Finite Group Databasebeta

← C2×#23774857 #35161230

Subgroups — C2×#23774857 #35161230

Order 20224.

1882 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099186C211yesmaximal, characteristic, complemented
2C2×#19099180C211yesmaximal, characteristic, complemented
3#23774857C2116yesmaximal, direct product factor
4C2×#19098857C211yesmaximal, characteristic, complemented
5C2×#19098856C211yesmaximal, characteristic, complemented
6C2×#19098842C211yesmaximal, characteristic, complemented
7C2×#19098841C211yesmaximal, characteristic, complemented
8C2×#19098809C211yesmaximal, characteristic, complemented
9C2×#19098802C211yesmaximal, characteristic, complemented
10C2×#19098797C211yesmaximal, characteristic
11C2×#19098788C211yesmaximal, characteristic, complemented
12C2×#19098783C211yesmaximal, characteristic, complemented
13C2×#19098780C211yesmaximal, characteristic, complemented
14C2×#19098777C211yesmaximal, characteristic, complemented
15C2×#19098591C211yesmaximal, characteristic, complemented
16C2×#468×C79C211yesmaximal, characteristic, complemented
17C22×#11929614C2211yescharacteristic
18C22×#11929613C2211yescharacteristic
19C22×#11929609C2211yescharacteristic
20C23×C79⋊C8C2211yescharacteristic
21#19099186—24no—
22#19099186C2218yescomplemented
23#19099180—24no—
24#19099180C2218yescomplemented
25C2×#14579160C2211yescharacteristic
26C2×#14579160C2211yescharacteristic
27C2×#14579156—21no—
28C2×#14579154—21no—
29C2×#14579150C2211yescharacteristic
30C2×#14579148—21no—
31C2×#14579148C2211yescharacteristic
32C2×#14579147—21no—
33C2×#14579143—21no—
34C2×#14579142—21no—
35C2×#14579141—21no—
36C2×#14579140C2211yescharacteristic
37C2×#14579138—21no—
38C2×#14579135C2211yescharacteristic
39C2×Q8×Dic79C2211yescharacteristic
40C2×#14579126C2211yescharacteristic
41C2×D4×Dic79C2211yescharacteristic
42C2×#14579123C2211yescharacteristic
43C2×#14579120C2211yescharacteristic
44#19098857C2218yescomplemented
45#19098856C2218yescomplemented
46#19098842C2218yescomplemented
47#19098841C2218yescomplemented
48#19098809C2218yescomplemented
49#19098802C2218yescomplemented
50#19098797C2218yes—
51#19098788C2218yescomplemented
52#19098783C2218yescomplemented
53#19098780C2218yescomplemented
54#19098777C2218yescomplemented
55C2×#14579095C2211yescharacteristic
56C2×#14579094C2211yescharacteristic
57C2×#14579094C2211yescharacteristic
58#19098591C2218yescomplemented
59C2×Dic79⋊C8C2211yescharacteristic
60C2×Dic79⋊C8C2211yescharacteristic
61C2×Dic79⋊C8C2211yescharacteristic
62C2×Dic79⋊C8C2211yescharacteristic
63C2×#14579086C2211yescharacteristic
64C2×#14579085C2211yescharacteristic
65C2×#14579084C2211yescharacteristic
66C2×#14579083C2211yescharacteristic
67C2×#14579082C2211yescharacteristic
68C2×#14579081C2211yescharacteristic
69C22×SD16×C79C2211yescharacteristic
70C22×M16×C79C2211yescharacteristic
71C2×C22⋊Q8×C79C2211yescharacteristic
72C2×#121×C79C2211yescharacteristic
73#468×C79C2218yescomplemented
74C2×#107×C79C2211yescharacteristic
