Finite Group Databasebeta

← #26005332

Subgroups — #26005332

Order 11008.

6670 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19149223C216yesmaximal, complemented
2#19149213C216yesmaximal, complemented
3#19149151C216yesmaximal, complemented
4#19149141C216yesmaximal, complemented
5#19148663C2112yesmaximal, complemented
6#19148649C2112yesmaximal, complemented
7#19148296C216yesmaximal, complemented
8#19148278C216yesmaximal, complemented
9#19147891C211yesmaximal, characteristic, complemented
10C22×#13063319C211yesmaximal, characteristic, complemented
11C43×#3444C211yesmaximal, characteristic, complemented
12#14583651C22112yescomplemented
13#14583648C22112yescomplemented
14#14583640C2214yescomplemented
15#14583636C2214yescomplemented
16#14583621C22112yescomplemented
17#14583617C22112yescomplemented
18#14583608C22112yescomplemented
19#14583603C22112yescomplemented
20#14583598C22112yescomplemented
21#14583598C22112yescomplemented
22#14583593C22112yescomplemented
23#14583592C22112yescomplemented
24#14583590C22112yescomplemented
25#14583586C22112yescomplemented
26#14583582C22112yescomplemented
27#14583582C22112yescomplemented
28#14583578C22112yescomplemented
29#14583578C22112yescomplemented
30#14583576C22112yescomplemented
31#14583573C22112yescomplemented
32#14583573C22112yescomplemented
33#14583572C22112yescomplemented
34#14583548C22112yescomplemented
35#14583547C22112yescomplemented
36#14583544C22112yescomplemented
37#14583541C22112yescomplemented
38#14583538C22112yescomplemented
39#14583537C22112yescomplemented
40#14583528C2216yescomplemented
41#14583524C2216yescomplemented
42#14583521C22112yescomplemented
43#14583513C22112yescomplemented
44#14583508C22112yescomplemented
45#14583507C22112yescomplemented
46#14583498C2216yescomplemented
47#14583497C22112yescomplemented
48#14583494C2216yescomplemented
49#14583491C22112yescomplemented
50#14583491C22112yescomplemented
51#14583489C2216yes—
52#14583486C2216yes—
53#14583483C22112yescomplemented
54#14583482C22112yes—
55#14583482C22112yescomplemented
56#14583476C2216yescomplemented
57#14583457C2216yescomplemented
58#14583456C2213yescomplemented
59#14583449C2213yescomplemented
60#14583433C2216yescomplemented
61#14583433C2216yescomplemented
62#14583433C22112yescomplemented
63#14583432C22112yescomplemented
64C2×#13063319C2216yescomplemented
65C2×#13063319C2216yescomplemented
66C2×#13063319C2216yescomplemented
67C2×#13063319C2216yescomplemented
68C2×#13063319C2214yescomplemented
69#126×D43C2214yescomplemented
70#14583410C2216yescomplemented
71#14583405C22112yescomplemented
72#120×D43C2214yes—
73#14583378C22112yescomplemented
74#14583371C22112yescomplemented
75C4×#10621898C2216yescomplemented
76C22×Dic43⋊C4C2213yescomplemented
