Finite Group Databasebeta

← C2×#23775786 #35166723

Subgroups — C2×#23775786 #35166723

Order 20224.

1930 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099263C211yesmaximal, characteristic
2C2×#19099251C211yesmaximal, characteristic, complemented
3#23775786C2116yesmaximal, direct product factor
4C2×#19098962C211yesmaximal, characteristic, complemented
5C2×#19098900C211yesmaximal, characteristic, complemented
6C2×#19098907C211yesmaximal, characteristic, complemented
7C2×#19098886C211yesmaximal, characteristic, complemented
8C2×#19098875C211yesmaximal, characteristic, complemented
9C2×#19098871C211yesmaximal, characteristic, complemented
10C2×#19098791C211yesmaximal, characteristic, complemented
11C2×#19098791C211yesmaximal, characteristic, complemented
12C2×C4×#11929612C211yesmaximal, characteristic, complemented
13C2×#19098628C211yesmaximal, characteristic, complemented
14C2×#19098600C211yesmaximal, characteristic, complemented
15C2×#106×D79C211yesmaximal, characteristic, complemented
16C2×#478×C79C211yesmaximal, characteristic, complemented
17C22×#11929612C2211yescharacteristic
18C22×C8×D79C2211yescharacteristic
19C22×C8×D79C2211yescharacteristic
20#19099263—24no—
21#19099263C2218yes—
22#19099251—24no—
23#19099251C2218yescomplemented
24C2×#14579156—21no—
25C2×#14579154—21no—
26C2×#14579153C2211yescharacteristic
27C2×#14579152—21no—
28C2×#14579146—21no—
29C2×#14579144—21no—
30C2×#14579141C2211yescharacteristic
31C2×#14579141C2211yescharacteristic
32C2×#14579134—21no—
33C2×#14579132C2211yescharacteristic
34C2×#14579132C2211yescharacteristic
35C2×C4×Dic158C2211yescharacteristic
36C2×C4×D316C2211yescharacteristic
37C2×C4×C22⋊D79—21no—
38C2×#14579119—21no—
39C2×#14579119C2211yescharacteristic
40C2×#14579119C2211yescharacteristic
41C2×C4⋊C4×D79C2211yescharacteristic
42C2×C4⋊C4×D79C2211yescharacteristic
43#19098962C2218yescomplemented
44#19098907C2218yescomplemented
45#19098900C2218yescomplemented
46#19098886C2218yescomplemented
47#19098875C2218yescomplemented
48#19098871C2218yescomplemented
49#19098791C2218yescomplemented
50#19098791C2218yescomplemented
51C4×#11929612C2218yescomplemented
52#19098628C2218yescomplemented
53#19098600C2218yescomplemented
54C2×#14579095C2211yescharacteristic
55C2×#14579094C2211yescharacteristic
56C2×#14579094C2211yescharacteristic
57C2×#14579093C2211yescharacteristic
58C2×#14579092C2211yescharacteristic
59C2×#14579092C2211yescharacteristic
60C2×#14579092C2211yescharacteristic
61#106×D79C2218yescomplemented
62C2×#14579086C2211yescharacteristic
63C2×#14579086C2211yescharacteristic
64C2×#14579084C2211yescharacteristic
65C2×#14579082C2211yescharacteristic
66C2×(C2×D79)⋊C8C2211yescharacteristic
67C2×(C2×D79)⋊C8C2211yescharacteristic
68C2×C4×C79⋊C8C2211yescharacteristic
69C2×#125×C79C2211yescharacteristic
70C2×C4×D4×C79C2211yescharacteristic
71#478×C79C2218yescomplemented
72C2×#107×C79C2211yescharacteristic
