Finite Group Databasebeta

← C2×#23777871 #35195898

Subgroups — C2×#23777871 #35195898

Order 20224.

7182 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777871C2132yesmaximal, direct product factor
2C2×#19099309C214yesmaximal, complemented
3C2×#19099298C211yesmaximal, characteristic, complemented
4C2×#19099298C212yesmaximal, complemented
5C2×#19099291C211yesmaximal, characteristic, complemented
6C2×#19099273C212yesmaximal, complemented
7C2×#19099235C211yesmaximal, characteristic, complemented
8C2×Q8×D316C211yesmaximal, characteristic, complemented
9C2×#19099223C212yesmaximal, complemented
10C2×#19099215C212yesmaximal, complemented
11C2×#19099187C212yesmaximal, complemented
12C2×#19099184C212yesmaximal, complemented
13C2×#19099168C212yesmaximal, complemented
14C2×#19099161C214yesmaximal, complemented
15C2×#19099138C212yesmaximal, complemented
16C2×#19099113C211yesmaximal, characteristic, complemented
17C2×#19099097C211yesmaximal, characteristic, complemented
18C2×#533×C79C211yesmaximal, characteristic, complemented
19C22×#11929625C2212yes—
20C22×#11929624C2212yes—
21C22×Q8×D79C2212yes—
22#19099309C22164yescomplemented
23#19099298C22116yescomplemented
24#19099298C22132yescomplemented
25#19099291C22116yescomplemented
26#19099273C22132yescomplemented
27#19099235C22116yescomplemented
28Q8×D316C22116yescomplemented
29#19099223C22132yescomplemented
30#19099215C22132yescomplemented
31#19099187C22132yescomplemented
32#19099184C22132yescomplemented
33#19099168C22132yescomplemented
34#19099161C22164yescomplemented
35#19099138C22132yescomplemented
36#19099113C22116yescomplemented
37C2×#14579161C2212yes—
38C2×#14579161C2211yescharacteristic
39C2×#14579159C2212yes—
40C2×#14579158C2211yescharacteristic
41C2×#14579158C2212yes—
42#19099097C22116yescomplemented
43C2×#14579156C2214yes—
44C2×#14579155C2212yes—
45C2×#14579153C2211yescharacteristic
46C2×#14579153C2212yes—
47C2×#14579151C2214yes—
48C2×#14579150C2214yes—
49C2×#14579150C2212yes—
50C2×#14579149C2212yes—
51C2×#14579149C2212yes—
52C2×#14579149C2211yescharacteristic
53C2×#14579147C2214yes—
54C2×#14579146C2214yes—
55C2×#14579146C2214yes—
56C2×#14579146C2214yes—
57C2×#14579146C2214yes—
58C2×#14579146C2214yes—
59C2×#14579144C2212yes—
60C2×#14579143C2214yes—
61C2×#14579141C2212yes—
62C2×#14579141C2214yes—
63C2×#14579140C2211yescharacteristic
64C2×#14579139C2214yes—
65C2×#14579139C2214yes—
66C2×#14579139C2214yes—
67C2×#14579137C2214yes—
68C2×#14579136C2212yes—
69C2×#14579136C2214yes—
70C2×#14579135C2212yes—
71C2×#14579135C2211yescharacteristic
72C2×#14579135C2212yes—
73C2×#14579134C2214yes—
74C2×#14579134C2214yes—
75C2×C4×Dic158C2212yes—
