Finite Group Databasebeta

← C2×#23776000 #35166991

Subgroups — C2×#23776000 #35166991

Order 20224.

1962 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099259C211yesmaximal, characteristic, complemented
2#23776000C2116yesmaximal, direct product factor
3C2×#19098962C211yesmaximal, characteristic, complemented
4C2×#19098887C211yesmaximal, characteristic, complemented
5C2×#19098884C211yesmaximal, characteristic, complemented
6C2×#19098876C211yesmaximal, characteristic, complemented
7C2×#19098874C211yesmaximal, characteristic, complemented
8C2×#19098863C211yesmaximal, characteristic, complemented
9C2×#19098860C211yesmaximal, characteristic, complemented
10C2×#19098814C211yesmaximal, characteristic, complemented
11C2×#19098814C211yesmaximal, characteristic, complemented
12C2×C4×#11929609C211yesmaximal, characteristic, complemented
13C2×#19098641C211yesmaximal, characteristic, complemented
14C2×#19098606C211yesmaximal, characteristic, complemented
15C2×#19098603C211yesmaximal, characteristic, complemented
16C2×#553×C79C211yesmaximal, characteristic, complemented
17C22×#11929609C2211yescharacteristic
18C22×#11929608C2211yescharacteristic
19C22×#11929608C2211yescharacteristic
20#19099259—24no—
21#19099259C2218yescomplemented
22C2×#14579156—21no—
23C2×#14579153C2211yescharacteristic
24C2×#14579143—21no—
25C2×#14579135C2211yescharacteristic
26C2×#14579135C2211yescharacteristic
27C2×#14579133—21no—
28C2×C4×D316C2211yescharacteristic
29C2×(C22⋊D79)⋊C4—21no—
30C2×#14579120C2211yescharacteristic
31C22×C4⋊Dic79C2211yescharacteristic
32#19098962C2218yescomplemented
33#19098887C2218yescomplemented
34#19098884C2218yescomplemented
35#19098876C2218yescomplemented
36#19098874C2218yescomplemented
37#19098863C2218yescomplemented
38#19098860C2218yescomplemented
39#19098814C2218yescomplemented
40#19098814C2218yescomplemented
41C4×#11929609C2218yescomplemented
42#19098641C2218yescomplemented
43#19098606C2218yescomplemented
44#19098603C2218yescomplemented
45C2×#14579094C2211yescharacteristic
46C2×#14579094C2211yescharacteristic
47C2×#14579094C2211yescharacteristic
48C2×#14579094C2211yescharacteristic
49C2×#14579094C2211yescharacteristic
50C2×#14579092C2211yescharacteristic
51C2×#14579092C2211yescharacteristic
52C2×#14579092C2211yescharacteristic
53C2×#14579092C2211yescharacteristic
54C2×C4⋊(C79⋊C8)C2211yescharacteristic
55C2×#14579082C2211yescharacteristic
56C2×#14579082C2211yescharacteristic
57C2×#14579082C2211yescharacteristic
58C2×#14579081C2211yescharacteristic
59C2×#14579081C2211yescharacteristic
60C2×#14579081C2211yescharacteristic
61C2×C22⋊(C79⋊C8)C2211yescharacteristic
62C2×C22⋊(C79⋊C8)C2211yescharacteristic
63C2×C4×C79⋊C8C2211yescharacteristic
64#553×C79—24no—
65#553×C79C2218yescomplemented
66C2×#126×C79—21no—
67C2×#125×C79C2211yescharacteristic
68C2×#123×C79—21no—
69C2×#121×C79—21no—
70C2×#121×C79C2211yescharacteristic
71C2×#121×C79C2211yescharacteristic
72C2×C4×D4×C79—21no—
73C2×C4×D4×C79C2211yescharacteristic
