Finite Group Databasebeta

← #11904668

Subgroups — #11904668

Order 1152.

3761 conjugacy classes of subgroups.

The subgroup lattice has 1258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#64307C211yesmaximal, characteristic, complemented
3C3×#5833C211yesmaximal, characteristic, complemented
4C3×#5830C211yesmaximal, characteristic, complemented
5#10595431C212yesmaximal, complemented
6#10595362C212yesmaximal, complemented
7#10595307C214yesmaximal, complemented
8#10595297C212yesmaximal, complemented
9#10595292C214yesmaximal, complemented
10#10595164C212yesmaximal, complemented
11#10595082C212yesmaximal, complemented
12#10595081C212yesmaximal, complemented
13#10595034C211yesmaximal, characteristic, complemented
14C2×#63916C211yesmaximal, characteristic, complemented
15#10594990C211yesmaximal, characteristic, complemented
16#10594923C212yesmaximal, complemented
17#10594922C212yesmaximal, complemented
18#86379—31nomaximal
19#86331—31nomaximal
20C2×C32×#41C2211yescharacteristic, complemented
21#41×C3⋊D3—28no—
22C2×#3832C2211yescharacteristic, complemented
23C2×Q8×C3⋊D3C2211yescharacteristic, complemented
24C2×#3830C2211yescharacteristic, complemented
25C2×#3830C2212yescomplemented
26C2×D4×C3⋊D3C2212yescomplemented
27C2×D4×C3⋊D3C2211yescharacteristic, complemented
28C2×#3828C2211yescharacteristic
29C2×#3828C2212yescomplemented
30C22×C4×C3⋊D3C2212yescomplemented
31C22×C4×C3⋊D3C2211yescharacteristic, complemented
32C2×C3×#235C2211yescharacteristic, complemented
33C22×C3×D12C2211yescharacteristic, complemented
34C2×#3811C2214yescomplemented
35C2×D3×#67C2214yescomplemented
36C22×#626C2212yescomplemented
37#64307—28no—
38C2×#3802C2212yescomplemented
39C2×D3×D12C2212yescomplemented
40C2×#3796C2212yescomplemented
41C2×#3795C2212yescomplemented
42C3×#947C2212yescomplemented
43C3×#946C2212yescomplemented
44C3×#940C2212yescomplemented
45C3×#939C2214yescomplemented
46C3×#938C2212yescomplemented
47C3×#937C2214yescomplemented
48C3×#930C2212yescomplemented
49C3×#930C2212yescomplemented
50C3×#930C2212yescomplemented
51C3×#926C2211yescharacteristic, complemented
52C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
53C3×#924C2212yescomplemented
54#63983C2214yescomplemented
55#63981C2214yescomplemented
56#63981C2212yescomplemented
57#63980C2214yescomplemented
58#63979C2214yescomplemented
59#67⋊Dic3C2214yescomplemented
60#63971C2214yescomplemented
61#63962C2212yescomplemented
62C2×(C2×D3)⋊Dic3C2212yescomplemented
63#63958C2214yescomplemented
64#63952C2214yescomplemented
65#63923C2214yescomplemented
66#63921C2214yescomplemented
67#63916C2211yescharacteristic, complemented
68#63916C2212yescomplemented
69#63916C2211yescharacteristic, complemented
70#63916C2212yescomplemented
71#63916C2212yescomplemented
72#63916C2212yescomplemented
73#63913C2214yescomplemented
74#63912C2214yescomplemented
75#63910C2214yescomplemented
76C4×#626C2212yescomplemented
77C4×#626C2212yescomplemented
78#63900C2212yescomplemented
79#63896C2214yescomplemented
80#63894C2212yescomplemented
81#63881C2214yescomplemented
82#63871C2211yescharacteristic, complemented
83#63871C2211yescharacteristic, complemented
