Finite Group Databasebeta

← C2×#23777443 #35196272

Subgroups — C2×#23777443 #35196272

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#23777443C2132yesmaximal, direct product factor
2C2×#19099284C211yesmaximal, characteristic, complemented
3C2×#19099267C212yesmaximal, complemented
4C2×#19099248C211yesmaximal, characteristic, complemented
5C2×#19099247C211yesmaximal, characteristic, complemented
6C2×#19099240C212yesmaximal, complemented
7C2×#19099239C212yesmaximal, complemented
8C2×Q8×C22⋊D79C211yesmaximal, characteristic, complemented
9C2×#19099224C211yesmaximal, characteristic, complemented
10C2×#19099223C211yesmaximal, characteristic, complemented
11C2×#19099215C211yesmaximal, characteristic, complemented
12C2×#19099214C211yesmaximal, characteristic, complemented
13C2×#19099203C212yesmaximal, complemented
14C2×#19099183C212yesmaximal, complemented
15C2×#19099160C212yesmaximal, complemented
16C2×#19099159C212yesmaximal, complemented
17C2×#19099115C211yesmaximal, characteristic, complemented
18C2×#19099099C211yesmaximal, characteristic, complemented
19C2×#19099076C211yesmaximal, characteristic, complemented
20C2×#19099074C211yesmaximal, characteristic, complemented
21C2×C22⋊Q8×D79C211yesmaximal, characteristic, complemented
22C2×#19099044C212yesmaximal, complemented
23C22×C4×C22⋊D79C211yesmaximal, characteristic, complemented
24C22×C22⋊Q8×C79C211yesmaximal, characteristic, complemented
25C22×#11929625C2211yescharacteristic, complemented
26C22×#11929624C2212yes—
27C22×#11929624C2211yescharacteristic, complemented
28C22×Q8×D79C2211yescharacteristic, complemented
29C23×C22⋊D79C2211yescharacteristic
30C23×C4×D79C2211yescharacteristic
31#19099284C22116yescomplemented
32#19099267C22132yescomplemented
33#19099248C22116yescomplemented
34#19099247C22116yescomplemented
35#19099240C22132yescomplemented
36#19099239C22132yescomplemented
37Q8×C22⋊D79C22116yescomplemented
38#19099224C22116yescomplemented
39#19099223C22116yescomplemented
40#19099215C22116yescomplemented
41#19099214C22116yescomplemented
42#19099203C22132yescomplemented
43#19099183C22132yescomplemented
44#19099160C22132yescomplemented
45#19099159C22132yescomplemented
46#19099115C22116yescomplemented
47C2×#14579160C2211yescharacteristic, complemented
48C2×#14579159C2212yescomplemented
49C2×#14579159C2211yescharacteristic, complemented
50#19099099C22116yescomplemented
51C2×#14579156C2212yescomplemented
52C2×#14579156C2212yescomplemented
53C2×#14579156C2212yescomplemented
54C2×#14579154C2212yescomplemented
55C2×#14579154C2212yescomplemented
56C2×#14579152C2211yescharacteristic, complemented
57C2×#14579151C2212yescomplemented
58C2×#14579151C2212yescomplemented
59C2×#14579151C2212yescomplemented
60C2×#14579150C2212yescomplemented
61C2×#14579150C2211yescharacteristic, complemented
62C2×#14579147C2212yes—
63C2×#14579147C2212yescomplemented
64#19099076C22116yescomplemented
65#19099074C22116yescomplemented
66C2×#14579146C2212yescomplemented
67C2×#14579146C2212yescomplemented
68C2×#14579146C2212yescomplemented
69C2×#14579145C2212yes—
70C2×#14579144C2212yes—
71C2×#14579144C2212yescomplemented
72C2×#14579144C2212yescomplemented
73C2×#14579143C2212yes—
74C2×#14579143C2212yescomplemented
75C2×#14579141C2211yescharacteristic, complemented
76C2×#14579140C2211yescharacteristic
77C2×#14579140C2212yescomplemented
78C2×#14579140C2211yescharacteristic, complemented
79C2×#14579139C2212yescomplemented
80C2×#14579139C2212yescomplemented
81C2×#14579139C2212yescomplemented
82C2×#14579138C2212yes—
83C2×#14579138C2212yes—
84C2×#14579137C2211yescharacteristic, complemented
85C2×#14579137C2212yescomplemented
86C2×#14579137C2212yescomplemented
87C2×#14579137C2211yescharacteristic, complemented
88C22⋊Q8×D79C22116yescomplemented
89C2×#14579136C2211yescharacteristic, complemented
90C2×#14579135C2212yes—
91C2×#14579135C2211yescharacteristic
92C2×#14579135C2211yescharacteristic, complemented
93C2×#14579134C2212yes—
94C2×#14579134C2212yes—
95C2×#14579131C2212yes—
96C2×#14579130C2212yes—
97#19099044C22132yescomplemented
98C2×Q8×Dic79C2211yescharacteristic, complemented
99C2×Q8×Dic79C2211yescharacteristic, complemented
100C2×#14579126C2212yescomplemented
101C2×#14579126C2212yescomplemented
102C2×#14579126C2211yescharacteristic, complemented
103C2×#14579123C2212yescomplemented
104C2×#14579123C2212yescomplemented
105C2×#14579123C2211yescharacteristic, complemented
106C2×C4×C22⋊D79C2211yescharacteristic
107C2×C4×C22⋊D79C2211yescharacteristic
108C2×C4×C22⋊D79C2211yescharacteristic
109C2×C4×C22⋊D79C2211yescharacteristic
