Finite Group Databasebeta

← #26005149

Subgroups — #26005149

Order 11008.

6930 conjugacy classes of subgroups.

The subgroup lattice has 1074 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148415C218yesmaximal, complemented
2#19148409C214yesmaximal, complemented
3#19148406C214yesmaximal, complemented
4#19148403C212yesmaximal, complemented
5#19148400C212yesmaximal, complemented
6#19148398C211yesmaximal, characteristic, complemented
7#19148395C214yesmaximal, complemented
8#19148393C212yesmaximal, complemented
9#19148391C214yesmaximal, complemented
10#19148174C214yesmaximal, complemented
11#19148174C218yesmaximal, complemented
12Q8×#10621900C214yesmaximal, complemented
13#19147999C212yesmaximal, complemented
14#19147997C214yesmaximal, complemented
15C2×#14583451C214yesmaximal, complemented
16#533×D43C212yesmaximal, complemented
17#19147793C212yesmaximal
18C2×C4×#10621900C211yesmaximal, characteristic
19C43×#3501C211yesmaximal, characteristic, complemented
20C22×#10621900C2211yescharacteristic
21Q8×Dic86C2214yescomplemented
22#14583629C2214yescomplemented
23#14583629C2218yescomplemented
24#14583627C2214yescomplemented
25#14583627C2218yescomplemented
26#14583626C2218yescomplemented
27#14583626C2218yescomplemented
28#14583626C2218yescomplemented
29#14583624C2214yescomplemented
30#14583624C2218yescomplemented
31#14583608C2218yescomplemented
32#14583608C2218yescomplemented
33#14583608C2218yescomplemented
34#14583607C2218yescomplemented
35#14583607C22116yescomplemented
36#14583606C2218yescomplemented
37#14583606C2214yescomplemented
38#14583604C2218yescomplemented
39#14583604C22116yescomplemented
40#14583603C22116yescomplemented
41#14583603C22116yescomplemented
42#14583603C22116yescomplemented
43D4×Dic86C2218yescomplemented
44D4×Dic86C2214yescomplemented
45Q8×C22⋊D43C2218yescomplemented
46#14583562C2218yescomplemented
47#14583562C22116yescomplemented
48#14583530C2212yes—
49#14583529C2218yescomplemented
50#14583528C2218yes—
51#14583528C2218yes—
52#14583528C22116yescomplemented
53#14583528C22116yescomplemented
54#14583527C2214yes—
55#14583526C2218yescomplemented
56#14583525C2218yes—
57#14583525C2214yes—
58#14583524C2218yes—
59#14583456C2212yes—
60#14583455C2214yescomplemented
61#14583455C2218yescomplemented
62#14583454C2212yescomplemented
63#14583454C2212yescomplemented
64#14583454C2218yescomplemented
65#14583453C2214yescomplemented
66#14583453C2214yescomplemented
67#14583452C2214yes—
68#14583451C2218yes—
69#14583451C2214yes—
70#14583451C2214yes—
71#14583451C2218yes—
72#14583451C2218yes—
73#14583451C2218yescomplemented
74#14583451C2218yescomplemented
75#14583451C2218yescomplemented
76#14583451C2218yescomplemented
77#14583451C22116yescomplemented
78#14583451C22116yescomplemented
79C2×#13063324C2214yescomplemented
80C2×#13063323C2214yescomplemented
81C4⋊Q8×D43C2212yescomplemented
82C4⋊Q8×D43C2212yescomplemented
83C2×#13063315C2218yescomplemented
84#125×D43C2214yescomplemented
85C2×#13063304C2214yes—
86C2×#13063302C2218yes—
87C22⋊Q8×D43C2214yes—
88C22⋊Q8×D43C2214yes—
89#14583378C2218yes—
90#14583378C2218yes—
91#14583376C2214yes—
92#14583374C2212yes—
93#14583372C2218yes—
94C4×#10621900C2218yes—
95C4×#10621900C2218yes—
96C4×#10621900C2214yes—
97C4×#10621900C2214yes—
98C4×#10621900C2214yes—