84#63853C2214yescomplemented
85#63849C2212yescomplemented
86#63844C2212yescomplemented
87C2×#1009—31no—
88C2×D3×#41—31no—
89C2×D3×#41—31no—
90C2×D3×#41—61no—
91C2×#1004—31no—
92C3×#537—31no—
93C3×#535—31no—
94#5833D311yescharacteristic, complemented
95#5830D311yescharacteristic, complemented
96#5828—31no—
97C2×#938—31no—
98#5718—32no—
99#5717—32no—
100#5677—32no—
101#5676—32no—
102#5633—32no—
103#5630—32no—
104#5629—32no—
105#5627—32no—
106#5610—34no—
107#5609—32no—
108#5609—34no—
109#5608—32no—
110#5607—32no—
111#5607—32no—
112#5606—32no—
113D3×#121—32no—
114D3×#121—32no—
115#5599—32no—
116#5591—34no—
117#5590—34no—
118#5524—31no—
119#5523—31no—
120C2×#895—31no—
121#5504—31no—
122C23×C3⋊D3C2311yescharacteristic
123C23×C3⋊D3C2312yes—
124C23×C3×D3C2312yes—
125C22×D32C2314yes—
126C32×#41—24no—
127C2×C32×Q8C2311yescharacteristic
128C2×C32×D4C2312yes—
129C2×C32×D4C2311yescharacteristic
130C22×C32×C4C2312yes—
131C22×C32×C4C2311yescharacteristic
132C2×#638C2312yes—
133C2×#638C2312yes—
134C2×#638C2312yes—
135C22×C3⋊Dic3C2311yescharacteristic
136C22×C3⋊Dic3C2312yes—
137#3832—24no—
138Q8×C3⋊D3—24no—
139#3830—28no—
140#3830—24no—
141D4×C3⋊D3—28no—
142D4×C3⋊D3—24no—
143#3828—28no—
144#3828D418yescomplemented
145C2×C4⋊(C3⋊D3)C2312yes—
146C2×C4⋊(C3⋊D3)C2311yescharacteristic
147C2×C4×C3⋊D3—24no—
148C2×C4×C3⋊D3—28no—
149C2×C4×C3⋊D3C2311yescharacteristic
150C2×C4×C3⋊D3C2311yescharacteristic
151C2×C4×C3⋊D3C2312yes—
152C2×C4×C3⋊D3C2311yescharacteristic
153C2×C4×C3⋊D3C2312yes—
154C2×C4×C3⋊D3C2311yescharacteristic
155C2×C4×C3⋊D3C2312yes—
156C2×#634C2312yes—
157C2×#634C2311yescharacteristic
158C2×C3×#67C2312yes—
159C2×C3×#67C2314yes—
160C2×C3×#67C2314yes—
161C2×C3×#67C2314yes—
162C22×C3×Dic3C2312yes—
163C3×#235—24no—
164C2×C3×D12—24no—
165C2×C3×D12C2312yes—
166C2×C3×D12C2312yes—
167C2×C3×D12C2311yescharacteristic
168C2×C3×C4×D3C2312yes—
169C2×C3×Dic6C2311yescharacteristic
170#3811—48no—
171D3×#67—216no—
172C2×#626—44no—
173C2×#626C2314yes—
174C2×#626C2314yes—
175C2×#626C2312yes—
176C2×#626C2314yes—
177C2×#626C2312yes—
178C2×#625C2314yes—
179C2×#624C2314yes—
180C2×D3×Dic3C2314yes—
181#3802—28no—
182D3×D12—28no—
183#3796—28no—
184#3795—28no—
185C3×#217C2314yes—
186C3×#217C2312yes—
187C3×(C2×D3)⋊C4C2314yes—
188C3×(C2×D3)⋊C4C2314yes—
189C3×(C2×D3)⋊C4C2314yes—
190C3×C4⋊Dic3C2312yes—
191C3×C4⋊Dic3C2312yes—
192C3×C4⋊Dic3C2311yescharacteristic
193C3×C4⋊Dic3C2311yescharacteristic
194C3×Dic3⋊C4C2314yes—
195C3×C4×Dic3C2312yes—
196#3724C2314yes—
197Dic3⋊Dic3C2312yes—
198Dic3⋊Dic3C2312yes—
199#3722C2314yes—
200#3722C2312yes—
201#3722C2312yes—
202(C2×D3)⋊Dic3C2314yes—
203(C2×D3)⋊Dic3C2314yes—
204(C2×D3)⋊Dic3C2312yes—
205(C2×D3)⋊Dic3C2312yes—
206Dic32C2314yes—
207#3488—91noSylow
208C2×C3×#41—21no—
209C2×C3×#41—31no—
210C2×C3×#41C2×D311yescharacteristic, complemented
211C2×C3×#41C2×D311yescharacteristic, complemented
212C22×C3×D4—31no—
213C22×#67—34no—
214C22×#67—32no—
215#1009—68no—
216D3×#41—68no—
217D3×#41—68no—
218D3×#41—616no—
219C2×#239—31no—
220C2×#239—31no—
221C2×#239—32no—
222C2×#239—61no—
223C2×D3×Q8—31no—
224C2×D3×Q8—31no—
225C2×D3×Q8—61no—
226#1004—68no—
227C2×#237—31no—
228C2×#237—32no—
229C2×#237—31no—
