Finite Group Databasebeta

← #26005419

Subgroups — #26005419

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#19149276C218yesmaximal, complemented
2#19149216C214yesmaximal, complemented
3#19149152C214yesmaximal, complemented
4#19149103C212yesmaximal, complemented
5#19149024C212yesmaximal, complemented
6#19148834C211yesmaximal, characteristic, complemented
7#19148824C212yesmaximal, complemented
8#19148589C214yesmaximal, complemented
9#19148570C214yesmaximal, complemented
10#19148557C214yesmaximal, complemented
11#19148540C214yesmaximal, complemented
12#19148522C218yesmaximal, complemented
13#19148518C212yesmaximal, complemented
14#19148494C212yesmaximal, complemented
15#19148316C214yesmaximal, complemented
16#19148289C214yesmaximal, complemented
17#19147887C211yesmaximal, characteristic, complemented
18C2×#14583435C212yesmaximal, complemented
19C43×#3538C211yesmaximal, characteristic, complemented
20#14583653C2218yescomplemented
21#14583648C2214yescomplemented
22#14583645C2218yescomplemented
23#14583639C2214yes—
24#14583639C2214yescomplemented
25#14583634C2214yescomplemented
26#14583631C2218yescomplemented
27#14583625C2214yescomplemented
28#14583623C2214yescomplemented
29#14583623C2218yescomplemented
30#14583623C2218yescomplemented
31#14583615C2218yescomplemented
32#14583615C2214yescomplemented
33#14583607C2214yescomplemented
34#14583607C2218yescomplemented
35#14583605C2214yescomplemented
36#14583602C2218yescomplemented
37#14583602C2218yescomplemented
38#14583600C2218yescomplemented
39#14583600C2218yescomplemented
40#14583595C2214yes—
41#14583595C2218yescomplemented
42#14583593C2214yescomplemented
43#14583587C2218yescomplemented
44#14583587C2218yescomplemented
45#14583585C2218yescomplemented
46#14583583C2218yescomplemented
47#14583583C2214yescomplemented
48#14583582C2218yescomplemented
49#14583581C2218yescomplemented
50#14583577C2214yescomplemented
51#14583576C2218yescomplemented
52#14583576C2218yescomplemented
53#14583574C2218yescomplemented
54#14583573C2218yescomplemented
55#14583572C2218yescomplemented
56#14583572C2218yescomplemented
57#14583560C2214yescomplemented
58#14583560C2214yescomplemented
59#14583550C2214yescomplemented
60#14583547C2218yescomplemented
61#14583544C2218yescomplemented
62#14583541C2218yescomplemented
63#14583540C2214yescomplemented
64#14583540C2214yescomplemented
65#14583539C2218yescomplemented
66D4×D172C2214yes—
67#14583531C2214yes—
68#14583524C2214yescomplemented
69#14583523C2218yescomplemented
70#14583522C2214yescomplemented
71#14583522C2218yescomplemented
72#14583522C2214yescomplemented
73#14583515C2218yescomplemented
74#14583510C2212yescomplemented
75#14583510C2218yescomplemented
76#14583508C2218yescomplemented
77#14583505C2212yescomplemented
78#14583504C2212yes—
79#14583501C2218yescomplemented
80#14583497C2218yescomplemented
81#14583496C2214yescomplemented
82#14583493C2218yescomplemented
83#14583490C2218yescomplemented
84#14583490C2218yescomplemented
85#14583489C2214yes—
86#14583489C2218yescomplemented
87#14583489C2218yescomplemented
88#14583489C2214yescomplemented
89#14583488C2218yescomplemented
90#14583483C2218yescomplemented
91#14583480C2214yescomplemented
92#14583479C2214yescomplemented
93#14583463C2212yes—
94#14583457C2214yes—
95#14583452C2212yescomplemented
96#14583452C2211yescharacteristic, complemented
97#14583451C2212yescomplemented
98#14583450C2212yescomplemented
99#14583445C2211yescharacteristic, complemented
100#14583444C2212yescomplemented
101#14583436C2214yescomplemented
102#14583435C2214yescomplemented
103#14583435C2214yescomplemented
104#14583435C2214yescomplemented
105#14583435C2212yescomplemented
106#14583435C2218yescomplemented
107#14583435C2214yescomplemented
108#14583435C2214yescomplemented
109#14583435C2214yescomplemented
110#14583435C2214yescomplemented
111#14583435C2214yescomplemented
112#14583435C2214yescomplemented
