Finite Group Databasebeta

← C2×#23773685 #35156609

Subgroups — C2×#23773685 #35156609

Order 20224.

2122 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099166C211yesmaximal, characteristic
2C2×#19099041C211yesmaximal, characteristic, complemented
3#23773685C2116yesmaximal, direct product factor
4C2×#19098888C211yesmaximal, characteristic, complemented
5C2×#19098884C211yesmaximal, characteristic, complemented
6C2×#19098872C211yesmaximal, characteristic, complemented
7C2×#19098868C211yesmaximal, characteristic, complemented
8C2×#19098761C211yesmaximal, characteristic, complemented
9C2×#19098761C211yesmaximal, characteristic, complemented
10C2×#19098702C211yesmaximal, characteristic, complemented
11C2×#19098666C211yesmaximal, characteristic, complemented
12C2×#19098664C211yesmaximal, characteristic, complemented
13C2×SD16×Dic79C211yesmaximal, characteristic, complemented
14C2×#19098648C211yesmaximal, characteristic, complemented
15C2×#19098621C211yesmaximal, characteristic, complemented
16C2×#448×C79C211yesmaximal, characteristic, complemented
17C22×#11929611C2211yescharacteristic
18C22×#11929611C2211yescharacteristic
19#19099166—24no—
20#19099166C2218yes—
21C2×#14579157C2211yescharacteristic
22C2×#14579152C2211yescharacteristic
23C2×#14579145—21no—
24C2×#14579143—21no—
25C2×#14579135C2211yescharacteristic
26C2×#14579133—21no—
27C2×#14579132—21no—
28#19099041—24no—
29#19099041C2218yescomplemented
30C2×Q8×Dic79—21no—
31C2×Q8×Dic79—21no—
32C2×Q8×Dic79C2211yescharacteristic
33C2×Q8×Dic79C2211yescharacteristic
34C2×Q8×Dic79C2211yescharacteristic
35C2×Q8×Dic79C2211yescharacteristic
36C2×D4×Dic79C2211yescharacteristic
37C2×#14579123C2211yescharacteristic
38C2×#14579120—21no—
39C2×#14579120—21no—
40C2×#14579120C2211yescharacteristic
41C2×#14579120C2211yescharacteristic
42#19098888C2218yescomplemented
43#19098884C2218yescomplemented
44#19098872C2218yescomplemented
45#19098868C2218yescomplemented
46#19098761C2218yescomplemented
47#19098761C2218yescomplemented
48#19098702C2218yescomplemented
49#19098666C2218yescomplemented
50#19098664C2218yescomplemented
51SD16×Dic79C2218yescomplemented
52#19098648C2218yescomplemented
53#19098621C2218yescomplemented
54C2×#14579095C2211yescharacteristic
55C2×#14579094C2211yescharacteristic
56C2×#14579093C2211yescharacteristic
57C2×#14579092C2211yescharacteristic
58C2×Dic79⋊C8C2211yescharacteristic
59C2×Dic79⋊C8C2211yescharacteristic
60C2×#14579085C2211yescharacteristic
61C2×#14579085C2211yescharacteristic
62C2×#14579083C2211yescharacteristic