76C2×C4×Dic158C2211yescharacteristic
77C2×#14579126C2212yes—
78C2×C4×D316C2212yes—
79C2×C4×D316C2211yescharacteristic
80C2×C4×D316C2212yes—
81C2×C4×D316C2212yes—
82C2×C4×D316C2212yes—
83C2×C4×D316C2212yes—
84C2×#14579123C2212yes—
85C2×#14579123C2214yes—
86C2×C4×C22⋊D79C2212yes—
87C2×#14579118C2212yes—
88C2×C4⋊C4×D79C2214yes—
89#533×C79C22116yescomplemented
90C2×C4⋊Q8×C79C2211yescharacteristic
91C2×C4⋊Q8×C79C2211yescharacteristic
92C2×#125×C79C2212yes—
93C2×C22⋊Q8×C79C2211yescharacteristic
94C2×C22⋊Q8×C79C2211yescharacteristic
95C2×C22⋊Q8×C79C2212yes—
96C2×C4×Q8×C79C2211yescharacteristic
97C2×C4×Q8×C79C2211yescharacteristic
98C2×C4×Q8×C79C2212yes—
99C2×#117×C79C2212yes—
100C22×C42×C79C2211yescharacteristic
101C2×#11929625—48no—
102C2×#11929625C23116yes—
103C2×#11929624—48no—
104C2×#11929624C23116yes—
105C22×Dic158C2312yes—
106C22×Dic158C2311yescharacteristic
107C22×Dic158C2314yes—
108C2×Q8×D79—48no—
109C2×Q8×D79C23116yes—
110C22×D316C2312yes—
111C22×D316C2312yes—
112C22×D316C2311yescharacteristic
113C22×D316C2314yes—
114C22×D316C2312yes—
115C22×D316C2314yes—
116C22×C22⋊D79C2312yes—
117C22×C22⋊D79C2314yes—
118C22×C4×D79C2312yes—
119C22×C4×D79C2314yes—
120C22×C4×D79C2314yes—
121C22×C4×D79C2314yes—
122C22×C4×D79C2314yes—
123#14579161C23116yes—
124#14579161C2318yes—
125#14579159C23116yes—
126#14579158C23116yes—
127#14579158C2318yes—
128#14579156C23132yes—
129#14579155C23116yes—
130#14579153C23116yes—
131#14579153C2318yes—
132#14579151C23132yes—
133#14579150C23116yes—
134#14579150C23132yes—
135#14579149C23116yes—
136#14579149C23116yes—
137#14579149C2318yes—
138#14579147C23132yes—
139#14579146C23132yes—
140#14579146C23132yes—
141#14579146C23132yes—
142#14579146C23132yes—
143#14579146C23132yes—
144#14579144C23116yes—
145#14579143C23132yes—
146#14579141C23132yes—
147#14579141C23116yes—
148#14579140C2318yes—
149#14579139C23132yes—
150#14579139C23132yes—
151#14579139C23132yes—
152#14579137C23132yes—
153#14579136C23132yes—
154#14579136C23116yes—
155#14579135C2318yes—
156#14579135C23116yes—
157#14579135C23116yes—
158#14579134C23132yes—
159#14579134C23132yes—
160C4×Dic158C23116yes—
161C4×Dic158C2318yes—
162#14579126C23116yes—
163C4×D316C23116yes—
164C4×D316C23116yes—
165C4×D316C23116yes—
166C4×D316C23116yes—
167C4×D316C2318yes—
168C4×D316C23116yes—
169#14579123C23132yes—
170#14579123C23116yes—
171C4×C22⋊D79C23116yes—
172#14579118C23116yes—
173C2×C4⋊Dic79C2314yes—
174C2×C4⋊Dic79C2311yescharacteristic
175C2×C4⋊Dic79C2311yescharacteristic
176C2×C4⋊Dic79C2312yes—
177C2×C4⋊Dic79C2312yes—
178C2×Dic79⋊C4C2312yes—
179C2×Dic79⋊C4C2314yes—
180C2×Dic79⋊C4C2312yes—
181C2×Dic79⋊C4C2312yes—
182C2×Dic79⋊C4C2314yes—
