Finite Group Databasebeta

← C2×#23775676 #35165147

Subgroups — C2×#23775676 #35165147

Order 20224.

2082 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×#19099284C211yesmaximal, characteristic
2C2×Q8×C22⋊D79C211yesmaximal, characteristic
3#23775676C2116yesmaximal, direct product factor
4C2×#19098912C211yesmaximal, characteristic, complemented
5C2×#19098905C211yesmaximal, characteristic, complemented
6C2×#19098903C211yesmaximal, characteristic, complemented
7C2×#19098846C211yesmaximal, characteristic, complemented
8C2×#19098819C211yesmaximal, characteristic, complemented
9C2×#19098818C211yesmaximal, characteristic, complemented
10C2×#19098771C211yesmaximal, characteristic, complemented
11C2×#19098717C211yesmaximal, characteristic, complemented
12C2×Q16×Dic79C211yesmaximal, characteristic, complemented
13C2×#19098638C211yesmaximal, characteristic
14C2×#19098572C211yesmaximal, characteristic, complemented
15C2×#19098570C211yesmaximal, characteristic, complemented
16C2×#451×C79C211yesmaximal, characteristic, complemented
17C22×Q8×D79C2211yescharacteristic
18C22×#11929614C2211yescharacteristic
19C22×#11929608C2211yescharacteristic
20C22×#11929607C2211yescharacteristic
21#19099284—24no—
22#19099284C2218yes—
23Q8×C22⋊D79—24no—
24Q8×C22⋊D79C2218yes—
25C2×#14579160C2211yescharacteristic
26C2×#14579159—21no—
27C2×#14579159C2211yescharacteristic
28C2×#14579156—21no—
29C2×#14579154—21no—
30C2×#14579147—21no—
31C2×#14579140—21no—
32C2×#14579140C2211yescharacteristic
33C2×#14579137—21no—
34C2×#14579137C2211yescharacteristic
35C2×#14579137C2211yescharacteristic
36C2×Q8×Dic79C2211yescharacteristic
37C2×Q8×Dic79C2211yescharacteristic
38C2×#14579126—21no—
39C2×C4×C22⋊D79—21no—
40C2×C4×C22⋊D79C2211yescharacteristic
41C2×#14579120C2211yescharacteristic
42C2×#14579119C2211yescharacteristic
43#19098912C2218yescomplemented
44#19098905C2218yescomplemented
45#19098903C2218yescomplemented
46#19098846C2218yescomplemented
47#19098819C2218yescomplemented
48#19098818C2218yescomplemented
49#19098771C2218yescomplemented
50#19098717C2218yescomplemented
51Q16×Dic79C2218yescomplemented
52#19098638C2218yes—
53C2×#14579095C2211yescharacteristic
54C2×#14579093C2211yescharacteristic
55C2×#14579092C2211yescharacteristic
56C2×Dic79⋊C8C2211yescharacteristic
57#19098572C2218yescomplemented
58#19098570C2218yescomplemented
59C2×#14579086C2211yescharacteristic
60C2×#14579086C2211yescharacteristic
61C2×#14579085C2211yescharacteristic
62C2×#14579085C2211yescharacteristic
63C2×#14579085C2211yescharacteristic
64C2×#14579085C2211yescharacteristic
65C2×#14579085C2211yescharacteristic
66C2×#14579084C2211yescharacteristic
67C2×(C2×D79)⋊C8C2211yescharacteristic
68C2×C8×Dic79C2211yescharacteristic
69C23×Q8×C79C2211yescharacteristic
