Finite Group Databasebeta

← C2×#23773954 #35157978

Subgroups — C2×#23773954 #35157978

Order 20224.

2286 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099115C211yesmaximal, characteristic, complemented
2C2×#19099108C211yesmaximal, characteristic
3#23773954C2116yesmaximal, direct product factor
4C2×#19098960C211yesmaximal, characteristic, complemented
5C2×#19098934C211yesmaximal, characteristic, complemented
6C2×#19098912C211yesmaximal, characteristic, complemented
7C2×#19098908C211yesmaximal, characteristic, complemented
8C2×#19098794C211yesmaximal, characteristic, complemented
9C2×#19098792C211yesmaximal, characteristic, complemented
10C2×#19098790C211yesmaximal, characteristic, complemented
11C2×#19098654C211yesmaximal, characteristic, complemented
12C2×SD16×Dic79C211yesmaximal, characteristic, complemented
13C2×#19098650C211yesmaximal, characteristic, complemented
14C2×#19098648C211yesmaximal, characteristic, complemented
15C22×C8×Dic79C211yesmaximal, characteristic, complemented
16C2×#465×C79C211yesmaximal, characteristic, complemented
17C22×#11929623—21no—
18C22×#11929613C2211yescharacteristic
19C22×#11929612C2211yescharacteristic
20C22×#11929611C2211yescharacteristic
21C23×C79⋊C8C2211yescharacteristic
22#19099115—24no—
23#19099115C2218yescomplemented
24#19099108—24no—
25#19099108C2218yes—
26C2×#14579160C2211yescharacteristic
27C2×#14579160C2211yescharacteristic
28C2×#14579159C2211yescharacteristic
29C2×#14579157C2211yescharacteristic
30C2×#14579151—21no—
31C2×#14579147—21no—
32C2×#14579140C2211yescharacteristic
33C2×#14579138—21no—
34C2×#14579135C2211yescharacteristic
35C2×#14579133—21no—
36C2×Q8×Dic79C2211yescharacteristic
37C2×#14579126—21no—
38C2×#14579126C2211yescharacteristic
39C2×D4×Dic79C2211yescharacteristic
40C2×#14579123C2211yescharacteristic
41C2×(C22⋊D79)⋊C4—21no—
42C2×#14579117—21no—
43C22×C4×Dic79C2211yescharacteristic
44#19098960C2218yescomplemented
45#19098934C2218yescomplemented
46#19098912C2218yescomplemented
47#19098908C2218yescomplemented
48#19098794C2218yescomplemented
49#19098792C2218yescomplemented
50#19098790C2218yescomplemented
51#19098654C2218yescomplemented
52SD16×Dic79C2218yescomplemented
53#19098650C2218yescomplemented
54#19098648C2218yescomplemented
55C2×#14579093C2211yescharacteristic
56C2×#14579092C2211yescharacteristic
57C2×#14579092C2211yescharacteristic
58C2×#14579086C2211yescharacteristic
59C2×#14579085C2211yescharacteristic
60C2×#14579084C2211yescharacteristic
61C2×#14579083C2211yescharacteristic
62C2×#14579082C2211yescharacteristic
63C2×#14579081C2211yescharacteristic
64C2×C8×Dic79C2211yescharacteristic
65C2×C8×Dic79C2211yescharacteristic
