Finite Group Databasebeta

← #26005401

Subgroups — #26005401

Order 11008.

6636 conjugacy classes of subgroups.

The subgroup lattice has 1316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19149252C218yesmaximal, complemented
2#19149221C214yesmaximal, complemented
3#19149137C214yesmaximal, complemented
4#19149100C212yesmaximal, complemented
5#19149019C212yesmaximal, complemented
6#19148844C211yesmaximal, characteristic, complemented
7#19148817C212yesmaximal, complemented
8#19148579C214yesmaximal, complemented
9#19148566C214yesmaximal, complemented
10#19148547C214yesmaximal, complemented
11#19148520C218yesmaximal, complemented
12#19148520C214yesmaximal, complemented
13#19148514C212yesmaximal, complemented
14#19148490C212yesmaximal, complemented
15#19148310C214yesmaximal, complemented
16#19148292C214yesmaximal, complemented
17#19147887C211yesmaximal, characteristic, complemented
18C2×#14583430C212yesmaximal, complemented
19C43×#3537C211yesmaximal, characteristic, complemented
20#14583652C2214yescomplemented
21#14583652C2218yescomplemented
22#14583649C2214yescomplemented
23#14583644C2218yescomplemented
24#14583638C2214yescomplemented
25#14583635C2214yescomplemented
26#14583635C2218yescomplemented
27#14583626C2214yescomplemented
28#14583619C2214yescomplemented
29#14583618C2218yescomplemented
30#14583616C2218yescomplemented
31#14583613C2218yescomplemented
32#14583611C2214yescomplemented
33#14583608C2214yescomplemented
34#14583608C2218yescomplemented
35#14583604C2214yescomplemented
36#14583596C2214yescomplemented
37#14583596C2218yescomplemented
38#14583594C2218yescomplemented
39#14583592C2218yescomplemented
40#14583592C2218yescomplemented
41#14583592C2218yescomplemented
42#14583589C2214yescomplemented
43#14583589C2218yescomplemented
44#14583588C2214yescomplemented
45#14583586C2218yescomplemented
46#14583586C2218yescomplemented
47#14583586C2218yescomplemented
48#14583586C2218yescomplemented
49#14583585C2218yescomplemented
50#14583580C2218yescomplemented
51#14583580C2218yescomplemented
52#14583580C2214yescomplemented
53#14583580C2218yescomplemented
54#14583580C2218yescomplemented
55#14583580C2214yescomplemented
56#14583580C2218yescomplemented
57#14583580C2218yescomplemented
58D4×Dic86C2214yescomplemented
59#14583555C2214yescomplemented
60#14583555C2214yescomplemented
61#14583549C2214yescomplemented
62#14583549C2218yescomplemented
63#14583543C2214yescomplemented
64#14583543C2218yescomplemented
65#14583543C2214yescomplemented
66#14583543C2218yescomplemented
67#14583543C2218yescomplemented
68#14583528C2214yescomplemented
69#14583525C2214yescomplemented
70#14583517C2218yescomplemented
71#14583516C2218yescomplemented
72#14583516C2214yescomplemented
73#14583516C2214yescomplemented
74#14583516C2218yescomplemented
75#14583512C2212yescomplemented
76#14583511C2212yescomplemented
77#14583506C2218yescomplemented
78#14583506C2218yescomplemented
79#14583503C2218yescomplemented
80#14583503C2212yescomplemented
81#14583494C2214yescomplemented
82#14583494C2218yescomplemented
83#14583494C2214yescomplemented
84#14583494C2218yescomplemented
85#14583494C2218yescomplemented
86#14583492C2218yescomplemented
87#14583487C2214yescomplemented
88#14583484C2218yescomplemented
89#14583484C2218yescomplemented
90#14583484C2218yescomplemented
91#14583484C2218yescomplemented
92#14583478C2214yescomplemented
93#14583476C2214yescomplemented
94#14583470C2212yescomplemented
95#14583452C2212yescomplemented
96#14583452C2211yescharacteristic, complemented
97#14583451C2212yescomplemented
98#14583447C2212yescomplemented
99#14583445C2211yescharacteristic, complemented
100#14583444C2212yescomplemented
101#14583435C2212yescomplemented
102#14583431C2214yescomplemented
103#14583430C2214yescomplemented
104#14583430C2214yescomplemented
105#14583430C2212yescomplemented
106#14583430C2214yescomplemented
107#14583430C2218yescomplemented
108#14583430C2214yescomplemented
109#14583430C2214yescomplemented
110#14583430C2214yescomplemented
111#14583430C2214yescomplemented
112#14583430C2214yescomplemented
