Finite Group Databasebeta

← C2×#23775452 #35164876

Subgroups — C2×#23775452 #35164876

Order 20224.

2094 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099252C211yesmaximal, characteristic
2C2×Q8×C22⋊D79C211yesmaximal, characteristic
3#23775452C2116yesmaximal, direct product factor
4C2×#19098930C211yesmaximal, characteristic, complemented
5C2×#19098904C211yesmaximal, characteristic, complemented
6C2×#19098892C211yesmaximal, characteristic, complemented
7C2×#19098868C211yesmaximal, characteristic, complemented
8C2×#19098821C211yesmaximal, characteristic, complemented
9C2×#19098803C211yesmaximal, characteristic, complemented
10C2×#19098772C211yesmaximal, characteristic, complemented
11C2×#19098720C211yesmaximal, characteristic, complemented
12C2×#19098719C211yesmaximal, characteristic, complemented
13C2×#19098667C211yesmaximal, characteristic, complemented
14C2×#19098632C211yesmaximal, characteristic
15C2×#103×D79C211yesmaximal, characteristic, complemented
16C2×#419×C79C211yesmaximal, characteristic, complemented
17C22×Q8×D79C2211yescharacteristic
18C22×Dic316C2211yescharacteristic
19C22×#11929614C2211yescharacteristic
20C22×#11929614C2211yescharacteristic
21C22×C8×D79C2211yescharacteristic
22#19099252—24no—
23#19099252C2218yes—
24Q8×C22⋊D79—24no—
25Q8×C22⋊D79C2218yes—
26C2×#14579159—21no—
27C2×#14579159C2211yescharacteristic
28C2×#14579154—21no—
29C2×#14579153—21no—
30C2×#14579152C2211yescharacteristic
31C2×#14579143—21no—
32C2×#14579141C2211yescharacteristic
33C2×#14579140—21no—
34C2×#14579140C2211yescharacteristic
35C2×#14579140C2211yescharacteristic
36C2×#14579137—21no—
37C2×#14579137C2211yescharacteristic
38C2×Q8×Dic79C2211yescharacteristic
39C2×#14579126C2211yescharacteristic
40C2×C4×C22⋊D79—21no—
41C2×C4×C22⋊D79C2211yescharacteristic
42C2×#14579118—21no—
43C2×C4⋊C4×D79C2211yescharacteristic
44#19098930C2218yescomplemented
45#19098904C2218yescomplemented
46#19098892C2218yescomplemented
47#19098868C2218yescomplemented
48#19098821C2218yescomplemented
49#19098803C2218yescomplemented
50#19098772C2218yescomplemented
51#19098720C2218yescomplemented
52#19098719C2218yescomplemented
53#19098667C2218yescomplemented
54#19098632C2218yes—
55C2×#14579094C2211yescharacteristic
56C2×#14579093C2211yescharacteristic
57C2×#14579092C2211yescharacteristic
58C2×Dic79⋊C8C2211yescharacteristic
59C2×#14579086C2211yescharacteristic
60C2×#14579086C2211yescharacteristic
61C2×#14579085C2211yescharacteristic
62C2×#14579085C2211yescharacteristic
63C2×#14579084C2211yescharacteristic
64C2×#14579084C2211yescharacteristic
65#103×D79C2218yescomplemented
