Finite Group Databasebeta

← C2×#23773587 #35156503

Subgroups — C2×#23773587 #35156503

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×#19099186C211yesmaximal, characteristic, complemented
2C2×#19099037C211yesmaximal, characteristic, complemented
3#23773587C2116yesmaximal, direct product factor
4C2×#19098887C211yesmaximal, characteristic, complemented
5C2×#19098852C211yesmaximal, characteristic, complemented
6C2×#19098842C211yesmaximal, characteristic, complemented
7C2×#19098781C211yesmaximal, characteristic, complemented
8C2×#19098781C211yesmaximal, characteristic, complemented
9C2×#19098713C211yesmaximal, characteristic, complemented
10C2×#19098699C211yesmaximal, characteristic
11C2×#19098674C211yesmaximal, characteristic, complemented
12C2×#19098666C211yesmaximal, characteristic, complemented
13C2×#19098648C211yesmaximal, characteristic, complemented
14C2×#19098645C211yesmaximal, characteristic, complemented
15C2×#19098621C211yesmaximal, characteristic, complemented
16C2×#485×C79C211yesmaximal, characteristic, complemented
17C23×D316C2211yescharacteristic
18C22×#11929611C2211yescharacteristic
19C22×#11929611C2211yescharacteristic
20C22×D632C2211yescharacteristic
21C22×D632C2211yescharacteristic
22#19099186—24no—
23#19099186C2218yescomplemented
24C2×#14579160C2211yescharacteristic, complemented
25C2×#14579156—21no—
26C2×#14579150C2211yescharacteristic, complemented
27C2×#14579147—21no—
28C2×#14579143—21no—
29C2×#14579141—21no—
30C2×#14579135C2211yescharacteristic
31#19099037—24no—
32#19099037C2218yescomplemented
33C2×Q8×Dic79C2211yescharacteristic, complemented
34C2×C4×D316—21no—
35C2×C4×D316—21no—
36C2×#14579123C2211yescharacteristic
37C2×#14579123C2211yescharacteristic
38C2×#14579123C2211yescharacteristic
39C2×#14579123C2211yescharacteristic
40C2×#14579123C2211yescharacteristic, complemented
41C2×#14579120C2211yescharacteristic
42C2×C22⋊C4×D79—21no—
43C2×C22⋊C4×D79—21no—
44#19098887C2218yescomplemented
45#19098852C2218yescomplemented
46#19098842C2218yescomplemented
47#19098781C2218yescomplemented
48#19098781C2218yescomplemented
49#19098713C2218yescomplemented
50#19098699C2218yes—
51#19098674C2218yescomplemented
52#19098666C2218yescomplemented
53#19098648C2218yescomplemented
54#19098645C2218yescomplemented
55#19098621C2218yescomplemented
56C2×#14579094C2211yescharacteristic, complemented
57C2×#14579092C2211yescharacteristic, complemented
58C2×Dic79⋊C8C2211yescharacteristic, complemented
59C2×Dic79⋊C8C2211yescharacteristic, complemented
60C2×#14579083C2211yescharacteristic
61C2×#14579083C2211yescharacteristic
62C2×#14579081C2211yescharacteristic
63C2×#14579081C2211yescharacteristic
64C2×#14579081C2211yescharacteristic, complemented
65C2×#14579081C2211yescharacteristic, complemented
66C2×C22⋊(C79⋊C8)C2211yescharacteristic
67C2×#14579071C2211yescharacteristic, complemented
68C2×C8×Dic79C2211yescharacteristic, complemented
69C2×C22⋊Q8×C79C2211yescharacteristic