113#14583430C2214yescomplemented
114#14583429C2218yescomplemented
115#14583429C2214yescomplemented
116#14583426C2214yescomplemented
117C2×#13063318C2214yescomplemented
118C2×#13063316C2212yescomplemented
119#125×D43C2212yescomplemented
120C2×#13063312C2212yescomplemented
121C2×#13063312C2212yescomplemented
122#14583410C2211yescharacteristic, complemented
123#14583405C2218yescomplemented
124#14583405C2214yescomplemented
125C2×#13063306C2218yescomplemented
126C2×#13063306C2214yescomplemented
127C2×#13063304C2212yescomplemented
128#14583378C2218yescomplemented
129#14583378C2214yescomplemented
130#14583376C2212yescomplemented
131#14583374C2218yescomplemented
132#14583374C2212yescomplemented
133#41×Dic43C2211yescharacteristic, complemented
134#14583367C2211yescharacteristic, complemented
135C4×#10621900C2214yescomplemented
136C2×#13063290C2212yescomplemented
137C2×D4×Dic43C2214yescomplemented
138C2×D4×Dic43C2212yescomplemented
139C2×#13063281C2214yescomplemented
140C22×C4×Dic43C2211yescharacteristic, complemented
141C43×#560C2214yes—
142C43×#553C2214yes—
143D42×C43C2214yes—
144D42×C43C2214yes—
145C43×#540C2212yes—
146C43×#538C2214yes—
147C43×#535C2212yes—
148C43×#534C2214yes—
149C43×#525C2211yescharacteristic
150C2×#121×C43C2212yes—
151C2×#10621898C2311yescharacteristic
152C2×#10621900C2314yes—
153C2×#10621900C2314yes—
154C2×#10621900C2318yes—
155C22×Dic86C2312yes—
156C22×Dic86C2312yes—
157C23×Dic43C2312yes—
158C23×Dic43C2314yes—
159#13063325C2312yes—
160#13063324C2318yes—
161#13063324C2314yes—
162#13063324C2318yes—
163#13063324C2312yes—
164#13063323C2314yes—
165#13063323C2311yescharacteristic
166#13063321C2311yescharacteristic
167#13063320C2318yes—
168#13063320C2314yes—
169#13063318C2314yes—
170#13063318C2318yes—
171#13063318C2318yes—
172#13063318C2318yes—
173#13063318C2318yes—
174#13063318C2318yes—
175#13063318C2318yes—
176#13063318C2318yes—
177#13063318C2318yes—
178#13063318C2318yes—
179#13063318C2318yes—
180#13063318C2318yes—
181#13063318C2318yes—
182#13063318C2318yes—
183#13063318C2318yes—
184#13063317C2318yes—
185#13063317C2312yes—
186#13063316C2314yes—
187#13063316C2312yes—
188#13063316C2318yes—
189#13063316C2314yes—
190#13063316C2314yes—
191#13063316C2314yes—
192#13063315C2318yes—
193#13063315C2318yes—
194#13063315C2318yes—
195#13063315C2318yes—
196#13063315C2318yes—
197#13063315C2318yes—
198#13063315C2314yes—
199#13063314C2311yescharacteristic
200#13063312C2314yes—
201#13063312C2314yes—
202#13063312C2311yescharacteristic
203#13063312C2314yes—
204#13063312C2318yes—
205#13063312C2318yes—
206#13063312C2314yes—
207#13063312C2318yes—
208#13063312C2318yes—
209#13063312C2314yes—
210#13063312C2314yes—
211#13063311C2318yes—
212#13063311C2318yes—
213#13063311C2314yes—
214#13063309C2314yes—
215#13063308C2312yes—
216#13063307C2318yes—
217#13063307C2318yes—
218#13063307C2318yes—
219#13063306C2314yes—
220#13063306C2314yes—
221#13063306C2318yes—
222#13063306C2318yes—
223#13063306C2318yes—
224#13063306C2318yes—
225#13063306C2318yes—
226#13063306C2318yes—
227#13063306C2318yes—
228#13063306C2318yes—
229#13063306C2318yes—
230#13063306C2318yes—
231#13063306C2318yes—
232#13063306C2318yes—
233#13063306C2318yes—
234#13063306C2314yes—
235#13063306C2318yes—
236#13063306C2318yes—
237#13063305C2314yes—
238#13063304C2314yes—
239#13063304C2314yes—
240#13063304C2318yes—
241#13063304C2318yes—
242#13063304C2318yes—
243#13063304C2314yes—
244#13063304C2314yes—
245#13063304C2314yes—
246#13063304C2312yes—
247#13063303C2318yes—
248#13063302C2318yes—
249#13063302C2318yes—
250#13063302C2318yes—
251#13063302C2318yes—
252#13063302C2318yes—
253#13063302C2314yes—
254#13063302C2318yes—
255#13063302C2318yes—
256#13063302C2318yes—
257#13063302C2318yes—
258#13063302C2318yes—
259#13063302C2318yes—
260#13063302C2314yes—
261#13063299C2312yes—
262#13063298C2318yes—
263#13063297C2318yes—
264#13063297C2318yes—
265#13063297C2318yes—
266#13063297C2318yes—
267#13063297C2314yes—
268#13063297C2318yes—
269#13063297C2318yes—
270#13063297C2314yes—
271#13063296C2318yes—
272#13063296C2318yes—
