Finite Group Databasebeta

← C2×#23773654 #35156575

Subgroups — C2×#23773654 #35156575

Order 20224.

2210 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×#19099176C211yesmaximal, characteristic, complemented
2C2×#19099035C211yesmaximal, characteristic
3#23773654C2116yesmaximal, direct product factor
4C2×#19098907C211yesmaximal, characteristic, complemented
5C2×#19098906C211yesmaximal, characteristic, complemented
6C2×#19098860C211yesmaximal, characteristic, complemented
7C2×#19098769C211yesmaximal, characteristic, complemented
8C2×#19098768C211yesmaximal, characteristic, complemented
9C2×#19098715C211yesmaximal, characteristic
10C2×#19098715C211yesmaximal, characteristic
11C2×#19098662C211yesmaximal, characteristic, complemented
12C2×#19098660C211yesmaximal, characteristic, complemented
13C2×#19098654C211yesmaximal, characteristic, complemented
14C2×#19098650C211yesmaximal, characteristic, complemented
15C2×#19098623C211yesmaximal, characteristic, complemented
16C2×#478×C79C211yesmaximal, characteristic, complemented
17C22×D4×D79C2211yescharacteristic
18C22×#11929613C2211yescharacteristic
19C22×#11929613C2211yescharacteristic
20C22×#11929612C2211yescharacteristic
21C22×#11929612C2211yescharacteristic
22#19099176—24no—
23#19099176C2218yescomplemented
24C2×#14579161C2211yescharacteristic, complemented
25C2×#14579156—21no—
26C2×#14579156—21no—
27C2×#14579152—21no—
28C2×#14579152—21no—
29C2×#14579141C2211yescharacteristic
30C2×#14579141C2211yescharacteristic
31#19099035—24no—
32#19099035C2218yes—
33C2×#14579126C2211yescharacteristic, complemented
34C2×#14579126C2211yescharacteristic, complemented
35C2×C4×D316C2211yescharacteristic
36C2×D4×Dic79C2211yescharacteristic
37C2×#14579123C2211yescharacteristic
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#19098906C2218yescomplemented
46#19098860C2218yescomplemented
47#19098769C2218yescomplemented
48#19098768C2218yescomplemented
49#19098715C2218yes—
50#19098715C2218yes—
51#19098662C2218yescomplemented
52#19098660C2218yescomplemented
53#19098654C2218yescomplemented
54#19098650C2218yescomplemented
55#19098623C2218yescomplemented
56C2×#14579094C2211yescharacteristic, complemented
57C2×#14579092C2211yescharacteristic, complemented
58C2×C4⋊(C79⋊C8)C2211yescharacteristic, complemented
59C2×#14579086C2211yescharacteristic, complemented
60C2×#14579086C2211yescharacteristic, complemented
61C2×#14579084C2211yescharacteristic, complemented
62C2×#14579084C2211yescharacteristic, complemented
63C2×#14579081C2211yescharacteristic
64C2×#14579081C2211yescharacteristic
65C2×(C2×D79)⋊C8C2211yescharacteristic
66C2×(C2×D79)⋊C8C2211yescharacteristic
67C2×#14579071C2211yescharacteristic, complemented
68C2×C8×Dic79C2211yescharacteristic, complemented