110C2×C4×C22⋊D79C2211yescharacteristic
111C2×C4×C22⋊D79C2211yescharacteristic
112C2×C4×C22⋊D79C2211yescharacteristic
113C2×C4×C22⋊D79C2211yescharacteristic
114C2×C4×C22⋊D79C2212yes—
115C2×C4×C22⋊D79C2212yes—
116C2×C4×C22⋊D79C22116yescomplemented
117C2×C4×C22⋊D79C2212yescomplemented
118C2×C4×C22⋊D79C2212yescomplemented
119C2×(C22⋊D79)⋊C4C2212yes—
120C2×(C22⋊D79)⋊C4C2212yes—
121C2×#14579120C2212yescomplemented
122C2×#14579120C2211yescharacteristic, complemented
123C2×#14579119C2212yescomplemented
124C2×#14579119C2212yescomplemented
125C2×#14579119C2211yescharacteristic, complemented
126C2×#14579117C2212yes—
127C22×Dic79⋊C4C2211yescharacteristic
128C2×C4⋊C4×D79C2212yescomplemented
129C2×C4⋊C4×D79C2212yescomplemented
130C2×C4⋊C4×D79C2211yescharacteristic, complemented
131C22×C22⋊Dic79C2211yescharacteristic
132C22×(C2×D79)⋊C4C2211yescharacteristic
133C2×C22⋊C4×D79C2212yes—
134C22×C4×Dic79C2211yescharacteristic
135C23×Q8×C79C2211yescharacteristic, complemented
136C24×C4×C79C2211yescharacteristic
137C2×C22⋊Q8×C79C2211yescharacteristic
138C2×C22⋊Q8×C79C2212yes—
139C2×C22⋊Q8×C79C2211yescharacteristic
140C2×C22⋊Q8×C79C2212yescomplemented
141C2×C22⋊Q8×C79C2211yescharacteristic, complemented
142C2×C22⋊Q8×C79C2211yescharacteristic, complemented
143C2×C22⋊Q8×C79C22116yescomplemented
144C22×C4⋊C4×C79C2212yescomplemented
145C22×C4⋊C4×C79C2211yescharacteristic, complemented
146C22×C22⋊C4×C79C2212yes—
147C24×D79C2311yescharacteristic
148C2×#11929625—44no—
149C2×#11929625C2318yescomplemented
150C2×#11929624—216no—
151C2×#11929624—44no—
152C2×#11929624C23116yes—
153C2×#11929624C2318yescomplemented
154C22×Dic158C2312yes—
155C22×Dic158C2311yescharacteristic
156C22×Dic158C2312yes—
157C2×Q8×D79—44no—
158C2×Q8×D79C2318yescomplemented
159C22×D316C2312yes—
160C22×D316C2311yescharacteristic
161C22×D316C2312yes—
162C22×C22⋊D79—28no—
163C22×C22⋊D79C2318yes—
164C22×C22⋊D79C2312yes—
165C22×C22⋊D79C2311yescharacteristic
166C22×C22⋊D79C2311yescharacteristic
167C22×C22⋊D79C2311yescharacteristic
168C22×C22⋊D79C2312yes—
169C22×C22⋊D79C2312yes—
170C22×C22⋊D79C2311yescharacteristic
171C23×Dic79C2311yescharacteristic
172C23×Dic79C2311yescharacteristic
173C23×Dic79C2311yescharacteristic
174C22×C4×D79—44no—
175C22×C4×D79C2312yes—
176C22×C4×D79C2312yes—
177C22×C4×D79C2311yescharacteristic
178C22×C4×D79C2311yescharacteristic
179C22×C4×D79C2312yes—
180C22×C4×D79C2311yescharacteristic
181C22×C4×D79C2312yes—
182C22×C4×D79C2312yes—
183C22×C4×D79C2311yescharacteristic
184C22×C4×D79C2318yes—
185#14579160C2318yescomplemented
186#14579159C23116yescomplemented
187#14579159C2318yescomplemented
188#14579156C23116yescomplemented
189#14579156C23116yescomplemented
190#14579156C23116yescomplemented
191#14579154C23116yescomplemented
192#14579154C23116yescomplemented
193#14579152C2318yescomplemented
194#14579151C23116yescomplemented
195#14579151C23116yescomplemented
196#14579151C23116yescomplemented
197#14579150C23116yescomplemented
198#14579150C2318yescomplemented
199#14579147C23116yes—
200#14579147C23116yescomplemented
201#14579146C23116yescomplemented
202#14579146C23116yescomplemented
203#14579146C23116yescomplemented
204#14579145C23116yes—
205#14579144C23116yes—
206#14579144C23116yescomplemented
207#14579144C23116yescomplemented
208#14579143C23116yes—
209#14579143C23116yescomplemented
210#14579141C2318yescomplemented
211#14579140C2318yes—
212#14579140C23116yescomplemented
213#14579140C2318yescomplemented
214#14579139C23116yescomplemented
215#14579139C23116yescomplemented
216#14579139C23116yescomplemented
217#14579138C23116yes—
218#14579138C23116yes—
219#14579137C23116yescomplemented
220#14579137C23116yescomplemented
221#14579137C2318yescomplemented
222#14579137C2318yescomplemented
223#14579136C2318yescomplemented
224#14579135C23116yes—
225#14579135C2318yes—
226#14579135C2318yescomplemented
227#14579134C23116yes—
228#14579134C23116yes—
229#14579131C23116yes—
230#14579130C23116yes—
231Q8×Dic79C2318yescomplemented
232Q8×Dic79C2318yescomplemented
233#14579126C23116yescomplemented
234#14579126C2318yescomplemented
235#14579126C23116yescomplemented
236#14579123C23116yescomplemented
237#14579123C2318yescomplemented
238#14579123C23116yescomplemented
239C4×C22⋊D79C2318yes—
240C4×C22⋊D79C2318yes—
241C4×C22⋊D79C2318yes—
242C4×C22⋊D79C23116yes—
243C4×C22⋊D79C2318yes—
244C4×C22⋊D79C2318yes—
245C4×C22⋊D79C2318yes—
246C4×C22⋊D79C2318yes—
247C4×C22⋊D79C23116yes—
248C4×C22⋊D79C2318yes—
249C4×C22⋊D79C23116yescomplemented
250C4×C22⋊D79C23116yescomplemented
251(C22⋊D79)⋊C4C23116yes—
252(C22⋊D79)⋊C4C23116yes—