273#13063296C2318yes—
274#13063296C2314yes—
275#13063294C2318yes—
276#13063294C2312yes—
277#13063294C2318yes—
278Q8×Dic43C2312yes—
279C4×Dic86C2314yes—
280C4×Dic86C2318yes—
281C4×Dic86C2318yes—
282C4×Dic86C2314yes—
283#13063290C2314yes—
284#13063290C2314yes—
285#13063290C2312yes—
286#13063290C2314yes—
287#13063290C2318yes—
288#13063290C2314yes—
289#13063290C2314yes—
290#13063290C2314yes—
291D4×Dic43C2318yes—
292D4×Dic43C2318yes—
293D4×Dic43C2318yes—
294D4×Dic43C2312yes—
295D4×Dic43C2318yes—
296D4×Dic43C2314yes—
297D4×Dic43C2314yes—
298D4×Dic43C2318yes—
299D4×Dic43C2318yes—
300D4×Dic43C2318yes—
301D4×Dic43C2318yes—
302D4×Dic43C2318yes—
303D4×Dic43C2314yes—
304D4×Dic43C2314yes—
305D4×Dic43C2318yes—
306D4×Dic43C2314yes—
307D4×Dic43C2314yes—
308D4×Dic43C2318yes—
309D4×Dic43C2314yes—
310#13063287C2312yes—
311C4×C22⋊D43C2314yes—
312C4×C22⋊D43C2314yes—
313C4×C22⋊D43C2318yes—
314C4×C22⋊D43C2318yes—
315C4×C22⋊D43C2318yes—
316(C22⋊D43)⋊C4C2318yes—
317(C22⋊D43)⋊C4C2314yes—
318(C22⋊D43)⋊C4C2318yes—
319(C22⋊D43)⋊C4C2314yes—
320(C22⋊D43)⋊C4C2314yes—
321#13063284C2318yes—
322#13063284C2318yes—
323#13063284C2312yes—
324#13063284C2312yes—
325#13063284C2311yescharacteristic
326#13063283C2314yes—
327#13063282C2318yes—
328#13063282C2312yes—
329#13063281C2314yes—
330#13063281C2318yes—
331#13063281C2318yes—
332#13063281C2314yes—
333#13063281C2318yes—
334#13063281C2318yes—
335#13063281C2318yes—
336#13063281C2318yes—
337#13063281C2318yes—
338#13063281C2318yes—
339C2×C4⋊Dic43C2312yes—
340C2×C4⋊Dic43C2314yes—
341C2×Dic43⋊C4C2318yes—
342C2×Dic43⋊C4C2318yes—
343C2×Dic43⋊C4C2314yes—
344C2×Dic43⋊C4C2314yes—
345C2×Dic43⋊C4C2314yes—
346C4⋊C4×D43C2318yes—
347C4⋊C4×D43C2314yes—
348C2×C22⋊Dic43C2318yes—
349C2×C22⋊Dic43C2318yes—
350C2×C22⋊Dic43C2318yes—
351C2×C22⋊Dic43C2314yes—
352C2×C22⋊Dic43C2314yes—
353C2×C22⋊Dic43C2314yes—
354C2×C22⋊Dic43C2318yes—
355C2×C22⋊Dic43C2314yes—
356C2×C4×Dic43C2312yes—
357C2×C4×Dic43C2312yes—
358C2×C4×Dic43C2312yes—
359C2×C4×Dic43C2311yescharacteristic
360C2×C4×Dic43C2312yes—
361C2×C4×Dic43C2312yes—
362C2×C4×Dic43C2311yescharacteristic
363C2×C4×Dic43C2314yes—
364C2×C4×Dic43C2312yes—
365C42×D43C2312yes—
366C2×#41×C43C2311yescharacteristic
367C22×D4×C43C2314yes—
368C22×D4×C43C2312yes—
369C22×D4×C43C2318yes—
370C22×D4×C43C2312yes—
371C23×C4×C43C2311yescharacteristic
372#127×C43C2314yes—
373#127×C43C2312yes—
374#126×C43C2318yes—
375#125×C43C2312yes—
376#124×C43C2314yes—
377#123×C43C2312yes—
378#123×C43C2318yes—
379#123×C43C2318yes—
380C22⋊Q8×C43C2312yes—
381#121×C43C2314yes—
382#121×C43C2314yes—
383#121×C43C2314yes—
384#121×C43C2314yes—
385#121×C43C2314yes—
386#121×C43C2312yes—
387#121×C43C2318yes—
388#121×C43C2318yes—
389#121×C43C2318yes—
390#120×C43C2312yes—
391#120×C43C2314yes—
392#120×C43C2318yes—
393#120×C43C2314yes—
394#120×C43C2318yes—
395C4×D4×C43C2314yes—
396C4×D4×C43C2318yes—
397C4×D4×C43C2314yes—
398#117×C43C2311yescharacteristic
399#117×C43C2312yes—
400C2×C4⋊C4×C43C2312yes—
401C2×C22⋊C4×C43C2314yes—
402C24×C43C2411yescharacteristic
403C24×C43C2414yes—
404C24×C43C2414yes—
405#41×C43—42no—
406C2×Q8×C43C2411yescharacteristic
407C2×D4×C43—48no—
408C2×D4×C43—416no—
409C2×D4×C43—44no—
410C2×D4×C43—44no—
411C2×D4×C43C2414yes—
412C2×D4×C43C2418yes—
413C2×D4×C43C2414yes—
414C2×D4×C43C2411yescharacteristic
415C2×D4×C43C2412yes—
416C2×D4×C43C2414yes—
417C2×D4×C43C2418yes—
418C2×D4×C43C2418yes—
419C2×D4×C43C2414yes—
420C2×D4×C43C2418yes—
421C22×C4×C43—42no—
422C22×C4×C43C2412yes—
423C22×C4×C43C2412yes—
424C22×C4×C43C2411yescharacteristic
425C22×C4×C43C2412yes—
426C22×C4×C43C2414yes—
427C22×C4×C43C2418yes—
428C22×C4×C43C2411yescharacteristic
429C2×C22⋊D43C2414yes—
430C2×C22⋊D43C2412yes—
431C2×C22⋊D43C2418yes—
432C2×C22⋊D43C2418yes—
433C2×C22⋊D43C2414yes—
434C22×Dic43—44no—
435C22×Dic43—48no—
436C22×Dic43C2412yes—
437C22×Dic43C2412yes—
438C22×Dic43C2414yes—
439C22×Dic43C2412yes—
440C22×Dic43C2412yes—
441C22×Dic43C2412yes—
442C22×Dic43C2412yes—
443C22×Dic43C2414yes—
444C22×Dic43C2414yes—
445C22×Dic43C2418yes—
446C22×Dic43C2418yes—
447C22×Dic43C2414yes—