113#14583430C2212yescomplemented
114#14583429C2218yescomplemented
115#14583429C2214yescomplemented
116#14583426C2214yescomplemented
117C2×#13063320C2214yescomplemented
118C2×#13063316C2212yescomplemented
119#125×D43C2212yescomplemented
120C2×#13063314C2212yescomplemented
121C2×#13063314C2212yescomplemented
122#14583411C2218yescomplemented
123#14583410C2211yescharacteristic, complemented
124#14583405C2214yescomplemented
125C2×#13063309C2214yescomplemented
126#123×D43C2218yescomplemented
127C2×#13063299C2212yes—
128#14583381C2214yescomplemented
129#14583379C2218yescomplemented
130#14583377C2212yescomplemented
131#14583373C2212yescomplemented
132#14583371C2218yescomplemented
133#41×Dic43C2211yescharacteristic, complemented
134#14583367C2211yescharacteristic, complemented
135C4×#10621900C2214yescomplemented
136C2×Q8×Dic43C2212yescomplemented
137C2×#13063287C2212yescomplemented
138C2×(C22⋊D43)⋊C4C2214yescomplemented
139C2×#13063283C2214yescomplemented
140C22×C4×Dic43C2211yescharacteristic, complemented
141C43×#563C2214yescomplemented
142C43×#552C2214yescomplemented
143C43×#551C2214yescomplemented
144D4×Q8×C43C2214yescomplemented
145C43×#544C2214yescomplemented
146C43×#541C2212yescomplemented
147C43×#539C2214yescomplemented
148C43×#536C2212yescomplemented
149C43×#525C2211yescharacteristic
150C2×C22⋊Q8×C43C2212yescomplemented
151C2×#10621902C2314yes—
152C2×#10621898C2311yescharacteristic
153C2×#10621898C2318yes—
154C2×#10621900C2314yes—
155C22×D172C2312yes—
156C22×D172C2312yes—
157C22×C22⋊D43C2314yes—
158C2×D4×D43C2318yes—
159C23×Dic43C2312yes—
160C22×C4×D43C2314yes—
161#13063324C2314yes—
162#13063324C2318yes—
163#13063324C2312yes—
164#13063323C2311yescharacteristic
165#13063322C2312yes—
166#13063321C2314yes—
167#13063321C2311yescharacteristic
168#13063320C2318yes—
169#13063320C2318yes—
170#13063320C2318yes—
171#13063320C2318yes—
172#13063320C2318yes—
173#13063320C2318yes—
174#13063320C2318yes—
175#13063320C2318yes—
176#13063320C2318yes—
177#13063320C2314yes—
178#13063320C2318yes—
179#13063320C2318yes—
180#13063320C2318yes—
181#13063319C2318yes—
182#13063318C2314yes—
183#13063318C2318yes—
184#13063317C2318yes—
185#13063317C2312yes—
186#13063316C2318yes—
187#13063316C2314yes—
188#13063316C2314yes—
189#13063316C2312yes—
190#13063316C2314yes—
191#13063316C2314yes—
192#13063315C2318yes—
193#13063315C2318yes—
194#13063315C2318yes—
195#13063315C2318yes—
196#13063315C2314yes—
197#13063314C2318yes—
198#13063314C2318yes—
199#13063314C2314yes—
200#13063314C2314yes—
201#13063314C2314yes—
202#13063314C2318yes—
203#13063314C2311yescharacteristic
204#13063314C2314yes—
205#13063314C2314yes—
206#13063314C2314yes—
207#13063313C2318yes—
208#13063312C2311yescharacteristic
209#13063311C2318yes—
210#13063311C2318yes—
211#13063311C2314yes—
212#13063310C2318yes—
213#13063310C2318yes—
214#13063310C2318yes—
215#13063310C2318yes—
216#13063310C2318yes—
217#13063310C2318yes—
218#13063310C2318yes—
219#13063310C2318yes—
220#13063309C2318yes—
221#13063309C2318yes—
222#13063309C2318yes—
223#13063309C2318yes—
224#13063309C2318yes—
225#13063309C2314yes—
226#13063308C2318yes—
227#13063308C2312yes—
228#13063307C2318yes—
229#13063307C2318yes—
230#13063307C2318yes—
231#13063307C2318yes—
232#13063307C2318yes—
233#13063306C2314yes—
234#13063305C2318yes—
235#13063305C2318yes—
236#13063305C2318yes—
237#13063305C2318yes—
238#13063305C2318yes—
239#13063304C2312yes—
240#13063303C2318yes—
241#13063303C2318yes—
242#13063303C2318yes—
243#13063303C2318yes—
244#13063302C2318yes—
245#13063302C2314yes—
246#13063302C2318yes—
247#13063302C2314yes—
248#13063301C2314yes—
249#13063301C2318yes—
250#13063301C2318yes—
251#13063300C2314yes—
252#13063300C2318yes—
253#13063300C2318yes—
254#13063300C2318yes—
255#13063300C2318yes—
256#13063300C2318yes—
257#13063300C2318yes—
258#13063299C2314yes—
259#13063299C2314yes—
260#13063299C2318yes—
261#13063299C2318yes—
