Finite Group Databasebeta

← C2×#23777442 #35196273

Subgroups — C2×#23777442 #35196273

Order 20224.

7910 conjugacy classes of subgroups.

The subgroup lattice has 1372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777442C2132yesmaximal, direct product factor
2C2×#19099284C211yesmaximal, characteristic, complemented
3C2×#19099267C212yesmaximal, complemented
4C2×#19099254C211yesmaximal, characteristic, complemented
5C2×#19099253C211yesmaximal, characteristic, complemented
6C2×#19099243C212yesmaximal, complemented
7C2×#19099242C212yesmaximal, complemented
8C2×Q8×C22⋊D79C211yesmaximal, characteristic, complemented
9C2×#19099221C211yesmaximal, characteristic, complemented
10C2×#19099213C211yesmaximal, characteristic, complemented
11C2×#19099212C211yesmaximal, characteristic, complemented
12C2×#19099202C212yesmaximal, complemented
13C2×#19099177C212yesmaximal, complemented
14C2×#19099159C212yesmaximal, complemented
15C2×#19099158C212yesmaximal, complemented
16C2×#19099117C211yesmaximal, characteristic, complemented
17C2×#19099092C211yesmaximal, characteristic, complemented
18C2×#19099073C211yesmaximal, characteristic, complemented
19C2×#19099070C211yesmaximal, characteristic, complemented
20C22×#14579137C211yesmaximal, characteristic, complemented
21C2×C22⋊Q8×D79C211yesmaximal, characteristic, complemented
22C2×#19099042C212yesmaximal, complemented
23C2×C4×D4×D79C211yesmaximal, characteristic, complemented
24C2×#548×C79C211yesmaximal, characteristic, complemented
25C22×#11929623C2212yes—
26C22×#11929623C2211yescharacteristic, complemented
27C22×Q8×D79C2211yescharacteristic, complemented
28C22×D4×D79C2211yescharacteristic
29C23×C4×D79C2211yescharacteristic
30C23×C4×D79C2211yescharacteristic
31#19099284C22116yescomplemented
32#19099267C22132yescomplemented
33#19099254C22116yescomplemented
34#19099253C22116yescomplemented
35#19099243C22132yescomplemented
36#19099242C22132yescomplemented
37Q8×C22⋊D79C22116yescomplemented
38#19099221C22116yescomplemented
39#19099213C22116yescomplemented
40#19099212C22116yescomplemented
41#19099202C22132yescomplemented
42#19099177C22132yescomplemented
43#19099159C22132yescomplemented
44#19099158C22132yescomplemented
45#19099117C22116yescomplemented
46C2×#14579160C2211yescharacteristic, complemented
47C2×#14579159C2212yescomplemented
48C2×#14579159C2211yescharacteristic, complemented
49#19099092C22116yescomplemented
50C2×#14579156C2212yescomplemented
51C2×#14579155C2212yescomplemented
52C2×#14579154C2212yescomplemented
53C2×#14579154C2212yescomplemented
54C2×#14579154C2212yescomplemented
55C2×#14579153C2211yescharacteristic, complemented
56C2×#14579151C2212yescomplemented
57C2×#14579151C2212yescomplemented
58C2×#14579151C2212yescomplemented
59C2×#14579147C2212yes—
60C2×#14579147C2212yescomplemented
61#19099073C22116yescomplemented
62#19099070C22116yescomplemented
63C2×#14579146C2212yes—
64C2×#14579144C2212yescomplemented
65C2×#14579143C2212yes—
66C2×#14579143C2212yescomplemented
67C2×#14579143C2212yescomplemented
68C2×#14579142C2212yes—
69C2×#14579142C2212yescomplemented
70C2×#14579142C2212yescomplemented
71C2×#14579142C2212yescomplemented
72C2×#14579141C2211yescharacteristic
73C2×#14579140C2211yescharacteristic, complemented
74C2×#14579140C2211yescharacteristic, complemented
75C2×#14579140C2212yescomplemented
76C2×#14579139C2212yes—
77C2×#14579139C2212yes—
78C2×#14579138C2212yescomplemented
79C2×#14579138C2212yescomplemented
80C2×#14579138C2212yescomplemented
81C2×#14579137C2211yescharacteristic
82C2×#14579137C2211yescharacteristic
83C2×#14579137C2212yes—
84C2×#14579137C2212yescomplemented
85C2×#14579137C2211yescharacteristic, complemented
86C2×#14579137C2211yescharacteristic, complemented
87C2×#14579137C2211yescharacteristic, complemented
88C2×#14579137C2212yescomplemented
89C2×#14579137C22116yescomplemented
90C22⋊Q8×D79C22116yescomplemented
91C2×#14579134C2212yes—
92C2×#14579133C2212yes—
93C2×#14579132C2211yescharacteristic
94C2×#14579132C2211yescharacteristic, complemented
95C2×#14579129C2212yes—
96C2×#14579129C2212yes—
97#19099042C22132yescomplemented
98C2×Q8×Dic79C2211yescharacteristic, complemented
99C2×C4×Dic158C2212yescomplemented
100C2×C4×Dic158C2211yescharacteristic, complemented
101C2×#14579126C2212yescomplemented
102C2×C4×D316C2211yescharacteristic
103C2×D4×Dic79C2211yescharacteristic
104C2×D4×Dic79C2212yescomplemented
105C2×D4×Dic79C2211yescharacteristic, complemented
106C2×#14579123C2211yescharacteristic
107C2×C4×C22⋊D79C2211yescharacteristic
108C2×C4×C22⋊D79C2211yescharacteristic
109C2×C4×C22⋊D79C2212yes—
110C2×C4×C22⋊D79C2212yes—
111C2×C4×C22⋊D79C2212yescomplemented
112C2×(C22⋊D79)⋊C4C2211yescharacteristic
113C2×(C22⋊D79)⋊C4C2211yescharacteristic
114C2×(C22⋊D79)⋊C4C2212yes—
115C2×(C22⋊D79)⋊C4C2212yes—
116C2×(C22⋊D79)⋊C4C2212yescomplemented