230C2×#237—32no—
231C2×#237—32no—
232C2×#237—32no—
233C2×#237—62no—
234C2×#237—61no—
235C2×D3×D4—34no—
236C2×D3×D4—31no—
237C2×D3×D4—32no—
238C2×D3×D4—32no—
239C2×D3×D4—31no—
240C2×D3×D4—34no—
241C2×D3×D4—34no—
242C2×D3×D4—32no—
243C2×D3×D4—32no—
244C2×D3×D4—32no—
245C2×D3×D4—62no—
246C2×D3×D4—61no—
247C2×#235—31no—
248C2×#235—31no—
249C2×#235—32no—
250C2×#235—32no—
251C2×#235—32no—
252C2×#235—61no—
253C2×#235—62no—
254C2×#235C2×D311yescharacteristic, complemented
255C22×D12—32no—
256C22×D12—32no—
257C22×D12C2×D311yescharacteristic, complemented
258C22×C4×D3—31no—
259C22×C4×D3—31no—
260C22×C4×D3—32no—
261C22×C4×D3—32no—
262C22×C4×D3—62no—
263C22×C4×D3—61no—
264C3×#127—32no—
265C3×#124—32no—
266C3×C22⋊Q8—32no—
267C3×C22⋊Q8—32no—
268C3×#121—32no—
269C3×#121—34no—
270C3×#121—32no—
271C3×#121—32no—
272C3×#121—32no—
273C3×#120—34no—
274C3×#117—31no—
275C2×C3×C4⋊C4—31no—
276C2×#217—32no—
277#947C2×D312yescomplemented
278#946—31no—
279#946—31no—
280#946C2×D312yescomplemented
281#940—34no—
282#940—34no—
283#940C2×D312yescomplemented
284#939—34no—
285#939—34no—
286#939—34no—
287#939C2×D314yescomplemented
288#938—34no—
289#938—32no—
290#938—32no—
291#938—32no—
292#938—32no—
293#938—31no—
294#938—31no—
295#938C2×D312yescomplemented
296#937—34no—
297#937—34no—
298#937—34no—
299#937—32no—
300#937C2×D314yescomplemented
301#935—32no—
302D4×Dic3—34no—
303#930C2×D312yescomplemented
304#930C2×D312yescomplemented
305#930C2×D312yescomplemented
306C4×#67—34no—
307C4×#67—32no—
308C4×#67—32no—
309C2×(C2×D3)⋊C4—32no—
310#926C2×D311yescharacteristic, complemented
311C2×C4⋊Dic3C2×D311yescharacteristic, complemented
312#924C2×D312yescomplemented
313#897—31no—
314#897—31no—
315#896—34no—
316#895—32no—
317#895—32no—
318#895—32no—
319#895—32no—
320#895—31no—
321#895—31no—
322#895—34no—
323#894—34no—
324#893—34no—
325#893—32no—
326#892—32no—
327#892—32no—
328D3×C4⋊C4—32no—
329D3×C4⋊C4—32no—
330#887—32no—
331#886—32no—
332#885—34no—
333#885—34no—
334#884—34no—
335#884—34no—
336#884—34no—
337#884—34no—
338#884—34no—
339#883—34no—
340#882—32no—
341#882—34no—
342#882—34no—
343#882—34no—
344#67⋊C4—34no—
345#67⋊C4—34no—
346#67⋊C4—34no—
347D3×C22⋊C4—34no—
348D3×C22⋊C4—34no—
349#878—34no—
350C4×D12—32no—
351C4×D12—32no—
352C4×D12—32no—
353C4×Dic6—32no—
354C23×C32C2412yes—
355C23×C32C2411yescharacteristic
356C22×C3⋊D3—22no—
357C22×C3⋊D3—24no—
358C22×C3⋊D3—22no—
359C22×C3⋊D3—24no—
360C22×C3⋊D3—42no—
361C22×C3⋊D3—41no—
362C22×C3⋊D3C2411yescharacteristic
363C22×C3⋊D3C2412yes—
364C22×C3⋊D3C2411yescharacteristic
365C22×C3×D3—24no—
366C22×C3×D3—42no—
367C22×C3×D3—42no—
368C22×C3×D3C2412yes—
369C22×C3×D3C2414yes—
370C2×D32—28no—
371C2×D32—44no—
372C2×D32—44no—
373C32×Q8—22no—
374C32×D4—24no—
375C32×D4—22no—
376C2×C32×C4—24no—
377C2×C32×C4C2×D414yescomplemented
378C2×C32×C4C2412yes—
379C2×C32×C4C2411yescharacteristic
380C2×C32×C4C2411yescharacteristic
381#638—24no—
382#638—24no—
383#638C2×D418yescomplemented
384C2×C3⋊Dic3—22no—
385C2×C3⋊Dic3—24no—
386C2×C3⋊Dic3C2411yescharacteristic
387C2×C3⋊Dic3C2411yescharacteristic
388C2×C3⋊Dic3C2412yes—
389C4⋊(C3⋊D3)—24no—
390C4⋊(C3⋊D3)C2×D414yescomplemented
391C4×C3⋊D3—24no—