66C2×C8×Dic79C2211yescharacteristic
67C2×C8×Dic79C2211yescharacteristic
68C2×C8×Dic79C2218yescomplemented
69C22×SD16×C79C2211yescharacteristic
70C23×C8×C79C2211yescharacteristic
71C2×C22⋊Q8×C79C2211yescharacteristic
72C2×#121×C79C2211yescharacteristic
73#465×C79C2218yescomplemented
74C2×#106×C79C2211yescharacteristic
75C2×#103×C79C2211yescharacteristic
76C2×#102×C79C2211yescharacteristic
77C2×#11929623—28no—
78C2×#11929623—48no—
79C22×Dic158—21no—
80C22×Dic158—21no—
81C22×Dic158C2311yescharacteristic
82C22×D316C2311yescharacteristic
83C22×C22⋊D79—21no—
84C22×C22⋊D79—21no—
85C22×C22⋊D79—21no—
86C23×Dic79—21no—
87C23×Dic79D411yescharacteristic
88C23×Dic79D411yescharacteristic
89C22×C4×D79—21no—
90C2×#11929613—24no—
91C2×#11929613C2314yes—
92C2×#11929612—24no—
93C2×#11929612C2314yes—
94C2×#11929611—24no—
95C2×#11929611C2314yes—
96C22×C79⋊C8—24no—
97C22×C79⋊C8C2311yescharacteristic
98C22×C79⋊C8C2314yes—
99C22×C79⋊C8C2311yescharacteristic
100#14579160—22no—
101#14579160—22no—
102#14579160C2314yes—
103#14579160C2314yes—
104#14579159—22no—
105#14579159C2314yes—
106#14579157—22no—
107#14579157C2314yes—
108#14579151—28no—
109#14579147—28no—
110#14579140—22no—
111#14579140C2314yes—
112#14579138—28no—
113#14579135—22no—
114#14579135C2314yes—
115#14579133—28no—
116Q8×Dic79—22no—
117Q8×Dic79C2314yes—
118#14579126—28no—
119#14579126—22no—
120#14579126C2314yes—
121D4×Dic79—22no—
122D4×Dic79C2314yes—
123#14579123—22no—
124#14579123C2314yes—
125(C22⋊D79)⋊C4—28no—
126#14579117—28no—
127C2×C4⋊Dic79—21no—
128C2×C4⋊Dic79C2311yescharacteristic
129C2×C4⋊Dic79C2311yescharacteristic
130C2×Dic79⋊C4—21no—
131C2×Dic79⋊C4—21no—
132C2×Dic79⋊C4—21no—
133C2×Dic79⋊C4—21no—
134C2×Dic79⋊C4—21no—
135C2×Dic79⋊C4—21no—
136C2×C22⋊Dic79—21no—
137C2×C22⋊Dic79—21no—
138C2×(C2×D79)⋊C4—21no—
139C2×(C2×D79)⋊C4—21no—
140C2×C4×Dic79—21no—
141C2×C4×Dic79—21no—
142C2×C4×Dic79D411yescharacteristic
143C2×C4×Dic79D411yescharacteristic
144C2×C4×Dic79D414yes—
145C2×C4×Dic79C2311yescharacteristic
146C2×C4×Dic79C2311yescharacteristic
147C2×C4×Dic79C2314yes—
148#14579093C2314yes—
149#14579092C2314yes—
150#14579092C2314yes—
151#14579086C2314yes—
152#14579085C2314yes—
153#14579084C2314yes—
154#14579083C2314yes—
155#14579082C2314yes—
156#14579081C2314yes—
157C8×Dic79C2314yes—
158C8×Dic79C2314yes—
159C8×Dic79C2314yes—
160C8×Dic79C2314yes—
161C22×Q8×C79C2311yescharacteristic
162C22×D4×C79—21no—
163C22×D4×C79C2311yescharacteristic
164C23×C4×C79C2311yescharacteristic
165C2×SD16×C79—24no—
166C2×SD16×C79C2314yes—
167C22×C8×C79—24no—
168C22×C8×C79C2314yes—
169C22×C8×C79C2311yescharacteristic
170C22×C8×C79C2311yescharacteristic
171C22⋊Q8×C79—22no—
172C22⋊Q8×C79C2314yes—
