Finite Group Databasebeta

← C2×#23777759 #35195909

Subgroups — C2×#23777759 #35195909

Order 20224.

8046 conjugacy classes of subgroups.

The subgroup lattice has 1412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777759C2132yesmaximal, direct product factor
2C2×#19099301C212yesmaximal, complemented
3C2×#19099300C212yesmaximal, complemented
4C2×#19099285C211yesmaximal, characteristic, complemented
5C2×#19099262C212yesmaximal, complemented
6C2×#19099233C211yesmaximal, characteristic, complemented
7C2×#19099231C211yesmaximal, characteristic, complemented
8C2×#19099212C211yesmaximal, characteristic, complemented
9C2×#19099209C211yesmaximal, characteristic, complemented
10C2×#19099202C212yesmaximal, complemented
11C2×#19099201C211yesmaximal, characteristic, complemented
12C2×#19099197C211yesmaximal, characteristic, complemented
13C2×#19099185C211yesmaximal, characteristic, complemented
14C2×#19099180C211yesmaximal, characteristic, complemented
15C2×#19099146C212yesmaximal, complemented
16C2×#19099145C212yesmaximal, complemented
17C2×#19099140C212yesmaximal, complemented
18C2×#19099127C211yesmaximal, characteristic, complemented
19C2×#19099126C212yesmaximal, complemented
20C2×#19099126C211yesmaximal, characteristic, complemented
21C2×#19099109C211yesmaximal, characteristic, complemented
22C2×#19099108C211yesmaximal, characteristic, complemented
23C2×#19099093C211yesmaximal, characteristic, complemented
24C2×#550×C79C211yesmaximal, characteristic, complemented
25C22×#11929624C2211yescharacteristic, complemented
26C22×#11929623C2212yescomplemented
27C22×#11929623C2211yescharacteristic, complemented
28C22×#11929623C2212yescomplemented
29C23×D316C2211yescharacteristic
30C22×D4×D79C2211yescharacteristic
31C22×D4×D79C2212yes—
32#19099301C22132yescomplemented
33#19099300C22132yescomplemented
34#19099285C22116yescomplemented
35#19099262C22132yescomplemented
36#19099233C22116yescomplemented
37#19099231C22116yescomplemented
38#19099212C22116yescomplemented
39#19099209C22116yescomplemented
40#19099202C22132yescomplemented
41#19099201C22116yescomplemented
42#19099197C22116yescomplemented
43#19099185C22116yescomplemented
44#19099180C22116yescomplemented
45#19099146C22132yescomplemented
46#19099145C22132yescomplemented
47#19099140C22132yescomplemented
48#19099127C22116yescomplemented
49#19099126C22132yescomplemented
50#19099126C22116yescomplemented
51#19099109C22116yescomplemented
52#19099108C22116yescomplemented
53C2×#14579160C2211yescharacteristic, complemented
54C2×#14579159C2211yescharacteristic, complemented
55C2×#14579157C2211yescharacteristic
56C2×#14579157C2211yescharacteristic
57C2×#14579157C2211yescharacteristic, complemented
58C2×#14579157C2212yescomplemented
59#19099093C22116yescomplemented
60C2×#14579156C2211yescharacteristic, complemented
61C2×#14579156C2212yescomplemented
62C2×#14579155C2212yescomplemented
63C2×#14579155C2212yescomplemented
64C2×#14579154C2212yescomplemented
65C2×#14579154C2211yescharacteristic, complemented
66C2×#14579151C2211yescharacteristic, complemented
67C2×#14579150C2211yescharacteristic
68C2×#14579150C2211yescharacteristic, complemented
69C2×#14579149C2211yescharacteristic
70C2×#14579149C2212yescomplemented
71C2×#14579148C2211yescharacteristic, complemented
72C2×#14579148C2212yescomplemented
73C2×#14579147C2211yescharacteristic
74C2×#14579147C2212yescomplemented
75C2×#14579146C2212yescomplemented
76C2×#14579146C2212yescomplemented
77C2×#14579145C2211yescharacteristic, complemented
78C2×#14579144C2212yescomplemented
79C2×#14579144C2212yescomplemented
80C2×#14579142C2212yescomplemented
81C2×#14579142C2212yescomplemented
82C2×#14579142C2211yescharacteristic, complemented
83C2×#14579140C2211yescharacteristic, complemented
84C2×#14579139C2212yescomplemented
85C2×#14579139C2212yescomplemented
86C2×#14579138C2212yescomplemented
87C2×#14579138C2211yescharacteristic, complemented
88C2×#14579137C2211yescharacteristic, complemented
89C2×#14579136C2211yescharacteristic
90C2×#14579135C2211yescharacteristic
91C2×#14579135C2212yescomplemented
92C2×#14579135C2212yescomplemented
93C2×#14579134C2212yes—
94C2×#14579134C2212yescomplemented
95C2×#14579134C2212yescomplemented
96C2×#14579133C2212yes—
97C2×#14579133C2211yescharacteristic
98C2×#14579133C2212yescomplemented
99C2×#14579133C2212yescomplemented
100C2×#14579133C2212yescomplemented
101C2×#14579133C2212yescomplemented
102C2×#14579133C2212yescomplemented
103C2×#14579133C2212yescomplemented
104C2×#14579133C2212yescomplemented
105C2×#14579133C2212yescomplemented
106C2×#14579133C2212yescomplemented
107C2×#14579132C2212yescomplemented
108C2×#14579131C2212yes—
109C2×#14579129C2212yes—
110C2×#14579129C2212yescomplemented
111C2×#14579129C2212yescomplemented
112C2×#14579129C2212yescomplemented
113C2×#14579129C2212yescomplemented
114C2×#14579129C2212yescomplemented
115C2×#14579129C2212yescomplemented
116C2×C4×Dic158C2211yescharacteristic, complemented
117C2×#14579126C2211yescharacteristic, complemented
118C2×C4×D316C2211yescharacteristic, complemented
119C2×D4×Dic79C2211yescharacteristic, complemented
