Finite Group Databasebeta

← C2×#23774065 #35158134

Subgroups — C2×#23774065 #35158134

Order 20224.

1906 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099182C211yesmaximal, characteristic
2C2×#19099174C211yesmaximal, characteristic, complemented
3#23774065C2116yesmaximal, direct product factor
4C2×#19098972C211yesmaximal, characteristic, complemented
5C2×#19098917C211yesmaximal, characteristic, complemented
6C2×#19098913C211yesmaximal, characteristic, complemented
7C2×#19098818C211yesmaximal, characteristic, complemented
8C2×#19098806C211yesmaximal, characteristic
9C2×#19098801C211yesmaximal, characteristic, complemented
10C2×#19098789C211yesmaximal, characteristic
11C2×#19098670C211yesmaximal, characteristic, complemented
12C2×#19098664C211yesmaximal, characteristic, complemented
13C2×Q16×Dic79C211yesmaximal, characteristic, complemented
14C2×SD16×Dic79C211yesmaximal, characteristic, complemented
15C2×#19098520C211yesmaximal, characteristic, complemented
16C2×#497×C79C211yesmaximal, characteristic, complemented
17C22×#11929607C2211yescharacteristic
18C22×C8×D79C2211yescharacteristic
19#19099182—24no—
20#19099182C2218yes—
21#19099174—24no—
22#19099174C2218yescomplemented
23C2×#14579161C2211yescharacteristic
24C2×#14579156—21no—
25C2×#14579156—21no—
26C2×#14579154—21no—
27C2×#14579153C2211yescharacteristic
28C2×#14579151—21no—
29C2×#14579151—21no—
30C2×#14579147—21no—
31C2×#14579145—21no—
32C2×#14579138—21no—
33C2×#14579137C2211yescharacteristic
34C2×#14579137C2211yescharacteristic
35C2×#14579137C2211yescharacteristic
36C2×#14579132C2211yescharacteristic
37C2×Q8×Dic79C2211yescharacteristic
38C2×Q8×Dic79C2211yescharacteristic
39C2×Q8×Dic79C2211yescharacteristic
40C2×D4×Dic79C2211yescharacteristic
41C2×#14579118C2211yescharacteristic
42#19098972C2218yescomplemented
43#19098917C2218yescomplemented
44#19098913C2218yescomplemented
45#19098818C2218yescomplemented
46#19098806C2218yes—
47#19098801C2218yescomplemented
48#19098789C2218yes—
49#19098670C2218yescomplemented
50#19098664C2218yescomplemented
51Q16×Dic79C2218yescomplemented
52SD16×Dic79C2218yescomplemented
53C2×#14579095C2211yescharacteristic
54C2×#14579095C2211yescharacteristic
55C2×#14579093C2211yescharacteristic
56C2×#14579093C2211yescharacteristic
57C2×#14579085C2211yescharacteristic
58C2×#14579085C2211yescharacteristic
59C2×#14579085C2211yescharacteristic
60C2×#14579085C2211yescharacteristic
61C2×#14579085C2211yescharacteristic
62C2×#14579085C2211yescharacteristic
63C2×#14579082C2211yescharacteristic
64C2×#14579082C2211yescharacteristic
65#19098520C2218yescomplemented
66C2×#14579071C2211yescharacteristic
67C2×C4×C79⋊C8C2211yescharacteristic
68C2×C8×Dic79C2211yescharacteristic
69C22×Q16×C79C2211yescharacteristic
70C22×Q16×C79C2211yescharacteristic
71C22×SD16×C79C2211yescharacteristic
72C22×SD16×C79C2211yescharacteristic
73C2×C4⋊Q8×C79C2211yescharacteristic