69C2×#125×C79C2211yescharacteristic, complemented
70C2×C4×D4×C79C2211yescharacteristic
71#478×C79C2218yescomplemented
72C2×#107×C79C2211yescharacteristic, complemented
73C2×#106×C79C2211yescharacteristic, complemented
74C2×C4⋊C8×C79C2211yescharacteristic, complemented
75C2×#102×C79C2211yescharacteristic
76C2×#102×C79C2211yescharacteristic
77C24×D79—21no—
78C22×Dic158C2311yescharacteristic
79C22×Dic158C2311yescharacteristic
80C22×D316C2311yescharacteristic
81C22×C22⋊D79—21no—
82C2×D4×D79—24no—
83C2×D4×D79—24no—
84C2×D4×D79—22no—
85C2×D4×D79C2314yes—
86C23×Dic79—21no—
87C22×C4×D79—21no—
88C22×C4×D79—21no—
89C22×C4×D79C2311yescharacteristic
90C2×#11929613—24no—
91C2×#11929613—24no—
92C2×#11929613C2314yes—
93C2×#11929613C2314yes—
94C2×#11929612—24no—
95C2×#11929612—24no—
96C2×#11929612C2314yes—
97C2×#11929612C2314yes—
98C22×C79⋊C8C2311yescharacteristic
99C22×C79⋊C8C2311yescharacteristic
100#14579161—22no—
101#14579161C2314yescomplemented
102#14579156—28no—
103#14579156—28no—
104#14579152—28no—
105#14579152—28no—
106#14579141—22no—
107#14579141—22no—
108#14579141C2314yes—
109#14579141C2314yes—
110#14579126—22no—
111#14579126—22no—
112#14579126C2314yescomplemented
113#14579126C2314yescomplemented
114C4×D316—22no—
115C4×D316C2314yes—
116D4×Dic79—22no—
117D4×Dic79C2314yes—
118#14579123—22no—
119#14579123C2314yes—
120C4×C22⋊D79—28no—
121(C22⋊D79)⋊C4—28no—
122#14579119—22no—
123#14579119C2314yes—
124#14579118D414yes—
125#14579118C2314yes—
126C2×C4⋊Dic79—21no—
127C2×C4⋊Dic79—21no—
128C2×C4⋊Dic79—21no—
129C2×C4⋊Dic79—21no—
130C2×C4⋊Dic79C2311yescharacteristic
131C2×Dic79⋊C4—21no—
132C2×Dic79⋊C4—21no—
133C2×Dic79⋊C4D411yescharacteristic
134C2×Dic79⋊C4D411yescharacteristic
135C2×C22⋊Dic79—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—28no—
142C2×(C2×D79)⋊C4D411yescharacteristic
143C2×(C2×D79)⋊C4D411yescharacteristic
144C22⋊C4×D79—28no—
145C2×C4×Dic79—21no—
146C2×C4×Dic79—21no—
147C2×C4×Dic79—21no—
148C2×C4×Dic79C2311yescharacteristic
149#14579094C2314yescomplemented
150#14579092C2314yescomplemented
151C4⋊(C79⋊C8)C2314yescomplemented
152#14579086C2314yescomplemented
153#14579086C2314yescomplemented
154#14579084C2314yescomplemented
155#14579084C2314yescomplemented
156#14579081C2314yes—
157#14579081C2314yes—
158(C2×D79)⋊C8C2314yes—
159(C2×D79)⋊C8C2314yes—
160#14579071C2314yescomplemented
161C8×Dic79C2314yescomplemented
162C22×D4×C79C2311yescharacteristic
163C23×C4×C79—21no—
164C22×C8×C79C2311yescharacteristic
165C22×C8×C79C2311yescharacteristic
166#125×C79—22no—
167#125×C79C2314yescomplemented
168C4×D4×C79—22no—
169C4×D4×C79C2314yes—
170C2×C4⋊C4×C79—21no—
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#107×C79C2314yescomplemented
178#106×C79C2314yescomplemented