392C4×C3⋊D3—22no—
393C4×C3⋊D3—22no—
394C4×C3⋊D3—22no—
395C4×C3⋊D3—22no—
396C4×C3⋊D3—24no—
397C4×C3⋊D3C2×D418yescomplemented
398#634—24no—
399#634C2×D414yescomplemented
400C3×#67—24no—
401C3×#67—44no—
402C3×#67—44no—
403C3×#67—44no—
404C2×C3×Dic3—42no—
405C2×C3×Dic3C2412yes—
406C2×C3×Dic3C2414yes—
407C2×C3×Dic3C2412yes—
408C2×C3×Dic3C2412yes—
409C3×D12—24no—
410C3×D12—24no—
411C3×D12—22no—
412C3×C4×D3—24no—
413C3×Dic6—22no—
414#626—28no—
415#626—28no—
416#626—24no—
417#626—44no—
418#626—42no—
419#625—28no—
420#624—44no—
421D3×Dic3—28no—
422C2×H(5,𝔽2)—91no—
423C22×#41—91no—
424#550—92no—
425#548—92no—
426#546—94no—
427#546—92no—
428D42—94no—
429D42—92no—
430#537—31no—
431#537—92no—
432#535—31no—
433#535—92no—
434#525—91no—
435#525—92no—
436C2×#121—91no—
437C2×#121—92no—
438#520—91no—
439C24×C3—32no—
440C23×D3—32no—
441C23×D3—31no—
442C23×D3—31no—
443C23×D3—32no—
444C23×D3—34no—
445C23×D3—34no—
446C23×D3—61no—
447C23×D3—62no—
448C23×D3C22×D312yes—
449C3×#41—28no—
450C3×#41—24no—
451C3×#41—24no—
452C3×#41—64no—
453C2×C3×Q8—21no—
454C2×C3×Q8—31no—
455C2×C3×Q8C22×D311yescharacteristic
456C2×C3×Q8C22×D311yescharacteristic
457C2×C3×D4—22no—
458C2×C3×D4—21no—
459C2×C3×D4—32no—
460C2×C3×D4—34no—
461C2×C3×D4—34no—
462C2×C3×D4—34no—
463C2×C3×D4—31no—
464C2×C3×D4—32no—
465C2×C3×D4—32no—
466C2×C3×D4—64no—
467C2×C3×D4C22×D312yes—
468C2×C3×D4C22×D311yescharacteristic
469C2×C3×D4C22×D312yes—
470C2×C3×D4C22×D311yescharacteristic
471C22×C3×C4—22no—
472C22×C3×C4—21no—
473C22×C3×C4—32no—
474C22×C3×C4—32no—
475C22×C3×C4C22×D312yes—
476C22×C3×C4C22×D312yes—
477C22×C3×C4C22×D311yescharacteristic
478C22×C3×C4C22×D311yescharacteristic
479C2×#67—32no—
480C2×#67—32no—
481C2×#67—32no—
482C2×#67—32no—
483C2×#67—32no—
484C2×#67—32no—
485C2×#67—34no—
486C2×#67—34no—
487C2×#67—34no—
488C2×#67—34no—
489C2×#67—32no—
490C2×#67—32no—
491C2×#67—34no—
492C2×#67—62no—
493C2×#67—62no—
494C2×#67—62no—
495C2×#67—616no—
496C2×#67—124no—
497C2×#67C22×D312yes—
498C2×#67C22×D314yes—
499C2×#67C22×D314yes—
500C2×#67C22×D314yes—
501C22×Dic3—32no—
502C22×Dic3—31no—
503C22×Dic3—31no—
504C22×Dic3—32no—
505C22×Dic3—34no—
506C22×Dic3—61no—
507C22×Dic3—62no—
508C22×Dic3C22×D312yes—
509#239—68no—
510#239—64no—
511#239—64no—
512#239—68no—
513D3×Q8—64no—
514D3×Q8—64no—
515D3×Q8—68no—
516#237—68no—
517#237—68no—
518#237—64no—
519#237—64no—
520#237—68no—
521#237—68no—
522#237—616no—
523#237—68no—
524D3×D4—68no—
525D3×D4—68no—
526D3×D4—68no—
527D3×D4—64no—
528D3×D4—64no—
529D3×D4—68no—
530D3×D4—68no—
531D3×D4—616no—
532D3×D4—68no—
533D3×D4—616no—
534D3×D4—128no—
535D3×D4—128no—
536#235—24no—
537#235—38no—
538#235—38no—
539#235—68no—
540#235—68no—
541#235—68no—
542#235—68no—
543#235—616no—
544C2×D12—24no—
545C2×D12—31no—
546C2×D12—31no—
547C2×D12—32no—
548C2×D12—34no—
549C2×D12—34no—
550C2×D12—32no—
551C2×D12—32no—
552C2×D12—32no—
553C2×D12—34no—
554C2×D12—61no—
555C2×D12—62no—
556C2×D12—68no—
557C2×D12—124no—
558C2×D12C22×D312yes—
559C2×D12C22×D311yescharacteristic
560C2×D12C22×D312yes—
561C2×C4×D3—32no—
562C2×C4×D3—32no—
563C2×C4×D3—34no—
564C2×C4×D3—31no—
565C2×C4×D3—31no—
566C2×C4×D3—32no—
567C2×C4×D3—32no—
568C2×C4×D3—32no—