77C22×(C2×D43)⋊C4C2213yes—
78C43×#533C2213yescomplemented
79C43×#532C2213yescomplemented
80C43×#529C2216yescomplemented
81C43×#529C2216yescomplemented
82C43×#525C2216yescomplemented
83C4×#41×C43C2216yescomplemented
84C22×C42×C43C2211yescharacteristic, complemented
85C24×D43C2311yescharacteristic
86C2×#10621898C2316yes—
87C2×#10621900C23112yes—
88C2×D4×D43C23112yes—
89C23×Dic43C2313yes—
90#13063325C2313yescomplemented
91#13063324C23112yescomplemented
92#13063323C23112yescomplemented
93#13063322C2311yescharacteristic, complemented
94#13063320C23112yes—
95#13063320C23112yes—
96#13063320C23112yes—
97#13063320C23112yescomplemented
98#13063319C23112yes—
99#13063319C23112yes—
100#13063319C23112yes—
101#13063319C2314yes—
102#13063319C2314yes—
103#13063319C2314yes—
104#13063319C2314yes—
105#13063319C23112yes—
106#13063319C23112yes—
107#13063319C23112yescomplemented
108#13063319C2314yescomplemented
109#13063319C2314yescomplemented
110#13063318C23112yescomplemented
111#13063318C23112yescomplemented
112#13063317C23112yescomplemented
113#13063317C2316yescomplemented
114#13063316C23112yescomplemented
115#13063315C23112yescomplemented
116#13063315C23112yescomplemented
117#13063315C23112yescomplemented
118#13063315C23112yescomplemented
119#13063314C23112yes—
120#13063313C23112yes—
121#13063313C2316yescomplemented
122#13063311C23112yes—
123#13063311C23112yes—
124#13063310C23112yes—
125#13063310C23112yes—
126#13063310C23112yes—
127#13063310C23112yescomplemented
128#13063309C23112yes—
129#13063309C23112yes—
130#13063308C23112yes—
131#13063308C23112yes—
132#13063308C23112yescomplemented
133#13063307C23112yes—
134#13063307C23112yescomplemented
135#13063306C23112yes—
136#13063306C23112yescomplemented
137#13063305C23112yes—
138#13063304C2316yes—
139#13063304C2316yes—
140#13063304C23112yescomplemented
141#13063303C23112yes—
142#13063303C23112yes—
143#13063303C23112yescomplemented
144#13063303C23112yescomplemented
145#13063302C23112yes—
146#13063302C23112yes—
147#13063302C23112yescomplemented
148#13063302C23112yescomplemented
149#13063301C23112yes—
150#13063301C23112yescomplemented
151#13063300C23112yes—
152#13063299C23112yes—
153#13063299C2316yes—
154#13063299C2316yes—
155#13063298C23112yes—
156#13063298C23112yescomplemented
157#13063297C23112yes—
158#13063297C23112yes—
159#13063297C23112yes—
160#13063297C23112yescomplemented
161#13063295C23112yes—
162#13063295C23112yes—
163#13063294C2314yes—
164#13063293C23112yes—
165#13063293C23112yes—
166C4×Dic86C2316yescomplemented
167C4×Dic86C23112yescomplemented
168C4×Dic86C2316yescomplemented
169#13063290C23112yescomplemented
170C4×D172C23112yes—
171C4×D172C2316yescomplemented
172C4×D172C2316yescomplemented
173D4×Dic43C23112yes—
174D4×Dic43C23112yes—
175#13063287C23112yes—
