Finite Group Databasebeta

← #36312992

Subgroups — #36312992

Order 21248.

7210 conjugacy classes of subgroups.

The subgroup lattice has 1216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24921384C214yesmaximal, complemented
2#24921372C214yesmaximal, complemented
3#24921362C212yesmaximal, complemented
4#24921358C212yesmaximal, complemented
5#24921348C212yesmaximal, complemented
6#24921338C212yesmaximal, complemented
7#24921327C214yesmaximal, complemented
8#24921314C214yesmaximal, complemented
9#24921300C218yesmaximal, complemented
10#24921060C218yesmaximal, complemented
11#24921023C218yesmaximal, complemented
12#24920851C214yesmaximal, complemented
13#24920792C211yesmaximal, characteristic, complemented
14#24920755C214yesmaximal, complemented
15C2×#19128254C211yesmaximal, characteristic, complemented
16C2×#19128247C211yesmaximal, characteristic, complemented
17#24920666C211yesmaximal, characteristic, complemented
18#24920664C211yesmaximal, characteristic, complemented
19C2×#41×Dic83C211yesmaximal, characteristic, complemented
20C83×#3449C211yesmaximal, characteristic, complemented
21C22×#13050590C2211yescharacteristic
22#19128437C2218yescomplemented
23#19128433C2218yescomplemented
24#19128433C2218yescomplemented
25#19128426C2218yescomplemented
26#19128425C2218yescomplemented
27#19128422C2218yescomplemented
28#19128420C2218yescomplemented
29#19128420C2218yescomplemented
30#19128415C2218yescomplemented
31#19128409C2218yescomplemented
32#19128403C2218yescomplemented
33#19128403C22116yescomplemented
34#19128398C2218yescomplemented
35#19128394C22116yescomplemented
36#19128394C22116yescomplemented
37#19128393C2218yescomplemented
38#19128388C22116yescomplemented
39#19128385C2218yescomplemented
40#19128382C22116yescomplemented
41#19128374C22116yescomplemented
42#19128371C2218yescomplemented
43#19128357C22116yescomplemented
44#19128351C2218yescomplemented
45#19128338C22116yescomplemented
46#19128324C2218yescomplemented
47#19128318C2218yescomplemented
48#19128311C2218yescomplemented
49#19128304C2218yescomplemented
50#19128295C22116yescomplemented
51#19128286C22116yescomplemented
52#19128279C2214yescomplemented
53#19128275C2212yescomplemented
54#19128272C2212yes—
55#19128268C2212yescomplemented
56#19128265C2212yes—
57#19128260C2214yes—
58#19128254C2212yescomplemented
59#19128254C2212yescomplemented
60#19128254C2212yescomplemented
61#19128254C2212yescomplemented
62#19128254C2214yescomplemented
63#19128254C2214yescomplemented
64#19128253C2218yescomplemented
65#19128247C2212yes—
66#19128247C2212yes—
67#19128247C2214yes—
68#19128247C2212yescomplemented
69#19128247C2212yescomplemented
70#19128247C2214yescomplemented
71#19128247C2214yescomplemented
72#19128246C2218yescomplemented
73C2×#14581791C2212yescomplemented
74C2×#14581790C2211yescharacteristic, complemented
75C2×#14581788C2211yescharacteristic, complemented
76#19128237C2218yescomplemented
77#19128233C22116yescomplemented
78#19128232C2218yescomplemented
79#19128231C22116yescomplemented
80#19128231C22116yescomplemented
81#19128228C22116yescomplemented
82C2×#14581783C2212yescomplemented
83C2×#14581781C2211yescharacteristic, complemented
84C2×#14581779C2211yescharacteristic, complemented
85#19128212C2214yescomplemented
86#19128208C2214yes—
87#19128207C22116yescomplemented
88C2×#14581769C2214yes—
89C2×#14581764C2214yes—
90#19128184C2214yescomplemented
91#19128184C2214yescomplemented
92#19128182C2214yescomplemented
93#19128181C2214yescomplemented
94#19128179C2212yescomplemented
95#19128178C2212yescomplemented
96#19128176C2214yes—
97#19128176C2212yescomplemented
98#19128175C2212yescomplemented
99#19128174C2214yes—
100#41×Dic83C2212yes—
101#41×Dic83C2212yes—
102#41×Dic83C2214yes—
103#41×Dic83C2214yescomplemented
104#41×Dic83C2212yescomplemented