253#14579120C23116yescomplemented
254#14579120C2318yescomplemented
255#14579119C23116yescomplemented
256#14579119C23116yescomplemented
257#14579119C2318yescomplemented
258#14579117C23116yes—
259C2×C4⋊Dic79C2312yes—
260C2×C4⋊Dic79C2311yescharacteristic
261C2×C4⋊Dic79C2312yes—
262C2×C4⋊Dic79C2311yescharacteristic
263C2×C4⋊Dic79C2312yes—
264C2×C4⋊Dic79C2312yes—
265C2×Dic79⋊C4C2318yes—
266C2×Dic79⋊C4C2311yescharacteristic
267C2×Dic79⋊C4C2312yes—
268C2×Dic79⋊C4C2312yes—
269C2×Dic79⋊C4C2312yes—
270C2×Dic79⋊C4C2312yes—
271C2×Dic79⋊C4C2311yescharacteristic
272C2×Dic79⋊C4C2311yescharacteristic
273C2×Dic79⋊C4C2311yescharacteristic
274C2×Dic79⋊C4C2312yes—
275C2×Dic79⋊C4C2312yes—
276C2×Dic79⋊C4C2312yes—
277C2×Dic79⋊C4C2312yes—
278C2×Dic79⋊C4C2312yes—
279C2×Dic79⋊C4C2312yes—
280C4⋊C4×D79C23116yescomplemented
281C4⋊C4×D79C2318yescomplemented
282C4⋊C4×D79C23116yescomplemented
283C2×C22⋊Dic79C2318yes—
284C2×C22⋊Dic79C2312yes—
285C2×C22⋊Dic79C2311yescharacteristic
286C2×C22⋊Dic79C2311yescharacteristic
287C2×C22⋊Dic79C2311yescharacteristic
288C2×C22⋊Dic79C2311yescharacteristic
289C2×C22⋊Dic79C2312yes—
290C2×C22⋊Dic79C2312yes—
291C2×(C2×D79)⋊C4C2318yes—
292C2×(C2×D79)⋊C4C2312yes—
293C2×(C2×D79)⋊C4C2312yes—
294C2×(C2×D79)⋊C4C2311yescharacteristic
295C2×(C2×D79)⋊C4C2311yescharacteristic
296C2×(C2×D79)⋊C4C2311yescharacteristic
297C2×(C2×D79)⋊C4C2311yescharacteristic
298C2×(C2×D79)⋊C4C2312yes—
299C2×(C2×D79)⋊C4C2312yes—
300C2×(C2×D79)⋊C4C2312yes—
301C2×(C2×D79)⋊C4C2312yes—
302C2×(C2×D79)⋊C4C2312yes—
303C2×(C2×D79)⋊C4C2312yes—
304C2×(C2×D79)⋊C4C2312yes—
305C2×(C2×D79)⋊C4C2312yes—
306C22⋊C4×D79C23116yes—
307C2×C4×Dic79C2311yescharacteristic
308C2×C4×Dic79C2311yescharacteristic
309C2×C4×Dic79C2311yescharacteristic
310C2×C4×Dic79C2311yescharacteristic
311C2×C4×Dic79C2318yes—
312C2×C4×Dic79C2312yes—
313C2×C4×Dic79C2312yes—
314C2×C4×Dic79C2312yes—
315C2×C4×Dic79C2312yes—
316C2×C4×Dic79C2312yes—
317C25×C79C2311yescharacteristic
318C22×Q8×C79—44no—
319C22×Q8×C79C2311yescharacteristic
320C22×Q8×C79C2311yescharacteristic
321C22×Q8×C79C2312yes—
322C22×Q8×C79C2318yescomplemented
323C23×C4×C79—44no—
324C23×C4×C79C2312yes—
325C23×C4×C79C2311yescharacteristic
326C23×C4×C79C2311yescharacteristic
327C23×C4×C79C2311yescharacteristic
328C23×C4×C79C2312yes—
329C23×C4×C79C2311yescharacteristic
330C23×C4×C79C2311yescharacteristic
331C23×C4×C79C2311yescharacteristic
332C23×C4×C79C2318yes—
333C22⋊Q8×C79C23116yes—
334C22⋊Q8×C79C2318yes—
335C22⋊Q8×C79C2318yes—
336C22⋊Q8×C79C23116yescomplemented
337C22⋊Q8×C79C2318yescomplemented
338C22⋊Q8×C79C2318yescomplemented
339C2×C4⋊C4×C79C2312yes—
340C2×C4⋊C4×C79C2312yes—
341C2×C4⋊C4×C79C2311yescharacteristic
342C2×C4⋊C4×C79C2311yescharacteristic
343C2×C4⋊C4×C79C2312yes—
344C2×C4⋊C4×C79C2312yes—
345C2×C4⋊C4×C79C2312yes—
346C2×C4⋊C4×C79C23116yescomplemented
347C2×C4⋊C4×C79C2318yescomplemented
348C2×C22⋊C4×C79C23116yes—
349C2×C22⋊C4×C79C2312yes—
350C2×C22⋊C4×C79C2312yes—
351C2×C22⋊C4×C79C2312yes—
352C2×C22⋊C4×C79C2312yes—
353C23×D79—24no—
354C23×D79—24no—
355C23×D79—42no—
356C23×D79C2411yescharacteristic
357C23×D79C2412yes—
358C23×D79C2414yes—
359C23×D79C2411yescharacteristic
360#11929625—416no—
361#11929624—264no—
362#11929624—416no—
363C2×Dic158—28no—
364C2×Dic158—24no—
365C2×Dic158—44no—
366C2×Dic158C2414yes—
367C2×Dic158C2418yes—
368C2×Dic158C2418yes—
369Q8×D79—416no—
370C2×D316—28no—
371C2×D316—24no—
372C2×D316—44no—
373C2×D316C2418yes—
374C2×D316C2414yes—
375C2×D316C2418yes—
376C2×C22⋊D79—24no—
377C2×C22⋊D79—28no—
378C2×C22⋊D79—24no—
379C2×C22⋊D79—28no—
380C2×C22⋊D79—24no—
381C2×C22⋊D79—232no—
382C2×C22⋊D79—44no—
383C2×C22⋊D79#4118yescomplemented
384C2×C22⋊D79C2418yes—
385C2×C22⋊D79C2418yes—
386C2×C22⋊D79C2414yes—
387C2×C22⋊D79C2414yes—
388C2×C22⋊D79C2414yes—
389C2×C22⋊D79C2418yes—
390C2×C22⋊D79C2414yes—
391C22×Dic79—24no—
392C22×Dic79—24no—
393C22×Dic79—42no—
394C22×Dic79C2412yes—
395C22×Dic79C2411yescharacteristic
396C22×Dic79C2412yes—
397C22×Dic79C2411yescharacteristic
398C22×Dic79C2412yes—
399C22×Dic79C2411yescharacteristic
400C22×Dic79C2414yes—
401C22×Dic79C2411yescharacteristic
402C22×Dic79C2411yescharacteristic
403C22×Dic79C2414yes—
404C22×Dic79C2414yes—
405C22×Dic79C2411yescharacteristic
406C2×C4×D79—28no—
407C2×C4×D79—28no—
408C2×C4×D79—24no—
409C2×C4×D79—24no—
410C2×C4×D79—44no—
411C2×C4×D79—44no—
412C2×C4×D79—44no—
413C2×C4×D79—42no—
414C2×C4×D79—42no—
415C2×C4×D79—416no—
416C2×C4×D79C2414yes—
417C2×C4×D79C2418yes—
418C2×C4×D79C2418yes—
419C2×C4×D79C2414yes—
420C2×C4×D79C2418yes—
421C2×C4×D79C2418yes—
422C2×C4×D79C2418yes—
423C2×C4×D79C2414yes—