63C2×#14579083C2211yescharacteristic
64C2×#14579082C2211yescharacteristic
65C2×#14579082C2211yescharacteristic
66C2×C22⋊(C79⋊C8)C2211yescharacteristic
67C2×#14579071C2211yescharacteristic
68C2×C8×Dic79C2211yescharacteristic
69C23×Q8×C79C2211yescharacteristic
70C22×SD16×C79C2211yescharacteristic
71C22×SD16×C79C2211yescharacteristic
72C2×#121×C79C2211yescharacteristic
73#448×C79C2218yescomplemented
74C2×#103×C79C2211yescharacteristic
75C2×#103×C79C2211yescharacteristic
76C2×C22⋊C8×C79C2211yescharacteristic
77C22×D316C2311yescharacteristic
78C22×C22⋊D79—21no—
79C22×C22⋊D79—21no—
80C22×C22⋊D79—21no—
81C23×Dic79—21no—
82C22×C4×D79—21no—
83C2×#11929611—24no—
84C2×#11929611—24no—
85C2×#11929611C2314yes—
86C2×#11929611C2314yes—
87C22×C79⋊C8C2311yescharacteristic
88C22×C79⋊C8C2311yescharacteristic
89#14579157—22no—
90#14579157C2314yes—
91#14579152—22no—
92#14579152C2314yes—
93#14579145—28no—
94#14579143—28no—
95#14579135—22no—
96#14579135C2314yes—
97#14579133—28no—
98#14579132—28no—
99Q8×Dic79—28no—
100Q8×Dic79—28no—
101Q8×Dic79—22no—
102Q8×Dic79—22no—
103Q8×Dic79—22no—
104Q8×Dic79—22no—
105Q8×Dic79C2314yes—
106Q8×Dic79C2314yes—
107Q8×Dic79C2314yes—
108Q8×Dic79C2314yes—
109D4×Dic79—22no—
110D4×Dic79C2314yes—
111#14579123—22no—
112#14579123C2314yes—
113#14579120—22no—
114#14579120—28no—
115#14579120—28no—
116#14579120D414yes—
117#14579120C2314yes—
118#14579120C2314yes—
119C2×C4⋊Dic79—21no—
120C2×C4⋊Dic79—21no—
121C2×C4⋊Dic79—21no—
122C2×C4⋊Dic79—21no—
123C2×C4⋊Dic79—21no—
124C2×C4⋊Dic79D411yescharacteristic
125C2×C4⋊Dic79D411yescharacteristic
126C2×C4⋊Dic79C2311yescharacteristic
127C2×C4⋊Dic79C2311yescharacteristic
128C2×C4⋊Dic79C2311yescharacteristic
129C2×Dic79⋊C4—21no—
130C2×C22⋊Dic79—21no—
131C2×C22⋊Dic79—21no—
132C2×C22⋊Dic79D411yescharacteristic
133C2×C22⋊Dic79D411yescharacteristic
134C2×(C2×D79)⋊C4—21no—
135C2×(C2×D79)⋊C4—21no—
136C2×C4×Dic79—21no—
137C2×C4×Dic79—21no—
138C2×C4×Dic79—21no—
139C2×C4×Dic79—21no—
140C2×C4×Dic79—21no—
141C2×C4×Dic79C2311yescharacteristic
142C2×C4×Dic79C2311yescharacteristic
143#14579095C2314yes—
144#14579094C2314yes—
145#14579093C2314yes—
146#14579092C2314yes—
147Dic79⋊C8C2314yes—
148Dic79⋊C8C2314yes—
149#14579085C2314yes—
150#14579085C2314yes—
151#14579083C2314yes—
152#14579083C2314yes—
153#14579082C2314yes—
154#14579082C2314yes—
155C22⋊(C79⋊C8)C2314yes—
156#14579071C2314yes—
157C8×Dic79C2314yes—
158C22×Q8×C79—24no—
159C22×Q8×C79—24no—
160C22×Q8×C79—21no—
161C22×Q8×C79—22no—
162C22×Q8×C79C2314yes—
163C22×Q8×C79C2311yescharacteristic
