Finite Group Databasebeta

← C2×#23773589 #35156505

Subgroups — C2×#23773589 #35156505

Order 20224.

2274 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099187C211yesmaximal, characteristic, complemented
2C2×#19099035C211yesmaximal, characteristic, complemented
3#23773589C2116yesmaximal, direct product factor
4C2×#19098907C211yesmaximal, characteristic, complemented
5C2×#19098889C211yesmaximal, characteristic, complemented
6C2×#19098840C211yesmaximal, characteristic, complemented
7C2×#19098779C211yesmaximal, characteristic, complemented
8C2×#19098778C211yesmaximal, characteristic, complemented
9C2×#19098715C211yesmaximal, characteristic, complemented
10C2×#19098698C211yesmaximal, characteristic
11C2×#19098674C211yesmaximal, characteristic, complemented
12C2×#19098660C211yesmaximal, characteristic, complemented
13C2×#19098650C211yesmaximal, characteristic, complemented
14C2×#19098643C211yesmaximal, characteristic, complemented
15C2×#19098623C211yesmaximal, characteristic, complemented
16C2×#476×C79C211yesmaximal, characteristic, complemented
17C22×D4×D79C2211yescharacteristic
18C22×#11929613C2211yescharacteristic
19C22×#11929612C2211yescharacteristic
20C22×D632C2211yescharacteristic
21C22×#11929609C2211yescharacteristic
22#19099187—24no—
23#19099187C2218yescomplemented
24C2×#14579156—21no—
25C2×#14579150—21no—
26C2×#14579149C2211yescharacteristic, complemented
27C2×#14579146—21no—
28C2×#14579141C2211yescharacteristic
29C2×#14579137—21no—
30C2×#14579136C2211yescharacteristic
31#19099035—24no—
32#19099035C2218yescomplemented
33C2×#14579126C2211yescharacteristic, complemented
34C2×C4×D316C2211yescharacteristic
35C2×D4×Dic79C2211yescharacteristic
36C2×#14579123C2211yescharacteristic
37C2×#14579123C2211yescharacteristic, complemented
38C2×C4×C22⋊D79—21no—
39C2×(C22⋊D79)⋊C4—21no—
40C2×#14579119C2211yescharacteristic
41C2×#14579118C2211yescharacteristic
42C22×(C2×D79)⋊C4—21no—
43C2×C22⋊C4×D79—21no—
44#19098907C2218yescomplemented
45#19098889C2218yescomplemented
46#19098840C2218yescomplemented
47#19098779C2218yescomplemented
48#19098778C2218yescomplemented
49#19098715C2218yescomplemented
50#19098698C2218yes—
51#19098674C2218yescomplemented
52#19098660C2218yescomplemented
53#19098650C2218yescomplemented
54#19098643C2218yescomplemented
55#19098623C2218yescomplemented
56C2×#14579094C2211yescharacteristic, complemented
57C2×#14579094C2211yescharacteristic, complemented
58C2×C4⋊(C79⋊C8)C2211yescharacteristic, complemented
59C2×#14579086C2211yescharacteristic, complemented
60C2×#14579084C2211yescharacteristic, complemented
61C2×#14579083C2211yescharacteristic, complemented
62C2×#14579081C2211yescharacteristic
63C2×#14579081C2211yescharacteristic
64C2×#14579081C2211yescharacteristic, complemented
65C2×(C2×D79)⋊C8C2211yescharacteristic
66C2×(C2×D79)⋊C8C2211yescharacteristic
67C2×#14579071C2211yescharacteristic, complemented