117C4×D4×D79C22116yescomplemented
118C2×#14579120C2211yescharacteristic, complemented
119C2×#14579119C2211yescharacteristic, complemented
120C2×#14579118C2212yes—
121C2×#14579118C2212yescomplemented
122C2×#14579117C2212yescomplemented
123C2×#14579117C2212yescomplemented
124C22×C4⋊Dic79C2211yescharacteristic, complemented
125C22×Dic79⋊C4C2212yescomplemented
126C22×Dic79⋊C4C2212yescomplemented
127C2×C4⋊C4×D79C2211yescharacteristic
128C2×C4⋊C4×D79C2212yescomplemented
129C2×C4⋊C4×D79C2211yescharacteristic, complemented
130C22×(C2×D79)⋊C4C2212yes—
131C2×C22⋊C4×D79C2211yescharacteristic
132C2×C22⋊C4×D79C2211yescharacteristic
133C2×C22⋊C4×D79C2212yes—
134C2×C42×D79C2211yescharacteristic
135C22×#41×C79C2211yescharacteristic, complemented
136C23×Q8×C79C2211yescharacteristic, complemented
137#548×C79C22116yescomplemented
138C2×#124×C79C2212yescomplemented
139C2×#124×C79C2211yescharacteristic, complemented
140C2×C22⋊Q8×C79C2211yescharacteristic, complemented
141C2×C22⋊Q8×C79C2212yescomplemented
142C2×#121×C79C2212yes—
143C2×#121×C79C2211yescharacteristic, complemented
144C2×C4×Q8×C79C2211yescharacteristic, complemented
145C2×C4×D4×C79C2211yescharacteristic
146C2×C4×D4×C79C2212yescomplemented
147C24×D79C2311yescharacteristic
148C24×D79C2311yescharacteristic
149C2×#11929623—216no—
150C2×#11929623—44no—
151C2×#11929623C23116yes—
152C2×#11929623C2318yescomplemented
153C22×Dic158C2312yes—
154C22×Dic158C2311yescharacteristic
155C22×Dic158C2312yes—
156C2×Q8×D79—44no—
157C2×Q8×D79C2318yescomplemented
158C22×D316C2311yescharacteristic
159C22×C22⋊D79C2312yes—
160C22×C22⋊D79C2311yescharacteristic
161C22×C22⋊D79C2312yes—
162C22×C22⋊D79C2312yes—
163C22×C22⋊D79C2311yescharacteristic
164C2×D4×D79—28no—
165C2×D4×D79C2318yes—
166C23×Dic79C2312yes—
167C23×Dic79C2312yes—
168C23×Dic79C2311yescharacteristic
169C23×Dic79C2312yes—
170C23×Dic79C2311yescharacteristic
171C22×C4×D79—44no—
172C22×C4×D79—44no—
173C22×C4×D79C2311yescharacteristic
174C22×C4×D79C2311yescharacteristic
175C22×C4×D79C2311yescharacteristic
176C22×C4×D79C2312yes—
177C22×C4×D79C2311yescharacteristic
178C22×C4×D79C2311yescharacteristic
179C22×C4×D79C2311yescharacteristic
180C22×C4×D79C2311yescharacteristic
181C22×C4×D79C2312yes—
182C22×C4×D79C2311yescharacteristic
183C22×C4×D79C2318yes—
184C22×C4×D79C2318yes—
185C22×C4×D79C2311yescharacteristic
186#14579160C2318yescomplemented
187#14579159C23116yescomplemented
188#14579159C2318yescomplemented
189#14579156C23116yescomplemented
190#14579155C23116yescomplemented
191#14579154C23116yescomplemented
192#14579154C23116yescomplemented
193#14579154C23116yescomplemented
194#14579153C2318yescomplemented
195#14579151C23116yescomplemented
196#14579151C23116yescomplemented
197#14579151C23116yescomplemented
198#14579147C23116yes—
199#14579147C23116yescomplemented
200#14579146C23116yes—
201#14579144C23116yescomplemented
202#14579143C23116yes—
203#14579143C23116yescomplemented
204#14579143C23116yescomplemented
205#14579142C23116yes—
206#14579142C23116yescomplemented
207#14579142C23116yescomplemented
208#14579142C23116yescomplemented
209#14579141C2318yes—
210#14579140C23116yescomplemented
211#14579140C2318yescomplemented
212#14579140C2318yescomplemented
213#14579139C23116yes—
214#14579139C23116yes—
215#14579138C23116yescomplemented
216#14579138C23116yescomplemented
217#14579138C23116yescomplemented
218#14579137C23116yes—
219#14579137C2318yes—
220#14579137C2318yes—
221#14579137C23116yescomplemented
222#14579137C23116yescomplemented
223#14579137C2318yescomplemented
224#14579137C2318yescomplemented
225#14579137C2318yescomplemented
226#14579134C23116yes—
227#14579133C23116yes—
228#14579132C2318yes—
229#14579132C2318yescomplemented
230#14579129C23116yes—
231#14579129C23116yes—
232Q8×Dic79C2318yescomplemented
233C4×Dic158C23116yescomplemented
234C4×Dic158C2318yescomplemented
235#14579126C23116yescomplemented
236C4×D316C2318yes—
237D4×Dic79C2318yes—
238D4×Dic79C23116yescomplemented
239D4×Dic79C2318yescomplemented
240#14579123C2318yes—
241C4×C22⋊D79C23116yes—
242C4×C22⋊D79C2318yes—
243C4×C22⋊D79C2318yes—
244C4×C22⋊D79C23116yes—
245C4×C22⋊D79C23116yescomplemented
246(C22⋊D79)⋊C4C2318yes—
247(C22⋊D79)⋊C4C23116yes—
248(C22⋊D79)⋊C4C23116yes—
249(C22⋊D79)⋊C4C2318yes—
250(C22⋊D79)⋊C4C23116yescomplemented
251#14579120C2318yescomplemented
252#14579119C2318yescomplemented
253#14579118C23116yes—
254#14579118C23116yescomplemented
255#14579117C23116yescomplemented
256#14579117C23116yescomplemented
257C2×C4⋊Dic79C2311yescharacteristic
258C2×C4⋊Dic79C2311yescharacteristic
259C2×C4⋊Dic79C2312yes—
260C2×C4⋊Dic79C2311yescharacteristic
261C2×C4⋊Dic79C2312yes—
262C2×C4⋊Dic79C2311yescharacteristic
263C2×C4⋊Dic79C2312yes—
264C2×C4⋊Dic79C2318yescomplemented
265C2×Dic79⋊C4C2311yescharacteristic
266C2×Dic79⋊C4C2311yescharacteristic
267C2×Dic79⋊C4C2312yes—