424C2×C4×D79C2414yes—
425C4⋊Dic79C2418yes—
426C4⋊Dic79C2414yes—
427C4⋊Dic79C2418yes—
428C4⋊Dic79C2414yes—
429C4⋊Dic79C2418yes—
430C4⋊Dic79C2418yes—
431Dic79⋊C4C2414yes—
432Dic79⋊C4C2418yes—
433Dic79⋊C4C2418yes—
434Dic79⋊C4C2418yes—
435Dic79⋊C4C2418yes—
436Dic79⋊C4C2414yes—
437Dic79⋊C4C2414yes—
438Dic79⋊C4C2414yes—
439Dic79⋊C4C2418yes—
440Dic79⋊C4C2418yes—
441Dic79⋊C4C2418yes—
442Dic79⋊C4C2418yes—
443Dic79⋊C4C2418yes—
444Dic79⋊C4C2418yes—
445C22⋊Dic79C2418yes—
446C22⋊Dic79C2414yes—
447C22⋊Dic79C2414yes—
448C22⋊Dic79C2414yes—
449C22⋊Dic79C2414yes—
450C22⋊Dic79C2418yes—
451C22⋊Dic79C2418yes—
452(C2×D79)⋊C4C2418yes—
453(C2×D79)⋊C4C2418yes—
454(C2×D79)⋊C4C2414yes—
455(C2×D79)⋊C4C2414yes—
456(C2×D79)⋊C4C2414yes—
457(C2×D79)⋊C4C2414yes—
458(C2×D79)⋊C4C2418yes—
459(C2×D79)⋊C4C2418yes—
460(C2×D79)⋊C4C2418yes—
461(C2×D79)⋊C4C2418yes—
462(C2×D79)⋊C4C2418yes—
463(C2×D79)⋊C4C2418yes—
464(C2×D79)⋊C4C2418yes—
465(C2×D79)⋊C4C2418yes—
466C4×Dic79C2414yes—
467C4×Dic79C2414yes—
468C4×Dic79C2414yes—
469C4×Dic79C2414yes—
470C4×Dic79C2418yes—
471C4×Dic79C2418yes—
472C4×Dic79C2418yes—
473C4×Dic79C2418yes—
474C4×Dic79C2418yes—
475C24×C79—24no—
476C24×C79—24no—
477C24×C79—42no—
478C24×C79C2411yescharacteristic
479C24×C79C2414yes—
480C24×C79C2411yescharacteristic
481C24×C79C2411yescharacteristic
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—
489C22×C4×C79—28no—
490C22×C4×C79—24no—
491C22×C4×C79—24no—
492C22×C4×C79—24no—
493C22×C4×C79—416no—
494C22×C4×C79—42no—
495C22×C4×C79—42no—
496C22×C4×C79—42no—
497C22×C4×C79—44no—
498C22×C4×C79C2412yes—
499C22×C4×C79C2412yes—
500C22×C4×C79C2418yes—
501C22×C4×C79C2414yes—
502C22×C4×C79C2412yes—
503C22×C4×C79C2412yes—
504C22×C4×C79C2411yescharacteristic
505C22×C4×C79C2411yescharacteristic
506C22×C4×C79C2411yescharacteristic
507C22×C4×C79C2414yes—
508C22×C4×C79C2414yes—
509C22×C4×C79C2418yes—
510C22×C4×C79C2414yes—
511C22×C4×C79C2414yes—
512C22×C4×C79C2414yes—
513C22×C4×C79C2411yescharacteristic
514C4⋊C4×C79C2418yes—
515C4⋊C4×C79C2418yes—
516C4⋊C4×C79C2414yes—
517C4⋊C4×C79C2414yes—
518C4⋊C4×C79C2418yes—
519C4⋊C4×C79C2418yes—
520C4⋊C4×C79C2418yes—
521C22⋊C4×C79C2418yes—
522C22⋊C4×C79C2418yes—
523C22⋊C4×C79C2418yes—
524C22⋊C4×C79C2418yes—
525C23×C79—22no—
526C23×C79—22no—
527C23×C79—22no—
528C23×C79—22no—
529C23×C79—28no—
530C23×C79—22no—
531C23×C79—22no—
532C23×C79—28no—
533C23×C79—22no—
534C23×C79—44no—
535C23×C79—416no—
536C23×C79C2×#4114yes—
537C23×C792−1+414yes—
538C23×C79C2512yes—
539C23×C79C2512yes—
540C23×C79C2512yes—
541C23×C79C2511yescharacteristic
542C22×D79—22no—
543C22×D79—22no—
544C22×D79—24no—
545C22×D79—22no—
546C22×D79—22no—
547C22×D79—24no—
548C22×D79—24no—
549C22×D79—28no—
550C22×D79—22no—
551C22×D79—28no—
552C22×D79—44no—
553C22×D79—416no—
554C22×D79C2×#4114yes—
555C22×D79C2512yes—
556C22×D79C2514yes—
557C22×D79C2512yes—
558Q8×C79—28no—
559Q8×C79—28no—
560Q8×C79—48no—
561C2×C4×C79—24no—
562C2×C4×C79—24no—
563C2×C4×C79—216no—
564C2×C4×C79—22no—
565C2×C4×C79—22no—
566C2×C4×C79—24no—
567C2×C4×C79—24no—
568C2×C4×C79—22no—
569C2×C4×C79—28no—
570C2×C4×C79—28no—
571C2×C4×C79—28no—
572C2×C4×C79—44no—
573C2×C4×C79—44no—
574C2×C4×C79—44no—
575C2×C4×C79—48no—
576C2×C4×C79H(5,𝔽2)14yes—
577C2×C4×C79C2512yes—
578C2×C4×C79C2512yes—
579C2×C4×C79C2514yes—
580C2×C4×C79C2514yes—
581C2×C4×C79C2514yes—
582C2×C4×C79C2512yes—
583C2×C4×C79C2514yes—
584C2×C4×C79C2512yes—
585C22⋊D79—28no—
586C22⋊D79—216no—
587C22⋊D79—216no—
588C22⋊D79—28no—
589C22⋊D79—28no—
590C22⋊D79—48no—
591C22⋊D79C2×#41116yescomplemented
592C2×Dic79—24no—
593C2×Dic79—22no—
594C2×Dic79—22no—
595C2×Dic79—22no—
596C2×Dic79—24no—
597C2×Dic79—28no—
598C2×Dic79—22no—
599C2×Dic79—22no—
600C2×Dic79—24no—
601C2×Dic79—28no—
602C2×Dic79—44no—
603C2×Dic79C2×#4114yes—
604C2×Dic79C2512yes—
605C2×Dic79C2514yes—
606C2×Dic79C2512yes—
607C2×Dic79C2514yes—
608C2×Dic79C2512yes—
609C2×Dic79C2512yes—
610C2×Dic79C2514yes—
611C2×Dic79C2512yes—
612C2×Dic79C2512yes—
613D316—216no—
614D316—28no—
615D316—48no—
616C4×D79—216no—
617C4×D79—28no—
618C4×D79—28no—
619C4×D79—216no—
620C4×D79—44no—
621C4×D79—44no—
622C4×D79—48no—
623C4×D79—48no—
624C4×D79—48no—
625Dic158—28no—
626Dic158—216no—
627Dic158—48no—
628C22×C79—22no—
629C22×C79—22no—
630C22×C79—22no—
631C22×C79—22no—
632C22×C79—28no—
633C22×C79—28no—
634C22×C79—22no—
635C22×C79—22no—
636C22×C79—22no—
637C22×C79—416no—
638C22×C79—44no—
639C22×C79C22×#4114yes—
640C22×C79C22×#4112yes—
641C22×C79C2×H(5,𝔽2)12yes—
642C22×C79C2×2−1+414yes—
643C22×C79C2×2−1+412yes—
644C22×C79C2611yescharacteristic
645C2×D79—22no—
646C2×D79—22no—
647C2×D79—28no—