173#121×C79—22no—
174#121×C79C2314yes—
175C2×C4⋊C4×C79—21no—
176C2×C4⋊C4×C79C2311yescharacteristic
177C2×C4⋊C4×C79C2311yescharacteristic
178C2×C22⋊C4×C79—21no—
179C2×C22⋊C4×C79—21no—
180#106×C79C2314yes—
181#103×C79C2314yes—
182#102×C79C2314yes—
183C23×D79—21no—
184#11929623—432no—
185C2×Dic158—24no—
186C2×Dic158—24no—
187C2×Dic158—21no—
188C2×Dic158—22no—
189C2×Dic158—22no—
190C2×Dic158—44no—
191C2×Dic158—44no—
192C2×Dic158C2412yes—
193C2×D316—21no—
194C2×D316—22no—
195C2×D316—22no—
196C2×D316C2412yes—
197C2×C22⋊D79—24no—
198C2×C22⋊D79—24no—
199C2×C22⋊D79—24no—
200C2×C22⋊D79—44no—
201C2×C22⋊D79—44no—
202C2×C22⋊D79—44no—
203C22×Dic79—24no—
204C22×Dic79—24no—
205C22×Dic79—21no—
206C22×Dic79—21no—
207C22×Dic79—21no—
208C22×Dic79—44no—
209C22×Dic79SD1618yescomplemented
210C22×Dic79C2×D411yescharacteristic
211C22×Dic79C2×D414yes—
212C22×Dic79C2×D411yescharacteristic
213C22×Dic79C2×D411yescharacteristic
214C22×Dic79C2×D414yes—
215C22×Dic79C2×D411yescharacteristic
216C2×C4×D79—24no—
217C2×C4×D79—44no—
218#11929613—28no—
219#11929612—28no—
220#11929611—28no—
221C2×C79⋊C8—28no—
222C2×C79⋊C8—22no—
223C2×C79⋊C8#4114yescomplemented
224C2×C79⋊C8C2412yes—
225C2×C79⋊C8C2412yes—
226C4⋊Dic79—24no—
227C4⋊Dic79—21no—
228C4⋊Dic79—21no—
229C4⋊Dic79C2412yes—
230C4⋊Dic79C2412yes—
231Dic79⋊C4—24no—
232Dic79⋊C4—24no—
233Dic79⋊C4—24no—
234Dic79⋊C4—24no—
235Dic79⋊C4—24no—
236Dic79⋊C4—24no—
237C22⋊Dic79—24no—
238C22⋊Dic79—24no—
239(C2×D79)⋊C4—24no—
240(C2×D79)⋊C4—24no—
241C4×Dic79—24no—
242C4×Dic79—24no—
243C4×Dic79C2×D414yes—
244C4×Dic79C2×D412yes—
245C4×Dic79C2×D414yes—
246C4×Dic79C2×D412yes—
247C4×Dic79C2412yes—
248C4×Dic79C2412yes—
249C24×C79—21no—
250C24×C79C2×D411yescharacteristic
251C2×Q8×C79—21no—
252C2×Q8×C79—22no—
253C2×Q8×C79—22no—
254C2×Q8×C79C2412yes—
255C2×D4×C79—24no—
256C2×D4×C79—21no—
257C2×D4×C79—22no—
258C2×D4×C79—22no—
259C2×D4×C79—44no—
260C2×D4×C79C2412yes—
261C22×C4×C79—22no—
262C22×C4×C79—22no—
263C22×C4×C79—21no—
264C22×C4×C79—21no—
265C22×C4×C79—21no—
266C22×C4×C79C2×D411yescharacteristic
267C22×C4×C79C2×D412yes—
268C22×C4×C79C2412yes—
269C22×C4×C79C2411yescharacteristic
270SD16×C79—28no—
271C2×C8×C79—28no—
272C2×C8×C79—22no—
273C2×C8×C79#4114yescomplemented
274C2×C8×C79C2412yes—
275C2×C8×C79C2412yes—
276C4⋊C4×C79—24no—
277C4⋊C4×C79—21no—
278C4⋊C4×C79—21no—
279C4⋊C4×C79C2412yes—
280C4⋊C4×C79C2412yes—
281C22⋊C4×C79—24no—
282C22⋊C4×C79—24no—
283C23×C79—22no—
284C23×C79—22no—
285C23×C79—22no—
286C23×C79—42no—
287C23×C79—42no—
288C23×C79—42no—
289C23×C79C2×SD1614yes—
290C23×C79C22×D412yes—
291C23×C79C22×D411yescharacteristic
292C22×D79—22no—
293C22×D79—42no—
294C22×D79—42no—
295C22×D79—42no—
296Q8×C79—22no—