120C2×D4×Dic79C2211yescharacteristic, complemented
121C2×#14579123C2211yescharacteristic
122C2×C4×C22⋊D79C2211yescharacteristic
123C2×C4×C22⋊D79C2211yescharacteristic, complemented
124C2×C4×C22⋊D79C2212yescomplemented
125C2×C4×C22⋊D79C2212yescomplemented
126C2×(C22⋊D79)⋊C4C2212yescomplemented
127C2×(C22⋊D79)⋊C4C2212yescomplemented
128C2×#14579120C2211yescharacteristic, complemented
129C2×#14579118C2211yescharacteristic, complemented
130C2×#14579118C2212yescomplemented
131C22×Dic79⋊C4C2212yescomplemented
132C22×(C2×D79)⋊C4C2212yescomplemented
133C2×C22⋊C4×D79C2212yescomplemented
134C22×C4×Dic79C2211yescharacteristic, complemented
135C22×#41×C79C2211yescharacteristic, complemented
136C22×#41×C79C2211yescharacteristic, complemented
137#550×C79C22116yescomplemented
138C2×#127×C79C2211yescharacteristic, complemented
139C2×#127×C79C2212yescomplemented
140C2×#121×C79C2211yescharacteristic
141C2×#121×C79C2212yescomplemented
142C2×#121×C79C2211yescharacteristic, complemented
143C2×#121×C79C2212yescomplemented
144C2×C4×Q8×C79C2211yescharacteristic, complemented
145C2×C4×D4×C79C2211yescharacteristic, complemented
146C2×C4×D4×C79C2212yescomplemented
147C24×D79C2312yes—
148C24×D79C2312yes—
149C2×#11929624—44no—
150C2×#11929624C2318yescomplemented
151C2×#11929623—48no—
152C2×#11929623—44no—
153C2×#11929623—48no—
154C2×#11929623C23116yescomplemented
155C2×#11929623C23116yescomplemented
156C2×#11929623C2318yescomplemented
157C22×Dic158C2311yescharacteristic
158C22×Dic158C2311yescharacteristic
159C22×Dic158C2312yes—
160C22×D316—44no—
161C22×D316C2311yescharacteristic
162C22×D316C2311yescharacteristic
163C22×D316C2318yes—
164C22×D316C2312yes—
165C22×D316C2312yes—
166C22×C22⋊D79C2311yescharacteristic
167C22×C22⋊D79C2312yes—
168C22×C22⋊D79C2312yes—
169C22×C22⋊D79C2312yes—
170C22×C22⋊D79C2312yes—
171C22×C22⋊D79C2311yescharacteristic
172C22×C22⋊D79C2312yes—
173C22×C22⋊D79C2312yes—
174C22×C22⋊D79C2312yes—
175C22×C22⋊D79C2312yes—
176C22×C22⋊D79C2312yes—
177C22×C22⋊D79C2312yes—
178C2×D4×D79—48no—
179C2×D4×D79—44no—
180C2×D4×D79C2318yes—
181C2×D4×D79C23116yes—
182C23×Dic79C2311yescharacteristic
183C23×Dic79C2312yes—
184C23×Dic79C2311yescharacteristic
185C23×Dic79C2312yes—
186C23×Dic79C2312yes—
187C22×C4×D79C2312yes—
188C22×C4×D79C2311yescharacteristic
189C22×C4×D79C2312yes—
190C22×C4×D79C2312yes—
191#14579160C2318yescomplemented
192#14579159C2318yescomplemented
193#14579157C2318yes—
194#14579157C2318yes—
195#14579157C2318yescomplemented
196#14579157C23116yescomplemented
197#14579156C23116yescomplemented
198#14579156C2318yescomplemented
199#14579155C23116yescomplemented
200#14579155C23116yescomplemented
201#14579154C2318yescomplemented
202#14579154C23116yescomplemented
203#14579151C2318yescomplemented
204#14579150C2318yes—
205#14579150C2318yescomplemented
206#14579149C2318yes—
207#14579149C23116yescomplemented
208#14579148C23116yescomplemented
209#14579148C2318yescomplemented
210#14579147C2318yes—
211#14579147C23116yescomplemented
212#14579146C23116yescomplemented
213#14579146C23116yescomplemented
214#14579145C2318yescomplemented
215#14579144C23116yescomplemented
216#14579144C23116yescomplemented
217#14579142C23116yescomplemented
218#14579142C23116yescomplemented
219#14579142C2318yescomplemented
220#14579140C2318yescomplemented
221#14579139C23116yescomplemented
222#14579139C23116yescomplemented
223#14579138C2318yescomplemented
224#14579138C23116yescomplemented
225#14579137C2318yescomplemented
226#14579136C2318yes—
227#14579135C2318yes—
228#14579135C23116yescomplemented
229#14579135C23116yescomplemented
230#14579134C23116yes—
231#14579134C23116yescomplemented
232#14579134C23116yescomplemented
233#14579133C23116yes—
234#14579133C2318yes—
235#14579133C23116yescomplemented
236#14579133C23116yescomplemented
237#14579133C23116yescomplemented
238#14579133C23116yescomplemented
239#14579133C23116yescomplemented
240#14579133C23116yescomplemented
241#14579133C23116yescomplemented
242#14579133C23116yescomplemented
243#14579133C23116yescomplemented
244#14579132C23116yescomplemented
245#14579131C23116yes—
246#14579129C23116yes—
247#14579129C23116yescomplemented
248#14579129C23116yescomplemented
249#14579129C23116yescomplemented
250#14579129C23116yescomplemented
251#14579129C23116yescomplemented
252#14579129C23116yescomplemented
253C4×Dic158C2318yescomplemented
254#14579126C2318yescomplemented
255C4×D316C2318yescomplemented
256D4×Dic79C2318yescomplemented
257D4×Dic79C2318yescomplemented
258#14579123C2318yes—
259C4×C22⋊D79C2318yes—
260C4×C22⋊D79C23116yescomplemented
261C4×C22⋊D79C2318yescomplemented
262C4×C22⋊D79C23116yescomplemented
263(C22⋊D79)⋊C4C23116yescomplemented
264(C22⋊D79)⋊C4C23116yescomplemented
265#14579120C2318yescomplemented
266#14579118C2318yescomplemented
267#14579118C23116yescomplemented
268C2×C4⋊Dic79C2311yescharacteristic
269C2×C4⋊Dic79C2311yescharacteristic
270C2×C4⋊Dic79C2311yescharacteristic
271C2×C4⋊Dic79C2311yescharacteristic
272C2×Dic79⋊C4C2311yescharacteristic
273C2×Dic79⋊C4C2312yes—
274C2×Dic79⋊C4C2312yes—
275C2×Dic79⋊C4C2312yes—
276C2×Dic79⋊C4C2311yescharacteristic