164C22×Q8×C79C2311yescharacteristic
165C22×D4×C79—21no—
166C22×D4×C79C2311yescharacteristic
167C23×C4×C79—21no—
168C23×C4×C79C2311yescharacteristic
169C2×SD16×C79—24no—
170C2×SD16×C79—24no—
171C2×SD16×C79C2314yes—
172C2×SD16×C79C2314yes—
173C22×C8×C79C2311yescharacteristic
174C22×C8×C79C2311yescharacteristic
175#121×C79—22no—
176#121×C79C2314yes—
177C2×C4⋊C4×C79C2311yescharacteristic
178C2×C22⋊C4×C79—21no—
179#103×C79C2314yes—
180#103×C79C2314yes—
181C22⋊C8×C79C2314yes—
182C23×D79—21no—
183C2×D316—21no—
184C2×D316—22no—
185C2×D316—22no—
186C2×D316C2412yes—
187C2×C22⋊D79—24no—
188C2×C22⋊D79—24no—
189C2×C22⋊D79—24no—
190C2×C22⋊D79—82no—
191C2×C22⋊D79—82no—
192C2×C22⋊D79—82no—
193C22×Dic79—24no—
194C22×Dic79—21no—
195C22×Dic79—21no—
196C22×Dic79—21no—
197C22×Dic79—82no—
198C22×Dic79C2×D411yescharacteristic
199C22×Dic79C2×D411yescharacteristic
200C22×Dic79C2×D411yescharacteristic
201C22×Dic79C2×D411yescharacteristic
202C2×C4×D79—24no—
203C2×C4×D79—82no—
204#11929611—28no—
205#11929611—28no—
206C2×C79⋊C8—22no—
207C2×C79⋊C8—22no—
208C2×C79⋊C8C2412yes—
209C2×C79⋊C8C2412yes—
210C4⋊Dic79—24no—
211C4⋊Dic79—24no—
212C4⋊Dic79—24no—
213C4⋊Dic79—24no—
214C4⋊Dic79—24no—
215C4⋊Dic79—21no—
216C4⋊Dic79—21no—
217C4⋊Dic79—21no—
218C4⋊Dic79C2×D414yes—
219C4⋊Dic79C2×D414yes—
220C4⋊Dic79C2412yes—
221C4⋊Dic79C2412yes—
222C4⋊Dic79C2412yes—
223Dic79⋊C4—24no—
224C22⋊Dic79—24no—
225C22⋊Dic79—24no—
226C22⋊Dic79C2×D414yes—
227C22⋊Dic79C2×D414yes—
228(C2×D79)⋊C4—24no—
229(C2×D79)⋊C4—24no—
230C4×Dic79—24no—
231C4×Dic79—24no—
232C4×Dic79—24no—
233C4×Dic79—24no—
234C4×Dic79—24no—
235C4×Dic79C2×D412yes—
236C4×Dic79C2×D412yes—
237C4×Dic79C2412yes—
238C4×Dic79C2412yes—
239C24×C79—21no—
240C24×C79C2×D411yescharacteristic
241C2×Q8×C79—216no—
242C2×Q8×C79—28no—
243C2×Q8×C79—28no—
244C2×Q8×C79—28no—
245C2×Q8×C79—24no—
246C2×Q8×C79—21no—
247C2×Q8×C79—21no—
248C2×Q8×C79—22no—
249C2×Q8×C79—22no—
250C2×Q8×C79#4114yes—
251C2×Q8×C79#4114yes—
252C2×Q8×C79C2412yes—
253C2×Q8×C79C2412yes—
254C2×D4×C79—24no—
255C2×D4×C79—21no—
256C2×D4×C79—22no—
257C2×D4×C79—22no—
258C2×D4×C79—82no—
259C2×D4×C79C2412yes—
260C22×C4×C79—28no—
261C22×C4×C79—21no—
262C22×C4×C79—21no—
263C22×C4×C79—24no—
264C22×C4×C79—22no—
265C22×C4×C79—22no—
266C22×C4×C79—21no—
267C22×C4×C79C2×D411yescharacteristic
268C22×C4×C79C2×D412yes—
269C22×C4×C79C2412yes—
270C22×C4×C79C2411yescharacteristic
271SD16×C79—28no—
272SD16×C79—28no—
273C2×C8×C79—22no—
274C2×C8×C79—22no—
275C2×C8×C79C2412yes—
276C2×C8×C79C2412yes—
277C4⋊C4×C79—21no—
278C4⋊C4×C79C2412yes—
279C22⋊C4×C79—24no—