66C2×C22⋊(C79⋊C8)C2211yescharacteristic
67C2×(C2×D79)⋊C8C2211yescharacteristic
68C2×#14579071C2211yescharacteristic
69C23×Q8×C79C2211yescharacteristic
70C22×M16×C79C2211yescharacteristic
71C2×#117×C79C2211yescharacteristic
72#419×C79C2218yescomplemented
73C2×#103×C79C2211yescharacteristic
74C2×#103×C79C2211yescharacteristic
75C2×#103×C79C2211yescharacteristic
76C2×#103×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×Dic158C2311yescharacteristic
79C22×Dic158C2311yescharacteristic
80C2×Q8×D79—22no—
81C2×Q8×D79—24no—
82C2×Q8×D79—42no—
83C2×Q8×D79C2314yes—
84C22×C22⋊D79D411yescharacteristic
85C22×C4×D79—21no—
86C22×C4×D79—21no—
87C22×C4×D79C2311yescharacteristic
88C2×Dic316—42no—
89C2×Dic316C2314yes—
90C2×#11929614—24no—
91C2×#11929614—42no—
92C2×#11929614C2314yes—
93C2×#11929614C2314yes—
94C22×C79⋊C8C2311yescharacteristic
95C22×C79⋊C8C2311yescharacteristic
96C2×C8×D79—42no—
97C2×C8×D79C2314yes—
98#14579159—28no—
99#14579159—22no—
100#14579159C2314yes—
101#14579154—28no—
102#14579153—28no—
103#14579152—22no—
104#14579152C2314yes—
105#14579143—28no—
106#14579141—22no—
107#14579141C2314yes—
108#14579140—22no—
109#14579140—22no—
110#14579140—28no—
111#14579140C2314yes—
112#14579140C2314yes—
113#14579137—22no—
114#14579137—28no—
115#14579137C2314yes—
116Q8×Dic79—22no—
117Q8×Dic79C2314yes—
118#14579126—22no—
119#14579126C2314yes—
120C4×C22⋊D79—28no—
121C4×C22⋊D79D414yes—
122C4×C22⋊D79C2314yes—
123#14579118—28no—
124C2×C4⋊Dic79—21no—
125C2×C4⋊Dic79—21no—
126C2×C4⋊Dic79—21no—
127C2×C4⋊Dic79C2311yescharacteristic
128C2×C4⋊Dic79C2311yescharacteristic
129C2×Dic79⋊C4—21no—
130C2×Dic79⋊C4—21no—
131C2×Dic79⋊C4—21no—
132C2×Dic79⋊C4—21no—
133C2×Dic79⋊C4—21no—
134C2×Dic79⋊C4—21no—
135C2×Dic79⋊C4—21no—
136C2×Dic79⋊C4—21no—
137C2×Dic79⋊C4D411yescharacteristic
138C4⋊C4×D79—22no—
139C4⋊C4×D79C2314yes—
140C2×C22⋊Dic79—21no—
141C2×C22⋊Dic79—21no—
142C2×C22⋊Dic79D411yescharacteristic
143C2×(C2×D79)⋊C4—21no—
144C2×(C2×D79)⋊C4—21no—
145C2×(C2×D79)⋊C4D411yescharacteristic
146C2×C4×Dic79—21no—
147C2×C4×Dic79—21no—
148C2×C4×Dic79C2311yescharacteristic
149#14579094C2314yes—
150#14579093C2314yes—
151#14579092C2314yes—
152Dic79⋊C8C2314yes—
153#14579086C2314yes—
154#14579086C2314yes—
155#14579085C2314yes—
156#14579085C2314yes—
157#14579084C2314yes—
158#14579084C2314yes—
159C22⋊(C79⋊C8)C2314yes—
160(C2×D79)⋊C8C2314yes—
161#14579071C2314yes—
162C22×Q8×C79—22no—
163C22×Q8×C79—21no—
164C22×Q8×C79—24no—
165C22×Q8×C79—42no—
166C22×Q8×C79C2311yescharacteristic
167C22×Q8×C79C2314yes—
168C22×Q8×C79C2311yescharacteristic
169C23×C4×C79—21no—
170C23×C4×C79C2311yescharacteristic