183C2×Dic79⋊C4C2314yes—
184C2×Dic79⋊C4C2312yes—
185C4⋊C4×D79C23132yes—
186C2×C22⋊Dic79C2312yes—
187C2×(C2×D79)⋊C4C2312yes—
188C2×(C2×D79)⋊C4C2312yes—
189C2×(C2×D79)⋊C4C2312yes—
190C2×(C2×D79)⋊C4C2314yes—
191C2×(C2×D79)⋊C4C2314yes—
192C2×(C2×D79)⋊C4C2314yes—
193C2×(C2×D79)⋊C4C2314yes—
194C2×(C2×D79)⋊C4C2314yes—
195C2×(C2×D79)⋊C4C2314yes—
196C2×(C2×D79)⋊C4C2314yes—
197C2×(C2×D79)⋊C4C2312yes—
198C2×C4×Dic79C2312yes—
199C2×C4×Dic79C2314yes—
200C22×Q8×C79C2311yescharacteristic
201C22×Q8×C79C2311yescharacteristic
202C22×Q8×C79C2312yes—
203C23×C4×C79C2311yescharacteristic
204C23×C4×C79C2311yescharacteristic
205C23×C4×C79C2311yescharacteristic
206C4⋊Q8×C79C2318yes—
207C4⋊Q8×C79C2318yes—
208#125×C79C23116yes—
209C22⋊Q8×C79C2318yes—
210C22⋊Q8×C79C2318yes—
211C22⋊Q8×C79C23116yes—
212C4×Q8×C79C2318yes—
213C4×Q8×C79C2318yes—
214C4×Q8×C79C23116yes—
215#117×C79C23116yes—
216C2×C4⋊C4×C79C2312yes—
217C2×C4⋊C4×C79C2312yes—
218C2×C4⋊C4×C79C2312yes—
219C2×C4⋊C4×C79C2312yes—
220C2×C4⋊C4×C79C2312yes—
221C2×C4⋊C4×C79C2312yes—
222C2×C4⋊C4×C79C2311yescharacteristic
223C2×C4⋊C4×C79C2311yescharacteristic
224C2×C4⋊C4×C79C2312yes—
225C2×C22⋊C4×C79C2312yes—
226C2×C22⋊C4×C79C2312yes—
227C2×C42×C79C2311yescharacteristic
228C2×C42×C79C2311yescharacteristic
229C2×C42×C79C2311yescharacteristic
230C2×C42×C79C2311yescharacteristic
231C2×C42×C79C2318yes—
232C2×C42×C79C2312yes—
233C2×C42×C79C2312yes—
234C23×D79C2412yes—
235C23×D79C2414yes—
236#11929625—432no—
237#11929624—432no—
238C2×Dic158—28no—
239C2×Dic158—24no—
240C2×Dic158—48no—
241C2×Dic158C2418yes—
242C2×Dic158C2414yes—
243C2×Dic158C24116yes—
244Q8×D79—432no—
245C2×D316—28no—
246C2×D316—28no—
247C2×D316—24no—
248C2×D316—48no—
249C2×D316—44no—
250C2×D316—48no—
251C2×D316C2418yes—
252C2×D316C2414yes—
253C2×D316C2418yes—
254C2×D316C24116yes—
255C2×D316C24116yes—
256C2×D316C2418yes—
257C2×C22⋊D79—48no—
258C2×C22⋊D79—44no—
259C2×C22⋊D79C24116yes—
260C2×C22⋊D79C2418yes—
261C22×Dic79C2414yes—
262C22×Dic79C2412yes—
263C22×Dic79C2412yes—
264C22×Dic79C2412yes—
265C2×C4×D79—28no—
266C2×C4×D79—48no—
267C2×C4×D79—48no—
268C2×C4×D79—48no—
269C2×C4×D79—48no—
270C2×C4×D79C2418yes—
271C2×C4×D79C24116yes—
272C2×C4×D79C24116yes—
273C2×C4×D79C24116yes—
274C2×C4×D79C24116yes—
275C4⋊Dic79C24116yes—
276C4⋊Dic79C2414yes—
277C4⋊Dic79C2414yes—
278C4⋊Dic79C2418yes—
279C4⋊Dic79C2418yes—
280Dic79⋊C4C2418yes—
281Dic79⋊C4C24116yes—
282Dic79⋊C4C2418yes—
283Dic79⋊C4C2418yes—
284Dic79⋊C4C24116yes—
285Dic79⋊C4C24116yes—
286Dic79⋊C4C2418yes—
287C22⋊Dic79C2418yes—
288(C2×D79)⋊C4C2418yes—
289(C2×D79)⋊C4C2418yes—
290(C2×D79)⋊C4C2418yes—
291(C2×D79)⋊C4C24116yes—
292(C2×D79)⋊C4C24116yes—
293(C2×D79)⋊C4C24116yes—