75C2×#103×C79C2211yescharacteristic
76C2×#102×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×Dic158—21no—
79C22×Dic158C2311yescharacteristic
80C22×D316C2311yescharacteristic
81C22×C22⋊D79—21no—
82C23×Dic79—21no—
83C22×C4×D79—21no—
84C2×#11929614—42no—
85C2×#11929614C2314yes—
86C2×#11929613—42no—
87C2×#11929613C2314yes—
88C2×#11929609—42no—
89C2×#11929609C2314yes—
90C22×C79⋊C8—42no—
91C22×C79⋊C8C2311yescharacteristic
92C22×C79⋊C8C2311yescharacteristic
93C22×C79⋊C8C2314yes—
94#14579160—22no—
95#14579160—22no—
96#14579160C2314yes—
97#14579160C2314yes—
98#14579156—28no—
99#14579154—28no—
100#14579150—22no—
101#14579150C2314yes—
102#14579148—28no—
103#14579148—22no—
104#14579148C2314yes—
105#14579147—28no—
106#14579143—28no—
107#14579142—28no—
108#14579141—28no—
109#14579140—22no—
110#14579140C2314yes—
111#14579138—28no—
112#14579135—22no—
113#14579135C2314yes—
114Q8×Dic79—22no—
115Q8×Dic79C2314yes—
116#14579126—22no—
117#14579126C2314yes—
118D4×Dic79—22no—
119D4×Dic79C2314yes—
120#14579123—22no—
121#14579123C2314yes—
122#14579120D414yes—
123#14579120C2314yes—
124C2×C4⋊Dic79—21no—
125C2×C4⋊Dic79D411yescharacteristic
126C2×C4⋊Dic79D411yescharacteristic
127C2×C4⋊Dic79C2311yescharacteristic
128C2×C4⋊Dic79C2311yescharacteristic
129C2×Dic79⋊C4—21no—
130C2×Dic79⋊C4—21no—
131C2×Dic79⋊C4—21no—
132C2×Dic79⋊C4—21no—
133C2×C22⋊Dic79—21no—
134C2×C22⋊Dic79—21no—
135C2×C22⋊Dic79—21no—
136C2×C22⋊Dic79—21no—
137C2×C22⋊Dic79D411yescharacteristic
138C2×C22⋊Dic79D411yescharacteristic
139C2×(C2×D79)⋊C4—21no—
140C2×(C2×D79)⋊C4—21no—
141C2×(C2×D79)⋊C4—21no—
142C2×(C2×D79)⋊C4—21no—
143C2×C4×Dic79—21no—
144C2×C4×Dic79—21no—
145C2×C4×Dic79C2311yescharacteristic
146C2×C4×Dic79C2311yescharacteristic
147#14579095C2314yes—
148#14579094C2314yes—
149#14579094C2314yes—
150Dic79⋊C8C2314yes—
151Dic79⋊C8C2314yes—
152Dic79⋊C8C2314yes—
153Dic79⋊C8C2314yes—
154#14579086C2314yes—
155#14579085C2314yes—
156#14579084C2314yes—
157#14579083C2314yes—
158#14579082C2314yes—
159#14579081C2314yes—
160C22×Q8×C79C2311yescharacteristic
161C22×D4×C79—21no—
162C22×D4×C79C2311yescharacteristic
163C23×C4×C79C2311yescharacteristic
164C2×SD16×C79—42no—
165C2×SD16×C79C2314yes—
166C2×M16×C79—42no—
167C2×M16×C79C2314yes—
168C22×C8×C79C2311yescharacteristic
169C22×C8×C79C2311yescharacteristic
170C22⋊Q8×C79—22no—
171C22⋊Q8×C79C2314yes—
172#121×C79—22no—
173#121×C79C2314yes—
174C2×C4⋊C4×C79—21no—
175C2×C4⋊C4×C79C2311yescharacteristic
176C2×C4⋊C4×C79C2311yescharacteristic
177C2×C22⋊C4×C79—21no—
178C2×C22⋊C4×C79—21no—
179#107×C79C2314yes—
180#103×C79C2314yes—
181#102×C79C2314yes—
182C23×D79—21no—
183C2×Dic158—24no—
184C2×Dic158—24no—
185C2×Dic158—21no—
186C2×Dic158—22no—
187C2×Dic158—22no—
188C2×Dic158—82no—
189C2×Dic158—82no—
190C2×Dic158C2412yes—
191C2×D316—21no—
192C2×D316—22no—
193C2×D316—22no—
194C2×D316C2412yes—
195C2×C22⋊D79—24no—
196C2×C22⋊D79—82no—
197C22×Dic79—24no—
198C22×Dic79—21no—
199C22×Dic79—21no—
200C22×Dic79—21no—