179C4⋊C8×C79C2314yescomplemented
180#102×C79C2314yes—
181#102×C79C2314yes—
182C23×D79—21no—
183C23×D79—28no—
184C23×D79—24no—
185C23×D79—82no—
186C23×D79—82no—
187C23×D79C2×D411yescharacteristic
188C2×Dic158—21no—
189C2×Dic158—21no—
190C2×Dic158—22no—
191C2×Dic158—22no—
192C2×Dic158—22no—
193C2×Dic158—22no—
194C2×Dic158C2412yes—
195C2×Dic158C2412yes—
196C2×D316—21no—
197C2×D316—22no—
198C2×D316#4114yes—
199C2×D316C2412yes—
200C2×C22⋊D79—28no—
201C2×C22⋊D79—24no—
202D4×D79—216no—
203D4×D79—28no—
204D4×D79—28no—
205C22×Dic79—24no—
206C22×Dic79—21no—
207C22×Dic79—21no—
208C22×Dic79—21no—
209C22×Dic79—82no—
210C22×Dic79C2×D411yescharacteristic
211C22×Dic79C2×D411yescharacteristic
212C22×Dic79C2×D411yescharacteristic
213C2×C4×D79—24no—
214C2×C4×D79—24no—
215C2×C4×D79—22no—
216C2×C4×D79—22no—
217C2×C4×D79—82no—
218C2×C4×D79—82no—
219C2×C4×D79C2×D412yes—
220C2×C4×D79C2412yes—
221#11929613—28no—
222#11929613—28no—
223#11929612—28no—
224#11929612—28no—
225C2×C79⋊C8—22no—
226C2×C79⋊C8—22no—
227C2×C79⋊C8C2412yes—
228C2×C79⋊C8C2412yes—
229C4⋊Dic79—24no—
230C4⋊Dic79—24no—
231C4⋊Dic79—24no—
232C4⋊Dic79—24no—
233C4⋊Dic79—21no—
234C4⋊Dic79C2412yes—
235Dic79⋊C4—24no—
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)⋊C4C2×D414yes—
246(C2×D79)⋊C4C2×D414yes—
247C4×Dic79—24no—
248C4×Dic79—24no—
249C4×Dic79—24no—
250C4×Dic79C2×D412yes—
251C4×Dic79C2412yes—
252C24×C79—21no—
253C2×D4×C79—21no—
254C2×D4×C79—22no—
255C2×D4×C79#4114yes—
256C2×D4×C79C2412yes—
257C22×C4×C79—21no—
258C22×C4×C79—21no—
259C22×C4×C79—21no—
260C22×C4×C79—24no—
261C22×C4×C79—82no—
262C22×C4×C79C2×D411yescharacteristic
263C22×C4×C79C2×D411yescharacteristic
264C22×C4×C79C2411yescharacteristic
265C2×C8×C79—22no—
266C2×C8×C79—22no—
267C2×C8×C79C2412yes—
268C2×C8×C79C2412yes—
269C4⋊C4×C79—24no—
270C4⋊C4×C79—24no—
271C4⋊C4×C79—21no—
272C4⋊C4×C79—21no—
273C4⋊C4×C79—21no—
274C4⋊C4×C79C2412yes—
275C4⋊C4×C79C2412yes—
276C4⋊C4×C79C2412yes—
277C22⋊C4×C79—24no—
278C42×C79C2×D412yes—
279C42×C79C2412yes—
280C23×C79—24no—
281C23×C79—22no—
282C23×C79—42no—
283C23×C79—42no—
284C23×C79C22×D411yescharacteristic
285C22×D79—22no—
286C22×D79—24no—
287C22×D79—22no—
288C22×D79—22no—
289C22×D79—22no—
290C22×D79—216no—
291C22×D79—42no—
292C22×D79—42no—
293C22×D79—84no—
294C22×D79—84no—
295C22×D79—816no—
296C22×D79C22×D412yes—
297D4×C79—24no—
298D4×C79—22no—
299D4×C79C2×#4114yes—
300C2×C4×C79—22no—
301C2×C4×C79—22no—
302C2×C4×C79—22no—
303C2×C4×C79—22no—
304C2×C4×C79—22no—
305C2×C4×C79—42no—
306C2×C4×C79—42no—
307C2×C4×C79—42no—
308C2×C4×C79—84no—
309C2×C4×C79C22×D412yes—
310C2×C4×C79C22×D412yes—
311C2×C4×C79C22×D411yescharacteristic
312C2×C4×C79C2×#4112yes—
313C2×C4×C79C2×#4112yes—
314C2×C4×C79C2511yescharacteristic
315C22⋊D79—216no—
316C2×Dic79—22no—