294(C2×D79)⋊C4C24116yes—
295(C2×D79)⋊C4C24116yes—
296(C2×D79)⋊C4C24116yes—
297(C2×D79)⋊C4C24116yes—
298(C2×D79)⋊C4C2418yes—
299C4×Dic79C2418yes—
300C4×Dic79C24116yes—
301C24×C79C2411yescharacteristic
302C2×Q8×C79—24no—
303C2×Q8×C79—24no—
304C2×Q8×C79—44no—
305C2×Q8×C79C2414yes—
306C2×Q8×C79C2414yes—
307C2×Q8×C79C2418yes—
308C22×C4×C79—24no—
309C22×C4×C79—24no—
310C22×C4×C79—42no—
311C22×C4×C79C2412yes—
312C22×C4×C79C2414yes—
313C22×C4×C79C2411yescharacteristic
314C22×C4×C79C2411yescharacteristic
315C22×C4×C79C2411yescharacteristic
316C22×C4×C79C2411yescharacteristic
317C22×C4×C79C2414yes—
318C22×C4×C79C2412yes—
319C22×C4×C79C2412yes—
320C22×C4×C79C2412yes—
321C22×C4×C79C2414yes—
322C22×C4×C79C2411yescharacteristic
323C22×C4×C79C2411yescharacteristic
324C4⋊C4×C79C2418yes—
325C4⋊C4×C79C2418yes—
326C4⋊C4×C79C2418yes—
327C4⋊C4×C79C2418yes—
328C4⋊C4×C79C2418yes—
329C4⋊C4×C79C2418yes—
330C4⋊C4×C79C2414yes—
331C4⋊C4×C79C2414yes—
332C4⋊C4×C79C2418yes—
333C22⋊C4×C79C2418yes—
334C22⋊C4×C79C2418yes—
335C42×C79C2414yes—
336C42×C79C2414yes—
337C42×C79C2414yes—
338C42×C79C2414yes—
339C42×C79C2418yes—
340C42×C79C2418yes—
341C23×C79—22no—
342C23×C79—22no—
343C23×C79—22no—
344C23×C79C2512yes—
345C23×C79C2511yescharacteristic
346C22×D79—24no—
347C22×D79—28no—
348C22×D79—24no—
349C22×D79—28no—
350C22×D79—28no—
351C22×D79—24no—
352C22×D79C2518yes—
353C22×D79C2514yes—
354Q8×C79—28no—
355Q8×C79—28no—
356Q8×C79—48no—
357C2×C4×C79—22no—
358C2×C4×C79—24no—
359C2×C4×C79—24no—
360C2×C4×C79—22no—
361C2×C4×C79—24no—
362C2×C4×C79—22no—
363C2×C4×C79—24no—
364C2×C4×C79—22no—
365C2×C4×C79—28no—
366C2×C4×C79—28no—
367C2×C4×C79—44no—
368C2×C4×C79H(5,𝔽2)14yes—
369C2×C4×C792−1+414yes—
370C2×C4×C79C2514yes—
371C2×C4×C79C2512yes—
372C2×C4×C79C2512yes—
373C2×C4×C79C2514yes—
374C2×C4×C79C2514yes—
375C2×C4×C79C2512yes—
376C2×C4×C79C2512yes—
377C2×C4×C79C2514yes—
378C2×C4×C79C2512yes—
379C2×C4×C79C2512yes—
380C22⋊D79—48no—
381C22⋊D79—416no—
382C2×Dic79—24no—
383C2×Dic79—28no—
384C2×Dic79—24no—
385C2×Dic79—24no—
386C2×Dic79C2514yes—
387C2×Dic79C2514yes—
388C2×Dic79C2518yes—
389C2×Dic79C2514yes—
390D316—216no—
391D316—28no—
392D316—216no—
393D316—48no—
394D316—416no—
395D316—416no—
396C4×D79—216no—
397C4×D79—416no—
398C4×D79—416no—
399C4×D79—416no—
400C4×D79—416no—
401Dic158—216no—
402Dic158—28no—
403Dic158—416no—
404C22×C79—22no—
405C22×C79—22no—
406C22×C79—22no—
407C22×C79—44no—
408C22×C79C2×H(5,𝔽2)12yes—
409C22×C79C2×2−1+412yes—
410C22×C79#58512yes—
411C22×C79C2611yescharacteristic
412C2×D79—28no—
413C2×D79—24no—
414C2×D79—28no—
415C2×D79—24no—
416C2×D79—24no—
417C2×D79—28no—
418C2×D79—48no—
419C2×D79—416no—
420C4×C79—22no—
