Finite Group Databasebeta

← C2×#23773217 #35155803

Subgroups — C2×#23773217 #35155803

Order 20224.

2142 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#125×D79C211yesmaximal, characteristic, complemented
2C2×C4×#11929623C211yesmaximal, characteristic
3#23773217C2116yesmaximal, direct product factor
4C2×#19098873C211yesmaximal, characteristic, complemented
5C2×#19098871C211yesmaximal, characteristic, complemented
6C2×#19098869C211yesmaximal, characteristic, complemented
7C2×#19098867C211yesmaximal, characteristic, complemented
8C2×#19098865C211yesmaximal, characteristic, complemented
9C2×#19098863C211yesmaximal, characteristic, complemented
10C2×#19098861C211yesmaximal, characteristic, complemented
11C2×#19098604C211yesmaximal, characteristic, complemented
12C2×#19098602C211yesmaximal, characteristic, complemented
13C2×#19098585C211yesmaximal, characteristic, complemented
14C2×#19098561C211yesmaximal, characteristic
15C2×#19098561C211yesmaximal, characteristic
16C2×#478×C79C211yesmaximal, characteristic, complemented
17C22×#11929623C2211yescharacteristic
18C22×#11929607C2211yescharacteristic
19C22×#11929607C2211yescharacteristic
20C2×#14579153C2211yescharacteristic
21C2×#14579152C2211yescharacteristic
22C2×#14579152C2211yescharacteristic
23C2×#14579151—21no—
24C2×#14579151—21no—
25#125×D79—24no—
26#125×D79C2218yescomplemented
27C4×#11929623—24no—
28C4×#11929623C2218yes—
29C2×C4×Dic158C2211yescharacteristic
30C2×#14579126C2211yescharacteristic
31C2×D4×Dic79C2211yescharacteristic
32C2×C4×C22⋊D79—21no—
33C2×(C22⋊D79)⋊C4—21no—
34C2×#14579119C2211yescharacteristic
35C2×#14579117—21no—
36C2×C4⋊C4×D79—21no—
37C2×C4⋊C4×D79—21no—
38C2×C4⋊C4×D79C2211yescharacteristic
39C2×C4⋊C4×D79C2211yescharacteristic
40C22×C4×Dic79—21no—
41C2×C42×D79C2211yescharacteristic
42#19098873C2218yescomplemented
43#19098871C2218yescomplemented
44#19098869C2218yescomplemented
45#19098867C2218yescomplemented
46#19098865C2218yescomplemented
47#19098863C2218yescomplemented
48#19098861C2218yescomplemented
49#19098604C2218yescomplemented
50#19098602C2218yescomplemented
51C2×#14579095C2211yescharacteristic
52C2×#14579094C2211yescharacteristic
53C2×#14579094C2211yescharacteristic
54C2×#14579093C2211yescharacteristic
55C2×#14579092C2211yescharacteristic
56C2×#14579092C2211yescharacteristic
57#19098585C2218yescomplemented
58C2×C4⋊(C79⋊C8)C2211yescharacteristic
59C2×Dic79⋊C8C2211yescharacteristic
60C2×Dic79⋊C8C2211yescharacteristic
61#19098561C2218yes—
62#19098561C2218yes—
63C2×#14579086C2211yescharacteristic
64C2×#14579086C2211yescharacteristic
65C2×#14579084C2211yescharacteristic
66C2×#14579084C2211yescharacteristic
67C2×#14579082C2211yescharacteristic
68C2×#14579082C2211yescharacteristic
69C2×#125×C79C2211yescharacteristic
70C2×C4×D4×C79C2211yescharacteristic
71#478×C79C2218yescomplemented
72C2×#107×C79C2211yescharacteristic