176C4×C22⋊D43C23112yes—
177C4×C22⋊D43C23112yes—
178C4×C22⋊D43C23112yes—
179C4×C22⋊D43C23112yescomplemented
180(C22⋊D43)⋊C4C23112yes—
181(C22⋊D43)⋊C4C23112yes—
182(C22⋊D43)⋊C4C23112yes—
183(C22⋊D43)⋊C4C23112yescomplemented
184#13063284C2316yes—
185#13063283C23112yes—
186#13063282C23112yes—
187#13063282C23112yescomplemented
188#13063282C23112yescomplemented
189#13063281C23112yes—
190#13063281C23112yescomplemented
191C2×Dic43⋊C4C2316yes—
192C2×Dic43⋊C4C2316yes—
193C2×Dic43⋊C4C2316yes—
194C2×Dic43⋊C4C2316yes—
195C2×Dic43⋊C4C2316yes—
196C2×Dic43⋊C4C2316yes—
197C2×Dic43⋊C4C23112yescomplemented
198C4⋊C4×D43C23112yescomplemented
199C2×(C2×D43)⋊C4C2316yes—
200C2×(C2×D43)⋊C4C2316yes—
201C2×(C2×D43)⋊C4C23112yes—
202C2×(C2×D43)⋊C4C2316yes—
203C2×(C2×D43)⋊C4C2316yes—
204C2×(C2×D43)⋊C4C2316yes—
205C2×(C2×D43)⋊C4C2316yes—
206C22⋊C4×D43C23112yes—
207C22⋊C4×D43C23112yes—
208C42×D43C2314yescomplemented
209C2×#41×C43C2316yes—
210C23×C4×C43C2313yes—
211C4⋊Q8×C43C2313yescomplemented
212#127×C43C2311yescharacteristic, complemented
213#126×C43C2314yescomplemented
214#126×C43C2314yescomplemented
215#125×C43C2316yescomplemented
216#124×C43C2316yescomplemented
217#123×C43C23112yes—
218C22⋊Q8×C43C2316yes—
219C22⋊Q8×C43C2316yes—
220#121×C43C2316yes—
221#121×C43C2316yes—
222#120×C43C2314yes—
223C4×Q8×C43C2316yescomplemented
224C4×Q8×C43C2316yescomplemented
225C4×D4×C43C23112yes—
226C4×D4×C43C23112yes—
227C4×D4×C43C2316yescomplemented
228C4×D4×C43C2316yescomplemented
229#117×C43C2316yes—
230#117×C43C23112yescomplemented
231C2×C42×C43C2313yes—
232C2×C42×C43C2313yes—
233C2×C42×C43C2313yes—
234C2×C42×C43C2313yes—
235C2×C42×C43C2314yescomplemented
236C24×C43C2411yescharacteristic
237C23×D43—46no—
238C23×D43C2416yes—
239C23×D43C2414yes—
240#41×C43—412no—
241C2×Q8×C43C2416yes—
242C2×D4×C43C24112yes—
243C2×D4×C43C2416yes—
244C22×C4×C43—46no—
245C22×C4×C43C2413yes—
246C22×C4×C43C2413yes—
247C22×C4×C43C2413yes—
248C22×C4×C43C2413yes—
249C22×C4×C43C2413yes—
250C22×C4×C43C2413yes—
251C22×C4×C43C24112yes—
252C2×C22⋊D43C24112yes—
253C2×C22⋊D43C24112yes—
254C2×C22⋊D43C24112yes—
255C22×Dic43—46no—
256C22×Dic43C2416yes—
257C22×Dic43C2416yes—
258C22×Dic43C2416yes—
259C22×Dic43C24112yes—
260#10621900—424no—
261D4×D43—424no—
262#10621898—412no—
263C2×D172C24112yes—
264C2×D172C2416yes—
265C2×C4×D43C24112yes—
266C2×C4×D43C24112yes—
267C2×C4×D43C24112yes—
268C2×Dic86C24112yes—
269C2×Dic86C2416yes—
270C4⋊C4×C43C2416yes—
271C4⋊C4×C43C2416yes—
272C4⋊C4×C43C24112yes—
273C4⋊C4×C43C24112yes—
274C22⋊C4×C43C24112yes—
275C22⋊C4×C43C24112yes—
276C22⋊C4×C43C24112yes—
277C42×C43C2411yescharacteristic
278C42×C43C2413yes—
279C42×C43C2413yes—
280C42×C43C2413yes—
281C42×C43C2413yes—
282C42×C43C2411yescharacteristic
283C42×C43C2411yescharacteristic