74C2×#124×C79C2211yescharacteristic
75#497×C79C2218yescomplemented
76C2×#97×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×C22⋊D79—21no—
79C23×Dic79—21no—
80C22×C4×D79C2311yescharacteristic
81C2×#11929607—24no—
82C2×#11929607C2314yes—
83C22×C79⋊C8C2311yescharacteristic
84C22×C79⋊C8C2311yescharacteristic
85C2×C8×D79—24no—
86C2×C8×D79C2314yes—
87#14579161—22no—
88#14579161C2314yes—
89#14579156—28no—
90#14579156—28no—
91#14579154—28no—
92#14579153—22no—
93#14579153C2314yes—
94#14579151—28no—
95#14579151—28no—
96#14579147—28no—
97#14579145—28no—
98#14579138—28no—
99#14579137—22no—
100#14579137—22no—
101#14579137—22no—
102#14579137C2314yes—
103#14579137C2314yes—
104#14579137C2314yes—
105#14579132—22no—
106#14579132C2314yes—
107Q8×Dic79—22no—
108Q8×Dic79—22no—
109Q8×Dic79—22no—
110Q8×Dic79C2314yes—
111Q8×Dic79C2314yes—
112Q8×Dic79C2314yes—
113D4×Dic79—22no—
114D4×Dic79C2314yes—
115#14579118D414yes—
116#14579118C2314yes—
117C2×C4⋊Dic79—21no—
118C2×C4⋊Dic79—21no—
119C2×C4⋊Dic79—21no—
120C2×C4⋊Dic79—21no—
121C2×C4⋊Dic79C2311yescharacteristic
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—
130C2×Dic79⋊C4D411yescharacteristic
131C2×Dic79⋊C4D411yescharacteristic
132C2×C22⋊Dic79—21no—
133C2×C22⋊Dic79—21no—
134C2×(C2×D79)⋊C4—21no—
135C2×(C2×D79)⋊C4—21no—
136C2×(C2×D79)⋊C4—21no—
137C2×(C2×D79)⋊C4D411yescharacteristic
138C2×(C2×D79)⋊C4D411yescharacteristic
139C2×C4×Dic79—21no—
140C2×C4×Dic79—21no—
141C2×C4×Dic79—21no—
142C2×C4×Dic79C2311yescharacteristic
143#14579095C2314yes—
144#14579095C2314yes—
145#14579093C2314yes—
146#14579093C2314yes—
147#14579085C2314yes—
148#14579085C2314yes—
149#14579085C2314yes—
150#14579085C2314yes—
151#14579085C2314yes—
152#14579085C2314yes—
153#14579082C2314yes—
154#14579082C2314yes—
155#14579071C2314yes—
156C4×C79⋊C8C2314yes—
157C8×Dic79C2314yes—
158C22×Q8×C79C2311yescharacteristic
159C22×Q8×C79C2311yescharacteristic
160C22×Q8×C79C2311yescharacteristic
161C22×D4×C79C2311yescharacteristic
162C2×Q16×C79—24no—
163C2×Q16×C79—24no—
164C2×Q16×C79C2314yes—
165C2×Q16×C79C2314yes—
166C2×SD16×C79—24no—
167C2×SD16×C79—24no—
168C2×SD16×C79C2314yes—
169C2×SD16×C79C2314yes—
170C22×C8×C79C2311yescharacteristic
171C22×C8×C79C2311yescharacteristic
172C4⋊Q8×C79—22no—
173C4⋊Q8×C79C2314yes—
174#124×C79—22no—
175#124×C79C2314yes—
176C2×C4⋊C4×C79—21no—
177C2×C4⋊C4×C79—21no—
178C2×C22⋊C4×C79—21no—
179C2×C22⋊C4×C79—21no—
180C2×C42×C79C2311yescharacteristic
181#97×C79C2314yes—
182C23×D79C2×D411yescharacteristic
183C2×Dic158—24no—
184C2×Dic158—82no—
185C2×C22⋊D79—24no—
186C2×C22⋊D79—82no—
187C22×Dic79—24no—
188C22×Dic79—21no—
189C22×Dic79—21no—
190C22×Dic79—21no—
191C22×Dic79—21no—
192C22×Dic79—82no—
193C22×Dic79C2×D411yescharacteristic
194C22×Dic79C2×D411yescharacteristic
195C22×Dic79C2×D411yescharacteristic
196C2×C4×D79—22no—
197C2×C4×D79—22no—
198C2×C4×D79C2×D412yes—
199C2×C4×D79C2412yes—