448C22×Dic43C2418yes—
449C22×Dic43C2418yes—
450#10621900—48no—
451#10621900—48no—
452#10621900—416no—
453#10621898—42no—
454C2×D172C2411yescharacteristic
455C2×C4×D43C2412yes—
456C2×C4×D43C2414yes—
457C2×C4×D43C2418yes—
458C2×Dic86—44no—
459C2×Dic86—44no—
460C2×Dic86C2414yes—
461C2×Dic86C2411yescharacteristic
462C2×Dic86C2414yes—
463C2×Dic86C2418yes—
464C2×Dic86C2414yes—
465C2×Dic86C2414yes—
466C4⋊C4×C43C2414yes—
467C4⋊C4×C43C2414yes—
468C4⋊C4×C43C2412yes—
469C4⋊C4×C43C2414yes—
470C4⋊C4×C43C2418yes—
471C22⋊C4×C43C2418yes—
472C22⋊C4×C43C2418yes—
473C22⋊C4×C43C2414yes—
474C22⋊C4×C43C2412yes—
475C22⋊C4×C43C2414yes—
476C22⋊C4×C43C2418yes—
477C22⋊C4×C43C2418yes—
478C22⋊C4×C43C2414yes—
479C42×C43C2412yes—
480C42×C43C2414yes—
481C22⋊Dic43C2418yes—
482C22⋊Dic43C2414yes—
483C22⋊Dic43C2418yes—
484C22⋊Dic43C2418yes—
485C22⋊Dic43C2414yes—
486C22⋊Dic43C2418yes—
487C22⋊Dic43C2414yes—
488C22⋊Dic43C2418yes—
489C22⋊Dic43C2414yes—
490C22⋊Dic43C2418yes—
491C22⋊Dic43C2418yes—
492C22⋊Dic43C2418yes—
493C22⋊Dic43C2418yes—
494C22⋊Dic43C2418yes—
495C22⋊Dic43C2418yes—
496C22⋊Dic43C2418yes—
497C22⋊Dic43C2418yes—
498C22⋊Dic43C2412yes—
499(C2×D43)⋊C4C2414yes—
500(C2×D43)⋊C4C2414yes—
501(C2×D43)⋊C4C2418yes—
502(C2×D43)⋊C4C2414yes—
503C4⋊Dic43C2414yes—
504C4⋊Dic43C2418yes—
505C4⋊Dic43C2418yes—
506C4⋊Dic43C2414yes—
507C4⋊Dic43C2414yes—
508C4⋊Dic43C2414yes—
509C4⋊Dic43C2418yes—
510C4⋊Dic43C2418yes—
511C4⋊Dic43C2412yes—
512Dic43⋊C4C2418yes—
513Dic43⋊C4C2418yes—
514Dic43⋊C4C2418yes—
515Dic43⋊C4C2414yes—
516Dic43⋊C4C2418yes—
517Dic43⋊C4C2414yes—
518Dic43⋊C4C2418yes—
519Dic43⋊C4C2418yes—
520Dic43⋊C4C2418yes—
521Dic43⋊C4C2418yes—
522Dic43⋊C4C2418yes—
523Dic43⋊C4C2418yes—
524Dic43⋊C4C2418yes—
525Dic43⋊C4C2414yes—
526Dic43⋊C4C2414yes—
527Dic43⋊C4C2414yes—
528Dic43⋊C4C2418yes—
529C4×Dic43C2411yescharacteristic
530C4×Dic43C2414yes—
531C4×Dic43C2411yescharacteristic
532C4×Dic43C2412yes—
533C4×Dic43C2412yes—
534C4×Dic43C2412yes—
535C4×Dic43C2411yescharacteristic
536C4×Dic43C2412yes—
537C4×Dic43C2412yes—
538C4×Dic43C2412yes—
539C4×Dic43C2411yescharacteristic
540C4×Dic43C2418yes—
541C4×Dic43C2414yes—
542C4×Dic43C2418yes—
543C4×Dic43C2412yes—
544C4×Dic43C2414yes—
545C4×Dic43C2418yes—
546C4×Dic43C2418yes—
547C23×C43—24no—
548C23×C43—28no—
549C23×C43—41no—
550C23×C43—44no—
551C23×C43—44no—
552C23×C43—48no—
553C23×C43—44no—
554C23×C43C2518yes—
555C23×C43C2512yes—
556C23×C43C2511yescharacteristic
557C23×C43C2512yes—
558C22×D43C2512yes—
559Q8×C43—41no—
560D4×C43—216no—
561D4×C43—28no—
562D4×C43—28no—
563D4×C43—44no—
564D4×C43—44no—
565D4×C43—48no—
566D4×C43—48no—
567D4×C43—48no—
568D4×C43—42no—
569D4×C43—41no—
570C2×C4×C43—24no—
571C2×C4×C43—24no—
572C2×C4×C43—22no—
573C2×C4×C43—41no—
574C2×C4×C43—42no—
575C2×C4×C43—44no—
576C2×C4×C43—48no—
577C2×C4×C43C2511yescharacteristic
578C2×C4×C43C2512yes—
579C2×C4×C43C2512yes—
580C2×C4×C43C2514yes—
581C2×C4×C43C2518yes—
582C2×C4×C43C2511yescharacteristic
583C22⋊D43—28no—
584C22⋊D43—42no—
585C22⋊D43—48no—
586C22⋊D43—44no—
587C22⋊D43—48no—
588C2×Dic43—24no—
589C2×Dic43—28no—
590C2×Dic43—24no—
591C2×Dic43—44no—
592C2×Dic43—44no—
593C2×Dic43—48no—
594C2×Dic43—48no—
595C2×Dic43—44no—
596C2×Dic43—42no—
597C2×Dic43—42no—
598C2×Dic43—48no—
599C2×Dic43—48no—
600C2×Dic43—42no—
601C2×Dic43—42no—
602C2×Dic43C2512yes—
603C2×Dic43C2512yes—
604C2×Dic43C2512yes—
605C2×Dic43C2512yes—
606C2×Dic43C2518yes—
607C2×Dic43C2514yes—
608C2×Dic43C2512yes—
609C2×Dic43C2518yes—
610D172—41no—
611C4×D43—24no—
612C4×D43—48no—
613C4×D43—44no—
614Dic86—28no—
615Dic86—44no—
616Dic86—44no—
617Dic86—41no—
618Dic86—44no—
619Dic86—48no—
620#62829—431nomaximal, Sylow
621C22×C43—22no—
622C22×C43—22no—
623C22×C43—28no—
624C22×C43—22no—
625C22×C43—22no—
626C22×C43—28no—
627C22×C43—28no—
628C22×C43—24no—
629C22×C43—21no—
630C22×C43—44no—
631C22×C43—88no—
632C22×C43—164no—
633C22×C43#58514yes—
634C22×C43C2611yescharacteristic
635C2×D43—22no—
636C2×D43—24no—
637C4×C43—22no—
638C4×C43—22no—
639C4×C43—24no—
640C4×C43—28no—
641C4×C43—21no—
642C4×C43#58512yes—
643Dic43—28no—
644Dic43—24no—