171C2×M16×C79—42no—
172C2×M16×C79C2314yes—
173C22×C8×C79C2311yescharacteristic
174C22×C8×C79C2311yescharacteristic
175#117×C79—22no—
176#117×C79C2314yes—
177C2×C4⋊C4×C79C2311yescharacteristic
178C2×C4⋊C4×C79C2311yescharacteristic
179C2×C22⋊C4×C79—21no—
180C2×C42×C79—21no—
181#103×C79C2314yes—
182#103×C79C2314yes—
183#103×C79C2314yes—
184#103×C79C2314yes—
185C23×D79C2×D411yescharacteristic
186C2×Dic158—24no—
187C2×Dic158—21no—
188C2×Dic158—21no—
189C2×Dic158—22no—
190C2×Dic158—22no—
191C2×Dic158—22no—
192C2×Dic158—22no—
193C2×Dic158—44no—
194C2×Dic158C2412yes—
195C2×Dic158C2412yes—
196Q8×D79—28no—
197Q8×D79—44no—
198Q8×D79—48no—
199C2×C22⋊D79—24no—
200C2×C22⋊D79C2×D414yes—
201C22×Dic79—21no—
202C22×Dic79—21no—
203C22×Dic79—21no—
204C22×Dic79—21no—
205C22×Dic79C2×D411yescharacteristic
206C22×Dic79C2×D411yescharacteristic
207C22×Dic79C2×D411yescharacteristic
208C2×C4×D79—24no—
209C2×C4×D79—24no—
210C2×C4×D79—22no—
211C2×C4×D79—22no—
212C2×C4×D79—44no—
213C2×C4×D79—44no—
214C2×C4×D79C2×D412yes—
215C2×C4×D79C2412yes—
216Dic316—44no—
217#11929614—28no—
218#11929614—44no—
219C2×C79⋊C8—22no—
220C2×C79⋊C8—22no—
221C2×C79⋊C8C2412yes—
222C2×C79⋊C8C2412yes—
223C8×D79—44no—
224C4⋊Dic79—24no—
225C4⋊Dic79—24no—
226C4⋊Dic79—24no—
227C4⋊Dic79—21no—
228C4⋊Dic79—21no—
229C4⋊Dic79C2412yes—
230C4⋊Dic79C2412yes—
231Dic79⋊C4—24no—
232Dic79⋊C4—24no—
233Dic79⋊C4—24no—
234Dic79⋊C4—24no—
235Dic79⋊C4—24no—
236Dic79⋊C4—24no—
237Dic79⋊C4—24no—
238Dic79⋊C4—24no—
239Dic79⋊C4C2×D414yes—
240C22⋊Dic79—24no—
241C22⋊Dic79—24no—
242C22⋊Dic79C2×D414yes—
243(C2×D79)⋊C4—24no—
244(C2×D79)⋊C4—24no—
245(C2×D79)⋊C4C2×D414yes—
246C4×Dic79—24no—
247C4×Dic79—24no—
248C4×Dic79C2×D412yes—
249C4×Dic79C2412yes—
250C24×C79C2×D411yescharacteristic
251C2×Q8×C79—21no—
252C2×Q8×C79—24no—
253C2×Q8×C79—21no—
254C2×Q8×C79—22no—
255C2×Q8×C79—28no—
256C2×Q8×C79—22no—
257C2×Q8×C79—22no—
258C2×Q8×C79—44no—
259C2×Q8×C79—44no—
260C2×Q8×C79—48no—
261C2×Q8×C79#4114yes—
262C2×Q8×C79C2412yes—
263C2×Q8×C79C2412yes—
264C22×C4×C79—21no—
265C22×C4×C79—22no—
266C22×C4×C79—22no—
267C22×C4×C79—21no—
268C22×C4×C79—21no—
269C22×C4×C79—21no—
270C22×C4×C79—24no—
271C22×C4×C79—44no—
272C22×C4×C79C2×D411yescharacteristic
273C22×C4×C79C2×D412yes—
274C22×C4×C79C2412yes—
275C22×C4×C79C2411yescharacteristic
276M16×C79—44no—
277C2×C8×C79—22no—
278C2×C8×C79—22no—
279C2×C8×C79C2412yes—
280C2×C8×C79C2412yes—
281C4⋊C4×C79—21no—
282C4⋊C4×C79—21no—
283C4⋊C4×C79C2412yes—
284C4⋊C4×C79C2412yes—
285C22⋊C4×C79—24no—
286C42×C79—24no—
287C23×C79—22no—
288C23×C79—22no—
289C23×C79—22no—
290C23×C79C22×D412yes—
291C23×C79C22×D411yescharacteristic