68C2×C8×Dic79C2211yescharacteristic, complemented
69C2×C4⋊Q8×C79C2211yescharacteristic, complemented
70C2×C4×D4×C79C2211yescharacteristic
71#476×C79C2218yescomplemented
72C2×#106×C79C2211yescharacteristic, complemented
73C2×#106×C79C2211yescharacteristic, complemented
74C2×C4⋊C8×C79C2211yescharacteristic, complemented
75C2×#102×C79C2211yescharacteristic
76C2×#102×C79C2211yescharacteristic
77C24×D79—21no—
78C22×Dic158C2311yescharacteristic
79C22×D316—21no—
80C22×D316C2311yescharacteristic
81C22×D316C2311yescharacteristic
82C22×C22⋊D79—21no—
83C2×D4×D79—24no—
84C2×D4×D79—24no—
85C2×D4×D79—22no—
86C2×D4×D79C2314yes—
87C23×Dic79—21no—
88C22×C4×D79—21no—
89C22×C4×D79—21no—
90C22×C4×D79—21no—
91C22×C4×D79C2311yescharacteristic
92C2×#11929613—24no—
93C2×#11929613C2314yes—
94C2×#11929612—24no—
95C2×#11929612C2314yes—
96C2×D632—24no—
97C2×D632C2314yes—
98C2×#11929609—24no—
99C2×#11929609C2314yes—
100C22×C79⋊C8C2311yescharacteristic
101C22×C79⋊C8C2311yescharacteristic
102#14579156—28no—
103#14579150—28no—
104#14579149—22no—
105#14579149C2314yescomplemented
106#14579146—28no—
107#14579141—22no—
108#14579141C2314yes—
109#14579137—28no—
110#14579136—22no—
111#14579136C2314yes—
112#14579126—22no—
113#14579126C2314yescomplemented
114C4×D316—22no—
115C4×D316C2314yes—
116D4×Dic79—22no—
117D4×Dic79C2314yes—
118#14579123—22no—
119#14579123—22no—
120#14579123C2314yes—
121#14579123C2314yescomplemented
122C4×C22⋊D79—28no—
123(C22⋊D79)⋊C4—28no—
124#14579119—22no—
125#14579119C2314yes—
126#14579118D414yes—
127#14579118C2314yes—
128C2×C4⋊Dic79—21no—
129C2×C4⋊Dic79C2311yescharacteristic
130C2×Dic79⋊C4—21no—
131C2×Dic79⋊C4D411yescharacteristic
132C2×Dic79⋊C4D411yescharacteristic
133C2×C22⋊Dic79—21no—
134C2×(C2×D79)⋊C4—21no—
135C2×(C2×D79)⋊C4—21no—
136C2×(C2×D79)⋊C4—21no—
137C2×(C2×D79)⋊C4—21no—
138C2×(C2×D79)⋊C4—21no—
139C2×(C2×D79)⋊C4—21no—
140C2×(C2×D79)⋊C4—21no—
141C2×(C2×D79)⋊C4—21no—
142C2×(C2×D79)⋊C4—28no—
143C2×(C2×D79)⋊C4D411yescharacteristic
144C2×(C2×D79)⋊C4D411yescharacteristic
145C22⋊C4×D79—28no—
146C2×C4×Dic79—21no—
147C2×C4×Dic79—21no—
148C2×C4×Dic79C2311yescharacteristic
149#14579094C2314yescomplemented
150#14579094C2314yescomplemented
151C4⋊(C79⋊C8)C2314yescomplemented
152#14579086C2314yescomplemented
153#14579084C2314yescomplemented
154#14579083C2314yescomplemented
155#14579081C2314yes—
156#14579081C2314yes—
157#14579081C2314yescomplemented
158(C2×D79)⋊C8C2314yes—
159(C2×D79)⋊C8C2314yes—
160#14579071C2314yescomplemented
161C8×Dic79C2314yescomplemented
162C22×Q8×C79—21no—
163C22×D4×C79C2311yescharacteristic
164C23×C4×C79—21no—
165C22×C8×C79C2311yescharacteristic
166C22×C8×C79C2311yescharacteristic
167C4⋊Q8×C79—22no—
168C4⋊Q8×C79C2314yescomplemented
169C4×D4×C79—22no—
170C4×D4×C79C2314yes—
171C2×C4⋊C4×C79—21no—
172C2×C4⋊C4×C79C2311yescharacteristic
173C2×C4⋊C4×C79C2311yescharacteristic
174C2×C4⋊C4×C79C2311yescharacteristic
175C2×C22⋊C4×C79—21no—