262#13063299C2314yes—
263#13063299C2314yes—
264#13063299C2314yes—
265#13063299C2312yes—
266#13063298C2318yes—
267#13063298C2318yes—
268#13063298C2318yes—
269#13063298C2318yes—
270#13063297C2318yes—
271#13063297C2314yes—
272#13063297C2314yes—
273#13063295C2318yes—
274#13063295C2318yes—
275#13063295C2318yes—
276#13063295C2318yes—
277#13063294C2312yes—
278#13063293C2314yes—
279#13063293C2314yes—
280Q8×Dic43C2314yes—
281Q8×Dic43C2314yes—
282Q8×Dic43C2314yes—
283Q8×Dic43C2318yes—
284Q8×Dic43C2314yes—
285Q8×Dic43C2314yes—
286Q8×Dic43C2312yes—
287C4×Dic86C2318yes—
288C4×Dic86C2318yes—
289C4×Dic86C2314yes—
290#13063290C2312yes—
291#13063290C2314yes—
292C4×D172C2318yes—
293C4×D172C2318yes—
294C4×D172C2318yes—
295C4×D172C2314yes—
296C4×D172C2318yes—
297C4×D172C2318yes—
298D4×Dic43C2312yes—
299D4×Dic43C2314yes—
300D4×Dic43C2314yes—
301#13063287C2314yes—
302#13063287C2318yes—
303#13063287C2314yes—
304#13063287C2318yes—
305#13063287C2312yes—
306#13063287C2314yes—
307#13063287C2314yes—
308#13063287C2314yes—
309C4×C22⋊D43C2318yes—
310C4×C22⋊D43C2318yes—
311C4×C22⋊D43C2314yes—
312C4×C22⋊D43C2314yes—
313(C22⋊D43)⋊C4C2318yes—
314(C22⋊D43)⋊C4C2318yes—
315(C22⋊D43)⋊C4C2318yes—
316(C22⋊D43)⋊C4C2318yes—
317(C22⋊D43)⋊C4C2318yes—
318(C22⋊D43)⋊C4C2314yes—
319(C22⋊D43)⋊C4C2318yes—
320(C22⋊D43)⋊C4C2318yes—
321(C22⋊D43)⋊C4C2314yes—
322(C22⋊D43)⋊C4C2314yes—
323#13063284C2318yes—
324#13063284C2312yes—
325#13063284C2312yes—
326#13063284C2311yescharacteristic
327#13063283C2318yes—
328#13063283C2318yes—
329#13063283C2318yes—
330#13063283C2318yes—
331#13063283C2318yes—
332#13063283C2318yes—
333#13063283C2318yes—
334#13063283C2314yes—
335#13063282C2318yes—
336#13063282C2318yes—
337#13063282C2312yes—
338#13063281C2314yes—
339#13063281C2314yes—
340C2×C4⋊Dic43C2312yes—
341C2×C4⋊Dic43C2314yes—
342C2×C4⋊Dic43C2314yes—
343C2×Dic43⋊C4C2314yes—
344C4⋊C4×D43C2318yes—
345C4⋊C4×D43C2314yes—
346C4⋊C4×D43C2318yes—
347C4⋊C4×D43C2318yes—
348C2×(C2×D43)⋊C4C2318yes—
349C2×(C2×D43)⋊C4C2314yes—
350C2×(C2×D43)⋊C4C2314yes—
351C2×(C2×D43)⋊C4C2314yes—
352C2×(C2×D43)⋊C4C2314yes—
353C22⋊C4×D43C2318yes—
354C22⋊C4×D43C2318yes—
355C22⋊C4×D43C2318yes—
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×Q8×C43C2312yes—
368C22×Q8×C43C2312yes—
369C23×C4×C43C2311yescharacteristic
370C4⋊Q8×C43C2314yes—
371C4⋊Q8×C43C2312yes—
372C4⋊Q8×C43C2318yes—
373#126×C43C2318yes—
374#126×C43C2318yes—
375#125×C43C2318yes—
376#125×C43C2318yes—
377#125×C43C2312yes—
378#124×C43C2314yes—
379#123×C43C2314yes—
380#123×C43C2314yes—
381#123×C43C2312yes—
382#123×C43C2318yes—
383C22⋊Q8×C43C2318yes—
384C22⋊Q8×C43C2318yes—
385C22⋊Q8×C43C2314yes—
386C22⋊Q8×C43C2314yes—
387C22⋊Q8×C43C2314yes—
388C22⋊Q8×C43C2314yes—
389C22⋊Q8×C43C2312yes—
390C22⋊Q8×C43C2314yes—
391#121×C43C2312yes—
392#120×C43C2312yes—
393C4×Q8×C43C2314yes—
394C4×D4×C43C2314yes—
395C4×D4×C43C2318yes—
396#117×C43C2318yes—
397#117×C43C2311yescharacteristic
398#117×C43C2312yes—
399C2×C4⋊C4×C43C2314yes—
400C2×C4⋊C4×C43C2312yes—
401C2×C22⋊C4×C43C2314yes—
402C24×C43C2411yescharacteristic
403C23×D43C2414yes—
404C23×D43C2414yes—
405#41×C43—42no—
406C2×Q8×C43—44no—
407C2×Q8×C43—44no—
408C2×Q8×C43C2414yes—
409C2×Q8×C43C2414yes—
410C2×Q8×C43C2414yes—
411C2×Q8×C43C2411yescharacteristic
412C2×D4×C43C2414yes—
413C2×D4×C43C2412yes—
414C2×D4×C43C2411yescharacteristic
415C22×C4×C43—42no—
416C22×C4×C43C2414yes—
417C22×C4×C43C2412yes—
418C22×C4×C43C2412yes—
419C22×C4×C43C2411yescharacteristic
420C22×C4×C43C2414yes—
421C22×C4×C43C2412yes—
422C22×C4×C43C2414yes—
423C22×C4×C43C2411yescharacteristic
424C2×C22⋊D43—48no—
425C2×C22⋊D43C2414yes—
426C2×C22⋊D43C2418yes—
427C2×C22⋊D43C2418yes—
428C2×C22⋊D43C2412yes—
429C2×C22⋊D43C2418yes—
430C2×C22⋊D43C2414yes—
431C22×Dic43—44no—
432C22×Dic43C2412yes—
433C22×Dic43C2412yes—
434C22×Dic43C2412yes—
435C22×Dic43C2412yes—
436C22×Dic43C2412yes—
437C22×Dic43C2412yes—
438C22×Dic43C2414yes—