201C22×Dic79—82no—
202C22×Dic79C2×D411yescharacteristic
203C22×Dic79C2×D411yescharacteristic
204C22×Dic79C2×D411yescharacteristic
205C22×Dic79C2×D411yescharacteristic
206C2×C4×D79—24no—
207C2×C4×D79—82no—
208#11929614—44no—
209#11929613—44no—
210#11929609—44no—
211C2×C79⋊C8—22no—
212C2×C79⋊C8—22no—
213C2×C79⋊C8—44no—
214C2×C79⋊C8C2412yes—
215C2×C79⋊C8C2412yes—
216C4⋊Dic79—24no—
217C4⋊Dic79—21no—
218C4⋊Dic79—21no—
219C4⋊Dic79C2×D414yes—
220C4⋊Dic79C2×D414yes—
221C4⋊Dic79C2412yes—
222C4⋊Dic79C2412yes—
223Dic79⋊C4—24no—
224Dic79⋊C4—24no—
225Dic79⋊C4—24no—
226Dic79⋊C4—24no—
227C22⋊Dic79—24no—
228C22⋊Dic79—24no—
229C22⋊Dic79—24no—
230C22⋊Dic79—24no—
231C22⋊Dic79C2×D414yes—
232C22⋊Dic79C2×D414yes—
233(C2×D79)⋊C4—24no—
234(C2×D79)⋊C4—24no—
235(C2×D79)⋊C4—24no—
236(C2×D79)⋊C4—24no—
237C4×Dic79—24no—
238C4×Dic79—24no—
239C4×Dic79C2×D412yes—
240C4×Dic79C2×D412yes—
241C4×Dic79C2412yes—
242C4×Dic79C2412yes—
243C24×C79—21no—
244C24×C79C2×D411yescharacteristic
245C2×Q8×C79—21no—
246C2×Q8×C79—22no—
247C2×Q8×C79—22no—
248C2×Q8×C79C2412yes—
249C2×D4×C79—24no—
250C2×D4×C79—21no—
251C2×D4×C79—22no—
252C2×D4×C79—22no—
253C2×D4×C79—82no—
254C2×D4×C79C2412yes—
255C22×C4×C79—22no—
256C22×C4×C79—22no—
257C22×C4×C79—21no—
258C22×C4×C79—21no—
259C22×C4×C79—21no—
260C22×C4×C79C2×D411yescharacteristic
261C22×C4×C79C2×D412yes—
262C22×C4×C79C2412yes—
263C22×C4×C79C2411yescharacteristic
264SD16×C79—44no—
265M16×C79—44no—
266C2×C8×C79—22no—
267C2×C8×C79—22no—
268C2×C8×C79C2412yes—
269C2×C8×C79C2412yes—
270C4⋊C4×C79—24no—
271C4⋊C4×C79—21no—
272C4⋊C4×C79—21no—
273C4⋊C4×C79C2412yes—
274C4⋊C4×C79C2412yes—
275C22⋊C4×C79—24no—
276C22⋊C4×C79—24no—
277C23×C79—22no—
278C23×C79—22no—
279C23×C79—22no—
280C23×C79—22no—
281C23×C79—42no—
282C23×C79—42no—
283C23×C79—42no—
284C23×C79C22×D412yes—
285C23×C79C22×D411yescharacteristic
286C22×D79—22no—
287C22×D79—42no—
288C22×D79—42no—
289C22×D79—42no—
290Q8×C79—22no—
291Q8×C79—22no—
292Q8×C79—42no—
293D4×C79—22no—
294D4×C79—22no—
295D4×C79—42no—
296D4×C79—84no—
297C2×C4×C79—22no—
298C2×C4×C79—24no—
299C2×C4×C79—22no—
300C2×C4×C79—22no—
301C2×C4×C79—22no—
302C2×C4×C79—22no—
303C2×C4×C79—22no—
304C2×C4×C79—42no—
305C2×C4×C79—42no—
306C2×C4×C79—42no—
307C2×C4×C79C22×D412yes—
308C2×C4×C79C22×D411yescharacteristic
309C2×C4×C79H(5,𝔽2)12yes—
310C2×C4×C792−1+412yes—
311C2×C4×C79C2511yescharacteristic
312C22⋊D79—84no—
313C2×Dic79—22no—
314C2×Dic79—22no—
315C2×Dic79—22no—
316C2×Dic79—22no—
317C2×Dic79—22no—
318C2×Dic79—22no—
319C2×Dic79—22no—
320C2×Dic79—42no—
321C2×Dic79—42no—
322C2×Dic79—42no—
323C2×Dic79—84no—
324C2×Dic79C22×D412yes—
325C2×Dic79C22×D412yes—
326C2×Dic79C22×D412yes—
327C2×Dic79C22×D412yes—
328D316—22no—
329D316—22no—
330D316—42no—
331C4×D79—84no—
332Dic158—22no—
333Dic158—22no—
334Dic158—42no—
335Dic158—84no—
336Dic158—84no—
337C8×C79—22no—
338C8×C79—22no—
339C79⋊C8—22no—
340C79⋊C8—22no—
341C22×C79—22no—
342C22×C79—22no—
343C22×C79—22no—
344C22×C79—44no—
345C22×C79—42no—
346C22×C79—42no—