105#41×Dic83C2212yescomplemented
106#41×Dic83C2214yescomplemented
107#41×Dic83C2214yescomplemented
108C4×#13050590C2214yescomplemented
109#19128169C2214yescomplemented
110C4×#13050589C22116yescomplemented
111C2×Q8×Dic83C2212yescomplemented
112C2×C4×Dic166C2214yescomplemented
113C2×D4×Dic83C2214yes—
114C2×D4×Dic83C2212yescomplemented
115C2×C4×C22⋊D83C2214yescomplemented
116C2×#14581751C2211yescharacteristic
117C2×#14581751C2211yescharacteristic
118C2×#14581751C2212yescomplemented
119C2×#14581751C2214yescomplemented
120#117×D83C2214yescomplemented
121C22×C4×Dic83C2211yescharacteristic
122C22×C4×Dic83C2212yescomplemented
123C22×#41×C83C2211yescharacteristic
124C22×#41×C83C2211yescharacteristic
125#537×C83C2214yescomplemented
126#536×C83C2212yes—
127#536×C83C2212yescomplemented
128#535×C83C2212yes—
129#535×C83C2212yescomplemented
130#534×C83C2214yes—
131#532×C83C2214yescomplemented
132#525×C83C2214yes—
133#525×C83C2214yescomplemented
134C2×#117×C83C2211yescharacteristic
135C2×#13050590—28no—
136C2×#13050590C2312yes—
137C2×#13050590C2312yes—
138C2×#13050590C2312yes—
139C2×#13050590C2312yes—
140C2×#13050589C23116yes—
141C22×Dic166C2311yescharacteristic
142C22×Dic166C2314yes—
143C22×D332C2311yescharacteristic
144C22×C22⋊D83C2312yes—
145C22×C22⋊D83C2314yes—
146C23×Dic83C2312yes—
147C23×Dic83C2314yes—
148C22×C4×D83C2312yes—
149#14581791C2314yes—
150#14581791C2314yes—
151#14581791C2314yes—
152#14581791C2314yes—
153#14581790C2314yes—
154#14581790C2314yes—
155#14581790C2312yes—
156#14581790C2312yes—
157#14581788C2314yes—
158#14581788C2314yes—
159#14581788C2312yes—
160#14581788C2312yes—
161#14581787C23116yes—
162#14581787C23116yes—
163#14581785C23116yes—
164#14581785C23116yes—
165#14581785C23116yes—
166#14581785C23116yes—
167#14581783C2314yes—
168#14581783C23116yes—
169#14581783C2314yes—
170#14581783C2314yes—
171#14581783C2314yes—
172#14581782C23116yes—
173#14581782C23116yes—
174#14581781C2312yes—
175#14581781C2314yes—
176#14581781C2314yes—
177#14581781C2312yes—
178#14581779C23116yes—
179#14581779C2314yes—
180#14581779C2314yes—
181#14581779C2312yes—
182#14581779C2312yes—
183#14581778C23116yes—
184#14581778C23116yes—
185#14581776C23116yes—
186#14581776C23116yes—
187#14581775C2318yes—
188#14581774C23116yes—
189#14581774C23116yes—
190#14581773C23116yes—
191#14581773C2318yes—
192#14581773C23116yes—
193#14581772C23116yes—
194#14581771C2318yes—
195#14581769C2318yes—
196#14581769C23116yes—
197#14581769C23116yes—
198#14581769C2318yes—
199#14581769C2318yes—
200#14581769C2318yes—
201#14581768C2318yes—
202#14581766C2318yes—
203#14581764C23116yes—
204#14581764C23116yes—
205#14581764C2318yes—
206#14581764C23116yes—
207#14581764C2318yes—
208#14581764C2318yes—
209#14581764C2318yes—
210#14581763C23116yes—
211#14581763C2318yes—
212#14581761C2318yes—
213#14581760C2318yes—
214Q8×Dic83C2318yes—
215Q8×Dic83C2314yes—
216Q8×Dic83C2314yes—
217Q8×Dic83C2314yes—
218Q8×Dic83C2318yes—
219Q8×Dic83C2314yes—
220C4×Dic166C2318yes—
221C4×Dic166C2318yes—
222C4×Dic166C2318yes—
223C4×Dic166C2318yes—
224C4×Dic166C2318yes—
225#14581757C23116yes—
226#14581757C2318yes—
227C4×D332C2318yes—
228D4×Dic83C2318yes—
229D4×Dic83C2314yes—
230D4×Dic83C2318yes—
231D4×Dic83C23116yes—
232D4×Dic83C2314yes—
233D4×Dic83C2318yes—
234D4×Dic83C2318yes—
235D4×Dic83C23116yes—
236D4×Dic83C2318yes—
237D4×Dic83C2314yes—
238D4×Dic83C2314yes—
239D4×Dic83C23116yes—
240D4×Dic83C2318yes—
241#14581754C2318yes—
242C4×C22⋊D83C2318yes—
243C4×C22⋊D83C23116yes—
244C4×C22⋊D83C2318yes—
245C4×C22⋊D83C2318yes—
246C4×C22⋊D83C2318yes—
247C4×C22⋊D83C23116yes—
248(C22⋊D83)⋊C4C23116yes—
249(C22⋊D83)⋊C4C23116yes—
250(C22⋊D83)⋊C4C23116yes—
251#14581751C2314yes—
252#14581751C2318yes—
253#14581751C2318yes—
254#14581751C2312yes—
255#14581751C2312yes—
256#14581751C2312yes—