284C42×C43C2411yescharacteristic
285C42×C43C24112yes—
286C22⋊Dic43C24112yes—
287C22⋊Dic43C24112yes—
288C22⋊Dic43C24112yes—
289(C2×D43)⋊C4C24112yes—
290(C2×D43)⋊C4C24112yes—
291(C2×D43)⋊C4C24112yes—
292(C2×D43)⋊C4C24112yes—
293(C2×D43)⋊C4C24112yes—
294(C2×D43)⋊C4C24112yes—
295(C2×D43)⋊C4C24112yes—
296(C2×D43)⋊C4C24112yes—
297(C2×D43)⋊C4C24112yes—
298(C2×D43)⋊C4C24112yes—
299C4⋊Dic43C24112yes—
300C4⋊Dic43C24112yes—
301C4⋊Dic43C2416yes—
302C4⋊Dic43C2416yes—
303Dic43⋊C4C24112yes—
304Dic43⋊C4C24112yes—
305Dic43⋊C4C24112yes—
306Dic43⋊C4C24112yes—
307Dic43⋊C4C24112yes—
308Dic43⋊C4C24112yes—
309Dic43⋊C4C24112yes—
310Dic43⋊C4C24112yes—
311Dic43⋊C4C24112yes—
312Dic43⋊C4C24112yes—
313C4×Dic43C24112yes—
314C4×Dic43C24112yes—
315C4×Dic43C24112yes—
316C23×C43—26no—
317C23×C43C2514yes—
318C23×C43C2513yes—
319C22×D43—212no—
320C22×D43—46no—
321C22×D43—46no—
322C22×D43—412no—
323C22×D43—88no—
324C22×D43C2514yes—
325C22×D43C2514yes—
326Q8×C43—46no—
327D4×C43—224no—
328D4×C43—46no—
329C2×C4×C43—26no—
330C2×C4×C43—26no—
331C2×C4×C43—43no—
332C2×C4×C43—43no—
333C2×C4×C43—43no—
334C2×C4×C43—43no—
335C2×C4×C43—412no—
336C2×C4×C43C2513yes—
337C2×C4×C43C25112yes—
338C2×C4×C43C2513yes—
339C2×C4×C43C2513yes—
340C2×C4×C43C2513yes—
341C22⋊D43—224no—
342C22⋊D43—412no—
343C22⋊D43—412no—
344C2×Dic43—212no—
345C2×Dic43—412no—
346C2×Dic43—46no—
347C2×Dic43—46no—
348C2×Dic43C25112yes—
349C2×Dic43C25112yes—
350D172—46no—
351D172—412no—
352C4×D43—412no—
353C4×D43—412no—
354C4×D43—412no—
355Dic86—46no—
356Dic86—412no—
357#62826—431nomaximal, Sylow
358C22×C43—28no—
359C22×C43—23no—
360C22×C43—23no—
361C22×C43—212no—
362C22×C43#58516yes—
363C22×C43C2611yescharacteristic
364C2×D43—212no—
365C2×D43—212no—
366C2×D43—812no—
367C2×D43—164no—
368C4×C43—23no—
369C4×C43—212no—
370C4×C43—23no—
371C4×C43—23no—
372C4×C43—23no—
373Dic43—212no—
374Dic43—212no—
375#3564—436no—
376#3564—436no—
377#3560—436no—
378#3560—436no—
379#3521—4312no—
380#3521—4312no—
381#3492—436no—
382#3490—436no—
383#3444—431no—
384#3444D4311yescharacteristic, complemented
385C22×#126—431no—
386C2×C43—26no—
387C2×C43—44no—
388C2×C43C2×#58513yes—
389D43—44no—
390D43—44no—
391#563—4312no—
392#563—4312no—
393#560—434no—
394#560—434no—
395#556—4312no—
396#556—4312no—
397#554—4312no—
398#554—4312no—
399#553—4312no—
400#553—4312no—
401#553—4312no—
402#553—4312no—
403#552—4312no—
404#552—4312no—
405#552—4312no—
406#552—4312no—
407#551—4312no—
408#551—4312no—
409#551—4312no—
410#551—4312no—
411#551—4312no—
412#551—4312no—
413#547—4312no—
414#547—4312no—
415#546—4312no—
416#546—4312no—
417#546—4312no—
418#546—4312no—
419#544—436no—
420#543—436no—
421#542—4312no—
422#542—4312no—
423#541—4312no—
424#541—4312no—
425#539—4312no—
426#539—436no—
427#539—436no—