268C2×Dic79⋊C4C2312yes—
269C2×Dic79⋊C4C2312yes—
270C2×Dic79⋊C4C2312yes—
271C2×Dic79⋊C4C2312yes—
272C2×Dic79⋊C4C2312yes—
273C2×Dic79⋊C4C2312yes—
274C2×Dic79⋊C4C2312yes—
275C2×Dic79⋊C4C2312yes—
276C2×Dic79⋊C4C2312yes—
277C2×Dic79⋊C4C2312yes—
278C2×Dic79⋊C4C2312yes—
279C2×Dic79⋊C4C2312yes—
280C2×Dic79⋊C4C2312yes—
281C2×Dic79⋊C4C23116yescomplemented
282C2×Dic79⋊C4C23116yescomplemented
283C4⋊C4×D79C2318yes—
284C4⋊C4×D79C23116yescomplemented
285C4⋊C4×D79C2318yescomplemented
286C2×C22⋊Dic79C2311yescharacteristic
287C2×C22⋊Dic79C2311yescharacteristic
288C2×C22⋊Dic79C2312yes—
289C2×C22⋊Dic79C2312yes—
290C2×C22⋊Dic79C2312yes—
291C2×C22⋊Dic79C2312yes—
292C2×C22⋊Dic79C2312yes—
293C2×C22⋊Dic79C2312yes—
294C2×(C2×D79)⋊C4C23116yes—
295C2×(C2×D79)⋊C4C2312yes—
296C2×(C2×D79)⋊C4C2312yes—
297C2×(C2×D79)⋊C4C2311yescharacteristic
298C2×(C2×D79)⋊C4C2311yescharacteristic
299C2×(C2×D79)⋊C4C2311yescharacteristic
300C2×(C2×D79)⋊C4C2311yescharacteristic
301C2×(C2×D79)⋊C4C2312yes—
302C2×(C2×D79)⋊C4C2312yes—
303C2×(C2×D79)⋊C4C2312yes—
304C2×(C2×D79)⋊C4C2312yes—
305C2×(C2×D79)⋊C4C2312yes—
306C22⋊C4×D79C23116yes—
307C22⋊C4×D79C2318yes—
308C22⋊C4×D79C2318yes—
309C2×C4×Dic79C2311yescharacteristic
310C2×C4×Dic79C2311yescharacteristic
311C2×C4×Dic79C2311yescharacteristic
312C2×C4×Dic79C2312yes—
313C2×C4×Dic79C2312yes—
314C2×C4×Dic79C2312yes—
315C2×C4×Dic79C2312yes—
316C42×D79C2318yes—
317C2×#41×C79—44no—
318C2×#41×C79C2318yescomplemented
319C22×Q8×C79—44no—
320C22×Q8×C79C2311yescharacteristic
321C22×Q8×C79C2311yescharacteristic
322C22×Q8×C79C2312yes—
323C22×Q8×C79C2318yescomplemented
324C22×D4×C79C2311yescharacteristic
325C22×D4×C79C2312yes—
326C22×D4×C79C2311yescharacteristic
327C22×D4×C79C2312yes—
328C23×C4×C79C2311yescharacteristic
329C23×C4×C79C2311yescharacteristic
330C23×C4×C79C2312yes—
331C23×C4×C79C2312yes—
332#124×C79C23116yescomplemented
333#124×C79C2318yescomplemented
334C22⋊Q8×C79C23116yescomplemented
335C22⋊Q8×C79C2318yescomplemented
336#121×C79C23116yes—
337#121×C79C2318yescomplemented
338C4×Q8×C79C2318yescomplemented
339C4×D4×C79C2318yes—
340C4×D4×C79C23116yescomplemented
341C2×C4⋊C4×C79C2311yescharacteristic
342C2×C4⋊C4×C79C2312yes—
343C2×C4⋊C4×C79C2312yes—
344C2×C4⋊C4×C79C2311yescharacteristic
345C2×C22⋊C4×C79C2311yescharacteristic
346C2×C22⋊C4×C79C2311yescharacteristic
347C2×C22⋊C4×C79C2312yes—
348C2×C22⋊C4×C79C2312yes—
349C2×C22⋊C4×C79C2312yes—
350C2×C22⋊C4×C79C2312yes—
351C2×C42×C79C2311yescharacteristic
352C2×C42×C79C2312yes—
353C23×D79—24no—
354C23×D79—24no—
355C23×D79—24no—
356C23×D79—24no—
357C23×D79—42no—
358C23×D79—42no—
359C23×D79C2411yescharacteristic
360C23×D79C2414yes—
361C23×D79C2414yes—
362C23×D79C2411yescharacteristic
363C23×D79C2411yescharacteristic
364#11929623—264no—
365#11929623—416no—
366C2×Dic158—28no—
367C2×Dic158—24no—
368C2×Dic158—44no—
369C2×Dic158C2414yes—
370C2×Dic158C2418yes—
371C2×Dic158C2418yes—
372Q8×D79—416no—
373C2×D316—24no—
374C2×D316C2414yes—
375C2×C22⋊D79—24no—
376C2×C22⋊D79—28no—
377C2×C22⋊D79—28no—
378C2×C22⋊D79—44no—
379C2×C22⋊D79#4118yescomplemented
380C2×C22⋊D79C2418yes—
381C2×C22⋊D79C2418yes—
382C2×C22⋊D79C2414yes—
383C2×C22⋊D79C2418yes—
384C2×C22⋊D79C2414yes—
385D4×D79—232no—
386C22×Dic79—28no—
387C22×Dic79—28no—
388C22×Dic79—44no—
389C22×Dic79—42no—
390C22×Dic79—42no—
391C22×Dic79C2412yes—
392C22×Dic79C2411yescharacteristic
393C22×Dic79C2412yes—
394C22×Dic79C2418yes—
395C22×Dic79C2418yes—
396C22×Dic79C2412yes—
397C22×Dic79C2411yescharacteristic
398C22×Dic79C2411yescharacteristic
399C22×Dic79C2411yescharacteristic
400C22×Dic79C2412yes—
401C22×Dic79C2418yes—
402C22×Dic79C2414yes—
403C22×Dic79C2414yes—
404C22×Dic79C2411yescharacteristic
405C2×C4×D79—24no—
406C2×C4×D79—28no—
407C2×C4×D79—24no—
408C2×C4×D79—24no—
409C2×C4×D79—24no—
410C2×C4×D79—24no—
411C2×C4×D79—44no—
412C2×C4×D79—42no—
413C2×C4×D79—42no—
414C2×C4×D79—42no—
415C2×C4×D79—42no—
416C2×C4×D79—416no—
417C2×C4×D79—416no—
418C2×C4×D79C2414yes—
419C2×C4×D79C2418yes—
420C2×C4×D79C2414yes—
421C2×C4×D79C2414yes—
422C2×C4×D79C2414yes—
423C2×C4×D79C2414yes—
424C2×C4×D79C2418yes—
425C2×C4×D79C2414yes—
426C2×C4×D79C2414yes—
427C2×C4×D79C2414yes—
428C2×C4×D79C2414yes—
429C4⋊Dic79C2414yes—
430C4⋊Dic79C2414yes—
431C4⋊Dic79C2418yes—
432C4⋊Dic79C2414yes—
433C4⋊Dic79C2418yes—
434C4⋊Dic79C2414yes—
435C4⋊Dic79C2418yes—
436Dic79⋊C4C2414yes—
437Dic79⋊C4C2414yes—
438Dic79⋊C4C2418yes—
439Dic79⋊C4C2418yes—
440Dic79⋊C4C2418yes—
441Dic79⋊C4C2418yes—
442Dic79⋊C4C2418yes—
443Dic79⋊C4C2418yes—
444Dic79⋊C4C2418yes—
445Dic79⋊C4C2418yes—
446Dic79⋊C4C2418yes—
447Dic79⋊C4C2418yes—
448Dic79⋊C4C2418yes—
449Dic79⋊C4C2418yes—
450Dic79⋊C4C2418yes—
451Dic79⋊C4C2418yes—
452C22⋊Dic79C2414yes—
453C22⋊Dic79C2414yes—
454C22⋊Dic79C2418yes—
455C22⋊Dic79C2418yes—
456C22⋊Dic79C2418yes—
457C22⋊Dic79C2418yes—
458C22⋊Dic79C2418yes—
459C22⋊Dic79C2418yes—