277C2×Dic79⋊C4C2311yescharacteristic
278C2×Dic79⋊C4C2311yescharacteristic
279C2×Dic79⋊C4C2311yescharacteristic
280C2×Dic79⋊C4C2312yes—
281C2×Dic79⋊C4C2312yes—
282C2×Dic79⋊C4C2312yes—
283C2×Dic79⋊C4C2311yescharacteristic
284C2×Dic79⋊C4C23116yescomplemented
285C2×C22⋊Dic79C2312yes—
286C2×C22⋊Dic79C2311yescharacteristic
287C2×C22⋊Dic79C2311yescharacteristic
288C2×C22⋊Dic79C2311yescharacteristic
289C2×C22⋊Dic79C2312yes—
290C2×C22⋊Dic79C2312yes—
291C2×C22⋊Dic79C2311yescharacteristic
292C2×C22⋊Dic79C2312yes—
293C2×C22⋊Dic79C2312yes—
294C2×(C2×D79)⋊C4C2312yes—
295C2×(C2×D79)⋊C4C2312yes—
296C2×(C2×D79)⋊C4C2311yescharacteristic
297C2×(C2×D79)⋊C4C2312yes—
298C2×(C2×D79)⋊C4C2312yes—
299C2×(C2×D79)⋊C4C2311yescharacteristic
300C2×(C2×D79)⋊C4C2312yes—
301C2×(C2×D79)⋊C4C2312yes—
302C2×(C2×D79)⋊C4C2311yescharacteristic
303C2×(C2×D79)⋊C4C2312yes—
304C2×(C2×D79)⋊C4C2311yescharacteristic
305C2×(C2×D79)⋊C4C2312yes—
306C2×(C2×D79)⋊C4C2312yes—
307C2×(C2×D79)⋊C4C2312yes—
308C2×(C2×D79)⋊C4C2312yes—
309C2×(C2×D79)⋊C4C23116yescomplemented
310C22⋊C4×D79C23116yescomplemented
311C2×C4×Dic79C2311yescharacteristic
312C2×C4×Dic79C2311yescharacteristic
313C2×C4×Dic79C2311yescharacteristic
314C2×C4×Dic79C2311yescharacteristic
315C2×C4×Dic79C2312yes—
316C2×C4×Dic79C2311yescharacteristic
317C2×C4×Dic79C2318yescomplemented
318C2×#41×C79—44no—
319C2×#41×C79—44no—
320C2×#41×C79C2318yescomplemented
321C2×#41×C79C2318yescomplemented
322C22×Q8×C79C2311yescharacteristic
323C22×D4×C79C2311yescharacteristic
324C22×D4×C79C2311yescharacteristic
325C22×D4×C79C2311yescharacteristic
326C22×D4×C79C2312yes—
327C22×D4×C79C2312yes—
328C22×D4×C79C2312yes—
329C22×D4×C79C2312yes—
330C22×D4×C79C2312yes—
331C22×D4×C79C2312yes—
332C23×C4×C79C2311yescharacteristic
333C23×C4×C79C2311yescharacteristic
334C23×C4×C79C2312yes—
335C23×C4×C79C2312yes—
336#127×C79C2318yescomplemented
337#127×C79C23116yescomplemented
338#121×C79C2318yes—
339#121×C79C23116yescomplemented
340#121×C79C23116yescomplemented
341#121×C79C2318yescomplemented
342C4×Q8×C79C2318yescomplemented
343C4×D4×C79C23116yescomplemented
344C4×D4×C79C2318yescomplemented
345C2×C4⋊C4×C79C2311yescharacteristic
346C2×C4⋊C4×C79C2311yescharacteristic
347C2×C4⋊C4×C79C2312yes—
348C2×C22⋊C4×C79C2312yes—
349C2×C22⋊C4×C79C2311yescharacteristic
350C2×C22⋊C4×C79C2312yes—
351C2×C22⋊C4×C79C2311yescharacteristic
352C2×C42×C79C2311yescharacteristic
353C2×C42×C79C2312yes—
354C23×D79—44no—
355C23×D79—44no—
356C23×D79—44no—
357C23×D79—44no—
358C23×D79—44no—
359C23×D79—44no—
360C23×D79C2411yescharacteristic
361C23×D79C2412yes—
362C23×D79C2412yes—
363C23×D79C2418yes—
364C23×D79C2418yes—
365#11929624—416no—
366#11929623—432no—
367#11929623—416no—
368#11929623—432no—
369C2×Dic158—24no—
370C2×Dic158—24no—
371C2×Dic158—44no—
372C2×Dic158C2414yes—
373C2×Dic158C2414yes—
374C2×Dic158C2418yes—
375C2×D316—24no—
376C2×D316—24no—
377C2×D316—44no—
378C2×D316—44no—
379C2×D316—416no—
380C2×D316C2414yes—
381C2×D316C2414yes—
382C2×D316C2418yes—
383C2×D316C2418yes—
384C2×C22⋊D79—28no—
385C2×C22⋊D79—24no—
386C2×C22⋊D79—44no—
387C2×C22⋊D79—44no—
388C2×C22⋊D79—44no—
389C2×C22⋊D79—44no—
390C2×C22⋊D79—44no—
391C2×C22⋊D79—44no—
392C2×C22⋊D79—44no—
393C2×C22⋊D79—44no—
394C2×C22⋊D79—42no—
395C2×C22⋊D79—44no—
396C2×C22⋊D79C2418yes—
397C2×C22⋊D79C2414yes—
398C2×C22⋊D79C2418yes—
399C2×C22⋊D79C2418yes—
400C2×C22⋊D79C2418yes—
401C2×C22⋊D79C2418yes—
402C2×C22⋊D79C2418yes—
403C2×C22⋊D79C2418yes—
404C2×C22⋊D79C2418yes—
405C2×C22⋊D79C2418yes—
406C2×C22⋊D79C2414yes—
407C2×C22⋊D79C2418yes—
408D4×D79—432no—
409D4×D79—416no—
410C22×Dic79—28no—
411C22×Dic79—24no—
412C22×Dic79—44no—
413C22×Dic79—44no—
414C22×Dic79—42no—
415C22×Dic79C2411yescharacteristic
416C22×Dic79C2411yescharacteristic
417C22×Dic79C2412yes—
418C22×Dic79C2412yes—
419C22×Dic79C2414yes—
420C22×Dic79C2418yes—
421C22×Dic79C2411yescharacteristic
422C22×Dic79C2411yescharacteristic
423C22×Dic79C2411yescharacteristic
424C22×Dic79C2411yescharacteristic
425C22×Dic79C2418yes—
426C22×Dic79C2418yes—
427C22×Dic79C2414yes—
428C22×Dic79C2411yescharacteristic
429C2×C4×D79—28no—
430C2×C4×D79—24no—
431C2×C4×D79—44no—
432C2×C4×D79—44no—
433C2×C4×D79C2418yes—
434C2×C4×D79C2414yes—
435C2×C4×D79C2418yes—
436C2×C4×D79C2418yes—
437C4⋊Dic79C2414yes—
438C4⋊Dic79C2414yes—
439C4⋊Dic79C2414yes—
440C4⋊Dic79C2414yes—
441Dic79⋊C4C2414yes—
442Dic79⋊C4C2418yes—
443Dic79⋊C4C2418yes—
444Dic79⋊C4C2418yes—
445Dic79⋊C4C2414yes—
446Dic79⋊C4C2414yes—
447Dic79⋊C4C2414yes—
448Dic79⋊C4C2414yes—
449Dic79⋊C4C2418yes—
450Dic79⋊C4C2418yes—
451Dic79⋊C4C2418yes—
452Dic79⋊C4C2414yes—
453C22⋊Dic79C2418yes—
454C22⋊Dic79C2414yes—
455C22⋊Dic79C2414yes—
456C22⋊Dic79C2414yes—
457C22⋊Dic79C2418yes—
458C22⋊Dic79C2418yes—
459C22⋊Dic79C2414yes—
460C22⋊Dic79C2418yes—
461C22⋊Dic79C2418yes—
462(C2×D79)⋊C4C2418yes—
463(C2×D79)⋊C4C2418yes—
464(C2×D79)⋊C4C2414yes—
465(C2×D79)⋊C4C2418yes—
466(C2×D79)⋊C4C2418yes—
467(C2×D79)⋊C4C2414yes—
468(C2×D79)⋊C4C2418yes—
469(C2×D79)⋊C4C2418yes—
470(C2×D79)⋊C4C2414yes—
471(C2×D79)⋊C4C2418yes—
472(C2×D79)⋊C4C2414yes—
473(C2×D79)⋊C4C2418yes—
474(C2×D79)⋊C4C2418yes—