257#14581751C2312yes—
258#14581751C2312yes—
259#14581751C2312yes—
260#14581751C2312yes—
261#14581751C2312yes—
262#14581751C2318yes—
263#14581751C2314yes—
264#14581751C2318yes—
265#14581750C23116yes—
266#14581750C2318yes—
267#14581749C2318yes—
268#14581748C2318yes—
269#14581748C23116yes—
270#14581748C23116yes—
271C2×C4⋊Dic83C2318yes—
272C2×C4⋊Dic83C2314yes—
273C2×C4⋊Dic83C2312yes—
274C2×C4⋊Dic83C2312yes—
275C2×C4⋊Dic83C2314yes—
276C2×Dic83⋊C4C2314yes—
277C2×Dic83⋊C4C2314yes—
278C2×Dic83⋊C4C2314yes—
279C4⋊C4×D83C2318yes—
280C2×C22⋊Dic83C2318yes—
281C2×C22⋊Dic83C2314yes—
282C2×C22⋊Dic83C2312yes—
283C2×C22⋊Dic83C2312yes—
284C2×C22⋊Dic83C2314yes—
285C2×(C2×D83)⋊C4C2314yes—
286C22⋊C4×D83C2318yes—
287C2×C4×Dic83C2311yescharacteristic
288C2×C4×Dic83C2311yescharacteristic
289C2×C4×Dic83C2312yes—
290C2×C4×Dic83C2312yes—
291C2×C4×Dic83C2312yes—
292C2×C4×Dic83C2311yescharacteristic
293C2×C4×Dic83C2311yescharacteristic
294C2×C4×Dic83C2311yescharacteristic
295C2×C4×Dic83C2311yescharacteristic
296C2×C4×Dic83C2312yes—
297C2×C4×Dic83C2314yes—
298C2×C4×Dic83C2318yes—
299C2×C4×Dic83C2314yes—
300C2×C4×Dic83C2314yes—
301C2×C4×Dic83C2312yes—
302C2×C4×Dic83C2318yes—
303C42×D83C2318yes—
304C2×#41×C83—28no—
305C2×#41×C83—28no—
306C2×#41×C83C2312yes—
307C2×#41×C83C2312yes—
308C2×#41×C83C2312yes—
309C2×#41×C83C2312yes—
310C2×#41×C83C2312yes—
311C2×#41×C83C2312yes—
312C2×#41×C83C2312yes—
313C2×#41×C83C2312yes—
314C22×Q8×C83C2311yescharacteristic
315C22×Q8×C83C2311yescharacteristic
316C22×D4×C83C2312yes—
317C22×D4×C83C2312yes—
318C22×D4×C83C2311yescharacteristic
319C22×D4×C83C2311yescharacteristic
320C23×C4×C83C2312yes—
321C23×C4×C83C2312yes—
322C23×C4×C83C2311yescharacteristic
323C4⋊Q8×C83C2314yes—
324#127×C83C2314yes—
325#124×C83C2314yes—
326#124×C83C2314yes—
327#123×C83C2318yes—
328#123×C83C2318yes—
329C22⋊Q8×C83C2318yes—
330C22⋊Q8×C83C2318yes—
331#121×C83C2318yes—
332#121×C83C23116yes—
333#121×C83C2318yes—
334#120×C83C2318yes—
335#120×C83C2318yes—
336C4×D4×C83C23116yes—
337#117×C83C2312yes—
338#117×C83C2312yes—
339#117×C83C2312yes—
340#117×C83C2312yes—
341C2×C4⋊C4×C83C2312yes—
342C2×C22⋊C4×C83C2312yes—
343C2×C42×C83C2312yes—
344C23×D83C2412yes—
345#13050590—28no—
346#13050590—28no—
347#13050590—28no—
348#13050590—28no—
349#13050589—432no—
350C2×Dic166—24no—
351C2×Dic166—48no—
352C2×Dic166C2418yes—
353C2×Dic166C2412yes—
354C2×Dic166C2412yes—
355C2×Dic166C2418yes—
356C2×D332—24no—
357C2×D332C2412yes—
358C2×D332C2412yes—
359C2×C22⋊D83—28no—
360C2×C22⋊D83—48no—
361C2×C22⋊D83C2414yes—
362C2×C22⋊D83C2414yes—
363C2×C22⋊D83C2418yes—
364C2×C22⋊D83C24116yes—
365C2×C22⋊D83C2418yes—
366C22×Dic83—44no—
367C22×Dic83—48no—
368C22×Dic83C2412yes—
369C22×Dic83C2412yes—
370C22×Dic83C2418yes—
371C22×Dic83C2412yes—
372C22×Dic83C2412yes—
373C22×Dic83C2412yes—
374C22×Dic83C2412yes—
375C22×Dic83C2414yes—
376C22×Dic83C24116yes—
377C22×Dic83C2412yes—
378C22×Dic83C2418yes—
379C22×Dic83C2414yes—
380C2×C4×D83—28no—
381C2×C4×D83C2414yes—
382C2×C4×D83C2414yes—
383C2×C4×D83C24116yes—
384C4⋊Dic83C2414yes—
385C4⋊Dic83C2418yes—
386C4⋊Dic83C2414yes—
387C4⋊Dic83C2418yes—
388C4⋊Dic83C2418yes—
389C4⋊Dic83C24116yes—
390C4⋊Dic83C2418yes—
391C4⋊Dic83C2414yes—
392C4⋊Dic83C2414yes—
393Dic83⋊C4C2418yes—
394Dic83⋊C4C2418yes—
395Dic83⋊C4C2418yes—
396Dic83⋊C4C2418yes—
397Dic83⋊C4C24116yes—
398Dic83⋊C4C2418yes—
399Dic83⋊C4C24116yes—
400Dic83⋊C4C2418yes—
401C22⋊Dic83C2414yes—
402C22⋊Dic83C2414yes—
403C22⋊Dic83C24116yes—
404C22⋊Dic83C2418yes—
405C22⋊Dic83C24116yes—
406C22⋊Dic83C2418yes—
407C22⋊Dic83C2418yes—
408C22⋊Dic83C2418yes—
409C22⋊Dic83C2414yes—
410C22⋊Dic83C2414yes—
411(C2×D83)⋊C4C24116yes—
412(C2×D83)⋊C4C2418yes—
413(C2×D83)⋊C4C24116yes—
414(C2×D83)⋊C4C2418yes—
415C4×Dic83C2418yes—
416C4×Dic83C24116yes—
417C4×Dic83C2411yescharacteristic