460(C2×D79)⋊C4C2418yes—
461(C2×D79)⋊C4C2418yes—
462(C2×D79)⋊C4C2414yes—
463(C2×D79)⋊C4C2414yes—
464(C2×D79)⋊C4C2414yes—
465(C2×D79)⋊C4C2414yes—
466(C2×D79)⋊C4C2418yes—
467(C2×D79)⋊C4C2418yes—
468(C2×D79)⋊C4C2418yes—
469(C2×D79)⋊C4C2418yes—
470(C2×D79)⋊C4C2418yes—
471C4×Dic79C2414yes—
472C4×Dic79C2414yes—
473C4×Dic79C2414yes—
474C4×Dic79C2418yes—
475C4×Dic79C2418yes—
476C4×Dic79C2418yes—
477C4×Dic79C2418yes—
478C24×C79C2411yescharacteristic
479C24×C79C2412yes—
480C24×C79C2411yescharacteristic
481#41×C79—416no—
482C2×Q8×C79—24no—
483C2×Q8×C79—24no—
484C2×Q8×C79—44no—
485C2×Q8×C79—416no—
486C2×Q8×C79C2414yes—
487C2×Q8×C79C2414yes—
488C2×Q8×C79C2418yes—
489C2×D4×C79—28no—
490C2×D4×C79—24no—
491C2×D4×C79—24no—
492C2×D4×C79—44no—
493C2×D4×C79C2418yes—
494C2×D4×C79C2414yes—
495C2×D4×C79C2414yes—
496C2×D4×C79C2418yes—
497C22×C4×C79—24no—
498C22×C4×C79—24no—
499C22×C4×C79—44no—
500C22×C4×C79—44no—
501C22×C4×C79C2412yes—
502C22×C4×C79C2412yes—
503C22×C4×C79C2411yescharacteristic
504C22×C4×C79C2411yescharacteristic
505C22×C4×C79C2412yes—
506C22×C4×C79C2411yescharacteristic
507C22×C4×C79C2411yescharacteristic
508C22×C4×C79C2414yes—
509C22×C4×C79C2414yes—
510C22×C4×C79C2418yes—
511C22×C4×C79C2418yes—
512C22×C4×C79C2411yescharacteristic
513C4⋊C4×C79C2414yes—
514C4⋊C4×C79C2418yes—
515C4⋊C4×C79C2418yes—
516C4⋊C4×C79C2414yes—
517C22⋊C4×C79C2414yes—
518C22⋊C4×C79C2414yes—
519C22⋊C4×C79C2418yes—
520C22⋊C4×C79C2418yes—
521C22⋊C4×C79C2418yes—
522C22⋊C4×C79C2418yes—
523C42×C79C2414yes—
524C42×C79C2418yes—
525C23×C79—22no—
526C23×C79—22no—
527C23×C79—24no—
528C23×C79—22no—
529C23×C79—24no—
530C23×C79—22no—
531C23×C79—24no—
532C23×C79—22no—
533C23×C79C2×#4114yes—
534C23×C79C2512yes—
535C23×C79C2514yes—
536C23×C79C2512yes—
537C23×C79C2511yescharacteristic
538C22×D79—22no—
539C22×D79—22no—
540C22×D79—22no—
541C22×D79—22no—
542C22×D79—28no—
543C22×D79—22no—
544C22×D79—22no—
545C22×D79—22no—
546C22×D79—28no—
547C22×D79—28no—
548C22×D79—28no—
549C22×D79—44no—
550C22×D79—44no—
551C22×D79—416no—
552C22×D79—416no—
553C22×D79C2×#4114yes—
554C22×D792−1+414yes—
555C22×D79C2512yes—
556C22×D79C2512yes—
557C22×D79C2512yes—
558Q8×C79—28no—
559Q8×C79—28no—
560Q8×C79—48no—
561D4×C79—28no—
562D4×C79—216no—
563D4×C79—28no—
564D4×C79—48no—
565C2×C4×C79—22no—
566C2×C4×C79—24no—
567C2×C4×C79—22no—
568C2×C4×C79—22no—
569C2×C4×C79—24no—
570C2×C4×C79—24no—
571C2×C4×C79—22no—
572C2×C4×C79—28no—
573C2×C4×C79—28no—
574C2×C4×C79—48no—
575C2×C4×C79—48no—
576C2×C4×C79H(5,𝔽2)14yes—
577C2×C4×C79C2512yes—
578C2×C4×C79C2512yes—
579C2×C4×C79C2514yes—
580C2×C4×C79C2514yes—
581C2×C4×C79C2512yes—
582C2×C4×C79C2514yes—
583C2×C4×C79C2512yes—
584C2×C4×C79C2512yes—
585C22⋊D79—216no—
586C22⋊D79—216no—
587C22⋊D79—28no—
588C22⋊D79—48no—
589C22⋊D79C2×#41116yescomplemented
590C2×Dic79—24no—
591C2×Dic79—24no—
592C2×Dic79—216no—
593C2×Dic79—22no—
594C2×Dic79—22no—
595C2×Dic79—22no—
596C2×Dic79—24no—
597C2×Dic79—22no—
598C2×Dic79—24no—
599C2×Dic79—216no—
600C2×Dic79—44no—
601C2×Dic79—44no—
602C2×Dic79—48no—
603C2×Dic79C2×#4114yes—
604C2×Dic79C2514yes—
605C2×Dic79C2512yes—
606C2×Dic79C2514yes—
607C2×Dic79C2512yes—
608C2×Dic79C2512yes—
609C2×Dic79C2514yes—
610C2×Dic79C2514yes—
611C2×Dic79C2512yes—
612C2×Dic79C2512yes—
613D316—28no—
614C4×D79—216no—
615C4×D79—28no—
616C4×D79—28no—
617C4×D79—28no—
618C4×D79—28no—
619C4×D79—28no—
620C4×D79—44no—
621C4×D79—44no—
622C4×D79—44no—
623C4×D79—44no—
624C4×D79—48no—
625Dic158—28no—
626Dic158—216no—
627Dic158—48no—
628C22×C79—22no—
629C22×C79—22no—
630C22×C79—28no—
631C22×C79—22no—
632C22×C79—24no—
633C22×C79—24no—
634C22×C79—22no—
635C22×C79—24no—
636C22×C79—22no—
637C22×C79—44no—
638C22×C79—48no—
639C22×C79C22×#4114yes—
640C22×C79C22×#4112yes—
641C22×C79C2×H(5,𝔽2)12yes—
642C22×C79C2×2−1+412yes—
643C22×C79C2611yescharacteristic
644C2×D79—22no—
645C2×D79—22no—
646C2×D79—22no—
647C2×D79—22no—
648C2×D79—28no—
649C2×D79—28no—
650C2×D79—22no—
651C2×D79—22no—
652C2×D79—22no—
653C2×D79—416no—
654C2×D79—416no—
655C2×D79—44no—
656C2×D79C22×#4114yes—
657C2×D79C2×2−1+414yes—
658C4×C79—24no—
659C4×C79—22no—
660C4×C79—22no—
661C4×C79—22no—
662C4×C79—24no—
663C4×C79—24no—
664C4×C79—22no—
665C4×C79C2×H(5,𝔽2)14yes—
666Dic79—24no—
667Dic79—24no—
668Dic79—24no—
669Dic79—22no—
670Dic79—22no—
671Dic79—22no—
672Dic79—24no—
673Dic79—22no—
674Dic79C22×#4114yes—
675C2×#3520—791nomaximal, Sylow
676C2×C79—24no—
677C2×C79—42no—
678C2×C79—44no—
679C2×C79#352014yescomplemented
680C2×C79C23×#4111yescharacteristic
681C2×C79C22×H(5,𝔽2)11yescharacteristic
682C2×C79C22×2−1+411yescharacteristic
683D79—24no—
684D79—24no—
685D79—42no—
686#3520—7932no—
687C2×#556—791no—
688C2×#554—792no—
689C2×#552—791no—
690C2×#552—791no—
691C2×#551—792no—
692C2×#551—792no—
693C2×D4×Q8—791no—
694C2×#548—791no—
695C2×#548D7911yescharacteristic, complemented
696C2×#547—791no—
697C2×#547—791no—