645Dic43—22no—
646Dic43—22no—
647Dic43—28no—
648Dic43—22no—
649Dic43—22no—
650Dic43—22no—
651#3566—438no—
652#3564—434no—
653#3560—434no—
654#3557—432no—
655#3551—432no—
656#3538—431no—
657#3537D4311yescharacteristic, complemented
658#3536—432no—
659#3516—434no—
660#3515—434no—
661#3514—434no—
662#3513—438no—
663#3513—434no—
664#3512—432no—
665#3510—432no—
666#3493—434no—
667#3491—434no—
668#3444—431no—
669C2×#529—432no—
670C2×C43—24no—
671C2×C43—41no—
672C2×C43—48no—
673C2×C43—42no—
674C2×C43C2×#58512yes—
675C2×C43C2×#58511yescharacteristic
676D43—42no—
677#563—434no—
678#563—434no—
679#563—438no—
680#562—438no—
681#560—434no—
682#560C2×D4314yes—
683#559—438no—
684#559—434no—
685#557—434no—
686#556—438no—
687#556—438no—
688#556—434no—
689#555—434no—
690#555—438no—
691#554—434no—
692#554—438no—
693#554—434no—
694#553—438no—
695#553—438no—
696#553—438no—
697#553—438no—
698#553—438no—
699#553—434no—
700#553C2×D4314yes—
701#552—438no—
702#552—438no—
703#552—438no—
704#552—438no—
705#552—438no—
706#552—434no—
707#552—438no—
708#552—434no—
709#551—434no—
710#551—438no—
711#551—438no—
712#551—438no—
713#551—438no—
714#551—434no—
715#551—438no—
716#551—438no—
717D4×Q8—434no—
718#548—434no—
719#548—434no—
720#547—434no—
721#547—438no—
722#546—438no—
723#546—438no—
724#546—434no—
725#546—434no—
726#546—438no—
727D42C2×D4314yes—
728D42C2×D4314yes—
729#544—434no—
730#543—434no—
731#542—438no—
732#542—434no—
733#542—434no—
734#542—438no—
735#542—438no—
736#541—438no—
737#541—438no—
738#541—432no—
739#541—432no—
740#540—432no—
741#540—438no—
742#540C2×D4312yes—
743#539—438no—
744#539—438no—
745#539—434no—
746#539—434no—
747#539—438no—
748#539—438no—
749#538—438no—
750#538—438no—
751#538—438no—
752#538—438no—
753#538—434no—
754#538C2×D4314yes—
755#537—434no—
756#537—434no—
757#536—432no—
758#535C2×D4312yes—
759#534C2×D4314yes—
760#533—432no—
761#533—431no—
762#533—432no—
763#532—431no—
764#532—432no—
765#532—432no—
766#529—434no—
767#529—432no—
768#529—434no—
769#529—434no—
770#529—434no—
771#529—434no—
772#529—434no—
773#529—434no—
774#529—434no—
775#529—434no—
776#529—432no—
777#529—438no—
778#529—434no—
779#529—434no—
780#529—438no—
781#529—434no—
782C2×#126—434no—
783C2×#125—432no—
784C2×#125—432no—
785C2×#124—432no—
786C2×#124—432no—
787#525—431no—
788#525—434no—
789#525—438no—
790#525C2×D4311yescharacteristic
791C2×#123—434no—
792C2×#123—438no—
793C2×C22⋊Q8—432no—
794C2×#121C2×D4312yes—
795#520—438no—
796#520—434no—
797#519—432no—
798#518—438no—
799#518—432no—
800C4×#41—431no—
801C4×#41—434no—
802C4×#41—431no—
803C2×C4×Q8—432no—
804C2×C4×D4—434no—
805C2×C4×D4—432no—
806C2×#117—434no—
807C22×C42—431no—
808C43#6282911yescharacteristic, complemented, Sylow
809C2×#41—434no—
810C2×#41—438no—
811C2×#41—434no—
812C2×#41—431no—
813C2×#41C22×D4311yescharacteristic
814C22×Q8—432no—
815C22×Q8—432no—
816C22×D4C22×D4314yes—
817C22×D4C22×D4312yes—
818C22×D4C22×D4318yes—
819C22×D4C22×D4312yes—
820C23×C4—434no—
821C23×C4—432no—
822C23×C4C22×D4311yescharacteristic
823C4⋊Q8—431no—
824C4⋊Q8—434no—
825C4⋊Q8—432no—
826C4⋊Q8—434no—
827C4⋊Q8—438no—
828C4⋊Q8—438no—
829C4⋊Q8—432no—
830#127—431no—
831#127C22×D4312yes—
832#127C22×D4314yes—
833#126—434no—
834#126—438no—
835#126—438no—
836#126—438no—
837#126—438no—
838#126—438no—
839#126—434no—
840#126—438no—
841#126—438no—
842#126—438no—
843#126—438no—
844#126—438no—
845#126—438no—
846#126—438no—
847#126—438no—
848#126—438no—
849#126—438no—
850#126C22×D4318yes—
851#125—434no—
852#125—434no—
853#125—434no—
854#125—434no—
855#125—438no—
856#125—434no—
857#125—432no—
858#125—438no—
859#125—438no—
860#125—438no—
861#125—438no—
862#125—438no—
863#125—438no—
864#125—432no—
865#125—438no—
866#125C22×D4312yes—
867#124—431no—
868#124—434no—
869#124—434no—
870#124—434no—
871#124—434no—
872#124—438no—
873#124—434no—
874#124—431no—
875#124—438no—
876#124—434no—
877#124—438no—
878#124—438no—
879#124—434no—
880#124—438no—
881#124—438no—
882#124C22×D4314yes—
883#123—438no—
884#123—434no—
885#123—438no—
886#123—438no—
887#123—438no—
