Finite Group Databasebeta

← C2×#23775274 #35164662

Subgroups — C2×#23775274 #35164662

Order 20224.

2158 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099268C211yesmaximal, characteristic
2C2×#19099226C211yesmaximal, characteristic
3#23775274C2116yesmaximal, direct product factor
4C2×#19098912C211yesmaximal, characteristic, complemented
5C2×#19098900C211yesmaximal, characteristic, complemented
6C2×#19098857C211yesmaximal, characteristic, complemented
7C2×#19098805C211yesmaximal, characteristic, complemented
8C2×#19098802C211yesmaximal, characteristic, complemented
9C2×#19098772C211yesmaximal, characteristic, complemented
10C2×#19098721C211yesmaximal, characteristic, complemented
11C2×#19098720C211yesmaximal, characteristic, complemented
12C2×#19098657C211yesmaximal, characteristic, complemented
13C2×(C22⋊D79)⋊C8C211yesmaximal, characteristic
14C22×#14579084C211yesmaximal, characteristic, complemented
15C2×#103×D79C211yesmaximal, characteristic, complemented
16C2×#484×C79C211yesmaximal, characteristic, complemented
17C23×Dic158C2211yescharacteristic
18C22×Q8×D79C2211yescharacteristic
19C22×Dic316C2211yescharacteristic
20C22×Dic316C2211yescharacteristic
21C22×#11929614C2211yescharacteristic
22C23×C79⋊C8C2211yescharacteristic
23C22×C8×D79C2211yescharacteristic
24#19099268—24no—
25#19099268C2218yes—
26#19099226—24no—
27#19099226C2218yes—
28C2×#14579160—21no—
29C2×#14579160C2211yescharacteristic
30C2×#14579159C2211yescharacteristic
31C2×#14579151—21no—
32C2×#14579141C2211yescharacteristic
33C2×#14579141C2211yescharacteristic
34C2×#14579140—21no—
35C2×#14579140C2211yescharacteristic
36C2×#14579139—21no—
37C2×#14579139—21no—
38C2×#14579138—21no—
39C2×#14579126C2211yescharacteristic
40C2×#14579126C2211yescharacteristic
41C2×C4×C22⋊D79—21no—
42C2×C4×C22⋊D79C2211yescharacteristic
43C2×(C22⋊D79)⋊C4—21no—
44C2×C4⋊C4×D79C2211yescharacteristic
45#19098912C2218yescomplemented
46#19098900C2218yescomplemented
47#19098857C2218yescomplemented
48#19098805C2218yescomplemented
49#19098802C2218yescomplemented
50#19098772C2218yescomplemented
51#19098721C2218yescomplemented
52#19098720C2218yescomplemented
53#19098657C2218yescomplemented
54(C22⋊D79)⋊C8C2218yes—
55C2×#14579094C2211yescharacteristic
56C2×Dic79⋊C8C2211yescharacteristic
57C2×#14579086C2211yescharacteristic
58C2×#14579086C2211yescharacteristic
59C2×#14579085C2211yescharacteristic
60C2×#14579084C2211yescharacteristic
61C2×#14579084C2211yescharacteristic
62C2×#14579084C2211yescharacteristic
63C2×#14579084C2211yescharacteristic
64C2×#14579084C2211yescharacteristic
65C2×#14579084C2218yescomplemented