99C4×#10621900C2214yes—
100C2×Q8×Dic43C2214yescomplemented
101C2×C4×Dic86C2211yescharacteristic
102C2×#13063290C2211yescharacteristic
103C2×#13063290C2218yescomplemented
104C2×#13063290C2214yescomplemented
105C4×Q8×D43C2214yescomplemented
106C4×Q8×D43C2214yescomplemented
107C2×D4×Dic43C2211yescharacteristic
108C2×C4×C22⋊D43C2212yes—
109C2×(C22⋊D43)⋊C4C2212yes—
110C2×#13063283C2211yescharacteristic
111C2×#13063281C2218yes—
112C2×#13063281C2212yes—
113#117×D43C2214yes—
114C22×C4×Dic43C2212yes—
115C2×C42×D43C2211yescharacteristic
116C43×#554C2214yescomplemented
117C43×#554C2218yescomplemented
118D4×Q8×C43C2214yescomplemented
119C43×#544C2212yes—
120C43×#543C2214yes—
121C43×#533C2212yes—
122C2×C22⋊Q8×C43C2214yes—
123C43×#518C2212yes—
124C2×C4×D4×C43C2211yescharacteristic
125C2×#10621900Q8116yescomplemented
126C2×#10621900C2314yes—
127C2×#10621900C2314yes—
128C22×Dic86C2318yes—
129C22×Dic86C2314yes—
130C22×Dic86C2311yescharacteristic
131C2×Q8×D43C2314yes—
132C2×Q8×D43C2314yes—
133C22×C22⋊D43C2312yes—
134C23×Dic43C2312yes—
135C23×Dic43C2312yes—
136C22×C4×D43C2311yescharacteristic
137C22×C4×D43C2311yescharacteristic
138C22×C4×D43C2311yescharacteristic
139#13063325C2312yes—
140#13063325C2318yes—
141#13063325C2312yes—
142#13063324C2318yes—
143#13063324C23116yes—
144#13063324C23116yes—
145#13063324C2314yes—
146#13063324C2318yes—
147#13063324C2318yes—
148#13063324C2318yes—
149#13063324C2314yes—
150#13063324C2314yes—
151#13063324C2314yes—
152#13063324C2318yes—
153#13063323C2318yes—
154#13063323C23116yes—
155#13063323C23116yes—
156#13063323C2318yes—
157#13063323C2314yes—
158#13063323C2314yes—
159#13063323C2318yes—
160#13063317C2314yes—
161#13063317C2318yes—
162#13063316C2314yes—
163#13063316C2318yes—
164#13063316C2318yes—
165#13063316C2314yes—
166#13063315C23116yes—
167#13063315C23116yes—
168#13063315C23116yes—
169#13063315C23116yes—
170#13063315C23116yes—
171#13063315C23116yes—
172#13063315C2318yes—
173#13063315C2318yes—
174#13063315C23116yes—
175#13063305C2314yes—
176#13063305C23116yes—
177#13063305C2314yes—
178#13063304C2318yes—
179#13063304C23116yes—
180#13063304C23116yes—
181#13063304C2318yes—
182#13063304C2314yes—
183#13063304C2314yes—
184#13063304C2318yes—
185#13063303C2318yes—
186#13063303C23116yes—
187#13063303C23116yes—
188#13063303C2318yes—
189#13063302C23116yes—
190#13063302C23116yes—
191#13063302C23116yes—
192#13063302C23116yes—
193#13063302C23116yes—
194#13063302C23116yes—
195#13063302C2318yes—
196#13063302C2318yes—
197#13063302C23116yes—
198#13063301C2314yes—
199#13063301C23116yes—
200#13063301C2314yes—
201Q8×Dic43C2318yes—
202Q8×Dic43C2318yes—
203Q8×Dic43C2314yes—
204Q8×Dic43C2314yes—
205Q8×Dic43C2318yes—
206C4×Dic86C2314yes—
207C4×Dic86C2318yes—
208C4×Dic86C2318yes—
209C4×Dic86C2314yes—
210C4×Dic86C2314yes—
211C4×Dic86C2314yes—
212C4×Dic86C2318yes—
213C4×Dic86C2318yes—
214#13063290C23116yes—
215#13063290C2318yes—
216#13063290C2318yes—
217#13063290C23116yes—
218#13063290C2314yes—
219#13063290C2318yes—
220#13063290C2314yes—
221#13063290C2318yes—
222#13063290C2314yes—
223#13063290C2314yes—
224#13063290C23116yes—
225#13063290C2318yes—
226#13063290C2318yes—
227#13063290C2318yes—
228D4×Dic43C2314yes—
229D4×Dic43C2318yes—
230D4×Dic43C2318yes—
231D4×Dic43C2314yes—