698C2×#546—792no—
699C2×#542—792no—
700C2×#539—792no—
701C2×#539—792no—
702C2×#533—791no—
703C2×#529—791no—
704C2×#525—791no—
705C2×#525—791no—
706C22×C22⋊Q8—791no—
707C22×C22⋊Q8—791no—
708C2×#520—792no—
709C22×C4×D4—791no—
710C79C2×#352011yescharacteristic, complemented, Sylow
711C22×#41—791no—
712C22×#41—792no—
713C22×#41C2×D7911yescharacteristic, complemented
714C23×Q8—791no—
715C23×Q8C2×D7911yescharacteristic, complemented
716C23×D4—791no—
717C24×C4—791no—
718C24×C4—791no—
719#556—7916no—
720#554—7932no—
721#552—7916no—
722#552—7916no—
723#551—7932no—
724#551—7932no—
725D4×Q8—7916no—
726#548—7916no—
727#548C2×D79116yescomplemented
728#547—7916no—
729#547—7916no—
730#546—7932no—
731#542—7932no—
732#539—7932no—
733#539—7932no—
734#533—7916no—
735C2×C4⋊Q8—791no—
736C2×C4⋊Q8—792no—
737C2×C4⋊Q8—791no—
738#529—7916no—
739C2×#126—792no—
740C2×#126—792no—
741C2×#126—792no—
742C2×#126—792no—
743C2×#126—792no—
744C2×#125—792no—
745C2×#125—792no—
746C2×#125—792no—
747C2×#125—791no—
748C2×#124—792no—
749C2×#124—792no—
750C2×#124C2×D7911yescharacteristic, complemented
751C2×#124C2×D7912yescomplemented
752#525—7916no—
753#525—7916no—
754C2×#123—792no—
755C2×#123—792no—
756C2×#123—792no—
757C2×#123—792no—
758C2×#123—792no—
759C2×#123—792no—
760C2×#123—792no—
761C2×#123—792no—
762C2×#123—792no—
763C2×C22⋊Q8—791no—
764C2×C22⋊Q8—791no—
765C2×C22⋊Q8—792no—
766C2×C22⋊Q8—791no—
767C2×C22⋊Q8—791no—
768C2×C22⋊Q8—792no—
769C2×C22⋊Q8—791no—
770C2×C22⋊Q8—792no—
771C2×C22⋊Q8—7916no—
772C2×C22⋊Q8—791no—
773C2×C22⋊Q8—791no—
774C2×C22⋊Q8—792no—
775C2×C22⋊Q8—7916no—
776C2×C22⋊Q8—791no—
777C2×C22⋊Q8—792no—
778C2×C22⋊Q8—792no—
779C2×C22⋊Q8—792no—
780C2×C22⋊Q8—792no—
781C2×C22⋊Q8—792no—
782C2×C22⋊Q8C2×D7911yescharacteristic, complemented
783C2×C22⋊Q8C2×D7912yescomplemented
784C2×#121—791no—
785C2×#121—791no—
786C2×#121—792no—
787C2×#121—792no—
788C2×#121C2×D7912yes—
789C2×#121C2×D7911yescharacteristic, complemented
790C2×#120—792no—
791C2×#120—792no—
792#520—7932no—
793C2×C4×Q8—791no—
794C2×C4×Q8—792no—
795C2×C4×Q8—792no—
796C2×C4×Q8—791no—
797C2×C4×Q8C2×D7911yescharacteristic, complemented
798C2×C4×D4—791no—
799C2×C4×D4—792no—
800C2×C4×D4—791no—
801C2×C4×D4—791no—
802C2×C4×D4—791no—
803C2×C4×D4—792no—
804C2×C4×D4—792no—
805C2×C4×D4—792no—
806C2×C4×D4—7916no—
807C2×C4×D4—791no—
808C2×C4×D4—791no—
809C2×C4×D4—791no—
810C2×C4×D4—792no—
811C2×C4×D4—792no—
812C2×C4×D4—792no—
813C2×C4×D4—791no—
814C2×C4×D4C2×D7911yescharacteristic
815C2×C4×D4C2×D7912yescomplemented
816C2×#117—791no—
817C2×#117—791no—
818C2×#117—792no—
819C2×#117—792no—
820C2×#117—792no—
821C2×#117—792no—
822C22×C4⋊C4—792no—
823C22×C4⋊C4—792no—
824C22×C4⋊C4—791no—
825C22×C4⋊C4—791no—
826C22×C4⋊C4—792no—
827C22×C4⋊C4—791no—
828C22×C22⋊C4—792no—
829C22×C22⋊C4—791no—
830C22×C22⋊C4—791no—
831C22×C22⋊C4—792no—
832C22×C42—791no—
833C25—791no—
834C25—791no—
835C2×#41—44no—
836C2×#41—3164no—
837C2×#41—798no—
838C2×#41—7916no—
839C2×#41—15816no—
840C2×#41C22×D7918yescomplemented
841C22×Q8—44no—
842C22×Q8—3164no—
843C22×Q8—798no—
844C22×Q8—792no—
845C22×Q8—792no—
846C22×Q8—791no—
847C22×Q8C22×D7911yescharacteristic
848C22×Q8C22×D7911yescharacteristic
849C22×Q8C22×D7912yes—
850C22×Q8C22×D7918yescomplemented
851C22×D4—792no—
852C22×D4—791no—
853C22×D4—792no—
854C22×D4—792no—
855C22×D4—791no—
856C22×D4—798no—
857C22×D4—791no—
858C22×D4—1588no—
859C22×D4C22×D7911yescharacteristic
860C22×D4C22×D7912yes—
861C22×D4C22×D7911yescharacteristic
862C22×D4C22×D7912yes—
863C23×C4—3164no—
864C23×C4—3164no—
865C23×C4—791no—
866C23×C4—792no—
867C23×C4—791no—
868C23×C4—792no—
869C23×C4—791no—
870C23×C4—791no—
871C23×C4—791no—
872C23×C4—791no—
873C23×C4—798no—
874C23×C4—798no—
875C23×C4—792no—
876C23×C4—792no—
877C23×C4—791no—
878C23×C4—792no—
879C23×C4—791no—
880C23×C4—791no—
881C23×C4—791no—
882C23×C4—791no—
883C23×C4C22×D7911yescharacteristic
884C23×C4C22×D7911yescharacteristic
885C23×C4C22×D7912yes—
886C23×C4C22×D7912yes—
887C4⋊Q8—798no—
888C4⋊Q8—7916no—
889C4⋊Q8—798no—
890#126—7916no—
891#126—7916no—
892#126—7916no—
893#126—7916no—
894#126—7916no—
895#125—7916no—
896#125—7916no—
897#125—7916no—
898#125—798no—
899#124—7916no—
900#124—7916no—
901#124C22×D7918yescomplemented
902#124C22×D79116yescomplemented
903#123—7916no—
904#123—7916no—
905#123—7916no—
906#123—7916no—
907#123—7916no—
908#123—7916no—
909#123—7916no—
910#123—7916no—
911#123—7916no—
912C22⋊Q8—798no—
913C22⋊Q8—798no—
914C22⋊Q8—7916no—
915C22⋊Q8—798no—
916C22⋊Q8—798no—
917C22⋊Q8—7916no—
918C22⋊Q8—798no—
919C22⋊Q8—7916no—
920C22⋊Q8—798no—
921C22⋊Q8—798no—
922C22⋊Q8—7916no—
923C22⋊Q8—798no—
924C22⋊Q8—7916no—
925C22⋊Q8—7916no—
926C22⋊Q8—7916no—
927C22⋊Q8—7916no—
928C22⋊Q8—7916no—
929C22⋊Q8C22×D7918yescomplemented
930C22⋊Q8C22×D79116yescomplemented
931#121—798no—
932#121—798no—
933#121—7916no—
934#121—7916no—