297Q8×C79—22no—
298Q8×C79—42no—
299D4×C79—22no—
300D4×C79—22no—
301D4×C79—48no—
302D4×C79—42no—
303C2×C4×C79—22no—
304C2×C4×C79—24no—
305C2×C4×C79—22no—
306C2×C4×C79—22no—
307C2×C4×C79—22no—
308C2×C4×C79—22no—
309C2×C4×C79—22no—
310C2×C4×C79—42no—
311C2×C4×C79—42no—
312C2×C4×C79—42no—
313C2×C4×C79C22×D412yes—
314C2×C4×C79C22×D411yescharacteristic
315C2×C4×C79C2×#4112yes—
316C2×C4×C79C2×#4112yes—
317C2×C4×C79C2511yescharacteristic
318C22⋊D79—48no—
319C22⋊D79—48no—
320C22⋊D79—48no—
321C2×Dic79—22no—
322C2×Dic79—28no—
323C2×Dic79—22no—
324C2×Dic79—22no—
325C2×Dic79—22no—
326C2×Dic79—42no—
327C2×Dic79—42no—
328C2×Dic79—42no—
329C2×Dic79—48no—
330C2×Dic79C2×SD1614yes—
331C2×Dic79C2×SD1614yes—
332C2×Dic79C2×SD16116yescomplemented
333C2×Dic79#13514yes—
334C2×Dic79C22×D412yes—
335C2×Dic79C22×D412yes—
336C2×Dic79C22×D412yes—
337C2×Dic79C22×D412yes—
338D316—22no—
339D316—22no—
340D316—42no—
341C4×D79—48no—
342Dic158—22no—
343Dic158—22no—
344Dic158—42no—
345Dic158—48no—
346Dic158—48no—
347C8×C79—22no—
348C8×C79C2×#4114yescomplemented
349C79⋊C8—22no—
350C79⋊C8C2×#4114yescomplemented
351C22×C79—28no—
352C22×C79—22no—
353C22×C79—22no—
354C22×C79—42no—
355C22×C79—42no—
356C22×C79—42no—
357C22×C79—84no—
358C22×C79#53212yes—
359C22×C79C22×SD1614yes—
360C22×C79C22×SD1612yes—
361C22×C79C2×#13512yes—
362C22×C79C23×D411yescharacteristic
363C2×D79—42no—
364C2×D79—42no—
365C2×D79—42no—
366C2×D79—84no—
367C4×C79—22no—
368C4×C79—42no—
369C4×C79—42no—
370C4×C79—42no—
371C4×C79#53212yes—
372C4×C79C22×#4111yescharacteristic
373C4×C79C22×#4111yescharacteristic
374Dic79—22no—
375Dic79—42no—
376Dic79—42no—
377Dic79—42no—
378Dic79C22×SD1614yes—
379Dic79C22×SD1614yes—
380Dic79C2×#13514yes—
381C2×#3167—791nomaximal, Sylow
382C2×C79—24no—
383C2×C79—82no—
384C2×C79#316714yescomplemented
385C2×C79C2×#53211yescharacteristic
386C2×C79C23×SD1611yescharacteristic
387C2×C79C22×#13511yescharacteristic
388D79—82no—
389C2×#533—791no—
390C2×#532—791no—
391#3167—7916no—
392C2×#498—791no—
393C2×#492—791no—
394C2×#487—791no—
395C2×#486—791no—
396C2×#465—791no—
397C2×#465—791no—
398C2×#465—791no—
399C2×#465D7911yescharacteristic, complemented
400C2×C4×SD16—791no—
401C2×C4×SD16—791no—
402C2×C4×SD16—791no—
403C2×C4×SD16—791no—
404C22×C4×C8—791no—
405C79C2×#316711yescharacteristic, complemented, Sylow
406C22×#41—1581no—
407C22×SD16—791no—
408C22×SD16—791no—
409C22×SD16—791no—
410C22×SD16C2×D7911yescharacteristic
411C23×C8—791no—
412C23×C8C2×D7911yescharacteristic
413#533—798no—
414#533—1584no—
415#532—798no—
416#532—1584no—
417C2×C4⋊Q8—791no—
418C2×C4⋊Q8—791no—
419C2×C4⋊Q8—791no—
420C2×#127—791no—
421C2×#125—1581no—
422C2×#124—1581no—
423C2×C22⋊Q8—791no—