347C22×C79—42no—
348C22×C79—84no—
349C22×C79#53712yes—
350C22×C79#57612yes—
351C22×C79#57812yes—
352C22×C79C23×D411yescharacteristic
353C2×D79—42no—
354C2×D79—42no—
355C2×D79—42no—
356C2×D79—84no—
357C4×C79—22no—
358C4×C79—42no—
359C4×C79—42no—
360C4×C79—42no—
361C4×C79#53712yes—
362C4×C79C2×H(5,𝔽2)11yescharacteristic
363C4×C79C2×2−1+411yescharacteristic
364Dic79—22no—
365Dic79—22no—
366Dic79—22no—
367Dic79—22no—
368Dic79—42no—
369Dic79—42no—
370Dic79—42no—
371C2×#3262—791nomaximal, Sylow
372C2×C79—42no—
373C2×C79—82no—
374C2×C79#326214yescomplemented
375C2×C79C2×#53711yescharacteristic
376C2×C79C2×#57611yescharacteristic
377C2×C79C2×#57811yescharacteristic
378D79—82no—
379C2×#542—791no—
380C2×#542—791no—
381#3262—7916no—
382C2×#477—791no—
383C2×#477—791no—
384C2×#474—791no—
385C2×#474—791no—
386C2×#468—791no—
387C2×#468D7911yescharacteristic, complemented
388C2×#467—791no—
389C2×#466—791no—
390C2×#464—791no—
391C2×#464—791no—
392C2×#463—791no—
393C2×#463—791no—
394C2×#424—791no—
395C79C2×#326211yescharacteristic, complemented, Sylow
396C22×Q16—791no—
397C22×SD16—791no—
398C22×SD16C2×D7911yescharacteristic
399C22×D8—791no—
400C22×M16C2×D7911yescharacteristic
401C23×C8—791no—
402#542—798no—
403#542—798no—
404#542—1584no—
405#542—1584no—
406C2×C4⋊Q8—791no—
407C2×C4⋊Q8—791no—
408C2×#126—1581no—
409C2×#126—1581no—
410C2×#124—791no—
411C2×#124—791no—
412C2×#124—1581no—
413C2×#124—1581no—
414C2×#123—1581no—
415C2×#123—1581no—
416C2×C22⋊Q8—791no—
417C2×C22⋊Q8—1581no—
418C2×C22⋊Q8—1581no—
419C2×C22⋊Q8C2×D7911yescharacteristic
420C2×#121—791no—
421C2×#121C2×D7911yescharacteristic
422C2×C4×Q8—791no—
423C2×C4×Q8—791no—
424C2×C4×D4—791no—
425C2×C4×D4—791no—
426C2×#117—791no—
427#477—798no—
428#477—798no—
429#474—798no—
430#474—798no—
431#468—798no—
432#468C2×D7918yescomplemented
433#467—798no—
434#466—798no—
435#464—798no—
436#464—798no—
437#463—798no—
438#463—798no—
439C2×#107—791no—
440C2×#107—791no—
441C2×#107—791no—
442C2×#107C2×D7911yescharacteristic
443#424—798no—
444C2×C4⋊C8—791no—
445C2×C4⋊C8—791no—
446C2×C4⋊C8—791no—
447C2×C4⋊C8—791no—
448C2×#103—791no—
449C2×#103—791no—
450C2×#103—791no—
451C2×#103C2×D7911yescharacteristic
452C2×#102—791no—
453C2×#102—791no—
454C2×#102—791no—
455C2×#102C2×D7911yescharacteristic
456C22×Q8—791no—
457C22×Q8—1581no—
458C22×Q8—1581no—
459C22×Q8C22×D7911yescharacteristic
460C22×D4—21no—
461C22×D4—791no—
462C22×D4—1581no—
463C22×D4C22×D7911yescharacteristic
464C23×C4—1581no—
465C23×C4—1581no—
466C23×C4C22×D7911yescharacteristic
467C2×Q16—3162no—
468C2×Q16—794no—
469C2×SD16—42no—
470C2×SD16—3162no—
471C2×SD16—794no—
472C2×SD16C22×D7914yes—
473C2×D8—3162no—
474C2×D8—794no—
475C2×M16—42no—
476C2×M16C22×D7914yes—
477C22×C8—3162no—
478C22×C8—794no—
479C22×C8—791no—
480C22×C8—791no—
481C22×C8C22×D7911yescharacteristic
482C22×C8C22×D7911yescharacteristic
483C4⋊Q8—794no—
484C4⋊Q8—794no—
485C4⋊Q8—1582no—
486C4⋊Q8—1582no—
487#126—1588no—
488#126—1588no—
489#124—794no—