418C4×Dic83C2411yescharacteristic
419C4×Dic83C2412yes—
420C4×Dic83C2414yes—
421C4×Dic83C24116yes—
422C4×Dic83C2411yescharacteristic
423C4×Dic83C2412yes—
424C4×Dic83C2418yes—
425C4×Dic83C2411yescharacteristic
426C4×Dic83C2412yes—
427C4×Dic83C2412yes—
428C4×Dic83C2414yes—
429C4×Dic83C2412yes—
430C4×Dic83C2412yes—
431C4×Dic83C2414yes—
432C4×Dic83C2414yes—
433C24×C83C2412yes—
434C24×C83C2412yes—
435C24×C83C2411yescharacteristic
436#41×C83—28no—
437#41×C83—28no—
438#41×C83—28no—
439#41×C83—28no—
440#41×C83—28no—
441#41×C83—28no—
442#41×C83—28no—
443#41×C83—28no—
444C2×Q8×C83—24no—
445C2×Q8×C83—24no—
446C2×Q8×C83C2412yes—
447C2×Q8×C83C2412yes—
448C2×Q8×C83C2412yes—
449C2×Q8×C83C2412yes—
450C2×D4×C83—28no—
451C2×D4×C83—28no—
452C2×D4×C83—24no—
453C2×D4×C83—24no—
454C2×D4×C83C2414yes—
455C2×D4×C83C2412yes—
456C2×D4×C83C2414yes—
457C2×D4×C83C2414yes—
458C2×D4×C83C2414yes—
459C2×D4×C83C2412yes—
460C2×D4×C83C2412yes—
461C2×D4×C83C2412yes—
462C2×D4×C83C24116yes—
463C22×C4×C83—28no—
464C22×C4×C83—28no—
465C22×C4×C83#4118yescomplemented
466C22×C4×C83C2414yes—
467C22×C4×C83C2412yes—
468C22×C4×C83C2414yes—
469C22×C4×C83C2414yes—
470C22×C4×C83C2414yes—
471C22×C4×C83C2412yes—
472C22×C4×C83C2414yes—
473C22×C4×C83C2411yescharacteristic
474C22×C4×C83C2411yescharacteristic
475C22×C4×C83C2411yescharacteristic
476C22×C4×C83C2411yescharacteristic
477C22×C4×C83C2411yescharacteristic
478C22×C4×C83C2411yescharacteristic
479C4⋊C4×C83C24116yes—
480C4⋊C4×C83C2414yes—
481C4⋊C4×C83C2414yes—
482C22⋊C4×C83C2414yes—
483C22⋊C4×C83C2414yes—
484C22⋊C4×C83C24116yes—
485C22⋊C4×C83C24116yes—
486C42×C83C2414yes—
487C42×C83C2414yes—
488C23×C83—24no—
489C23×C83—24no—
490C23×C83—42no—
491C23×C83—44no—
492C23×C83—44no—
493C23×C83C2×#4114yes—
494C23×C83C2514yes—
495C23×C83C2514yes—
496C23×C83C2511yescharacteristic
497C23×C83C2511yescharacteristic
498C23×C83C2511yescharacteristic
499C22×D83—24no—
500C22×D83—44no—
501C22×D83C2514yes—
502Q8×C83—24no—
503Q8×C83—24no—
504Q8×C83—24no—
505Q8×C83—24no—
506D4×C83—28no—
507D4×C83—28no—
508D4×C83—28no—
509D4×C83—28no—
510D4×C83—24no—
511D4×C83—24no—
512D4×C83—24no—
513D4×C83—24no—
514D4×C83—416no—
515C2×C4×C83—24no—
516C2×C4×C83—24no—
517C2×C4×C83—28no—
518C2×C4×C83—28no—
519C2×C4×C83—28no—
520C2×C4×C83—28no—
521C2×C4×C83—44no—
522C2×C4×C83C2×#4114yes—
523C2×C4×C83C2×#4114yes—
524C2×C4×C83C2×#4114yes—
525C2×C4×C83C2×#4114yes—
526C2×C4×C83C2×#4114yes—
527C2×C4×C83C2×#4114yes—
528C2×C4×C83C2518yes—
529C2×C4×C83C2514yes—
530C2×C4×C83C2514yes—
531C2×C4×C83C2511yescharacteristic
532C2×C4×C83C2511yescharacteristic
533C2×C4×C83C2511yescharacteristic
534C2×C4×C83C2511yescharacteristic
535C22⋊D83—28no—
536C22⋊D83—28no—
537C22⋊D83—216no—
538C22⋊D83—48no—
539C22⋊D83—416no—
540C2×Dic83—24no—
541C2×Dic83—24no—
542C2×Dic83—24no—
543C2×Dic83—24no—
544C2×Dic83—216no—
545C2×Dic83—42no—
546C2×Dic83—42no—
547C2×Dic83—44no—
548C2×Dic83—48no—
549C2×Dic83—42no—
550C2×Dic83—44no—
551C2×Dic83—416no—
552C2×Dic83C2512yes—
553C2×Dic83C2518yes—
554C2×Dic83C2512yes—
555C2×Dic83C2518yes—
556C2×Dic83C2514yes—
557C2×Dic83C2512yes—
558C2×Dic83C2512yes—
559D332—24no—
560D332—24no—
561C4×D83—28no—
562C4×D83—28no—
563C4×D83—416no—
564Dic166—24no—
565Dic166—24no—
566Dic166—216no—
567Dic166—48no—
568C22×C83—22no—
569C22×C83—22no—
570C22×C83—22no—
571C22×C83—24no—
572C22×C83—24no—
573C22×C83—28no—
574C22×C83—28no—
575C22×C83—44no—
576C22×C83—48no—
577C22×C83—84no—
578C22×C83C22×#4112yes—
579C22×C83C22×#4112yes—
580C22×C83C22×#4112yes—
581C22×C83C2611yescharacteristic
582C2×D83—24no—
583C2×D83—28no—
584C2×D83—84no—
585C4×C83—24no—
586C4×C83—24no—
587C4×C83—28no—
588C4×C83C22×#4112yes—
589C4×C83C22×#4112yes—
590C4×C83C22×#4112yes—
591C4×C83C22×#4112yes—
592Dic83—24no—
593Dic83—28no—
594Dic83—22no—
595Dic83—28no—
596Dic83—22no—