424C2×C22⋊Q8—1581no—
425C2×C22⋊Q8C2×D7911yescharacteristic
426C2×#121—791no—
427C2×#121—1581no—
428C2×#121C2×D7911yescharacteristic
429C2×C4×Q8—791no—
430C2×C4×Q8—791no—
431C2×C4×Q8—1581no—
432C2×C4×D4—791no—
433C2×C4×D4—791no—
434C2×C4×D4—1581no—
435C2×#117—1581no—
436C22×C42—791no—
437#498—798no—
438#492—798no—
439#487—798no—
440#486—798no—
441#465—798no—
442#465—798no—
443#465—798no—
444#465C2×D7918yescomplemented
445C4×SD16—798no—
446C4×SD16—798no—
447C4×SD16—798no—
448C4×SD16—798no—
449C2×#106—791no—
450C2×#106—791no—
451C2×#106—791no—
452C2×#106C2×D7911yescharacteristic
453C2×#103—791no—
454C2×#103—791no—
455C2×#103—791no—
456C2×#103C2×D7911yescharacteristic
457C2×#102—791no—
458C2×#102—791no—
459C2×#102—791no—
460C2×#102C2×D7911yescharacteristic
461C2×C4×C8—791no—
462C2×C4×C8—791no—
463C2×C4×C8—798no—
464C2×C4×C8—791no—
465C2×C4×C8—791no—
466C2×#41—3168no—
467C2×#41—1588no—
468C22×Q8—791no—
469C22×Q8—1581no—
470C22×Q8—1581no—
471C22×Q8C22×D7911yescharacteristic
472C22×D4—21no—
473C22×D4—791no—
474C22×D4—1581no—
475C22×D4—1581no—
476C22×D4—1581no—
477C22×D4C22×D7911yescharacteristic
478C23×C4—791no—
479C23×C4—791no—
480C23×C4—1581no—
481C23×C4—1581no—
482C23×C4C22×D7911yescharacteristic
483C2×SD16—24no—
484C2×SD16—794no—
485C2×SD16—794no—
486C2×SD16—794no—
487C2×SD16—1584no—
488C2×SD16—1584no—
489C2×SD16—1584no—
490C2×SD16C22×D7914yes—
491C22×C8—24no—
492C22×C8—791no—
493C22×C8—791no—
494C22×C8—794no—
495C22×C8—1584no—
496C22×C8C22×D7911yescharacteristic
497C22×C8C22×D7914yes—
498C22×C8C22×D7911yescharacteristic
499C4⋊Q8—794no—
500C4⋊Q8—794no—
501C4⋊Q8—794no—
502C4⋊Q8—1582no—
503C4⋊Q8—1582no—
504C4⋊Q8—1582no—
505#127—794no—
506#127—1582no—
507#125—1588no—
508#124—1588no—
509C22⋊Q8—22no—
510C22⋊Q8—794no—
511C22⋊Q8—1588no—
512C22⋊Q8—1582no—
513C22⋊Q8C22×D7914yes—
514#121—22no—
515#121—794no—
516#121—1588no—
517#121—1582no—
518#121C22×D7914yes—
519C4×Q8—794no—
520C4×Q8—794no—
521C4×Q8—1582no—
522C4×Q8—1588no—
523C4×Q8—1582no—
524C4×D4—794no—
525C4×D4—794no—
526C4×D4—1588no—
527C4×D4—1582no—
528C4×D4—1582no—
529#117—1588no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—791no—
532C2×C4⋊C4—791no—
533C2×C4⋊C4—1581no—
534C2×C4⋊C4—1581no—
535C2×C4⋊C4—1581no—
536C2×C4⋊C4—1581no—
537C2×C4⋊C4—1581no—
538C2×C4⋊C4—1581no—
539C2×C4⋊C4—1581no—
540C2×C4⋊C4C22×D7911yescharacteristic
541C2×C4⋊C4C22×D7911yescharacteristic
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—1581no—
545C2×C22⋊C4—1581no—
546C2×C22⋊C4—1581no—
547C2×C22⋊C4—1581no—
548C2×C42—791no—
549C2×C42—791no—
550C2×C42—794no—
551C2×C42—791no—
552C2×C42—791no—
553C2×C42—794no—
554C2×C42—1581no—
555C2×C42—1581no—
556#106—794no—
557#106—794no—