569C2×C4×D3—32no—
570C2×C4×D3—31no—
571C2×C4×D3—31no—
572C2×C4×D3—31no—
573C2×C4×D3—31no—
574C2×C4×D3—31no—
575C2×C4×D3—31no—
576C2×C4×D3—34no—
577C2×C4×D3—34no—
578C2×C4×D3—61no—
579C2×C4×D3—62no—
580C2×C4×D3—61no—
581C2×C4×D3—62no—
582C2×C4×D3—61no—
583C2×C4×D3—62no—
584C2×C4×D3—61no—
585C2×C4×D3—68no—
586C2×C4×D3—68no—
587C2×C4×D3—616no—
588C2×C4×D3—68no—
589C2×C4×D3—64no—
590C2×C4×D3—64no—
591C2×C4×D3C22×D312yes—
592C2×Dic6—31no—
593C2×Dic6—31no—
594C2×Dic6—32no—
595C2×Dic6—32no—
596C2×Dic6—61no—
597C2×Dic6—62no—
598C2×Dic6C22×D311yescharacteristic
599C3×C4⋊C4—32no—
600C3×C4⋊C4—31no—
601C3×C4⋊C4—32no—
602C3×C4⋊C4—31no—
603C3×C4⋊C4—34no—
604C3×C22⋊C4—32no—
605C3×C22⋊C4—34no—
606C3×C22⋊C4—34no—
607C3×C22⋊C4—34no—
608C3×C22⋊C4—34no—
609C3×C42—32no—
610#217—34no—
611#217—32no—
612#217—34no—
613#217—32no—
614#217C22×D314yes—
615#217C22×D312yes—
616(C2×D3)⋊C4—32no—
617(C2×D3)⋊C4—32no—
618(C2×D3)⋊C4—34no—
619(C2×D3)⋊C4—34no—
620(C2×D3)⋊C4—32no—
621(C2×D3)⋊C4—34no—
622(C2×D3)⋊C4—32no—
623(C2×D3)⋊C4—34no—
624(C2×D3)⋊C4—32no—
625(C2×D3)⋊C4—32no—
626(C2×D3)⋊C4C22×D314yes—
627(C2×D3)⋊C4C22×D314yes—
628(C2×D3)⋊C4C22×D314yes—
629C4⋊Dic3—32no—
630C4⋊Dic3—32no—
631C4⋊Dic3C22×D312yes—
632C4⋊Dic3C22×D311yescharacteristic
633C4⋊Dic3C22×D312yes—
634C4⋊Dic3C22×D311yescharacteristic
635Dic3⋊C4—34no—
636Dic3⋊C4—32no—
637Dic3⋊C4—34no—
638Dic3⋊C4—32no—
639Dic3⋊C4C22×D314yes—
640C4×Dic3—34no—
641C4×Dic3—34no—
642C4×Dic3C22×D312yes—
643C22×C32—22no—
644C22×C32—21no—
645C22×C32—21no—
646C22×C32—22no—
647C22×C32—22no—
648C22×C32C22×D412yes—
649C22×C32C2511yescharacteristic
650C2×C3⋊D3—21no—
651C2×C3⋊D3—21no—
652C2×C3⋊D3—21no—
653C2×C3⋊D3—22no—
654C2×C3⋊D3—22no—
655C2×C3⋊D3—21no—
656C2×C3⋊D3—21no—
657C2×C3⋊D3—48no—
658C2×C3⋊D3—44no—
659C2×C3⋊D3C22×D414yes—
660C2×C3⋊D3H(5,𝔽2)12yescomplemented
661C2×C3×D3—24no—
662C2×C3×D3—22no—
663C2×C3×D3—24no—
664C2×C3×D3—22no—
665C2×C3×D3—22no—
666C2×C3×D3—24no—
667C2×C3×D3—84no—
668D32—88no—
669C32×C4—22no—
670C32×C4C22×D412yes—
671C32×C4C22×D412yes—
672C3⋊Dic3—21no—
673C3⋊Dic3—21no—
674C3⋊Dic3C22×D414yes—
675C3×Dic3—22no—
676C3×Dic3—22no—
677C3×Dic3—24no—
678C3×Dic3—22no—
679H(5,𝔽2)—188no—
680C2×#41—31no—
681C2×#41—92no—
682C2×#41—92no—
683C2×#41—91no—
684C2×#41—92no—
685C2×#41—91no—
686C2×#41—91no—
687C2×#41—92no—
688C2×#41—188no—
689C2×#41D3211yescharacteristic, complemented
690C22×Q8—91no—
691C22×D4—31no—
692C22×D4—92no—
693C22×D4—92no—
694C22×D4—92no—
695C22×D4—94no—
696C22×D4—94no—
697C22×D4—92no—
698C22×D4—91no—
699C23×C4—92no—
700C23×C4—91no—
701#127—32no—
702#127—94no—
703#124—32no—
704#124—94no—
705#123—94no—
706#123—92no—
707C22⋊Q8—32no—
708C22⋊Q8—32no—
709C22⋊Q8—94no—
710C22⋊Q8—91no—
711C22⋊Q8—91no—
712#121—34no—
713#121—32no—
714#121—32no—
715#121—32no—
716#121—32no—
717#121—94no—
718#121—94no—
719#121—94no—
720#121—94no—
721#121—92no—
722#121—91no—
723#121—92no—
724#121—92no—
725#121—92no—
726#121—91no—
727#121—94no—
728#120—34no—
729#120—94no—
730#120—92no—
731#120—94no—
732#120—94no—
733C4×Q8—92no—
734C4×D4—92no—
735C4×D4—92no—
736C4×D4—92no—
737C4×D4—94no—
738C4×D4—94no—
739C4×D4—94no—
740#117—31no—
741#117—92no—
742C2×C4⋊C4—31no—
743C2×C4⋊C4—92no—