428#539—4312no—
429#539—4312no—
430#538—4312no—
431#538—436no—
432#538—436no—
433#538—4312no—
434#538—4312no—
435#537—436no—
436#534—436no—
437#533—433no—
438#533C2×D4313yescomplemented
439#532—433no—
440#532C2×D4313yescomplemented
441#529—4312no—
442#529—436no—
443#529—436no—
444#529—4312no—
445#529C2×D4316yescomplemented
446#529C2×D4316yescomplemented
447C2×#126—434no—
448C2×#126—436no—
449C2×#126—436no—
450C2×#126—436no—
451C2×#126—436no—
452C2×#126—434no—
453#525—436no—
454#525—4312no—
455#525C2×D4316yescomplemented
456C2×#120—434no—
457#520—4312no—
458#518—4312no—
459C4×#41—436no—
460C4×#41C2×D4316yescomplemented
461C22×C4⋊C4—433no—
462C22×C22⋊C4—433no—
463C22×C42C2×D4311yescharacteristic, complemented
464C43#6282611yescharacteristic, complemented, Sylow
465C25—431no—
466C2×#41—4312no—
467C2×#41—436no—
468C2×#41C22×D4316yes—
469C22×D4—4312no—
470C23×C4—433no—
471C23×C4C22×D4313yes—
472C4⋊Q8—4312no—
473C4⋊Q8—4312no—
474C4⋊Q8—433no—
475C4⋊Q8C22×D4313yescomplemented
476#127—431no—
477#127C22×D4311yescharacteristic, complemented
478#126—4312no—
479#126—4312no—
480#126—4312no—
481#126—4312no—
482#126—4312no—
483#126—4312no—
484#126—434no—
485#126—434no—
486#126—4312no—
487#126—4312no—
488#126—4312no—
489#126—4312no—
490#126—434no—
491#126—434no—
492#126—434no—
493#126—4312no—
494#126—4312no—
495#126—434no—
496#126C22×D4314yescomplemented
497#126C22×D4314yescomplemented
498#125—4312no—
499#125—4312no—
500#125—4312no—
501#125—4312no—
502#125—4312no—
503#125—436no—
504#125—4312no—
505#125C22×D4316yescomplemented
506#124—4312no—
507#124—4312no—
508#124—4312no—
509#124—436no—
510#124—4312no—
511#124C22×D4316yescomplemented
512#123—4312no—
513#123—4312no—
514#123—4312no—
515#123—4312no—
516#123—4312no—
517#123—4312no—
518#123—4312no—
519#123—4312no—
520#123—4312no—
521#123—4312no—
522#123—4312no—
523#123—4312no—
524#123—4312no—
525#123C22×D43112yes—
526C22⋊Q8—4312no—
527C22⋊Q8—4312no—
528C22⋊Q8—436no—
529C22⋊Q8—436no—
530C22⋊Q8—4312no—
531C22⋊Q8—4312no—
532C22⋊Q8—4312no—
533C22⋊Q8—4312no—
534C22⋊Q8—4312no—
535C22⋊Q8—4312no—
536C22⋊Q8—4312no—
537C22⋊Q8—4312no—
538C22⋊Q8—4312no—
539C22⋊Q8—4312no—
540C22⋊Q8C22×D4316yes—
541C22⋊Q8C22×D4316yes—
542#121—4312no—
543#121—4312no—
544#121—4312no—
545#121—4312no—
546#121—436no—
547#121—436no—
548#121—4312no—
549#121—4312no—
550#121—4312no—
551#121—4312no—
552#121C22×D4316yes—
553#121C22×D4316yes—
554#120—434no—
555#120—4312no—
556#120—4312no—
557#120—4312no—
558#120—4312no—
559#120C22×D4314yes—
560C4×Q8—4312no—
561C4×Q8—436no—
562C4×Q8—436no—
563C4×Q8—4312no—
564C4×Q8C22×D4316yescomplemented
565C4×Q8C22×D4316yescomplemented
566C4×D4—4312no—
567C4×D4—4312no—
568C4×D4—4312no—
569C4×D4—4312no—
570C4×D4—4312no—
571C4×D4—4312no—
572C4×D4—4312no—