490#124—794no—
491#124—1582no—
492#124—1582no—
493#124—1588no—
494#124—1588no—
495#123—1588no—
496#123—1588no—
497C22⋊Q8—22no—
498C22⋊Q8—794no—
499C22⋊Q8—1588no—
500C22⋊Q8—1588no—
501C22⋊Q8—1582no—
502C22⋊Q8C22×D7914yes—
503#121—22no—
504#121—794no—
505#121—1582no—
506#121C22×D7914yes—
507C4×Q8—794no—
508C4×Q8—794no—
509C4×Q8—1582no—
510C4×Q8—1582no—
511C4×D4—794no—
512C4×D4—794no—
513C4×D4—1582no—
514C4×D4—1582no—
515#117—794no—
516#117—794no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—791no—
519C2×C4⋊C4—791no—
520C2×C4⋊C4—791no—
521C2×C4⋊C4—791no—
522C2×C4⋊C4—1581no—
523C2×C4⋊C4—1581no—
524C2×C4⋊C4—1581no—
525C2×C4⋊C4—1581no—
526C2×C4⋊C4—1581no—
527C2×C4⋊C4C22×D7911yescharacteristic
528C2×C4⋊C4C22×D7911yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—791no—
532C2×C22⋊C4—791no—
533C2×C22⋊C4—1581no—
534C2×C22⋊C4—1581no—
535C2×C22⋊C4—1581no—
536C2×C22⋊C4—1581no—
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—
545#107—794no—
546#107—794no—
547#107—794no—
548#107C22×D7914yes—
549C4⋊C8—794no—
550C4⋊C8—794no—
551C4⋊C8—794no—
552C4⋊C8—794no—
553#103—794no—
554#103—794no—
555#103—794no—
556#103C22×D7914yes—
557#102—794no—
558#102—794no—
559#102—794no—
560#102C22×D7914yes—
561C24—21no—
562C24—1581no—
563C24D4×D7911yescharacteristic
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—792no—
568C2×Q8—6322no—
569C2×Q8—6322no—
570C2×Q8—1584no—
571C2×Q8—1584no—
572C2×Q8—1582no—
573C2×Q8—1582no—
574C2×Q8—1581no—
575C2×Q8C23×D7912yes—
576C2×D4—24no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—21no—
580C2×D4—82no—
581C2×D4—792no—
582C2×D4—6322no—
583C2×D4—1584no—
584C2×D4—1582no—
585C2×D4—1582no—
586C2×D4—1581no—
587C2×D4C23×D7912yes—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—791no—
594C22×C4—791no—
595C22×C4—791no—
596C22×C4—791no—
597C22×C4—6322no—
598C22×C4—6322no—
599C22×C4—1584no—
600C22×C4—1581no—
601C22×C4—1581no—
602C22×C4—1581no—
603C22×C4—1584no—
604C22×C4D4×D7912yes—
605C22×C4D4×D7911yescharacteristic
606C22×C4C23×D7912yes—
607C22×C4C23×D7911yescharacteristic
608Q16—3164no—
609SD16—44no—
610SD16—3164no—
611D8—3164no—
612M16—44no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—3164no—
616C2×C8—792no—
617C2×C8—792no—
618C2×C8—1582no—
619C2×C8—1582no—
620C2×C8C23×D7912yes—
621C2×C8C23×D7912yes—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—794no—
626C4⋊C4—794no—
627C4⋊C4—792no—
628C4⋊C4—792no—
629C4⋊C4—1584no—
630C4⋊C4—1584no—
631C4⋊C4—1584no—
632C4⋊C4—1584no—
633C4⋊C4—1584no—
634C4⋊C4—1581no—
635C4⋊C4—1581no—
636C4⋊C4C23×D7912yes—
637C4⋊C4C23×D7912yes—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—794no—
641C22⋊C4—794no—
642C22⋊C4—1584no—
643C22⋊C4—1584no—
644C22⋊C4—1584no—
645C22⋊C4—1584no—
646C22⋊C4—1584no—
647C22⋊C4—1584no—
648C22⋊C4—1584no—
649C22⋊C4—1584no—
650C42—792no—
651C42—792no—
652C42—792no—
653C42—792no—
654C42—1584no—
655C42—1584no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—3162no—
664C23—3162no—
665C23—3162no—