200#11929607—28no—
201C2×C79⋊C8—22no—
202C2×C79⋊C8—22no—
203C2×C79⋊C8C2412yes—
204C2×C79⋊C8C2412yes—
205C8×D79—28no—
206C4⋊Dic79—24no—
207C4⋊Dic79—24no—
208C4⋊Dic79—24no—
209C4⋊Dic79—24no—
210C4⋊Dic79—21no—
211C4⋊Dic79—21no—
212C4⋊Dic79—21no—
213C4⋊Dic79—21no—
214C4⋊Dic79C2412yes—
215C4⋊Dic79C2412yes—
216C4⋊Dic79C2412yes—
217C4⋊Dic79C2412yes—
218Dic79⋊C4—24no—
219Dic79⋊C4—24no—
220Dic79⋊C4—24no—
221Dic79⋊C4—24no—
222Dic79⋊C4—24no—
223Dic79⋊C4C2×D414yes—
224Dic79⋊C4C2×D414yes—
225C22⋊Dic79—24no—
226C22⋊Dic79—24no—
227(C2×D79)⋊C4—24no—
228(C2×D79)⋊C4—24no—
229(C2×D79)⋊C4—24no—
230(C2×D79)⋊C4C2×D414yes—
231(C2×D79)⋊C4C2×D414yes—
232C4×Dic79—24no—
233C4×Dic79—24no—
234C4×Dic79—24no—
235C4×Dic79C2×D412yes—
236C4×Dic79C2412yes—
237C24×C79—21no—
238C2×Q8×C79—21no—
239C2×Q8×C79—21no—
240C2×Q8×C79—21no—
241C2×Q8×C79—22no—
242C2×Q8×C79—22no—
243C2×Q8×C79—22no—
244C2×Q8×C79—22no—
245C2×Q8×C79—22no—
246C2×Q8×C79—22no—
247C2×Q8×C79C2412yes—
248C2×Q8×C79C2412yes—
249C2×Q8×C79C2412yes—
250C2×D4×C79—21no—
251C2×D4×C79—22no—
252C2×D4×C79—22no—
253C2×D4×C79C2412yes—
254C22×C4×C79—21no—
255C22×C4×C79—21no—
256C22×C4×C79—21no—
257C22×C4×C79C2×D411yescharacteristic
258C22×C4×C79C2×D411yescharacteristic
259C22×C4×C79C2411yescharacteristic
260Q16×C79—28no—
261Q16×C79—28no—
262SD16×C79—28no—
263SD16×C79—28no—
264C2×C8×C79#4114yes—
265C2×C8×C79#4114yes—
266C2×C8×C79C2412yes—
267C2×C8×C79C2412yes—
268C4⋊C4×C79—24no—
269C4⋊C4×C79—24no—
270C22⋊C4×C79—24no—
271C22⋊C4×C79—24no—
272C42×C79C2×D412yes—
273C42×C79C2412yes—
274C23×C79—22no—
275C23×C79—42no—
276C23×C79—42no—
277C23×C79—42no—
278C23×C79C22×D411yescharacteristic
279C22×D79—22no—
280C22×D79—22no—
281C22×D79—22no—
282C22×D79C22×D412yes—
283Q8×C79—22no—
284Q8×C79—22no—
285Q8×C79—22no—
286Q8×C79—22no—
287Q8×C79—22no—
288Q8×C79—22no—
289Q8×C79—42no—
290Q8×C79—42no—
291Q8×C79—42no—
292D4×C79—22no—
293D4×C79—22no—
294D4×C79—42no—
295C2×C4×C79—22no—
296C2×C4×C79—22no—
297C2×C4×C79—22no—
298C2×C4×C79—22no—
299C2×C4×C79—22no—
300C2×C4×C79—42no—
301C2×C4×C79—42no—
302C2×C4×C79—42no—
303C2×C4×C79C22×D412yes—
304C2×C4×C79C22×D412yes—
305C2×C4×C79C22×D411yescharacteristic
306C2×C4×C79C2×#4112yes—
307C2×C4×C79C2×#4112yes—
308C2×C4×C79C2511yescharacteristic
309C22⋊D79—84no—
310C2×Dic79—22no—
311C2×Dic79—22no—
312C2×Dic79—22no—
313C2×Dic79—22no—
314C2×Dic79—22no—
315C2×Dic79—22no—
316C2×Dic79—22no—
317C2×Dic79—42no—
318C2×Dic79—42no—
319C2×Dic79—42no—
320C2×Dic79—42no—
321C2×Dic79—84no—
322C2×Dic79C22×D412yes—
323C2×Dic79C22×D412yes—
324C2×Dic79C22×D412yes—
325C4×D79—24no—
326C4×D79—22no—
327C4×D79—22no—
328Dic158—84no—
329C8×C79C2×#4114yes—
330C8×C79C2×#4114yes—
331C79⋊C8—22no—
332C79⋊C8—22no—
333C22×C79—42no—
334C22×C79—42no—
335C22×C79—42no—
336C22×C79—84no—
337C22×C79#53212yes—
338C22×C79#57712yes—
339C22×C79#57812yes—
340C22×C79C23×D411yescharacteristic
341C2×D79—22no—
342C2×D79—22no—