475(C2×D79)⋊C4C2418yes—
476(C2×D79)⋊C4C2418yes—
477C4×Dic79C2414yes—
478C4×Dic79C2414yes—
479C4×Dic79C2414yes—
480C4×Dic79C2414yes—
481C4×Dic79C2418yes—
482C4×Dic79C2414yes—
483C24×C79C2411yescharacteristic
484C24×C79C2412yes—
485C24×C79C2412yes—
486C24×C79C2411yescharacteristic
487#41×C79—416no—
488#41×C79—416no—
489C2×Q8×C79—24no—
490C2×Q8×C79C2414yes—
491C2×D4×C79—24no—
492C2×D4×C79—24no—
493C2×D4×C79—44no—
494C2×D4×C79—44no—
495C2×D4×C79—42no—
496C2×D4×C79—44no—
497C2×D4×C79—44no—
498C2×D4×C79—44no—
499C2×D4×C79—44no—
500C2×D4×C79C2414yes—
501C2×D4×C79C2414yes—
502C2×D4×C79C2418yes—
503C2×D4×C79C2418yes—
504C2×D4×C79C2414yes—
505C2×D4×C79C2418yes—
506C2×D4×C79C2418yes—
507C2×D4×C79C2418yes—
508C2×D4×C79C2418yes—
509C22×C4×C79—24no—
510C22×C4×C79—24no—
511C22×C4×C79—44no—
512C22×C4×C79—44no—
513C22×C4×C79C2412yes—
514C22×C4×C79C2411yescharacteristic
515C22×C4×C79C2414yes—
516C22×C4×C79C2411yescharacteristic
517C22×C4×C79C2412yes—
518C22×C4×C79C2411yescharacteristic
519C22×C4×C79C2411yescharacteristic
520C22×C4×C79C2414yes—
521C22×C4×C79C2418yes—
522C22×C4×C79C2418yes—
523C22×C4×C79C2411yescharacteristic
524C4⋊C4×C79C2414yes—
525C4⋊C4×C79C2414yes—
526C4⋊C4×C79C2418yes—
527C22⋊C4×C79C2418yes—
528C22⋊C4×C79C2414yes—
529C22⋊C4×C79C2418yes—
530C22⋊C4×C79C2414yes—
531C42×C79C2414yes—
532C42×C79C2418yes—
533C23×C79—24no—
534C23×C79—22no—
535C23×C79—24no—
536C23×C79—24no—
537C23×C79—22no—
538C23×C79—22no—
539C23×C79—24no—
540C23×C79—22no—
541C23×C79—22no—
542C23×C79—24no—
543C23×C79—24no—
544C23×C79—22no—
545C23×C79C2512yes—
546C23×C79C2514yes—
547C23×C79C2512yes—
548C23×C79C2514yes—
549C23×C79C2511yescharacteristic
550C22×D79—24no—
551C22×D79—22no—
552C22×D79—24no—
553C22×D79—24no—
554C22×D79—22no—
555C22×D79—24no—
556C22×D79—24no—
557C22×D79—22no—
558C22×D79—24no—
559C22×D79—48no—
560C22×D79—48no—
561C22×D79—48no—
562C22×D79—48no—
563C22×D79—48no—
564C22×D79—48no—
565C22×D79—816no—
566C22×D79—816no—
567C22×D79C2512yes—
568C22×D79C2514yes—
569C22×D79C2514yes—
570Q8×C79—28no—
571D4×C79—28no—
572D4×C79—28no—
573D4×C79—48no—
574D4×C79—48no—
575D4×C79—48no—
576D4×C79—48no—
577D4×C79—44no—
578D4×C79—48no—
579D4×C79—48no—
580C2×C4×C79—24no—
581C2×C4×C79—22no—
582C2×C4×C79—22no—
583C2×C4×C79—22no—
584C2×C4×C79—24no—
585C2×C4×C79—22no—
586C2×C4×C79—28no—
587C2×C4×C79—28no—
588C2×C4×C79—48no—
589C2×C4×C79—48no—
590C2×C4×C79H(5,𝔽2)14yes—
591C2×C4×C79C2512yes—
592C2×C4×C79C2514yes—
593C2×C4×C79C2512yes—
594C2×C4×C79C2514yes—
595C2×C4×C79C2512yes—
596C2×C4×C79C2512yes—
597C2×C4×C79C2512yes—
598C22⋊D79—28no—
599C22⋊D79—216no—
600C22⋊D79—48no—
601C22⋊D79—48no—
602C22⋊D79—44no—
603C22⋊D79—48no—
604C22⋊D79—48no—
605C22⋊D79—48no—
606C22⋊D79—48no—
607C22⋊D79—48no—
608C22⋊D79—48no—
609C22⋊D79—48no—
610C2×Dic79—22no—
611C2×Dic79—24no—
612C2×Dic79—24no—
613C2×Dic79—22no—
614C2×Dic79—22no—
615C2×Dic79—22no—
616C2×Dic79—22no—
617C2×Dic79—22no—
618C2×Dic79—28no—
619C2×Dic79—216no—
620C2×Dic79—44no—
621C2×Dic79—48no—
622C2×Dic79—48no—
623C2×Dic79H(5,𝔽2)14yes—
624C2×Dic79C2512yes—
625C2×Dic79C2512yes—
626C2×Dic79C2512yes—
627C2×Dic79C2512yes—
628C2×Dic79C2512yes—
629C2×Dic79C2514yes—
630C2×Dic79C2514yes—
631C2×Dic79C2512yes—
632C2×Dic79C2512yes—
633D316—28no—
634D316—28no—
635D316—48no—
636D316—48no—
637C4×D79—28no—
638C4×D79—216no—
639C4×D79—48no—
640C4×D79—48no—
641Dic158—28no—
642Dic158—28no—
643Dic158—48no—
644C22×C79—22no—
645C22×C79—24no—
646C22×C79—22no—
647C22×C79—22no—
648C22×C79—24no—
649C22×C79—24no—
650C22×C79—24no—
651C22×C79—22no—
652C22×C79—24no—
653C22×C79—24no—
654C22×C79—22no—
655C22×C79—22no—
656C22×C79—44no—
657C22×C79—48no—
658C22×C79—48no—
659C22×C79—44no—
660C22×C79C2×H(5,𝔽2)12yes—
661C22×C79C2×H(5,𝔽2)12yes—
662C22×C79#58512yes—
663C22×C79C2611yescharacteristic
664C2×D79—24no—
665C2×D79—22no—
666C2×D79—24no—
667C2×D79—22no—
668C2×D79—24no—
669C2×D79—24no—
670C2×D79—24no—
671C2×D79—22no—
672C2×D79—24no—
673C2×D79—48no—
674C2×D79—44no—
675C2×D79—48no—
676C2×D79—816no—
677C2×D79—816no—
678C4×C79—22no—
679C4×C79—22no—
680C4×C79—24no—
681C4×C79—22no—
682C4×C79—24no—
683C4×C79—22no—
684C4×C79C2×H(5,𝔽2)14yes—
685Dic79—24no—
686Dic79—22no—
687Dic79—22no—
688Dic79—22no—
689Dic79—24no—
690Dic79—22no—
691Dic79—22no—
692Dic79—22no—
693Dic79C2×H(5,𝔽2)14yes—
694C2×#3546—791nomaximal, Sylow
695C2×C79—42no—
696C2×C79—44no—
697C2×C79—42no—
698C2×C79—44no—
699C2×C79#354614yescomplemented
700C2×C79C22×H(5,𝔽2)11yescharacteristic
701C2×C79C22×H(5,𝔽2)11yescharacteristic
702C2×C79C2×#58511yescharacteristic
703D79—44no—
704D79—42no—
705D79—44no—
706#3546—7932no—
707C2×#560—792no—
708C2×#560—792no—
709C2×#556—791no—
710C2×#553—792no—
711C2×#550—791no—
712C2×#550—791no—
713C2×#550D7911yescharacteristic, complemented
714C2×#547—791no—
715C2×#546—791no—
716C2×#546—792no—
717C2×#546—791no—
718C2×D42—791no—
719C2×#542—791no—
720C2×#542—791no—
721C2×#538—792no—
722C2×#538—792no—
723C2×#537—792no—
724C2×#535—791no—
725C2×#535—791no—
726C2×#535—792no—
727C2×#532—791no—
728C2×#532—791no—
729C2×#529—791no—
730C79C2×#354611yescharacteristic, complemented, Sylow
731C22×#41—792no—
732C22×#41—791no—