888#123—438no—
889#123—438no—
890#123—438no—
891#123—438no—
892#123—438no—
893#123—438no—
894#123—438no—
895#123—434no—
896#123—434no—
897#123—438no—
898#123—438no—
899#123—438no—
900#123—438no—
901#123—432no—
902#123—434no—
903#123—438no—
904#123—438no—
905#123—438no—
906#123C22×D4312yes—
907#123C22×D4318yes—
908#123C22×D4318yes—
909C22⋊Q8—434no—
910C22⋊Q8—434no—
911C22⋊Q8—434no—
912C22⋊Q8—434no—
913C22⋊Q8—432no—
914C22⋊Q8—434no—
915C22⋊Q8—438no—
916C22⋊Q8—438no—
917C22⋊Q8—438no—
918C22⋊Q8—434no—
919C22⋊Q8—438no—
920C22⋊Q8—434no—
921C22⋊Q8—434no—
922C22⋊Q8—438no—
923C22⋊Q8—438no—
924C22⋊Q8—438no—
925C22⋊Q8—438no—
926C22⋊Q8—438no—
927C22⋊Q8—438no—
928C22⋊Q8—438no—
929C22⋊Q8—438no—
930C22⋊Q8—438no—
931C22⋊Q8—438no—
932C22⋊Q8—438no—
933C22⋊Q8C22×D4312yes—
934#121—434no—
935#121—434no—
936#121—438no—
937#121—438no—
938#121—438no—
939#121—434no—
940#121—438no—
941#121—438no—
942#121—438no—
943#121—438no—
944#121—438no—
945#121—438no—
946#121—432no—
947#121—438no—
948#121C22×D4314yes—
949#121C22×D4314yes—
950#121C22×D4314yes—
951#121C22×D4314yes—
952#121C22×D4312yes—
953#121C22×D4318yes—
954#121C22×D4314yes—
955#121C22×D4318yes—
956#121C22×D4318yes—
957#120—432no—
958#120—438no—
959#120—438no—
960#120C22×D4312yes—
961#120C22×D4318yes—
962#120C22×D4314yes—
963#120C22×D4318yes—
964#120C22×D4314yes—
965C4×Q8—432no—
966C4×Q8—434no—
967C4×Q8—434no—
968C4×Q8—434no—
969C4×Q8—434no—
970C4×Q8—434no—
971C4×Q8—432no—
972C4×Q8—434no—
973C4×Q8—438no—
974C4×Q8—434no—
975C4×Q8—438no—
976C4×Q8—434no—
977C4×Q8—438no—
978C4×D4—438no—
979C4×D4—434no—
980C4×D4—434no—
981C4×D4—438no—
982C4×D4—438no—
983C4×D4—434no—
984C4×D4—434no—
985C4×D4—438no—
986C4×D4—434no—
987C4×D4—434no—
988C4×D4—432no—
989C4×D4—438no—
990C4×D4—438no—
991C4×D4—438no—
992C4×D4—438no—
993C4×D4—438no—
994C4×D4—438no—
995C4×D4—434no—
996C4×D4—438no—
997C4×D4—434no—
998C4×D4—434no—
999C4×D4—438no—
1000C4×D4—438no—
1001C4×D4—438no—
1002C4×D4—432no—
1003C4×D4—434no—
1004C4×D4—434no—
1005C4×D4—434no—
1006C4×D4—438no—
1007C4×D4—438no—
1008C4×D4C22×D4314yes—
1009C4×D4C22×D4318yes—
1010C4×D4C22×D4314yes—
1011#117—432no—
1012#117—431no—
1013#117—438no—
1014#117—438no—
1015#117—432no—
1016#117—434no—
1017#117—438no—
1018#117—438no—
1019#117—438no—
1020#117—438no—
1021#117—434no—
1022#117—434no—
1023#117—438no—
1024#117—438no—
1025#117—438no—
1026#117—438no—
1027#117—432no—
1028#117—438no—
1029#117C22×D4311yescharacteristic
1030#117C22×D4312yes—
1031C2×C4⋊C4—434no—
1032C2×C4⋊C4—434no—
1033C2×C4⋊C4—432no—
1034C2×C4⋊C4—434no—
1035C2×C4⋊C4—434no—
1036C2×C4⋊C4—438no—
1037C2×C4⋊C4—438no—
1038C2×C4⋊C4—434no—
1039C2×C4⋊C4—438no—
1040C2×C4⋊C4C22×D4312yes—
1041C2×C22⋊C4—434no—
1042C2×C22⋊C4—434no—
1043C2×C22⋊C4—434no—
1044C2×C22⋊C4—434no—
1045C2×C22⋊C4—438no—
1046C2×C22⋊C4—438no—
1047C2×C22⋊C4—438no—
1048C2×C22⋊C4—438no—
1049C2×C22⋊C4C22×D4314yes—
1050C2×C42—432no—
1051C2×C42—434no—
1052C2×C42—432no—
1053C2×C42—432no—
1054C2×C42—432no—
1055C2×C42—431no—
1056C2×C42—432no—
1057C2×C42—432no—
1058C2×C42—431no—
1059C2×C42—432no—
1060C24C23×D4311yescharacteristic
1061C24C23×D4314yes—
1062C24C23×D4314yes—
1063#41—42no—
1064#41—1722no—
1065#41—1728no—
1066#41—17216no—
1067#41—1728no—
1068C2×Q8—434no—
1069C2×Q8—431no—
1070C2×Q8—438no—
1071C2×Q8—434no—
1072C2×Q8—434no—
1073C2×Q8—434no—
1074C2×Q8—1724no—
1075C2×Q8—1724no—
1076C2×Q8C23×D4311yescharacteristic
1077C2×D4—44no—
1078C2×D4—44no—
1079C2×D4—48no—
1080C2×D4—416no—
1081C2×D4—434no—
1082C2×D4—438no—
1083C2×D4—438no—
1084C2×D4—434no—
1085C2×D4—432no—
1086C2×D4—431no—
1087C2×D4C23×D4318yes—
1088C2×D4C23×D4314yes—
1089C2×D4C23×D4314yes—
1090C2×D4C23×D4311yescharacteristic
1091C2×D4C23×D4312yes—
1092C2×D4C23×D4314yes—
1093C2×D4C23×D4318yes—
1094C2×D4C23×D4318yes—
1095C2×D4C23×D4314yes—
1096C2×D4C23×D4318yes—
1097C22×C4—42no—
1098C22×C4—432no—
1099C22×C4—432no—
1100C22×C4—434no—
1101C22×C4—432no—
1102C22×C4—432no—
1103C22×C4—432no—
1104C22×C4—432no—
1105C22×C4—434no—
1106C22×C4—434no—
1107C22×C4—438no—
1108C22×C4—438no—
1109C22×C4—434no—
1110C22×C4—438no—
1111C22×C4—438no—