597Dic83—22no—
598Dic83#58514yes—
599#62815—831nomaximal, Sylow
600C2×C83—22no—
601C2×C83—22no—
602C2×C83—22no—
603C2×C83—44no—
604C2×C83—44no—
605C2×C83C23×#4111yescharacteristic
606C2×C83C2×#58512yes—
607D83—44no—
608#3512—834no—
609#3511—834no—
610#3510—832no—
611#3510—832no—
612#3509—832no—
613#3508—832no—
614#3507—834no—
615#3506—834no—
616#3505—838no—
617#3480—838no—
618#3475—838no—
619#3455—834no—
620#3449—831no—
621#3449D8311yescharacteristic, complemented
622#3444—834no—
623C2×#533—831no—
624C2×#532—831no—
625#3428—831no—
626#3428—831no—
627C2×C4×#41—831no—
628C83#6281511yescharacteristic, complemented, Sylow
629C22×#41—831no—
630C22×#41C2×D8311yescharacteristic
631C22×#41C2×D8311yescharacteristic
632#559—838no—
633#559—838no—
634#559—838no—
635#557—838no—
636#556—838no—
637#556—838no—
638#556—838no—
639#556—838no—
640#555—838no—
641#554—838no—
642#553—8316no—
643#553—8316no—
644#553—838no—
645#553—838no—
646#553—8316no—
647#552—8316no—
648#552—838no—
649#552—838no—
650#551—8316no—
651#551—8316no—
652#550—838no—
653#548—8316no—
654#547—838no—
655#546—8316no—
656#542—838no—
657#542—838no—
658#541—838no—
659#540—838no—
660#539—8316no—
661#538—8316no—
662#537—834no—
663#537C2×D8314yescomplemented
664#536—832no—
665#536—832no—
666#536C2×D8312yes—
667#536C2×D8312yescomplemented
668#535—832no—
669#535—832no—
670#535C2×D8312yes—
671#535C2×D8312yescomplemented
672#534—834no—
673#534C2×D8314yes—
674#533—838no—
675#533—832no—
676#533—832no—
677#533—834no—
678#533—834no—
679#533—832no—
680#533—832no—
681#532—832no—
682#532—832no—
683#532—834no—
684#532—834no—
685#532—832no—
686#532—832no—
687#532—834no—
688#532—838no—
689#532C2×D8314yescomplemented
690C2×C4⋊Q8—831no—
691C2×C4⋊Q8—832no—
692C2×#127—831no—
693#529—8316no—
694#529—838no—
695#529—838no—
696#529—8316no—
697#529—8316no—
698#529—8316no—
699C2×#125—832no—
700C2×#124—831no—
701C2×#124—831no—
702#525—834no—
703#525—834no—
704#525—8316no—
705#525C2×D8314yes—
706#525C2×D8314yescomplemented
707C2×C22⋊Q8—834no—
708C2×#121—834no—
709#520—834no—
710#520—834no—
711#520—834no—
712#520—834no—
713#519—832no—
714#519—832no—
715#518—834no—
716#518—832no—
717#518—832no—
718#518—834no—
719C4×#41—834no—
720C4×#41—832no—
721C4×#41—832no—
722C4×#41—834no—
723C4×#41—832no—
724C4×#41—832no—
725C4×#41—834no—
726C4×#41—834no—
727C4×#41—8316no—
728C4×#41—834no—
729C4×#41—834no—
730C2×C4×Q8—832no—
731C2×C4×Q8—834no—
732C2×C4×D4—834no—
733C2×C4×D4—832no—
734C2×C4×D4—834no—
735C2×#117—831no—
736C2×#117—831no—
737C2×#117—832no—
738C2×#117—834no—
739C2×#117—834no—
740C2×#117C2×D8311yescharacteristic
741C22×C42—831no—
742C22×C42—832no—
743C2×#41—28no—
744C2×#41—28no—
745C2×#41—8316no—
746C2×#41—832no—
747C2×#41—832no—
748C2×#41—832no—
749C2×#41—832no—
750C2×#41—1668no—
751C2×#41C22×D8312yes—
752C2×#41C22×D8312yes—
753C2×#41C22×D8312yes—
754C2×#41C22×D8312yes—
755C2×#41C22×D8312yes—
756C2×#41C22×D8312yes—
757C2×#41C22×D8312yes—
758C2×#41C22×D8312yes—
759C22×Q8—834no—
760C22×Q8—831no—
761C22×Q8C22×D8311yescharacteristic
762C22×Q8C22×D8311yescharacteristic
763C22×D4—834no—
764C22×D4—832no—
765C22×D4—831no—
766C22×D4C22×D8312yes—
767C22×D4C22×D8311yescharacteristic
768C22×D4C22×D8312yes—
769C22×D4C22×D8311yescharacteristic
770C23×C4—832no—
771C23×C4—834no—
772C23×C4—832no—
773C23×C4C22×D8312yes—
774C23×C4C22×D8312yes—
775C23×C4C22×D8311yescharacteristic
776C4⋊Q8—832no—
777C4⋊Q8—832no—
778C4⋊Q8—834no—
779C4⋊Q8—834no—
780C4⋊Q8—834no—
781C4⋊Q8—834no—
782C4⋊Q8—834no—
783C4⋊Q8—834no—
784C4⋊Q8C22×D8314yes—
785#127—832no—
786#127—832no—
787#127—834no—
788#127—834no—
789#127C22×D8314yes—
790#126—8316no—
791#126—8316no—
792#126—8316no—
793#126—8316no—
794#126—8316no—
795#126—8316no—
796#125—834no—
797#125—834no—
798#125—834no—
799#125—834no—
800#125—8316no—
801#125—8316no—