176C2×C42×C79C2311yescharacteristic
177#106×C79C2314yescomplemented
178#106×C79C2314yescomplemented
179C4⋊C8×C79C2314yescomplemented
180#102×C79C2314yes—
181#102×C79C2314yes—
182C23×D79—21no—
183C23×D79—28no—
184C23×D79—24no—
185C23×D79—21no—
186C23×D79—82no—
187C23×D79—82no—
188C23×D79C2×D411yescharacteristic
189C2×Dic158—21no—
190C2×Dic158—22no—
191C2×Dic158—22no—
192C2×Dic158C2412yes—
193C2×D316—24no—
194C2×D316—21no—
195C2×D316—21no—
196C2×D316—22no—
197C2×D316—22no—
198C2×D316—22no—
199C2×D316—82no—
200C2×D316#4114yes—
201C2×D316C2412yes—
202C2×D316C2412yes—
203C2×C22⋊D79—28no—
204C2×C22⋊D79—24no—
205D4×D79—216no—
206D4×D79—28no—
207D4×D79—28no—
208C22×Dic79—24no—
209C22×Dic79—21no—
210C22×Dic79—21no—
211C22×Dic79—82no—
212C22×Dic79C2×D411yescharacteristic
213C22×Dic79C2×D411yescharacteristic
214C22×Dic79C2×D411yescharacteristic
215C2×C4×D79—24no—
216C2×C4×D79—24no—
217C2×C4×D79—24no—
218C2×C4×D79—22no—
219C2×C4×D79—22no—
220C2×C4×D79—82no—
221C2×C4×D79—82no—
222C2×C4×D79—82no—
223C2×C4×D79C2×D412yes—
224C2×C4×D79C2412yes—
225#11929613—28no—
226#11929612—28no—
227D632—28no—
228#11929609—28no—
229C2×C79⋊C8—22no—
230C2×C79⋊C8—22no—
231C2×C79⋊C8C2412yes—
232C2×C79⋊C8C2412yes—
233C4⋊Dic79—24no—
234C4⋊Dic79—21no—
235C4⋊Dic79C2412yes—
236Dic79⋊C4—24no—
237Dic79⋊C4C2×D414yes—
238Dic79⋊C4C2×D414yes—
239C22⋊Dic79—24no—
240(C2×D79)⋊C4—24no—
241(C2×D79)⋊C4—24no—
242(C2×D79)⋊C4—24no—
243(C2×D79)⋊C4—24no—
244(C2×D79)⋊C4—24no—
245(C2×D79)⋊C4—24no—
246(C2×D79)⋊C4—24no—
247(C2×D79)⋊C4—24no—
248(C2×D79)⋊C4C2×D414yes—
249(C2×D79)⋊C4C2×D414yes—
250C4×Dic79—24no—
251C4×Dic79—24no—
252C4×Dic79C2×D412yes—
253C4×Dic79C2412yes—
254C24×C79—21no—
255C2×Q8×C79—24no—
256C2×Q8×C79—82no—
257C2×D4×C79—21no—
258C2×D4×C79—22no—
259C2×D4×C79#4114yes—
260C2×D4×C79C2412yes—
261C22×C4×C79—21no—
262C22×C4×C79—21no—
263C22×C4×C79—21no—
264C22×C4×C79—24no—
265C22×C4×C79—82no—
266C22×C4×C79C2×D411yescharacteristic
267C22×C4×C79C2×D411yescharacteristic
268C22×C4×C79C2411yescharacteristic
269C2×C8×C79—22no—
270C2×C8×C79—22no—
271C2×C8×C79C2412yes—
272C2×C8×C79C2412yes—
273C4⋊C4×C79—24no—
274C4⋊C4×C79—21no—
275C4⋊C4×C79—21no—
276C4⋊C4×C79—21no—
277C4⋊C4×C79C2412yes—
278C4⋊C4×C79C2412yes—
279C4⋊C4×C79C2412yes—
280C22⋊C4×C79—24no—
281C42×C79C2×D412yes—
282C42×C79C2412yes—
283C23×C79—24no—
284C23×C79—22no—
285C23×C79—42no—
286C23×C79—42no—
287C23×C79C22×D411yescharacteristic
288C22×D79—22no—
289C22×D79—24no—
290C22×D79—22no—
291C22×D79—22no—
292C22×D79—22no—
293C22×D79—216no—
294C22×D79—22no—
295C22×D79—42no—
296C22×D79—42no—
297C22×D79—42no—
298C22×D79—42no—
299C22×D79—42no—
300C22×D79—84no—
301C22×D79—84no—
302C22×D79—816no—
303C22×D79C22×D412yes—
304Q8×C79—84no—
305D4×C79—24no—
306D4×C79—22no—
307D4×C79C2×#4114yes—
308C2×C4×C79—22no—
309C2×C4×C79—22no—
310C2×C4×C79—22no—
311C2×C4×C79—22no—
312C2×C4×C79—22no—
313C2×C4×C79—42no—
314C2×C4×C79—42no—
315C2×C4×C79—42no—