573C4×D4—4312no—
574C4×D4—4312no—
575C4×D4—4312no—
576C4×D4—4312no—
577C4×D4—436no—
578C4×D4—436no—
579C4×D4—4312no—
580C4×D4C22×D43112yes—
581C4×D4C22×D43112yes—
582C4×D4C22×D4316yescomplemented
583C4×D4C22×D4316yescomplemented
584#117—436no—
585#117—4312no—
586#117—4312no—
587#117—4312no—
588#117—4312no—
589#117—4312no—
590#117—4312no—
591#117C22×D4316yes—
592#117C22×D43112yescomplemented
593C2×C4⋊C4—436no—
594C2×C4⋊C4—436no—
595C2×C4⋊C4—436no—
596C2×C4⋊C4—436no—
597C2×C4⋊C4—436no—
598C2×C4⋊C4—436no—
599C2×C4⋊C4—4312no—
600C2×C4⋊C4—4312no—
601C2×C22⋊C4—436no—
602C2×C22⋊C4—436no—
603C2×C22⋊C4—436no—
604C2×C22⋊C4—436no—
605C2×C22⋊C4—436no—
606C2×C22⋊C4—436no—
607C2×C22⋊C4—4312no—
608C2×C22⋊C4—4312no—
609C2×C22⋊C4—4312no—
610C2×C42—434no—
611C2×C42C22×D4313yes—
612C2×C42C22×D4313yes—
613C2×C42C22×D4313yes—
614C2×C42C22×D4313yes—
615C2×C42C22×D4314yescomplemented
616C24—436no—
617C24—434no—
618C24—1726no—
619C24C23×D4311yescharacteristic
620#41—412no—
621#41—17212no—
622#41—17224no—
623C2×Q8—4312no—
624C2×Q8—436no—
625C2×Q8C23×D4316yes—
626C2×D4—4312no—
627C2×D4—4312no—
628C2×D4—4312no—
629C2×D4—4312no—
630C2×D4—436no—
631C2×D4—17224no—
632C2×D4C23×D43112yes—
633C2×D4C23×D4316yes—
634C22×C4—46no—
635C22×C4—436no—
636C22×C4—436no—
637C22×C4—436no—
638C22×C4—4312no—
639C22×C4—4312no—
640C22×C4—4312no—
641C22×C4—4312no—
642C22×C4—1726no—
643C22×C4C23×D4313yes—
644C22×C4C23×D4313yes—
645C22×C4C23×D4313yes—
646C22×C4C23×D4313yes—
647C22×C4C23×D4313yes—
648C22×C4C23×D4313yes—
649C22×C4C23×D43112yes—
650C4⋊C4—4312no—
651C4⋊C4—4312no—
652C4⋊C4—4312no—
653C4⋊C4—4312no—
654C4⋊C4—4312no—
655C4⋊C4—4312no—
656C4⋊C4—4312no—
657C4⋊C4—4312no—
658C4⋊C4—4312no—
659C4⋊C4—4312no—
660C4⋊C4—4312no—
661C4⋊C4—4312no—
662C4⋊C4—436no—
663C4⋊C4—436no—
664C4⋊C4C23×D43112yes—
665C4⋊C4C23×D4316yes—
666C4⋊C4C23×D4316yes—
667C4⋊C4C23×D43112yes—
668C22⋊C4—4312no—
669C22⋊C4—4312no—
670C22⋊C4—4312no—
671C22⋊C4—4312no—
672C22⋊C4—4312no—
673C22⋊C4—4312no—
674C22⋊C4—4312no—
675C22⋊C4—4312no—
676C22⋊C4—4312no—
677C22⋊C4—4312no—
678C22⋊C4—4312no—
679C22⋊C4—4312no—
680C22⋊C4—4312no—
681C22⋊C4C23×D43112yes—
682C22⋊C4C23×D43112yes—
683C22⋊C4C23×D43112yes—
684C42—4312no—
685C42—4312no—
686C42—4312no—
687C42C23×D4311yescharacteristic
688C42C23×D4311yescharacteristic
689C42C23×D4313yes—
690C42C23×D4313yes—
691C42C23×D4313yes—
692C42C23×D4313yes—
693C42C23×D4311yescharacteristic
694C42C23×D4311yescharacteristic
695C42C23×D43112yes—
696C23—26no—
697C23—434no—
698C23—434no—
699C23—8612no—
700C23—3448no—
701C23—1726no—
702C23—1726no—
703C23—17212no—
704C23C24×D4314yes—
705C23C24×D4313yes—
706Q8—46no—
707Q8—1726no—
708Q8—17212no—
709D4—224no—
710D4—46no—
711D4—8624no—
712D4—17212no—
713D4—1726no—
714D4—17212no—
715D4—17212no—
716C2×C4—26no—