280C23×C79—22no—
281C23×C79—22no—
282C23×C79—22no—
283C23×C79—22no—
284C23×C79—42no—
285C23×C79—42no—
286C23×C79—42no—
287C23×C79C22×D412yes—
288C23×C79C22×D411yescharacteristic
289C22×D79—22no—
290C22×D79—42no—
291C22×D79—42no—
292C22×D79—42no—
293Q8×C79—216no—
294Q8×C79—24no—
295Q8×C79—24no—
296Q8×C79—22no—
297Q8×C79—22no—
298Q8×C79C2×#4114yes—
299Q8×C79C2×#4114yes—
300D4×C79—22no—
301D4×C79—22no—
302D4×C79—42no—
303D4×C79—84no—
304C2×C4×C79—216no—
305C2×C4×C79—24no—
306C2×C4×C79—24no—
307C2×C4×C79—22no—
308C2×C4×C79—22no—
309C2×C4×C79—22no—
310C2×C4×C79—24no—
311C2×C4×C79—22no—
312C2×C4×C79—22no—
313C2×C4×C79—22no—
314C2×C4×C79—42no—
315C2×C4×C79C22×D412yes—
316C2×C4×C79C22×D411yescharacteristic
317C2×C4×C79C2×#4112yes—
318C2×C4×C79C2×#4112yes—
319C2×C4×C79C2511yescharacteristic
320C22⋊D79—84no—
321C22⋊D79—84no—
322C22⋊D79—84no—
323C2×Dic79—22no—
324C2×Dic79—22no—
325C2×Dic79—22no—
326C2×Dic79—22no—
327C2×Dic79—22no—
328C2×Dic79—22no—
329C2×Dic79—22no—
330C2×Dic79—42no—
331C2×Dic79—42no—
332C2×Dic79—42no—
333C2×Dic79—84no—
334C2×Dic79C22×D412yes—
335C2×Dic79C22×D412yes—
336C2×Dic79C22×D412yes—
337C2×Dic79C22×D412yes—
338D316—22no—
339D316—22no—
340D316—42no—
341C4×D79—84no—
342C8×C79—22no—
343C8×C79—22no—
344C79⋊C8—22no—
345C79⋊C8—22no—
346C22×C79—22no—
347C22×C79—22no—
348C22×C79—22no—
349C22×C79—44no—
350C22×C79—42no—
351C22×C79—42no—
352C22×C79—42no—
353C22×C79—84no—
354C22×C79#52512yes—
355C22×C79#57712yes—
356C22×C79#57712yes—
357C22×C79C23×D411yescharacteristic
358C2×D79—42no—
359C2×D79—42no—
360C2×D79—42no—
361C2×D79—84no—
362C4×C79—24no—
363C4×C79—24no—
364C4×C79—22no—
365C4×C79—42no—
366C4×C79#52512yes—
367C4×C79C22×#4111yescharacteristic
368C4×C79C22×#4111yescharacteristic
369Dic79—22no—
370Dic79—22no—
371Dic79—22no—
372Dic79—22no—
373Dic79—42no—
374Dic79—42no—
375Dic79—42no—
376C2×#3126—791nomaximal, Sylow
377C2×C79—42no—
378C2×C79—82no—
379C2×C79#312614yescomplemented
380C2×C79C2×#52511yescharacteristic
381C2×C79C2×#57711yescharacteristic
382C2×C79C2×#57711yescharacteristic
383D79—82no—
384C2×#540—791no—
385C2×#519—791no—
386#3126—7916no—
387C2×#482—791no—
388C2×#482—791no—
389C2×#479—791no—
390C2×#479—791no—
391C2×#460—791no—
392C2×#460—791no—
393C2×#448—791no—
394C2×#448D7911yescharacteristic, complemented
395C2×#440—791no—
396C2×#440—791no—
397C2×C4×SD16—791no—
398C2×C4×SD16—791no—
399C2×#433—791no—
400C79C2×#312611yescharacteristic, complemented, Sylow
401C23×Q8C2×D7911yescharacteristic
402C22×SD16—791no—
403C22×SD16—791no—
404C22×SD16C2×D7911yescharacteristic