66#103×D79C2218yescomplemented
67C2×(C2×D79)⋊C8C2211yescharacteristic
68C2×C8×Dic79C2211yescharacteristic
69C2×C22⋊Q8×C79C2211yescharacteristic
70C22×C4⋊C4×C79C2211yescharacteristic
71#484×C79C2218yescomplemented
72C2×#107×C79C2211yescharacteristic
73C2×#107×C79C2211yescharacteristic
74C2×#103×C79C2211yescharacteristic
75C2×#103×C79C2211yescharacteristic
76C2×C22⋊C8×C79C2211yescharacteristic
77C22×Dic158—22no—
78C22×Dic158—21no—
79C22×Dic158—21no—
80C22×Dic158—21no—
81C22×Dic158—24no—
82C22×Dic158—42no—
83C22×Dic158C2311yescharacteristic
84C22×Dic158C2311yescharacteristic
85C22×Dic158C2314yes—
86C22×Dic158C2311yescharacteristic
87C2×Q8×D79—22no—
88C2×Q8×D79—24no—
89C2×Q8×D79—42no—
90C2×Q8×D79C2314yes—
91C22×C22⋊D79D411yescharacteristic
92C23×Dic79—21no—
93C22×C4×D79—21no—
94C22×C4×D79—21no—
95C22×C4×D79C2311yescharacteristic
96C2×Dic316—24no—
97C2×Dic316—42no—
98C2×Dic316C2314yes—
99C2×Dic316C2314yes—
100C2×#11929614—42no—
101C2×#11929614C2314yes—
102C22×C79⋊C8—42no—
103C22×C79⋊C8C2311yescharacteristic
104C22×C79⋊C8C2311yescharacteristic
105C22×C79⋊C8C2314yes—
106C2×C8×D79—42no—
107C2×C8×D79C2314yes—
108#14579160—28no—
109#14579160—22no—
110#14579160C2314yes—
111#14579159—22no—
112#14579159C2314yes—
113#14579151—28no—
114#14579141—22no—
115#14579141—22no—
116#14579141C2314yes—
117#14579141C2314yes—
118#14579140—22no—
119#14579140—28no—
120#14579140C2314yes—
121#14579139—28no—
122#14579139—28no—
123#14579138—28no—
124#14579126—22no—
125#14579126—22no—
126#14579126C2314yes—
127#14579126C2314yes—
128C4×C22⋊D79—28no—
129C4×C22⋊D79D414yes—
130C4×C22⋊D79C2314yes—
131(C22⋊D79)⋊C4—28no—
132C2×C4⋊Dic79—21no—
133C2×C4⋊Dic79—21no—
134C2×C4⋊Dic79C2311yescharacteristic
135C2×Dic79⋊C4—21no—
136C2×Dic79⋊C4—21no—
137C2×Dic79⋊C4—21no—
138C2×Dic79⋊C4—21no—
139C2×Dic79⋊C4—21no—
140C2×Dic79⋊C4—21no—
141C2×Dic79⋊C4—21no—
142C2×Dic79⋊C4D411yescharacteristic
143C4⋊C4×D79—22no—
144C4⋊C4×D79C2314yes—
145C2×C22⋊Dic79—21no—
146C2×C22⋊Dic79D411yescharacteristic
147C2×(C2×D79)⋊C4—21no—
148C2×(C2×D79)⋊C4—21no—
149C2×(C2×D79)⋊C4D411yescharacteristic
150C2×C4×Dic79—21no—
151C2×C4×Dic79—21no—
152C2×C4×Dic79C2311yescharacteristic
153#14579094C2314yes—
154Dic79⋊C8C2314yes—
155#14579086C2314yes—
156#14579086C2314yes—
157#14579085C2314yes—
158#14579084C2314yes—
159#14579084C2314yes—
160#14579084C2314yes—
161#14579084C2314yes—
162#14579084C2314yes—
163(C2×D79)⋊C8C2314yes—
164C8×Dic79C2314yes—
165C22×Q8×C79C2311yescharacteristic
166C23×C4×C79—21no—
167C23×C4×C79C2311yescharacteristic
168C22×C8×C79C2311yescharacteristic
169C22×C8×C79C2311yescharacteristic
170C22⋊Q8×C79—22no—
171C22⋊Q8×C79C2314yes—