744C2×C22⋊C4—94no—
745C2×C22⋊C4—92no—
746C23×C3—22no—
747C23×C3—21no—
748C23×C3—34no—
749C23×C3—32no—
750C23×C3—64no—
751C23×C3—122no—
752C23×C3—122no—
753C23×C3C23×D312yes—
754C23×C3C23×D312yes—
755C23×C3C23×D311yescharacteristic
756C23×C3C23×D311yescharacteristic
757C22×D3—24no—
758C22×D3—32no—
759C22×D3—31no—
760C22×D3—32no—
761C22×D3—31no—
762C22×D3—31no—
763C22×D3—31no—
764C22×D3—42no—
765C22×D3—42no—
766C22×D3—61no—
767C22×D3—62no—
768C22×D3—61no—
769C22×D3—68no—
770C22×D3—68no—
771C22×D3—64no—
772C22×D3—64no—
773C22×D3—62no—
774C22×D3—64no—
775C22×D3—64no—
776C22×D3—62no—
777C22×D3—68no—
778C22×D3—64no—
779C22×D3—62no—
780C22×D3—62no—
781C22×D3—122no—
782C22×D3—124no—
783C22×D3—124no—
784C22×D3—124no—
785C22×D3—124no—
786C22×D3—124no—
787C22×D3—122no—
788C22×D3—121no—
789C22×D3—122no—
790C22×D3—121no—
791C22×D3—122no—
792C22×D3—124no—
793C22×D3C23×D314yes—
794C22×D3C23×D312yes—
795C3×Q8—24no—
796C3×Q8—22no—
797C3×Q8—22no—
798C3×Q8—62no—
799C3×D4—28no—
800C3×D4—24no—
801C3×D4—24no—
802C3×D4—24no—
803C3×D4—22no—
804C3×D4—22no—
805C3×D4—64no—
806C3×D4—62no—
807C3×D4—64no—
808C3×D4—64no—
809C3×D4—124no—
810C3×D4—124no—
811C3×D4—124no—
812C2×C3×C4—28no—
813C2×C3×C4—24no—
814C2×C3×C4—24no—
815C2×C3×C4—22no—
816C2×C3×C4—21no—
817C2×C3×C4—21no—
818C2×C3×C4—24no—
819C2×C3×C4—32no—
820C2×C3×C4—34no—
821C2×C3×C4—32no—
822C2×C3×C4—32no—
823C2×C3×C4—64no—
824C2×C3×C4—122no—
825C2×C3×C4D3×D414yescomplemented
826C2×C3×C4D3×D414yescomplemented
827C2×C3×C4C23×D312yes—
828C2×C3×C4C23×D312yes—
829C2×C3×C4C23×D311yescharacteristic
830C2×C3×C4C23×D311yescharacteristic
831C2×C3×C4C23×D311yescharacteristic
832C2×C3×C4C23×D311yescharacteristic
833#67—24no—
834#67—38no—
835#67—38no—
836#67—44no—
837#67—44no—
838#67—44no—
839#67—68no—
840#67—68no—
841#67—64no—
842#67—68no—
843#67—68no—
844#67—68no—
845#67—64no—
846#67—64no—
847#67—64no—
848#67—64no—
849#67—68no—
850#67—68no—
851#67—122no—
852#67—124no—
853C2×Dic3—32no—
854C2×Dic3—32no—
855C2×Dic3—31no—
856C2×Dic3—31no—
857C2×Dic3—31no—
858C2×Dic3—31no—
859C2×Dic3—42no—
860C2×Dic3—62no—
861C2×Dic3—61no—
862C2×Dic3—61no—
863C2×Dic3—68no—
864C2×Dic3—64no—
865C2×Dic3—64no—
866C2×Dic3—68no—
867C2×Dic3—64no—
868C2×Dic3—62no—
869C2×Dic3—62no—
870C2×Dic3C23×D312yes—
871C2×Dic3C23×D314yes—
872C2×Dic3C23×D312yes—
873C2×Dic3C23×D312yes—
874D12—24no—
875D12—24no—
876D12—22no—
877D12—34no—
878D12—34no—
879D12—64no—
880D12—64no—
881D12—64no—
882D12—68no—
883D12—68no—
884D12—68no—
885D12—64no—
886D12—122no—
887D12—124no—
888C4×D3—24no—
889C4×D3—38no—
890C4×D3—38no—
891C4×D3—68no—
892C4×D3—64no—
893C4×D3—64no—
894C4×D3—68no—
895C4×D3—64no—
896C4×D3—64no—
897C4×D3—64no—
898C4×D3—64no—
899C4×D3—68no—
900C4×D3—64no—
901C4×D3—68no—
902C4×D3—64no—
903C4×D3—62no—
904C4×D3—62no—
905C4×D3—62no—
906C4×D3—62no—
907C4×D3—62no—
908C4×D3—62no—
909C4×D3—62no—
910C4×D3—62no—
911C4×D3—124no—
912C4×D3—124no—
913Dic6—22no—
914Dic6—34no—
915Dic6—34no—
916Dic6—64no—
917Dic6—64no—
918Dic6—64no—
919Dic6—68no—
920C2×C32—22no—
921C2×C32—42no—
922C2×C32C23×D411yescharacteristic
923C2×C32C2×H(5,𝔽2)11yescharacteristic
924C2×C32#58511yescharacteristic
925C3⋊D3—22no—
926C3⋊D3—24no—