439C22×Dic43C2414yes—
440#10621902—48no—
441#10621900—48no—
442D4×D43—416no—
443#10621898—42no—
444#10621898—416no—
445C2×D172—44no—
446C2×D172—44no—
447C2×D172C2414yes—
448C2×D172C2414yes—
449C2×D172C2411yescharacteristic
450C2×D172C2418yes—
451C2×D172C2418yes—
452C2×D172C2418yes—
453C2×D172C2414yes—
454C2×C4×D43—48no—
455C2×C4×D43C2412yes—
456C2×C4×D43C2414yes—
457C2×C4×D43C2418yes—
458C2×C4×D43C2418yes—
459C2×C4×D43C2418yes—
460C2×C4×D43C2418yes—
461C2×C4×D43C2418yes—
462C2×C4×D43C2418yes—
463C2×Dic86C2411yescharacteristic
464C2×Dic86C2414yes—
465C2×Dic86C2418yes—
466C4⋊C4×C43C2414yes—
467C4⋊C4×C43C2418yes—
468C4⋊C4×C43C2418yes—
469C4⋊C4×C43C2414yes—
470C4⋊C4×C43C2412yes—
471C4⋊C4×C43C2418yes—
472C4⋊C4×C43C2418yes—
473C4⋊C4×C43C2418yes—
474C4⋊C4×C43C2414yes—
475C4⋊C4×C43C2418yes—
476C22⋊C4×C43C2418yes—
477C22⋊C4×C43C2418yes—
478C22⋊C4×C43C2414yes—
479C22⋊C4×C43C2412yes—
480C22⋊C4×C43C2414yes—
481C22⋊C4×C43C2414yes—
482C22⋊C4×C43C2418yes—
483C42×C43C2414yes—
484C42×C43C2412yes—
485C42×C43C2418yes—
486C22⋊Dic43C2414yes—
487C22⋊Dic43C2414yes—
488C22⋊Dic43C2414yes—
489C22⋊Dic43C2414yes—
490C22⋊Dic43C2412yes—
491(C2×D43)⋊C4C2418yes—
492(C2×D43)⋊C4C2418yes—
493(C2×D43)⋊C4C2418yes—
494(C2×D43)⋊C4C2418yes—
495(C2×D43)⋊C4C2418yes—
496(C2×D43)⋊C4C2418yes—
497(C2×D43)⋊C4C2418yes—
498(C2×D43)⋊C4C2418yes—
499(C2×D43)⋊C4C2418yes—
500(C2×D43)⋊C4C2418yes—
501(C2×D43)⋊C4C2418yes—
502(C2×D43)⋊C4C2418yes—
503(C2×D43)⋊C4C2414yes—
504(C2×D43)⋊C4C2418yes—
505(C2×D43)⋊C4C2414yes—
506(C2×D43)⋊C4C2414yes—
507(C2×D43)⋊C4C2418yes—
508(C2×D43)⋊C4C2418yes—
509C4⋊Dic43C2418yes—
510C4⋊Dic43C2418yes—
511C4⋊Dic43C2414yes—
512C4⋊Dic43C2418yes—
513C4⋊Dic43C2414yes—
514C4⋊Dic43C2418yes—
515C4⋊Dic43C2414yes—
516C4⋊Dic43C2414yes—
517C4⋊Dic43C2412yes—
518C4⋊Dic43C2418yes—
519Dic43⋊C4C2414yes—
520Dic43⋊C4C2414yes—
521Dic43⋊C4C2418yes—
522Dic43⋊C4C2418yes—
523Dic43⋊C4C2418yes—
524Dic43⋊C4C2418yes—
525Dic43⋊C4C2418yes—
526Dic43⋊C4C2414yes—
527Dic43⋊C4C2414yes—
528Dic43⋊C4C2414yes—
529Dic43⋊C4C2418yes—
530C4×Dic43C2411yescharacteristic
531C4×Dic43C2414yes—
532C4×Dic43C2412yes—
533C4×Dic43C2411yescharacteristic
534C4×Dic43C2411yescharacteristic
535C4×Dic43C2412yes—
536C4×Dic43C2412yes—
537C4×Dic43C2412yes—
538C4×Dic43C2412yes—
539C4×Dic43C2412yes—
540C4×Dic43C2411yescharacteristic
541C4×Dic43C2414yes—
542C4×Dic43C2418yes—
543C4×Dic43C2418yes—
544C4×Dic43C2412yes—
545C4×Dic43C2418yes—
546C4×Dic43C2414yes—
547C23×C43—24no—
548C23×C43—41no—
549C23×C43C2512yes—
550C23×C43C2511yescharacteristic
551C23×C43C2512yes—
552C22×D43—28no—
553C22×D43—44no—
554C22×D43—44no—
555C22×D43—44no—
556C22×D43—48no—
557C22×D43C2518yes—
558C22×D43C2512yes—
559Q8×C43—28no—
560Q8×C43—44no—
561Q8×C43—44no—
562Q8×C43—41no—
563D4×C43—28no—
564D4×C43—41no—
565D4×C43—42no—
566C2×C4×C43—28no—
567C2×C4×C43—24no—
568C2×C4×C43—24no—
569C2×C4×C43—22no—
570C2×C4×C43—42no—
571C2×C4×C43—41no—
572C2×C4×C43—44no—
573C2×C4×C43—44no—
574C2×C4×C43C2512yes—
575C2×C4×C43C2512yes—
576C2×C4×C43C2511yescharacteristic
577C2×C4×C43C2518yes—
578C2×C4×C43C2514yes—
579C2×C4×C43C2518yes—
580C2×C4×C43C2511yescharacteristic
581C22⋊D43—28no—
582C22⋊D43—216no—
583C22⋊D43—42no—
584C22⋊D43—48no—
585C22⋊D43—44no—
586C22⋊D43—48no—
587C2×Dic43—24no—
588C2×Dic43—24no—
589C2×Dic43—44no—
590C2×Dic43—42no—
591C2×Dic43—42no—
592C2×Dic43—42no—
593C2×Dic43—42no—
594C2×Dic43—44no—
595C2×Dic43C2512yes—
596C2×Dic43C2512yes—
597C2×Dic43C2512yes—
598C2×Dic43C2512yes—
599C2×Dic43C2518yes—
600C2×Dic43C2514yes—
601C2×Dic43C2512yes—
602D172—28no—
603D172—44no—
604D172—44no—
605D172—48no—
606D172—41no—
607D172—48no—
608D172—48no—
609C4×D43—24no—
610C4×D43—48no—
611C4×D43—48no—
612C4×D43—48no—
613C4×D43—48no—
614C4×D43—48no—
615C4×D43—44no—
616C4×D43—48no—
617Dic86—48no—
618Dic86—41no—
619Dic86—44no—
620#62829—431nomaximal, Sylow
621C22×C43—22no—
622C22×C43—22no—
623C22×C43—24no—
624C22×C43—22no—
625C22×C43—22no—