70C22×Q16×C79C2211yescharacteristic
71C22×Q16×C79C2211yescharacteristic
72C2×C22⋊Q8×C79C2211yescharacteristic
73#451×C79C2218yescomplemented
74C2×#103×C79C2211yescharacteristic
75C2×#103×C79C2211yescharacteristic
76C2×C22⋊C8×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×Dic158—21no—
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×D79C2311yescharacteristic
87C2×#11929614—42no—
88C2×#11929614C2314yes—
89C2×#11929608—42no—
90C2×#11929608C2314yes—
91C2×#11929607—42no—
92C2×#11929607C2314yes—
93C22×C79⋊C8C2311yescharacteristic
94C22×C79⋊C8C2311yescharacteristic
95#14579160—22no—
96#14579160C2314yes—
97#14579159—28no—
98#14579159—22no—
99#14579159C2314yes—
100#14579156—28no—
101#14579154—28no—
102#14579147—28no—
103#14579140—22no—
104#14579140—28no—
105#14579140C2314yes—
106#14579137—22no—
107#14579137—22no—
108#14579137—28no—
109#14579137C2314yes—
110#14579137C2314yes—
111Q8×Dic79—22no—
112Q8×Dic79—22no—
113Q8×Dic79C2314yes—
114Q8×Dic79C2314yes—
115#14579126—28no—
116C4×C22⋊D79—28no—
117C4×C22⋊D79D414yes—
118C4×C22⋊D79C2314yes—
119#14579120—22no—
120#14579120C2314yes—
121#14579119—22no—
122#14579119C2314yes—
123C2×C4⋊Dic79—21no—
124C2×C4⋊Dic79—21no—
125C2×C4⋊Dic79C2311yescharacteristic
126C2×C4⋊Dic79C2311yescharacteristic
127C2×C4⋊Dic79C2311yescharacteristic
128C2×Dic79⋊C4—21no—
129C2×Dic79⋊C4—21no—
130C2×Dic79⋊C4—21no—
131C2×Dic79⋊C4—21no—
132C2×Dic79⋊C4—21no—
133C2×Dic79⋊C4—21no—
134C2×Dic79⋊C4D411yescharacteristic
135C2×C22⋊Dic79—21no—
136C2×C22⋊Dic79—21no—
137C2×C22⋊Dic79D411yescharacteristic
138C2×(C2×D79)⋊C4—21no—
139C2×(C2×D79)⋊C4—21no—
140C2×(C2×D79)⋊C4—21no—
141C2×(C2×D79)⋊C4D411yescharacteristic
142C2×C4×Dic79—21no—
143C2×C4×Dic79—21no—
144C2×C4×Dic79—21no—
145C2×C4×Dic79—21no—
146C2×C4×Dic79C2311yescharacteristic
147#14579095C2314yes—
148#14579093C2314yes—
149#14579092C2314yes—
150Dic79⋊C8C2314yes—
151#14579086C2314yes—
152#14579086C2314yes—
153#14579085C2314yes—
154#14579085C2314yes—
155#14579085C2314yes—
156#14579085C2314yes—
157#14579085C2314yes—
158#14579084C2314yes—
159(C2×D79)⋊C8C2314yes—
160C8×Dic79C2314yes—
161C22×Q8×C79—22no—
162C22×Q8×C79—21no—
163C22×Q8×C79—24no—
164C22×Q8×C79—42no—
165C22×Q8×C79C2311yescharacteristic
166C22×Q8×C79C2311yescharacteristic
167C22×Q8×C79C2314yes—
168C22×Q8×C79C2311yescharacteristic
169C23×C4×C79—21no—
170C23×C4×C79C2311yescharacteristic
171C2×Q16×C79—24no—
172C2×Q16×C79—42no—
173C2×Q16×C79C2314yes—
174C2×Q16×C79C2314yes—
175C22×C8×C79C2311yescharacteristic
176C22×C8×C79C2311yescharacteristic
177C22⋊Q8×C79—22no—
178C22⋊Q8×C79C2314yes—
179C2×C4⋊C4×C79—21no—
180C2×C4⋊C4×C79C2311yescharacteristic
181C2×C22⋊C4×C79—21no—
182#103×C79C2314yes—
183#103×C79C2314yes—
184C22⋊C8×C79C2314yes—
185C23×D79C2×D411yescharacteristic
186C2×Dic158—24no—
187C2×Dic158—24no—