317C2×Dic79—22no—
318C2×Dic79—22no—
319C2×Dic79—22no—
320C2×Dic79—22no—
321C2×Dic79—22no—
322C2×Dic79—42no—
323C2×Dic79—42no—
324C2×Dic79—42no—
325C2×Dic79—84no—
326C2×Dic79C22×D412yes—
327C2×Dic79C22×D412yes—
328C2×Dic79C22×D412yes—
329D316—24no—
330D316—22no—
331D316C2×#4114yes—
332C4×D79—24no—
333C4×D79—22no—
334C4×D79—22no—
335C4×D79—84no—
336C4×D79—84no—
337Dic158—22no—
338Dic158—22no—
339Dic158—22no—
340Dic158—22no—
341Dic158—42no—
342Dic158—42no—
343C8×C79—22no—
344C8×C79—22no—
345C79⋊C8—22no—
346C79⋊C8—22no—
347C22×C79—24no—
348C22×C79—48no—
349C22×C79—42no—
350C22×C79—42no—
351C22×C79#52512yes—
352C22×C79#57712yes—
353C22×C79#57712yes—
354C22×C79C23×D411yescharacteristic
355C2×D79—24no—
356C2×D79—22no—
357C2×D79—22no—
358C2×D79—22no—
359C2×D79—44no—
360C2×D79—48no—
361C2×D79—42no—
362C2×D79—42no—
363C2×D79—816no—
364C4×C79—22no—
365C4×C79—22no—
366C4×C79—42no—
367C4×C79—42no—
368C4×C79—42no—
369C4×C79#52512yes—
370C4×C79C22×#4111yescharacteristic
371C4×C79C22×#4111yescharacteristic
372Dic79—22no—
373Dic79—22no—
374Dic79—22no—
375Dic79—42no—
376Dic79—42no—
377Dic79—42no—
378C2×#3123—791nomaximal, Sylow
379C2×C79—44no—
380C2×C79#312314yescomplemented
381C2×C79C2×#52511yescharacteristic
382C2×C79C2×#57711yescharacteristic
383C2×C79C2×#57711yescharacteristic
384D79—42no—
385D79—44no—
386C2×#541—791no—
387C2×#518—791no—
388#3123—7916no—
389C2×#485—791no—
390C2×#485—791no—
391C2×#478—791no—
392C2×#478D7911yescharacteristic, complemented
393C2×#461—791no—
394C2×#461—791no—
395C2×#450—791no—
396C2×#450—791no—
397C2×#440—791no—
398C2×#440—791no—
399C2×C4×SD16—791no—
400C2×C4×SD16—791no—
401C2×#433—791no—
402C79C2×#312311yescharacteristic, complemented, Sylow
403C23×D4—791no—
404C22×SD16—791no—
405C22×SD16—791no—
406C22×SD16—791no—
407C22×SD16—791no—
408#541—798no—
409#541—1584no—
410C2×C4⋊Q8—791no—
411C2×#126—1581no—
412C2×#126—1581no—
413C2×#125—1581no—
414C2×#125—1581no—
415C2×#125C2×D7911yescharacteristic, complemented
416C2×C22⋊Q8—791no—
417C2×C22⋊Q8—791no—
418#518—798no—
419#518—1584no—
420C2×C4×Q8—791no—
421C2×C4×Q8—791no—
422C2×C4×D4—791no—
423C2×C4×D4—791no—
424C2×C4×D4—791no—
425C2×C4×D4—1581no—
426C2×C4×D4—1581no—
427C2×C4×D4C2×D7911yescharacteristic
428C2×#117—791no—
429C2×#117—791no—
430C22×C22⋊C4—1581no—
431C22×C22⋊C4—1581no—
432#485—798no—
433#485—798no—
434#478—798no—
435#478C2×D7918yescomplemented
436#461—798no—
437#461—798no—
438#450—798no—
439#450—798no—
440#440—798no—
441#440—798no—
442C4×SD16—798no—
443C4×SD16—798no—
444#433—798no—
445C2×#107—791no—
446C2×#107C2×D7911yescharacteristic, complemented
447C2×#106—791no—
448C2×#106C2×D7911yescharacteristic, complemented
449C2×C4⋊C8—791no—
450C2×C4⋊C8C2×D7911yescharacteristic, complemented
451C2×#103—791no—