343C2×D79—22no—
344C2×D79—44no—
345C4×C79—22no—
346C4×C79—22no—
347C4×C79—42no—
348C4×C79—42no—
349C4×C79—42no—
350C4×C79#53212yes—
351C4×C79C22×#4111yescharacteristic
352C4×C79C22×#4111yescharacteristic
353Dic79—22no—
354Dic79—22no—
355Dic79—22no—
356Dic79—42no—
357Dic79—42no—
358Dic79—42no—
359Dic79—42no—
360C2×#3178—791nomaximal, Sylow
361C2×C79—82no—
362C2×C79#317814yescomplemented
363C2×C79C2×#53211yescharacteristic
364C2×C79C2×#57711yescharacteristic
365C2×C79C2×#57811yescharacteristic
366D79—42no—
367C2×#542—791no—
368C2×#541—791no—
369#3178—7916no—
370C2×#501—791no—
371C2×#497D7911yescharacteristic, complemented
372C2×#488—791no—
373C2×#487—791no—
374C2×#470—791no—
375C2×#468—791no—
376C2×#467—791no—
377C2×#465—791no—
378C2×#441—791no—
379C2×#440—791no—
380C2×C4×Q16—791no—
381C2×C4×SD16—791no—
382C2×#405—791no—
383C79C2×#317811yescharacteristic, complemented, Sylow
384C22×Q16C2×D7911yescharacteristic
385C22×Q16C2×D7911yescharacteristic
386C22×SD16C2×D7911yescharacteristic
387C22×SD16C2×D7911yescharacteristic
388C22×M16—791no—
389C23×C8—791no—
390#542—798no—
391#542—1584no—
392#541—798no—
393#541—1584no—
394C2×C4⋊Q8—791no—
395C2×C4⋊Q8C2×D7911yescharacteristic
396C2×#126—1581no—
397C2×#126—1581no—
398C2×#126—1581no—
399C2×#125—791no—
400C2×#125—1581no—
401C2×#125—1581no—
402C2×#124—1581no—
403C2×#124C2×D7911yescharacteristic
404C2×#123—1581no—
405C2×C22⋊Q8—791no—
406C2×C22⋊Q8—791no—
407C2×C22⋊Q8—791no—
408C2×C22⋊Q8—1581no—
409C2×#121—791no—
410C2×C4×Q8—791no—
411C2×C4×Q8—791no—
412C2×C4×Q8—791no—
413C2×C4×D4—791no—
414C2×#117—791no—
415#501—798no—
416#497C2×D7918yescomplemented
417#488—798no—
418#487—798no—
419#470—798no—
420#468—798no—
421#467—798no—
422#465—798no—
423#441—798no—
424#440—798no—
425C4×Q16—798no—
426C4×SD16—798no—
427C2×#107—791no—
428C2×#107—791no—
429C2×#106—791no—
430C2×#106—791no—
431C2×#103—791no—
432C2×#103—791no—
433C2×#103—791no—
434C2×#103—791no—
435C2×#103—791no—
436C2×#103—791no—
437C2×#102—791no—
438C2×#102—791no—
439#405—798no—
440C2×#97—791no—
441C2×#97C2×D7911yescharacteristic
442C2×C4×C8—791no—
443C2×C4×C8—791no—
444C22×Q8—1581no—
445C22×Q8C22×D7911yescharacteristic
446C22×Q8C22×D7911yescharacteristic
447C22×Q8C22×D7911yescharacteristic
448C22×D4—1581no—
449C22×D4C22×D7911yescharacteristic
450C23×C4—791no—
451C23×C4—1581no—
452C2×Q16—24no—
453C2×Q16—24no—
454C2×Q16C22×D7914yes—
455C2×Q16C22×D7914yes—
456C2×SD16—24no—
457C2×SD16—24no—
458C2×SD16C22×D7914yes—
459C2×SD16C22×D7914yes—
460C2×M16—794no—
461C2×M16—1584no—
462C22×C8—791no—
463C22×C8—791no—
464C22×C8—794no—
465C22×C8—1584no—
466C22×C8C22×D7911yescharacteristic
467C22×C8C22×D7911yescharacteristic
468C4⋊Q8—22no—
469C4⋊Q8—794no—
470C4⋊Q8—1582no—
471C4⋊Q8C22×D7914yes—
472#126—1588no—
473#126—1588no—
474#126—1588no—
475#125—794no—
476#125—1588no—
477#125—1588no—
478#125—1582no—
479#124—22no—
480#124—1588no—
481#124C22×D7914yes—