74C2×C4×D4×C79C2211yescharacteristic
75C2×#117×C79C2211yescharacteristic
76C22×C4⋊C4×C79C2211yescharacteristic
77C22×D316C2311yescharacteristic
78C22×C22⋊D79—21no—
79C22×C22⋊D79—21no—
80C23×Dic79—21no—
81C22×C4×D79—21no—
82C2×#11929609—24no—
83C2×#11929609C2314yes—
84C2×#11929608—24no—
85C2×#11929608—24no—
86C2×#11929608C2314yes—
87C2×#11929608C2314yes—
88C22×C79⋊C8C2311yescharacteristic
89C22×C79⋊C8C2311yescharacteristic
90C22×C79⋊C8C2311yescharacteristic
91C22×C79⋊C8C2311yescharacteristic
92#14579156—28no—
93#14579153—22no—
94#14579153C2314yes—
95#14579143—28no—
96#14579135—22no—
97#14579135—22no—
98#14579135C2314yes—
99#14579135C2314yes—
100#14579133—28no—
101C4×D316—22no—
102C4×D316C2314yes—
103(C22⋊D79)⋊C4—28no—
104#14579120—22no—
105#14579120C2314yes—
106C2×C4⋊Dic79—22no—
107C2×C4⋊Dic79—21no—
108C2×C4⋊Dic79C2314yes—
109C2×C4⋊Dic79C2311yescharacteristic
110C2×C4⋊Dic79C2311yescharacteristic
111C2×C4⋊Dic79C2311yescharacteristic
112C2×Dic79⋊C4—21no—
113C2×Dic79⋊C4—21no—
114C2×C22⋊Dic79—21no—
115C2×(C2×D79)⋊C4—21no—
116C2×(C2×D79)⋊C4—21no—
117C2×(C2×D79)⋊C4—21no—
118C2×C4×Dic79—21no—
119#14579094C2314yes—
120#14579094C2314yes—
121#14579094C2314yes—
122#14579094C2314yes—
123#14579094C2314yes—
124#14579092C2314yes—
125#14579092C2314yes—
126#14579092C2314yes—
127#14579092C2314yes—
128C4⋊(C79⋊C8)C2314yes—
129#14579082C2314yes—
130#14579082C2314yes—
131#14579082C2314yes—
132#14579081C2314yes—
133#14579081C2314yes—
134#14579081C2314yes—
135C22⋊(C79⋊C8)C2314yes—
136C22⋊(C79⋊C8)C2314yes—
137C4×C79⋊C8C2314yes—
138C22×D4×C79—21no—
139C22×D4×C79—21no—
140C22×D4×C79D411yescharacteristic
141C22×D4×C79C2311yescharacteristic
142C23×C4×C79—21no—
143C23×C4×C79—21no—
144C23×C4×C79C2311yescharacteristic
145C23×C4×C79C2311yescharacteristic
146#126×C79—28no—
147#125×C79—22no—
148#125×C79C2314yes—
149#123×C79—28no—
150#121×C79—28no—
151#121×C79—22no—
152#121×C79—22no—
153#121×C79C2314yes—
154#121×C79C2314yes—
155C4×D4×C79—28no—
156C4×D4×C79—22no—
157C4×D4×C79D414yes—
158C4×D4×C79C2314yes—
159C4×D4×C79C2314yes—
160#117×C79—22no—
161#117×C79C2314yes—
162C2×C4⋊C4×C79—21no—
163C2×C4⋊C4×C79—22no—
164C2×C4⋊C4×C79—21no—
165C2×C4⋊C4×C79—21no—
166C2×C4⋊C4×C79D411yescharacteristic
167C2×C4⋊C4×C79C2311yescharacteristic
168C2×C4⋊C4×C79C2311yescharacteristic
169C2×C4⋊C4×C79C2314yes—
170C2×C4⋊C4×C79C2311yescharacteristic
171C2×C22⋊C4×C79—21no—
172C2×C22⋊C4×C79—21no—
173C2×C22⋊C4×C79—21no—
174C2×C22⋊C4×C79—21no—
175C2×C22⋊C4×C79D411yescharacteristic
176C2×C22⋊C4×C79D411yescharacteristic
177C2×C42×C79—21no—
178C2×C42×C79C2311yescharacteristic
179C23×D79—21no—
180C2×D316—21no—
181C2×D316—22no—
182C2×D316—22no—
183C2×D316C2412yes—
184C2×C22⋊D79—24no—
185C2×C22⋊D79—24no—
186C2×C22⋊D79—44no—
187C2×C22⋊D79—82no—
188C22×Dic79—21no—
189C22×Dic79—21no—
190C22×Dic79—21no—
191C22×Dic79—24no—
192C22×Dic79—82no—
193C2×C4×D79—24no—
194C2×C4×D79—82no—
195#11929609—28no—
196#11929608—28no—
197#11929608—28no—
198C2×C79⋊C8—22no—