452C2×#103—791no—
453C2×#103—791no—
454C2×#103—791no—
455C2×#102—791no—
456C2×#102—791no—
457C2×#102C2×D7911yescharacteristic
458C2×#102C2×D7911yescharacteristic
459C2×C22⋊C8—791no—
460C2×C22⋊C8—791no—
461C2×#97—791no—
462C2×C4×C8—791no—
463C25—1581no—
464C22×Q8—791no—
465C22×Q8—791no—
466C22×D4—794no—
467C22×D4—791no—
468C22×D4—1582no—
469C22×D4—1581no—
470C22×D4—1584no—
471C22×D4—1584no—
472C22×D4C22×D7911yescharacteristic
473C23×C4—21no—
474C23×C4—791no—
475C23×C4—1581no—
476C23×C4—1581no—
477C23×C4—1581no—
478C2×SD16—794no—
479C2×SD16—794no—
480C2×SD16—794no—
481C2×SD16—794no—
482C2×SD16—1584no—
483C2×SD16—1584no—
484C2×SD16—1584no—
485C2×SD16—1584no—
486C22×C8—791no—
487C22×C8—791no—
488C22×C8C22×D7911yescharacteristic
489C22×C8C22×D7911yescharacteristic
490C4⋊Q8—794no—
491C4⋊Q8—1582no—
492#126—1588no—
493#126—1588no—
494#125—22no—
495#125—1588no—
496#125—1588no—
497#125C22×D7914yescomplemented
498C22⋊Q8—794no—
499C22⋊Q8—794no—
500C22⋊Q8—1582no—
501C22⋊Q8—1582no—
502C4×Q8—794no—
503C4×Q8—794no—
504C4×Q8—1582no—
505C4×Q8—1582no—
506C4×D4—22no—
507C4×D4—794no—
508C4×D4—794no—
509C4×D4—794no—
510C4×D4—1582no—
511C4×D4—1582no—
512C4×D4—1588no—
513C4×D4—1588no—
514C4×D4—1582no—
515C4×D4C22×D7914yes—
516#117—794no—
517#117—794no—
518#117—794no—
519#117—1582no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—791no—
523C2×C4⋊C4—791no—
524C2×C4⋊C4—791no—
525C2×C4⋊C4—1581no—
526C2×C4⋊C4—1581no—
527C2×C4⋊C4—1581no—
528C2×C4⋊C4—1581no—
529C2×C4⋊C4—1581no—
530C2×C4⋊C4—1581no—
531C2×C4⋊C4C22×D7911yescharacteristic
532C2×C4⋊C4C22×D7911yescharacteristic
533C2×C4⋊C4C22×D7911yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—791no—
536C2×C22⋊C4—791no—
537C2×C22⋊C4—1588no—
538C2×C22⋊C4—1588no—
539C2×C22⋊C4—1581no—
540C2×C22⋊C4—1581no—
541C2×C22⋊C4—1581no—
542C2×C22⋊C4—1581no—
543C2×C22⋊C4—1581no—
544C2×C22⋊C4—1581no—
545C2×C42—791no—
546C2×C42—1581no—
547C2×C42—1581no—
548C2×C42—1581no—
549C2×C42C22×D7911yescharacteristic
550#107—794no—
551#107C22×D7914yescomplemented
552#106—794no—
553#106C22×D7914yescomplemented
554C4⋊C8—794no—
555C4⋊C8C22×D7914yescomplemented
556#103—794no—
557#103—794no—
558#103—794no—
559#103—794no—
560#102—794no—
561#102—794no—
562#102C22×D7914yes—
563#102C22×D7914yes—
564C22⋊C8—794no—
565C22⋊C8—794no—
566#97—794no—
567C4×C8—794no—
568C24—21no—
569C24—791no—
570C24—6322no—
571C24—6322no—
572C24—1584no—
573C24—1588no—
574C24—1581no—
575C2×Q8—792no—
576C2×Q8—792no—
577C2×Q8—1582no—
578C2×Q8—1582no—
579C2×Q8—1582no—
580C2×Q8—1582no—
581C2×Q8—1581no—
582C2×Q8—1581no—
583C2×D4—22no—
584C2×D4—21no—
585C2×D4—794no—
586C2×D4—792no—
587C2×D4—1584no—
588C2×D4—1588no—
589C2×D4—15816no—
590C2×D4—1588no—
591C2×D4—1588no—
592C2×D4—1582no—
593C2×D4—1581no—
594C2×D4#1192962514yes—