405C22×SD16C2×D7911yescharacteristic
406#540—798no—
407#540—1584no—
408C2×#127—791no—
409C2×#125—791no—
410C2×#123—1581no—
411C2×#123—1581no—
412C2×#121—791no—
413C2×#121—1581no—
414C2×#121—1581no—
415C2×#121C2×D7911yescharacteristic
416#519—798no—
417#519—1584no—
418C2×C4×Q8—791no—
419C2×C4×Q8—791no—
420C2×C4×Q8—791no—
421C2×C4×Q8—791no—
422C2×C4×Q8—1581no—
423C2×C4×Q8—1581no—
424C2×C4×D4—791no—
425C2×C4×D4—791no—
426C2×#117—791no—
427C2×#117—791no—
428C2×#117—1581no—
429C2×#117—1581no—
430#482—798no—
431#482—798no—
432#479—798no—
433#479—798no—
434#460—798no—
435#460—798no—
436#448—798no—
437#448C2×D7918yescomplemented
438#440—798no—
439#440—798no—
440C4×SD16—798no—
441C4×SD16—798no—
442#433—798no—
443C2×#107—791no—
444C2×#107—791no—
445C2×#106—791no—
446C2×#106—791no—
447C2×C4⋊C8—791no—
448C2×C4⋊C8—791no—
449C2×#103—791no—
450C2×#103—791no—
451C2×#103C2×D7911yescharacteristic
452C2×#103C2×D7911yescharacteristic
453C2×#102—791no—
454C2×#102—791no—
455C2×#102—791no—
456C2×#102—791no—
457C2×C22⋊C8—791no—
458C2×C22⋊C8C2×D7911yescharacteristic
459C2×#97—791no—
460C2×C4×C8—791no—
461C22×Q8—24no—
462C22×Q8—24no—
463C22×Q8—21no—
464C22×Q8—22no—
465C22×Q8C22×D7914yes—
466C22×Q8C22×D7911yescharacteristic
467C22×Q8C22×D7911yescharacteristic
468C22×D4—21no—
469C22×D4—791no—
470C22×D4—1581no—
471C22×D4—1581no—
472C22×D4—1581no—
473C22×D4C22×D7911yescharacteristic
474C23×C4—21no—
475C23×C4—1581no—
476C23×C4—1581no—
477C23×C4C22×D7911yescharacteristic
478C2×SD16—24no—
479C2×SD16—24no—
480C2×SD16—794no—
481C2×SD16—794no—
482C2×SD16—1584no—
483C2×SD16—1584no—
484C2×SD16C22×D7914yes—
485C2×SD16C22×D7914yes—
486C22×C8—791no—
487C22×C8—791no—
488C22×C8C22×D7911yescharacteristic
489C22×C8C22×D7911yescharacteristic
490#127—794no—
491#127—1582no—
492#125—794no—
493#125—1582no—
494#123—1588no—
495#123—1588no—
496#121—22no—
497#121—794no—
498#121—1588no—
499#121—1588no—
500#121—1582no—
501#121C22×D7914yes—
502C4×Q8—794no—
503C4×Q8—794no—
504C4×Q8—794no—
505C4×Q8—794no—
506C4×Q8—1582no—
507C4×Q8—1582no—
508C4×Q8—1582no—
509C4×Q8—1582no—
510C4×Q8—1588no—
511C4×Q8—1588no—
512C4×D4—794no—
513C4×D4—794no—
514C4×D4—1582no—
515C4×D4—1582no—
516#117—794no—
517#117—794no—
518#117—794no—
519#117—1588no—
520#117—1588no—
521#117—1582no—
522C2×C4⋊C4—791no—
523C2×C4⋊C4—791no—
524C2×C4⋊C4—791no—
525C2×C4⋊C4—791no—
526C2×C4⋊C4—791no—
527C2×C4⋊C4—1581no—
528C2×C4⋊C4—1581no—
529C2×C4⋊C4—1581no—
530C2×C4⋊C4—1581no—
531C2×C4⋊C4—1581no—
532C2×C4⋊C4—1581no—
533C2×C4⋊C4C22×D7911yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—791no—