188C2×Dic158—21no—
189C2×Dic158—22no—
190C2×Dic158—22no—
191C2×Dic158—44no—
192C2×Dic158—44no—
193C2×Dic158C2412yes—
194Q8×D79—28no—
195Q8×D79—44no—
196Q8×D79—48no—
197C2×C22⋊D79—24no—
198C2×C22⋊D79C2×D414yes—
199C22×Dic79—21no—
200C22×Dic79—21no—
201C22×Dic79—21no—
202C22×Dic79—21no—
203C22×Dic79C2×D411yescharacteristic
204C22×Dic79C2×D411yescharacteristic
205C22×Dic79C2×D411yescharacteristic
206C2×C4×D79—24no—
207C2×C4×D79—22no—
208C2×C4×D79—22no—
209C2×C4×D79—44no—
210C2×C4×D79C2×D412yes—
211C2×C4×D79C2412yes—
212#11929614—44no—
213#11929608—44no—
214#11929607—44no—
215C2×C79⋊C8—22no—
216C2×C79⋊C8—22no—
217C2×C79⋊C8C2412yes—
218C2×C79⋊C8C2412yes—
219C4⋊Dic79—24no—
220C4⋊Dic79—24no—
221C4⋊Dic79—21no—
222C4⋊Dic79—21no—
223C4⋊Dic79—21no—
224C4⋊Dic79C2412yes—
225C4⋊Dic79C2412yes—
226C4⋊Dic79C2412yes—
227Dic79⋊C4—24no—
228Dic79⋊C4—24no—
229Dic79⋊C4—24no—
230Dic79⋊C4—24no—
231Dic79⋊C4—24no—
232Dic79⋊C4—24no—
233Dic79⋊C4C2×D414yes—
234C22⋊Dic79—24no—
235C22⋊Dic79—24no—
236C22⋊Dic79C2×D414yes—
237(C2×D79)⋊C4—24no—
238(C2×D79)⋊C4—24no—
239(C2×D79)⋊C4—24no—
240(C2×D79)⋊C4C2×D414yes—
241C4×Dic79—24no—
242C4×Dic79—24no—
243C4×Dic79—24no—
244C4×Dic79—24no—
245C4×Dic79C2×D412yes—
246C4×Dic79C2412yes—
247C24×C79C2×D411yescharacteristic
248C2×Q8×C79—21no—
249C2×Q8×C79—21no—
250C2×Q8×C79—24no—
251C2×Q8×C79—21no—
252C2×Q8×C79—22no—
253C2×Q8×C79—28no—
254C2×Q8×C79—22no—
255C2×Q8×C79—22no—
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—
264C2×Q8×C79C2412yes—
265C22×C4×C79—21no—
266C22×C4×C79—22no—
267C22×C4×C79—22no—
268C22×C4×C79—21no—
269C22×C4×C79—21no—
270C22×C4×C79—21no—
271C22×C4×C79—24no—
272C22×C4×C79—44no—
273C22×C4×C79C2×D411yescharacteristic
274C22×C4×C79C2×D412yes—
275C22×C4×C79C2412yes—
276C22×C4×C79C2411yescharacteristic
277Q16×C79—28no—
278Q16×C79—44no—
279C2×C8×C79—22no—
280C2×C8×C79—22no—
281C2×C8×C79C2412yes—
282C2×C8×C79C2412yes—
283C4⋊C4×C79—24no—
284C4⋊C4×C79—21no—
285C4⋊C4×C79C2412yes—
286C22⋊C4×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—22no—
295C22×D79C22×D412yes—
296Q8×C79—24no—
297Q8×C79—22no—
298Q8×C79—22no—
299Q8×C79—22no—
300Q8×C79—22no—
301Q8×C79—22no—
302Q8×C79—48no—
303Q8×C79—42no—
304Q8×C79—42no—
305Q8×C79C2×#4114yes—
306C2×C4×C79—24no—
307C2×C4×C79—22no—
308C2×C4×C79—22no—
309C2×C4×C79—24no—
310C2×C4×C79—22no—
311C2×C4×C79—22no—
312C2×C4×C79—22no—
313C2×C4×C79—22no—
314C2×C4×C79—22no—
315C2×C4×C79—48no—
316C2×C4×C79—42no—
317C2×C4×C79—42no—
318C2×C4×C79—42no—
319C2×C4×C79C22×D412yes—
320C2×C4×C79C22×D411yescharacteristic
321C2×C4×C79C2×#4112yes—
322C2×C4×C79H(5,𝔽2)12yes—
323C2×C4×C79C2511yescharacteristic
324C22⋊D79—28no—
325C2×Dic79—22no—
326C2×Dic79—22no—
327C2×Dic79—22no—
328C2×Dic79—22no—
329C2×Dic79—22no—
330C2×Dic79—22no—
331C2×Dic79—42no—
332C2×Dic79—42no—