935#121C22×D79116yes—
936#121C22×D7918yescomplemented
937#120—7916no—
938#120—7916no—
939C4×Q8—798no—
940C4×Q8—7916no—
941C4×Q8—7916no—
942C4×Q8—798no—
943C4×Q8C22×D7918yescomplemented
944C4×D4—798no—
945C4×D4—7916no—
946C4×D4—798no—
947C4×D4—798no—
948C4×D4—798no—
949C4×D4—7916no—
950C4×D4—7916no—
951C4×D4—7916no—
952C4×D4—798no—
953C4×D4—798no—
954C4×D4—798no—
955C4×D4—7916no—
956C4×D4—7916no—
957C4×D4—7916no—
958C4×D4—798no—
959C4×D4C22×D7918yes—
960C4×D4C22×D79116yescomplemented
961#117—798no—
962#117—798no—
963#117—7916no—
964#117—7916no—
965#117—7916no—
966#117—7916no—
967C2×C4⋊C4—791no—
968C2×C4⋊C4—792no—
969C2×C4⋊C4—792no—
970C2×C4⋊C4—792no—
971C2×C4⋊C4—791no—
972C2×C4⋊C4—791no—
973C2×C4⋊C4—791no—
974C2×C4⋊C4—791no—
975C2×C4⋊C4—792no—
976C2×C4⋊C4—792no—
977C2×C4⋊C4—792no—
978C2×C4⋊C4—792no—
979C2×C4⋊C4—7916no—
980C2×C4⋊C4—7916no—
981C2×C4⋊C4—792no—
982C2×C4⋊C4—792no—
983C2×C4⋊C4—798no—
984C2×C4⋊C4—792no—
985C2×C4⋊C4—791no—
986C2×C4⋊C4—792no—
987C2×C4⋊C4—792no—
988C2×C4⋊C4—792no—
989C2×C4⋊C4—792no—
990C2×C4⋊C4—792no—
991C2×C4⋊C4—792no—
992C2×C4⋊C4—792no—
993C2×C4⋊C4—798no—
994C2×C4⋊C4—7916no—
995C2×C4⋊C4—798no—
996C2×C4⋊C4C22×D7911yescharacteristic
997C2×C4⋊C4C22×D7911yescharacteristic
998C2×C4⋊C4C22×D7912yes—
999C2×C4⋊C4C22×D7912yes—
1000C2×C22⋊C4—791no—
1001C2×C22⋊C4—791no—
1002C2×C22⋊C4—792no—
1003C2×C22⋊C4—792no—
1004C2×C22⋊C4—792no—
1005C2×C22⋊C4—792no—
1006C2×C22⋊C4—792no—
1007C2×C22⋊C4—792no—
1008C2×C22⋊C4—792no—
1009C2×C22⋊C4—791no—
1010C2×C22⋊C4—792no—
1011C2×C22⋊C4—792no—
1012C2×C22⋊C4—791no—
1013C2×C22⋊C4—791no—
1014C2×C22⋊C4—791no—
1015C2×C22⋊C4—792no—
1016C2×C22⋊C4—792no—
1017C2×C22⋊C4—7916no—
1018C2×C22⋊C4—792no—
1019C2×C22⋊C4—792no—
1020C2×C22⋊C4—798no—
1021C2×C22⋊C4—798no—
1022C2×C22⋊C4—7916no—
1023C2×C22⋊C4C22×D7911yescharacteristic
1024C2×C22⋊C4C22×D7911yescharacteristic
1025C2×C22⋊C4C22×D7912yes—
1026C2×C22⋊C4C22×D7912yes—
1027C2×C22⋊C4C22×D7912yes—
1028C2×C22⋊C4C22×D7912yes—
1029C2×C42—791no—
1030C2×C42—792no—
1031C2×C42—792no—
1032C2×C42—792no—
1033C2×C42—792no—
1034C2×C42—791no—
1035C2×C42—791no—
1036C2×C42—798no—
1037C2×C42C22×D7912yes—
1038C2×C42C22×D7911yescharacteristic
1039C24—3162no—
1040C24—3162no—
1041C24—794no—
1042C24—794no—
1043C24—791no—
1044C24—791no—
1045C24—791no—
1046C24—1584no—
1047C24—1584no—
1048C24—1584no—
1049C24—1584no—
1050C24C23×D7911yescharacteristic
1051C24C23×D7912yes—
1052C24C23×D7911yescharacteristic
1053#41—416no—
1054#41—31616no—
1055#41—15864no—
1056C2×Q8—24no—
1057C2×Q8—24no—
1058C2×Q8—44no—
1059C2×Q8—416no—
1060C2×Q8—3164no—
1061C2×Q8—31616no—
1062C2×Q8—798no—
1063C2×Q8—798no—
1064C2×Q8—794no—
1065C2×Q8—1588no—
1066C2×Q8—1584no—
1067C2×Q8C23×D7914yes—
1068C2×Q8C23×D7914yes—
1069C2×Q8C23×D7918yes—
1070C2×D4—24no—
1071C2×D4—28no—
1072C2×D4—24no—
1073C2×D4—44no—
1074C2×D4—3164no—
1075C2×D4—798no—
1076C2×D4—798no—
1077C2×D4—794no—
1078C2×D4—798no—
1079C2×D4—798no—
1080C2×D4—794no—
1081C2×D4—794no—
1082C2×D4—1584no—
1083C2×D4—1584no—
1084C2×D4—15832no—
1085C2×D4—1588no—
1086C2×D4—1588no—
1087C2×D4C23×D7914yes—
1088C2×D4C23×D7918yes—
1089C2×D4C23×D7914yes—
1090C2×D4C23×D7918yes—
1091C22×C4—24no—
1092C22×C4—24no—
1093C22×C4—44no—
1094C22×C4—44no—
1095C22×C4—3162no—
1096C22×C4—3162no—
1097C22×C4—3162no—
1098C22×C4—3162no—
1099C22×C4—3164no—
1100C22×C4—31616no—
1101C22×C4—31616no—
1102C22×C4—3162no—
1103C22×C4—3162no—
1104C22×C4—3164no—
1105C22×C4—794no—
1106C22×C4—798no—
1107C22×C4—794no—
1108C22×C4—798no—
1109C22×C4—794no—
1110C22×C4—794no—
1111C22×C4—794no—
1112C22×C4—794no—
1113C22×C4—791no—
1114C22×C4—798no—
1115C22×C4—798no—
1116C22×C4—792no—
1117C22×C4—791no—
1118C22×C4—792no—
1119C22×C4—791no—
1120C22×C4—791no—
1121C22×C4—792no—
1122C22×C4—792no—
1123C22×C4—791no—
1124C22×C4—794no—
1125C22×C4—794no—
1126C22×C4—794no—
1127C22×C4—798no—
1128C22×C4—794no—
1129C22×C4—794no—
1130C22×C4—1584no—
1131C22×C4—1584no—
1132C22×C4—1588no—
1133C22×C4—1588no—
1134C22×C4—1588no—
1135C22×C4—1584no—
1136C22×C4—1584no—
1137C22×C4—1584no—
1138C22×C4C23×D7914yes—
1139C22×C4C23×D7914yes—
1140C22×C4C23×D7911yescharacteristic
1141C22×C4C23×D7911yescharacteristic
1142C22×C4C23×D7912yes—
1143C22×C4C23×D7911yescharacteristic
1144C22×C4C23×D7912yes—
1145C22×C4C23×D7912yes—
1146C22×C4C23×D7911yescharacteristic
1147C22×C4C23×D7918yes—
1148C22×C4C23×D7918yes—
1149C22×C4C23×D7911yescharacteristic
1150C4⋊C4—794no—
1151C4⋊C4—798no—
1152C4⋊C4—798no—
1153C4⋊C4—798no—
1154C4⋊C4—794no—
1155C4⋊C4—798no—
1156C4⋊C4—798no—
1157C4⋊C4—798no—
1158C4⋊C4—798no—
1159C4⋊C4—798no—
1160C4⋊C4—798no—
1161C4⋊C4—798no—
1162C4⋊C4—798no—
1163C4⋊C4—798no—
1164C4⋊C4—798no—
1165C4⋊C4—798no—
1166C4⋊C4—794no—
1167C4⋊C4—794no—
1168C4⋊C4—794no—
1169C4⋊C4—798no—
1170C4⋊C4—798no—
1171C4⋊C4—794no—
1172C4⋊C4—798no—
1173C4⋊C4C23×D7914yes—
1174C4⋊C4C23×D7914yes—
1175C4⋊C4C23×D7918yes—
1176C4⋊C4C23×D7918yes—