733C22×#41—792no—
734C22×#41—791no—
735C22×#41C2×D7911yescharacteristic, complemented
736C22×#41C2×D7911yescharacteristic, complemented
737C23×D4—791no—
738C23×D4—792no—
739C23×D4—791no—
740#560—7932no—
741#560—7932no—
742#556—7916no—
743#553—7932no—
744#550—7916no—
745#550—7916no—
746#550C2×D79116yescomplemented
747#547—7916no—
748#546—7916no—
749#546—7932no—
750#546—7916no—
751D42—7916no—
752#542—7916no—
753#542—7916no—
754#538—7932no—
755#538—7932no—
756#537—7932no—
757#535—7916no—
758#535—7916no—
759#535—7932no—
760#532—7916no—
761#532—7916no—
762C2×C4⋊Q8—791no—
763C2×C4⋊Q8—791no—
764C2×#127—791no—
765C2×#127—791no—
766C2×#127—791no—
767C2×#127—792no—
768C2×#127C2×D7911yescharacteristic, complemented
769C2×#127C2×D7912yescomplemented
770#529—7916no—
771C2×#126—791no—
772C2×#126—792no—
773C2×#126—791no—
774C2×#126—792no—
775C2×#126—792no—
776C2×#126—792no—
777C2×#125—791no—
778C2×#124—791no—
779C2×#124—791no—
780C2×#124—791no—
781C2×#124—792no—
782C2×#124—791no—
783C2×#124—792no—
784C2×#124—792no—
785C2×#124—791no—
786C2×#123—791no—
787C2×#123—792no—
788C2×#123—792no—
789C2×#123—792no—
790C2×#123—792no—
791C2×#123—792no—
792C2×#123—792no—
793C2×#123—791no—
794C2×C22⋊Q8—791no—
795C2×C22⋊Q8—791no—
796C2×C22⋊Q8—792no—
797C2×C22⋊Q8—792no—
798C2×C22⋊Q8—791no—
799C2×C22⋊Q8—792no—
800C2×#121—791no—
801C2×#121—792no—
802C2×#121—792no—
803C2×#121—792no—
804C2×#121—792no—
805C2×#121—792no—
806C2×#121—792no—
807C2×#121—792no—
808C2×#121—792no—
809C2×#121—792no—
810C2×#121—792no—
811C2×#121—792no—
812C2×#121—791no—
813C2×#121—792no—
814C2×#121—792no—
815C2×#121—791no—
816C2×#121—792no—
817C2×#121—792no—
818C2×#121—792no—
819C2×#121C2×D7911yescharacteristic
820C2×#121C2×D7911yescharacteristic, complemented
821C2×#121C2×D7912yescomplemented
822C2×#121C2×D7912yescomplemented
823C2×#120—792no—
824C2×#120—792no—
825C2×#120—792no—
826C2×#120—792no—
827C2×#120—792no—
828C2×#120—792no—
829C2×#120—792no—
830C2×#120—792no—
831C2×C4×Q8—791no—
832C2×C4×Q8—791no—
833C2×C4×Q8C2×D7911yescharacteristic, complemented
834C2×C4×D4—791no—
835C2×C4×D4—791no—
836C2×C4×D4—791no—
837C2×C4×D4—791no—
838C2×C4×D4—792no—
839C2×C4×D4—792no—
840C2×C4×D4—791no—
841C2×C4×D4—792no—
842C2×C4×D4—792no—
843C2×C4×D4—791no—
844C2×C4×D4C2×D7911yescharacteristic, complemented
845C2×C4×D4C2×D7912yescomplemented
846C2×#117—791no—
847C2×#117—791no—
848C2×#117—792no—
849C22×C4⋊C4—792no—
850C22×C22⋊C4—792no—
851C22×C22⋊C4—792no—
852C22×C42—791no—
853C25—792no—
854C25—792no—
855C2×#41—44no—
856C2×#41—44no—
857C2×#41—3164no—
858C2×#41—3164no—
859C2×#41—3168no—
860C2×#41—3168no—
861C2×#41—7916no—
862C2×#41—798no—
863C2×#41—7916no—
864C2×#41—798no—
865C2×#41C22×D7918yescomplemented
866C2×#41C22×D7918yescomplemented
867C22×Q8—792no—
868C22×Q8—791no—
869C22×Q8—791no—
870C22×Q8C22×D7911yescharacteristic
871C22×D4—3164no—
872C22×D4—3164no—
873C22×D4—3168no—
874C22×D4—792no—
875C22×D4—792no—
876C22×D4—791no—
877C22×D4—792no—
878C22×D4—792no—
879C22×D4—792no—
880C22×D4—792no—
881C22×D4—792no—
882C22×D4—792no—
883C22×D4—792no—
884C22×D4—798no—
885C22×D4—7916no—
886C22×D4—791no—
887C22×D4—792no—
888C22×D4—792no—
889C22×D4—792no—
890C22×D4—798no—
891C22×D4—791no—
892C22×D4—791no—
893C22×D4C22×D7911yescharacteristic
894C22×D4C22×D7911yescharacteristic
895C22×D4C22×D7911yescharacteristic
896C22×D4C22×D7912yes—
897C22×D4C22×D7912yes—
898C22×D4C22×D7912yes—
899C22×D4C22×D7912yes—
900C22×D4C22×D7912yes—
901C22×D4C22×D7912yes—
902C23×C4—792no—
903C23×C4—792no—
904C23×C4—791no—
905C23×C4—792no—
906C23×C4—792no—
907C23×C4—792no—
908C23×C4—791no—
909C23×C4—792no—
910C23×C4—791no—
911C23×C4C22×D7911yescharacteristic
912C23×C4C22×D7911yescharacteristic
913C23×C4C22×D7912yes—
914C23×C4C22×D7912yes—
915C4⋊Q8—798no—
916C4⋊Q8—798no—
917#127—798no—
918#127—798no—
919#127—798no—
920#127—7916no—
921#127C22×D7918yescomplemented
922#127C22×D79116yescomplemented
923#126—798no—
924#126—7916no—
925#126—798no—
926#126—7916no—
927#126—7916no—
928#126—7916no—
929#125—798no—
930#124—798no—
931#124—798no—
932#124—798no—
933#124—7916no—
934#124—798no—
935#124—7916no—
936#124—7916no—
937#124—798no—
938#123—798no—
939#123—7916no—
940#123—7916no—
941#123—7916no—
942#123—7916no—
943#123—7916no—
944#123—7916no—
945#123—798no—
946C22⋊Q8—798no—
947C22⋊Q8—798no—
948C22⋊Q8—7916no—
949C22⋊Q8—7916no—
950C22⋊Q8—798no—
951C22⋊Q8—7916no—
952#121—798no—
953#121—7916no—
954#121—7916no—
955#121—7916no—
956#121—7916no—
957#121—7916no—
958#121—7916no—
959#121—7916no—
960#121—7916no—
961#121—7916no—
962#121—7916no—
963#121—7916no—
964#121—798no—
965#121—7916no—
966#121—7916no—
967#121—798no—
968#121—7916no—
969#121—7916no—
970#121—7916no—
971#121C22×D7918yes—
972#121C22×D7918yescomplemented
973#121C22×D79116yescomplemented
974#121C22×D79116yescomplemented
975#120—7916no—
976#120—7916no—
977#120—7916no—
978#120—7916no—
979#120—7916no—
980#120—7916no—
981#120—7916no—
982#120—7916no—
983C4×Q8—798no—
984C4×Q8—798no—
985C4×Q8C22×D7918yescomplemented
986C4×D4—798no—
987C4×D4—798no—
988C4×D4—798no—
989C4×D4—798no—
990C4×D4—7916no—
991C4×D4—7916no—
992C4×D4—798no—