927C3⋊D3—41no—
928C3×D3—42no—
929C3×D3—44no—
930C24—32no—
931C24—94no—
932C24—92no—
933C24—91no—
934#41—24no—
935#41—64no—
936#41—98no—
937#41—188no—
938#41—188no—
939#41—188no—
940#41—188no—
941#41—184no—
942#41—184no—
943C2×Q8—31no—
944C2×Q8—91no—
945C2×Q8—92no—
946C2×Q8—184no—
947C2×Q8C2×D3211yescharacteristic
948C2×D4—32no—
949C2×D4—34no—
950C2×D4—34no—
951C2×D4—34no—
952C2×D4—32no—
953C2×D4—31no—
954C2×D4—32no—
955C2×D4—64no—
956C2×D4—92no—
957C2×D4—94no—
958C2×D4—94no—
959C2×D4—92no—
960C2×D4—94no—
961C2×D4—92no—
962C2×D4—94no—
963C2×D4—92no—
964C2×D4—92no—
965C2×D4—91no—
966C2×D4—92no—
967C2×D4—188no—
968C2×D4—188no—
969C2×D4—188no—
970C2×D4—184no—
971C2×D4—1816no—
972C2×D4—364no—
973C2×D4—368no—
974C2×D4C2×D3212yes—
975C2×D4C2×D3211yescharacteristic
976C22×C4—32no—
977C22×C4—32no—
978C22×C4—94no—
979C22×C4—94no—
980C22×C4—92no—
981C22×C4—91no—
982C22×C4—92no—
983C22×C4—92no—
984C22×C4—92no—
985C22×C4—91no—
986C22×C4—91no—
987C22×C4—91no—
988C22×C4—91no—
989C22×C4—188no—
990C22×C4—184no—
991C22×C4C2×D3212yes—
992C22×C4C2×D3211yescharacteristic
993C4⋊C4—32no—
994C4⋊C4—32no—
995C4⋊C4—31no—
996C4⋊C4—31no—
997C4⋊C4—34no—
998C4⋊C4—94no—
999C4⋊C4—92no—
1000C4⋊C4—92no—
1001C22⋊C4—32no—
1002C22⋊C4—34no—
1003C22⋊C4—34no—
1004C22⋊C4—34no—
1005C22⋊C4—34no—
1006C22⋊C4—94no—
1007C22⋊C4—92no—
1008C22⋊C4—92no—
1009C22⋊C4—92no—
1010C22⋊C4—94no—
1011C22⋊C4—94no—
1012C22⋊C4—92no—
1013C42—32no—
1014C42—94no—
1015C22×C3—21no—
1016C22×C3—21no—
1017C22×C3—21no—
1018C22×C3—21no—
1019C22×C3—24no—
1020C22×C3—22no—
1021C22×C3—22no—
1022C22×C3—22no—
1023C22×C3—22no—
1024C22×C3—22no—
1025C22×C3—22no—
1026C22×C3—22no—
1027C22×C3—21no—
1028C22×C3—41no—
1029C22×C3—41no—
1030C22×C3—42no—
1031C22×C3—42no—
1032C22×C3—64no—
1033C22×C3—62no—
1034C22×C3—64no—
1035C22×C3—62no—
1036C22×C3—62no—
1037C22×C3—64no—
1038C22×C3—244no—
1039C22×C3C2×D3×D412yes—
1040C22×C3C2×D3×D412yes—
1041C22×C3C24×D311yescharacteristic
1042C22×C3C24×D311yescharacteristic
1043C2×D3—22no—
1044C2×D3—24no—
1045C2×D3—24no—
1046C2×D3—22no—
1047C2×D3—24no—
1048C2×D3—22no—
1049C2×D3—34no—
1050C2×D3—34no—
1051C2×D3—32no—
1052C2×D3—32no—
1053C2×D3—62no—
1054C2×D3—64no—
1055C2×D3—62no—
1056C2×D3—62no—
1057C2×D3—61no—
1058C2×D3—61no—
1059C2×D3—62no—
1060C2×D3—62no—
1061C2×D3—61no—
1062C2×D3—62no—
1063C2×D3—61no—
1064C2×D3—62no—
1065C2×D3—62no—
1066C2×D3—61no—
1067C2×D3—61no—
1068C2×D3—61no—
1069C2×D3—61no—
1070C2×D3—61no—
1071C2×D3—61no—
1072C2×D3—84no—
1073C2×D3—122no—
1074C2×D3—122no—
1075C2×D3—121no—
1076C2×D3—121no—
1077C2×D3—128no—
1078C2×D3—128no—
1079C2×D3—124no—
1080C2×D3—124no—
1081C2×D3—128no—
1082C2×D3—1216no—
1083C2×D3—248no—
1084C2×D3—248no—
1085C3×C4—24no—
1086C3×C4—22no—
1087C3×C4—22no—
1088C3×C4—22no—
1089C3×C4—22no—
1090C3×C4—62no—
1091C3×C4—62no—
1092C3×C4—64no—
1093C3×C4—62no—
1094C3×C4C2×D3×D412yes—
1095C3×C4C2×D3×D412yes—
1096C3×C4C2×D3×D412yes—
1097C3×C4C2×D3×D412yes—
1098Dic3—22no—
1099Dic3—22no—
1100Dic3—24no—
1101Dic3—22no—
1102Dic3—34no—
1103Dic3—34no—
1104Dic3—64no—
1105Dic3—62no—
1106Dic3—62no—
1107Dic3—61no—
1108Dic3—61no—
1109Dic3—61no—
1110Dic3—61no—
1111C32#348811yescharacteristic, complemented, Sylow
1112C23—32no—