292C22×D79—22no—
293C22×D79—22no—
294C22×D79#13714yes—
295C22×D79C22×D412yes—
296Q8×C79—24no—
297Q8×C79—22no—
298Q8×C79—22no—
299Q8×C79—22no—
300Q8×C79—48no—
301Q8×C79—42no—
302Q8×C79C2×#4114yes—
303C2×C4×C79—24no—
304C2×C4×C79—22no—
305C2×C4×C79—22no—
306C2×C4×C79—24no—
307C2×C4×C79—22no—
308C2×C4×C79—22no—
309C2×C4×C79—22no—
310C2×C4×C79—22no—
311C2×C4×C79—22no—
312C2×C4×C79—48no—
313C2×C4×C79—42no—
314C2×C4×C79—42no—
315C2×C4×C79—42no—
316C2×C4×C79C22×D412yes—
317C2×C4×C79C22×D411yescharacteristic
318C2×C4×C79C2×#4112yes—
319C2×C4×C79H(5,𝔽2)12yes—
320C2×C4×C79C2511yescharacteristic
321C22⋊D79—28no—
322C2×Dic79—22no—
323C2×Dic79—22no—
324C2×Dic79—22no—
325C2×Dic79—22no—
326C2×Dic79—22no—
327C2×Dic79—22no—
328C2×Dic79—22no—
329C2×Dic79—42no—
330C2×Dic79—42no—
331C2×Dic79—42no—
332C2×Dic79—42no—
333C2×Dic79C22×D412yes—
334C2×Dic79C22×D412yes—
335C2×Dic79C22×D412yes—
336C4×D79—24no—
337C4×D79—22no—
338C4×D79—22no—
339C4×D79—48no—
340C4×D79—48no—
341Dic158—22no—
342Dic158—22no—
343Dic158—22no—
344Dic158—22no—
345Dic158—48no—
346Dic158—42no—
347Dic158—42no—
348C8×C79—22no—
349C8×C79—22no—
350C79⋊C8—22no—
351C79⋊C8—22no—
352C22×C79—22no—
353C22×C79—22no—
354C22×C79—22no—
355C22×C79—44no—
356C22×C79#54612yes—
357C22×C79C2×#13712yes—
358C22×C79#57812yes—
359C22×C79C23×D411yescharacteristic
360C2×D79—22no—
361C2×D79—28no—
362C2×D79—22no—
363C2×D79C2×#13714yes—
364C4×C79—22no—
365C4×C79—24no—
366C4×C79—42no—
367C4×C79—42no—
368C4×C79—42no—
369C4×C79#54612yes—
370C4×C79C22×#4111yescharacteristic
371C4×C79C2×H(5,𝔽2)11yescharacteristic
372Dic79—22no—
373Dic79—22no—
374Dic79—22no—
375Dic79—42no—
376Dic79—42no—
377Dic79—42no—
378Dic79—42no—
379C2×#3312—791nomaximal, Sylow
380C2×C79—42no—
381C2×C79#331214yescomplemented
382C2×C79C2×#54611yescharacteristic
383C2×C79C22×#13711yescharacteristic
384C2×C79C2×#57811yescharacteristic
385D79—24no—
386C2×#552—791no—
387C2×D4×Q8—791no—
388#3312—7916no—
389C2×#491—791no—
390C2×#485—791no—
391C2×#483—791no—
392C2×#479—791no—
393C2×#470—791no—
394C2×#467—791no—
395C2×#462—791no—
396C2×#451—791no—
397C2×#451—791no—
398C2×#441—791no—
399C2×#435—791no—
400C2×#419D7911yescharacteristic, complemented
401C22×#103—791no—
402C79C2×#331211yescharacteristic, complemented, Sylow
403C23×Q8—791no—
404C23×Q8C2×D7911yescharacteristic
405C22×Q16—791no—
406C22×Q16—791no—
407C22×Q16—791no—
408C22×M16C2×D7911yescharacteristic
409C23×C8—791no—
410#552—798no—
411#552—1584no—
412D4×Q8—798no—
413D4×Q8—1584no—
414C2×C4⋊Q8—791no—
415C2×C4⋊Q8—1581no—
416C2×#126—1581no—
417C2×#125—791no—
418C2×#125—1581no—
419C2×#123—1581no—