717C2×C4—26no—
718C2×C4—43no—
719C2×C4—43no—
720C2×C4—43no—
721C2×C4—43no—
722C2×C4—412no—
723C2×C4—4312no—
724C2×C4—4312no—
725C2×C4—8612no—
726C2×C4—17212no—
727C2×C4—17212no—
728C2×C4—17212no—
729C2×C4—1726no—
730C2×C4—1726no—
731C2×C4—17212no—
732C2×C4C24×D4313yes—
733C2×C4C24×D43112yes—
734C2×C4C24×D4313yes—
735C2×C4C24×D4313yes—
736C2×C4C24×D4313yes—
737C22—28no—
738C22—23no—
739C22—23no—
740C22—212no—
741C22—8612no—
742C22—8612no—
743C22—34412no—
744C22—6884no—
745C22#1458373516yes—
746C22C25×D4311yescharacteristic
747C4—23no—
748C4—23no—
749C4—23no—
750C4—23no—
751C4—212no—
752C4—8612no—
753C4—8612no—
754C2—26no—
755C2—44no—
756C2—1724no—
757C2—1724no—
758C2C2×#1458373513yes—
subgroupG/H
center, FrattiniC22C25×D43
commutator, socle, cosocleC22×C43C26
FittingC43×#3444C2
hypercenter#3444D43
hypocenterC43#62826
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #3444

Complements

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

NH ≅ G/Ntype
1. #19149223C2semidirect
2. #19149213C2semidirect
3. #19149151C2semidirect
4. #19149141C2semidirect
5. #19148663C2semidirect
6. #19148649C2semidirect
7. #19148296C2semidirect
8. #19148278C2semidirect
9. #19147891C2semidirect
10. C22×#13063319C2semidirect
11. C43×#3444C2semidirect
12. #14583651C22semidirect
13. #14583648C22semidirect
14. #14583640C22semidirect
15. #14583636C22semidirect
16. #14583621C22semidirect
17. #14583617C22semidirect
18. #14583608C22semidirect
19. #14583603C22semidirect
20. #14583598C22semidirect
21. #14583598C22semidirect
22. #14583593C22semidirect
23. #14583592C22semidirect
24. #14583590C22semidirect
25. #14583586C22semidirect
26. #14583582C22semidirect
27. #14583582C22semidirect
28. #14583578C22semidirect
29. #14583578C22semidirect
30. #14583576C22semidirect
31. #14583573C22semidirect
32. #14583573C22semidirect
33. #14583572C22semidirect
34. #14583548C22semidirect
35. #14583547C22semidirect
36. #14583544C22semidirect
37. #14583541C22semidirect
38. #14583538C22semidirect
39. #14583537C22semidirect
40. #14583528C22semidirect
41. #14583524C22semidirect
42. #14583521C22semidirect
43. #14583513C22semidirect
44. #14583508C22semidirect
45. #14583507C22semidirect
46. #14583498C22semidirect
47. #14583497C22semidirect
48. #14583494C22semidirect
49. #14583491C22semidirect
50. #14583491C22semidirect
53. #14583483C22semidirect
55. #14583482C22semidirect
56. #14583476C22semidirect
57. #14583457C22semidirect
58. #14583456C22semidirect
59. #14583449C22semidirect
60. #14583433C22semidirect
61. #14583433C22semidirect
62. #14583433C22semidirect
63. #14583432C22semidirect
64. C2×#13063319C22semidirect
65. C2×#13063319C22semidirect
66. C2×#13063319C22semidirect
67. C2×#13063319C22semidirect
68. C2×#13063319C22semidirect