199C2×C79⋊C8—22no—
200C2×C79⋊C8—22no—
201C2×C79⋊C8#4114yes—
202C2×C79⋊C8C2412yes—
203C2×C79⋊C8C2412yes—
204C2×C79⋊C8C2412yes—
205C2×C79⋊C8C2412yes—
206C4⋊Dic79—21no—
207C4⋊Dic79—21no—
208C4⋊Dic79—24no—
209C4⋊Dic79—21no—
210C4⋊Dic79C2412yes—
211C4⋊Dic79C2412yes—
212C4⋊Dic79C2412yes—
213Dic79⋊C4—24no—
214Dic79⋊C4—24no—
215C22⋊Dic79—24no—
216(C2×D79)⋊C4—24no—
217(C2×D79)⋊C4—24no—
218(C2×D79)⋊C4—24no—
219C4×Dic79—24no—
220C24×C79—21no—
221C24×C79C2×D411yescharacteristic
222C24×C79C2×D411yescharacteristic
223C2×D4×C79—24no—
224C2×D4×C79—24no—
225C2×D4×C79—21no—
226C2×D4×C79—22no—
227C2×D4×C79—22no—
228C2×D4×C79—42no—
229C2×D4×C79—44no—
230C2×D4×C79—82no—
231C2×D4×C79C2×D414yes—
232C2×D4×C79C2412yes—
233C22×C4×C79—22no—
234C22×C4×C79—22no—
235C22×C4×C79—22no—
236C22×C4×C79—22no—
237C22×C4×C79—21no—
238C22×C4×C79—21no—
239C22×C4×C79—21no—
240C22×C4×C79—24no—
241C22×C4×C79—24no—
242C22×C4×C79—82no—
243C22×C4×C79—82no—
244C22×C4×C79C2×D411yescharacteristic
245C22×C4×C79C2×D411yescharacteristic
246C22×C4×C79C2×D411yescharacteristic
247C22×C4×C79C2×D411yescharacteristic
248C22×C4×C79C2×D412yes—
249C22×C4×C79C2×D412yes—
250C22×C4×C79C2412yes—
251C22×C4×C79C2412yes—
252C22×C4×C79C2411yescharacteristic
253C4⋊C4×C79—21no—
254C4⋊C4×C79—21no—
255C4⋊C4×C79—24no—
256C4⋊C4×C79—24no—
257C4⋊C4×C79—24no—
258C4⋊C4×C79—21no—
259C4⋊C4×C79C2×D414yes—
260C4⋊C4×C79C2412yes—
261C4⋊C4×C79C2412yes—
262C4⋊C4×C79C2412yes—
263C22⋊C4×C79—24no—
264C22⋊C4×C79—24no—
265C22⋊C4×C79—24no—
266C22⋊C4×C79—24no—
267C22⋊C4×C79C2×D414yes—
268C22⋊C4×C79C2×D414yes—
269C42×C79—24no—
270C42×C79C2×D412yes—
271C42×C79C2412yes—
272C23×C79—22no—
273C23×C79—22no—
274C23×C79—22no—
275C23×C79—22no—
276C23×C79—22no—
277C23×C79—22no—
278C23×C79—22no—
279C23×C79—42no—
280C23×C79—42no—
281C23×C79—42no—
282C23×C79C22×D412yes—
283C23×C79C22×D412yes—
284C23×C79C22×D411yescharacteristic
285C22×D79—22no—
286C22×D79—42no—
287C22×D79—42no—
288C22×D79—42no—
289D4×C79—22no—
290D4×C79—22no—
291D4×C79—44no—
292D4×C79—48no—
293D4×C79—42no—
294D4×C79—84no—
295C2×C4×C79—22no—
296C2×C4×C79—22no—
297C2×C4×C79—22no—
298C2×C4×C79—22no—
299C2×C4×C79—24no—
300C2×C4×C79—24no—
301C2×C4×C79—22no—
302C2×C4×C79—22no—
303C2×C4×C79—22no—
304C2×C4×C79—22no—
305C2×C4×C79—22no—
306C2×C4×C79—22no—
307C2×C4×C79—22no—
308C2×C4×C79—42no—
309C2×C4×C79—42no—
310C2×C4×C79—42no—
311C2×C4×C79—84no—
312C2×C4×C79—84no—
313C2×C4×C79C22×D412yes—
314C2×C4×C79C22×D412yes—
315C2×C4×C79C22×D412yes—
316C2×C4×C79C22×D412yes—
317C2×C4×C79C22×D411yescharacteristic
318C2×C4×C79C2×#4112yes—
319C2×C4×C792−1+412yes—
320C2×C4×C79C2511yescharacteristic
321C22⋊D79—48no—
322C22⋊D79—84no—
323C2×Dic79—22no—
324C2×Dic79—22no—
325C2×Dic79—22no—
326C2×Dic79—42no—
327C2×Dic79—42no—
328C2×Dic79—42no—
329C2×Dic79—84no—
330D316—22no—
331D316—22no—
332D316—42no—
333C4×D79—84no—
334C79⋊C8—22no—
335C79⋊C8—22no—
336C79⋊C8—22no—
337C79⋊C8C2×#4114yes—
338C22×C79—22no—
339C22×C79—22no—
340C22×C79—22no—
341C22×C79—22no—