420C2×C22⋊Q8—791no—
421C2×C22⋊Q8—791no—
422C2×C22⋊Q8—791no—
423C2×C22⋊Q8—791no—
424C2×C22⋊Q8—1581no—
425C2×C22⋊Q8—1581no—
426C2×C4×Q8—791no—
427C2×C4×Q8—791no—
428C2×C4×D4—791no—
429C2×C4×D4—1581no—
430C2×#117—1581no—
431C2×#117C2×D7911yescharacteristic
432C22×C4⋊C4—791no—
433#491—798no—
434#485—798no—
435#483—798no—
436#479—798no—
437#470—798no—
438#467—798no—
439#462—798no—
440#451—798no—
441#451—798no—
442#441—798no—
443#435—798no—
444C2×#107—791no—
445C2×#106—791no—
446C2×#106—791no—
447C2×C4⋊C8—791no—
448#419C2×D7918yescomplemented
449C2×#103—791no—
450C2×#103—791no—
451C2×#103—791no—
452C2×#103—791no—
453C2×#103—791no—
454C2×#103—791no—
455C2×#103—798no—
456C2×#103C2×D7911yescharacteristic
457C2×#103C2×D7911yescharacteristic
458C2×#103C2×D7911yescharacteristic
459C2×#103C2×D7911yescharacteristic
460C2×C22⋊C8—791no—
461C2×C22⋊C8—791no—
462C2×#97—791no—
463C22×Q8—21no—
464C22×Q8—22no—
465C22×Q8—24no—
466C22×Q8—42no—
467C22×Q8—3162no—
468C22×Q8—794no—
469C22×Q8—791no—
470C22×Q8—791no—
471C22×Q8—1581no—
472C22×Q8—1584no—
473C22×Q8—1582no—
474C22×Q8C22×D7911yescharacteristic
475C22×Q8C22×D7914yes—
476C22×Q8C22×D7911yescharacteristic
477C22×D4—791no—
478C23×C4—21no—
479C23×C4—791no—
480C23×C4—1581no—
481C23×C4—1581no—
482C23×C4C22×D7911yescharacteristic
483C2×Q16—3162no—
484C2×Q16—3162no—
485C2×Q16—794no—
486C2×Q16—794no—
487C2×Q16—794no—
488C2×Q16—1584no—
489C2×M16—42no—
490C2×M16C22×D7914yes—
491C22×C8—3162no—
492C22×C8—794no—
493C22×C8—791no—
494C22×C8—791no—
495C22×C8C22×D7911yescharacteristic
496C22×C8C22×D7911yescharacteristic
497C4⋊Q8—794no—
498C4⋊Q8—1582no—
499C4⋊Q8—1588no—
500#126—1588no—
501#125—794no—
502#125—1588no—
503#125—1582no—
504#123—1588no—
505C22⋊Q8—794no—
506C22⋊Q8—794no—
507C22⋊Q8—794no—
508C22⋊Q8—794no—
509C22⋊Q8—1588no—
510C22⋊Q8—1588no—
511C22⋊Q8—1582no—
512C22⋊Q8—1582no—
513C22⋊Q8—1582no—
514C22⋊Q8—1582no—
515C4×Q8—794no—
516C4×Q8—794no—
517C4×Q8—1582no—
518C4×Q8—1582no—
519C4×D4—794no—
520C4×D4—794no—
521C4×D4—1588no—
522#117—22no—
523#117—1588no—
524#117C22×D7914yes—
525C2×C4⋊C4—791no—
526C2×C4⋊C4—791no—
527C2×C4⋊C4—791no—
528C2×C4⋊C4—794no—
529C2×C4⋊C4—1582no—
530C2×C4⋊C4—1581no—
531C2×C4⋊C4—1581no—
532C2×C4⋊C4—1581no—
533C2×C4⋊C4—1581no—
534C2×C4⋊C4—1581no—
535C2×C4⋊C4—1581no—
536C2×C4⋊C4—1581no—
537C2×C4⋊C4—1581no—
538C2×C4⋊C4—1581no—
539C2×C4⋊C4—1581no—
540C2×C4⋊C4—1581no—
541C2×C4⋊C4C22×D7911yescharacteristic
542C2×C4⋊C4C22×D7911yescharacteristic
543C2×C22⋊C4—21no—
544C2×C22⋊C4—791no—
545C2×C22⋊C4—791no—
546C2×C22⋊C4—1581no—
547C2×C22⋊C4—1581no—
548C2×C22⋊C4—1581no—
549C2×C22⋊C4—1581no—