421C4×C79—24no—
422C4×C79—24no—
423C4×C79—22no—
424C4×C79—22no—
425C4×C79—22no—
426C4×C79—24no—
427C4×C79—24no—
428C4×C79C2×H(5,𝔽2)14yes—
429C4×C79C2×2−1+414yes—
430Dic79—28no—
431Dic79—24no—
432Dic79—24no—
433Dic79—24no—
434C2×#3554—791nomaximal, Sylow
435C2×C79—42no—
436C2×C79#355414yescomplemented
437C2×C79C22×H(5,𝔽2)11yescharacteristic
438C2×C79C22×2−1+411yescharacteristic
439C2×C79C2×#58511yescharacteristic
440D79—48no—
441D79—44no—
442#3554—7932no—
443C2×#562—794no—
444C2×#559—792no—
445C2×#559—791no—
446C2×#557—791no—
447C2×#554—792no—
448C2×#550—791no—
449C2×D4×Q8—791no—
450C2×#548—792no—
451C2×#547—792no—
452C2×#542—792no—
453C2×#542—792no—
454C2×#540—792no—
455C2×#539—794no—
456C2×#536—792no—
457C2×#533D7911yescharacteristic, complemented
458C2×#532—791no—
459C2×#529—791no—
460C79C2×#355411yescharacteristic, complemented, Sylow
461C22×#41—792no—
462C22×#41—792no—
463C23×Q8—792no—
464#562—7964no—
465#559—7932no—
466#559—7916no—
467#557—7916no—
468#554—7932no—
469#550—7916no—
470D4×Q8—7916no—
471#548—7932no—
472#547—7932no—
473#542—7932no—
474#542—7932no—
475#540—7932no—
476#539—7964no—
477#536—7932no—
478#533C2×D79116yescomplemented
479#532—7916no—
480C2×C4⋊Q8—792no—
481C2×C4⋊Q8—791no—
482C2×C4⋊Q8—792no—
483C2×C4⋊Q8C2×D7911yescharacteristic
484C2×C4⋊Q8C2×D7911yescharacteristic
485C2×#127—791no—
486C2×#127—792no—
487#529—7916no—
488C2×#126—794no—
489C2×#126—792no—
490C2×#125—794no—
491C2×#125—791no—
492C2×#125—792no—
493C2×#125C2×D7912yes—
494C2×#124—792no—
495C2×#124—794no—
496C2×#124—794no—
497C2×#124—791no—
498C2×#124—792no—
499C2×#124—792no—
500C2×#123—792no—
501C2×#123—794no—
502C2×#123—794no—
503C2×#123—794no—
504C2×#123—794no—
505C2×#123—794no—
506C2×#123—794no—
507C2×C22⋊Q8—794no—
508C2×C22⋊Q8—791no—
509C2×C22⋊Q8—794no—
510C2×C22⋊Q8—794no—
511C2×C22⋊Q8—794no—
512C2×C22⋊Q8—794no—
513C2×C22⋊Q8—792no—
514C2×C22⋊Q8C2×D7911yescharacteristic
515C2×C22⋊Q8C2×D7911yescharacteristic
516C2×C22⋊Q8C2×D7912yes—
517C2×#121—791no—
518C2×#121—792no—
519C2×#121—792no—
520C2×#121—794no—
521C2×#121—792no—
522C2×#121—794no—
523C2×#121—794no—
524C2×C4×Q8—792no—
525C2×C4×Q8—791no—
526C2×C4×Q8—792no—
527C2×C4×Q8C2×D7911yescharacteristic
528C2×C4×Q8C2×D7911yescharacteristic
529C2×C4×Q8C2×D7912yes—
530C2×C4×D4—792no—
531C2×C4×D4—794no—
532C2×C4×D4—792no—
533C2×C4×D4—791no—
534C2×C4×D4—792no—
535C2×C4×D4—792no—
536C2×C4×D4—792no—
537C2×C4×D4—792no—
538C2×C4×D4—792no—
539C2×#117—792no—
540C2×#117C2×D7912yes—
541C22×C4⋊C4—794no—
542C22×C42C2×D7911yescharacteristic
543C2×#41—3168no—
544C2×#41—3168no—
545C2×#41—7916no—
546C2×#41—7916no—
547C22×Q8—3168no—
548C22×Q8—7916no—
549C22×Q8—794no—
550C22×Q8—791no—