802#125—8316no—
803#124—832no—
804#124—832no—
805#124—834no—
806#124—834no—
807#124—832no—
808#124—832no—
809#124—834no—
810#124—8316no—
811#124—834no—
812#124—8316no—
813#124—8316no—
814#124C22×D8314yes—
815#124C22×D8314yes—
816#123—8316no—
817#123—838no—
818#123—8316no—
819#123—838no—
820#123—8316no—
821#123—8316no—
822#123—8316no—
823#123—8316no—
824#123C22×D8318yes—
825#123C22×D8318yes—
826C22⋊Q8—838no—
827C22⋊Q8—838no—
828C22⋊Q8—8316no—
829C22⋊Q8—838no—
830C22⋊Q8—838no—
831C22⋊Q8—838no—
832C22⋊Q8—838no—
833C22⋊Q8—8316no—
834C22⋊Q8—8316no—
835C22⋊Q8C22×D8318yes—
836C22⋊Q8C22×D8318yes—
837#121—838no—
838#121—8316no—
839#121—838no—
840#121—838no—
841#121—838no—
842#121—838no—
843#121—8316no—
844#121—8316no—
845#121—8316no—
846#121—838no—
847#121C22×D8318yes—
848#121C22×D8318yes—
849#121C22×D83116yes—
850#120—838no—
851#120—838no—
852#120C22×D8318yes—
853#120C22×D8318yes—
854C4×Q8—834no—
855C4×Q8—834no—
856C4×Q8—834no—
857C4×Q8—834no—
858C4×Q8—838no—
859C4×Q8—838no—
860C4×Q8—838no—
861C4×Q8—8316no—
862C4×Q8—838no—
863C4×Q8—838no—
864C4×Q8—838no—
865C4×Q8—838no—
866C4×Q8—838no—
867C4×D4—838no—
868C4×D4—834no—
869C4×D4—838no—
870C4×D4—834no—
871C4×D4—838no—
872C4×D4—838no—
873C4×D4—834no—
874C4×D4—834no—
875C4×D4—8316no—
876C4×D4—838no—
877C4×D4—8316no—
878C4×D4—838no—
879C4×D4—8316no—
880C4×D4—838no—
881C4×D4—838no—
882C4×D4—838no—
883C4×D4—838no—
884C4×D4—8316no—
885C4×D4—8316no—
886C4×D4—838no—
887C4×D4—8316no—
888C4×D4—8316no—
889C4×D4—8316no—
890C4×D4—838no—
891C4×D4C22×D83116yes—
892#117—832no—
893#117—832no—
894#117—832no—
895#117—832no—
896#117—832no—
897#117—832no—
898#117—838no—
899#117—838no—
900#117—834no—
901#117—834no—
902#117—832no—
903#117—838no—
904#117—832no—
905#117—838no—
906#117—838no—
907#117—8316no—
908#117—838no—
909#117—8316no—
910#117—8316no—
911#117—838no—
912#117C22×D8312yes—
913#117C22×D8312yes—
914#117C22×D8312yes—
915#117C22×D8312yes—
916C2×C4⋊C4—832no—
917C2×C4⋊C4—834no—
918C2×C4⋊C4—832no—
919C2×C4⋊C4—838no—
920C2×C4⋊C4—834no—
921C2×C4⋊C4—834no—
922C2×C4⋊C4—834no—
923C2×C4⋊C4—834no—
924C2×C4⋊C4—838no—
925C2×C4⋊C4C22×D8312yes—
926C2×C22⋊C4—832no—
927C2×C22⋊C4—834no—
928C2×C22⋊C4—832no—
929C2×C22⋊C4—838no—
930C2×C22⋊C4—834no—
931C2×C22⋊C4—834no—
932C2×C22⋊C4—838no—
933C2×C22⋊C4C22×D8312yes—
934C2×C42—832no—
935C2×C42—831no—
936C2×C42—832no—
937C2×C42—838no—
938C2×C42—832no—
939C2×C42—834no—
940C2×C42—832no—
941C2×C42—832no—
942C2×C42—838no—
943C2×C42—831no—
944C2×C42—831no—
945C2×C42—834no—
946C2×C42—831no—
947C2×C42—831no—
948C2×C42—834no—
949C2×C42—831no—
950C2×C42—838no—
951C2×C42C22×D8312yes—
952C24—832no—
953C24C23×D8312yes—
954C24C23×D8312yes—
955C24C23×D8311yescharacteristic
956#41—28no—
957#41—28no—
958#41—28no—
959#41—28no—
960#41—28no—
961#41—28no—
962#41—28no—
963#41—28no—
964#41—33232no—
965#41—1668no—
966#41—1668no—
967#41—1668no—
968#41—1668no—
969C2×Q8—24no—
970C2×Q8—24no—
971C2×Q8—3328no—
972C2×Q8—838no—
973C2×Q8—838no—
974C2×Q8—832no—
975C2×Q8—832no—
976C2×Q8—1664no—
977C2×Q8C23×D8312yes—
978C2×Q8C23×D8312yes—
979C2×Q8C23×D8312yes—
980C2×Q8C23×D8312yes—
981C2×D4—28no—
982C2×D4—28no—
983C2×D4—24no—
984C2×D4—24no—
985C2×D4—3328no—
986C2×D4—8316no—
987C2×D4—838no—
988C2×D4—834no—
989C2×D4—834no—
990C2×D4—838no—
991C2×D4—832no—
992C2×D4—832no—
993C2×D4—1668no—
994C2×D4—1664no—
995C2×D4C23×D8314yes—
996C2×D4C23×D8314yes—
997C2×D4C23×D8314yes—
998C2×D4C23×D8314yes—
999C2×D4C23×D8312yes—
1000C2×D4C23×D8312yes—
1001C2×D4C23×D8312yes—
1002C2×D4C23×D8312yes—
1003C2×D4C23×D83116yes—
1004C22×C4—28no—
1005C22×C4—28no—
1006C22×C4—3324no—
1007C22×C4—3328no—
1008C22×C4—832no—
1009C22×C4—834no—
1010C22×C4—832no—
1011C22×C4—832no—
1012C22×C4—838no—
1013C22×C4—834no—
1014C22×C4—8316no—
1015C22×C4—8316no—
1016C22×C4—832no—
1017C22×C4—832no—
1018C22×C4—832no—