1177C22⋊C4—794no—
1178C22⋊C4—794no—
1179C22⋊C4—798no—
1180C22⋊C4—798no—
1181C22⋊C4—798no—
1182C22⋊C4—798no—
1183C22⋊C4—798no—
1184C22⋊C4—798no—
1185C22⋊C4—798no—
1186C22⋊C4—794no—
1187C22⋊C4—798no—
1188C22⋊C4—798no—
1189C22⋊C4—794no—
1190C22⋊C4—794no—
1191C22⋊C4—794no—
1192C22⋊C4—798no—
1193C22⋊C4—798no—
1194C22⋊C4—798no—
1195C22⋊C4—798no—
1196C22⋊C4C23×D7914yes—
1197C22⋊C4C23×D7914yes—
1198C22⋊C4C23×D7918yes—
1199C22⋊C4C23×D7918yes—
1200C22⋊C4C23×D7918yes—
1201C22⋊C4C23×D7918yes—
1202C42—794no—
1203C42—794no—
1204C42—794no—
1205C42—798no—
1206C42—798no—
1207C42—798no—
1208C42—798no—
1209C42C23×D7914yes—
1210C42C23×D7918yes—
1211C23—22no—
1212C23—22no—
1213C23—22no—
1214C23—24no—
1215C23—24no—
1216C23—22no—
1217C23—24no—
1218C23—22no—
1219C23—31616no—
1220C23—3164no—
1221C23—3164no—
1222C23—31616no—
1223C23—794no—
1224C23—792no—
1225C23—792no—
1226C23—794no—
1227C23—792no—
1228C23—1588no—
1229C23—1588no—
1230C23—1588no—
1231C23—1582no—
1232C23—1582no—
1233C23—1588no—
1234C23—1582no—
1235C23—1582no—
1236C23—1582no—
1237C23—1582no—
1238C23—1582no—
1239C23#41×D7914yes—
1240C23C24×D7912yes—
1241C23C24×D7914yes—
1242C23C24×D7912yes—
1243C23C24×D7911yescharacteristic
1244Q8—28no—
1245Q8—28no—
1246Q8—48no—
1247Q8—3168no—
1248Q8—15816no—
1249Q8—1588no—
1250D4—28no—
1251D4—216no—
1252D4—28no—
1253D4—48no—
1254D4—3168no—
1255D4—7916no—
1256D4—1588no—
1257D4—1588no—
1258D4—15816no—
1259D4—15816no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—24no—
1263C2×C4—24no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—24no—
1267C2×C4—28no—
1268C2×C4—28no—
1269C2×C4—48no—
1270C2×C4—48no—
1271C2×C4—3164no—
1272C2×C4—3164no—
1273C2×C4—3164no—
1274C2×C4—3164no—
1275C2×C4—3168no—
1276C2×C4—3164no—
1277C2×C4—3164no—
1278C2×C4—3168no—
1279C2×C4—792no—
1280C2×C4—794no—
1281C2×C4—794no—
1282C2×C4—792no—
1283C2×C4—794no—
1284C2×C4—792no—
1285C2×C4—792no—
1286C2×C4—794no—
1287C2×C4—794no—
1288C2×C4—792no—
1289C2×C4—1588no—
1290C2×C4—15816no—
1291C2×C4—1588no—
1292C2×C4—15816no—
1293C2×C4—1582no—
1294C2×C4—1582no—
1295C2×C4—1582no—
1296C2×C4—1584no—
1297C2×C4—1582no—
1298C2×C4—1584no—
1299C2×C4—1584no—
1300C2×C4—1584no—
1301C2×C4—15816no—
1302C2×C4—1588no—
1303C2×C4—1588no—
1304C2×C4—1588no—
1305C2×C4#1457920614yes—
1306C2×C4C24×D7912yes—
1307C2×C4C24×D7912yes—
1308C2×C4C24×D7914yes—
1309C2×C4C24×D7912yes—
1310C2×C4C24×D7914yes—
1311C2×C4C24×D7914yes—
1312C2×C4C24×D7912yes—
1313C2×C4C24×D7912yes—
1314C22—22no—
1315C22—22no—
1316C22—28no—
1317C22—24no—
1318C22—22no—
1319C22—22no—
1320C22—24no—
1321C22—24no—
1322C22—22no—
1323C22—44no—
1324C22—48no—
1325C22—31616no—
1326C22—31616no—
1327C22—3164no—
1328C22—794no—
1329C22—794no—
1330C22—1582no—
1331C22—1582no—
1332C22—1582no—
1333C22—1582no—
1334C22—1582no—
1335C22—1582no—
1336C22—1582no—
1337C22—1588no—
1338C22—1588no—
1339C22C2×#41×D7914yes—
1340C22C2×#41×D7912yes—
1341C22C2×#1457920612yes—
1342C222−1+4×D7912yes—
1343C22C25×D7911yescharacteristic
1344C4—22no—
1345C4—24no—
1346C4—22no—
1347C4—22no—
1348C4—24no—
1349C4—24no—
1350C4—22no—
1351C4—794no—
1352C4—1584no—
1353C4—1584no—
1354C4—1582no—
1355C4—1582no—
1356C4—1582no—
1357C4—1584no—
1358C4—1582no—
1359C4—1584no—
1360C4C2×#1457920614yes—
1361C2—24no—
1362C2—42no—
1363C2—44no—
1364C2—3162no—
1365C2—1584no—
1366C2—1584no—
1367C2#2377744214yesdirect product factor
1368C2C22×#41×D7911yescharacteristic
1369C2C22×#1457920611yescharacteristic
1370C2C2×2−1+4×D7911yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#548×C79C2
socleC23×C79C25
hypercenterC2×#548D79
hypocenterC79C2×#3520
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. #23777442C2direct (N × H)
2. C2×#19099284C2semidirect
3. C2×#19099267C2semidirect
4. C2×#19099254C2semidirect
5. C2×#19099253C2semidirect
6. C2×#19099243C2semidirect
7. C2×#19099242C2semidirect
8. C2×Q8×C22⋊D79C2semidirect
9. C2×#19099221C2semidirect
10. C2×#19099213C2semidirect
11. C2×#19099212C2semidirect
12. C2×#19099202C2semidirect
13. C2×#19099177C2semidirect
14. C2×#19099159C2semidirect
15. C2×#19099158C2semidirect
16. C2×#19099117C2semidirect
17. C2×#19099092C2semidirect
18. C2×#19099073C2semidirect
19. C2×#19099070C2semidirect
20. C22×#14579137C2semidirect
21. C2×C22⋊Q8×D79C2semidirect
22. C2×#19099042C2semidirect
23. C2×C4×D4×D79C2semidirect
24. C2×#548×C79C2semidirect
26. C22×#11929623C22semidirect
27. C22×Q8×D79C22semidirect
31. #19099284C22semidirect
32. #19099267C22semidirect
33. #19099254C22semidirect
34. #19099253C22semidirect
35. #19099243C22semidirect
36. #19099242C22semidirect
37. Q8×C22⋊D79C22semidirect
38. #19099221C22semidirect
39. #19099213C22semidirect
40. #19099212C22semidirect
41. #19099202C22semidirect
42. #19099177C22semidirect
43. #19099159C22semidirect
44. #19099158C22semidirect
45. #19099117C22semidirect
46. C2×#14579160C22semidirect