73C2×#106×C79C2211yescharacteristic
74C2×C4⋊C8×C79C2211yescharacteristic
75C2×#102×C79C2211yescharacteristic
76C2×#102×C79C2211yescharacteristic
77C22×Dic158C2311yescharacteristic
78C22×D316D411yescharacteristic
79C22×C22⋊D79—21no—
80C22×C22⋊D79—21no—
81C22×C4×D79—21no—
82C22×C4×D79—21no—
83C22×C4×D79C2311yescharacteristic
84C22×C4×D79C2311yescharacteristic
85C2×#11929612—24no—
86C2×#11929612C2314yes—
87C22×C79⋊C8C2311yescharacteristic
88C22×C79⋊C8C2311yescharacteristic
89C2×C8×D79—24no—
90C2×C8×D79—24no—
91C2×C8×D79C2314yes—
92C2×C8×D79C2314yes—
93#14579156—28no—
94#14579154—28no—
95#14579153—22no—
96#14579153C2314yes—
97#14579152—28no—
98#14579146—28no—
99#14579144—28no—
100#14579141—22no—
101#14579141—22no—
102#14579141C2314yes—
103#14579141C2314yes—
104#14579134—28no—
105#14579132—22no—
106#14579132—22no—
107#14579132C2314yes—
108#14579132C2314yes—
109C4×Dic158—22no—
110C4×Dic158C2314yes—
111C4×D316D414yes—
112C4×D316C2314yes—
113C4×C22⋊D79—28no—
114#14579119—22no—
115#14579119—22no—
116#14579119—28no—
117#14579119C2314yes—
118#14579119C2314yes—
119C2×C4⋊Dic79—21no—
120C2×C4⋊Dic79—21no—
121C2×C4⋊Dic79D411yescharacteristic
122C2×C4⋊Dic79C2311yescharacteristic
123C2×C4⋊Dic79C2311yescharacteristic
124C2×C4⋊Dic79C2311yescharacteristic
125C2×Dic79⋊C4—21no—
126C2×Dic79⋊C4—21no—
127C2×Dic79⋊C4—21no—
128C2×Dic79⋊C4—21no—
129C2×Dic79⋊C4—21no—
130C4⋊C4×D79—22no—
131C4⋊C4×D79—22no—
132C4⋊C4×D79C2314yes—
133C4⋊C4×D79C2314yes—
134C2×C22⋊Dic79—21no—
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)⋊C4D411yescharacteristic
141C2×(C2×D79)⋊C4D411yescharacteristic
142C2×C4×Dic79—21no—
143C2×C4×Dic79—21no—
144C2×C4×Dic79—21no—
145#14579095C2314yes—
146#14579094C2314yes—
147#14579094C2314yes—
148#14579093C2314yes—
149#14579092C2314yes—
150#14579092C2314yes—
151#14579092C2314yes—
152#14579086C2314yes—
153#14579086C2314yes—
154#14579084C2314yes—
155#14579082C2314yes—
156(C2×D79)⋊C8C2314yes—
157(C2×D79)⋊C8C2314yes—
158C4×C79⋊C8C2314yes—
159C22×D4×C79C2311yescharacteristic
160C23×C4×C79—21no—
161C22×C8×C79C2311yescharacteristic
162C22×C8×C79C2311yescharacteristic
163#125×C79—22no—
164#125×C79C2314yes—
165C4×D4×C79—22no—
166C4×D4×C79C2314yes—
167C2×C4⋊C4×C79—21no—
168C2×C4⋊C4×C79—21no—
169C2×C4⋊C4×C79C2311yescharacteristic
170C2×C4⋊C4×C79C2311yescharacteristic
171C2×C4⋊C4×C79C2311yescharacteristic
172C2×C22⋊C4×C79—21no—
173C2×C42×C79C2311yescharacteristic
174#107×C79C2314yes—
175#106×C79C2314yes—
176C4⋊C8×C79C2314yes—
177#102×C79C2314yes—
178#102×C79C2314yes—
179C23×D79C2×D411yescharacteristic
180C23×D79C2×D411yescharacteristic
181C2×Dic158—21no—
182C2×Dic158—22no—
183C2×Dic158—22no—
184C2×Dic158C2412yes—
185C2×D316—24no—
186C2×D316C2×D414yes—
187C2×C22⋊D79—24no—
188C2×C22⋊D79—24no—
189C2×C22⋊D79—44no—
190C2×C22⋊D79—82no—
191C22×Dic79—21no—
192C22×Dic79—21no—
193C22×Dic79—21no—
194C22×Dic79—21no—
195C22×Dic79C2×D411yescharacteristic
196C22×Dic79C2×D411yescharacteristic
197C2×C4×D79—24no—