1019C22×C4—838no—
1020C22×C4—832no—
1021C22×C4—834no—
1022C22×C4—834no—
1023C22×C4—1668no—
1024C22×C4#1305058918yescomplemented
1025C22×C4C23×D8312yes—
1026C22×C4C23×D8314yes—
1027C22×C4C23×D8312yes—
1028C22×C4C23×D8314yes—
1029C22×C4C23×D8314yes—
1030C22×C4C23×D8314yes—
1031C22×C4C23×D8314yes—
1032C22×C4C23×D8311yescharacteristic
1033C22×C4C23×D8311yescharacteristic
1034C22×C4C23×D8311yescharacteristic
1035C22×C4C23×D8311yescharacteristic
1036C22×C4C23×D8311yescharacteristic
1037C22×C4C23×D8311yescharacteristic
1038C4⋊C4—834no—
1039C4⋊C4—834no—
1040C4⋊C4—834no—
1041C4⋊C4—838no—
1042C4⋊C4—838no—
1043C4⋊C4—834no—
1044C4⋊C4—838no—
1045C4⋊C4—838no—
1046C4⋊C4—8316no—
1047C4⋊C4—8316no—
1048C4⋊C4—838no—
1049C4⋊C4—838no—
1050C4⋊C4—838no—
1051C4⋊C4—838no—
1052C4⋊C4—838no—
1053C4⋊C4—838no—
1054C4⋊C4—8316no—
1055C4⋊C4C23×D8314yes—
1056C4⋊C4C23×D8314yes—
1057C4⋊C4C23×D83116yes—
1058C22⋊C4—834no—
1059C22⋊C4—834no—
1060C22⋊C4—834no—
1061C22⋊C4—834no—
1062C22⋊C4—838no—
1063C22⋊C4—8316no—
1064C22⋊C4—838no—
1065C22⋊C4—838no—
1066C22⋊C4—838no—
1067C22⋊C4—8316no—
1068C22⋊C4—838no—
1069C22⋊C4—8316no—
1070C22⋊C4—838no—
1071C22⋊C4—8316no—
1072C22⋊C4C23×D8314yes—
1073C22⋊C4C23×D8314yes—
1074C22⋊C4C23×D83116yes—
1075C22⋊C4C23×D83116yes—
1076C42—831no—
1077C42—831no—
1078C42—834no—
1079C42—838no—
1080C42—831no—
1081C42—831no—
1082C42—832no—
1083C42—832no—
1084C42—838no—
1085C42—832no—
1086C42—832no—
1087C42—8316no—
1088C42—8316no—
1089C42—834no—
1090C42—834no—
1091C42—832no—
1092C42—832no—
1093C42—834no—
1094C42C23×D8314yes—
1095C42C23×D8314yes—
1096C23—24no—
1097C23—24no—
1098C23—42no—
1099C23—44no—
1100C23—44no—
1101C23—3324no—
1102C23—834no—
1103C23—1664no—
1104C23C2×#1305058914yes—
1105C23C24×D8314yes—
1106C23C24×D8314yes—
1107C23C24×D8311yescharacteristic
1108C23C24×D8311yescharacteristic
1109C23C24×D8311yescharacteristic
1110Q8—24no—
1111Q8—24no—
1112Q8—24no—
1113Q8—24no—
1114Q8—3328no—
1115Q8—16616no—
1116Q8—1664no—
1117Q8—1664no—
1118D4—28no—
1119D4—28no—
1120D4—28no—
1121D4—28no—
1122D4—24no—
1123D4—24no—
1124D4—24no—
1125D4—24no—
1126D4—416no—
1127D4—3328no—
1128D4—33216no—
1129D4—16616no—
1130D4—1668no—
1131D4—1668no—
1132D4—1664no—
1133D4—1664no—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—28no—
1137C2×C4—28no—
1138C2×C4—28no—
1139C2×C4—28no—
1140C2×C4—44no—
1141C2×C4—33216no—
1142C2×C4—3324no—
1143C2×C4—3328no—
1144C2×C4—3322no—
1145C2×C4—3322no—
1146C2×C4—3322no—
1147C2×C4—3324no—
1148C2×C4—33216no—
1149C2×C4—832no—
1150C2×C4—832no—
1151C2×C4—838no—
1152C2×C4—832no—
1153C2×C4—834no—
1154C2×C4—838no—
1155C2×C4—832no—
1156C2×C4—1664no—
1157C2×C4—1664no—
1158C2×C4—1664no—
1159C2×C4—16616no—
1160C2×C4—1664no—
1161C2×C4—1668no—
1162C2×C4—1668no—
1163C2×C4C2×#1305058914yes—
1164C2×C4C2×#1305058914yes—
1165C2×C4C2×#1305058914yes—
1166C2×C4C2×#1305058914yes—
1167C2×C4C2×#1305058914yes—
1168C2×C4C2×#1305058914yes—
1169C2×C4C24×D8314yes—
1170C2×C4C24×D8314yes—
1171C2×C4C24×D8318yes—
1172C2×C4C24×D8311yescharacteristic
1173C2×C4C24×D8311yescharacteristic
1174C2×C4C24×D8311yescharacteristic
1175C2×C4C24×D8311yescharacteristic
1176C22—22no—
1177C22—22no—
1178C22—22no—
1179C22—24no—
1180C22—24no—
1181C22—28no—
1182C22—28no—
1183C22—44no—
1184C22—48no—
1185C22—84no—
1186C22—6644no—
1187C22—1664no—
1188C22—1668no—
1189C22C22×#1305058912yes—
1190C22C22×#1305058912yes—
1191C22C22×#1305058912yes—
1192C22C25×D8311yescharacteristic
1193C4—24no—
1194C4—24no—
1195C4—28no—
1196C4—834no—
1197C4—1664no—
1198C4—1668no—
1199C4—1662no—
1200C4—1668no—
1201C4—1662no—
1202C4—1662no—
1203C4C22×#1305058912yes—
1204C4C22×#1305058912yes—
1205C4C22×#1305058912yes—
1206C4C22×#1305058912yes—
1207C2—22no—
1208C2—22no—
1209C2—22no—
1210C2—44no—
1211C2—44no—
1212C2—3324no—
1213C2C23×#1305058911yescharacteristic