550C2×C42—21no—
551C2×C42—791no—
552C2×C42—1581no—
553C2×C42—1581no—
554#107—794no—
555#106—794no—
556#106—794no—
557C4⋊C8—794no—
558#103—794no—
559#103—794no—
560#103—794no—
561#103—794no—
562#103—794no—
563#103—794no—
564#103C22×D7914yes—
565#103C22×D7914yes—
566#103C22×D7914yes—
567#103C22×D7914yes—
568C22⋊C8—794no—
569C22⋊C8—794no—
570#97—794no—
571C24—791no—
572C24D4×D7911yescharacteristic
573C2×Q8—22no—
574C2×Q8—21no—
575C2×Q8—24no—
576C2×Q8—21no—
577C2×Q8—28no—
578C2×Q8—22no—
579C2×Q8—22no—
580C2×Q8—44no—
581C2×Q8—44no—
582C2×Q8—48no—
583C2×Q8—3164no—
584C2×Q8—3168no—
585C2×Q8—3164no—
586C2×Q8—792no—
587C2×Q8—792no—
588C2×Q8—1584no—
589C2×Q8—1588no—
590C2×Q8—1582no—
591C2×Q8—1582no—
592C2×Q8—1582no—
593C2×Q8—1582no—
594C2×Q8—1581no—
595C2×Q8—1581no—
596C2×Q8#1192962414yes—
597C2×Q8C23×D7912yes—
598C2×Q8C23×D7912yes—
599C2×D4—794no—
600C2×D4—1584no—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—24no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—44no—
609C22×C4—3164no—
610C22×C4—3164no—
611C22×C4—791no—
612C22×C4—791no—
613C22×C4—791no—
614C22×C4—792no—
615C22×C4—792no—
616C22×C4—1584no—
617C22×C4—1584no—
618C22×C4—1581no—
619C22×C4—1581no—
620C22×C4—1581no—
621C22×C4—1581no—
622C22×C4—1582no—
623C22×C4—1582no—
624C22×C4D4×D7912yes—
625C22×C4D4×D7911yescharacteristic
626C22×C4C23×D7912yes—
627C22×C4C23×D7911yescharacteristic
628Q16—3164no—
629Q16—3164no—
630Q16—1588no—
631M16—44no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—3164no—
635C2×C8—792no—
636C2×C8—792no—
637C2×C8—1582no—
638C2×C8—1582no—
639C2×C8C23×D7912yes—
640C2×C8C23×D7912yes—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—794no—
644C4⋊C4—792no—
645C4⋊C4—792no—
646C4⋊C4—1584no—
647C4⋊C4—1584no—
648C4⋊C4—1584no—
649C4⋊C4—1584no—
650C4⋊C4—1584no—
651C4⋊C4—1584no—
652C4⋊C4—1584no—
653C4⋊C4—1584no—
654C4⋊C4—1584no—
655C4⋊C4—1584no—
656C4⋊C4—1584no—
657C4⋊C4—1581no—
658C4⋊C4—1581no—
659C4⋊C4C23×D7912yes—
660C4⋊C4C23×D7912yes—
661C22⋊C4—24no—
662C22⋊C4—794no—
663C22⋊C4—794no—
664C22⋊C4—1584no—
665C22⋊C4—1584no—
666C22⋊C4—1584no—
667C22⋊C4—1584no—
668C42—24no—
669C42—792no—
670C42—792no—
671C42—1584no—
672C42—1584no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—794no—
677C23—792no—
678C23—1582no—
679C23—1582no—
680C23C2×D4×D7912yes—
681C23C2×D4×D7911yescharacteristic
682Q8—22no—
683Q8—24no—
684Q8—22no—
685Q8—22no—
686Q8—48no—
687Q8—42no—
688Q8—3168no—
689Q8—3162no—
690Q8—3162no—
691Q8—1582no—
692Q8—1582no—
693Q8—1582no—
694Q8—1582no—
695Q8C2×#1192962414yes—
696D4—1588no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—48no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—3168no—