232C4×C22⋊D43C2318yes—
233C4×C22⋊D43C23116yes—
234C4×C22⋊D43C23116yes—
235C4×C22⋊D43C2318yes—
236(C22⋊D43)⋊C4C2318yes—
237(C22⋊D43)⋊C4C23116yes—
238(C22⋊D43)⋊C4C23116yes—
239(C22⋊D43)⋊C4C2318yes—
240#13063284C2314yes—
241#13063283C2314yes—
242#13063283C2314yes—
243#13063283C2314yes—
244#13063283C2314yes—
245#13063282C2318yes—
246#13063281C2318yes—
247#13063281C2318yes—
248#13063281C23116yes—
249#13063281C2318yes—
250#13063281C23116yes—
251#13063281C23116yes—
252C2×C4⋊Dic43C2318yes—
253C2×C4⋊Dic43C2314yes—
254C2×C4⋊Dic43C2311yescharacteristic
255C2×Dic43⋊C4C2318yes—
256C2×Dic43⋊C4C2318yes—
257C2×Dic43⋊C4C2318yes—
258C2×Dic43⋊C4C2312yes—
259C2×Dic43⋊C4C2312yes—
260C2×Dic43⋊C4C2318yes—
261C2×Dic43⋊C4C2318yes—
262C4⋊C4×D43C2314yes—
263C4⋊C4×D43C2318yes—
264C4⋊C4×D43C2318yes—
265C4⋊C4×D43C2314yes—
266C4⋊C4×D43C2314yes—
267C4⋊C4×D43C2314yes—
268C2×C22⋊Dic43C2312yes—
269C2×C22⋊Dic43C2318yes—
270C2×(C2×D43)⋊C4C2312yes—
271C22⋊C4×D43C2318yes—
272C2×C4×Dic43C2311yescharacteristic
273C2×C4×Dic43C2311yescharacteristic
274C2×C4×Dic43C2311yescharacteristic
275C2×C4×Dic43C2312yes—
276C2×C4×Dic43C2312yes—
277C2×C4×Dic43C2312yes—
278C2×C4×Dic43C2314yes—
279C2×C4×Dic43C2314yes—
280C2×C4×Dic43C2314yes—
281C2×C4×Dic43C2314yes—
282C2×C4×Dic43C2318yes—
283C2×C4×Dic43C2318yes—
284C42×D43C2312yes—
285C42×D43C2312yes—
286C42×D43C2312yes—
287C42×D43C2312yes—
288C42×D43C2318yes—
289C22×Q8×C43C2314yes—
290C22×D4×C43C2311yescharacteristic
291C23×C4×C43C2312yes—
292C4⋊Q8×C43C2312yes—
293C4⋊Q8×C43C2312yes—
294C4⋊Q8×C43C2318yes—
295#125×C43C2314yes—
296#125×C43C2318yes—
297C22⋊Q8×C43C2318yes—
298C22⋊Q8×C43C23116yes—
299C22⋊Q8×C43C2314yes—
300C22⋊Q8×C43C2318yes—
301C22⋊Q8×C43C2318yes—
302C22⋊Q8×C43C2314yes—
303C22⋊Q8×C43C23116yes—
304C4×Q8×C43C2314yes—
305C4×Q8×C43C2314yes—
306C4×D4×C43C2314yes—
307C4×D4×C43C2318yes—
308C4×D4×C43C2314yes—
309C4×D4×C43C2318yes—
310#117×C43C2314yes—
311C2×C4⋊C4×C43C2311yescharacteristic
312C2×C4⋊C4×C43C2318yes—
313C2×C4⋊C4×C43C2314yes—
314C2×C22⋊C4×C43C2312yes—
315C2×C22⋊C4×C43C2318yes—
316C2×C42×C43C2311yescharacteristic
317C24×C43C2412yes—
318C23×D43C2411yescharacteristic
319C2×Q8×C43—48no—
320C2×Q8×C43C2414yes—
321C2×Q8×C43C2414yes—
322C2×Q8×C43C2418yes—
323C2×D4×C43C2×Q818yescomplemented
324C2×D4×C43C2414yes—
325C22×C4×C43—44no—
326C22×C4×C43C2411yescharacteristic
327C22×C4×C43C2414yes—
328C22×C4×C43C2411yescharacteristic
329C22×C4×C43C2418yes—
330C22×C4×C43C2418yes—
331C22×C4×C43C2412yes—
332C22×C4×C43C2414yes—
333C22×C4×C43C2411yescharacteristic
334C2×C22⋊D43C2×Q8116yescomplemented
335C2×C22⋊D43C2418yes—
336C22×Dic43—44no—
337C22×Dic43C2×Q8116yescomplemented
338C22×Dic43C2411yescharacteristic
339C22×Dic43C2414yes—
340C22×Dic43C2412yes—
341C22×Dic43C2411yescharacteristic
342C22×Dic43C2414yes—
343C22×Dic43C2418yes—
344C22×Dic43C2418yes—
345C22×Dic43C2414yes—
346C22×Dic43C2411yescharacteristic
347C22×Dic43C2414yes—
348C22×Dic43C2412yes—
349Q8×D43—48no—
350Q8×D43—48no—
351#10621900C2×Q8132yescomplemented
352#10621900C2×Q8132yescomplemented
353C2×C4×D43—42no—
354C2×C4×D43—42no—
355C2×C4×D43C2×Q818yescomplemented
356C2×C4×D43C2412yes—
357C2×C4×D43C2412yes—
358C2×C4×D43C2412yes—
359C2×C4×D43C2412yes—
360C2×C4×D43C2418yes—
361C2×C4×D43C2418yes—
362C2×C4×D43C2412yes—
363C2×C4×D43C2412yes—