47. C2×#14579159C22semidirect
48. C2×#14579159C22semidirect
49. #19099092C22semidirect
50. C2×#14579156C22semidirect
51. C2×#14579155C22semidirect
52. C2×#14579154C22semidirect
53. C2×#14579154C22semidirect
54. C2×#14579154C22semidirect
55. C2×#14579153C22semidirect
56. C2×#14579151C22semidirect
57. C2×#14579151C22semidirect
58. C2×#14579151C22semidirect
60. C2×#14579147C22semidirect
61. #19099073C22semidirect
62. #19099070C22semidirect
64. C2×#14579144C22semidirect
66. C2×#14579143C22semidirect
67. C2×#14579143C22semidirect
69. C2×#14579142C22semidirect
70. C2×#14579142C22semidirect
71. C2×#14579142C22semidirect
73. C2×#14579140C22semidirect
74. C2×#14579140C22semidirect
75. C2×#14579140C22semidirect
78. C2×#14579138C22semidirect
79. C2×#14579138C22semidirect
80. C2×#14579138C22semidirect
84. C2×#14579137C22semidirect
85. C2×#14579137C22semidirect
86. C2×#14579137C22semidirect
87. C2×#14579137C22semidirect
88. C2×#14579137C22semidirect
89. C2×#14579137C22semidirect
90. C22⋊Q8×D79C22semidirect
94. C2×#14579132C22semidirect
97. #19099042C22semidirect
98. C2×Q8×Dic79C22semidirect
99. C2×C4×Dic158C22semidirect
100. C2×C4×Dic158C22semidirect
101. C2×#14579126C22semidirect
104. C2×D4×Dic79C22semidirect
105. C2×D4×Dic79C22semidirect
111. C2×C4×C22⋊D79C22semidirect
116. C2×(C22⋊D79)⋊C4C22semidirect
117. C4×D4×D79C22semidirect
118. C2×#14579120C22semidirect
119. C2×#14579119C22semidirect
121. C2×#14579118C22semidirect
122. C2×#14579117C22semidirect
123. C2×#14579117C22semidirect
124. C22×C4⋊Dic79C22semidirect
125. C22×Dic79⋊C4C22semidirect
126. C22×Dic79⋊C4C22semidirect
128. C2×C4⋊C4×D79C22semidirect
129. C2×C4⋊C4×D79C22semidirect
135. C22×#41×C79C22semidirect
136. C23×Q8×C79C22semidirect
137. #548×C79C22semidirect
138. C2×#124×C79C22semidirect
139. C2×#124×C79C22semidirect
140. C2×C22⋊Q8×C79C22semidirect
141. C2×C22⋊Q8×C79C22semidirect
143. C2×#121×C79C22semidirect
144. C2×C4×Q8×C79C22semidirect
146. C2×C4×D4×C79C22semidirect
152. C2×#11929623C23semidirect
157. C2×Q8×D79C23semidirect
186. #14579160C23semidirect
187. #14579159C23semidirect
188. #14579159C23semidirect
189. #14579156C23semidirect
190. #14579155C23semidirect
191. #14579154C23semidirect
192. #14579154C23semidirect
193. #14579154C23semidirect
194. #14579153C23semidirect
195. #14579151C23semidirect
196. #14579151C23semidirect
197. #14579151C23semidirect
199. #14579147C23semidirect
201. #14579144C23semidirect
203. #14579143C23semidirect
204. #14579143C23semidirect
206. #14579142C23semidirect
207. #14579142C23semidirect
208. #14579142C23semidirect
210. #14579140C23semidirect
211. #14579140C23semidirect
212. #14579140C23semidirect
215. #14579138C23semidirect
216. #14579138C23semidirect
217. #14579138C23semidirect
221. #14579137C23semidirect
222. #14579137C23semidirect
223. #14579137C23semidirect
224. #14579137C23semidirect
225. #14579137C23semidirect
229. #14579132C23semidirect
232. Q8×Dic79C23semidirect
233. C4×Dic158C23semidirect
234. C4×Dic158C23semidirect
235. #14579126C23semidirect
238. D4×Dic79C23semidirect
239. D4×Dic79C23semidirect
245. C4×C22⋊D79C23semidirect
250. (C22⋊D79)⋊C4C23semidirect
251. #14579120C23semidirect
252. #14579119C23semidirect
254. #14579118C23semidirect
255. #14579117C23semidirect
256. #14579117C23semidirect
264. C2×C4⋊Dic79C23semidirect
281. C2×Dic79⋊C4C23semidirect
282. C2×Dic79⋊C4C23semidirect
284. C4⋊C4×D79C23semidirect
285. C4⋊C4×D79C23semidirect
318. C2×#41×C79C23semidirect
323. C22×Q8×C79C23semidirect
332. #124×C79C23semidirect
333. #124×C79C23semidirect
334. C22⋊Q8×C79C23semidirect
335. C22⋊Q8×C79C23semidirect
337. #121×C79C23semidirect
338. C4×Q8×C79C23semidirect
340. C4×D4×C79C23semidirect
379. C2×C22⋊D79#41semidirect
589. C22⋊D79C2×#41semidirect
679. C2×C79#3520semidirect
695. C2×#548D79semidirect
710. C79C2×#3520semidirect
713. C22×#41C2×D79semidirect
715. C23×Q8C2×D79semidirect
727. #548C2×D79semidirect
750. C2×#124C2×D79semidirect
751. C2×#124C2×D79semidirect
782. C2×C22⋊Q8C2×D79semidirect
783. C2×C22⋊Q8C2×D79semidirect
789. C2×#121C2×D79semidirect
797. C2×C4×Q8C2×D79semidirect
815. C2×C4×D4C2×D79semidirect
840. C2×#41C22×D79semidirect
850. C22×Q8C22×D79semidirect
901. #124C22×D79semidirect
902. #124C22×D79semidirect
929. C22⋊Q8C22×D79semidirect
930. C22⋊Q8C22×D79semidirect
936. #121C22×D79semidirect
943. C4×Q8C22×D79semidirect
960. C4×D4C22×D79semidirect
1367. C2#23777442direct (N × H)

Maximal subgroups

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

subgroupindex
#237774422
C2×#190992842
C2×#190992672
C2×#190992542
C2×#190992532
C2×#190992432
C2×#190992422
C2×Q8×C22⋊D792
C2×#190992212
C2×#190992132
C2×#190992122
C2×#190992022
C2×#190991772
C2×#190991592
C2×#190991582
C2×#190991172
C2×#190990922
C2×#190990732
C2×#190990702
C22×#145791372
C2×C22⋊Q8×D792
C2×#190990422
C2×C4×D4×D792
C2×#548×C792
C2×#352079