172C2×C4⋊C4×C79—22no—
173C2×C4⋊C4×C79—21no—
174C2×C4⋊C4×C79—21no—
175C2×C4⋊C4×C79C2311yescharacteristic
176C2×C4⋊C4×C79C2311yescharacteristic
177C2×C4⋊C4×C79C2311yescharacteristic
178C2×C4⋊C4×C79C2314yes—
179C2×C22⋊C4×C79—21no—
180#107×C79C2314yes—
181#107×C79C2314yes—
182#103×C79C2314yes—
183#103×C79C2314yes—
184C22⋊C8×C79C2314yes—
185C23×D79C2×D411yescharacteristic
186C2×Dic158—28no—
187C2×Dic158—24no—
188C2×Dic158—24no—
189C2×Dic158—21no—
190C2×Dic158—24no—
191C2×Dic158—21no—
192C2×Dic158—21no—
193C2×Dic158—22no—
194C2×Dic158—22no—
195C2×Dic158—22no—
196C2×Dic158—22no—
197C2×Dic158—22no—
198C2×Dic158—44no—
199C2×Dic158—48no—
200C2×Dic158—44no—
201C2×Dic158—44no—
202C2×Dic158—82no—
203C2×Dic158#4114yes—
204C2×Dic158C2412yes—
205C2×Dic158C2412yes—
206C2×Dic158C2412yes—
207Q8×D79—28no—
208Q8×D79—44no—
209Q8×D79—48no—
210C2×C22⋊D79Q1618yescomplemented
211C2×C22⋊D79C2×D414yes—
212C22×Dic79—21no—
213C22×Dic79—21no—
214C22×Dic79—24no—
215C22×Dic79—21no—
216C22×Dic79—21no—
217C22×Dic79—44no—
218C22×Dic79C2×D411yescharacteristic
219C22×Dic79C2×D411yescharacteristic
220C22×Dic79C2×D411yescharacteristic
221C2×C4×D79—24no—
222C2×C4×D79—24no—
223C2×C4×D79—22no—
224C2×C4×D79—22no—
225C2×C4×D79—44no—
226C2×C4×D79—82no—
227C2×C4×D79C2×D412yes—
228C2×C4×D79C2412yes—
229Dic316—28no—
230Dic316—44no—
231#11929614—44no—
232C2×C79⋊C8—22no—
233C2×C79⋊C8—22no—
234C2×C79⋊C8—44no—
235C2×C79⋊C8C2412yes—
236C2×C79⋊C8C2412yes—
237C8×D79—44no—
238C4⋊Dic79—24no—
239C4⋊Dic79—24no—
240C4⋊Dic79—21no—
241C4⋊Dic79C2412yes—
242Dic79⋊C4—24no—
243Dic79⋊C4—24no—
244Dic79⋊C4—24no—
245Dic79⋊C4—24no—
246Dic79⋊C4—24no—
247Dic79⋊C4—24no—
248Dic79⋊C4—24no—
249Dic79⋊C4C2×D414yes—
250C22⋊Dic79—24no—
251C22⋊Dic79C2×D414yes—
252(C2×D79)⋊C4—24no—
253(C2×D79)⋊C4—24no—
254(C2×D79)⋊C4C2×D414yes—
255C4×Dic79—24no—
256C4×Dic79—24no—
257C4×Dic79C2×D412yes—
258C4×Dic79C2412yes—
259C24×C79C2×D411yescharacteristic
260C2×Q8×C79—21no—
261C2×Q8×C79—22no—
262C2×Q8×C79—22no—
263C2×Q8×C79C2412yes—
264C22×C4×C79—22no—
265C22×C4×C79—22no—
266C22×C4×C79—21no—
267C22×C4×C79—21no—
268C22×C4×C79—21no—
269C22×C4×C79—21no—
270C22×C4×C79—24no—
271C22×C4×C79—82no—
272C22×C4×C79C2×D411yescharacteristic
273C22×C4×C79C2×D412yes—
274C22×C4×C79C2412yes—
275C22×C4×C79C2411yescharacteristic
276C2×C8×C79—22no—
277C2×C8×C79—22no—
278C2×C8×C79C2412yes—
279C2×C8×C79C2412yes—
280C4⋊C4×C79—21no—
281C4⋊C4×C79—24no—
282C4⋊C4×C79—21no—
283C4⋊C4×C79—24no—
284C4⋊C4×C79—21no—
285C4⋊C4×C79C2412yes—
286C4⋊C4×C79C2412yes—
287C4⋊C4×C79C2412yes—
288C22⋊C4×C79—24no—
289C23×C79—22no—
290C23×C79—22no—
291C23×C79C2×Q1614yes—
292C23×C79C22×D412yes—