342C22×C79—22no—
343C22×C79—22no—
344C22×C79—44no—
345C22×C79—44no—
346C22×C79—42no—
347C22×C79—42no—
348C22×C79—42no—
349C22×C79—84no—
350C22×C79#54712yes—
351C22×C79#57512yes—
352C22×C79#57612yes—
353C22×C79C23×D411yescharacteristic
354C2×D79—42no—
355C2×D79—42no—
356C2×D79—42no—
357C2×D79—84no—
358C4×C79—22no—
359C4×C79—22no—
360C4×C79—22no—
361C4×C79—22no—
362C4×C79—42no—
363C4×C79—42no—
364C4×C79—42no—
365C4×C79#54712yes—
366C4×C79C22×#4111yescharacteristic
367C4×C79C2×2−1+411yescharacteristic
368Dic79—42no—
369Dic79—42no—
370Dic79—42no—
371C2×#3355—791nomaximal, Sylow
372C2×C79—42no—
373C2×C79—42no—
374C2×C79—82no—
375C2×C79#335514yescomplemented
376C2×C79C2×#54711yescharacteristic
377C2×C79C2×#57511yescharacteristic
378C2×C79C2×#57611yescharacteristic
379D79—82no—
380C2×#553—791no—
381C2×#553D7911yescharacteristic, complemented
382#3355—7916no—
383C2×#499—791no—
384C2×#482—791no—
385C2×#482—791no—
386C2×#480—791no—
387C2×#480—791no—
388C2×#478—791no—
389C2×#478—791no—
390C2×#469—791no—
391C2×#469—791no—
392C2×C4×D8—791no—
393C2×#436—791no—
394C2×#428—791no—
395C2×#428—791no—
396C79C2×#335511yescharacteristic, complemented, Sylow
397C22×D8—791no—
398C22×M16—791no—
399C22×M16—791no—
400#553—24no—
401#553—798no—
402#553—1584no—
403#553C2×D7918yescomplemented
404C2×#126—21no—
405C2×#126—1581no—
406C2×#125—791no—
407C2×#125C2×D7911yescharacteristic
408C2×#123—21no—
409C2×#123—1581no—
410C2×#121—21no—
411C2×#121—791no—
412C2×#121—791no—
413C2×#121—1581no—
414C2×#121C2×D7911yescharacteristic
415C2×#121C2×D7911yescharacteristic
416C2×C4×D4—21no—
417C2×C4×D4—791no—
418C2×C4×D4—1581no—
419C2×C4×D4C2×D7911yescharacteristic
420C2×C4×D4C2×D7911yescharacteristic
421C2×#117—791no—
422C2×#117C2×D7911yescharacteristic
423C22×C4⋊C4—791no—
424C22×C4⋊C4C2×D7911yescharacteristic
425#499—798no—
426#482—798no—
427#482—798no—
428#480—798no—
429#480—798no—
430#478—798no—
431#478—798no—
432#469—798no—
433#469—798no—
434C4×D8—798no—
435#436—798no—
436#428—798no—
437#428—798no—
438C2×#107—791no—
439C2×#107—791no—
440C2×#107—791no—
441C2×#107—791no—
442C2×#107—791no—
443C2×#106—791no—
444C2×#106—791no—
445C2×#106—791no—
446C2×#106—791no—
447C2×C4⋊C8—791no—
448C2×#102—791no—
449C2×#102—791no—
450C2×#102—791no—
451C2×#102—791no—
452C2×#102—791no—
453C2×#102—791no—
454C2×C22⋊C8—791no—
455C2×C22⋊C8—791no—
456C2×C4×C8—791no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—791no—
460C22×D4—1581no—
461C22×D4—1581no—
462C22×D4C22⋊D7911yescharacteristic
463C22×D4C22×D7911yescharacteristic
464C23×C4—21no—
465C23×C4—21no—
466C23×C4—1581no—
467C23×C4—1581no—
468C23×C4C22×D7911yescharacteristic
469C23×C4C22×D7911yescharacteristic
470C2×D8—794no—
471C2×D8—1584no—
472C2×M16—794no—
473C2×M16—794no—
474C2×M16—1584no—
475C2×M16—1584no—
476C22×C8—791no—
477C22×C8—791no—
478C22×C8—791no—
479C22×C8—791no—
480#126—28no—
481#126—1588no—
482#125—22no—
483#125—794no—
484#125—1582no—
485#125C22×D7914yes—
486#123—28no—
487#123—1588no—