73C2×#106×C79C2211yescharacteristic
74C2×C4⋊C8×C79C2211yescharacteristic
75C2×#102×C79C2211yescharacteristic
76C2×#102×C79C2211yescharacteristic
77C2×#11929623—22no—
78C2×#11929623—24no—
79C2×#11929623Q818yes—
80C2×#11929623C2314yes—
81C22×Dic158C2311yescharacteristic
82C22×C22⋊D79—21no—
83C23×Dic79—21no—
84C23×Dic79—21no—
85C22×C4×D79—21no—
86C22×C4×D79—21no—
87C22×C4×D79D411yescharacteristic
88C22×C4×D79D411yescharacteristic
89C22×C4×D79C2311yescharacteristic
90C2×#11929607—24no—
91C2×#11929607—24no—
92C2×#11929607C2314yes—
93C2×#11929607C2314yes—
94C22×C79⋊C8C2311yescharacteristic
95C22×C79⋊C8C2311yescharacteristic
96#14579153—22no—
97#14579153C2314yes—
98#14579152—22no—
99#14579152—22no—
100#14579152C2314yes—
101#14579152C2314yes—
102#14579151—28no—
103#14579151—28no—
104C4×Dic158—22no—
105C4×Dic158C2314yes—
106#14579126—22no—
107#14579126C2314yes—
108D4×Dic79—22no—
109D4×Dic79C2314yes—
110C4×C22⋊D79—28no—
111(C22⋊D79)⋊C4—28no—
112#14579119—22no—
113#14579119C2314yes—
114#14579117—28no—
115C2×C4⋊Dic79—21no—
116C2×C4⋊Dic79—21no—
117C2×C4⋊Dic79C2311yescharacteristic
118C2×C4⋊Dic79C2311yescharacteristic
119C2×C4⋊Dic79C2311yescharacteristic
120C2×Dic79⋊C4—21no—
121C2×Dic79⋊C4—21no—
122C2×Dic79⋊C4—21no—
123C2×Dic79⋊C4—21no—
124C2×Dic79⋊C4—21no—
125C2×Dic79⋊C4—21no—
126C2×Dic79⋊C4—21no—
127C2×Dic79⋊C4—21no—
128C4⋊C4×D79—28no—
129C4⋊C4×D79—28no—
130C4⋊C4×D79—22no—
131C4⋊C4×D79—22no—
132C4⋊C4×D79C2314yes—
133C4⋊C4×D79C2314yes—
134C2×C22⋊Dic79—21no—
135C2×(C2×D79)⋊C4—21no—
136C2×C4×Dic79—21no—
137C2×C4×Dic79—21no—
138C2×C4×Dic79—21no—
139C2×C4×Dic79—28no—
140C2×C4×Dic79D411yescharacteristic
141C2×C4×Dic79D411yescharacteristic
142C2×C4×Dic79C2311yescharacteristic
143C42×D79D414yes—
144C42×D79C2314yes—
145#14579095C2314yes—
146#14579094C2314yes—
147#14579094C2314yes—
148#14579093C2314yes—
149#14579092C2314yes—
150#14579092C2314yes—
151C4⋊(C79⋊C8)C2314yes—
152Dic79⋊C8C2314yes—
153Dic79⋊C8C2314yes—
154#14579086C2314yes—
155#14579086C2314yes—
156#14579084C2314yes—
157#14579084C2314yes—
158#14579082C2314yes—
159#14579082C2314yes—
160C22×D4×C79C2311yescharacteristic
161C23×C4×C79—21no—
162C22×C8×C79C2311yescharacteristic
163C22×C8×C79C2311yescharacteristic
164#125×C79—22no—
165#125×C79C2314yes—
166C4×D4×C79—22no—
167C4×D4×C79C2314yes—
168C2×C4⋊C4×C79—21no—
169C2×C4⋊C4×C79—21no—
170C2×C4⋊C4×C79C2311yescharacteristic
171C2×C4⋊C4×C79C2311yescharacteristic
172C2×C4⋊C4×C79C2311yescharacteristic
173C2×C22⋊C4×C79—21no—
174C2×C42×C79C2311yescharacteristic
175#107×C79C2314yes—
176#106×C79C2314yes—
177C4⋊C8×C79C2314yes—
178#102×C79C2314yes—
179#102×C79C2314yes—
180C23×D79C2×D411yescharacteristic
181#11929623—216no—
182#11929623—28no—
183#11929623C2×Q8116yes—
184C2×Dic158—21no—
185C2×Dic158—22no—
186C2×Dic158C2×Q814yes—
187C2×Dic158C2412yes—
188C2×C22⋊D79—28no—
189C2×C22⋊D79—24no—
190C22×Dic79—28no—