293C23×C79C22×D411yescharacteristic
294C22×D79—22no—
295C22×D79—22no—
296C22×D79C2×Q1614yes—
297C22×D79C22×D412yes—
298Q8×C79—22no—
299Q8×C79—22no—
300Q8×C79—42no—
301C2×C4×C79—22no—
302C2×C4×C79—24no—
303C2×C4×C79—22no—
304C2×C4×C79—22no—
305C2×C4×C79—22no—
306C2×C4×C79—22no—
307C2×C4×C79—22no—
308C2×C4×C79—22no—
309C2×C4×C79—42no—
310C2×C4×C79—42no—
311C2×C4×C79—42no—
312C2×C4×C79—42no—
313C2×C4×C79—84no—
314C2×C4×C79C22×D412yes—
315C2×C4×C79C22×D411yescharacteristic
316C2×C4×C79C2×#4112yes—
317C2×C4×C79H(5,𝔽2)12yes—
318C2×C4×C79C2511yescharacteristic
319C22⋊D79C2×Q16116yescomplemented
320C2×Dic79—22no—
321C2×Dic79—24no—
322C2×Dic79—22no—
323C2×Dic79—22no—
324C2×Dic79—22no—
325C2×Dic79—22no—
326C2×Dic79—22no—
327C2×Dic79—48no—
328C2×Dic79—42no—
329C2×Dic79—42no—
330C2×Dic79—42no—
331C2×Dic79C2×Q1614yes—
332C2×Dic79C22×D412yes—
333C2×Dic79C22×D412yes—
334C2×Dic79C22×D412yes—
335C4×D79—24no—
336C4×D79—22no—
337C4×D79—22no—
338C4×D79—48no—
339C4×D79—84no—
340Dic158—24no—
341Dic158—22no—
342Dic158—22no—
343Dic158—22no—
344Dic158—22no—
345Dic158—22no—
346Dic158—48no—
347Dic158—48no—
348Dic158—42no—
349Dic158—42no—
350Dic158—84no—
351Dic158C2×#4114yes—
352C8×C79—22no—
353C8×C79—22no—
354C79⋊C8—22no—
355C79⋊C8—22no—
356C22×C79—22no—
357C22×C79—28no—
358C22×C79—22no—
359C22×C79#54612yes—
360C22×C79C22×Q1614yes—
361C22×C79C22×Q1612yes—
362C22×C79#57712yes—
363C22×C79C23×D411yescharacteristic
364C2×D79—22no—
365C2×D79—28no—
366C2×D79—22no—
367C2×D79C22×Q1614yes—
368C4×C79—22no—
369C4×C79—42no—
370C4×C79—42no—
371C4×C79—42no—
372C4×C79—42no—
373C4×C79#54612yes—
374C4×C79C22×#4111yescharacteristic
375C4×C79C2×H(5,𝔽2)11yescharacteristic
376Dic79—24no—
377Dic79—22no—
378Dic79—22no—
379Dic79—42no—
380Dic79—42no—
381Dic79—42no—
382Dic79C22×Q1614yes—
383C2×#3299—791nomaximal, Sylow
384C2×C79—24no—
385C2×C79#329914yescomplemented
386C2×C79C2×#54611yescharacteristic
387C2×C79C23×Q1611yescharacteristic
388C2×C79C2×#57711yescharacteristic
389D79—24no—
390C2×#554—791no—
391C2×D4×Q8—791no—
392#3299—7916no—
393C2×#487—791no—
394C2×#484—791no—
395C2×#484D7911yescharacteristic, complemented
396C2×#477—791no—
397C2×#467—791no—
398C2×#467—791no—
399C2×#462—791no—
400C2×#451—791no—
401C2×#451—791no—
402C2×C4×Q16—791no—
403C2×C8×D4—791no—
404C22×#103—791no—
405C22×#103—791no—
406C79C2×#329911yescharacteristic, complemented, Sylow
407C23×Q8—791no—
408C23×Q8—791no—
409C22×Q16—791no—
410C22×Q16—791no—
411C22×Q16—791no—
412C23×C8—791no—
413C23×C8—791no—
414#554—798no—
415#554—1584no—
416D4×Q8—798no—
417D4×Q8—1584no—
418C2×C4⋊Q8—791no—
419C2×C4⋊Q8—791no—
420C2×C4⋊Q8—1581no—
421C2×#125—1581no—