626C22×C43—21no—
627C22×C43—44no—
628C22×C43#58514yes—
629C22×C43C2611yescharacteristic
630C2×D43—28no—
631C2×D43—28no—
632C2×D43—28no—
633C2×D43—22no—
634C2×D43—24no—
635C2×D43—88no—
636C2×D43—164no—
637C4×C43—28no—
638C4×C43—24no—
639C4×C43—21no—
640C4×C43—28no—
641C4×C43—22no—
642C4×C43—22no—
643C4×C43#58512yes—
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#3538D4311yescharacteristic, complemented
657#3537—431no—
658#3536—432no—
659#3516—434no—
660#3515—434no—
661#3514—434no—
662#3513—434no—
663#3513—438no—
664#3512—432no—
665#3510—432no—
666#3493—434no—
667#3491—434no—
668#3444—431no—
669C2×#529—432no—
670C2×C43—24no—
671C2×C43—42no—
672C2×C43—41no—
673C2×C43C2×#58511yescharacteristic
674C2×C43C2×#58512yes—
675D43—42no—
676D43—48no—
677#563—434no—
678#563—438no—
679#563C2×D4314yescomplemented
680#562—438no—
681#560—434no—
682#560—434no—
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—434no—
699#553—438no—
700#553—434no—
701#552—438no—
702#552—438no—
703#552—438no—
704#552—438no—
705#552—438no—
706#552—434no—
707#552—438no—
708#552C2×D4314yescomplemented
709#551—438no—
710#551—438no—
711#551—438no—
712#551—434no—
713#551—438no—
714#551—438no—
715#551—438no—
716#551C2×D4314yescomplemented
717D4×Q8C2×D4314yescomplemented
718#548—434no—
719#548—434no—
720#547—438no—
721#547—434no—
722#546—438no—
723#546—434no—
724#546—434no—
725#546—438no—
726#546—438no—
727D42—434no—
728D42—434no—
729#544C2×D4314yescomplemented
730#543—434no—
731#542—438no—
732#542—438no—
733#542—434no—
734#542—434no—
735#542—438no—
736#541—432no—
737#541—438no—
738#541—438no—
739#541C2×D4312yescomplemented
740#540—432no—
741#540—438no—
742#540—432no—
743#539—438no—
744#539—438no—
745#539—438no—
746#539—438no—
747#539—434no—
748#539C2×D4314yescomplemented
749#538—438no—
750#538—438no—
751#538—438no—
752#538—434no—
753#538—434no—
754#538—438no—
755#537—434no—
756#537—434no—
757#536C2×D4312yescomplemented
758#535—432no—
759#534—434no—
760#533—432no—
761#533—431no—
762#533—432no—
763#532—431no—
764#532—432no—
765#532—432no—
766#529—434no—
767#529—434no—
768#529—434no—
769#529—434no—
770#529—434no—
771#529—434no—
772#529—434no—
773#529—434no—
774#529—434no—
775#529—432no—
776#529—438no—
777#529—434no—
778#529—432no—
779#529—434no—
780#529—434no—
781#529—438no—
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—438no—
792C2×#123—434no—
793C2×C22⋊Q8C2×D4312yescomplemented
794C2×#121—432no—
795#520—434no—
796#520—438no—
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—432no—
805C2×C4×D4—434no—
806C2×#117—434no—
807C22×C42—431no—
808C43#6282911yescharacteristic, complemented, Sylow
809C2×#41—434no—
810C2×#41—434no—
811C2×#41—431no—
812C2×#41—438no—
813C2×#41C22×D4311yescharacteristic
814C22×Q8C22×D4312yes—
815C22×Q8C22×D4312yes—
816C22×D4—434no—
817C22×D4—438no—
818C22×D4—432no—
819C22×D4—432no—
820C23×C4—432no—
821C23×C4—434no—
822C23×C4C22×D4311yescharacteristic
823C4⋊Q8—431no—
824C4⋊Q8—432no—
825C4⋊Q8—434no—
826C4⋊Q8—438no—
827C4⋊Q8C22×D4312yes—
828C4⋊Q8C22×D4314yes—
829C4⋊Q8C22×D4318yes—
830#127—431no—
831#127—434no—
832#127—432no—
833#126—438no—
834#126—438no—
835#126—438no—
836#126—438no—
837#126—434no—
838#126—438no—
839#126—438no—
840#126—438no—
841#126—438no—
842#126—438no—
843#126—438no—
844#126—438no—
845#126—438no—
846#126—434no—
847#126—438no—
848#126—438no—
849#126C22×D4318yes—
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—432no—
863#125—438no—
864#125C22×D4312yes—
865#125C22×D4318yes—
866#125C22×D4318yes—
867#124—434no—
868#124—434no—
869#124—434no—
870#124—434no—
871#124—438no—
872#124—434no—
873#124—431no—
874#124—438no—
875#124—434no—
876#124—438no—
877#124—431no—
878#124—434no—
879#124—438no—
880#124—438no—
881#124—438no—
882#124C22×D4314yes—
883#123—434no—
884#123—438no—
885#123—432no—
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—438no—
896#123—438no—
897#123—438no—