70C2×#117×C79C2211yescharacteristic
71#485×C79C2218yescomplemented
72C2×#107×C79C2211yescharacteristic, complemented
73C2×#106×C79C2211yescharacteristic, complemented
74C2×#103×C79C2211yescharacteristic, complemented
75C2×#103×C79C2211yescharacteristic, complemented
76C2×C22⋊C8×C79C2211yescharacteristic
77C24×D79—21no—
78C22×Dic158—21no—
79C22×D316—21no—
80C22×D316—22no—
81C22×D316—24no—
82C22×D316—24no—
83C22×D316C2314yes—
84C22×D316C2311yescharacteristic
85C22×D316C2311yescharacteristic
86C22×D316C2311yescharacteristic
87C22×C22⋊D79—21no—
88C22×C4×D79—21no—
89C22×C4×D79—21no—
90C22×C4×D79—21no—
91C22×C4×D79—21no—
92C22×C4×D79—21no—
93C2×#11929611—24no—
94C2×#11929611—24no—
95C2×#11929611C2314yes—
96C2×#11929611C2314yes—
97C2×D632—24no—
98C2×D632—24no—
99C2×D632C2314yes—
100C2×D632C2314yes—
101C22×C79⋊C8C2311yescharacteristic
102C22×C79⋊C8C2311yescharacteristic
103#14579160—22no—
104#14579160C2314yescomplemented
105#14579156—28no—
106#14579150—22no—
107#14579150C2314yescomplemented
108#14579147—28no—
109#14579143—28no—
110#14579141—28no—
111#14579135—22no—
112#14579135C2314yes—
113Q8×Dic79—22no—
114Q8×Dic79C2314yescomplemented
115C4×D316—28no—
116C4×D316—28no—
117#14579123—22no—
118#14579123—22no—
119#14579123—22no—
120#14579123—22no—
121#14579123—22no—
122#14579123C2314yes—
123#14579123C2314yes—
124#14579123C2314yes—
125#14579123C2314yes—
126#14579123C2314yescomplemented
127#14579120D414yes—
128#14579120C2314yes—
129C2×C4⋊Dic79—21no—
130C2×C4⋊Dic79D411yescharacteristic
131C2×C4⋊Dic79D411yescharacteristic
132C2×C4⋊Dic79C2311yescharacteristic
133C2×Dic79⋊C4—21no—
134C2×C22⋊Dic79D411yescharacteristic
135C2×C22⋊Dic79D411yescharacteristic
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—21no—
143C2×(C2×D79)⋊C4—21no—
144C22⋊C4×D79—28no—
145C22⋊C4×D79—28no—
146C2×C4×Dic79—21no—
147C2×C4×Dic79C2311yescharacteristic
148C2×C4×Dic79C2311yescharacteristic
149#14579094C2314yescomplemented
150#14579092C2314yescomplemented
151Dic79⋊C8C2314yescomplemented
152Dic79⋊C8C2314yescomplemented
153#14579083C2314yes—
154#14579083C2314yes—
155#14579081C2314yes—
156#14579081C2314yes—
157#14579081C2314yescomplemented
158#14579081C2314yescomplemented
159C22⋊(C79⋊C8)C2314yes—
160#14579071C2314yescomplemented
161C8×Dic79C2314yescomplemented
162C22×Q8×C79C2311yescharacteristic
163C23×C4×C79C2311yescharacteristic
164C22×C8×C79C2311yescharacteristic
165C22×C8×C79C2311yescharacteristic
166C22⋊Q8×C79—22no—
167C22⋊Q8×C79C2314yes—
168#117×C79—22no—
169#117×C79C2314yes—
170C2×C4⋊C4×C79—21no—
171C2×C4⋊C4×C79C2311yescharacteristic
172C2×C4⋊C4×C79C2311yescharacteristic
173C2×C4⋊C4×C79C2311yescharacteristic
174C2×C22⋊C4×C79—21no—
175C2×C22⋊C4×C79—21no—
176C2×C42×C79—21no—
177#107×C79C2314yescomplemented
178#106×C79C2314yescomplemented
179#103×C79C2314yescomplemented
180#103×C79C2314yescomplemented
181C22⋊C8×C79C2314yes—
182C23×D79—21no—
183C23×D79—21no—
184C23×D79—28no—
185C23×D79—24no—