198C2×C4×D79—24no—
199C2×C4×D79—22no—
200C2×C4×D79—22no—
201C2×C4×D79—22no—
202C2×C4×D79—22no—
203C2×C4×D79—44no—
204C2×C4×D79—82no—
205C2×C4×D79C2×D412yes—
206C2×C4×D79C2×D412yes—
207C2×C4×D79C2412yes—
208C2×C4×D79C2412yes—
209#11929612—28no—
210C2×C79⋊C8—22no—
211C2×C79⋊C8#4114yes—
212C2×C79⋊C8C2412yes—
213C2×C79⋊C8C2412yes—
214C8×D79—28no—
215C8×D79—28no—
216C4⋊Dic79—24no—
217C4⋊Dic79—24no—
218C4⋊Dic79—21no—
219C4⋊Dic79—21no—
220C4⋊Dic79—21no—
221C4⋊Dic79C2×D414yes—
222C4⋊Dic79C2412yes—
223C4⋊Dic79C2412yes—
224C4⋊Dic79C2412yes—
225Dic79⋊C4—24no—
226Dic79⋊C4—24no—
227Dic79⋊C4—24no—
228Dic79⋊C4—24no—
229Dic79⋊C4—24no—
230C22⋊Dic79—24no—
231C22⋊Dic79—24no—
232(C2×D79)⋊C4—24no—
233(C2×D79)⋊C4—24no—
234(C2×D79)⋊C4—24no—
235(C2×D79)⋊C4—24no—
236(C2×D79)⋊C4C2×D414yes—
237(C2×D79)⋊C4C2×D414yes—
238C4×Dic79—24no—
239C4×Dic79—24no—
240C4×Dic79—24no—
241C24×C79—21no—
242C2×D4×C79—21no—
243C2×D4×C79—22no—
244C2×D4×C79—22no—
245C2×D4×C79C2412yes—
246C22×C4×C79—21no—
247C22×C4×C79—21no—
248C22×C4×C79—21no—
249C22×C4×C79—24no—
250C22×C4×C79—82no—
251C22×C4×C79C2×D411yescharacteristic
252C22×C4×C79C2×D411yescharacteristic
253C22×C4×C79C2411yescharacteristic
254C2×C8×C79—22no—
255C2×C8×C79—22no—
256C2×C8×C79C2412yes—
257C2×C8×C79C2412yes—
258C4⋊C4×C79—24no—
259C4⋊C4×C79—24no—
260C4⋊C4×C79—21no—
261C4⋊C4×C79—21no—
262C4⋊C4×C79—21no—
263C4⋊C4×C79C2412yes—
264C4⋊C4×C79C2412yes—
265C4⋊C4×C79C2412yes—
266C22⋊C4×C79—24no—
267C42×C79C2×D412yes—
268C42×C79C2412yes—
269C23×C79—22no—
270C23×C79—42no—
271C23×C79—42no—
272C23×C79—42no—
273C23×C79C22×D411yescharacteristic
274C22×D79—22no—
275C22×D79—22no—
276C22×D79—22no—
277C22×D79—22no—
278C22×D79—22no—
279C22×D79#13514yes—
280C22×D79C22×D412yes—
281C22×D79C22×D412yes—
282D4×C79—22no—
283D4×C79—22no—
284D4×C79—42no—
285C2×C4×C79—22no—
286C2×C4×C79—22no—
287C2×C4×C79—22no—
288C2×C4×C79—22no—
289C2×C4×C79—22no—
290C2×C4×C79—42no—
291C2×C4×C79—42no—
292C2×C4×C79—42no—
293C2×C4×C79—84no—
294C2×C4×C79C22×D412yes—
295C2×C4×C79C22×D412yes—
296C2×C4×C79C22×D411yescharacteristic
297C2×C4×C79C2×#4112yes—
298C2×C4×C792−1+412yes—
299C2×C4×C79C2511yescharacteristic
300C22⋊D79—48no—
301C22⋊D79—84no—
302C2×Dic79—22no—
303C2×Dic79—22no—
304C2×Dic79—22no—
305C2×Dic79—22no—
306C2×Dic79—22no—
307C2×Dic79—22no—
308C2×Dic79—42no—
309C2×Dic79—42no—
310C2×Dic79—42no—
311C2×Dic79—42no—
312C2×Dic79C22×D412yes—
313C2×Dic79C22×D412yes—
314D316—28no—
315C4×D79—24no—
316C4×D79—24no—
317C4×D79—22no—
318C4×D79—22no—
319C4×D79—22no—
320C4×D79—22no—
321C4×D79—48no—
322C4×D79—84no—
323Dic158—22no—
324Dic158—22no—
325Dic158—42no—
326C8×C79—22no—
327C8×C79—22no—
328C79⋊C8—22no—
329C79⋊C8C2×#4114yes—
330C22×C79—42no—
331C22×C79—42no—
332C22×C79—42no—
333C22×C79—84no—
334C22×C79#54712yes—
335C22×C79C2×#13512yes—
336C22×C79#57712yes—
337C22×C79C23×D411yescharacteristic
338C2×D79—28no—
339C2×D79—22no—
340C2×D79—22no—
341C2×D79—22no—
342C2×D79—22no—