191C22×Dic79—24no—
192C22×Dic79—24no—
193C22×Dic79—21no—
194C22×Dic79—21no—
195C22×Dic79—21no—
196C22×Dic79—21no—
197C22×Dic79—44no—
198C22×Dic79C2×D411yescharacteristic
199C22×Dic79C2×D411yescharacteristic
200C22×Dic79C2×D411yescharacteristic
201C2×C4×D79—24no—
202C2×C4×D79—24no—
203C2×C4×D79—42no—
204C2×C4×D79—42no—
205C2×C4×D79—44no—
206C2×C4×D79—44no—
207C2×C4×D79C2×D414yes—
208C2×C4×D79C2×D414yes—
209C2×C4×D79C2×D412yes—
210C2×C4×D79C2×Q814yes—
211C2×C4×D79#4114yes—
212C2×C4×D79C2412yes—
213#11929607—28no—
214#11929607—28no—
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⋊C4—24no—
234Dic79⋊C4—24no—
235C22⋊Dic79—24no—
236(C2×D79)⋊C4—24no—
237C4×Dic79—24no—
238C4×Dic79—24no—
239C4×Dic79—24no—
240C4×Dic79C2×D412yes—
241C4×Dic79C2×D414yes—
242C4×Dic79C2×D414yes—
243C4×Dic79C2412yes—
244C24×C79—21no—
245C2×D4×C79—21no—
246C2×D4×C79—22no—
247C2×D4×C79C2×Q814yes—
248C2×D4×C79C2412yes—
249C22×C4×C79—21no—
250C22×C4×C79—21no—
251C22×C4×C79—21no—
252C22×C4×C79—24no—
253C22×C4×C79—44no—
254C22×C4×C79C2×D411yescharacteristic
255C22×C4×C79C2×D411yescharacteristic
256C22×C4×C79C2411yescharacteristic
257C2×C8×C79—22no—
258C2×C8×C79—22no—
259C2×C8×C79C2412yes—
260C2×C8×C79C2412yes—
261C4⋊C4×C79—24no—
262C4⋊C4×C79—24no—
263C4⋊C4×C79—21no—
264C4⋊C4×C79—21no—
265C4⋊C4×C79—21no—
266C4⋊C4×C79C2412yes—
267C4⋊C4×C79C2412yes—
268C4⋊C4×C79C2412yes—
269C22⋊C4×C79—24no—
270C42×C79C2×D412yes—
271C42×C79C2412yes—
272C23×C79—24no—
273C23×C79—22no—
274C23×C79—42no—
275C23×C79—42no—
276C23×C79C22×D411yescharacteristic
277C22×D79—22no—
278C22×D79—22no—
279C22×D79C22⋊Q814yes—
280C22×D79C22×D412yes—
281D4×C79—24no—
282D4×C79—22no—
283D4×C79C22×Q814yes—
284C2×C4×C79—22no—
285C2×C4×C79—22no—
286C2×C4×C79—22no—
287C2×C4×C79—22no—
288C2×C4×C79—22no—
289C2×C4×C79—48no—
290C2×C4×C79—42no—
291C2×C4×C79—42no—
292C2×C4×C79—42no—
293C2×C4×C79C22×D412yes—
294C2×C4×C79C22×D412yes—
295C2×C4×C79C22×D411yescharacteristic
296C2×C4×C79C22×Q812yes—
297C2×C4×C79C2×#4112yes—
298C2×C4×C79C2511yescharacteristic
299C22⋊D79—216no—
300C2×Dic79—24no—
301C2×Dic79—22no—
302C2×Dic79—22no—
303C2×Dic79—22no—
304C2×Dic79—216no—
305C2×Dic79—22no—
306C2×Dic79—22no—
307C2×Dic79—22no—
308C2×Dic79—48no—
309C2×Dic79—42no—
310C2×Dic79—42no—
311C2×Dic79—42no—
312C2×Dic79C22⋊Q814yes—
313C2×Dic79C22×D412yes—
314C2×Dic79C22×D412yes—
315C2×Dic79C22×D412yes—
316C4×D79—44no—
317C4×D79—44no—
318C4×D79—48no—
319C4×D79—48no—
320C4×D79C22⋊Q818yes—
321C4×D79C22×Q814yes—
322C4×D79C2×#4114yes—
323Dic158—24no—
324Dic158—22no—
325Dic158C22×Q814yes—
326C8×C79—22no—
327C8×C79—22no—
328C79⋊C8—22no—
329C79⋊C8—22no—
330C22×C79—24no—
331C22×C79—48no—
332C22×C79—42no—
333C22×C79—42no—
334C22×C79C2×C22⋊Q812yes—
335C22×C79#57512yes—
336C22×C79#57512yes—
337C22×C79C23×D411yescharacteristic
338C2×D79—28no—
339C2×D79—22no—
340C2×D79—22no—
341C2×D79C2×C22⋊Q814yes—