422C2×C22⋊Q8—791no—
423C2×C22⋊Q8—791no—
424C2×C22⋊Q8—791no—
425C2×C22⋊Q8—1581no—
426C2×C22⋊Q8—1581no—
427C2×C22⋊Q8—1581no—
428C2×C22⋊Q8—1581no—
429C2×C22⋊Q8C2×D7911yescharacteristic
430C2×C4×Q8—791no—
431C2×C4×Q8—791no—
432C2×C4×D4—791no—
433C2×C4×D4—1581no—
434C2×C4×D4—1581no—
435C22×C4⋊C4—791no—
436C22×C4⋊C4C2×D7911yescharacteristic
437#487—798no—
438#484—798no—
439#484C2×D7918yescomplemented
440#477—798no—
441#467—798no—
442#467—798no—
443#462—798no—
444#451—798no—
445#451—798no—
446C4×Q16—798no—
447C8×D4—798no—
448C2×#107—791no—
449C2×#107C2×D7911yescharacteristic
450C2×#107C2×D7911yescharacteristic
451C2×C4⋊C8—791no—
452C2×#103—791no—
453C2×#103—791no—
454C2×#103—791no—
455C2×#103—791no—
456C2×#103—791no—
457C2×#103—791no—
458C2×#103—791no—
459C2×#103—798no—
460C2×#103—791no—
461C2×#103—798no—
462C2×#103C2×D7911yescharacteristic
463C2×#103C2×D7911yescharacteristic
464C2×C22⋊C8—791no—
465C2×C22⋊C8C2×D7911yescharacteristic
466C2×C4×C8—791no—
467C22×Q8—3162no—
468C22×Q8—3162no—
469C22×Q8—794no—
470C22×Q8—794no—
471C22×Q8—791no—
472C22×Q8—791no—
473C22×Q8—791no—
474C22×Q8—1584no—
475C22×Q8—1581no—
476C22×Q8—1581no—
477C22×Q8—1584no—
478C22×Q8—1582no—
479C22×Q8—1581no—
480C22×Q8—1582no—
481C22×Q8C22×D7911yescharacteristic
482C22×D4—791no—
483C23×C4—21no—
484C23×C4—791no—
485C23×C4—1581no—
486C23×C4—1581no—
487C23×C4—1581no—
488C23×C4C22×D7911yescharacteristic
489C2×Q16—3162no—
490C2×Q16—3162no—
491C2×Q16—794no—
492C2×Q16—794no—
493C2×Q16—794no—
494C2×Q16—1584no—
495C22×C8—3162no—
496C22×C8—3162no—
497C22×C8—794no—
498C22×C8—794no—
499C22×C8—791no—
500C22×C8—791no—
501C22×C8C22×D7911yescharacteristic
502C22×C8C22×D7911yescharacteristic
503C4⋊Q8—794no—
504C4⋊Q8—794no—
505C4⋊Q8—1582no—
506C4⋊Q8—1582no—
507C4⋊Q8—1588no—
508#125—1588no—
509C22⋊Q8—22no—
510C22⋊Q8—794no—
511C22⋊Q8—794no—
512C22⋊Q8—794no—
513C22⋊Q8—1588no—
514C22⋊Q8—1588no—
515C22⋊Q8—1588no—
516C22⋊Q8—1588no—
517C22⋊Q8—1582no—
518C22⋊Q8—1582no—
519C22⋊Q8—1582no—
520C22⋊Q8C22×D7914yes—
521C4×Q8—794no—
522C4×Q8—794no—
523C4×Q8—1582no—
524C4×Q8—1582no—
525C4×D4—794no—
526C4×D4—794no—
527C4×D4—1588no—
528C4×D4—1588no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—22no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—791no—
533C2×C4⋊C4—791no—
534C2×C4⋊C4—794no—
535C2×C4⋊C4—1582no—
536C2×C4⋊C4—1581no—
537C2×C4⋊C4—1581no—
538C2×C4⋊C4—1581no—
539C2×C4⋊C4—1581no—
540C2×C4⋊C4—1581no—
541C2×C4⋊C4—1581no—
542C2×C4⋊C4—1581no—
543C2×C4⋊C4—1581no—
544C2×C4⋊C4—1581no—
545C2×C4⋊C4C22×D7911yescharacteristic
546C2×C4⋊C4C22×D7911yescharacteristic
547C2×C4⋊C4C22×D7914yes—
548C2×C4⋊C4C22×D7911yescharacteristic