558#106—794no—
559#106C22×D7914yes—
560#103—794no—
561#103—794no—
562#103—794no—
563#103C22×D7914yes—
564#102—794no—
565#102—794no—
566#102—794no—
567#102C22×D7914yes—
568C4×C8—794no—
569C4×C8—794no—
570C4×C8—794no—
571C4×C8—794no—
572C24—21no—
573C24—1581no—
574C24D4×D7911yescharacteristic
575#41—31632no—
576C2×Q8—21no—
577C2×Q8—22no—
578C2×Q8—22no—
579C2×Q8—3164no—
580C2×Q8—3164no—
581C2×Q8—792no—
582C2×Q8—1584no—
583C2×Q8—1584no—
584C2×Q8—1582no—
585C2×Q8—1582no—
586C2×Q8—1581no—
587C2×Q8C23×D7912yes—
588C2×D4—24no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—21no—
592C2×D4—44no—
593C2×D4—3164no—
594C2×D4—3164no—
595C2×D4—3164no—
596C2×D4—792no—
597C2×D4—1584no—
598C2×D4—1584no—
599C2×D4—1584no—
600C2×D4—1582no—
601C2×D4—1582no—
602C2×D4—1581no—
603C2×D4C23×D7912yes—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—3164no—
610C22×C4—3164no—
611C22×C4—798no—
612C22×C4—794no—
613C22×C4—791no—
614C22×C4—791no—
615C22×C4—791no—
616C22×C4—794no—
617C22×C4—791no—
618C22×C4—1584no—
619C22×C4—1584no—
620C22×C4—1581no—
621C22×C4—1581no—
622C22×C4—1581no—
623C22×C4—1584no—
624C22×C4D4×D7912yes—
625C22×C4D4×D7911yescharacteristic
626C22×C4C23×D7912yes—
627C22×C4C23×D7911yescharacteristic
628SD16—28no—
629SD16—1588no—
630SD16—1588no—
631SD16—1588no—
632C2×C8—22no—
633C2×C8—28no—
634C2×C8—794no—
635C2×C8—792no—
636C2×C8—792no—
637C2×C8—1588no—
638C2×C8—1582no—
639C2×C8#1192962314yescomplemented
640C2×C8C23×D7912yes—
641C2×C8C23×D7912yes—
642C4⋊C4—24no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—792no—
646C4⋊C4—792no—
647C4⋊C4—1584no—
648C4⋊C4—1584no—
649C4⋊C4—1584no—
650C4⋊C4—1584no—
651C4⋊C4—1584no—
652C4⋊C4—1584no—
653C4⋊C4—1584no—
654C4⋊C4—1581no—
655C4⋊C4—1581no—
656C4⋊C4C23×D7912yes—
657C4⋊C4C23×D7912yes—
658C22⋊C4—24no—
659C22⋊C4—24no—
660C22⋊C4—1584no—
661C22⋊C4—1584no—
662C22⋊C4—1584no—
663C22⋊C4—1584no—
664C42—792no—
665C42—792no—
666C42—794no—
667C42—792no—
668C42—794no—
669C42—792no—
670C42—1584no—
671C42—1584no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—3162no—
679C23—3162no—
680C23—3162no—
681C23—1582no—
682C23SD16×D7914yes—
683C23C2×D4×D7912yes—
684C23C2×D4×D7911yescharacteristic
685Q8—22no—
686Q8—22no—
687Q8—42no—
688Q8—3168no—
689Q8—3168no—
690Q8—3162no—
691Q8—1582no—
692Q8—1582no—
693D4—22no—
694D4—22no—
695D4—48no—
696D4—42no—
697D4—3168no—
698D4—3168no—
699D4—3168no—
700D4—3162no—
701D4—1582no—
702D4—1582no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—3168no—
714C2×C4—3162no—
715C2×C4—3162no—
716C2×C4—3162no—
717C2×C4—3168no—
718C2×C4—794no—
719C2×C4—794no—
720C2×C4—7916no—
721C2×C4—794no—
722C2×C4—792no—
723C2×C4—792no—
724C2×C4—792no—
725C2×C4—792no—