342C4×C79—22no—
343C4×C79—22no—
344C4×C79—42no—
345C4×C79—42no—
346C4×C79—42no—
347C4×C79C2×C22⋊Q812yes—
348C4×C79C23×Q811yescharacteristic
349C4×C79C22×#4111yescharacteristic
350Dic79—24no—
351Dic79—22no—
352Dic79—22no—
353Dic79—42no—
354Dic79—42no—
355Dic79—42no—
356Dic79C2×C22⋊Q814yes—
357C2×#3080—791nomaximal, Sylow
358C2×C79—44no—
359C2×C79#308014yescomplemented
360C2×C79C22×C22⋊Q811yescharacteristic
361C2×C79C2×#57511yescharacteristic
362C2×C79C2×#57511yescharacteristic
363D79—24no—
364C22×#125—791no—
365C2×C4×#41—791no—
366#3080—7916no—
367C2×#479—791no—
368C2×#479—791no—
369C2×#479—791no—
370C2×#479—791no—
371C2×#478—791no—
372C2×#478—791no—
373C2×#478—791no—
374C2×#478D7911yescharacteristic, complemented
375C2×#428—791no—
376C2×#428—791no—
377C2×#423—791no—
378C2×#417—791no—
379C2×#417—791no—
380C79C2×#308011yescharacteristic, complemented, Sylow
381C22×#41—791no—
382C22×M16—791no—
383C22×M16—791no—
384C2×#125—798no—
385C2×#125—791no—
386C2×#125—791no—
387C2×#125—791no—
388C2×#125—1581no—
389C2×#125—1581no—
390C2×#125—1584no—
391C2×#125C2×D7911yescharacteristic
392C4×#41—798no—
393C4×#41—1584no—
394C2×C4×Q8—791no—
395C2×C4×Q8—791no—
396C2×C4×D4—791no—
397C2×C4×D4—1581no—
398C2×C4×D4—1581no—
399C2×C4×D4C2×D7911yescharacteristic
400C2×#117—791no—
401C2×#117—1581no—
402C22×C4⋊C4—791no—
403C22×C4⋊C4—791no—
404C22×C4⋊C4—1581no—
405C22×C4⋊C4—1581no—
406C22×C42—791no—
407C22×C42—1581no—
408#479—798no—
409#479—798no—
410#479—798no—
411#479—798no—
412#478—798no—
413#478—798no—
414#478—798no—
415#478C2×D7918yescomplemented
416#428—798no—
417#428—798no—
418C2×#107—791no—
419C2×#107—791no—
420C2×#107—791no—
421C2×#107C2×D7911yescharacteristic
422C2×#106—791no—
423C2×#106—791no—
424C2×#106—791no—
425C2×#106C2×D7911yescharacteristic
426#423—798no—
427C2×C4⋊C8—791no—
428C2×C4⋊C8—791no—
429C2×C4⋊C8—791no—
430C2×C4⋊C8C2×D7911yescharacteristic
431#417—798no—
432#417—798no—
433C2×#103—791no—
434C2×#103—791no—
435C2×#103—791no—
436C2×#103—791no—
437C2×#102—791no—
438C2×#102—791no—
439C2×#102C2×D7911yescharacteristic
440C2×#102C2×D7911yescharacteristic
441C2×#41—798no—
442C2×#41—794no—
443C2×#41—1582no—
444C2×#41—1584no—
445C22×Q8—791no—
446C22×D4—1581no—
447C22×D4C22×D7911yescharacteristic
448C23×C4—21no—
449C23×C4—791no—
450C23×C4—791no—
451C23×C4—791no—
452C23×C4—1581no—
453C23×C4—1581no—
454C23×C4—1581no—
455C23×C4—1581no—
456C2×M16—794no—
457C2×M16—794no—
458C2×M16—1584no—
459C2×M16—1584no—
460C22×C8—791no—
461C22×C8—791no—
462C22×C8C22×D7911yescharacteristic
463C22×C8C22×D7911yescharacteristic
464#125—22no—
465#125—794no—
466#125—794no—
467#125—794no—
468#125—1588no—
469#125—1588no—
470#125—1582no—
471#125—1582no—
472#125—1582no—
473#125C22×D7914yes—
474C4×Q8—794no—
475C4×Q8—794no—
476C4×Q8—1582no—
477C4×Q8—1582no—
478C4×D4—22no—
479C4×D4—794no—
480C4×D4—1582no—
481C4×D4—1588no—
482C4×D4—1588no—