993C4×D4—7916no—
994C4×D4—7916no—
995C4×D4—798no—
996C4×D4C22×D7918yescomplemented
997C4×D4C22×D79116yescomplemented
998#117—798no—
999#117—798no—
1000#117—7916no—
1001C2×C4⋊C4—791no—
1002C2×C4⋊C4—792no—
1003C2×C4⋊C4—792no—
1004C2×C4⋊C4—792no—
1005C2×C4⋊C4—7916no—
1006C2×C4⋊C4—791no—
1007C2×C4⋊C4—791no—
1008C2×C4⋊C4—791no—
1009C2×C4⋊C4—791no—
1010C2×C4⋊C4—791no—
1011C2×C4⋊C4—791no—
1012C2×C4⋊C4—791no—
1013C2×C4⋊C4—792no—
1014C2×C4⋊C4—792no—
1015C2×C4⋊C4—792no—
1016C2×C4⋊C4—791no—
1017C2×C4⋊C4—791no—
1018C2×C4⋊C4C22×D7911yescharacteristic
1019C2×C4⋊C4C22×D7911yescharacteristic
1020C2×C4⋊C4C22×D7912yes—
1021C2×C22⋊C4—792no—
1022C2×C22⋊C4—791no—
1023C2×C22⋊C4—791no—
1024C2×C22⋊C4—791no—
1025C2×C22⋊C4—792no—
1026C2×C22⋊C4—792no—
1027C2×C22⋊C4—792no—
1028C2×C22⋊C4—791no—
1029C2×C22⋊C4—792no—
1030C2×C22⋊C4—791no—
1031C2×C22⋊C4—792no—
1032C2×C22⋊C4—792no—
1033C2×C22⋊C4—792no—
1034C2×C22⋊C4—792no—
1035C2×C22⋊C4—7916no—
1036C2×C22⋊C4—792no—
1037C2×C22⋊C4—792no—
1038C2×C22⋊C4—791no—
1039C2×C22⋊C4—791no—
1040C2×C22⋊C4—792no—
1041C2×C22⋊C4—791no—
1042C2×C22⋊C4—792no—
1043C2×C22⋊C4—792no—
1044C2×C22⋊C4—792no—
1045C2×C22⋊C4—792no—
1046C2×C22⋊C4—7916no—
1047C2×C22⋊C4C22×D7911yescharacteristic
1048C2×C22⋊C4C22×D7912yes—
1049C2×C22⋊C4C22×D7912yes—
1050C2×C22⋊C4C22×D7911yescharacteristic
1051C2×C42—791no—
1052C2×C42—791no—
1053C2×C42—792no—
1054C2×C42—791no—
1055C2×C42—791no—
1056C2×C42—791no—
1057C2×C42—798no—
1058C2×C42C22×D7911yescharacteristic
1059C2×C42C22×D7912yes—
1060C24—3164no—
1061C24—3164no—
1062C24—3164no—
1063C24—3164no—
1064C24—3164no—
1065C24—3164no—
1066C24—798no—
1067C24—798no—
1068C24—792no—
1069C24—791no—
1070C24—792no—
1071C24C23×D7911yescharacteristic
1072C24C23×D7912yes—
1073C24C23×D7911yescharacteristic
1074C24C23×D7912yes—
1075#41—416no—
1076#41—416no—
1077#41—31616no—
1078#41—31616no—
1079#41—31632no—
1080#41—31632no—
1081C2×Q8—24no—
1082C2×Q8—3164no—
1083C2×Q8—798no—
1084C2×Q8—794no—
1085C2×Q8—794no—
1086C2×Q8—1584no—
1087C2×Q8—1584no—
1088C2×Q8C23×D7914yes—
1089C2×D4—24no—
1090C2×D4—24no—
1091C2×D4—44no—
1092C2×D4—44no—
1093C2×D4—44no—
1094C2×D4—44no—
1095C2×D4—44no—
1096C2×D4—42no—
1097C2×D4—44no—
1098C2×D4—3164no—
1099C2×D4—3164no—
1100C2×D4—31616no—
1101C2×D4—31616no—
1102C2×D4—31632no—
1103C2×D4—3164no—
1104C2×D4—3164no—
1105C2×D4—3164no—
1106C2×D4—3162no—
1107C2×D4—3164no—
1108C2×D4—3164no—
1109C2×D4—3164no—
1110C2×D4—3164no—
1111C2×D4—3164no—
1112C2×D4—3164no—
1113C2×D4—798no—
1114C2×D4—798no—
1115C2×D4—794no—
1116C2×D4—798no—
1117C2×D4—798no—
1118C2×D4—798no—
1119C2×D4—798no—
1120C2×D4—798no—
1121C2×D4—798no—
1122C2×D4—798no—
1123C2×D4—794no—
1124C2×D4—798no—
1125C2×D4—798no—
1126C2×D4—798no—
1127C2×D4—794no—
1128C2×D4—794no—
1129C2×D4—1584no—
1130C2×D4—1588no—
1131C2×D4—1584no—
1132C2×D4—1584no—
1133C2×D4C23×D7914yes—
1134C2×D4C23×D7914yes—
1135C2×D4C23×D7914yes—
1136C2×D4C23×D7918yes—
1137C2×D4C23×D7918yes—
1138C2×D4C23×D7918yes—
1139C2×D4C23×D7918yes—
1140C2×D4C23×D7918yes—
1141C2×D4C23×D7918yes—
1142C22×C4—24no—
1143C22×C4—24no—
1144C22×C4—44no—
1145C22×C4—44no—
1146C22×C4—3164no—
1147C22×C4—3164no—
1148C22×C4—3162no—
1149C22×C4—3164no—
1150C22×C4—3164no—
1151C22×C4—794no—
1152C22×C4—798no—
1153C22×C4—798no—
1154C22×C4—798no—
1155C22×C4—798no—
1156C22×C4—791no—
1157C22×C4—794no—
1158C22×C4—798no—
1159C22×C4—791no—
1160C22×C4—791no—
1161C22×C4—791no—
1162C22×C4—791no—
1163C22×C4—791no—
1164C22×C4—792no—
1165C22×C4—792no—
1166C22×C4—791no—
1167C22×C4—798no—
1168C22×C4—794no—
1169C22×C4—1588no—
1170C22×C4—1588no—
1171C22×C4—1584no—
1172C22×C4—1584no—
1173C22×C4C23×D7914yes—
1174C22×C4C23×D7914yes—
1175C22×C4C23×D7911yescharacteristic
1176C22×C4C23×D7912yes—
1177C22×C4C23×D7911yescharacteristic
1178C22×C4C23×D7912yes—
1179C22×C4C23×D7911yescharacteristic
1180C22×C4C23×D7911yescharacteristic
1181C22×C4C23×D7918yes—
1182C22×C4C23×D7918yes—
1183C22×C4C23×D7911yescharacteristic
1184C4⋊C4—794no—
1185C4⋊C4—798no—
1186C4⋊C4—798no—
1187C4⋊C4—798no—
1188C4⋊C4—794no—
1189C4⋊C4—794no—
1190C4⋊C4—794no—
1191C4⋊C4—794no—
1192C4⋊C4—798no—
1193C4⋊C4—798no—
1194C4⋊C4—798no—
1195C4⋊C4—794no—
1196C4⋊C4—794no—
1197C4⋊C4—794no—
1198C4⋊C4—794no—
1199C4⋊C4—794no—
1200C4⋊C4C23×D7914yes—
1201C4⋊C4C23×D7914yes—
1202C4⋊C4C23×D7918yes—
1203C22⋊C4—798no—
1204C22⋊C4—794no—
1205C22⋊C4—794no—
1206C22⋊C4—794no—
1207C22⋊C4—798no—
1208C22⋊C4—798no—
1209C22⋊C4—798no—
1210C22⋊C4—794no—
1211C22⋊C4—798no—
1212C22⋊C4—794no—
1213C22⋊C4—798no—
1214C22⋊C4—798no—
1215C22⋊C4—798no—
1216C22⋊C4—798no—
1217C22⋊C4—798no—
1218C22⋊C4—798no—
1219C22⋊C4—794no—
1220C22⋊C4—794no—
1221C22⋊C4—798no—
1222C22⋊C4—794no—
1223C22⋊C4—798no—
1224C22⋊C4—798no—
1225C22⋊C4—798no—
1226C22⋊C4—798no—
1227C22⋊C4C23×D7914yes—
1228C22⋊C4C23×D7918yes—
1229C22⋊C4C23×D7918yes—
1230C22⋊C4C23×D7914yes—
1231C42—794no—
1232C42—794no—
1233C42—794no—
1234C42—794no—
1235C42—794no—
1236C42—798no—
1237C42C23×D7914yes—
1238C42C23×D7918yes—
1239C23—24no—
1240C23—22no—
1241C23—24no—
1242C23—22no—
1243C23—22no—
1244C23—22no—
1245C23—24no—
1246C23—24no—
1247C23—22no—
1248C23—24no—
1249C23—24no—
1250C23—22no—
1251C23—3168no—