898#123—438no—
899#123—438no—
900#123—434no—
901#123—438no—
902#123—438no—
903#123—438no—
904#123—438no—
905#123C22×D4318yes—
906#123C22×D4312yes—
907#123C22×D4314yes—
908#123C22×D4314yes—
909C22⋊Q8—434no—
910C22⋊Q8—438no—
911C22⋊Q8—438no—
912C22⋊Q8—432no—
913C22⋊Q8—438no—
914C22⋊Q8—438no—
915C22⋊Q8—438no—
916C22⋊Q8—438no—
917C22⋊Q8—438no—
918C22⋊Q8—438no—
919C22⋊Q8—438no—
920C22⋊Q8—438no—
921C22⋊Q8—438no—
922C22⋊Q8—434no—
923C22⋊Q8—434no—
924C22⋊Q8—438no—
925C22⋊Q8—438no—
926C22⋊Q8C22×D4314yes—
927C22⋊Q8C22×D4314yes—
928C22⋊Q8C22×D4314yes—
929C22⋊Q8C22×D4314yes—
930C22⋊Q8C22×D4312yes—
931C22⋊Q8C22×D4314yes—
932C22⋊Q8C22×D4318yes—
933C22⋊Q8C22×D4318yes—
934#121—434no—
935#121—434no—
936#121—438no—
937#121—434no—
938#121—434no—
939#121—434no—
940#121—434no—
941#121—432no—
942#121—434no—
943#121—438no—
944#121—438no—
945#121—438no—
946#121—438no—
947#121—434no—
948#121—438no—
949#121—438no—
950#121—438no—
951#121—438no—
952#121—438no—
953#121—438no—
954#121—438no—
955#121—438no—
956#121C22×D4312yes—
957#120—432no—
958#120—434no—
959#120—434no—
960#120—438no—
961#120—438no—
962#120—438no—
963#120—438no—
964#120C22×D4312yes—
965C4×Q8—434no—
966C4×Q8—434no—
967C4×Q8—434no—
968C4×Q8—434no—
969C4×Q8—432no—
970C4×Q8—438no—
971C4×Q8—434no—
972C4×Q8—434no—
973C4×Q8—432no—
974C4×Q8—434no—
975C4×Q8—438no—
976C4×Q8—438no—
977C4×Q8C22×D4314yes—
978C4×D4—434no—
979C4×D4—434no—
980C4×D4—432no—
981C4×D4—434no—
982C4×D4—434no—
983C4×D4—438no—
984C4×D4—438no—
985C4×D4—434no—
986C4×D4—434no—
987C4×D4—434no—
988C4×D4—434no—
989C4×D4—432no—
990C4×D4—434no—
991C4×D4—438no—
992C4×D4—438no—
993C4×D4—438no—
994C4×D4—438no—
995C4×D4—438no—
996C4×D4—438no—
997C4×D4—434no—
998C4×D4—434no—
999C4×D4—434no—
1000C4×D4—438no—
1001C4×D4—438no—
1002C4×D4—438no—
1003C4×D4—438no—
1004C4×D4—438no—
1005C4×D4—438no—
1006C4×D4—438no—
1007C4×D4—438no—
1008C4×D4—434no—
1009C4×D4C22×D4314yes—
1010C4×D4C22×D4318yes—
1011#117—432no—
1012#117—431no—
1013#117—438no—
1014#117—432no—
1015#117—438no—
1016#117—438no—
1017#117—438no—
1018#117—438no—
1019#117—434no—
1020#117—438no—
1021#117—438no—
1022#117—438no—
1023#117—434no—
1024#117—434no—
1025#117—432no—
1026#117—438no—
1027#117—438no—
1028#117C22×D4311yescharacteristic
1029#117C22×D4312yes—
1030#117C22×D4318yes—
1031C2×C4⋊C4—434no—
1032C2×C4⋊C4—434no—
1033C2×C4⋊C4—432no—
1034C2×C4⋊C4—434no—
1035C2×C4⋊C4—438no—
1036C2×C4⋊C4—438no—
1037C2×C4⋊C4—434no—
1038C2×C4⋊C4—438no—
1039C2×C4⋊C4C22×D4314yes—
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—
1060C24—434no—
1061C24—434no—
1062C24C23×D4311yescharacteristic
1063#41—42no—
1064#41—1722no—
1065#41—17216no—
1066#41—1728no—
1067#41—1728no—
1068C2×Q8—44no—
1069C2×Q8—44no—
1070C2×Q8—431no—
1071C2×Q8—438no—
1072C2×Q8—434no—
1073C2×Q8C23×D4314yes—
1074C2×Q8C23×D4314yes—
1075C2×Q8C23×D4314yes—
1076C2×Q8C23×D4311yescharacteristic
1077C2×D4—434no—
1078C2×D4—438no—
1079C2×D4—434no—
1080C2×D4—438no—
1081C2×D4—432no—
1082C2×D4—438no—
1083C2×D4—434no—
1084C2×D4—438no—
1085C2×D4—438no—
1086C2×D4—434no—
1087C2×D4—438no—
1088C2×D4—434no—
1089C2×D4—431no—
1090C2×D4—1724no—
1091C2×D4—1724no—
1092C2×D4—17216no—
1093C2×D4—1728no—
1094C2×D4C23×D4314yes—
1095C2×D4C23×D4311yescharacteristic
1096C2×D4C23×D4312yes—
1097C22×C4—42no—
1098C22×C4—432no—
1099C22×C4—432no—
1100C22×C4—432no—
1101C22×C4—432no—
1102C22×C4—432no—
1103C22×C4—432no—
1104C22×C4—434no—
1105C22×C4—434no—
1106C22×C4—432no—
1107C22×C4—434no—
1108C22×C4—438no—
1109C22×C4—438no—
1110C22×C4—438no—
1111C22×C4—438no—
1112C22×C4—438no—
1113C22×C4—438no—
1114C22×C4—1728no—
1115C22×C4—1724no—
1116C22×C4C23×D4312yes—
1117C22×C4C23×D4311yescharacteristic
1118C22×C4C23×D4312yes—
1119C22×C4C23×D4314yes—
1120C22×C4C23×D4312yes—
1121C22×C4C23×D4311yescharacteristic
1122C22×C4C23×D4314yes—
1123C22×C4C23×D4314yes—
1124C4⋊C4—434no—
1125C4⋊C4—438no—
1126C4⋊C4—438no—
1127C4⋊C4—438no—
1128C4⋊C4—434no—