549C2×C22⋊C4—21no—
550C2×C22⋊C4—791no—
551C2×C22⋊C4—791no—
552C2×C22⋊C4—1581no—
553C2×C22⋊C4—1581no—
554C2×C22⋊C4—1581no—
555C2×C42—791no—
556C2×C42—1581no—
557C2×C42—1581no—
558#107—794no—
559#107C22×D7914yes—
560#107C22×D7914yes—
561C4⋊C8—794no—
562#103—794no—
563#103—794no—
564#103—794no—
565#103—794no—
566#103—794no—
567#103—794no—
568#103—794no—
569#103—794no—
570#103C22×D7914yes—
571#103C22×D7914yes—
572C22⋊C8—794no—
573C22⋊C8C22×D7914yes—
574C4×C8—794no—
575C24—791no—
576C24D4×D7911yescharacteristic
577C2×Q8—21no—
578C2×Q8—22no—
579C2×Q8—22no—
580C2×Q8—3168no—
581C2×Q8—3164no—
582C2×Q8—3164no—
583C2×Q8—3164no—
584C2×Q8—3164no—
585C2×Q8—3168no—
586C2×Q8—794no—
587C2×Q8—792no—
588C2×Q8—792no—
589C2×Q8—792no—
590C2×Q8—6322no—
591C2×Q8—1588no—
592C2×Q8—1584no—
593C2×Q8—1584no—
594C2×Q8—1588no—
595C2×Q8—1582no—
596C2×Q8—1582no—
597C2×Q8—1582no—
598C2×Q8—1582no—
599C2×Q8—1582no—
600C2×Q8—1581no—
601C2×Q8—1581no—
602C2×Q8—1584no—
603C2×Q8—1581no—
604C2×Q8C23×D7912yes—
605C2×D4—798no—
606C2×D4—794no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—24no—
614C22×C4—82no—
615C22×C4—3164no—
616C22×C4—3164no—
617C22×C4—791no—
618C22×C4—791no—
619C22×C4—791no—
620C22×C4—792no—
621C22×C4—792no—
622C22×C4—6322no—
623C22×C4—1584no—
624C22×C4—1584no—
625C22×C4—1584no—
626C22×C4—1581no—
627C22×C4—1581no—
628C22×C4—1581no—
629C22×C4—1581no—
630C22×C4—1582no—
631C22×C4—1582no—
632C22×C4D4×D7912yes—
633C22×C4D4×D7911yescharacteristic
634C22×C4C23×D7912yes—
635C22×C4C23×D7911yescharacteristic
636Q16—3164no—
637Q16—3164no—
638Q16—1588no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—3164no—
642C2×C8—3164no—
643C2×C8—792no—
644C2×C8—792no—
645C2×C8—1582no—
646C2×C8—1582no—
647C2×C8C23×D7912yes—
648C2×C8C23×D7912yes—
649C4⋊C4—21no—
650C4⋊C4—24no—
651C4⋊C4—21no—
652C4⋊C4—24no—
653C4⋊C4—21no—
654C4⋊C4—794no—
655C4⋊C4—792no—
656C4⋊C4—1584no—
657C4⋊C4—1584no—
658C4⋊C4—1584no—
659C4⋊C4—1584no—
660C4⋊C4—1584no—
661C4⋊C4—1584no—
662C4⋊C4—1584no—
663C4⋊C4—1584no—
664C4⋊C4—1584no—
665C4⋊C4—1581no—
666C4⋊C4C23×D7912yes—
667C4⋊C4C23×D7912yes—
668C4⋊C4C23×D7912yes—
669C22⋊C4—24no—
670C22⋊C4—794no—
671C22⋊C4—794no—
672C22⋊C4—1584no—
673C22⋊C4—1584no—
674C22⋊C4—1584no—
675C42—792no—
676C42—792no—
677C42—1584no—
678C42—1584no—
679C23—22no—
680C23—22no—
681C23—794no—
682C23—792no—
683C23—1582no—
684C23—1582no—
685C23Q16×D7914yes—
686C23C2×D4×D7912yes—
687C23C2×D4×D7911yescharacteristic
688Q8—22no—
689Q8—22no—
690Q8—42no—
691Q8—3168no—
692Q8—3168no—
693Q8—3162no—
694Q8—3162no—
695Q8—794no—
696Q8—6324no—
697Q8—1582no—
698Q8—1582no—
699Q8—1582no—
700Q8—1582no—
701Q8—1582no—
702Q8—1584no—