711C2×C4—3168no—
712C2×C4—3162no—
713C2×C4—3162no—
714C2×C4—3162no—
715C2×C4—3162no—
716C2×C4—792no—
717C2×C4—792no—
718C2×C4—792no—
719C2×C4—1582no—
720C2×C4—1582no—
721C2×C4—1582no—
722C2×C4—1582no—
723C2×C4—1582no—
724C2×C4—1582no—
725C2×C4—1582no—
726C2×C4—1582no—
727C2×C4—1584no—
728C2×C4—1582no—
729C2×C4C2×D4×D7912yes—
730C2×C4C2×D4×D7911yescharacteristic
731C2×C4C2×#1192962412yes—
732C2×C4#1457920612yes—
733C2×C4C24×D7911yescharacteristic
734C8—22no—
735C8—22no—
736C8—1582no—
737C8—1582no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—44no—
742C22—794no—
743C22—1582no—
744C22—1582no—
745C22—1588no—
746C22#1909920312yes—
747C22#137×D7912yes—
748C22#1909937912yes—
749C22C22×D4×D7911yescharacteristic
750C4—22no—
751C4—24no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—3162no—
756C4—3162no—
757C4—3162no—
758C4—3162no—
759C4—1582no—
760C4—1582no—
761C4—1582no—
762C4#1909920312yes—
763C4C22×#1192962411yescharacteristic
764C4C2×#1457920611yescharacteristic
765C2—42no—
766C2—1584no—
767C2#2377545214yesdirect product factor
768C2C2×#1909920311yescharacteristic
769C2C2×#137×D7911yescharacteristic
770C2C2×#1909937911yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#419×C79C2
socleC23×C79C22×D4
prime radicalC22×C22⋊D79D4
hypercenterC2×#419D79
hypocenterC79C2×#3312
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#419

Complements

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

NH ≅ G/Ntype
3. #23775452C2direct (N × H)
4. C2×#19098930C2semidirect
5. C2×#19098904C2semidirect
6. C2×#19098892C2semidirect
7. C2×#19098868C2semidirect
8. C2×#19098821C2semidirect
9. C2×#19098803C2semidirect
10. C2×#19098772C2semidirect
11. C2×#19098720C2semidirect
12. C2×#19098719C2semidirect
13. C2×#19098667C2semidirect
15. C2×#103×D79C2semidirect
16. C2×#419×C79C2semidirect
44. #19098930C22semidirect
45. #19098904C22semidirect
46. #19098892C22semidirect
47. #19098868C22semidirect
48. #19098821C22semidirect
49. #19098803C22semidirect
50. #19098772C22semidirect
51. #19098720C22semidirect
52. #19098719C22semidirect
53. #19098667C22semidirect
65. #103×D79C22semidirect
72. #419×C79C22semidirect
381. C2×C79#3312semidirect
400. C2×#419D79semidirect
402. C79C2×#3312semidirect
448. #419C2×D79semidirect
767. C2#23775452direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992522
C2×Q8×C22⋊D792
#237754522
C2×#190989302
C2×#190989042
C2×#190988922
C2×#190988682
C2×#190988212
C2×#190988032
C2×#190987722
C2×#190987202
C2×#190987192
C2×#190986672
C2×#190986322
C2×#103×D792
C2×#419×C792
C2×#331279