316C2×C4×C79—84no—
317C2×C4×C79C22×D412yes—
318C2×C4×C79C22×D412yes—
319C2×C4×C79C22×D411yescharacteristic
320C2×C4×C79C2×#4112yes—
321C2×C4×C79C2×#4112yes—
322C2×C4×C79C2511yescharacteristic
323C22⋊D79—216no—
324C2×Dic79—22no—
325C2×Dic79—22no—
326C2×Dic79—22no—
327C2×Dic79—22no—
328C2×Dic79—22no—
329C2×Dic79—42no—
330C2×Dic79—42no—
331C2×Dic79—84no—
332C2×Dic79C22×D412yes—
333C2×Dic79C22×D412yes—
334C2×Dic79C22×D412yes—
335D316—24no—
336D316—22no—
337D316—22no—
338D316—22no—
339D316—42no—
340D316—84no—
341D316C2×#4114yes—
342C4×D79—24no—
343C4×D79—22no—
344C4×D79—22no—
345C4×D79—84no—
346C4×D79—84no—
347C4×D79—84no—
348Dic158—22no—
349Dic158—22no—
350Dic158—42no—
351C8×C79—22no—
352C8×C79—22no—
353C79⋊C8—22no—
354C79⋊C8—22no—
355C22×C79—24no—
356C22×C79—48no—
357C22×C79—42no—
358C22×C79—42no—
359C22×C79#52512yes—
360C22×C79#57612yes—
361C22×C79#57712yes—
362C22×C79C23×D411yescharacteristic
363C2×D79—24no—
364C2×D79—22no—
365C2×D79—22no—
366C2×D79—22no—
367C2×D79—44no—
368C2×D79—48no—
369C2×D79—42no—
370C2×D79—42no—
371C2×D79—42no—
372C2×D79—42no—
373C2×D79—42no—
374C2×D79—816no—
375C2×D79—84no—
376C4×C79—22no—
377C4×C79—22no—
378C4×C79—42no—
379C4×C79—42no—
380C4×C79—42no—
381C4×C79#52512yes—
382C4×C79C22×#4111yescharacteristic
383C4×C79C22×#4111yescharacteristic
384Dic79—22no—
385Dic79—22no—
386Dic79—22no—
387Dic79—42no—
388Dic79—42no—
389C2×#3118—791nomaximal, Sylow
390C2×C79—44no—
391C2×C79#311814yescomplemented
392C2×C79C2×#52511yescharacteristic
393C2×C79C2×#57611yescharacteristic
394C2×C79C2×#57711yescharacteristic
395D79—42no—
396D79—44no—
397D79—82no—
398C2×#542—791no—
399C2×#518—791no—
400#3118—7916no—
401C2×#485—791no—
402C2×#482—791no—
403C2×#476D7911yescharacteristic, complemented
404C2×#474—791no—
405C2×#463—791no—
406C2×#463—791no—
407C2×#450—791no—
408C2×#447—791no—
409C2×#442—791no—
410C2×#440—791no—
411C2×C4×SD16—791no—
412C2×C4×D8—791no—
413C2×#433—791no—
414C79C2×#311811yescharacteristic, complemented, Sylow
415C23×D4—791no—
416C22×SD16—791no—
417C22×SD16—791no—
418C22×D8—791no—
419C22×D8—791no—
420#542—798no—
421#542—1584no—
422C2×C4⋊Q8C2×D7911yescharacteristic, complemented
423C2×#126—1581no—
424C2×#124—791no—
425C2×#124—1581no—
426C2×#123—1581no—
427C2×C22⋊Q8—791no—
428C2×C22⋊Q8—1581no—
429C2×#121—791no—
430#518—798no—
431#518—1584no—
432C2×C4×Q8—791no—
433C2×C4×D4—791no—
434C2×C4×D4—791no—
435C2×C4×D4—791no—
436C2×C4×D4—791no—
437C2×C4×D4—1581no—
438C2×C4×D4—1581no—
439C2×C4×D4C2×D7911yescharacteristic
440C2×#117—791no—
441C2×#117—791no—
442C22×C22⋊C4—1581no—
443C22×C22⋊C4—1581no—
444#485—798no—
445#482—798no—
446#476C2×D7918yescomplemented
447#474—798no—
448#463—798no—
449#463—798no—
450#450—798no—
451#447—798no—
452#442—798no—
453#440—798no—
454C4×SD16—798no—
455C4×D8—798no—
456#433—798no—
457C2×#107—791no—
458C2×#107—791no—
459C2×#106C2×D7911yescharacteristic, complemented