364C2×Dic86—416no—
365C2×Dic86—48no—
366C2×Dic86C2×Q818yescomplemented
367C2×Dic86C2418yes—
368C2×Dic86C2414yes—
369C2×Dic86C24116yes—
370C2×Dic86C2418yes—
371C2×Dic86C2414yes—
372C2×Dic86C2418yes—
373C2×Dic86C2414yes—
374C4⋊C4×C43C2418yes—
375C4⋊C4×C43C2414yes—
376C4⋊C4×C43C2414yes—
377C4⋊C4×C43C2418yes—
378C4⋊C4×C43C24116yes—
379C4⋊C4×C43C2414yes—
380C4⋊C4×C43C2414yes—
381C4⋊C4×C43C2418yes—
382C4⋊C4×C43C2414yes—
383C22⋊C4×C43C2418yes—
384C22⋊C4×C43C2418yes—
385C22⋊C4×C43C24116yes—
386C42×C43C2412yes—
387C42×C43C2412yes—
388C42×C43C2418yes—
389C22⋊Dic43C2418yes—
390C22⋊Dic43C24116yes—
391C22⋊Dic43C2418yes—
392(C2×D43)⋊C4C2418yes—
393(C2×D43)⋊C4C2418yes—
394(C2×D43)⋊C4C2418yes—
395C4⋊Dic43C2414yes—
396C4⋊Dic43C2418yes—
397C4⋊Dic43C2414yes—
398C4⋊Dic43C2414yes—
399C4⋊Dic43C2414yes—
400C4⋊Dic43C2418yes—
401C4⋊Dic43C2414yes—
402C4⋊Dic43C24116yes—
403C4⋊Dic43C2418yes—
404Dic43⋊C4C2418yes—
405Dic43⋊C4C2418yes—
406Dic43⋊C4C2418yes—
407Dic43⋊C4C2418yes—
408Dic43⋊C4C2418yes—
409Dic43⋊C4C2418yes—
410Dic43⋊C4C2418yes—
411Dic43⋊C4C2418yes—
412Dic43⋊C4C2418yes—
413Dic43⋊C4C24116yes—
414Dic43⋊C4C24116yes—
415Dic43⋊C4C2418yes—
416Dic43⋊C4C24116yes—
417Dic43⋊C4C24116yes—
418Dic43⋊C4C24116yes—
419C4×Dic43C2411yescharacteristic
420C4×Dic43C2411yescharacteristic
421C4×Dic43C2411yescharacteristic
422C4×Dic43C2411yescharacteristic
423C4×Dic43C2412yes—
424C4×Dic43C2412yes—
425C4×Dic43C2412yes—
426C4×Dic43C2412yes—
427C4×Dic43C2418yes—
428C4×Dic43C2418yes—
429C4×Dic43C2418yes—
430C4×Dic43C2414yes—
431C4×Dic43C2414yes—
432C4×Dic43C2414yes—
433C4×Dic43C2414yes—
434C4×Dic43C2414yes—
435C4×Dic43C2414yes—
436C4×Dic43C24116yes—
437C4×Dic43C24116yes—
438C23×C43—42no—
439C23×C43—42no—
440C23×C43C22×Q818yes—
441C23×C43C2511yescharacteristic
442C23×C43C2514yes—
443C22×D43—41no—
444C22×D43—41no—
445C22×D43C22×Q814yes—
446C22×D43C2512yes—
447Q8×C43—28no—
448Q8×C43—44no—
449Q8×C43—48no—
450D4×C43C22×Q8116yes—
451C2×C4×C43—28no—
452C2×C4×C43—22no—
453C2×C4×C43—48no—
454C2×C4×C43—41no—
455C2×C4×C43—42no—
456C2×C4×C43—44no—
457C2×C4×C43—48no—
458C2×C4×C43C22×Q814yes—
459C2×C4×C43C2511yescharacteristic
460C2×C4×C43C2514yes—
461C2×C4×C43C2518yes—
462C2×C4×C43C2518yes—
463C2×C4×C43C2512yes—
464C2×C4×C43C2512yes—
465C2×C4×C43C2511yescharacteristic
466C22⋊D43C22×Q8132yes—
467C2×Dic43—28no—
468C2×Dic43—22no—
469C2×Dic43—48no—
470C2×Dic43—48no—
471C2×Dic43—41no—
472C2×Dic43—42no—
473C2×Dic43—44no—
474C2×Dic43C22×Q818yes—
475C2×Dic43C22×Q814yes—
476C2×Dic43C22×Q8116yes—
477C2×Dic43C22×Q8116yes—
478C2×Dic43C2511yescharacteristic
479C2×Dic43C2518yes—
480C2×Dic43C2512yes—
481C2×Dic43C2514yes—
482C2×Dic43C2518yes—
483C2×Dic43C2511yescharacteristic
484C2×Dic43C2514yes—
485C2×Dic43C2511yescharacteristic
486C2×Dic43C2511yescharacteristic
487C4×D43—24no—
488C4×D43—24no—
489C4×D43—42no—
490C4×D43—42no—
491C4×D43—48no—
492C4×D43—48no—
493C4×D43C22×Q818yes—
494C4×D43C22×Q818yes—
495Dic86—28no—
496Dic86—216no—
497Dic86—48no—
498Dic86—416no—
499Dic86—44no—
500Dic86—48no—
501Dic86C22×Q8116yes—
502#62813—431nomaximal, Sylow
503C22×C43—21no—
504C22×C43—21no—
505C22×C43—24no—
506C22×C43—24no—
507C22×C43—48no—
508C22×C43C23×Q812yes—
509C22×C43C23×Q818yes—
510C22×C43C2611yescharacteristic
511C2×D43—22no—
512C2×D43—22no—
513C2×D43—44no—