343C2×D79—22no—
344C2×D79—44no—
345C2×D79C2×#13514yes—
346C4×C79—22no—
347C4×C79—22no—
348C4×C79—42no—
349C4×C79—42no—
350C4×C79—42no—
351C4×C79#54712yes—
352C4×C79C22×#4111yescharacteristic
353C4×C79C2×2−1+411yescharacteristic
354Dic79—22no—
355Dic79—22no—
356Dic79—42no—
357Dic79—42no—
358Dic79—42no—
359Dic79—42no—
360C2×#3337—791nomaximal, Sylow
361C2×C79—82no—
362C2×C79#333714yescomplemented
363C2×C79C2×#54711yescharacteristic
364C2×C79C22×#13511yescharacteristic
365C2×C79C2×#57711yescharacteristic
366D79—24no—
367D79—42no—
368C2×#553—791no—
369C2×#552—791no—
370#3337—7916no—
371C2×#499—791no—
372C2×#484—791no—
373C2×#485—791no—
374C2×#482—791no—
375C2×#480—791no—
376C2×#479—791no—
377C2×#478D7911yescharacteristic, complemented
378C2×#465—791no—
379C2×#465—791no—
380C2×C4×SD16—791no—
381C2×C8×D4—791no—
382C2×#427—791no—
383C22×#106—791no—
384C79C2×#333711yescharacteristic, complemented, Sylow
385C22×SD16—791no—
386C23×C8—791no—
387C23×C8—791no—
388#553—798no—
389#553—1584no—
390#552—798no—
391#552—1584no—
392C2×#126—1581no—
393C2×#126—1581no—
394C2×#125—791no—
395C2×#125—1581no—
396C2×#125C2×D7911yescharacteristic
397C2×#123—1581no—
398C2×#123—1581no—
399C2×C22⋊Q8—791no—
400C2×C22⋊Q8—791no—
401C2×#121—791no—
402C2×#121—791no—
403C2×#121—1581no—
404C2×C4×Q8—791no—
405C2×C4×D4—791no—
406C2×C4×D4—1581no—
407C2×C4×D4C2×D7911yescharacteristic
408C2×#117—791no—
409C2×#117—791no—
410C2×#117—1581no—
411C22×C4⋊C4—791no—
412C22×C4⋊C4—791no—
413#499—798no—
414#485—798no—
415#484—798no—
416#482—798no—
417#480—798no—
418#479—798no—
419#478C2×D7918yescomplemented
420#465—798no—
421#465—798no—
422C4×SD16—798no—
423C8×D4—798no—
424#427—798no—
425C2×#107—791no—
426C2×#107—791no—
427C2×#107—791no—
428C2×#107C2×D7911yescharacteristic
429C2×#106—791no—
430C2×#106—791no—
431C2×#106—791no—
432C2×#106—791no—
433C2×#106—798no—
434C2×#106C2×D7911yescharacteristic
435C2×C4⋊C8C2×D7911yescharacteristic
436C2×#103—791no—
437C2×#103—791no—
438C2×#103—791no—
439C2×#102—791no—
440C2×#102C2×D7911yescharacteristic
441C2×#102C2×D7911yescharacteristic
442C2×C22⋊C8—791no—
443C2×C22⋊C8—791no—
444C2×C4×C8—791no—
445C22×Q8—791no—
446C22×D4—791no—
447C22×D4—1581no—
448C22×D4—1581no—
449C22×D4C22×D7911yescharacteristic
450C23×C4—21no—
451C23×C4—791no—
452C23×C4—791no—
453C23×C4—1581no—
454C23×C4—1581no—
455C2×SD16—794no—
456C2×SD16—1584no—
457C22×C8—791no—
458C22×C8—791no—
459C22×C8—794no—
460C22×C8—794no—
461C22×C8—1584no—
462C22×C8—1584no—
463C22×C8C22×D7911yescharacteristic
464C22×C8C22×D7911yescharacteristic
465#126—1588no—
466#126—1588no—
467#125—22no—
468#125—794no—
469#125—1588no—
470#125—1582no—
471#125C22×D7914yes—
472#123—1588no—
473#123—1588no—
474C22⋊Q8—794no—
475C22⋊Q8—794no—
476C22⋊Q8—1582no—
477C22⋊Q8—1582no—
478#121—794no—
479#121—794no—
480#121—1588no—
481#121—1582no—
482#121—1582no—
483C4×Q8—794no—
484C4×Q8—1582no—
485C4×D4—22no—
486C4×D4—794no—
487C4×D4—794no—
488C4×D4—1588no—