648C2×D79—22no—
649C2×D79—24no—
650C2×D79—24no—
651C2×D79—22no—
652C2×D79—24no—
653C2×D79—22no—
654C2×D79—416no—
655C2×D79—48no—
656C2×D79—44no—
657C2×D79C22×#4114yes—
658C4×C79—24no—
659C4×C79—24no—
660C4×C79—22no—
661C4×C79—22no—
662C4×C79—22no—
663C4×C79—24no—
664C4×C79—24no—
665C4×C79C2×H(5,𝔽2)14yes—
666Dic79—22no—
667Dic79—24no—
668Dic79—24no—
669Dic79—22no—
670Dic79—22no—
671Dic79—24no—
672Dic79—22no—
673Dic79—22no—
674Dic79C22×#4114yes—
675C2×#3520—791nomaximal, Sylow
676C2×C79—24no—
677C2×C79—24no—
678C2×C79—42no—
679C2×C79#352014yescomplemented
680C2×C79C23×#4111yescharacteristic
681C2×C79C22×H(5,𝔽2)11yescharacteristic
682C2×C79C22×2−1+411yescharacteristic
683D79—24no—
684D79—44no—
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×#548—791no—
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⋊Q8D7911yescharacteristic, complemented
708C2×#520—792no—
709C22×C4×D4—791no—
710C79C2×#352011yescharacteristic, complemented, Sylow
711C22×#41—791no—
712C22×#41—791no—
713C22×#41—792no—
714C23×Q8—791no—
715C23×Q8C2×D7911yescharacteristic, complemented
716C23×D4—791no—
717C24×C4—791no—
718C24×C4C2×D7911yescharacteristic
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#548—7916no—
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—791no—
745C2×#125—792no—
746C2×#125—792no—
747C2×#125—792no—
748C2×#124—791no—
749C2×#124—792no—
750C2×#124—792no—
751C2×#124—792no—
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—792no—
767C2×C22⋊Q8—791no—
768C2×C22⋊Q8—791no—
769C2×C22⋊Q8—792no—
770C2×C22⋊Q8—7916no—
771C2×C22⋊Q8—792no—
772C2×C22⋊Q8—791no—
773C2×C22⋊Q8—792no—
774C2×C22⋊Q8—792no—
775C2×C22⋊Q8—792no—
776C2×C22⋊Q8—792no—
777C2×C22⋊Q8C2×D7911yescharacteristic
778C2×C22⋊Q8C2×D7911yescharacteristic
779C2×C22⋊Q8C2×D7912yes—
780C2×C22⋊Q8C2×D7912yescomplemented
781C2×C22⋊Q8C2×D7911yescharacteristic, complemented
782C2×C22⋊Q8C2×D7911yescharacteristic, complemented
783C2×C22⋊Q8C2×D79116yescomplemented
784C2×#121—791no—
785C2×#121—791no—
786C2×#121—792no—
787C2×#121—791no—
788C2×#121—792no—
789C2×#121—792no—
790C2×#120—792no—
791C2×#120—792no—
792#520—7932no—
793C2×C4×Q8—791no—
794C2×C4×Q8—791no—
795C2×C4×Q8—792no—
796C2×C4×Q8—792no—
797C2×C4×Q8—791no—
798C2×C4×D4—791no—
799C2×C4×D4—791no—
800C2×C4×D4—791no—
801C2×C4×D4—791no—
802C2×C4×D4—791no—
803C2×C4×D4—791no—
804C2×C4×D4—791no—
805C2×C4×D4—791no—
806C2×C4×D4—7916no—
807C2×C4×D4—792no—
808C2×C4×D4—792no—
809C2×C4×D4—792no—
810C2×C4×D4—792no—
811C2×C4×D4—792no—
812C2×C4×D4—792no—
813C2×C4×D4—791no—
814C2×C4×D4—792no—
815C2×C4×D4—792no—
816C2×#117—792no—
817C2×#117—791no—
818C2×#117—792no—
819C2×#117—792no—
820C2×#117—791no—
821C2×#117—792no—
822C22×C4⋊C4—791no—
823C22×C4⋊C4—792no—
824C22×C4⋊C4—792no—
825C22×C4⋊C4—791no—
826C22×C4⋊C4C2×D7912yescomplemented
827C22×C4⋊C4C2×D7911yescharacteristic, complemented
828C22×C22⋊C4—791no—
829C22×C22⋊C4—791no—
830C22×C22⋊C4—792no—
831C22×C22⋊C4C2×D7912yes—
832C22×C42—791no—
833C25—791no—
834C25C22×D7911yescharacteristic
835C2×#41—3164no—
836C2×#41—3164no—
837C2×#41—798no—
838C2×#41—798no—
839C2×#41—7916no—
840C2×#41—15816no—
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—791no—
857C22×D4—791no—
858C22×D4—798no—
859C22×D4—792no—
860C22×D4—792no—
861C22×D4—791no—
862C22×D4—1588no—
863C23×C4—44no—
864C23×C4—3164no—
865C23×C4—791no—
866C23×C4—792no—
867C23×C4—791no—
868C23×C4—792no—
869C23×C4—792no—
870C23×C4—791no—
871C23×C4—798no—
872C23×C4—791no—
873C23×C4—791no—
874C23×C4—792no—
875C23×C4—792no—
876C23×C4—791no—
877C23×C4—791no—
878C23×C4C22×D7912yes—
879C23×C4C22×D7911yescharacteristic
880C23×C4C22×D7911yescharacteristic
881C23×C4C22×D7911yescharacteristic
882C23×C4C22×D7911yescharacteristic
883C23×C4C22×D7912yes—
884C23×C4C22×D7911yescharacteristic
885C23×C4C22×D7911yescharacteristic
886C23×C4C22×D7918yes—
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—798no—
896#125—7916no—
897#125—7916no—
898#125—7916no—
899#124—798no—
900#124—7916no—
901#124—7916no—
902#124—7916no—
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—7916no—
916C22⋊Q8—798no—
917C22⋊Q8—798no—
918C22⋊Q8—7916no—
919C22⋊Q8—7916no—
920C22⋊Q8—798no—
921C22⋊Q8—7916no—
922C22⋊Q8—7916no—
923C22⋊Q8—7916no—
924C22⋊Q8—7916no—
925C22⋊Q8C22×D7918yes—
926C22⋊Q8C22×D7918yes—
927C22⋊Q8C22×D79116yes—
928C22⋊Q8C22×D79116yescomplemented
929C22⋊Q8C22×D7918yescomplemented
930C22⋊Q8C22×D7918yescomplemented
931#121—798no—
932#121—798no—
933#121—7916no—
934#121—798no—
935#121—7916no—
936#121—7916no—
937#120—7916no—
938#120—7916no—
939C4×Q8—798no—
940C4×Q8—798no—
941C4×Q8—7916no—
942C4×Q8—7916no—