69. #126×D43C22semidirect
70. #14583410C22semidirect
71. #14583405C22semidirect
73. #14583378C22semidirect
74. #14583371C22semidirect
75. C4×#10621898C22semidirect
76. C22×Dic43⋊C4C22semidirect
78. C43×#533C22semidirect
79. C43×#532C22semidirect
80. C43×#529C22semidirect
81. C43×#529C22semidirect
82. C43×#525C22semidirect
83. C4×#41×C43C22semidirect
84. C22×C42×C43C22semidirect
90. #13063325C23semidirect
91. #13063324C23semidirect
92. #13063323C23semidirect
93. #13063322C23semidirect
97. #13063320C23semidirect
107. #13063319C23semidirect
108. #13063319C23semidirect
109. #13063319C23semidirect
110. #13063318C23semidirect
111. #13063318C23semidirect
112. #13063317C23semidirect
113. #13063317C23semidirect
114. #13063316C23semidirect
115. #13063315C23semidirect
116. #13063315C23semidirect
117. #13063315C23semidirect
118. #13063315C23semidirect
121. #13063313C23semidirect
127. #13063310C23semidirect
132. #13063308C23semidirect
134. #13063307C23semidirect
136. #13063306C23semidirect
140. #13063304C23semidirect
143. #13063303C23semidirect
144. #13063303C23semidirect
147. #13063302C23semidirect
148. #13063302C23semidirect
150. #13063301C23semidirect
156. #13063298C23semidirect
160. #13063297C23semidirect
166. C4×Dic86C23semidirect
167. C4×Dic86C23semidirect
168. C4×Dic86C23semidirect
169. #13063290C23semidirect
171. C4×D172C23semidirect
172. C4×D172C23semidirect
179. C4×C22⋊D43C23semidirect
183. (C22⋊D43)⋊C4C23semidirect
187. #13063282C23semidirect
188. #13063282C23semidirect
190. #13063281C23semidirect
197. C2×Dic43⋊C4C23semidirect
198. C4⋊C4×D43C23semidirect
208. C42×D43C23semidirect
211. C4⋊Q8×C43C23semidirect
212. #127×C43C23semidirect
213. #126×C43C23semidirect
214. #126×C43C23semidirect
215. #125×C43C23semidirect
216. #124×C43C23semidirect
223. C4×Q8×C43C23semidirect
224. C4×Q8×C43C23semidirect
227. C4×D4×C43C23semidirect
228. C4×D4×C43C23semidirect
230. #117×C43C23semidirect
235. C2×C42×C43C23semidirect
384. #3444D43semidirect
438. #533C2×D43semidirect
440. #532C2×D43semidirect
445. #529C2×D43semidirect
446. #529C2×D43semidirect
455. #525C2×D43semidirect
460. C4×#41C2×D43semidirect
463. C22×C42C2×D43semidirect
464. C43#62826semidirect
475. C4⋊Q8C22×D43semidirect
477. #127C22×D43semidirect
496. #126C22×D43semidirect
497. #126C22×D43semidirect
505. #125C22×D43semidirect
511. #124C22×D43semidirect
564. C4×Q8C22×D43semidirect
565. C4×Q8C22×D43semidirect
582. C4×D4C22×D43semidirect
583. C4×D4C22×D43semidirect
592. #117C22×D43semidirect
615. C2×C42C22×D43semidirect

Maximal subgroups

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

subgroupindex
#191492232
#191492132
#191491512
#191491412
#191486632
#191486492
#191482962
#191482782
#191478912
C22×#130633192
C43×#34442
#6282643