536C2×C22⋊C4—791no—
537C2×C22⋊C4—1581no—
538C2×C22⋊C4—1581no—
539C2×C22⋊C4—1581no—
540C2×C22⋊C4—1581no—
541C2×C42—791no—
542C2×C42—791no—
543C2×C42—1581no—
544C2×C42—1581no—
545C2×C42—1581no—
546C2×C42—1581no—
547C2×C42—1581no—
548#107—794no—
549#107—794no—
550#106—794no—
551#106—794no—
552C4⋊C8—794no—
553C4⋊C8—794no—
554#103—794no—
555#103—794no—
556#103C22×D7914yes—
557#103C22×D7914yes—
558#102—794no—
559#102—794no—
560#102—794no—
561#102—794no—
562C22⋊C8—794no—
563C22⋊C8C22×D7914yes—
564#97—794no—
565C4×C8—794no—
566C24—21no—
567C24—1581no—
568C24D4×D7911yescharacteristic
569C2×Q8—216no—
570C2×Q8—28no—
571C2×Q8—28no—
572C2×Q8—28no—
573C2×Q8—22no—
574C2×Q8—22no—
575C2×Q8—24no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8#1192962314yes—
579C2×Q8#1192962314yes—
580C2×Q8C23×D7912yes—
581C2×Q8C23×D7912yes—
582C2×D4—24no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—21no—
586C2×D4—82no—
587C2×D4—792no—
588C2×D4—6322no—
589C2×D4—6322no—
590C2×D4—6322no—
591C2×D4—1584no—
592C2×D4—1584no—
593C2×D4—1584no—
594C2×D4—1582no—
595C2×D4—1582no—
596C2×D4—1581no—
597C2×D4C23×D7912yes—
598C22×C4—28no—
599C22×C4—24no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—21no—
605C22×C4—791no—
606C22×C4—791no—
607C22×C4—791no—
608C22×C4—791no—
609C22×C4—6322no—
610C22×C4—6322no—
611C22×C4—1584no—
612C22×C4—1581no—
613C22×C4—1581no—
614C22×C4—1581no—
615C22×C4—1584no—
616C22×C4D4×D7912yes—
617C22×C4D4×D7911yescharacteristic
618C22×C4C23×D7912yes—
619C22×C4C23×D7911yescharacteristic
620SD16—28no—
621SD16—28no—
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—21no—
633C4⋊C4—794no—
634C4⋊C4—794no—
635C4⋊C4—792no—
636C4⋊C4—792no—
637C4⋊C4—792no—
638C4⋊C4—1584no—
639C4⋊C4—1584no—
640C4⋊C4—1584no—
641C4⋊C4—1584no—
642C4⋊C4—1584no—
643C4⋊C4—1584no—
644C4⋊C4—1581no—
645C4⋊C4—1581no—
646C4⋊C4—1581no—
647C4⋊C4C23×D7912yes—
648C22⋊C4—24no—
649C22⋊C4—794no—
650C22⋊C4—794no—
651C22⋊C4—1584no—
652C22⋊C4—1584no—
653C22⋊C4—1584no—
654C22⋊C4—1584no—
655C42—792no—
656C42—792no—
657C42—792no—
658C42—792no—
659C42—1584no—
660C42—1584no—
661C42—1584no—
662C42—1584no—
663C42—1584no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—3162no—
672C23—3162no—
673C23—3162no—
674C23—1582no—
675C23C2×D4×D7912yes—
676C23C2×D4×D7911yescharacteristic
677Q8—216no—
678Q8—24no—
679Q8—24no—
680Q8—22no—
681Q8—22no—
682Q8C2×#1192962314yes—
683Q8C2×#1192962314yes—
684D4—22no—
685D4—22no—
686D4—42no—
687D4—84no—
688D4—3162no—
689D4—6324no—
690D4—6324no—
691D4—6324no—