514C2×D43C23×Q814yes—
515C4×C43—28no—
516C4×C43—22no—
517C4×C43—24no—
518C4×C43—28no—
519C4×C43—21no—
520C4×C43C23×Q814yes—
521C4×C43#58512yes—
522Dic43—28no—
523Dic43—28no—
524Dic43—22no—
525Dic43—24no—
526Dic43—21no—
527Dic43C23×Q818yes—
528Dic43C23×Q812yes—
529Dic43C23×Q812yes—
530Dic43#58512yes—
531#3504—438no—
532#3503—434no—
533#3503—434no—
534#3502—432no—
535#3502—432no—
536#3501—434no—
537#3501—434no—
538#3501—432no—
539#3501—431no—
540#3501D4311yescharacteristic, complemented
541Q8×#41—434no—
542Q8×#41—438no—
543Q8×#41—434no—
544#3458—432no—
545#3458—434no—
546C2×#533—432no—
547C2×#533—434no—
548#3428—432no—
549C2×C4×#41—431no—
550C2×C43—22no—
551C2×C43—28no—
552C2×C43C24×Q811yescharacteristic
553C2×C43C2×#58511yescharacteristic
554C2×C43C2×#58511yescharacteristic
555D43—24no—
556C22×#41—431no—
557Q82—438no—
558Q82—434no—
559Q82—434no—
560#557—434no—
561#557—438no—
562#557—438no—
563#557—438no—
564#557—438no—
565#557—434no—
566#557—438no—
567#554—4316no—
568#554—4316no—
569#554—4316no—
570#554—438no—
571#554—4316no—
572#554—434no—
573#554—438no—
574#554—438no—
575#554—438no—
576#554—438no—
577#554—438no—
578#554—4316no—
579#554C2×D4314yescomplemented
580#554C2×D4318yescomplemented
581D4×Q8—438no—
582D4×Q8—438no—
583D4×Q8—4316no—
584D4×Q8—438no—
585D4×Q8—434no—
586D4×Q8C2×D4314yescomplemented
587#544—438no—
588#544—438no—
589#544—438no—
590#544—438no—
591#544—4316no—
592#544—4316no—
593#544—434no—
594#544—432no—
595#544C2×D4312yes—
596#543—438no—
597#543—438no—
598#543—434no—
599#543C2×D4314yes—
600#533—432no—
601#533—432no—
602#533—438no—
603#533—434no—
604#533—438no—
605#533—434no—
606#533—434no—
607#533—438no—
608#533—438no—
609#533—438no—
610#533—438no—
611#533—438no—
612#533—438no—
613#533—438no—
614#533—4316no—
615#533—4316no—
616#533—434no—
617#533—434no—
618#533—434no—
619#533—432no—
620#533C2×D4312yes—
621C2×C4⋊Q8—434no—
622C2×C4⋊Q8—432no—
623C2×C4⋊Q8—432no—
624C2×C4⋊Q8—434no—
625C2×#125—434no—
626C2×#125—438no—
627C2×C22⋊Q8—434no—
628C2×C22⋊Q8—434no—
629C2×C22⋊Q8—434no—
630C2×C22⋊Q8—438no—
631C2×C22⋊Q8C2×D4314yes—
632#520—438no—
633#520—438no—
634#519—434no—
635#518—432no—
636#518—438no—
637#518C2×D4312yes—
638C4×#41—434no—
639C4×#41—434no—
640C4×#41—434no—
641C4×#41—434no—
642C4×#41—438no—
643C4×#41—438no—
644C2×C4×Q8—434no—
645C2×C4×Q8—434no—
646C2×C4×Q8—434no—
647C2×C4×Q8—431no—
648C2×C4×Q8—434no—
649C2×C4×Q8—438no—
650C2×C4×Q8—431no—
651C2×C4×D4—431no—
652C2×C4×D4—432no—
653C2×C4×D4—432no—
654C2×C4×D4C2×D4311yescharacteristic
655C2×#117—434no—
656C2×#117—431no—
657C2×#117—432no—
658C2×#117—438no—
659C22×C42—432no—
660C22×C42—431no—
661C43#6281311yescharacteristic, complemented, Sylow
662C2×#41—4316no—
663C2×#41—434no—
664C2×#41—434no—
665C22×Q8—434no—
666C22×Q8—434no—
667C22×Q8—431no—
668C22×Q8—438no—
669C22×Q8—434no—
670C22×Q8C22×D4314yes—
671C22×D4—432no—
672C22×D4C22×D4311yescharacteristic
673C23×C4—432no—
674C23×C4—431no—
675C23×C4—432no—
676C23×C4—431no—
677C23×C4—431no—
678C23×C4C22×D4312yes—
679C4⋊Q8—434no—
680C4⋊Q8—438no—
681C4⋊Q8—434no—
682C4⋊Q8—438no—
683C4⋊Q8—438no—
684C4⋊Q8—4316no—
685C4⋊Q8—4316no—
686C4⋊Q8—434no—
687C4⋊Q8—434no—
688C4⋊Q8—438no—
689C4⋊Q8—438no—
690C4⋊Q8—434no—
691C4⋊Q8—434no—
692C4⋊Q8—438no—
693C4⋊Q8—4316no—
694C4⋊Q8—4316no—