1214C2#585×D8312yes—
subgroupG/H
centerC2×C4C24×D83
commutator, socle, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC83×#3449C2
hypercenter#3449D83
hypocenterC83#62815
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. #24921384C2semidirect
2. #24921372C2semidirect
3. #24921362C2semidirect
4. #24921358C2semidirect
5. #24921348C2semidirect
6. #24921338C2semidirect
7. #24921327C2semidirect
8. #24921314C2semidirect
9. #24921300C2semidirect
10. #24921060C2semidirect
11. #24921023C2semidirect
12. #24920851C2semidirect
13. #24920792C2semidirect
14. #24920755C2semidirect
15. C2×#19128254C2semidirect
16. C2×#19128247C2semidirect
17. #24920666C2semidirect
18. #24920664C2semidirect
19. C2×#41×Dic83C2semidirect
20. C83×#3449C2semidirect
22. #19128437C22semidirect
23. #19128433C22semidirect
24. #19128433C22semidirect
25. #19128426C22semidirect
26. #19128425C22semidirect
27. #19128422C22semidirect
28. #19128420C22semidirect
29. #19128420C22semidirect
30. #19128415C22semidirect
31. #19128409C22semidirect
32. #19128403C22semidirect
33. #19128403C22semidirect
34. #19128398C22semidirect
35. #19128394C22semidirect
36. #19128394C22semidirect
37. #19128393C22semidirect
38. #19128388C22semidirect
39. #19128385C22semidirect
40. #19128382C22semidirect
41. #19128374C22semidirect
42. #19128371C22semidirect
43. #19128357C22semidirect
44. #19128351C22semidirect
45. #19128338C22semidirect
46. #19128324C22semidirect
47. #19128318C22semidirect
48. #19128311C22semidirect
49. #19128304C22semidirect
50. #19128295C22semidirect
51. #19128286C22semidirect
52. #19128279C22semidirect
53. #19128275C22semidirect
55. #19128268C22semidirect
58. #19128254C22semidirect
59. #19128254C22semidirect
60. #19128254C22semidirect
61. #19128254C22semidirect
62. #19128254C22semidirect
63. #19128254C22semidirect
64. #19128253C22semidirect
68. #19128247C22semidirect
69. #19128247C22semidirect
70. #19128247C22semidirect
71. #19128247C22semidirect
72. #19128246C22semidirect
73. C2×#14581791C22semidirect
74. C2×#14581790C22semidirect
75. C2×#14581788C22semidirect
76. #19128237C22semidirect
77. #19128233C22semidirect
78. #19128232C22semidirect
79. #19128231C22semidirect
80. #19128231C22semidirect
81. #19128228C22semidirect
82. C2×#14581783C22semidirect
83. C2×#14581781C22semidirect
84. C2×#14581779C22semidirect
85. #19128212C22semidirect
87. #19128207C22semidirect
90. #19128184C22semidirect
91. #19128184C22semidirect
92. #19128182C22semidirect
93. #19128181C22semidirect
94. #19128179C22semidirect
95. #19128178C22semidirect
97. #19128176C22semidirect
98. #19128175C22semidirect
103. #41×Dic83C22semidirect
104. #41×Dic83C22semidirect
105. #41×Dic83C22semidirect
106. #41×Dic83C22semidirect
107. #41×Dic83C22semidirect
108. C4×#13050590C22semidirect
109. #19128169C22semidirect
110. C4×#13050589C22semidirect
111. C2×Q8×Dic83C22semidirect
112. C2×C4×Dic166C22semidirect
114. C2×D4×Dic83C22semidirect
115. C2×C4×C22⋊D83C22semidirect
118. C2×#14581751C22semidirect
119. C2×#14581751C22semidirect
120. #117×D83C22semidirect
122. C22×C4×Dic83C22semidirect
125. #537×C83C22semidirect
127. #536×C83C22semidirect
129. #535×C83C22semidirect
131. #532×C83C22semidirect
133. #525×C83C22semidirect
465. C22×C4×C83#41semidirect
621. #3449D83semidirect
628. C83#62815semidirect
663. #537C2×D83semidirect
667. #536C2×D83semidirect
671. #535C2×D83semidirect
689. #532C2×D83semidirect
706. #525C2×D83semidirect
1024. C22×C4#13050589semidirect

Maximal subgroups

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

subgroupindex
#249213842
#249213722
#249213622
#249213582
#249213482
#249213382
#249213272
#249213142
#249213002
#249210602
#249210232
#249208512
#249207922
#249207552
C2×#191282542
C2×#191282472
#249206662
#249206642
C2×#41×Dic832
C83×#34492
#6281583