460C2×#106C2×D7911yescharacteristic, complemented
461C2×C4⋊C8—791no—
462C2×C4⋊C8C2×D7911yescharacteristic, complemented
463C2×#103—791no—
464C2×#103—791no—
465C2×#102—791no—
466C2×#102—791no—
467C2×#102—791no—
468C2×#102—791no—
469C2×#102C2×D7911yescharacteristic
470C2×#102C2×D7911yescharacteristic
471C2×C22⋊C8—791no—
472C2×C22⋊C8—791no—
473C2×#97—791no—
474C2×C4×C8—791no—
475C25—1581no—
476C22×Q8—21no—
477C22×Q8—791no—
478C22×D4—794no—
479C22×D4—791no—
480C22×D4—791no—
481C22×D4—1581no—
482C22×D4—1582no—
483C22×D4—1581no—
484C22×D4—1584no—
485C22×D4—1584no—
486C22×D4C22×D7911yescharacteristic
487C23×C4—21no—
488C23×C4—791no—
489C23×C4—1581no—
490C23×C4—1581no—
491C23×C4—1581no—
492C23×C4—1581no—
493C2×SD16—794no—
494C2×SD16—794no—
495C2×SD16—1584no—
496C2×SD16—1584no—
497C2×D8—794no—
498C2×D8—794no—
499C2×D8—1584no—
500C2×D8—1584no—
501C22×C8—791no—
502C22×C8—791no—
503C22×C8C22×D7911yescharacteristic
504C22×C8C22×D7911yescharacteristic
505C4⋊Q8—22no—
506C4⋊Q8C22×D7914yescomplemented
507#126—1588no—
508#124—794no—
509#124—1588no—
510#124—1582no—
511#123—1588no—
512C22⋊Q8—794no—
513C22⋊Q8—1582no—
514C22⋊Q8—1588no—
515#121—794no—
516#121—1582no—
517C4×Q8—794no—
518C4×Q8—1582no—
519C4×D4—22no—
520C4×D4—794no—
521C4×D4—794no—
522C4×D4—794no—
523C4×D4—794no—
524C4×D4—1582no—
525C4×D4—1582no—
526C4×D4—1582no—
527C4×D4—1588no—
528C4×D4—1588no—
529C4×D4—1582no—
530C4×D4C22×D7914yes—
531#117—794no—
532#117—794no—
533#117—794no—
534#117—1582no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—791no—
537C2×C4⋊C4—791no—
538C2×C4⋊C4—791no—
539C2×C4⋊C4—1581no—
540C2×C4⋊C4—1581no—
541C2×C4⋊C4C22×D7911yescharacteristic
542C2×C4⋊C4C22×D7911yescharacteristic
543C2×C4⋊C4C22×D7911yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—791no—
546C2×C22⋊C4—791no—
547C2×C22⋊C4—1588no—
548C2×C22⋊C4—1588no—
549C2×C22⋊C4—1581no—
550C2×C22⋊C4—1581no—
551C2×C22⋊C4—1581no—
552C2×C22⋊C4—1581no—
553C2×C22⋊C4—1581no—
554C2×C22⋊C4—1581no—
555C2×C22⋊C4—1581no—
556C2×C22⋊C4—1581no—
557C2×C22⋊C4—1581no—
558C2×C42—791no—
559C2×C42—1581no—
560C2×C42—1581no—
561C2×C42C22×D7911yescharacteristic
562#107—794no—
563#107—794no—
564#106C22×D7914yescomplemented
565#106C22×D7914yescomplemented
566C4⋊C8—794no—
567C4⋊C8C22×D7914yescomplemented
568#103—794no—
569#103—794no—
570#102—794no—
571#102—794no—
572#102—794no—
573#102—794no—
574#102C22×D7914yes—
575#102C22×D7914yes—
576C22⋊C8—794no—
577C22⋊C8—794no—
578#97—794no—
579C4×C8—794no—
580C24—21no—
581C24—791no—
582C24—6322no—
583C24—6322no—
584C24—1584no—
585C24—1588no—
586C24—1581no—
587C24—1581no—
588C2×Q8—24no—
589C2×Q8—82no—
590C2×Q8—792no—
591C2×Q8—1582no—
592C2×Q8—1582no—
593C2×Q8—1581no—
594C2×D4—22no—
595C2×D4—21no—
596C2×D4—794no—
597C2×D4—792no—
598C2×D4—792no—
599C2×D4—6322no—
600C2×D4—1584no—
601C2×D4—1584no—
602C2×D4—1588no—
603C2×D4—15816no—
604C2×D4—1588no—
605C2×D4—1588no—
606C2×D4—1582no—
607C2×D4—1582no—
608C2×D4—1582no—