695C4⋊Q8—438no—
696C4⋊Q8—438no—
697C4⋊Q8—432no—
698C4⋊Q8—432no—
699C4⋊Q8—438no—
700C4⋊Q8C22×D4312yes—
701C4⋊Q8C22×D4312yes—
702C4⋊Q8C22×D4318yes—
703#125—438no—
704#125—438no—
705#125—4316no—
706#125—4316no—
707#125—4316no—
708#125—434no—
709#125—434no—
710#125—4316no—
711#125—4316no—
712#125—4316no—
713#125—4316no—
714#125—438no—
715#125—438no—
716#125—434no—
717#125—438no—
718#125C22×D4314yes—
719#125C22×D4318yes—
720C22⋊Q8—434no—
721C22⋊Q8—434no—
722C22⋊Q8—4316no—
723C22⋊Q8—434no—
724C22⋊Q8—438no—
725C22⋊Q8—434no—
726C22⋊Q8—438no—
727C22⋊Q8—438no—
728C22⋊Q8—4316no—
729C22⋊Q8—4316no—
730C22⋊Q8—438no—
731C22⋊Q8—434no—
732C22⋊Q8—438no—
733C22⋊Q8—434no—
734C22⋊Q8—4316no—
735C22⋊Q8—4316no—
736C22⋊Q8—4316no—
737C22⋊Q8—438no—
738C22⋊Q8—438no—
739C22⋊Q8—4316no—
740C22⋊Q8—4316no—
741C22⋊Q8—4316no—
742C22⋊Q8—4316no—
743C22⋊Q8—4316no—
744C22⋊Q8—4316no—
745C22⋊Q8—4316no—
746C22⋊Q8C22×D4314yes—
747C22⋊Q8C22×D4314yes—
748C22⋊Q8C22×D4318yes—
749C22⋊Q8C22×D4318yes—
750C22⋊Q8C22×D4318yes—
751C22⋊Q8C22×D43116yes—
752C22⋊Q8C22×D43116yes—
753C4×Q8—434no—
754C4×Q8—438no—
755C4×Q8—434no—
756C4×Q8—438no—
757C4×Q8—438no—
758C4×Q8—434no—
759C4×Q8—438no—
760C4×Q8—434no—
761C4×Q8—434no—
762C4×Q8—434no—
763C4×Q8—438no—
764C4×Q8—4316no—
765C4×Q8—438no—
766C4×Q8—4316no—
767C4×Q8—438no—
768C4×Q8—438no—
769C4×Q8—4316no—
770C4×Q8—438no—
771C4×Q8—438no—
772C4×Q8—434no—
773C4×Q8—434no—
774C4×Q8—438no—
775C4×Q8—434no—
776C4×Q8—438no—
777C4×Q8—434no—
778C4×Q8—438no—
779C4×Q8—438no—
780C4×Q8C22×D4314yes—
781C4×Q8C22×D4314yes—
782C4×D4—434no—
783C4×D4—434no—
784C4×D4—438no—
785C4×D4—438no—
786C4×D4—438no—
787C4×D4—438no—
788C4×D4—4316no—
789C4×D4—4316no—
790C4×D4—438no—
791C4×D4—438no—
792C4×D4—4316no—
793C4×D4—4316no—
794C4×D4C22×D4314yes—
795C4×D4C22×D4314yes—
796C4×D4C22×D4318yes—
797C4×D4C22×D4318yes—
798#117—434no—
799#117—434no—
800#117—434no—
801#117—434no—
802#117—434no—
803#117—438no—
804#117—438no—
805#117—4316no—
806#117—438no—
807#117—4316no—
808#117—4316no—
809#117—438no—
810#117C22×D4314yes—
811C2×C4⋊C4—432no—
812C2×C4⋊C4—432no—
813C2×C4⋊C4—431no—
814C2×C4⋊C4—438no—
815C2×C4⋊C4—438no—
816C2×C4⋊C4—438no—
817C2×C4⋊C4—438no—
818C2×C4⋊C4—438no—
819C2×C4⋊C4—438no—
820C2×C4⋊C4—434no—
821C2×C4⋊C4—434no—
822C2×C4⋊C4—434no—
823C2×C4⋊C4—438no—
824C2×C4⋊C4—438no—
825C2×C4⋊C4—434no—
826C2×C4⋊C4—434no—
827C2×C4⋊C4C22×D4311yescharacteristic
828C2×C4⋊C4C22×D4318yes—
829C2×C4⋊C4C22×D4314yes—
830C2×C22⋊C4—432no—
831C2×C22⋊C4—438no—
832C2×C22⋊C4—432no—
833C2×C22⋊C4—438no—
834C2×C22⋊C4C22×D4312yes—
835C2×C22⋊C4C22×D4318yes—
836C2×C42—432no—
837C2×C42—431no—
838C2×C42—438no—
839C2×C42—438no—
840C2×C42—432no—
841C2×C42—432no—
842C2×C42—431no—
843C2×C42—434no—
844C2×C42—434no—
845C2×C42—434no—
846C2×C42—434no—
847C2×C42—431no—
848C2×C42—438no—
849C2×C42—432no—
850C2×C42—432no—
851C2×C42—432no—
852C2×C42—432no—
853C2×C42C22×D4311yescharacteristic
854C24—431no—
855C24C23×D4312yes—
856#41—4332no—
857#41—4332no—
858C2×Q8—48no—
859C2×Q8—438no—
860C2×Q8—434no—
861C2×Q8—438no—
862C2×Q8—434no—
863C2×Q8—438no—
864C2×Q8—438no—
865C2×Q8—4316no—
866C2×Q8—434no—
867C2×Q8—1728no—
868C2×Q8—17216no—
869C2×Q8—1728no—
870C2×Q8—1728no—
871C2×Q8C23×D4314yes—
872C2×Q8C23×D4318yes—
873C2×Q8C23×D4314yes—
874C2×D4—4316no—
875C2×D4—438no—