482#123—1588no—
483C22⋊Q8—794no—
484C22⋊Q8—794no—
485C22⋊Q8—794no—
486C22⋊Q8—1588no—
487C22⋊Q8—1582no—
488C22⋊Q8—1582no—
489C22⋊Q8—1582no—
490#121—794no—
491#121—1582no—
492C4×Q8—794no—
493C4×Q8—794no—
494C4×Q8—794no—
495C4×Q8—1582no—
496C4×Q8—1582no—
497C4×Q8—1582no—
498C4×D4—794no—
499C4×D4—1582no—
500#117—794no—
501#117—794no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—791no—
505C2×C4⋊C4—791no—
506C2×C4⋊C4—791no—
507C2×C4⋊C4—791no—
508C2×C4⋊C4—791no—
509C2×C4⋊C4—791no—
510C2×C4⋊C4—1581no—
511C2×C4⋊C4—1581no—
512C2×C4⋊C4—1581no—
513C2×C4⋊C4—1581no—
514C2×C4⋊C4—1581no—
515C2×C4⋊C4—1581no—
516C2×C4⋊C4—1581no—
517C2×C4⋊C4—1581no—
518C2×C4⋊C4—1581no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—791no—
522C2×C22⋊C4—791no—
523C2×C22⋊C4—1581no—
524C2×C22⋊C4—1581no—
525C2×C22⋊C4—1581no—
526C2×C22⋊C4—1581no—
527C2×C22⋊C4—1581no—
528C2×C42—791no—
529C2×C42—1581no—
530C2×C42—1581no—
531C2×C42—1581no—
532C2×C42C22×D7911yescharacteristic
533#107—794no—
534#107—794no—
535#106—794no—
536#106—794no—
537#103—794no—
538#103—794no—
539#103—794no—
540#103—794no—
541#103—794no—
542#103—794no—
543#102—794no—
544#102—794no—
545#97—794no—
546#97C22×D7914yes—
547C4×C8—794no—
548C4×C8—794no—
549C24—21no—
550C24—791no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—6322no—
561C2×Q8—1584no—
562C2×Q8C23×D7912yes—
563C2×Q8C23×D7912yes—
564C2×Q8C23×D7912yes—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—21no—
568C2×D4—6322no—
569C2×D4—1584no—
570C2×D4C23×D7912yes—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—791no—
575C22×C4—791no—
576C22×C4—791no—
577C22×C4—792no—
578C22×C4—792no—
579C22×C4—6322no—
580C22×C4—1581no—
581C22×C4—1581no—
582C22×C4—1581no—
583C22×C4—1581no—
584C22×C4—1584no—
585C22×C4—1582no—
586C22×C4—1582no—
587C22×C4D4×D7911yescharacteristic
588C22×C4D4×D7911yescharacteristic
589C22×C4C23×D7911yescharacteristic
590Q16—28no—
591Q16—28no—
592SD16—28no—
593SD16—28no—
594M16—1588no—
595C2×C8—792no—
596C2×C8—792no—
597C2×C8—1582no—
598C2×C8—1582no—
599C2×C8—1588no—
600C2×C8#1192962314yes—
601C2×C8#1192962314yes—
602C2×C8C23×D7912yes—
603C2×C8C23×D7912yes—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—794no—
607C4⋊C4—794no—
608C4⋊C4—792no—
609C4⋊C4—792no—
610C4⋊C4—792no—
611C4⋊C4—792no—
612C4⋊C4—1584no—
613C4⋊C4—1584no—
614C4⋊C4—1584no—
615C4⋊C4—1584no—
616C4⋊C4—1584no—
617C4⋊C4—1584no—
618C4⋊C4—1584no—
619C4⋊C4—1584no—
620C4⋊C4—1581no—
621C4⋊C4—1581no—
622C4⋊C4—1581no—
623C4⋊C4—1581no—
624C4⋊C4—1584no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—794no—
628C22⋊C4—794no—
629C22⋊C4—1584no—
630C22⋊C4—1584no—
631C22⋊C4—1584no—
632C22⋊C4—1584no—
633C22⋊C4—1584no—
634C42—792no—
635C42—792no—
636C42—1584no—
637C42—1584no—
638C42—1584no—
639C42D4×D7912yes—
640C42C23×D7912yes—
641C23—22no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—792no—
646C23—1582no—
647C23—1582no—