551C22×Q8—792no—
552C22×Q8C22×D7911yescharacteristic
553C22×Q8C22×D7911yescharacteristic
554C22×Q8C22×D7912yes—
555C22×D4—792no—
556C22×D4—794no—
557C22×D4—792no—
558C22×D4—794no—
559C22×D4—794no—
560C22×D4—791no—
561C22×D4—792no—
562C22×D4—792no—
563C23×C4—794no—
564C23×C4—794no—
565C23×C4—794no—
566C23×C4—794no—
567C23×C4—792no—
568C23×C4C22×D7911yescharacteristic
569C23×C4C22×D7911yescharacteristic
570C23×C4C22×D7911yescharacteristic
571C4⋊Q8—7916no—
572C4⋊Q8—798no—
573C4⋊Q8—7916no—
574C4⋊Q8C22×D7918yes—
575C4⋊Q8C22×D7918yes—
576#127—798no—
577#127—7916no—
578#126—7932no—
579#126—7916no—
580#125—7932no—
581#125—798no—
582#125—7916no—
583#125C22×D79116yes—
584#124—7916no—
585#124—7932no—
586#124—7932no—
587#124—798no—
588#124—7916no—
589#124—7916no—
590#123—7916no—
591#123—7932no—
592#123—7932no—
593#123—7932no—
594#123—7932no—
595#123—7932no—
596#123—7932no—
597C22⋊Q8—7932no—
598C22⋊Q8—798no—
599C22⋊Q8—7932no—
600C22⋊Q8—7932no—
601C22⋊Q8—7932no—
602C22⋊Q8—7932no—
603C22⋊Q8—7916no—
604C22⋊Q8C22×D7918yes—
605C22⋊Q8C22×D7918yes—
606C22⋊Q8C22×D79116yes—
607#121—798no—
608#121—7916no—
609#121—7916no—
610#121—7932no—
611#121—7916no—
612#121—7932no—
613#121—7932no—
614C4×Q8—7916no—
615C4×Q8—798no—
616C4×Q8—7916no—
617C4×Q8C22×D7918yes—
618C4×Q8C22×D7918yes—
619C4×Q8C22×D79116yes—
620C4×D4—7916no—
621C4×D4—7932no—
622C4×D4—7916no—
623C4×D4—798no—
624C4×D4—7916no—
625C4×D4—7916no—
626C4×D4—7916no—
627C4×D4—7916no—
628C4×D4—7916no—
629#117—7916no—
630#117C22×D79116yes—
631C2×C4⋊C4—792no—
632C2×C4⋊C4—794no—
633C2×C4⋊C4—794no—
634C2×C4⋊C4—792no—
635C2×C4⋊C4—792no—
636C2×C4⋊C4—791no—
637C2×C4⋊C4—791no—
638C2×C4⋊C4—792no—
639C2×C4⋊C4—792no—
640C2×C4⋊C4—794no—
641C2×C4⋊C4—794no—
642C2×C4⋊C4—792no—
643C2×C4⋊C4—7932no—
644C2×C4⋊C4C22×D7912yes—
645C2×C4⋊C4C22×D7912yes—
646C2×C4⋊C4C22×D7912yes—
647C2×C4⋊C4C22×D7912yes—
648C2×C4⋊C4C22×D7911yescharacteristic
649C2×C4⋊C4C22×D7911yescharacteristic
650C2×C4⋊C4C22×D7912yes—
651C2×C4⋊C4C22×D7912yes—
652C2×C4⋊C4C22×D7912yes—
653C2×C22⋊C4—792no—
654C2×C22⋊C4—792no—
655C2×C22⋊C4—792no—
656C2×C22⋊C4—792no—
657C2×C22⋊C4—792no—
658C2×C22⋊C4—794no—
659C2×C22⋊C4—794no—
660C2×C22⋊C4—794no—
661C2×C22⋊C4—794no—
662C2×C22⋊C4—794no—
663C2×C22⋊C4—794no—
664C2×C22⋊C4—794no—
665C2×C22⋊C4C22×D7912yes—
666C2×C22⋊C4C22×D7912yes—
667C2×C42—792no—
668C2×C42—794no—
669C2×C42C22×D7911yescharacteristic
670C2×C42C22×D7912yes—
671C2×C42C22×D7912yes—
672C2×C42C22×D7911yescharacteristic
673C2×C42C22×D7911yescharacteristic
674C2×C42C22×D7911yescharacteristic
675C2×C42C22×D7918yes—
676C24—792no—
677C24—794no—
678C24C23×D7911yescharacteristic
679#41—31632no—
680#41—31632no—
681C2×Q8—24no—