876C2×D4Q8×D4318yescomplemented
877C2×D4C23×D4314yes—
878C22×C4—44no—
879C22×C4—4316no—
880C22×C4—434no—
881C22×C4—431no—
882C22×C4—434no—
883C22×C4—432no—
884C22×C4—438no—
885C22×C4—432no—
886C22×C4—432no—
887C22×C4—431no—
888C22×C4—434no—
889C22×C4—431no—
890C22×C4—432no—
891C22×C4—434no—
892C22×C4—438no—
893C22×C4—438no—
894C22×C4—432no—
895C22×C4—432no—
896C22×C4—432no—
897C22×C4—432no—
898C22×C4—438no—
899C22×C4—438no—
900C22×C4—1722no—
901C22×C4—1722no—
902C22×C4—1724no—
903C22×C4C23×D4311yescharacteristic
904C22×C4C23×D4314yes—
905C22×C4C23×D4312yes—
906C22×C4C23×D4314yes—
907C22×C4C23×D4311yescharacteristic
908C22×C4C23×D4318yes—
909C22×C4C23×D4318yes—
910C22×C4C23×D4311yescharacteristic
911C4⋊C4—438no—
912C4⋊C4—438no—
913C4⋊C4—438no—
914C4⋊C4—438no—
915C4⋊C4—438no—
916C4⋊C4—438no—
917C4⋊C4—434no—
918C4⋊C4—438no—
919C4⋊C4—4316no—
920C4⋊C4—4316no—
921C4⋊C4—438no—
922C4⋊C4—434no—
923C4⋊C4—434no—
924C4⋊C4—434no—
925C4⋊C4—4316no—
926C4⋊C4—4316no—
927C4⋊C4—438no—
928C4⋊C4—4316no—
929C4⋊C4—438no—
930C4⋊C4—438no—
931C4⋊C4—438no—
932C4⋊C4—4316no—
933C4⋊C4—438no—
934C4⋊C4—434no—
935C4⋊C4C23×D4318yes—
936C4⋊C4C23×D4314yes—
937C4⋊C4C23×D4314yes—
938C4⋊C4C23×D4314yes—
939C4⋊C4C23×D4314yes—
940C4⋊C4C23×D4318yes—
941C4⋊C4C23×D4314yes—
942C4⋊C4C23×D43116yes—
943C4⋊C4C23×D4318yes—
944C22⋊C4—438no—
945C22⋊C4—438no—
946C22⋊C4—4316no—
947C22⋊C4—438no—
948C22⋊C4—438no—
949C22⋊C4—438no—
950C22⋊C4C23×D4318yes—
951C22⋊C4C23×D4318yes—
952C22⋊C4C23×D43116yes—
953C42—431no—
954C42—431no—
955C42—431no—
956C42—431no—
957C42—434no—
958C42—438no—
959C42—438no—
960C42—432no—
961C42—434no—
962C42—432no—
963C42—434no—
964C42—434no—
965C42—432no—
966C42—434no—
967C42—434no—
968C42—432no—
969C42—4316no—
970C42—4316no—
971C42—438no—
972C42C23×D4312yes—
973C42C23×D4312yes—
974C42C23×D4318yes—
975C23—42no—
976C23—42no—
977C23—432no—
978C23—434no—
979C23—1721no—
980C23—1721no—
981C23C2×Q8×D4318yes—
982C23C24×D4311yescharacteristic
983C23C24×D4314yes—
984Q8—28no—
985Q8—48no—
986Q8—44no—
987Q8—4316no—
988Q8—8616no—
989Q8—868no—
990Q8—17216no—
991Q8—1724no—
992Q8—1728no—
993Q8—1728no—
994D4—4332no—
995D4C2×Q8×D43116yes—
996C2×C4—22no—
997C2×C4—28no—
998C2×C4—44no—
999C2×C4—42no—
1000C2×C4—41no—
1001C2×C4—48no—
1002C2×C4—48no—
1003C2×C4—434no—
1004C2×C4—438no—
1005C2×C4—4316no—
1006C2×C4—4316no—
1007C2×C4—431no—
1008C2×C4—434no—
1009C2×C4—431no—
1010C2×C4—431no—
1011C2×C4—438no—
1012C2×C4—438no—
1013C2×C4—431no—
1014C2×C4—434no—
1015C2×C4—438no—
1016C2×C4—432no—
1017C2×C4—438no—
1018C2×C4—864no—
1019C2×C4—862no—
1020C2×C4—868no—
1021C2×C4—864no—
1022C2×C4—1722no—
1023C2×C4—1722no—
1024C2×C4—1728no—
1025C2×C4—1728no—
1026C2×C4—1724no—
1027C2×C4—1722no—
1028C2×C4—1721no—
1029C2×C4—1728no—
1030C2×C4—1728no—
1031C2×C4C2×Q8×D4314yes—
1032C2×C4C24×D4311yescharacteristic
1033C2×C4C24×D4314yes—
1034C2×C4C24×D4318yes—
1035C2×C4C24×D4318yes—
1036C2×C4C24×D4312yes—
1037C2×C4C24×D4312yes—
1038C2×C4C24×D4311yescharacteristic
1039C22—24no—
1040C22—21no—
1041C22—24no—
1042C22—21no—
1043C22—48no—
1044C22—434no—
1045C22—862no—
1046C22—862no—
1047C22—1724no—
1048C22C22×Q8×D4312yes—
1049C22C22×Q8×D4318yes—
1050C22C25×D4311yescharacteristic
1051C4—28no—
1052C4—22no—
1053C4—21no—
1054C4—24no—
1055C4—28no—
1056C4—432no—
1057C4—432no—