1252C23—3168no—
1253C23—3168no—
1254C23—3168no—
1255C23—3168no—
1256C23—3168no—
1257C23—794no—
1258C23—792no—
1259C23—794no—
1260C23—63216no—
1261C23—63216no—
1262C23—1584no—
1263C23—1584no—
1264C23—1582no—
1265C23—1584no—
1266C23—1582no—
1267C23—1584no—
1268C23—1584no—
1269C23—1584no—
1270C23—1582no—
1271C23C24×D7912yes—
1272C23C24×D7914yes—
1273C23C24×D7912yes—
1274C23C24×D7914yes—
1275C23C24×D7911yescharacteristic
1276Q8—28no—
1277Q8—3168no—
1278Q8—1588no—
1279Q8—1588no—
1280D4—28no—
1281D4—28no—
1282D4—48no—
1283D4—44no—
1284D4—48no—
1285D4—48no—
1286D4—48no—
1287D4—48no—
1288D4—48no—
1289D4—3168no—
1290D4—3168no—
1291D4—3168no—
1292D4—3168no—
1293D4—3168no—
1294D4—3164no—
1295D4—3168no—
1296D4—3168no—
1297D4—3168no—
1298D4—3168no—
1299D4—3168no—
1300D4—3168no—
1301D4—1588no—
1302D4—15816no—
1303D4—1588no—
1304D4—1588no—
1305C2×C4—22no—
1306C2×C4—24no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—24no—
1310C2×C4—22no—
1311C2×C4—28no—
1312C2×C4—28no—
1313C2×C4—48no—
1314C2×C4—48no—
1315C2×C4—3168no—
1316C2×C4—3168no—
1317C2×C4—3168no—
1318C2×C4—3168no—
1319C2×C4—3164no—
1320C2×C4—794no—
1321C2×C4—792no—
1322C2×C4—792no—
1323C2×C4—792no—
1324C2×C4—792no—
1325C2×C4—792no—
1326C2×C4—792no—
1327C2×C4—794no—
1328C2×C4—794no—
1329C2×C4—792no—
1330C2×C4—15816no—
1331C2×C4—15816no—
1332C2×C4—1588no—
1333C2×C4—1584no—
1334C2×C4—1582no—
1335C2×C4—1582no—
1336C2×C4—1582no—
1337C2×C4—1584no—
1338C2×C4—1582no—
1339C2×C4—1582no—
1340C2×C4—1582no—
1341C2×C4—1588no—
1342C2×C4#1457920614yes—
1343C2×C4C24×D7912yes—
1344C2×C4C24×D7914yes—
1345C2×C4C24×D7912yes—
1346C2×C4C24×D7914yes—
1347C2×C4C24×D7912yes—
1348C2×C4C24×D7912yes—
1349C2×C4C24×D7912yes—
1350C22—24no—
1351C22—22no—
1352C22—24no—
1353C22—22no—
1354C22—22no—
1355C22—22no—
1356C22—24no—
1357C22—24no—
1358C22—22no—
1359C22—24no—
1360C22—24no—
1361C22—22no—
1362C22—44no—
1363C22—48no—
1364C22—44no—
1365C22—48no—
1366C22—3168no—
1367C22—3164no—
1368C22—3168no—
1369C22—63216no—
1370C22—63216no—
1371C22—1584no—
1372C22—1584no—
1373C22—1582no—
1374C22—1584no—
1375C22—1582no—
1376C22—1584no—
1377C22—1584no—
1378C22—1584no—
1379C22—1582no—
1380C22H(5,𝔽2)×D7912yes—
1381C22C2×#1457920612yes—
1382C22#1909939912yes—
1383C22C25×D7911yescharacteristic
1384C4—22no—
1385C4—24no—
1386C4—22no—
1387C4—22no—
1388C4—24no—
1389C4—22no—
1390C4—794no—
1391C4—1584no—
1392C4—1582no—
1393C4—1582no—
1394C4—1582no—
1395C4—1584no—
1396C4—1582no—
1397C4—1582no—
1398C4—1582no—
1399C4C2×#1457920614yes—
1400C2—42no—
1401C2—44no—
1402C2—42no—
1403C2—44no—
1404C2—3164no—
1405C2—3162no—
1406C2—3164no—
1407C2#2377775914yesdirect product factor
1408C2C2×H(5,𝔽2)×D7911yescharacteristic
1409C2C22×#1457920611yescharacteristic
1410C2C2×#1909939911yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#550×C79C2
socleC23×C79C25
hypercenterC2×#550D79
hypocenterC79C2×#3546
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#550

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #23777759C2direct (N × H)
2. C2×#19099301C2semidirect
3. C2×#19099300C2semidirect
4. C2×#19099285C2semidirect
5. C2×#19099262C2semidirect
6. C2×#19099233C2semidirect
7. C2×#19099231C2semidirect
8. C2×#19099212C2semidirect
9. C2×#19099209C2semidirect
10. C2×#19099202C2semidirect
11. C2×#19099201C2semidirect
12. C2×#19099197C2semidirect
13. C2×#19099185C2semidirect
14. C2×#19099180C2semidirect
15. C2×#19099146C2semidirect
16. C2×#19099145C2semidirect
17. C2×#19099140C2semidirect
18. C2×#19099127C2semidirect
19. C2×#19099126C2semidirect
20. C2×#19099126C2semidirect
21. C2×#19099109C2semidirect
22. C2×#19099108C2semidirect
23. C2×#19099093C2semidirect
24. C2×#550×C79C2semidirect
25. C22×#11929624C22semidirect
26. C22×#11929623C22semidirect
27. C22×#11929623C22semidirect
28. C22×#11929623C22semidirect
32. #19099301C22semidirect
33. #19099300C22semidirect
34. #19099285C22semidirect
35. #19099262C22semidirect
36. #19099233C22semidirect
37. #19099231C22semidirect
38. #19099212C22semidirect
39. #19099209C22semidirect
40. #19099202C22semidirect
41. #19099201C22semidirect
42. #19099197C22semidirect
43. #19099185C22semidirect
44. #19099180C22semidirect
45. #19099146C22semidirect
46. #19099145C22semidirect
47. #19099140C22semidirect
48. #19099127C22semidirect
49. #19099126C22semidirect
50. #19099126C22semidirect
51. #19099109C22semidirect
52. #19099108C22semidirect
53. C2×#14579160C22semidirect
54. C2×#14579159C22semidirect
57. C2×#14579157C22semidirect
58. C2×#14579157C22semidirect
59. #19099093C22semidirect
60. C2×#14579156C22semidirect
61. C2×#14579156C22semidirect
62. C2×#14579155C22semidirect
63. C2×#14579155C22semidirect
64. C2×#14579154C22semidirect
65. C2×#14579154C22semidirect
66. C2×#14579151C22semidirect
68. C2×#14579150C22semidirect
70. C2×#14579149C22semidirect
71. C2×#14579148C22semidirect
72. C2×#14579148C22semidirect
74. C2×#14579147C22semidirect
75. C2×#14579146C22semidirect
76. C2×#14579146C22semidirect
77. C2×#14579145C22semidirect
78. C2×#14579144C22semidirect
79. C2×#14579144C22semidirect
80. C2×#14579142C22semidirect
81. C2×#14579142C22semidirect
82. C2×#14579142C22semidirect