186C23×D79—21no—
187C23×D79—82no—
188C23×D79—82no—
189C2×Dic158—24no—
190C2×Dic158—82no—
191C2×D316—28no—
192C2×D316—216no—
193C2×D316—28no—
194C2×D316—28no—
195C2×D316—21no—
196C2×D316—21no—
197C2×D316—24no—
198C2×D316—21no—
199C2×D316—22no—
200C2×D316—22no—
201C2×D316—22no—
202C2×D316—22no—
203C2×D316#4114yes—
204C2×D316#4114yes—
205C2×D316C2412yes—
206C2×D316C2412yes—
207C2×D316C2412yes—
208C2×C22⋊D79—24no—
209C2×C22⋊D79—82no—
210C22×Dic79—21no—
211C22×Dic79C2×D411yescharacteristic
212C22×Dic79C2×D411yescharacteristic
213C22×Dic79C2×D411yescharacteristic
214C22×Dic79C2×D411yescharacteristic
215C2×C4×D79—24no—
216C2×C4×D79—24no—
217C2×C4×D79—24no—
218C2×C4×D79—24no—
219C2×C4×D79—24no—
220C2×C4×D79—82no—
221C2×C4×D79—82no—
222C2×C4×D79—82no—
223C2×C4×D79—82no—
224C2×C4×D79—82no—
225#11929611—28no—
226#11929611—28no—
227D632—28no—
228D632—28no—
229C2×C79⋊C8—22no—
230C2×C79⋊C8—22no—
231C2×C79⋊C8C2412yes—
232C2×C79⋊C8C2412yes—
233C4⋊Dic79—24no—
234C4⋊Dic79—21no—
235C4⋊Dic79C2×D414yes—
236C4⋊Dic79C2×D414yes—
237C4⋊Dic79C2412yes—
238Dic79⋊C4—24no—
239C22⋊Dic79C2×D414yes—
240C22⋊Dic79C2×D414yes—
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)⋊C4—24no—
249C4×Dic79—24no—
250C4×Dic79C2×D412yes—
251C4×Dic79C2×D412yes—
252C4×Dic79C2412yes—
253C4×Dic79C2412yes—
254C24×C79C2×D411yescharacteristic
255C2×Q8×C79—21no—
256C2×Q8×C79—22no—
257C2×Q8×C79—22no—
258C2×Q8×C79C2412yes—
259C22×C4×C79—22no—
260C22×C4×C79—22no—
261C22×C4×C79—21no—
262C22×C4×C79—21no—
263C22×C4×C79—21no—
264C22×C4×C79—21no—
265C22×C4×C79C2×D411yescharacteristic
266C22×C4×C79C2×D412yes—
267C22×C4×C79C2412yes—
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—
281C22⋊C4×C79—24no—
282C42×C79—24no—
283C23×C79—22no—
284C23×C79—22no—
285C23×C79—22no—
286C23×C79C22×D412yes—
287C23×C79C22×D411yescharacteristic
288C22×D79—24no—
289C22×D79—24no—
290C22×D79—22no—
291C22×D79—22no—
292C22×D79—216no—
293C22×D79—22no—
294C22×D79—42no—
295C22×D79—42no—
296C22×D79—42no—
297C22×D79—42no—
298C22×D79—42no—
299C22×D79—42no—
300C22×D79—42no—
301C22×D79—84no—
302C22×D79—84no—
303C22×D79—816no—
304Q8×C79—22no—
305Q8×C79—22no—
306Q8×C79—42no—
307C2×C4×C79—22no—
308C2×C4×C79—24no—
309C2×C4×C79—22no—
310C2×C4×C79—22no—
311C2×C4×C79—22no—
312C2×C4×C79—22no—
313C2×C4×C79—22no—
314C2×C4×C79—22no—
315C2×C4×C79—42no—
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×C79C2×#4112yes—
323C2×C4×C79C2511yescharacteristic
324C22⋊D79—84no—
325C2×Dic79—22no—
326C2×Dic79—22no—
327C2×Dic79—22no—
328C2×Dic79—22no—
329C2×Dic79—22no—
330C2×Dic79—42no—
331C2×Dic79C22×D412yes—
332C2×Dic79C22×D412yes—
333C2×Dic79C22×D412yes—
334C2×Dic79C22×D412yes—
335D316—216no—
336D316—24no—
337D316—24no—
338D316—22no—
339D316—22no—
340D316—22no—
341D316—22no—
342D316—42no—
343D316C2×#4114yes—
344D316C2×#4114yes—
345C4×D79—84no—
346C4×D79—84no—
347C4×D79—84no—
348C4×D79—84no—
349C4×D79—84no—
350Dic158—84no—
351C8×C79—22no—
352C8×C79—22no—
353C79⋊C8—22no—