488#121—28no—
489#121—22no—
490#121—22no—
491#121—794no—
492#121—794no—
493#121—1588no—
494#121—1582no—
495#121—1582no—
496#121C22×D7914yes—
497#121C22×D7914yes—
498C4×D4—28no—
499C4×D4—22no—
500C4×D4—794no—
501C4×D4—1588no—
502C4×D4—1582no—
503C4×D4C22⋊D7914yes—
504C4×D4C22×D7914yes—
505C4×D4C22×D7914yes—
506#117—22no—
507#117—794no—
508#117—1582no—
509#117C22×D7914yes—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—22no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—791no—
515C2×C4⋊C4—791no—
516C2×C4⋊C4—794no—
517C2×C4⋊C4—791no—
518C2×C4⋊C4—1581no—
519C2×C4⋊C4—1582no—
520C2×C4⋊C4—1581no—
521C2×C4⋊C4—1581no—
522C2×C4⋊C4C22⋊D7911yescharacteristic
523C2×C4⋊C4C22×D7911yescharacteristic
524C2×C4⋊C4C22×D7911yescharacteristic
525C2×C4⋊C4C22×D7914yes—
526C2×C4⋊C4C22×D7911yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—1581no—
532C2×C22⋊C4—1581no—
533C2×C22⋊C4—1581no—
534C2×C22⋊C4—1581no—
535C2×C22⋊C4C22⋊D7911yescharacteristic
536C2×C22⋊C4C22⋊D7911yescharacteristic
537C2×C42—21no—
538C2×C42—1581no—
539C2×C42C22×D7911yescharacteristic
540#107—794no—
541#107—794no—
542#107—794no—
543#107—794no—
544#107—794no—
545#106—794no—
546#106—794no—
547#106—794no—
548#106—794no—
549C4⋊C8—794no—
550#102—794no—
551#102—794no—
552#102—794no—
553#102—794no—
554#102—794no—
555#102—794no—
556C22⋊C8—794no—
557C22⋊C8—794no—
558C4×C8—794no—
559C24—21no—
560C24—1581no—
561C24C2×C22⋊D7911yescharacteristic
562C24C2×C22⋊D7911yescharacteristic
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—21no—
568C2×D4—42no—
569C2×D4—44no—
570C2×D4—82no—
571C2×D4—3164no—
572C2×D4—792no—
573C2×D4—6322no—
574C2×D4—1584no—
575C2×D4—1584no—
576C2×D4—1582no—
577C2×D4—1582no—
578C2×D4—1581no—
579C2×D4C2×C22⋊D7914yes—
580C2×D4C23×D7912yes—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—82no—
591C22×C4—82no—
592C22×C4—6322no—
593C22×C4—6322no—
594C22×C4—1581no—
595C22×C4—1581no—
596C22×C4—1581no—
597C22×C4—1584no—
598C22×C4—1584no—
599C22×C4C2×C22⋊D7912yes—
600C22×C4C2×C22⋊D7912yes—
601C22×C4C2×C22⋊D7911yescharacteristic
602C22×C4C2×C22⋊D7911yescharacteristic
603C22×C4C2×C22⋊D7911yescharacteristic
604C22×C4C2×C22⋊D7911yescharacteristic
605C22×C4C23×D7912yes—
606C22×C4C23×D7912yes—
607C22×C4C23×D7911yescharacteristic
608D8—1588no—
609M16—1588no—
610M16—1588no—
611C2×C8—794no—
612C2×C8—792no—
613C2×C8—792no—
614C2×C8—792no—
615C2×C8—792no—
616C2×C8—1582no—
617C2×C8—1582no—
618C2×C8—1582no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—21no—
625C4⋊C4—792no—
626C4⋊C4—792no—
627C4⋊C4—792no—
628C4⋊C4—1584no—
629C4⋊C4—1584no—
630C4⋊C4—1581no—
631C4⋊C4—1581no—
632C4⋊C4—1584no—
633C4⋊C4—1581no—
634C4⋊C4C2×C22⋊D7914yes—
635C4⋊C4C23×D7912yes—
636C4⋊C4C23×D7912yes—
637C4⋊C4C23×D7912yes—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—1584no—
643C22⋊C4—1584no—
644C22⋊C4—1584no—
645C22⋊C4—1584no—
646C22⋊C4C2×C22⋊D7914yes—
647C22⋊C4C2×C22⋊D7914yes—
648C42—24no—
649C42—1584no—
650C42C2×C22⋊D7912yes—