609C2×D4—1581no—
610C2×D4—1581no—
611C2×D4#1192962514yes—
612C2×D4C23×D7912yes—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—24no—
617C22×C4—82no—
618C22×C4—791no—
619C22×C4—791no—
620C22×C4—791no—
621C22×C4—792no—
622C22×C4—792no—
623C22×C4—6322no—
624C22×C4—6322no—
625C22×C4—6322no—
626C22×C4—6322no—
627C22×C4—1584no—
628C22×C4—1584no—
629C22×C4—1581no—
630C22×C4—1581no—
631C22×C4—1584no—
632C22×C4—1584no—
633C22×C4—1582no—
634C22×C4—1582no—
635C22×C4D4×D7911yescharacteristic
636C22×C4D4×D7911yescharacteristic
637C22×C4C23×D7911yescharacteristic
638SD16—1588no—
639SD16—1588no—
640D8—1588no—
641D8—1588no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—792no—
645C2×C8—792no—
646C2×C8—1582no—
647C2×C8—1582no—
648C2×C8C23×D7912yes—
649C2×C8C23×D7912yes—
650C4⋊C4—24no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—794no—
655C4⋊C4—794no—
656C4⋊C4—792no—
657C4⋊C4—1584no—
658C4⋊C4—1584no—
659C4⋊C4—1581no—
660C4⋊C4C23×D7912yes—
661C4⋊C4C23×D7912yes—
662C4⋊C4C23×D7912yes—
663C22⋊C4—24no—
664C22⋊C4—794no—
665C22⋊C4—794no—
666C22⋊C4—1584no—
667C22⋊C4—1584no—
668C22⋊C4—1584no—
669C22⋊C4—1584no—
670C22⋊C4—1584no—
671C22⋊C4—1584no—
672C22⋊C4—1584no—
673C22⋊C4—1584no—
674C22⋊C4—1584no—
675C42—792no—
676C42—792no—
677C42—1584no—
678C42—1584no—
679C42D4×D7912yes—
680C42C23×D7912yes—
681C23—24no—
682C23—22no—
683C23—42no—
684C23—42no—
685C23—3162no—
686C23—3162no—
687C23—3162no—
688C23—3162no—
689C23—3162no—
690C23—792no—
691C23—63216no—
692C23—6324no—
693C23—6324no—
694C23—15816no—
695C23—1582no—
696C23—1582no—
697C23—1584no—
698C23—1582no—
699C23—1582no—
700C23—1582no—
701C23C2×D4×D7911yescharacteristic
702Q8—84no—
703Q8—3162no—
704Q8—1582no—
705Q8—1582no—
706D4—24no—
707D4—22no—
708D4—3162no—
709D4—794no—
710D4—6324no—
711D4—15816no—
712D4—1584no—
713D4—1582no—
714D4—1582no—
715D4—1582no—
716D4C2×#1192962514yes—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—84no—
726C2×C4—3162no—
727C2×C4—3162no—
728C2×C4—792no—
729C2×C4—792no—
730C2×C4—792no—
731C2×C4—6324no—
732C2×C4—6324no—
733C2×C4—6324no—
734C2×C4—6324no—
735C2×C4—1582no—
736C2×C4—1582no—
737C2×C4—1582no—
738C2×C4—1582no—
739C2×C4—1582no—
740C2×C4—1584no—
741C2×C4—1582no—
742C2×C4—1582no—
743C2×C4C2×D4×D7912yes—
744C2×C4C2×D4×D7912yes—
745C2×C4C2×D4×D7911yescharacteristic
746C2×C4#41×D7912yes—
747C2×C4C2×#1192962512yes—
748C2×C4C24×D7911yescharacteristic
749C8—22no—
750C8—22no—
751C8—1582no—
752C8—1582no—
753C22—24no—
754C22—42no—
755C22—42no—
756C22—48no—
757C22—3162no—
758C22—3162no—
759C22—3168no—
760C22—3164no—
761C22—3162no—
762C22—3162no—
763C22—3162no—
764C22—63216no—
765C22—6324no—
766C22—1582no—
767C22—1582no—
768C22—1582no—
769C22—1584no—
770C22#1909907612yes—
771C22#1909936712yes—
772C22#1909936912yes—
773C22C22×D4×D7911yescharacteristic
774C4—22no—
775C4—22no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—3162no—
780C4—3162no—
781C4—1582no—