726C2×C4—1582no—
727C2×C4—1582no—
728C2×C4—1582no—
729C2×C4—1588no—
730C2×C4—1582no—
731C2×C4C2×D4×D7912yes—
732C2×C4C2×D4×D7911yescharacteristic
733C2×C4#41×D7912yes—
734C2×C4C2×#1192962312yes—
735C2×C4C24×D7911yescharacteristic
736C8—22no—
737C8—794no—
738C8—1582no—
739C8C2×#1192962314yescomplemented
740C22—28no—
741C22—22no—
742C22—22no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—84no—
747C22—3162no—
748C22—3162no—
749C22—3162no—
750C22—6324no—
751C22#1909910812yes—
752C22C2×SD16×D7914yes—
753C22C2×SD16×D7912yes—
754C22#135×D7912yes—
755C22C22×D4×D7911yescharacteristic
756C4—22no—
757C4—42no—
758C4—42no—
759C4—42no—
760C4—3162no—
761C4—3162no—
762C4—3162no—
763C4—794no—
764C4—794no—
765C4—794no—
766C4—1582no—
767C4#1909910812yes—
768C4C2×#41×D7911yescharacteristic
769C4C22×#1192962311yescharacteristic
770C2—24no—
771C2—82no—
772C2—6322no—
773C2#2377395414yesdirect product factor
774C2C2×#1909910811yescharacteristic
775C2C22×SD16×D7911yescharacteristic
776C2C2×#135×D7911yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#465×C79C2
socleC23×C79C22×D4
prime radicalC2×#19099108C2
hypercenterC2×#465D79
hypocenterC79C2×#3167
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#19099115C2semidirect
3. #23773954C2direct (N × H)
4. C2×#19098960C2semidirect
5. C2×#19098934C2semidirect
6. C2×#19098912C2semidirect
7. C2×#19098908C2semidirect
8. C2×#19098794C2semidirect
9. C2×#19098792C2semidirect
10. C2×#19098790C2semidirect
11. C2×#19098654C2semidirect
12. C2×SD16×Dic79C2semidirect
13. C2×#19098650C2semidirect
14. C2×#19098648C2semidirect
15. C22×C8×Dic79C2semidirect
16. C2×#465×C79C2semidirect
23. #19099115C22semidirect
44. #19098960C22semidirect
45. #19098934C22semidirect
46. #19098912C22semidirect
47. #19098908C22semidirect
48. #19098794C22semidirect
49. #19098792C22semidirect
50. #19098790C22semidirect
51. #19098654C22semidirect
52. SD16×Dic79C22semidirect
53. #19098650C22semidirect
54. #19098648C22semidirect
68. C2×C8×Dic79C22semidirect
73. #465×C79C22semidirect
209. C22×Dic79SD16semidirect
223. C2×C79⋊C8#41semidirect
273. C2×C8×C79#41semidirect
332. C2×Dic79C2×SD16semidirect
348. C8×C79C2×#41semidirect
350. C79⋊C8C2×#41semidirect
384. C2×C79#3167semidirect
399. C2×#465D79semidirect
405. C79C2×#3167semidirect
444. #465C2×D79semidirect
639. C2×C8#11929623semidirect
739. C8C2×#11929623semidirect
773. C2#23773954direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991152
C2×#190991082
#237739542
C2×#190989602
C2×#190989342
C2×#190989122
C2×#190989082
C2×#190987942
C2×#190987922
C2×#190987902
C2×#190986542
C2×SD16×Dic792
C2×#190986502
C2×#190986482
C22×C8×Dic792
C2×#465×C792
C2×#316779