333C2×Dic79—42no—
334C2×Dic79—42no—
335C2×Dic79#13714yes—
336C2×Dic79C22×D412yes—
337C2×Dic79C22×D412yes—
338C2×Dic79C22×D412yes—
339C4×D79—24no—
340C4×D79—22no—
341C4×D79—22no—
342C4×D79—48no—
343Dic158—22no—
344Dic158—22no—
345Dic158—48no—
346Dic158—42no—
347Dic158—48no—
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—22no—
362C2×D79—22no—
363C2×D79—44no—
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—42no—
375Dic79—42no—
376Dic79—42no—
377Dic79—42no—
378Dic79C2×#13714yes—
379C2×#3328—791nomaximal, Sylow
380C2×C79—42no—
381C2×C79#332814yescomplemented
382C2×C79C2×#54611yescharacteristic
383C2×C79C22×#13711yescharacteristic
384C2×C79C2×#57811yescharacteristic
385D79—42no—
386C2×#556—791no—
387C2×D4×Q8—791no—
388#3328—7916no—
389C2×#487—791no—
390C2×#485—791no—
391C2×#485—791no—
392C2×#475—791no—
393C2×#470—791no—
394C2×#470—791no—
395C2×#462—791no—
396C2×#451—791no—
397C2×#451D7911yescharacteristic, complemented
398C2×C4×Q16—791no—
399C2×#436—791no—
400C2×#419—791no—
401C2×#419—791no—
402C79C2×#332811yescharacteristic, complemented, Sylow
403C23×Q8—791no—
404C23×Q8C2×D7911yescharacteristic
405C22×Q16—791no—
406C22×Q16C2×D7911yescharacteristic
407C22×Q16C2×D7911yescharacteristic
408C22×M16—791no—
409C22×M16—791no—
410#556—798no—
411#556—1584no—
412D4×Q8—798no—
413D4×Q8—1584no—
414C2×C4⋊Q8—791no—
415C2×C4⋊Q8—791no—
416C2×C4⋊Q8—1581no—
417C2×#126—1581no—
418C2×#126—1581no—
419C2×#124—1581no—
420C2×C22⋊Q8—791no—
421C2×C22⋊Q8—791no—
422C2×C22⋊Q8—791no—
423C2×C22⋊Q8—1581no—
424C2×C22⋊Q8—1581no—
425C2×C22⋊Q8C2×D7911yescharacteristic
426C2×C4×Q8—791no—
427C2×C4×Q8—791no—
428C2×C4×Q8—1581no—
429C2×C4×D4—791no—
430C2×C4×D4—1581no—
431C2×#117—791no—
432C2×#117—791no—
433#487—798no—
434#485—798no—
435#485—798no—
436#475—798no—
437#470—798no—
438#470—798no—
439#462—798no—
440#451—798no—
441#451C2×D7918yescomplemented
442C4×Q16—798no—
443#436—798no—
444C2×#107—791no—
445C2×#106—791no—
446C2×#106—791no—
447C2×C4⋊C8—791no—
448#419—798no—
449#419—798no—
450C2×#103—791no—
451C2×#103—791no—
452C2×#103—791no—
453C2×#103—791no—
454C2×#103—791no—
455C2×#103—791no—
456C2×#103—791no—
457C2×#103—791no—
458C2×#103C2×D7911yescharacteristic
459C2×#103C2×D7911yescharacteristic
460C2×C22⋊C8—791no—
461C2×C22⋊C8C2×D7911yescharacteristic
462C2×C4×C8—791no—
463C22×Q8—21no—
464C22×Q8—22no—
465C22×Q8—24no—
466C22×Q8—42no—
467C22×Q8—3162no—
468C22×Q8—794no—
469C22×Q8—791no—
470C22×Q8—1581no—
471C22×Q8—1581no—
472C22×Q8—1584no—
473C22×Q8—1582no—
474C22×Q8C22×D7911yescharacteristic
475C22×Q8C22×D7911yescharacteristic
476C22×Q8C22×D7914yes—
477C22×Q8C22×D7911yescharacteristic
478C22×D4—791no—
479C23×C4—21no—
480C23×C4—791no—
481C23×C4—1581no—
482C23×C4C22×D7911yescharacteristic
483C2×Q16—24no—
484C2×Q16—42no—
485C2×Q16—3162no—