782C4—1582no—
783C4—1582no—
784C4#1909907612yes—
785C4C2×#41×D7911yescharacteristic
786C4C22×#1192962511yescharacteristic
787C2—44no—
788C2—3164no—
789C2—3162no—
790C2—6322no—
791C2#2377358914yesdirect product factor
792C2C2×#1909907611yescharacteristic
793C2C2×#1909936711yescharacteristic
794C2C2×#1909936911yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#476×C79C2
socleC23×C79C22×D4
prime radicalC2×#19098698C2
hypercenterC2×#476D79
hypocenterC79C2×#3118
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#19099187C2semidirect
2. C2×#19099035C2semidirect
3. #23773589C2direct (N × H)
4. C2×#19098907C2semidirect
5. C2×#19098889C2semidirect
6. C2×#19098840C2semidirect
7. C2×#19098779C2semidirect
8. C2×#19098778C2semidirect
9. C2×#19098715C2semidirect
11. C2×#19098674C2semidirect
12. C2×#19098660C2semidirect
13. C2×#19098650C2semidirect
14. C2×#19098643C2semidirect
15. C2×#19098623C2semidirect
16. C2×#476×C79C2semidirect
23. #19099187C22semidirect
26. C2×#14579149C22semidirect
32. #19099035C22semidirect
33. C2×#14579126C22semidirect
37. C2×#14579123C22semidirect
44. #19098907C22semidirect
45. #19098889C22semidirect
46. #19098840C22semidirect
47. #19098779C22semidirect
48. #19098778C22semidirect
49. #19098715C22semidirect
51. #19098674C22semidirect
52. #19098660C22semidirect
53. #19098650C22semidirect
54. #19098643C22semidirect
55. #19098623C22semidirect
56. C2×#14579094C22semidirect
57. C2×#14579094C22semidirect
58. C2×C4⋊(C79⋊C8)C22semidirect
59. C2×#14579086C22semidirect
60. C2×#14579084C22semidirect
61. C2×#14579083C22semidirect
64. C2×#14579081C22semidirect
67. C2×#14579071C22semidirect
68. C2×C8×Dic79C22semidirect
69. C2×C4⋊Q8×C79C22semidirect
71. #476×C79C22semidirect
72. C2×#106×C79C22semidirect
73. C2×#106×C79C22semidirect
74. C2×C4⋊C8×C79C22semidirect
105. #14579149C23semidirect
113. #14579126C23semidirect
121. #14579123C23semidirect
149. #14579094C23semidirect
150. #14579094C23semidirect
151. C4⋊(C79⋊C8)C23semidirect
152. #14579086C23semidirect
153. #14579084C23semidirect
154. #14579083C23semidirect
157. #14579081C23semidirect
160. #14579071C23semidirect
161. C8×Dic79C23semidirect
168. C4⋊Q8×C79C23semidirect
177. #106×C79C23semidirect
178. #106×C79C23semidirect
179. C4⋊C8×C79C23semidirect
391. C2×C79#3118semidirect
403. C2×#476D79semidirect
414. C79C2×#3118semidirect
422. C2×C4⋊Q8C2×D79semidirect
446. #476C2×D79semidirect
459. C2×#106C2×D79semidirect
460. C2×#106C2×D79semidirect
462. C2×C4⋊C8C2×D79semidirect
506. C4⋊Q8C22×D79semidirect
564. #106C22×D79semidirect
565. #106C22×D79semidirect
567. C4⋊C8C22×D79semidirect
791. C2#23773589direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991872
C2×#190990352
#237735892
C2×#190989072
C2×#190988892
C2×#190988402
C2×#190987792
C2×#190987782
C2×#190987152
C2×#190986982
C2×#190986742
C2×#190986602
C2×#190986502
C2×#190986432
C2×#190986232
C2×#476×C792
C2×#311879