595C2×D4C23×D7912yes—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—24no—
600C22×C4—82no—
601C22×C4—791no—
602C22×C4—791no—
603C22×C4—791no—
604C22×C4—792no—
605C22×C4—792no—
606C22×C4—6322no—
607C22×C4—6322no—
608C22×C4—6322no—
609C22×C4—1584no—
610C22×C4—1581no—
611C22×C4—1581no—
612C22×C4—1581no—
613C22×C4—1584no—
614C22×C4—1584no—
615C22×C4—1582no—
616C22×C4—1582no—
617C22×C4D4×D7911yescharacteristic
618C22×C4D4×D7911yescharacteristic
619C22×C4C23×D7911yescharacteristic
620SD16—1588no—
621SD16—1588no—
622SD16—1588no—
623SD16—1588no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—792no—
627C2×C8—792no—
628C2×C8—1582no—
629C2×C8—1582no—
630C2×C8C23×D7912yes—
631C2×C8C23×D7912yes—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—794no—
638C4⋊C4—794no—
639C4⋊C4—792no—
640C4⋊C4—1584no—
641C4⋊C4—1584no—
642C4⋊C4—1584no—
643C4⋊C4—1584no—
644C4⋊C4—1581no—
645C4⋊C4—1584no—
646C4⋊C4—1584no—
647C4⋊C4C23×D7912yes—
648C4⋊C4C23×D7912yes—
649C4⋊C4C23×D7912yes—
650C22⋊C4—24no—
651C22⋊C4—794no—
652C22⋊C4—794no—
653C22⋊C4—1584no—
654C22⋊C4—1584no—
655C22⋊C4—1584no—
656C22⋊C4—1584no—
657C22⋊C4—1584no—
658C22⋊C4—1584no—
659C42—792no—
660C42—792no—
661C42—1584no—
662C42—1584no—
663C42—1584no—
664C42D4×D7912yes—
665C42C23×D7912yes—
666C23—24no—
667C23—22no—
668C23—42no—
669C23—42no—
670C23—3162no—
671C23—3162no—
672C23—792no—
673C23—63216no—
674C23—6324no—
675C23—6324no—
676C23—15816no—
677C23—1582no—
678C23—1584no—
679C23—1582no—
680C23—1582no—
681C23—1582no—
682C23C2×D4×D7911yescharacteristic
683Q8—3162no—
684Q8—3162no—
685Q8—1582no—
686Q8—1582no—
687Q8—1582no—
688Q8—1582no—
689D4—24no—
690D4—22no—
691D4—794no—
692D4—15816no—
693D4—1584no—
694D4—1582no—
695D4C2×#1192962514yes—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—84no—
705C2×C4—3162no—
706C2×C4—3162no—
707C2×C4—3162no—
708C2×C4—792no—
709C2×C4—792no—
710C2×C4—792no—
711C2×C4—6324no—
712C2×C4—6324no—
713C2×C4—6324no—
714C2×C4—1582no—
715C2×C4—1582no—
716C2×C4—1582no—
717C2×C4—1582no—
718C2×C4—1582no—
719C2×C4—1582no—
720C2×C4—1584no—
721C2×C4—1582no—
722C2×C4—1582no—
723C2×C4C2×D4×D7912yes—
724C2×C4C2×D4×D7912yes—
725C2×C4C2×D4×D7911yescharacteristic
726C2×C4#41×D7912yes—
727C2×C4C2×#1192962512yes—
728C2×C4C24×D7911yescharacteristic
729C8—22no—
730C8—22no—
731C8—1582no—
732C8—1582no—
733C22—24no—
734C22—42no—
735C22—42no—
736C22—48no—
737C22—3162no—
738C22—3162no—
739C22—3168no—
740C22—3164no—
741C22—63216no—
742C22—1582no—
743C22—1582no—
744C22—1582no—
745C22—1584no—
746C22#1909907612yes—
747C22#1909937012yes—
748C22#1909937312yes—
749C22C22×D4×D7911yescharacteristic
750C4—22no—
751C4—22no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—3162no—
756C4—3162no—
757C4—3162no—
758C4—1582no—
759C4—1582no—