682C2×Q8—24no—
683C2×Q8—44no—
684C2×Q8—3168no—
685C2×Q8—31632no—
686C2×Q8—7916no—
687C2×Q8—794no—
688C2×Q8—798no—
689C2×Q8—1588no—
690C2×Q8—1584no—
691C2×Q8C23×D7914yes—
692C2×Q8C23×D7914yes—
693C2×Q8C23×D7918yes—
694C2×D4—3164no—
695C2×D4—3168no—
696C2×D4—3168no—
697C2×D4—3164no—
698C2×D4—3168no—
699C2×D4—798no—
700C2×D4—7916no—
701C2×D4—798no—
702C2×D4—7916no—
703C2×D4—7916no—
704C2×D4—794no—
705C2×D4—798no—
706C2×D4—798no—
707C2×D4—1588no—
708C2×D4—1584no—
709C2×D4—1588no—
710C22×C4—24no—
711C22×C4—24no—
712C22×C4—42no—
713C22×C4—3168no—
714C22×C4—3168no—
715C22×C4—3168no—
716C22×C4—3168no—
717C22×C4—7916no—
718C22×C4—7916no—
719C22×C4—7916no—
720C22×C4—7916no—
721C22×C4—792no—
722C22×C4—792no—
723C22×C4—794no—
724C22×C4—792no—
725C22×C4—798no—
726C22×C4—1588no—
727C22×C4C23×D7914yes—
728C22×C4C23×D7914yes—
729C22×C4C23×D7912yes—
730C22×C4C23×D7911yescharacteristic
731C22×C4C23×D7911yescharacteristic
732C22×C4C23×D7911yescharacteristic
733C22×C4C23×D7911yescharacteristic
734C22×C4C23×D7912yes—
735C22×C4C23×D7912yes—
736C22×C4C23×D7912yes—
737C22×C4C23×D7914yes—
738C22×C4C23×D7911yescharacteristic
739C22×C4C23×D7911yescharacteristic
740C4⋊C4—798no—
741C4⋊C4—7916no—
742C4⋊C4—798no—
743C4⋊C4—798no—
744C4⋊C4—7916no—
745C4⋊C4—7916no—
746C4⋊C4—798no—
747C4⋊C4—7916no—
748C4⋊C4—794no—
749C4⋊C4—794no—
750C4⋊C4—798no—
751C4⋊C4—798no—
752C4⋊C4C23×D7918yes—
753C4⋊C4C23×D7918yes—
754C4⋊C4C23×D7918yes—
755C4⋊C4C23×D7918yes—
756C4⋊C4C23×D7914yes—
757C4⋊C4C23×D7914yes—
758C4⋊C4C23×D7918yes—
759C4⋊C4C23×D7918yes—
760C4⋊C4C23×D7918yes—
761C22⋊C4—798no—
762C22⋊C4—798no—
763C22⋊C4—798no—
764C22⋊C4—798no—
765C22⋊C4—798no—
766C22⋊C4—7916no—
767C22⋊C4—7916no—
768C22⋊C4—7916no—
769C22⋊C4—7916no—
770C22⋊C4—7916no—
771C22⋊C4—7916no—
772C22⋊C4—7916no—
773C22⋊C4C23×D7918yes—
774C22⋊C4C23×D7918yes—
775C42—798no—
776C42—7916no—
777C42C23×D7914yes—
778C42C23×D7914yes—
779C42C23×D7914yes—
780C42C23×D7914yes—
781C42C23×D7918yes—
782C42C23×D7918yes—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—794no—
787C23—798no—
788C23—1584no—
789C23—1588no—
790C23—1584no—
791C23—1588no—
792C23—1588no—
793C23—1584no—
794C23C24×D7912yes—
795C23C24×D7911yescharacteristic
796Q8—28no—
797Q8—28no—
798Q8—48no—
799Q8—31616no—
800Q8—15816no—
801Q8—1588no—
802D4—31616no—
803D4—3168no—
804D4—31616no—
805D4—3168no—
806D4—31616no—
807D4—15816no—
808D4—1588no—
809D4—15816no—
810C2×C4—22no—
811C2×C4—24no—
812C2×C4—24no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—28no—
819C2×C4—28no—
820C2×C4—44no—
821C2×C4—31616no—
822C2×C4—31616no—
823C2×C4—31616no—
824C2×C4—31616no—
825C2×C4—794no—
826C2×C4—794no—
827C2×C4—798no—
828C2×C4—794no—