651C42C23×D7912yes—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—3162no—
663C23—3162no—
664C23—3162no—
665C23—1582no—
666C23C22×C22⋊D7912yes—
667C23C22×C22⋊D7912yes—
668C23C22×C22⋊D7911yescharacteristic
669D4—22no—
670D4—22no—
671D4—44no—
672D4—48no—
673D4—42no—
674D4—84no—
675D4—3168no—
676D4—3162no—
677D4—6324no—
678D4—1582no—
679D4—1582no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—84no—
697C2×C4—84no—
698C2×C4—3162no—
699C2×C4—3162no—
700C2×C4—3162no—
701C2×C4—6324no—
702C2×C4—6324no—
703C2×C4—1582no—
704C2×C4—1582no—
705C2×C4—1582no—
706C2×C4C22×C22⋊D7912yes—
707C2×C4C22×C22⋊D7912yes—
708C2×C4C22×C22⋊D7912yes—
709C2×C4C22×C22⋊D7912yes—
710C2×C4C22×C22⋊D7911yescharacteristic
711C2×C4#41×D7912yes—
712C2×C4#1457920812yes—
713C2×C4C24×D7911yescharacteristic
714C8—794no—
715C8—1582no—
716C8—1582no—
717C8—1582no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—44no—
725C22—44no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—84no—
730C22—3162no—
731C22—3162no—
732C22—3162no—
733C22—6324no—
734C22#1909921212yes—
735C22#1909936112yes—
736C22#1909936612yes—
737C22C23×C22⋊D7911yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—22no—
742C4—42no—
743C4—42no—
744C4—42no—
745C4—3162no—
746C4—3162no—
747C4—3162no—
748C4#1909921212yes—
749C4C2×#41×D7911yescharacteristic
750C4C2×#1457920811yescharacteristic
751C2—42no—
752C2—42no—
753C2—82no—
754C2—6322no—
755C2#2377600014yesdirect product factor
756C2C2×#1909921211yescharacteristic
757C2C2×#1909936111yescharacteristic
758C2C2×#1909936611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#553×C79C2
socleC23×C79C22×D4
hypercenterC2×#553D79
hypocenterC79C2×#3355
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#19099259C2semidirect
2. #23776000C2direct (N × H)
3. C2×#19098962C2semidirect
4. C2×#19098887C2semidirect
5. C2×#19098884C2semidirect
6. C2×#19098876C2semidirect
7. C2×#19098874C2semidirect
8. C2×#19098863C2semidirect
9. C2×#19098860C2semidirect
10. C2×#19098814C2semidirect
11. C2×#19098814C2semidirect
12. C2×C4×#11929609C2semidirect
13. C2×#19098641C2semidirect
14. C2×#19098606C2semidirect
15. C2×#19098603C2semidirect
16. C2×#553×C79C2semidirect
21. #19099259C22semidirect
32. #19098962C22semidirect
33. #19098887C22semidirect
34. #19098884C22semidirect
35. #19098876C22semidirect
36. #19098874C22semidirect
37. #19098863C22semidirect
38. #19098860C22semidirect
39. #19098814C22semidirect
40. #19098814C22semidirect
41. C4×#11929609C22semidirect
42. #19098641C22semidirect
43. #19098606C22semidirect
44. #19098603C22semidirect
65. #553×C79C22semidirect
375. C2×C79#3355semidirect
381. C2×#553D79semidirect
396. C79C2×#3355semidirect
403. #553C2×D79semidirect
755. C2#23776000direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992592
#237760002
C2×#190989622
C2×#190988872
C2×#190988842
C2×#190988762
C2×#190988742
C2×#190988632
C2×#190988602
C2×#190988142
C2×C4×#119296092
C2×#190986412
C2×#190986062
C2×#190986032
C2×#553×C792
C2×#335579