483C4×D4C22×D7914yes—
484#117—794no—
485#117—1588no—
486#117—1582no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—791no—
490C2×C4⋊C4—791no—
491C2×C4⋊C4—791no—
492C2×C4⋊C4—794no—
493C2×C4⋊C4—794no—
494C2×C4⋊C4—1582no—
495C2×C4⋊C4—1582no—
496C2×C4⋊C4—1588no—
497C2×C4⋊C4—1588no—
498C2×C4⋊C4—1581no—
499C2×C4⋊C4—1581no—
500C2×C4⋊C4—1581no—
501C2×C4⋊C4—1581no—
502C2×C4⋊C4—1581no—
503C2×C4⋊C4—1581no—
504C2×C4⋊C4—1581no—
505C2×C4⋊C4—1581no—
506C2×C4⋊C4—1581no—
507C2×C4⋊C4—1581no—
508C2×C4⋊C4C22×D7911yescharacteristic
509C2×C4⋊C4C22×D7911yescharacteristic
510C2×C4⋊C4C22×D7911yescharacteristic
511C2×C22⋊C4—21no—
512C2×C22⋊C4—1581no—
513C2×C22⋊C4—1581no—
514C2×C42—791no—
515C2×C42—791no—
516C2×C42—791no—
517C2×C42—794no—
518C2×C42—794no—
519C2×C42—1588no—
520C2×C42—1581no—
521C2×C42—1581no—
522C2×C42—1581no—
523C2×C42C22×D7911yescharacteristic
524#107—794no—
525#107—794no—
526#107—794no—
527#107C22×D7914yes—
528#106—794no—
529#106—794no—
530#106—794no—
531#106C22×D7914yes—
532C4⋊C8—794no—
533C4⋊C8—794no—
534C4⋊C8—794no—
535C4⋊C8C22×D7914yes—
536#103—794no—
537#103—794no—
538#103—794no—
539#103—794no—
540#102—794no—
541#102—794no—
542#102C22×D7914yes—
543#102C22×D7914yes—
544C24—21no—
545C24—791no—
546#41—7916no—
547#41—15816no—
548#41—1588no—
549C2×Q8—794no—
550C2×Q8—792no—
551C2×Q8—1582no—
552C2×Q8—1581no—
553C2×D4—22no—
554C2×D4—21no—
555C2×D4—1584no—
556C2×D4—1588no—
557C2×D4Q8×D7914yes—
558C2×D4C23×D7912yes—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—24no—
563C22×C4—44no—
564C22×C4—3162no—
565C22×C4—3162no—
566C22×C4—3164no—
567C22×C4—3164no—
568C22×C4—3164no—
569C22×C4—794no—
570C22×C4—794no—
571C22×C4—791no—
572C22×C4—794no—
573C22×C4—794no—
574C22×C4—792no—
575C22×C4—792no—
576C22×C4—791no—
577C22×C4—791no—
578C22×C4—1584no—
579C22×C4—1584no—
580C22×C4—1584no—
581C22×C4—1581no—
582C22×C4—1581no—
583C22×C4—1581no—
584C22×C4—1584no—
585C22×C4—1588no—
586C22×C4—1581no—
587C22×C4D4×D7911yescharacteristic
588C22×C4D4×D7911yescharacteristic
589C22×C4C23×D7911yescharacteristic
590M16—1588no—
591M16—1588no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—792no—
595C2×C8—792no—
596C2×C8—1582no—
597C2×C8—1582no—
598C2×C8C23×D7912yes—
599C2×C8C23×D7912yes—
600C4⋊C4—24no—
601C4⋊C4—24no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—792no—
606C4⋊C4—792no—
607C4⋊C4—792no—
608C4⋊C4—1584no—
609C4⋊C4—1584no—
610C4⋊C4—1584no—
611C4⋊C4—1584no—
612C4⋊C4—1584no—
613C4⋊C4—1584no—
614C4⋊C4—1584no—
615C4⋊C4—1584no—
616C4⋊C4—1584no—
617C4⋊C4—1584no—
618C4⋊C4—1581no—
619C4⋊C4—1581no—
620C4⋊C4—1581no—
621C4⋊C4C23×D7912yes—
622C4⋊C4C23×D7912yes—
623C4⋊C4C23×D7912yes—
624C22⋊C4—24no—
625C22⋊C4—1584no—
626C22⋊C4—1584no—
627C42—792no—
628C42—794no—
629C42—794no—
630C42—792no—
631C42—1584no—
632C42—1584no—
633C42—1584no—
634C42D4×D7912yes—
635C42C23×D7912yes—
636C23—24no—
637C23—22no—