1058C4—438no—
1059C4—432no—
1060C4—861no—
1061C4—864no—
1062C4—868no—
1063C4—862no—
1064C4—868no—
1065C4C22×Q8×D4314yes—
1066C4#1458373412yes—
1067C2—22no—
1068C2—28no—
1069C2—864no—
1070C2C23×Q8×D4311yescharacteristic
1071C2#585×D4311yescharacteristic
1072C2C2×#1458373411yescharacteristic
subgroupG/H
center, FrattiniC22C25×D43
commutator, socle, cosocleC22×C43C26
FittingC43×#3501C2
prime radicalC22×#10621900C22
hypercenter#3501D43
hypocenterC43#62813
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. #19148415C2semidirect
2. #19148409C2semidirect
3. #19148406C2semidirect
4. #19148403C2semidirect
5. #19148400C2semidirect
6. #19148398C2semidirect
7. #19148395C2semidirect
8. #19148393C2semidirect
9. #19148391C2semidirect
10. #19148174C2semidirect
11. #19148174C2semidirect
12. Q8×#10621900C2semidirect
13. #19147999C2semidirect
14. #19147997C2semidirect
15. C2×#14583451C2semidirect
16. #533×D43C2semidirect
19. C43×#3501C2semidirect
21. Q8×Dic86C22semidirect
22. #14583629C22semidirect
23. #14583629C22semidirect
24. #14583627C22semidirect
25. #14583627C22semidirect
26. #14583626C22semidirect
27. #14583626C22semidirect
28. #14583626C22semidirect
29. #14583624C22semidirect
30. #14583624C22semidirect
31. #14583608C22semidirect
32. #14583608C22semidirect
33. #14583608C22semidirect
34. #14583607C22semidirect
35. #14583607C22semidirect
36. #14583606C22semidirect
37. #14583606C22semidirect
38. #14583604C22semidirect
39. #14583604C22semidirect
40. #14583603C22semidirect
41. #14583603C22semidirect
42. #14583603C22semidirect
43. D4×Dic86C22semidirect
44. D4×Dic86C22semidirect
45. Q8×C22⋊D43C22semidirect
46. #14583562C22semidirect
47. #14583562C22semidirect
49. #14583529C22semidirect
52. #14583528C22semidirect
53. #14583528C22semidirect
55. #14583526C22semidirect
60. #14583455C22semidirect
61. #14583455C22semidirect
62. #14583454C22semidirect
63. #14583454C22semidirect
64. #14583454C22semidirect
65. #14583453C22semidirect
66. #14583453C22semidirect
73. #14583451C22semidirect
74. #14583451C22semidirect
75. #14583451C22semidirect
76. #14583451C22semidirect
77. #14583451C22semidirect
78. #14583451C22semidirect
79. C2×#13063324C22semidirect
80. C2×#13063323C22semidirect
81. C4⋊Q8×D43C22semidirect
82. C4⋊Q8×D43C22semidirect
83. C2×#13063315C22semidirect
84. #125×D43C22semidirect
100. C2×Q8×Dic43C22semidirect
103. C2×#13063290C22semidirect
104. C2×#13063290C22semidirect
105. C4×Q8×D43C22semidirect
106. C4×Q8×D43C22semidirect
116. C43×#554C22semidirect
117. C43×#554C22semidirect
118. D4×Q8×C43C22semidirect
125. C2×#10621900Q8semidirect
323. C2×D4×C43C2×Q8semidirect
334. C2×C22⋊D43C2×Q8semidirect
337. C22×Dic43C2×Q8semidirect
351. #10621900C2×Q8semidirect
352. #10621900C2×Q8semidirect
355. C2×C4×D43C2×Q8semidirect
366. C2×Dic86C2×Q8semidirect
540. #3501D43semidirect
579. #554C2×D43semidirect
580. #554C2×D43semidirect
586. D4×Q8C2×D43semidirect
661. C43#62813semidirect
876. C2×D4Q8×D43semidirect

Maximal subgroups

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

subgroupindex
#191484152
#191484092
#191484062
#191484032
#191484002
#191483982
#191483952
#191483932
#191483912
#191481742
Q8×#106219002
#191479992
#191479972
C2×#145834512
#533×D432
#191477932
C2×C4×#106219002
C43×#35012
#6281343