486C2×Q16—794no—
487C2×Q16C22×D7914yes—
488C2×Q16C22×D7914yes—
489C2×M16—3162no—
490C2×M16—3162no—
491C2×M16—794no—
492C2×M16—794no—
493C22×C8—791no—
494C22×C8—791no—
495C22×C8C22×D7911yescharacteristic
496C22×C8C22×D7911yescharacteristic
497C4⋊Q8—794no—
498C4⋊Q8—794no—
499C4⋊Q8—1582no—
500C4⋊Q8—1582no—
501C4⋊Q8—1588no—
502#126—1588no—
503#126—1588no—
504#124—1588no—
505C22⋊Q8—22no—
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⋊Q8C22×D7914yes—
515C4×Q8—794no—
516C4×Q8—794no—
517C4×Q8—1582no—
518C4×Q8—1582no—
519C4×Q8—1588no—
520C4×D4—794no—
521C4×D4—794no—
522C4×D4—1588no—
523#117—794no—
524#117—794no—
525#117—1582no—
526#117—1582no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—791no—
529C2×C4⋊C4—791no—
530C2×C4⋊C4—791no—
531C2×C4⋊C4—791no—
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⋊C4C22×D7911yescharacteristic
541C2×C22⋊C4—21no—
542C2×C22⋊C4—791no—
543C2×C22⋊C4—791no—
544C2×C22⋊C4—1581no—
545C2×C22⋊C4—1581no—
546C2×C22⋊C4—1581no—
547C2×C22⋊C4—1581no—
548C2×C22⋊C4—1581no—
549C2×C42—791no—
550C2×C42—1581no—
551C2×C42—1581no—
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#103—794no—
565#103—794no—
566#103C22×D7914yes—
567#103C22×D7914yes—
568C22⋊C8—794no—
569C22⋊C8C22×D7914yes—
570C4×C8—794no—
571C24—791no—
572C24D4×D7911yescharacteristic
573C2×Q8—22no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—24no—
577C2×Q8—21no—
578C2×Q8—28no—
579C2×Q8—22no—
580C2×Q8—22no—
581C2×Q8—22no—
582C2×Q8—22no—
583C2×Q8—44no—
584C2×Q8—44no—
585C2×Q8—48no—
586C2×Q8—3164no—
587C2×Q8—3164no—
588C2×Q8—3168no—
589C2×Q8—3164no—
590C2×Q8—792no—
591C2×Q8—1584no—
592C2×Q8—1584no—
593C2×Q8—1588no—
594C2×Q8—1582no—
595C2×Q8—1582no—
596C2×Q8—1581no—
597C2×Q8#1192962314yes—
598C2×Q8C23×D7912yes—
599C2×Q8C23×D7912yes—
600C2×Q8C23×D7912yes—
601C2×D4—794no—
602C2×D4—1584no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—24no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—44no—
611C22×C4—3164no—
612C22×C4—791no—
613C22×C4—791no—
614C22×C4—791no—
615C22×C4—792no—
616C22×C4—792no—
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—28no—
629Q16—44no—
630Q16—3164no—
631M16—3164no—
632M16—3164no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—792no—
636C2×C8—792no—
637C2×C8—1582no—
638C2×C8—1582no—
639C2×C8C23×D7912yes—
640C2×C8C23×D7912yes—
641C4⋊C4—24no—
642C4⋊C4—21no—
643C4⋊C4—794no—
644C4⋊C4—792no—
645C4⋊C4—792no—
646C4⋊C4—792no—
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—1581no—
656C4⋊C4—1581no—
657C4⋊C4—1581no—
658C4⋊C4C23×D7912yes—
659C22⋊C4—24no—
660C22⋊C4—794no—
661C22⋊C4—794no—
662C22⋊C4—1584no—
663C22⋊C4—1584no—
664C22⋊C4—1584no—
665C22⋊C4—1584no—
666C22⋊C4—1584no—
667C42—792no—
668C42—792no—
669C42—1584no—
670C42—1584no—
671C42—1584no—