354C79⋊C8—22no—
355C22×C79—22no—
356C22×C79—22no—
357C22×C79—22no—
358C22×C79—44no—
359C22×C79#52512yes—
360C22×C79#57612yes—
361C22×C79#57712yes—
362C22×C79C23×D411yescharacteristic
363C2×D79—24no—
364C2×D79—24no—
365C2×D79—48no—
366C2×D79—48no—
367C2×D79—42no—
368C2×D79—42no—
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—42no—
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—22no—
388Dic79—42no—
389C2×#3118—791nomaximal, Sylow
390C2×C79—42no—
391C2×C79#311814yescomplemented
392C2×C79C2×#52511yescharacteristic
393C2×C79C2×#57611yescharacteristic
394C2×C79C2×#57711yescharacteristic
395D79—44no—
396D79—44no—
397D79—82no—
398C2×#542—791no—
399C2×#518—791no—
400#3118—7916no—
401C2×#485D7911yescharacteristic, complemented
402C2×#482—791no—
403C2×#476—791no—
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⋊Q8—791no—
423C2×#126—1581no—
424C2×#124—791no—
425C2×#124—1581no—
426C2×#123—1581no—
427C2×C22⋊Q8—1581no—
428C2×C22⋊Q8C2×D7911yescharacteristic
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—791no—
438C2×C4×D4—1581no—
439C2×C4×D4—1581no—
440C2×#117—791no—
441C2×#117C2×D7911yescharacteristic
442C22×C22⋊C4—1581no—
443C22×C22⋊C4—1581no—
444#485C2×D7918yescomplemented
445#482—798no—
446#476—798no—
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×#107C2×D7911yescharacteristic, complemented
459C2×#106—791no—
460C2×#106C2×D7911yescharacteristic, complemented
461C2×C4⋊C8—791no—
462C2×C4⋊C8—791no—
463C2×#103C2×D7911yescharacteristic, complemented
464C2×#103C2×D7911yescharacteristic, complemented
465C2×#102—791no—
466C2×#102—791no—
467C2×#102—791no—
468C2×#102—791no—
469C2×#102—791no—
470C2×#102—791no—
471C2×C22⋊C8—791no—
472C2×C22⋊C8C2×D7911yescharacteristic
473C2×#97—791no—
474C2×C4×C8—791no—
475C25—1581no—
476C22×Q8—1581no—
477C22×Q8C22×D7911yescharacteristic
478C22×D4—791no—
479C22×D4—791no—
480C22×D4—791no—
481C22×D4—794no—
482C22×D4—1584no—
483C22×D4—1584no—
484C22×D4—1581no—
485C22×D4—1581no—
486C22×D4—1582no—
487C23×C4—1581no—
488C23×C4—1581no—
489C23×C4—1581no—
490C23×C4—1581no—
491C23×C4—1581no—
492C23×C4C22×D7911yescharacteristic
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—794no—
506C4⋊Q8—1582no—
507#126—1588no—
508#124—794no—
509#124—1582no—
510#124—1588no—
511#123—1588no—
512C22⋊Q8—22no—
513C22⋊Q8—1588no—
514C22⋊Q8C22×D7914yes—
515#121—794no—
516#121—1582no—
517C4×Q8—794no—
518C4×Q8—1582no—
519C4×D4—794no—
520C4×D4—794no—
521C4×D4—794no—
522C4×D4—794no—
523C4×D4—794no—
524C4×D4—1588no—
525C4×D4—1588no—
526C4×D4—1582no—
527C4×D4—1582no—
528C4×D4—1582no—
529C4×D4—1582no—
530C4×D4—1582no—
531#117—22no—
532#117—794no—
533#117—794no—
534#117C22×D7914yes—
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—21no—
546C2×C22⋊C4—791no—
547C2×C22⋊C4—791no—
548C2×C22⋊C4—1588no—
549C2×C22⋊C4—1588no—
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—21no—
559C2×C42—791no—
560C2×C42—791no—
561C2×C42—1581no—
562#107—794no—