489C4×D4C22×D7914yes—
490#117—794no—
491#117—794no—
492#117—1588no—
493#117—1582no—
494#117—1582no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—791no—
498C2×C4⋊C4—791no—
499C2×C4⋊C4—791no—
500C2×C4⋊C4—791no—
501C2×C4⋊C4—794no—
502C2×C4⋊C4—794no—
503C2×C4⋊C4—1582no—
504C2×C4⋊C4—1582no—
505C2×C4⋊C4—1581no—
506C2×C4⋊C4—1581no—
507C2×C4⋊C4—1581no—
508C2×C4⋊C4—1581no—
509C2×C4⋊C4—1581no—
510C2×C4⋊C4—1581no—
511C2×C4⋊C4—1581no—
512C2×C4⋊C4C22×D7911yescharacteristic
513C2×C4⋊C4C22×D7911yescharacteristic
514C2×C4⋊C4C22×D7911yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—791no—
517C2×C22⋊C4—791no—
518C2×C22⋊C4—1581no—
519C2×C22⋊C4—1581no—
520C2×C22⋊C4—1581no—
521C2×C22⋊C4—1581no—
522C2×C22⋊C4—1581no—
523C2×C22⋊C4—1581no—
524C2×C42—1581no—
525C2×C42—1581no—
526C2×C42—1581no—
527C2×C42C22×D7911yescharacteristic
528#107—794no—
529#107—794no—
530#107—794no—
531#107C22×D7914yes—
532#106—794no—
533#106—794no—
534#106—794no—
535#106—794no—
536#106C22×D7914yes—
537C4⋊C8C22×D7914yes—
538#103—794no—
539#103—794no—
540#103—794no—
541#102—794no—
542#102C22×D7914yes—
543#102C22×D7914yes—
544C22⋊C8—794no—
545C22⋊C8—794no—
546C4×C8—794no—
547C24—21no—
548C24—791no—
549C24—791no—
550C2×Q8—792no—
551C2×Q8—1582no—
552C2×Q8—1582no—
553C2×Q8—1581no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—21no—
557C2×D4—3164no—
558C2×D4—794no—
559C2×D4—6322no—
560C2×D4—1584no—
561C2×D4—1584no—
562C2×D4—1584no—
563C2×D4C23×D7912yes—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—24no—
568C22×C4—82no—
569C22×C4—3164no—
570C22×C4—791no—
571C22×C4—791no—
572C22×C4—792no—
573C22×C4—792no—
574C22×C4—792no—
575C22×C4—792no—
576C22×C4—6322no—
577C22×C4—1584no—
578C22×C4—1584no—
579C22×C4—1581no—
580C22×C4—1581no—
581C22×C4—1581no—
582C22×C4—1581no—
583C22×C4—1582no—
584C22×C4—1582no—
585C22×C4—1582no—
586C22×C4—1582no—
587C22×C4D4×D7911yescharacteristic
588C22×C4D4×D7911yescharacteristic
589C22×C4C23×D7911yescharacteristic
590SD16—1588no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—794no—
594C2×C8—792no—
595C2×C8—792no—
596C2×C8—1588no—
597C2×C8—1588no—
598C2×C8—1582no—
599C2×C8C23×D7912yes—
600C2×C8C23×D7912yes—
601C4⋊C4—24no—
602C4⋊C4—24no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—794no—
607C4⋊C4—792no—
608C4⋊C4—792no—
609C4⋊C4—792no—
610C4⋊C4—1584no—
611C4⋊C4—1584no—
612C4⋊C4—1584no—
613C4⋊C4—1584no—
614C4⋊C4—1584no—
615C4⋊C4—1584no—
616C4⋊C4—1584no—
617C4⋊C4—1581no—
618C4⋊C4—1581no—
619C4⋊C4—1581no—
620C4⋊C4C23×D7912yes—
621C4⋊C4C23×D7912yes—
622C4⋊C4C23×D7912yes—
623C22⋊C4—24no—
624C22⋊C4—794no—
625C22⋊C4—794no—
626C22⋊C4—1584no—
627C22⋊C4—1584no—
628C22⋊C4—1584no—
629C22⋊C4—1584no—
630C22⋊C4—1584no—
631C22⋊C4—1584no—
632C42—1584no—
633C42—1584no—
634C42—1584no—
635C42D4×D7912yes—
636C42C23×D7912yes—
637C23—22no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—794no—
642C23—792no—
643C23—792no—
644C23—1582no—
645C23—1582no—
646C23—1582no—