692D4—1582no—
693D4—1582no—
694C2×C4—216no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—42no—
705C2×C4—3162no—
706C2×C4—3162no—
707C2×C4—3162no—
708C2×C4—792no—
709C2×C4—792no—
710C2×C4—792no—
711C2×C4—792no—
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—1582no—
721C2×C4C2×D4×D7912yes—
722C2×C4C2×D4×D7911yescharacteristic
723C2×C4C2×#1192962312yes—
724C2×C4C2×#1192962312yes—
725C2×C4C24×D7911yescharacteristic
726C8—22no—
727C8—22no—
728C8—1582no—
729C8—1582no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—84no—
738C22—3162no—
739C22—3162no—
740C22—3162no—
741C22—6324no—
742C22#1909906912yes—
743C22#1909936912yes—
744C22#1909937212yes—
745C22C22×D4×D7911yescharacteristic
746C4—24no—
747C4—24no—
748C4—22no—
749C4—42no—
750C4—3162no—
751C4—3162no—
752C4—3162no—
753C4—1582no—
754C4—1582no—
755C4—1582no—
756C4—1582no—
757C4#1909906912yes—
758C4C22×#1192962311yescharacteristic
759C4C22×#1192962311yescharacteristic
760C2—42no—
761C2—82no—
762C2—6322no—
763C2#2377368514yesdirect product factor
764C2C2×#1909906911yescharacteristic
765C2C2×#1909936911yescharacteristic
766C2C2×#1909937211yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#448×C79C2
socleC23×C79C22×D4
prime radicalC2×#19099166C2
hypercenterC2×#448D79
hypocenterC79C2×#3126
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
2. C2×#19099041C2semidirect
3. #23773685C2direct (N × H)
4. C2×#19098888C2semidirect
5. C2×#19098884C2semidirect
6. C2×#19098872C2semidirect
7. C2×#19098868C2semidirect
8. C2×#19098761C2semidirect
9. C2×#19098761C2semidirect
10. C2×#19098702C2semidirect
11. C2×#19098666C2semidirect
12. C2×#19098664C2semidirect
13. C2×SD16×Dic79C2semidirect
14. C2×#19098648C2semidirect
15. C2×#19098621C2semidirect
16. C2×#448×C79C2semidirect
29. #19099041C22semidirect
42. #19098888C22semidirect
43. #19098884C22semidirect
44. #19098872C22semidirect
45. #19098868C22semidirect
46. #19098761C22semidirect
47. #19098761C22semidirect
48. #19098702C22semidirect
49. #19098666C22semidirect
50. #19098664C22semidirect
51. SD16×Dic79C22semidirect
52. #19098648C22semidirect
53. #19098621C22semidirect
73. #448×C79C22semidirect
379. C2×C79#3126semidirect
394. C2×#448D79semidirect
400. C79C2×#3126semidirect
437. #448C2×D79semidirect
763. C2#23773685direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991662
C2×#190990412
#237736852
C2×#190988882
C2×#190988842
C2×#190988722
C2×#190988682
C2×#190987612
C2×#190987022
C2×#190986662
C2×#190986642
C2×SD16×Dic792
C2×#190986482
C2×#190986212
C2×#448×C792
C2×#312679