648C23—1582no—
649C23C2×D4×D7911yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—22no—
653Q8—22no—
654Q8—22no—
655Q8—22no—
656Q8—42no—
657Q8—42no—
658Q8—42no—
659Q8—6324no—
660D4—22no—
661D4—22no—
662D4—42no—
663D4—6324no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—3162no—
673C2×C4—3162no—
674C2×C4—3162no—
675C2×C4—3162no—
676C2×C4—792no—
677C2×C4—792no—
678C2×C4—792no—
679C2×C4—6324no—
680C2×C4—1582no—
681C2×C4—1582no—
682C2×C4—1582no—
683C2×C4—1582no—
684C2×C4—1582no—
685C2×C4—1582no—
686C2×C4—1582no—
687C2×C4—1584no—
688C2×C4—1582no—
689C2×C4—1582no—
690C2×C4C2×D4×D7912yes—
691C2×C4C2×D4×D7912yes—
692C2×C4C2×D4×D7911yescharacteristic
693C2×C4C2×#1192962312yes—
694C2×C4C2×#1192962312yes—
695C2×C4C24×D7911yescharacteristic
696C8—1582no—
697C8—1582no—
698C8C2×#1192962314yes—
699C8C2×#1192962314yes—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—84no—
704C22—3164no—
705C22—1582no—
706C22—1582no—
707C22—1582no—
708C22#1909911112yes—
709C22#1909937212yes—
710C22#1909937912yes—
711C22C22×D4×D7911yescharacteristic
712C4—22no—
713C4—22no—
714C4—42no—
715C4—42no—
716C4—42no—
717C4—3162no—
718C4—3162no—
719C4—3162no—
720C4—3162no—
721C4—1582no—
722C4—1582no—
723C4—1582no—
724C4#1909911112yes—
725C4C22×#1192962311yescharacteristic
726C4C22×#1192962311yescharacteristic
727C2—82no—
728C2—3162no—
729C2#2377406514yesdirect product factor
730C2C2×#1909911111yescharacteristic
731C2C2×#1909937211yescharacteristic
732C2C2×#1909937911yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#497×C79C2
socleC23×C79C22×D4
prime radicalC2×#14579132C22
hypercenterC2×#497D79
hypocenterC79C2×#3178
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#497

Complements

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

NH ≅ G/Ntype
2. C2×#19099174C2semidirect
3. #23774065C2direct (N × H)
4. C2×#19098972C2semidirect
5. C2×#19098917C2semidirect
6. C2×#19098913C2semidirect
7. C2×#19098818C2semidirect
9. C2×#19098801C2semidirect
11. C2×#19098670C2semidirect
12. C2×#19098664C2semidirect
13. C2×Q16×Dic79C2semidirect
14. C2×SD16×Dic79C2semidirect
15. C2×#19098520C2semidirect
16. C2×#497×C79C2semidirect
22. #19099174C22semidirect
42. #19098972C22semidirect
43. #19098917C22semidirect
44. #19098913C22semidirect
45. #19098818C22semidirect
47. #19098801C22semidirect
49. #19098670C22semidirect
50. #19098664C22semidirect
51. Q16×Dic79C22semidirect
52. SD16×Dic79C22semidirect
65. #19098520C22semidirect
75. #497×C79C22semidirect
362. C2×C79#3178semidirect
371. C2×#497D79semidirect
383. C79C2×#3178semidirect
416. #497C2×D79semidirect
729. C2#23774065direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991822
C2×#190991742
#237740652
C2×#190989722
C2×#190989172
C2×#190989132
C2×#190988182
C2×#190988062
C2×#190988012
C2×#190987892
C2×#190986702
C2×#190986642
C2×Q16×Dic792
C2×SD16×Dic792
C2×#190985202
C2×#497×C792
C2×#317879