647C23—1582no—
648C23—1582no—
649C23C2×D4×D7911yescharacteristic
650Q8—3162no—
651Q8—1582no—
652Q8—1582no—
653D4—22no—
654D4—22no—
655D4—42no—
656D4—3168no—
657D4—6324no—
658D4—1588no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—84no—
668C2×C4—3168no—
669C2×C4—3162no—
670C2×C4—3162no—
671C2×C4—3162no—
672C2×C4—3162no—
673C2×C4—792no—
674C2×C4—792no—
675C2×C4—6324no—
676C2×C4—1582no—
677C2×C4—1582no—
678C2×C4—1582no—
679C2×C4—1582no—
680C2×C4—1582no—
681C2×C4—1582no—
682C2×C4—1582no—
683C2×C4—1582no—
684C2×C4—1584no—
685C2×C4—1584no—
686C2×C4—1582no—
687C2×C4—1582no—
688C2×C4C2×D4×D7912yes—
689C2×C4C2×D4×D7912yes—
690C2×C4C2×D4×D7911yescharacteristic
691C2×C4#41×D7912yes—
692C2×C4#1457920912yes—
693C2×C4C24×D7911yescharacteristic
694C8—22no—
695C8—22no—
696C8—794no—
697C8—1582no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—84no—
702C22—3164no—
703C22—794no—
704C22—1582no—
705C22—1582no—
706C22—1582no—
707C22—1588no—
708C22—1582no—
709C22—1582no—
710C22#1909921512yes—
711C22#135×D7912yes—
712C22#1909937312yes—
713C22C22×D4×D7911yescharacteristic
714C4—22no—
715C4—22no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—3162no—
720C4—3162no—
721C4—3162no—
722C4—3162no—
723C4—1582no—
724C4—1582no—
725C4#1909921512yes—
726C4C2×#41×D7911yescharacteristic
727C4C2×#1457920911yescharacteristic
728C2—82no—
729C2—3162no—
730C2—1584no—
731C2#2377578614yesdirect product factor
732C2C2×#1909921511yescharacteristic
733C2C2×#135×D7911yescharacteristic
734C2C2×#1909937311yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#478×C79C2
socleC23×C79C22×D4
prime radicalC2×#19099263C2
hypercenterC2×#478D79
hypocenterC79C2×#3337
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
2. C2×#19099251C2semidirect
3. #23775786C2direct (N × H)
4. C2×#19098962C2semidirect
5. C2×#19098900C2semidirect
6. C2×#19098907C2semidirect
7. C2×#19098886C2semidirect
8. C2×#19098875C2semidirect
9. C2×#19098871C2semidirect
10. C2×#19098791C2semidirect
11. C2×#19098791C2semidirect
12. C2×C4×#11929612C2semidirect
13. C2×#19098628C2semidirect
14. C2×#19098600C2semidirect
15. C2×#106×D79C2semidirect
16. C2×#478×C79C2semidirect
23. #19099251C22semidirect
43. #19098962C22semidirect
44. #19098907C22semidirect
45. #19098900C22semidirect
46. #19098886C22semidirect
47. #19098875C22semidirect
48. #19098871C22semidirect
49. #19098791C22semidirect
50. #19098791C22semidirect
51. C4×#11929612C22semidirect
52. #19098628C22semidirect
53. #19098600C22semidirect
61. #106×D79C22semidirect
71. #478×C79C22semidirect
362. C2×C79#3337semidirect
377. C2×#478D79semidirect
384. C79C2×#3337semidirect
419. #478C2×D79semidirect
731. C2#23775786direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992632
C2×#190992512
#237757862
C2×#190989622
C2×#190989002
C2×#190989072
C2×#190988862
C2×#190988752
C2×#190988712
C2×#190987912
C2×C4×#119296122
C2×#190986282
C2×#190986002
C2×#106×D792
C2×#478×C792
C2×#333779