1112C22×C4—432no—
1113C22×C4—434no—
1114C22×C4—438no—
1115C22×C4—1724no—
1116C22×C4—1728no—
1117C22×C4C23×D4312yes—
1118C22×C4C23×D4311yescharacteristic
1119C22×C4C23×D4312yes—
1120C22×C4C23×D4312yes—
1121C22×C4C23×D4311yescharacteristic
1122C22×C4C23×D4314yes—
1123C22×C4C23×D4318yes—
1124C4⋊C4—438no—
1125C4⋊C4—438no—
1126C4⋊C4—434no—
1127C4⋊C4—434no—
1128C4⋊C4—438no—
1129C4⋊C4—438no—
1130C4⋊C4—434no—
1131C4⋊C4—438no—
1132C4⋊C4—438no—
1133C4⋊C4—438no—
1134C4⋊C4—438no—
1135C4⋊C4—438no—
1136C4⋊C4—434no—
1137C4⋊C4—438no—
1138C4⋊C4—438no—
1139C4⋊C4—438no—
1140C4⋊C4—434no—
1141C4⋊C4—438no—
1142C4⋊C4—434no—
1143C4⋊C4—438no—
1144C4⋊C4—438no—
1145C4⋊C4—432no—
1146C4⋊C4—434no—
1147C4⋊C4—434no—
1148C4⋊C4—434no—
1149C4⋊C4—438no—
1150C4⋊C4C23×D4314yes—
1151C4⋊C4C23×D4318yes—
1152C4⋊C4C23×D4314yes—
1153C4⋊C4C23×D4314yes—
1154C4⋊C4C23×D4312yes—
1155C22⋊C4—438no—
1156C22⋊C4—438no—
1157C22⋊C4—434no—
1158C22⋊C4—438no—
1159C22⋊C4—434no—
1160C22⋊C4—438no—
1161C22⋊C4—434no—
1162C22⋊C4—438no—
1163C22⋊C4—434no—
1164C22⋊C4—438no—
1165C22⋊C4—438no—
1166C22⋊C4—438no—
1167C22⋊C4—438no—
1168C22⋊C4—438no—
1169C22⋊C4—438no—
1170C22⋊C4—438no—
1171C22⋊C4—438no—
1172C22⋊C4—432no—
1173C22⋊C4—434no—
1174C22⋊C4—434no—
1175C22⋊C4—438no—
1176C22⋊C4—434no—
1177C22⋊C4C23×D4318yes—
1178C22⋊C4C23×D4318yes—
1179C22⋊C4C23×D4314yes—
1180C22⋊C4C23×D4314yes—
1181C22⋊C4C23×D4318yes—
1182C22⋊C4C23×D4318yes—
1183C22⋊C4C23×D4314yes—
1184C22⋊C4C23×D4312yes—
1185C42—431no—
1186C42—432no—
1187C42—431no—
1188C42—431no—
1189C42—432no—
1190C42—432no—
1191C42—432no—
1192C42—432no—
1193C42—432no—
1194C42—431no—
1195C42—434no—
1196C42—438no—
1197C42—438no—
1198C42—434no—
1199C42—432no—
1200C42—438no—
1201C42—434no—
1202C42—438no—
1203C42C23×D4312yes—
1204C42C23×D4314yes—
1205C23—24no—
1206C23—28no—
1207C23—41no—
1208C23—44no—
1209C23—44no—
1210C23—44no—
1211C23—48no—
1212C23—432no—
1213C23C24×D4312yes—
1214C23C24×D4318yes—
1215C23C24×D4311yescharacteristic
1216C23C24×D4312yes—
1217Q8—41no—
1218Q8—868no—
1219Q8—1724no—
1220Q8—1724no—
1221Q8—1721no—
1222Q8—1728no—
1223Q8—1724no—
1224D4—216no—
1225D4—28no—
1226D4—28no—
1227D4—44no—
1228D4—44no—
1229D4—48no—
1230D4—48no—
1231D4—48no—
1232D4—41no—
1233D4—42no—
1234D4—868no—
1235D4—1721no—
1236D4—1722no—
1237D4—1728no—
1238D4—1724no—
1239D4—1728no—
1240C2×C4—24no—
1241C2×C4—22no—
1242C2×C4—24no—
1243C2×C4—41no—
1244C2×C4—42no—
1245C2×C4—44no—
1246C2×C4—48no—
1247C2×C4—432no—
1248C2×C4—432no—
1249C2×C4—432no—
1250C2×C4—434no—
1251C2×C4—438no—
1252C2×C4—432no—
1253C2×C4—432no—
1254C2×C4—438no—
1255C2×C4—864no—
1256C2×C4—864no—
1257C2×C4—868no—
1258C2×C4—864no—
1259C2×C4—1724no—
1260C2×C4—1728no—
1261C2×C4—1722no—
1262C2×C4—1722no—
1263C2×C4—1728no—
1264C2×C4—1728no—
1265C2×C4—1722no—
1266C2×C4—1722no—
1267C2×C4—1724no—
1268C2×C4—1724no—
1269C2×C4—1724no—
1270C2×C4—1728no—
1271C2×C4—1728no—
1272C2×C4C24×D4312yes—
1273C2×C4C24×D4312yes—
1274C2×C4C24×D4311yescharacteristic
1275C2×C4C24×D4314yes—
1276C2×C4C24×D4318yes—
1277C2×C4C24×D4311yescharacteristic
1278C22—22no—
1279C22—22no—
1280C22—21no—
1281C22—22no—
1282C22—28no—
1283C22—22no—
1284C22—28no—
1285C22—28no—
1286C22—24no—
1287C22—44no—
1288C22—88no—
1289C22—164no—
1290C22—862no—
1291C22—864no—
1292C22#1458373414yes—
1293C22C25×D4311yescharacteristic
1294C4—22no—
1295C4—21no—
1296C4—22no—
1297C4—28no—
1298C4—24no—
1299C4—862no—
1300C4—862no—
1301C4—862no—
1302C4—868no—
1303C4—862no—
1304C4—862no—
1305C4—864no—
1306C4—868no—
1307C4#1458373412yes—
1308C2—24no—
1309C2—41no—
1310C2—48no—
1311C2—42no—
1312C2—1722no—
1313C2C2×#1458373412yes—
1314C2C2×#1458373411yescharacteristic
subgroupG/H
center, FrattiniC22C25×D43
commutator, socle, cosocleC22×C43C26
FittingC43×#3537C2
hypercenter#3537D43
hypocenterC43#62829
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #3537

Complements

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

NH ≅ G/Ntype
1. #19149252C2semidirect
2. #19149221C2semidirect
3. #19149137C2semidirect
4. #19149100C2semidirect
5. #19149019C2semidirect
6. #19148844C2semidirect
7. #19148817C2semidirect