760C4—1582no—
761C4#1909907612yes—
762C4C2×#41×D7911yescharacteristic
763C4C22×#1192962511yescharacteristic
764C2—44no—
765C2—3164no—
766C2—3162no—
767C2#2377365414yesdirect product factor
768C2C2×#1909907611yescharacteristic
769C2C2×#1909937011yescharacteristic
770C2C2×#1909937311yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#478×C79C2
socleC23×C79C22×D4
prime radicalC22×D4×D79C22
hypercenterC2×#478D79
hypocenterC79C2×#3123
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×#19099176C2semidirect
3. #23773654C2direct (N × H)
4. C2×#19098907C2semidirect
5. C2×#19098906C2semidirect
6. C2×#19098860C2semidirect
7. C2×#19098769C2semidirect
8. C2×#19098768C2semidirect
11. C2×#19098662C2semidirect
12. C2×#19098660C2semidirect
13. C2×#19098654C2semidirect
14. C2×#19098650C2semidirect
15. C2×#19098623C2semidirect
16. C2×#478×C79C2semidirect
23. #19099176C22semidirect
24. C2×#14579161C22semidirect
33. C2×#14579126C22semidirect
34. C2×#14579126C22semidirect
44. #19098907C22semidirect
45. #19098906C22semidirect
46. #19098860C22semidirect
47. #19098769C22semidirect
48. #19098768C22semidirect
51. #19098662C22semidirect
52. #19098660C22semidirect
53. #19098654C22semidirect
54. #19098650C22semidirect
55. #19098623C22semidirect
56. C2×#14579094C22semidirect
57. C2×#14579092C22semidirect
58. C2×C4⋊(C79⋊C8)C22semidirect
59. C2×#14579086C22semidirect
60. C2×#14579086C22semidirect
61. C2×#14579084C22semidirect
62. C2×#14579084C22semidirect
67. C2×#14579071C22semidirect
68. C2×C8×Dic79C22semidirect
69. C2×#125×C79C22semidirect
71. #478×C79C22semidirect
72. C2×#107×C79C22semidirect
73. C2×#106×C79C22semidirect
74. C2×C4⋊C8×C79C22semidirect
101. #14579161C23semidirect
112. #14579126C23semidirect
113. #14579126C23semidirect
149. #14579094C23semidirect
150. #14579092C23semidirect
151. C4⋊(C79⋊C8)C23semidirect
152. #14579086C23semidirect
153. #14579086C23semidirect
154. #14579084C23semidirect
155. #14579084C23semidirect
160. #14579071C23semidirect
161. C8×Dic79C23semidirect
167. #125×C79C23semidirect
177. #107×C79C23semidirect
178. #106×C79C23semidirect
179. C4⋊C8×C79C23semidirect
380. C2×C79#3123semidirect
392. C2×#478D79semidirect
402. C79C2×#3123semidirect
415. C2×#125C2×D79semidirect
435. #478C2×D79semidirect
446. C2×#107C2×D79semidirect
448. C2×#106C2×D79semidirect
450. C2×C4⋊C8C2×D79semidirect
497. #125C22×D79semidirect
551. #107C22×D79semidirect
553. #106C22×D79semidirect
555. C4⋊C8C22×D79semidirect
767. C2#23773654direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991762
C2×#190990352
#237736542
C2×#190989072
C2×#190989062
C2×#190988602
C2×#190987692
C2×#190987682
C2×#190987152
C2×#190986622
C2×#190986602
C2×#190986542
C2×#190986502
C2×#190986232
C2×#478×C792
C2×#312379