943C4×Q8—798no—
944C4×D4—798no—
945C4×D4—798no—
946C4×D4—798no—
947C4×D4—798no—
948C4×D4—798no—
949C4×D4—798no—
950C4×D4—798no—
951C4×D4—798no—
952C4×D4—7916no—
953C4×D4—7916no—
954C4×D4—7916no—
955C4×D4—7916no—
956C4×D4—7916no—
957C4×D4—7916no—
958C4×D4—798no—
959C4×D4—7916no—
960C4×D4—7916no—
961#117—7916no—
962#117—798no—
963#117—7916no—
964#117—7916no—
965#117—798no—
966#117—7916no—
967C2×C4⋊C4—791no—
968C2×C4⋊C4—792no—
969C2×C4⋊C4—791no—
970C2×C4⋊C4—791no—
971C2×C4⋊C4—791no—
972C2×C4⋊C4—791no—
973C2×C4⋊C4—798no—
974C2×C4⋊C4—792no—
975C2×C4⋊C4—792no—
976C2×C4⋊C4—792no—
977C2×C4⋊C4—792no—
978C2×C4⋊C4—792no—
979C2×C4⋊C4—791no—
980C2×C4⋊C4—792no—
981C2×C4⋊C4—792no—
982C2×C4⋊C4—792no—
983C2×C4⋊C4—792no—
984C2×C4⋊C4—792no—
985C2×C4⋊C4—792no—
986C2×C4⋊C4—792no—
987C2×C4⋊C4—792no—
988C2×C4⋊C4—7916no—
989C2×C4⋊C4—7916no—
990C2×C4⋊C4—798no—
991C2×C4⋊C4C22×D7912yes—
992C2×C4⋊C4C22×D7912yes—
993C2×C4⋊C4C22×D7911yescharacteristic
994C2×C4⋊C4C22×D7911yescharacteristic
995C2×C4⋊C4C22×D7912yes—
996C2×C4⋊C4C22×D7912yes—
997C2×C4⋊C4C22×D7912yes—
998C2×C4⋊C4C22×D79116yescomplemented
999C2×C4⋊C4C22×D7918yescomplemented
1000C2×C22⋊C4—791no—
1001C2×C22⋊C4—792no—
1002C2×C22⋊C4—791no—
1003C2×C22⋊C4—791no—
1004C2×C22⋊C4—791no—
1005C2×C22⋊C4—798no—
1006C2×C22⋊C4—792no—
1007C2×C22⋊C4—792no—
1008C2×C22⋊C4—791no—
1009C2×C22⋊C4—791no—
1010C2×C22⋊C4—791no—
1011C2×C22⋊C4—791no—
1012C2×C22⋊C4—798no—
1013C2×C22⋊C4—792no—
1014C2×C22⋊C4—792no—
1015C2×C22⋊C4—792no—
1016C2×C22⋊C4—792no—
1017C2×C22⋊C4—792no—
1018C2×C22⋊C4—792no—
1019C2×C22⋊C4—792no—
1020C2×C22⋊C4—792no—
1021C2×C22⋊C4—792no—
1022C2×C22⋊C4—792no—
1023C2×C22⋊C4—7916no—
1024C2×C22⋊C4C22×D7912yes—
1025C2×C22⋊C4C22×D7912yes—
1026C2×C22⋊C4C22×D7912yes—
1027C2×C22⋊C4C22×D7912yes—
1028C2×C22⋊C4C22×D79116yes—
1029C2×C42—791no—
1030C2×C42—792no—
1031C2×C42—792no—
1032C2×C42—792no—
1033C2×C42—792no—
1034C2×C42—792no—
1035C2×C42—791no—
1036C2×C42—791no—
1037C2×C42—791no—
1038C2×C42—798no—
1039C24—24no—
1040C24—24no—
1041C24—42no—
1042C24—3162no—
1043C24—794no—
1044C24—791no—
1045C24—791no—
1046C24—792no—
1047C24—1584no—
1048C24—1584no—
1049C24C23×D7911yescharacteristic
1050C24C23×D7914yes—
1051C24C23×D7911yescharacteristic
1052C24C23×D7911yescharacteristic
1053#41—31616no—
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—3164no—
1071C2×D4—3164no—
1072C2×D4—798no—
1073C2×D4—798no—
1074C2×D4—794no—
1075C2×D4—798no—
1076C2×D4—798no—
1077C2×D4—794no—
1078C2×D4—794no—
1079C2×D4—794no—
1080C2×D4—798no—
1081C2×D4—798no—
1082C2×D4—794no—
1083C2×D4—1588no—
1084C2×D4—1584no—
1085C2×D4—15832no—
1086C2×D4—1584no—
1087C2×D4—1584no—
1088C2×D4—1588no—
1089C2×D4—1588no—
1090C2×D4—1584no—
1091C22×C4—28no—
1092C22×C4—24no—
1093C22×C4—24no—
1094C22×C4—24no—
1095C22×C4—416no—
1096C22×C4—42no—
1097C22×C4—42no—
1098C22×C4—42no—
1099C22×C4—44no—
1100C22×C4—3162no—
1101C22×C4—3162no—
1102C22×C4—3164no—
1103C22×C4—3164no—
1104C22×C4—3164no—
1105C22×C4—31616no—
1106C22×C4—3162no—
1107C22×C4—794no—
1108C22×C4—798no—
1109C22×C4—794no—
1110C22×C4—798no—
1111C22×C4—798no—
1112C22×C4—794no—
1113C22×C4—791no—
1114C22×C4—794no—
1115C22×C4—794no—
1116C22×C4—791no—
1117C22×C4—792no—
1118C22×C4—791no—
1119C22×C4—792no—
1120C22×C4—791no—
1121C22×C4—791no—
1122C22×C4—792no—
1123C22×C4—791no—
1124C22×C4—798no—
1125C22×C4—798no—
1126C22×C4—794no—
1127C22×C4—794no—
1128C22×C4—1588no—
1129C22×C4—1588no—
1130C22×C4—1584no—
1131C22×C4—1584no—
1132C22×C4—1584no—
1133C22×C4—1584no—
1134C22×C4C23×D7914yes—
1135C22×C4C23×D7918yes—
1136C22×C4C23×D7914yes—
1137C22×C4C23×D7914yes—
1138C22×C4C23×D7912yes—
1139C22×C4C23×D7911yescharacteristic
1140C22×C4C23×D7911yescharacteristic
1141C22×C4C23×D7912yes—
1142C22×C4C23×D7912yes—
1143C22×C4C23×D7911yescharacteristic
1144C22×C4C23×D7912yes—
1145C22×C4C23×D7914yes—
1146C22×C4C23×D7918yes—
1147C22×C4C23×D7914yes—
1148C22×C4C23×D7914yes—
1149C22×C4C23×D7911yescharacteristic
1150C4⋊C4—794no—
1151C4⋊C4—794no—
1152C4⋊C4—794no—
1153C4⋊C4—794no—
1154C4⋊C4—798no—
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—794no—
1166C4⋊C4—798no—
1167C4⋊C4—794no—
1168C4⋊C4—798no—
1169C4⋊C4—798no—
1170C4⋊C4C23×D7918yes—
1171C4⋊C4C23×D7918yes—
1172C4⋊C4C23×D7914yes—
1173C4⋊C4C23×D7914yes—
1174C4⋊C4C23×D7918yes—
1175C4⋊C4C23×D7918yes—
1176C4⋊C4C23×D7918yes—
1177C22⋊C4—794no—
1178C22⋊C4—798no—
1179C22⋊C4—794no—
1180C22⋊C4—794no—
1181C22⋊C4—794no—
1182C22⋊C4—798no—
1183C22⋊C4—798no—
1184C22⋊C4—794no—
1185C22⋊C4—794no—
1186C22⋊C4—794no—
1187C22⋊C4—794no—
1188C22⋊C4—798no—
1189C22⋊C4—798no—
1190C22⋊C4—798no—
1191C22⋊C4—798no—
1192C22⋊C4—798no—