8. #19148579C2semidirect
9. #19148566C2semidirect
10. #19148547C2semidirect
11. #19148520C2semidirect
12. #19148520C2semidirect
13. #19148514C2semidirect
14. #19148490C2semidirect
15. #19148310C2semidirect
16. #19148292C2semidirect
17. #19147887C2semidirect
18. C2×#14583430C2semidirect
19. C43×#3537C2semidirect
20. #14583652C22semidirect
21. #14583652C22semidirect
22. #14583649C22semidirect
23. #14583644C22semidirect
24. #14583638C22semidirect
25. #14583635C22semidirect
26. #14583635C22semidirect
27. #14583626C22semidirect
28. #14583619C22semidirect
29. #14583618C22semidirect
30. #14583616C22semidirect
31. #14583613C22semidirect
32. #14583611C22semidirect
33. #14583608C22semidirect
34. #14583608C22semidirect
35. #14583604C22semidirect
36. #14583596C22semidirect
37. #14583596C22semidirect
38. #14583594C22semidirect
39. #14583592C22semidirect
40. #14583592C22semidirect
41. #14583592C22semidirect
42. #14583589C22semidirect
43. #14583589C22semidirect
44. #14583588C22semidirect
45. #14583586C22semidirect
46. #14583586C22semidirect
47. #14583586C22semidirect
48. #14583586C22semidirect
49. #14583585C22semidirect
50. #14583580C22semidirect
51. #14583580C22semidirect
52. #14583580C22semidirect
53. #14583580C22semidirect
54. #14583580C22semidirect
55. #14583580C22semidirect
56. #14583580C22semidirect
57. #14583580C22semidirect
58. D4×Dic86C22semidirect
59. #14583555C22semidirect
60. #14583555C22semidirect
61. #14583549C22semidirect
62. #14583549C22semidirect
63. #14583543C22semidirect
64. #14583543C22semidirect
65. #14583543C22semidirect
66. #14583543C22semidirect
67. #14583543C22semidirect
68. #14583528C22semidirect
69. #14583525C22semidirect
70. #14583517C22semidirect
71. #14583516C22semidirect
72. #14583516C22semidirect
73. #14583516C22semidirect
74. #14583516C22semidirect
75. #14583512C22semidirect
76. #14583511C22semidirect
77. #14583506C22semidirect
78. #14583506C22semidirect
79. #14583503C22semidirect
80. #14583503C22semidirect
81. #14583494C22semidirect
82. #14583494C22semidirect
83. #14583494C22semidirect
84. #14583494C22semidirect
85. #14583494C22semidirect
86. #14583492C22semidirect
87. #14583487C22semidirect
88. #14583484C22semidirect
89. #14583484C22semidirect
90. #14583484C22semidirect
91. #14583484C22semidirect
92. #14583478C22semidirect
93. #14583476C22semidirect
94. #14583470C22semidirect
95. #14583452C22semidirect
96. #14583452C22semidirect
97. #14583451C22semidirect
98. #14583447C22semidirect
99. #14583445C22semidirect
100. #14583444C22semidirect
101. #14583435C22semidirect
102. #14583431C22semidirect
103. #14583430C22semidirect
104. #14583430C22semidirect
105. #14583430C22semidirect
106. #14583430C22semidirect
107. #14583430C22semidirect
108. #14583430C22semidirect
109. #14583430C22semidirect
110. #14583430C22semidirect
111. #14583430C22semidirect
112. #14583430C22semidirect
113. #14583430C22semidirect
114. #14583429C22semidirect
115. #14583429C22semidirect
116. #14583426C22semidirect
117. C2×#13063318C22semidirect
118. C2×#13063316C22semidirect
119. #125×D43C22semidirect
120. C2×#13063312C22semidirect
121. C2×#13063312C22semidirect
122. #14583410C22semidirect
123. #14583405C22semidirect
124. #14583405C22semidirect
125. C2×#13063306C22semidirect
126. C2×#13063306C22semidirect
127. C2×#13063304C22semidirect
128. #14583378C22semidirect
129. #14583378C22semidirect
130. #14583376C22semidirect
131. #14583374C22semidirect
132. #14583374C22semidirect
133. #41×Dic43C22semidirect
134. #14583367C22semidirect
135. C4×#10621900C22semidirect
136. C2×#13063290C22semidirect
137. C2×D4×Dic43C22semidirect
138. C2×D4×Dic43C22semidirect
139. C2×#13063281C22semidirect
140. C22×C4×Dic43C22semidirect
657. #3537D43semidirect
808. C43#62829semidirect

Maximal subgroups

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

subgroupindex
#191492522
#191492212
#191491372
#191491002
#191490192
#191488442
#191488172
#191485792
#191485662
#191485472
#191485202
#191485142
#191484902
#191483102
#191482922
#191478872
C2×#145834302
C43×#35372
#6282943