672C42—1584no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—792no—
677C23—1582no—
678C23—1582no—
679C23—1582no—
680C23C2×D4×D7912yes—
681C23C2×D4×D7911yescharacteristic
682Q8—22no—
683Q8—24no—
684Q8—22no—
685Q8—22no—
686Q8—22no—
687Q8—22no—
688Q8—48no—
689Q8—42no—
690Q8—42no—
691Q8—3168no—
692Q8—3168no—
693Q8—3162no—
694Q8—1582no—
695Q8—1582no—
696Q8C2×#1192962314yes—
697D4—1588no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—48no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—3168no—
712C2×C4—3162no—
713C2×C4—3162no—
714C2×C4—3162no—
715C2×C4—3162no—
716C2×C4—794no—
717C2×C4—792no—
718C2×C4—792no—
719C2×C4—792no—
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×#1192962312yes—
732C2×C4#1457920612yes—
733C2×C4C24×D7911yescharacteristic
734C8—22no—
735C8—22no—
736C8—1582no—
737C8—1582no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—44no—
742C22—3164no—
743C22—1582no—
744C22—1582no—
745C22—1582no—
746C22#1909920012yes—
747C22#137×D7912yes—
748C22#1909937612yes—
749C22C22×D4×D7911yescharacteristic
750C4—22no—
751C4—24no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—3162no—
756C4—3162no—
757C4—3162no—
758C4—3162no—
759C4—794no—
760C4—1582no—
761C4—1582no—
762C4#1909920012yes—
763C4C22×#1192962311yescharacteristic
764C4C2×#1457920611yescharacteristic
765C2—42no—
766C2—3162no—
767C2#2377567614yesdirect product factor
768C2C2×#1909920011yescharacteristic
769C2C2×#137×D7911yescharacteristic
770C2C2×#1909937611yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#451×C79C2
socleC23×C79C22×D4
prime radicalC22×C22⋊D79D4
hypercenterC2×#451D79
hypocenterC79C2×#3328
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
3. #23775676C2direct (N × H)
4. C2×#19098912C2semidirect
5. C2×#19098905C2semidirect
6. C2×#19098903C2semidirect
7. C2×#19098846C2semidirect
8. C2×#19098819C2semidirect
9. C2×#19098818C2semidirect
10. C2×#19098771C2semidirect
11. C2×#19098717C2semidirect
12. C2×Q16×Dic79C2semidirect
14. C2×#19098572C2semidirect
15. C2×#19098570C2semidirect
16. C2×#451×C79C2semidirect
43. #19098912C22semidirect
44. #19098905C22semidirect
45. #19098903C22semidirect
46. #19098846C22semidirect
47. #19098819C22semidirect
48. #19098818C22semidirect
49. #19098771C22semidirect
50. #19098717C22semidirect
51. Q16×Dic79C22semidirect
57. #19098572C22semidirect
58. #19098570C22semidirect
73. #451×C79C22semidirect
381. C2×C79#3328semidirect
397. C2×#451D79semidirect
402. C79C2×#3328semidirect
441. #451C2×D79semidirect
767. C2#23775676direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992842
C2×Q8×C22⋊D792
#237756762
C2×#190989122
C2×#190989052
C2×#190989032
C2×#190988462
C2×#190988192
C2×#190988182
C2×#190987712
C2×#190987172
C2×Q16×Dic792
C2×#190986382
C2×#190985722
C2×#190985702
C2×#451×C792
C2×#332879