703D4—7916no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—84no—
717C2×C4—3168no—
718C2×C4—3162no—
719C2×C4—3162no—
720C2×C4—3162no—
721C2×C4—3168no—
722C2×C4—794no—
723C2×C4—792no—
724C2×C4—792no—
725C2×C4—792no—
726C2×C4—6324no—
727C2×C4—1582no—
728C2×C4—1582no—
729C2×C4—1582no—
730C2×C4—1584no—
731C2×C4—1582no—
732C2×C4—1582no—
733C2×C4—1582no—
734C2×C4—1582no—
735C2×C4—1584no—
736C2×C4—1582no—
737C2×C4C2×D4×D7912yes—
738C2×C4C2×D4×D7911yescharacteristic
739C2×C4#41×D7912yes—
740C2×C4#1457920712yes—
741C2×C4C24×D7911yescharacteristic
742C8—22no—
743C8—22no—
744C8—1582no—
745C8—1582no—
746C22—28no—
747C22—22no—
748C22—22no—
749C22—794no—
750C22—1588no—
751C22—1582no—
752C22—1582no—
753C22#1909920512yes—
754C22C2×Q16×D7914yes—
755C22C2×Q16×D7912yes—
756C22#1909937312yes—
757C22C22×D4×D7911yescharacteristic
758C4—22no—
759C4—42no—
760C4—42no—
761C4—42no—
762C4—42no—
763C4—3162no—
764C4—3162no—
765C4—3162no—
766C4—794no—
767C4—1584no—
768C4—1582no—
769C4—1582no—
770C4#1909920512yes—
771C4C2×#41×D7911yescharacteristic
772C4C2×#1457920711yescharacteristic
773C2—24no—
774C2—1584no—
775C2#2377527414yesdirect product factor
776C2C2×#1909920511yescharacteristic
777C2C22×Q16×D7911yescharacteristic
778C2C2×#1909937311yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#484×C79C2
socleC23×C79C22×D4
prime radicalC22×C22⋊D79D4
hypercenterC2×#484D79
hypocenterC79C2×#3299
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
3. #23775274C2direct (N × H)
4. C2×#19098912C2semidirect
5. C2×#19098900C2semidirect
6. C2×#19098857C2semidirect
7. C2×#19098805C2semidirect
8. C2×#19098802C2semidirect
9. C2×#19098772C2semidirect
10. C2×#19098721C2semidirect
11. C2×#19098720C2semidirect
12. C2×#19098657C2semidirect
14. C22×#14579084C2semidirect
15. C2×#103×D79C2semidirect
16. C2×#484×C79C2semidirect
45. #19098912C22semidirect
46. #19098900C22semidirect
47. #19098857C22semidirect
48. #19098805C22semidirect
49. #19098802C22semidirect
50. #19098772C22semidirect
51. #19098721C22semidirect
52. #19098720C22semidirect
53. #19098657C22semidirect
65. C2×#14579084C22semidirect
66. #103×D79C22semidirect
71. #484×C79C22semidirect
210. C2×C22⋊D79Q16semidirect
319. C22⋊D79C2×Q16semidirect
385. C2×C79#3299semidirect
395. C2×#484D79semidirect
406. C79C2×#3299semidirect
439. #484C2×D79semidirect
775. C2#23775274direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992682
C2×#190992262
#237752742
C2×#190989122
C2×#190989002
C2×#190988572
C2×#190988052
C2×#190988022
C2×#190987722
C2×#190987212
C2×#190987202
C2×#190986572
C2×(C22⋊D79)⋊C82
C22×#145790842
C2×#103×D792
C2×#484×C792
C2×#329979