1193C22⋊C4—798no—
1194C22⋊C4—798no—
1195C22⋊C4—798no—
1196C22⋊C4—798no—
1197C22⋊C4—798no—
1198C22⋊C4C23×D7918yes—
1199C22⋊C4C23×D7918yes—
1200C22⋊C4C23×D7918yes—
1201C22⋊C4C23×D7918yes—
1202C42—794no—
1203C42—794no—
1204C42—794no—
1205C42—794no—
1206C42—798no—
1207C42—798no—
1208C42—798no—
1209C42—798no—
1210C42—798no—
1211C23—22no—
1212C23—22no—
1213C23—22no—
1214C23—22no—
1215C23—22no—
1216C23—28no—
1217C23—22no—
1218C23—28no—
1219C23—22no—
1220C23—44no—
1221C23—416no—
1222C23—31616no—
1223C23—3164no—
1224C23—792no—
1225C23—794no—
1226C23—792no—
1227C23—794no—
1228C23—1588no—
1229C23—1584no—
1230C23—1582no—
1231C23—1584no—
1232C23—1588no—
1233C23—1582no—
1234C23—1584no—
1235C23—1582no—
1236C23—1582no—
1237C23—1582no—
1238C23#41×D7914yes—
1239C23#1457920914yes—
1240C23C24×D7912yes—
1241C23C24×D7912yes—
1242C23C24×D7912yes—
1243C23C24×D7911yescharacteristic
1244Q8—28no—
1245Q8—28no—
1246Q8—48no—
1247Q8—3168no—
1248Q8—15816no—
1249Q8—1588no—
1250D4—3168no—
1251D4—3168no—
1252D4—7916no—
1253D4—15816no—
1254D4—1588no—
1255D4—1588no—
1256D4—15816no—
1257D4—1588no—
1258D4—15816no—
1259D4—1588no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—216no—
1268C2×C4—28no—
1269C2×C4—28no—
1270C2×C4—28no—
1271C2×C4—44no—
1272C2×C4—44no—
1273C2×C4—44no—
1274C2×C4—48no—
1275C2×C4—3164no—
1276C2×C4—3164no—
1277C2×C4—3168no—
1278C2×C4—3168no—
1279C2×C4—3168no—
1280C2×C4—3164no—
1281C2×C4—792no—
1282C2×C4—794no—
1283C2×C4—792no—
1284C2×C4—794no—
1285C2×C4—792no—
1286C2×C4—794no—
1287C2×C4—792no—
1288C2×C4—792no—
1289C2×C4—794no—
1290C2×C4—792no—
1291C2×C4—15816no—
1292C2×C4—15816no—
1293C2×C4—1588no—
1294C2×C4—1582no—
1295C2×C4—1582no—
1296C2×C4—1584no—
1297C2×C4—1588no—
1298C2×C4—1582no—
1299C2×C4—1582no—
1300C2×C4—1584no—
1301C2×C4—1582no—
1302C2×C4—1584no—
1303C2×C4—1588no—
1304C2×C4—1588no—
1305C2×C4#1457920614yes—
1306C2×C4C24×D7914yes—
1307C2×C4C24×D7912yes—
1308C2×C4C24×D7912yes—
1309C2×C4C24×D7914yes—
1310C2×C4C24×D7914yes—
1311C2×C4C24×D7912yes—
1312C2×C4C24×D7914yes—
1313C2×C4C24×D7912yes—
1314C22—22no—
1315C22—22no—
1316C22—22no—
1317C22—22no—
1318C22—28no—
1319C22—28no—
1320C22—22no—
1321C22—22no—
1322C22—22no—
1323C22—416no—
1324C22—44no—
1325C22—31616no—
1326C22—3164no—
1327C22—3168no—
1328C22—794no—
1329C22—1584no—
1330C22—1582no—
1331C22—1584no—
1332C22—1582no—
1333C22—1584no—
1334C22—1582no—
1335C22—1582no—
1336C22—1582no—
1337C22—1588no—
1338C22C2×#41×D7914yes—
1339C22C2×#41×D7912yes—
1340C22C2×#1457920612yes—
1341C22C2×#1457920914yes—
1342C22C2×#1457920912yes—
1343C22C25×D7911yescharacteristic
1344C4—24no—
1345C4—24no—
1346C4—22no—
1347C4—22no—
1348C4—22no—
1349C4—24no—
1350C4—24no—
1351C4—794no—
1352C4—1582no—
1353C4—1584no—
1354C4—1582no—
1355C4—1582no—
1356C4—1584no—
1357C4—1582no—
1358C4—1582no—
1359C4—1584no—
1360C4C2×#1457920614yes—
1361C2—24no—
1362C2—24no—
1363C2—42no—
1364C2—3162no—
1365C2—3164no—
1366C2—1584no—
1367C2#2377744314yesdirect product factor
1368C2C22×#41×D7911yescharacteristic
1369C2C22×#1457920611yescharacteristic
1370C2C22×#1457920911yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC22×C22⋊Q8×C79C2
socleC23×C79C25
hypercenterC22×C22⋊Q8D79
hypocenterC79C2×#3520
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #23777443C2direct (N × H)
2. C2×#19099284C2semidirect
3. C2×#19099267C2semidirect
4. C2×#19099248C2semidirect
5. C2×#19099247C2semidirect
6. C2×#19099240C2semidirect
7. C2×#19099239C2semidirect
8. C2×Q8×C22⋊D79C2semidirect
9. C2×#19099224C2semidirect
10. C2×#19099223C2semidirect
11. C2×#19099215C2semidirect
12. C2×#19099214C2semidirect
13. C2×#19099203C2semidirect
14. C2×#19099183C2semidirect
15. C2×#19099160C2semidirect
16. C2×#19099159C2semidirect
17. C2×#19099115C2semidirect
18. C2×#19099099C2semidirect
19. C2×#19099076C2semidirect
20. C2×#19099074C2semidirect
21. C2×C22⋊Q8×D79C2semidirect
22. C2×#19099044C2semidirect
23. C22×C4×C22⋊D79C2semidirect
24. C22×C22⋊Q8×C79C2semidirect
25. C22×#11929625C22semidirect
27. C22×#11929624C22semidirect
28. C22×Q8×D79C22semidirect
31. #19099284C22semidirect
32. #19099267C22semidirect
33. #19099248C22semidirect
34. #19099247C22semidirect
35. #19099240C22semidirect
36. #19099239C22semidirect
37. Q8×C22⋊D79C22semidirect
38. #19099224C22semidirect
39. #19099223C22semidirect
40. #19099215C22semidirect
41. #19099214C22semidirect
42. #19099203C22semidirect
43. #19099183C22semidirect
44. #19099160C22semidirect
45. #19099159C22semidirect
46. #19099115C22semidirect
47. C2×#14579160C22semidirect
48. C2×#14579159C22semidirect
49. C2×#14579159C22semidirect
50. #19099099C22semidirect