1129C4⋊C4—434no—
1130C4⋊C4—438no—
1131C4⋊C4—438no—
1132C4⋊C4—438no—
1133C4⋊C4—438no—
1134C4⋊C4—438no—
1135C4⋊C4—434no—
1136C4⋊C4—438no—
1137C4⋊C4—434no—
1138C4⋊C4—434no—
1139C4⋊C4—438no—
1140C4⋊C4—432no—
1141C4⋊C4—434no—
1142C4⋊C4—434no—
1143C4⋊C4—434no—
1144C4⋊C4—438no—
1145C4⋊C4C23×D4318yes—
1146C4⋊C4C23×D4314yes—
1147C4⋊C4C23×D4318yes—
1148C4⋊C4C23×D4318yes—
1149C4⋊C4C23×D4318yes—
1150C4⋊C4C23×D4314yes—
1151C4⋊C4C23×D4318yes—
1152C4⋊C4C23×D4318yes—
1153C4⋊C4C23×D4314yes—
1154C4⋊C4C23×D4312yes—
1155C22⋊C4—434no—
1156C22⋊C4—434no—
1157C22⋊C4—434no—
1158C22⋊C4—434no—
1159C22⋊C4—432no—
1160C22⋊C4—438no—
1161C22⋊C4—438no—
1162C22⋊C4—438no—
1163C22⋊C4—438no—
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—434no—
1173C22⋊C4—434no—
1174C22⋊C4—438no—
1175C22⋊C4—438no—
1176C22⋊C4—438no—
1177C22⋊C4—434no—
1178C22⋊C4C23×D4314yes—
1179C22⋊C4C23×D4318yes—
1180C22⋊C4C23×D4318yes—
1181C22⋊C4C23×D4318yes—
1182C22⋊C4C23×D4314yes—
1183C22⋊C4C23×D4314yes—
1184C22⋊C4C23×D4312yes—
1185C42—431no—
1186C42—431no—
1187C42—432no—
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—
1202C42C23×D4312yes—
1203C42C23×D4318yes—
1204C42C23×D4314yes—
1205C23—24no—
1206C23—41no—
1207C23—438no—
1208C23—432no—
1209C23—868no—
1210C23—1724no—
1211C23—1724no—
1212C23—1724no—
1213C23—1728no—
1214C23C24×D4312yes—
1215C23C24×D4311yescharacteristic
1216C23C24×D4312yes—
1217Q8—28no—
1218Q8—44no—
1219Q8—44no—
1220Q8—41no—
1221Q8—1721no—
1222Q8—1728no—
1223Q8—1724no—
1224D4—28no—
1225D4—41no—
1226D4—42no—
1227D4—8616no—
1228D4—868no—
1229D4—868no—
1230D4—1724no—
1231D4—1724no—
1232D4—1728no—
1233D4—1721no—
1234D4—1728no—
1235D4—1728no—
1236D4—1728no—
1237D4—1728no—
1238D4—1722no—
1239D4—1724no—
1240C2×C4—28no—
1241C2×C4—24no—
1242C2×C4—22no—
1243C2×C4—24no—
1244C2×C4—42no—
1245C2×C4—41no—
1246C2×C4—44no—
1247C2×C4—44no—
1248C2×C4—432no—
1249C2×C4—432no—
1250C2×C4—432no—
1251C2×C4—434no—
1252C2×C4—432no—
1253C2×C4—438no—
1254C2×C4—432no—
1255C2×C4—864no—
1256C2×C4—864no—
1257C2×C4—864no—
1258C2×C4—1728no—
1259C2×C4—1728no—
1260C2×C4—1728no—
1261C2×C4—1728no—
1262C2×C4—1728no—
1263C2×C4—1728no—
1264C2×C4—1724no—
1265C2×C4—1722no—
1266C2×C4—1722no—
1267C2×C4—1722no—
1268C2×C4—1722no—
1269C2×C4—1724no—
1270C2×C4—1724no—
1271C2×C4C24×D4312yes—
1272C2×C4C24×D4311yescharacteristic
1273C2×C4C24×D4312yes—
1274C2×C4C24×D4318yes—
1275C2×C4C24×D4314yes—
1276C2×C4C24×D4318yes—
1277C2×C4C24×D4311yescharacteristic
1278C22—22no—
1279C22—22no—
1280C22—22no—
1281C22—21no—
1282C22—22no—
1283C22—24no—
1284C22—44no—
1285C22—862no—
1286C22—868no—
1287C22—864no—
1288C22—868no—
1289C22—868no—
1290C22—3448no—
1291C22—6884no—
1292C22#1458373614yes—
1293C22C25×D4311yescharacteristic
1294C4—21no—
1295C4—22no—
1296C4—22no—
1297C4—28no—
1298C4—28no—
1299C4—24no—
1300C4—862no—
1301C4—862no—
1302C4—862no—
1303C4—862no—
1304C4—862no—
1305C4—868no—
1306C4—864no—
1307C4#1458373412yes—
1308C2—24no—
1309C2—41no—
1310C2—42no—
1311C2—1728no—
1312C2—1722no—
1313C2C2×#1458373411yescharacteristic
1314C2C2×#1458373612yes—
subgroupG/H
center, FrattiniC22C25×D43
commutator, socle, cosocleC22×C43C26
FittingC43×#3538C2
hypercenter#3538D43
hypocenterC43#62829
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #3538

Complements

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

NH ≅ G/Ntype
1. #19149276C2semidirect
2. #19149216C2semidirect
3. #19149152C2semidirect
4. #19149103C2semidirect
5. #19149024C2semidirect
6. #19148834C2semidirect
7. #19148824C2semidirect
8. #19148589C2semidirect
9. #19148570C2semidirect
10. #19148557C2semidirect
11. #19148540C2semidirect
12. #19148522C2semidirect
13. #19148518C2semidirect
14. #19148494C2semidirect
15. #19148316C2semidirect
16. #19148289C2semidirect
17. #19147887C2semidirect
18. C2×#14583435C2semidirect
19. C43×#3538C2semidirect
20. #14583653C22semidirect
21. #14583648C22semidirect
22. #14583645C22semidirect