829C2×C4—1584no—
830C2×C4—1588no—
831C2×C4—1584no—
832C2×C4—1584no—
833C2×C4—15816no—
834C2×C4#1457920714yes—
835C2×C4#1457920914yes—
836C2×C4C24×D7914yes—
837C2×C4C24×D7912yes—
838C2×C4C24×D7912yes—
839C2×C4C24×D7912yes—
840C2×C4C24×D7912yes—
841C2×C4C24×D7914yes—
842C2×C4C24×D7914yes—
843C2×C4C24×D7914yes—
844C2×C4C24×D7912yes—
845C2×C4C24×D7912yes—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—44no—
850C22—3168no—
851C22—31616no—
852C22—1584no—
853C22—1588no—
854C22—1584no—
855C22—1588no—
856C22—1588no—
857C22—1584no—
858C22C2×#1457920712yes—
859C22C2×#1457920912yes—
860C22#1909939912yes—
861C22C25×D7911yescharacteristic
862C4—22no—
863C4—24no—
864C4—24no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—24no—
869C4—24no—
870C4—1584no—
871C4—1588no—
872C4—1584no—
873C4—1584no—
874C4C2×#1457920714yes—
875C4C2×#1457920914yes—
876C2—42no—
877C2—3164no—
878C2—3168no—
879C2#2377787114yesdirect product factor
880C2C22×#1457920711yescharacteristic
881C2C22×#1457920911yescharacteristic
882C2C2×#1909939911yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#533×C79C2
socleC23×C79C25
hypercenterC2×#533D79
hypocenterC79C2×#3554
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #23777871C2direct (N × H)
2. C2×#19099309C2semidirect
3. C2×#19099298C2semidirect
4. C2×#19099298C2semidirect
5. C2×#19099291C2semidirect
6. C2×#19099273C2semidirect
7. C2×#19099235C2semidirect
8. C2×Q8×D316C2semidirect
9. C2×#19099223C2semidirect
10. C2×#19099215C2semidirect
11. C2×#19099187C2semidirect
12. C2×#19099184C2semidirect
13. C2×#19099168C2semidirect
14. C2×#19099161C2semidirect
15. C2×#19099138C2semidirect
16. C2×#19099113C2semidirect
17. C2×#19099097C2semidirect
18. C2×#533×C79C2semidirect
22. #19099309C22semidirect
23. #19099298C22semidirect
24. #19099298C22semidirect
25. #19099291C22semidirect
26. #19099273C22semidirect
27. #19099235C22semidirect
28. Q8×D316C22semidirect
29. #19099223C22semidirect
30. #19099215C22semidirect
31. #19099187C22semidirect
32. #19099184C22semidirect
33. #19099168C22semidirect
34. #19099161C22semidirect
35. #19099138C22semidirect
36. #19099113C22semidirect
42. #19099097C22semidirect
89. #533×C79C22semidirect
436. C2×C79#3554semidirect
457. C2×#533D79semidirect
460. C79C2×#3554semidirect
478. #533C2×D79semidirect
879. C2#23777871direct (N × H)

Maximal subgroups

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

subgroupindex
#237778712
C2×#190993092
C2×#190992982
C2×#190992912
C2×#190992732
C2×#190992352
C2×Q8×D3162
C2×#190992232
C2×#190992152
C2×#190991872
C2×#190991842
C2×#190991682
C2×#190991612
C2×#190991382
C2×#190991132
C2×#190990972
C2×#533×C792
C2×#355479