51. C2×#14579156C22semidirect
52. C2×#14579156C22semidirect
53. C2×#14579156C22semidirect
54. C2×#14579154C22semidirect
55. C2×#14579154C22semidirect
56. C2×#14579152C22semidirect
57. C2×#14579151C22semidirect
58. C2×#14579151C22semidirect
59. C2×#14579151C22semidirect
60. C2×#14579150C22semidirect
61. C2×#14579150C22semidirect
63. C2×#14579147C22semidirect
64. #19099076C22semidirect
65. #19099074C22semidirect
66. C2×#14579146C22semidirect
67. C2×#14579146C22semidirect
68. C2×#14579146C22semidirect
71. C2×#14579144C22semidirect
72. C2×#14579144C22semidirect
74. C2×#14579143C22semidirect
75. C2×#14579141C22semidirect
77. C2×#14579140C22semidirect
78. C2×#14579140C22semidirect
79. C2×#14579139C22semidirect
80. C2×#14579139C22semidirect
81. C2×#14579139C22semidirect
84. C2×#14579137C22semidirect
85. C2×#14579137C22semidirect
86. C2×#14579137C22semidirect
87. C2×#14579137C22semidirect
88. C22⋊Q8×D79C22semidirect
89. C2×#14579136C22semidirect
92. C2×#14579135C22semidirect
97. #19099044C22semidirect
98. C2×Q8×Dic79C22semidirect
99. C2×Q8×Dic79C22semidirect
100. C2×#14579126C22semidirect
101. C2×#14579126C22semidirect
102. C2×#14579126C22semidirect
103. C2×#14579123C22semidirect
104. C2×#14579123C22semidirect
105. C2×#14579123C22semidirect
116. C2×C4×C22⋊D79C22semidirect
117. C2×C4×C22⋊D79C22semidirect
118. C2×C4×C22⋊D79C22semidirect
121. C2×#14579120C22semidirect
122. C2×#14579120C22semidirect
123. C2×#14579119C22semidirect
124. C2×#14579119C22semidirect
125. C2×#14579119C22semidirect
128. C2×C4⋊C4×D79C22semidirect
129. C2×C4⋊C4×D79C22semidirect
130. C2×C4⋊C4×D79C22semidirect
135. C23×Q8×C79C22semidirect
140. C2×C22⋊Q8×C79C22semidirect
141. C2×C22⋊Q8×C79C22semidirect
142. C2×C22⋊Q8×C79C22semidirect
143. C2×C22⋊Q8×C79C22semidirect
144. C22×C4⋊C4×C79C22semidirect
145. C22×C4⋊C4×C79C22semidirect
149. C2×#11929625C23semidirect
153. C2×#11929624C23semidirect
158. C2×Q8×D79C23semidirect
185. #14579160C23semidirect
186. #14579159C23semidirect
187. #14579159C23semidirect
188. #14579156C23semidirect
189. #14579156C23semidirect
190. #14579156C23semidirect
191. #14579154C23semidirect
192. #14579154C23semidirect
193. #14579152C23semidirect
194. #14579151C23semidirect
195. #14579151C23semidirect
196. #14579151C23semidirect
197. #14579150C23semidirect
198. #14579150C23semidirect
200. #14579147C23semidirect
201. #14579146C23semidirect
202. #14579146C23semidirect
203. #14579146C23semidirect
206. #14579144C23semidirect
207. #14579144C23semidirect
209. #14579143C23semidirect
210. #14579141C23semidirect
212. #14579140C23semidirect
213. #14579140C23semidirect
214. #14579139C23semidirect
215. #14579139C23semidirect
216. #14579139C23semidirect
219. #14579137C23semidirect
220. #14579137C23semidirect
221. #14579137C23semidirect
222. #14579137C23semidirect
223. #14579136C23semidirect
226. #14579135C23semidirect
231. Q8×Dic79C23semidirect
232. Q8×Dic79C23semidirect
233. #14579126C23semidirect
234. #14579126C23semidirect
235. #14579126C23semidirect
236. #14579123C23semidirect
237. #14579123C23semidirect
238. #14579123C23semidirect
249. C4×C22⋊D79C23semidirect
250. C4×C22⋊D79C23semidirect
253. #14579120C23semidirect
254. #14579120C23semidirect
255. #14579119C23semidirect
256. #14579119C23semidirect
257. #14579119C23semidirect
280. C4⋊C4×D79C23semidirect
281. C4⋊C4×D79C23semidirect
282. C4⋊C4×D79C23semidirect
322. C22×Q8×C79C23semidirect
336. C22⋊Q8×C79C23semidirect
337. C22⋊Q8×C79C23semidirect
338. C22⋊Q8×C79C23semidirect
346. C2×C4⋊C4×C79C23semidirect
347. C2×C4⋊C4×C79C23semidirect
383. C2×C22⋊D79#41semidirect
591. C22⋊D79C2×#41semidirect
679. C2×C79#3520semidirect
707. C22×C22⋊Q8D79semidirect
710. C79C2×#3520semidirect
715. C23×Q8C2×D79semidirect
780. C2×C22⋊Q8C2×D79semidirect
781. C2×C22⋊Q8C2×D79semidirect
782. C2×C22⋊Q8C2×D79semidirect
783. C2×C22⋊Q8C2×D79semidirect
826. C22×C4⋊C4C2×D79semidirect
827. C22×C4⋊C4C2×D79semidirect
850. C22×Q8C22×D79semidirect
928. C22⋊Q8C22×D79semidirect
929. C22⋊Q8C22×D79semidirect
930. C22⋊Q8C22×D79semidirect
998. C2×C4⋊C4C22×D79semidirect
999. C2×C4⋊C4C22×D79semidirect
1367. C2#23777443direct (N × H)

Maximal subgroups

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

subgroupindex
#237774432
C2×#190992842
C2×#190992672
C2×#190992482
C2×#190992472
C2×#190992402
C2×#190992392
C2×Q8×C22⋊D792
C2×#190992242
C2×#190992232
C2×#190992152
C2×#190992142
C2×#190992032
C2×#190991832
C2×#190991602
C2×#190991592
C2×#190991152
C2×#190990992
C2×#190990762
C2×#190990742
C2×C22⋊Q8×D792
C2×#190990442
C22×C4×C22⋊D792
C22×C22⋊Q8×C792
C2×#352079