24. #14583639C22semidirect
25. #14583634C22semidirect
26. #14583631C22semidirect
27. #14583625C22semidirect
28. #14583623C22semidirect
29. #14583623C22semidirect
30. #14583623C22semidirect
31. #14583615C22semidirect
32. #14583615C22semidirect
33. #14583607C22semidirect
34. #14583607C22semidirect
35. #14583605C22semidirect
36. #14583602C22semidirect
37. #14583602C22semidirect
38. #14583600C22semidirect
39. #14583600C22semidirect
41. #14583595C22semidirect
42. #14583593C22semidirect
43. #14583587C22semidirect
44. #14583587C22semidirect
45. #14583585C22semidirect
46. #14583583C22semidirect
47. #14583583C22semidirect
48. #14583582C22semidirect
49. #14583581C22semidirect
50. #14583577C22semidirect
51. #14583576C22semidirect
52. #14583576C22semidirect
53. #14583574C22semidirect
54. #14583573C22semidirect
55. #14583572C22semidirect
56. #14583572C22semidirect
57. #14583560C22semidirect
58. #14583560C22semidirect
59. #14583550C22semidirect
60. #14583547C22semidirect
61. #14583544C22semidirect
62. #14583541C22semidirect
63. #14583540C22semidirect
64. #14583540C22semidirect
65. #14583539C22semidirect
68. #14583524C22semidirect
69. #14583523C22semidirect
70. #14583522C22semidirect
71. #14583522C22semidirect
72. #14583522C22semidirect
73. #14583515C22semidirect
74. #14583510C22semidirect
75. #14583510C22semidirect
76. #14583508C22semidirect
77. #14583505C22semidirect
79. #14583501C22semidirect
80. #14583497C22semidirect
81. #14583496C22semidirect
82. #14583493C22semidirect
83. #14583490C22semidirect
84. #14583490C22semidirect
86. #14583489C22semidirect
87. #14583489C22semidirect
88. #14583489C22semidirect
89. #14583488C22semidirect
90. #14583483C22semidirect
91. #14583480C22semidirect
92. #14583479C22semidirect
95. #14583452C22semidirect
96. #14583452C22semidirect
97. #14583451C22semidirect
98. #14583450C22semidirect
99. #14583445C22semidirect
100. #14583444C22semidirect
101. #14583436C22semidirect
102. #14583435C22semidirect
103. #14583435C22semidirect
104. #14583435C22semidirect
105. #14583435C22semidirect
106. #14583435C22semidirect
107. #14583435C22semidirect
108. #14583435C22semidirect
109. #14583435C22semidirect
110. #14583435C22semidirect
111. #14583435C22semidirect
112. #14583435C22semidirect
113. #14583430C22semidirect
114. #14583429C22semidirect
115. #14583429C22semidirect
116. #14583426C22semidirect
117. C2×#13063320C22semidirect
118. C2×#13063316C22semidirect
119. #125×D43C22semidirect
120. C2×#13063314C22semidirect
121. C2×#13063314C22semidirect
122. #14583411C22semidirect
123. #14583410C22semidirect
124. #14583405C22semidirect
125. C2×#13063309C22semidirect
126. #123×D43C22semidirect
128. #14583381C22semidirect
129. #14583379C22semidirect
130. #14583377C22semidirect
131. #14583373C22semidirect
132. #14583371C22semidirect
133. #41×Dic43C22semidirect
134. #14583367C22semidirect
135. C4×#10621900C22semidirect
136. C2×Q8×Dic43C22semidirect
137. C2×#13063287C22semidirect
138. C2×(C22⋊D43)⋊C4C22semidirect
139. C2×#13063283C22semidirect
140. C22×C4×Dic43C22semidirect
141. C43×#563C22semidirect
142. C43×#552C22semidirect
143. C43×#551C22semidirect
144. D4×Q8×C43C22semidirect
145. C43×#544C22semidirect
146. C43×#541C22semidirect
147. C43×#539C22semidirect
148. C43×#536C22semidirect
150. C2×C22⋊Q8×C43C22semidirect
656. #3538D43semidirect
679. #563C2×D43semidirect
708. #552C2×D43semidirect
716. #551C2×D43semidirect
717. D4×Q8C2×D43semidirect
729. #544C2×D43semidirect
739. #541C2×D43semidirect
748. #539C2×D43semidirect
757. #536C2×D43semidirect
793. C2×C22⋊Q8C2×D43semidirect
808. C43#62829semidirect

Maximal subgroups

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

subgroupindex
#191492762
#191492162
#191491522
#191491032
#191490242
#191488342
#191488242
#191485892
#191485702
#191485572
#191485402
#191485222
#191485182
#191484942
#191483162
#191482892
#191478872
C2×#145834352
C43×#35382
#6282943