638C23—42no—
639C23—42no—
640C23—794no—
641C23—792no—
642C23—1582no—
643C23—1582no—
644C23C2×D4×D7911yescharacteristic
645Q8—794no—
646Q8—1584no—
647Q8—1582no—
648D4—24no—
649D4—22no—
650D4—15816no—
651D4C2×Q8×D7914yes—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—48no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—3164no—
662C2×C4—3164no—
663C2×C4—3168no—
664C2×C4—3168no—
665C2×C4—3162no—
666C2×C4—3162no—
667C2×C4—3162no—
668C2×C4—3168no—
669C2×C4—794no—
670C2×C4—792no—
671C2×C4—798no—
672C2×C4—794no—
673C2×C4—794no—
674C2×C4—792no—
675C2×C4—792no—
676C2×C4—1582no—
677C2×C4—1582no—
678C2×C4—1582no—
679C2×C4—15816no—
680C2×C4—1584no—
681C2×C4—1582no—
682C2×C4—1582no—
683C2×C4—1582no—
684C2×C4C2×D4×D7912yes—
685C2×C4C2×D4×D7912yes—
686C2×C4C2×D4×D7911yescharacteristic
687C2×C4C2×Q8×D7912yes—
688C2×C4#41×D7912yes—
689C2×C4C24×D7911yescharacteristic
690C8—22no—
691C8—22no—
692C8—1582no—
693C8—1582no—
694C22—24no—
695C22—48no—
696C22—42no—
697C22—42no—
698C22—794no—
699C22—1588no—
700C22—1582no—
701C22—1582no—
702C22C22⋊Q8×D7912yes—
703C22#1909935912yes—
704C22#1909936012yes—
705C22C22×D4×D7911yescharacteristic
706C4—22no—
707C4—22no—
708C4—42no—
709C4—42no—
710C4—42no—
711C4—3162no—
712C4—3162no—
713C4—3162no—
714C4—794no—
715C4—1582no—
716C4—1582no—
717C4—1584no—
718C4C22⋊Q8×D7912yes—
719C4C22×Q8×D7911yescharacteristic
720C4C2×#41×D7911yescharacteristic
721C2—44no—
722C2—1584no—
723C2#2377321714yesdirect product factor
724C2C2×C22⋊Q8×D7911yescharacteristic
725C2C2×#1909935911yescharacteristic
726C2C2×#1909936011yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#478×C79C2
socleC23×C79C22×D4
prime radicalC22×#11929623C22
hypercenterC2×#478D79
hypocenterC79C2×#3080
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#125×D79C2semidirect
3. #23773217C2direct (N × H)
4. C2×#19098873C2semidirect
5. C2×#19098871C2semidirect
6. C2×#19098869C2semidirect
7. C2×#19098867C2semidirect
8. C2×#19098865C2semidirect
9. C2×#19098863C2semidirect
10. C2×#19098861C2semidirect
11. C2×#19098604C2semidirect
12. C2×#19098602C2semidirect
13. C2×#19098585C2semidirect
16. C2×#478×C79C2semidirect
26. #125×D79C22semidirect
42. #19098873C22semidirect
43. #19098871C22semidirect
44. #19098869C22semidirect
45. #19098867C22semidirect
46. #19098865C22semidirect
47. #19098863C22semidirect
48. #19098861C22semidirect
49. #19098604C22semidirect
50. #19098602C22semidirect
57. #19098585C22semidirect
71. #478×C79C22semidirect
359. C2×C79#3080semidirect
374. C2×#478D79semidirect
380. C79C2×#3080semidirect
415. #478C2×D79semidirect
723. C2#23773217direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#125×D792
C2×C4×#119296232
#237732172
C2×#190988732
C2×#190988712
C2×#190988692
C2×#190988672
C2×#190988652
C2×#190988632
C2×#190988612
C2×#190986042
C2×#190986022
C2×#190985852
C2×#190985612
C2×#478×C792
C2×#308079