563#107C22×D7914yescomplemented
564#106—794no—
565#106C22×D7914yescomplemented
566C4⋊C8—794no—
567C4⋊C8—794no—
568#103C22×D7914yescomplemented
569#103C22×D7914yescomplemented
570#102—794no—
571#102—794no—
572#102—794no—
573#102—794no—
574#102—794no—
575#102—794no—
576C22⋊C8—794no—
577C22⋊C8C22×D7914yes—
578#97—794no—
579C4×C8—794no—
580C24—6322no—
581C24—6322no—
582C24—1588no—
583C24—1581no—
584C24—1581no—
585C24—1581no—
586C24—1584no—
587C24D4×D7911yescharacteristic
588C2×Q8—21no—
589C2×Q8—22no—
590C2×Q8—22no—
591C2×Q8—6322no—
592C2×Q8—1584no—
593C2×Q8C23×D7912yes—
594C2×D4—794no—
595C2×D4—794no—
596C2×D4—792no—
597C2×D4—792no—
598C2×D4—792no—
599C2×D4—6322no—
600C2×D4—1588no—
601C2×D4—1588no—
602C2×D4—1588no—
603C2×D4—15816no—
604C2×D4—1584no—
605C2×D4—1582no—
606C2×D4—1582no—
607C2×D4—1582no—
608C2×D4—1582no—
609C2×D4—1581no—
610C2×D4—1584no—
611C2×D4—1581no—
612C2×D4—1581no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—791no—
620C22×C4—791no—
621C22×C4—791no—
622C22×C4—791no—
623C22×C4—6322no—
624C22×C4—6322no—
625C22×C4—6322no—
626C22×C4—6322no—
627C22×C4—6322no—
628C22×C4—1584no—
629C22×C4—1584no—
630C22×C4—1584no—
631C22×C4—1584no—
632C22×C4—1584no—
633C22×C4—1581no—
634C22×C4D4×D7912yes—
635C22×C4D4×D7911yescharacteristic
636C22×C4C23×D7912yes—
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—24no—
665C22⋊C4—794no—
666C22⋊C4—794no—
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—24no—
676C42—792no—
677C42—792no—
678C42—792no—
679C42—792no—
680C42—1584no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—3162no—
685C23—3162no—
686C23—3162no—
687C23—3162no—
688C23—3162no—
689C23—3162no—
690C23—3162no—
691C23—6324no—
692C23—6324no—
693C23—63216no—
694C23—15816no—
695C23—1582no—
696C23—1584no—
697C23—1584no—
698C23—1582no—
699C23—1582no—
700C23C2×D4×D7912yes—
701C23C2×D4×D7911yescharacteristic
702Q8—22no—
703Q8—22no—
704Q8—42no—
705Q8—6324no—
706D4—3162no—
707D4—794no—
708D4—794no—
709D4—6324no—
710D4—15816no—
711D4—1584no—
712D4—1584no—
713D4—1582no—
714D4—1582no—
715D4—1582no—
716D4—1582no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—3162no—
730C2×C4—792no—
731C2×C4—792no—
732C2×C4—792no—
733C2×C4—792no—
734C2×C4—6324no—
735C2×C4—6324no—
736C2×C4—6324no—
737C2×C4—6324no—
738C2×C4—6324no—
739C2×C4—1582no—
740C2×C4—1582no—
741C2×C4—1582no—
742C2×C4—1582no—
743C2×C4—1582no—
744C2×C4C2×D4×D7912yes—
745C2×C4C2×D4×D7911yescharacteristic
746C2×C4#41×D7912yes—
747C2×C4#41×D7912yes—
748C2×C4C24×D7911yescharacteristic
749C8—22no—
750C8—22no—
751C8—1582no—
752C8—1582no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—44no—
757C22—3162no—
758C22—3162no—
759C22—3162no—
760C22—3162no—
761C22—3168no—
762C22—3168no—
763C22—3162no—
764C22—3162no—
765C22—3162no—
766C22—63216no—
767C22—6324no—
768C22—1584no—
769C22—1584no—
770C22#1909907112yes—
771C22#1909936512yes—
772C22#1909937212yes—
773C22C22×D4×D7911yescharacteristic