666C23—1582no—
667C23C2×D4×D7912yes—
668C23C2×D4×D7911yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—3162no—
673Q8—6324no—
674Q8—6324no—
675Q8—1582no—
676Q8—1582no—
677D4—22no—
678D4—22no—
679D4—42no—
680D4—84no—
681D4—3162no—
682D4—6324no—
683D4—1582no—
684D4—1582no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—24no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—3162no—
696C2×C4—3162no—
697C2×C4—3162no—
698C2×C4—792no—
699C2×C4—792no—
700C2×C4—792no—
701C2×C4—792no—
702C2×C4—6324no—
703C2×C4—6324no—
704C2×C4—1582no—
705C2×C4—1582no—
706C2×C4—1582no—
707C2×C4—1582no—
708C2×C4—1582no—
709C2×C4—1582no—
710C2×C4—1582no—
711C2×C4C2×D4×D7912yes—
712C2×C4C2×D4×D7911yescharacteristic
713C2×C4#1457920612yes—
714C2×C4#1457920812yes—
715C2×C4C24×D7911yescharacteristic
716C8—22no—
717C8—22no—
718C8—1582no—
719C8—1582no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—44no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—84no—
728C22—3162no—
729C22—3162no—
730C22—3162no—
731C22—6324no—
732C22#1909914012yes—
733C22#1909936712yes—
734C22#1909937912yes—
735C22C22×D4×D7911yescharacteristic
736C4—22no—
737C4—42no—
738C4—42no—
739C4—42no—
740C4—3162no—
741C4—3162no—
742C4—3162no—
743C4—1582no—
744C4—1582no—
745C4—1582no—
746C4—1582no—
747C4#1909914012yes—
748C4C2×#1457920611yescharacteristic
749C4C2×#1457920811yescharacteristic
750C2—42no—
751C2—82no—
752C2—6322no—
753C2#2377485714yesdirect product factor
754C2C2×#1909914011yescharacteristic
755C2C2×#1909936711yescharacteristic
756C2C2×#1909937911yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#468×C79C2
socleC23×C79C22×D4
prime radicalC2×#19098797C2
hypercenterC2×#468D79
hypocenterC79C2×#3262
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#19099186C2semidirect
2. C2×#19099180C2semidirect
3. #23774857C2direct (N × H)
4. C2×#19098857C2semidirect
5. C2×#19098856C2semidirect
6. C2×#19098842C2semidirect
7. C2×#19098841C2semidirect
8. C2×#19098809C2semidirect
9. C2×#19098802C2semidirect
11. C2×#19098788C2semidirect
12. C2×#19098783C2semidirect
13. C2×#19098780C2semidirect
14. C2×#19098777C2semidirect
15. C2×#19098591C2semidirect
16. C2×#468×C79C2semidirect
22. #19099186C22semidirect
24. #19099180C22semidirect
44. #19098857C22semidirect
45. #19098856C22semidirect
46. #19098842C22semidirect
47. #19098841C22semidirect
48. #19098809C22semidirect
49. #19098802C22semidirect
51. #19098788C22semidirect
52. #19098783C22semidirect
53. #19098780C22semidirect
54. #19098777C22semidirect
58. #19098591C22semidirect
73. #468×C79C22semidirect
374. C2×C79#3262semidirect
387. C2×#468D79semidirect
395. C79C2×#3262semidirect
432. #468C2×D79semidirect
753. C2#23774857direct (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×#190991802
#237748572
C2×#190988572
C2×#190988562
C2×#190988422
C2×#190988412
C2×#190988092
C2×#190988022
C2×#190987972
C2×#190987882
C2×#190987832
C2×#190987802
C2×#190987772
C2×#190985912
C2×#468×C792
C2×#326279