83. C2×#14579140C22semidirect
84. C2×#14579139C22semidirect
85. C2×#14579139C22semidirect
86. C2×#14579138C22semidirect
87. C2×#14579138C22semidirect
88. C2×#14579137C22semidirect
91. C2×#14579135C22semidirect
92. C2×#14579135C22semidirect
94. C2×#14579134C22semidirect
95. C2×#14579134C22semidirect
98. C2×#14579133C22semidirect
99. C2×#14579133C22semidirect
100. C2×#14579133C22semidirect
101. C2×#14579133C22semidirect
102. C2×#14579133C22semidirect
103. C2×#14579133C22semidirect
104. C2×#14579133C22semidirect
105. C2×#14579133C22semidirect
106. C2×#14579133C22semidirect
107. C2×#14579132C22semidirect
110. C2×#14579129C22semidirect
111. C2×#14579129C22semidirect
112. C2×#14579129C22semidirect
113. C2×#14579129C22semidirect
114. C2×#14579129C22semidirect
115. C2×#14579129C22semidirect
116. C2×C4×Dic158C22semidirect
117. C2×#14579126C22semidirect
118. C2×C4×D316C22semidirect
119. C2×D4×Dic79C22semidirect
120. C2×D4×Dic79C22semidirect
123. C2×C4×C22⋊D79C22semidirect
124. C2×C4×C22⋊D79C22semidirect
125. C2×C4×C22⋊D79C22semidirect
126. C2×(C22⋊D79)⋊C4C22semidirect
127. C2×(C22⋊D79)⋊C4C22semidirect
128. C2×#14579120C22semidirect
129. C2×#14579118C22semidirect
130. C2×#14579118C22semidirect
131. C22×Dic79⋊C4C22semidirect
132. C22×(C2×D79)⋊C4C22semidirect
133. C2×C22⋊C4×D79C22semidirect
134. C22×C4×Dic79C22semidirect
135. C22×#41×C79C22semidirect
136. C22×#41×C79C22semidirect
137. #550×C79C22semidirect
138. C2×#127×C79C22semidirect
139. C2×#127×C79C22semidirect
141. C2×#121×C79C22semidirect
142. C2×#121×C79C22semidirect
143. C2×#121×C79C22semidirect
144. C2×C4×Q8×C79C22semidirect
145. C2×C4×D4×C79C22semidirect
146. C2×C4×D4×C79C22semidirect
150. C2×#11929624C23semidirect
154. C2×#11929623C23semidirect
155. C2×#11929623C23semidirect
156. C2×#11929623C23semidirect
191. #14579160C23semidirect
192. #14579159C23semidirect
195. #14579157C23semidirect
196. #14579157C23semidirect
197. #14579156C23semidirect
198. #14579156C23semidirect
199. #14579155C23semidirect
200. #14579155C23semidirect
201. #14579154C23semidirect
202. #14579154C23semidirect
203. #14579151C23semidirect
205. #14579150C23semidirect
207. #14579149C23semidirect
208. #14579148C23semidirect
209. #14579148C23semidirect
211. #14579147C23semidirect
212. #14579146C23semidirect
213. #14579146C23semidirect
214. #14579145C23semidirect
215. #14579144C23semidirect
216. #14579144C23semidirect
217. #14579142C23semidirect
218. #14579142C23semidirect
219. #14579142C23semidirect
220. #14579140C23semidirect
221. #14579139C23semidirect
222. #14579139C23semidirect
223. #14579138C23semidirect
224. #14579138C23semidirect
225. #14579137C23semidirect
228. #14579135C23semidirect
229. #14579135C23semidirect
231. #14579134C23semidirect
232. #14579134C23semidirect
235. #14579133C23semidirect
236. #14579133C23semidirect
237. #14579133C23semidirect
238. #14579133C23semidirect
239. #14579133C23semidirect
240. #14579133C23semidirect
241. #14579133C23semidirect
242. #14579133C23semidirect
243. #14579133C23semidirect
244. #14579132C23semidirect
247. #14579129C23semidirect
248. #14579129C23semidirect
249. #14579129C23semidirect
250. #14579129C23semidirect
251. #14579129C23semidirect
252. #14579129C23semidirect
253. C4×Dic158C23semidirect
254. #14579126C23semidirect
255. C4×D316C23semidirect
256. D4×Dic79C23semidirect
257. D4×Dic79C23semidirect
260. C4×C22⋊D79C23semidirect
261. C4×C22⋊D79C23semidirect
262. C4×C22⋊D79C23semidirect
263. (C22⋊D79)⋊C4C23semidirect
264. (C22⋊D79)⋊C4C23semidirect
265. #14579120C23semidirect
266. #14579118C23semidirect
267. #14579118C23semidirect
284. C2×Dic79⋊C4C23semidirect
309. C2×(C2×D79)⋊C4C23semidirect
310. C22⋊C4×D79C23semidirect
317. C2×C4×Dic79C23semidirect
320. C2×#41×C79C23semidirect
321. C2×#41×C79C23semidirect
336. #127×C79C23semidirect
337. #127×C79C23semidirect
339. #121×C79C23semidirect
340. #121×C79C23semidirect
341. #121×C79C23semidirect
342. C4×Q8×C79C23semidirect
343. C4×D4×C79C23semidirect
344. C4×D4×C79C23semidirect
699. C2×C79#3546semidirect
713. C2×#550D79semidirect
730. C79C2×#3546semidirect
735. C22×#41C2×D79semidirect
736. C22×#41C2×D79semidirect
746. #550C2×D79semidirect
768. C2×#127C2×D79semidirect
769. C2×#127C2×D79semidirect
820. C2×#121C2×D79semidirect
821. C2×#121C2×D79semidirect
822. C2×#121C2×D79semidirect
833. C2×C4×Q8C2×D79semidirect
844. C2×C4×D4C2×D79semidirect
845. C2×C4×D4C2×D79semidirect
865. C2×#41C22×D79semidirect
866. C2×#41C22×D79semidirect
921. #127C22×D79semidirect
922. #127C22×D79semidirect
972. #121C22×D79semidirect
973. #121C22×D79semidirect
974. #121C22×D79semidirect
985. C4×Q8C22×D79semidirect
996. C4×D4C22×D79semidirect
997. C4×D4C22×D79semidirect
1407. C2#23777759direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237777592
C2×#190993012
C2×#190993002
C2×#190992852
C2×#190992622
C2×#190992332
C2×#190992312
C2×#190992122
C2×#190992092
C2×#190992022
C2×#190992012
C2×#190991972
C2×#190991852
C2×#190991802
C2×#190991462
C2×#190991452
C2×#190991402
C2×#190991272
C2×#190991262
C2×#190991092
C2×#190991082
C2×#190990932
C2×#550×C792
C2×#354679