774C4—22no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—3162no—
780C4—1582no—
781C4—1582no—
782C4—1582no—
783C4—1582no—
784C4#1909907112yes—
785C4C2×#41×D7911yescharacteristic
786C4C2×#41×D7911yescharacteristic
787C2—42no—
788C2—3164no—
789C2—3164no—
790C2—6322no—
791C2#2377358714yesdirect product factor
792C2C2×#1909907111yescharacteristic
793C2C2×#1909936511yescharacteristic
794C2C2×#1909937211yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#485×C79C2
socleC23×C79C22×D4
prime radicalC2×#19098699C2
hypercenterC2×#485D79
hypocenterC79C2×#3118
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
1. C2×#19099186C2semidirect
2. C2×#19099037C2semidirect
3. #23773587C2direct (N × H)
4. C2×#19098887C2semidirect
5. C2×#19098852C2semidirect
6. C2×#19098842C2semidirect
7. C2×#19098781C2semidirect
8. C2×#19098781C2semidirect
9. C2×#19098713C2semidirect
11. C2×#19098674C2semidirect
12. C2×#19098666C2semidirect
13. C2×#19098648C2semidirect
14. C2×#19098645C2semidirect
15. C2×#19098621C2semidirect
16. C2×#485×C79C2semidirect
23. #19099186C22semidirect
24. C2×#14579160C22semidirect
26. C2×#14579150C22semidirect
32. #19099037C22semidirect
33. C2×Q8×Dic79C22semidirect
40. C2×#14579123C22semidirect
44. #19098887C22semidirect
45. #19098852C22semidirect
46. #19098842C22semidirect
47. #19098781C22semidirect
48. #19098781C22semidirect
49. #19098713C22semidirect
51. #19098674C22semidirect
52. #19098666C22semidirect
53. #19098648C22semidirect
54. #19098645C22semidirect
55. #19098621C22semidirect
56. C2×#14579094C22semidirect
57. C2×#14579092C22semidirect
58. C2×Dic79⋊C8C22semidirect
59. C2×Dic79⋊C8C22semidirect
64. C2×#14579081C22semidirect
65. C2×#14579081C22semidirect
67. C2×#14579071C22semidirect
68. C2×C8×Dic79C22semidirect
71. #485×C79C22semidirect
72. C2×#107×C79C22semidirect
73. C2×#106×C79C22semidirect
74. C2×#103×C79C22semidirect
75. C2×#103×C79C22semidirect
104. #14579160C23semidirect
107. #14579150C23semidirect
114. Q8×Dic79C23semidirect
126. #14579123C23semidirect
149. #14579094C23semidirect
150. #14579092C23semidirect
151. Dic79⋊C8C23semidirect
152. Dic79⋊C8C23semidirect
157. #14579081C23semidirect
158. #14579081C23semidirect
160. #14579071C23semidirect
161. C8×Dic79C23semidirect
177. #107×C79C23semidirect
178. #106×C79C23semidirect
179. #103×C79C23semidirect
180. #103×C79C23semidirect
391. C2×C79#3118semidirect
401. C2×#485D79semidirect
414. C79C2×#3118semidirect
444. #485C2×D79semidirect
458. C2×#107C2×D79semidirect
460. C2×#106C2×D79semidirect
463. C2×#103C2×D79semidirect
464. C2×#103C2×D79semidirect
563. #107C22×D79semidirect
565. #106C22×D79semidirect
568. #103C22×D79semidirect
569. #103C22×D79semidirect
791. C2#23773587direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991862
C2×#190990372
#237735872
C2×#190988872
C2×#190988522
C2×#190988422
C2×#190987812
C2×#190987132
C2×#190986992
C2×#190986742
C2×#190986662
C2×#190986482
C2×#190986452
C2×#190986212
C2×#485×C792
C2×#311879