1113C23—34no—
1114C23—64no—
1115C23—91no—
1116C23—92no—
1117C23—91no—
1118C23—122no—
1119C23—122no—
1120C23—184no—
1121C23—182no—
1122C23—184no—
1123C23—188no—
1124C23—182no—
1125C23—361no—
1126C23—362no—
1127C23—364no—
1128C23—364no—
1129C23C22×D3212yes—
1130C23C22×D3211yescharacteristic
1131Q8—22no—
1132Q8—62no—
1133Q8—94no—
1134Q8—184no—
1135D4—24no—
1136D4—22no—
1137D4—64no—
1138D4—64no—
1139D4—64no—
1140D4—62no—
1141D4—98no—
1142D4—94no—
1143D4—124no—
1144D4—124no—
1145D4—124no—
1146D4—184no—
1147D4—188no—
1148D4—188no—
1149D4—184no—
1150D4—184no—
1151D4—188no—
1152D4—184no—
1153D4—364no—
1154D4—362no—
1155C2×C4—24no—
1156C2×C4—32no—
1157C2×C4—32no—
1158C2×C4—34no—
1159C2×C4—32no—
1160C2×C4—64no—
1161C2×C4—92no—
1162C2×C4—98no—
1163C2×C4—91no—
1164C2×C4—91no—
1165C2×C4—122no—
1166C2×C4—184no—
1167C2×C4—184no—
1168C2×C4—188no—
1169C2×C4—184no—
1170C2×C4—182no—
1171C2×C4—182no—
1172C2×C4—182no—
1173C2×C4—182no—
1174C2×C4—182no—
1175C2×C4—364no—
1176C2×C4#381114yescomplemented
1177C2×C4C22×D3212yes—
1178C2×C4C22×D3211yescharacteristic
1179C2×C4C22×D3211yescharacteristic
1180C2×C3—22no—
1181C2×C3—22no—
1182C2×C3—21no—
1183C2×C3—21no—
1184C2×C3—21no—
1185C2×C3—42no—
1186C2×C3—44no—
1187C2×C3—42no—
1188C2×C3—42no—
1189C2×C3—122no—
1190C2×C3—124no—
1191C2×C3C22×D3×D411yescharacteristic
1192C2×C3C22×D3×D411yescharacteristic
1193C2×C3D3×H(5,𝔽2)11yescharacteristic
1194C2×C3D3×H(5,𝔽2)11yescharacteristic
1195C2×C3#596611yescharacteristic
1196C2×C3#596811yescharacteristic
1197D3—44no—
1198D3—42no—
1199D3—64no—
1200D3—62no—
1201D3—64no—
1202D3—62no—
1203D3—64no—
1204D3—124no—
1205D3—122no—
1206D3—121no—
1207D3—121no—
1208C22—21no—
1209C22—21no—
1210C22—22no—
1211C22—22no—
1212C22—22no—
1213C22—62no—
1214C22—64no—
1215C22—64no—
1216C22—62no—
1217C22—62no—
1218C22—64no—
1219C22—92no—
1220C22—94no—
1221C22—182no—
1222C22—181no—
1223C22—182no—
1224C22—181no—
1225C22—181no—
1226C22—181no—
1227C22—181no—
1228C22—244no—
1229C22—364no—
1230C22—368no—
1231C22—728no—
1232C22C2×#381112yes—
1233C22C23×D3211yescharacteristic
1234C4—22no—
1235C4—64no—
1236C4—62no—
1237C4—62no—
1238C4—62no—
1239C4—94no—
1240C4—181no—
1241C4—181no—
1242C4C2×#381112yes—
1243C4C2×#381112yes—
1244C3—21no—
1245C3#8633111yescharacteristic, complemented
1246C3#8637911yescharacteristic, complemented
1247C2—22no—
1248C2—42no—
1249C2—124no—
1250C2—122no—
1251C2—182no—
1252C2—184no—
1253C2—361no—
1254C2#1059669211yescharacteristic
1255C2#1059669811yescharacteristic
1256C2C22×#381111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×#41C22
hypercenterC2×#41D32
hypocenterC32#3488
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#41×C3⋊D3C2semidirect
2. C2×#64307C2semidirect
3. C3×#5833C2semidirect
4. C3×#5830C2semidirect
5. #10595431C2semidirect
6. #10595362C2semidirect
7. #10595307C2semidirect
8. #10595297C2semidirect
9. #10595292C2semidirect
10. #10595164C2semidirect
11. #10595082C2semidirect
12. #10595081C2semidirect
13. #10595034C2semidirect
14. C2×#63916C2semidirect
15. #10594990C2semidirect
16. #10594923C2semidirect
17. #10594922C2semidirect
20. C2×C32×#41C22semidirect
22. C2×#3832C22semidirect
23. C2×Q8×C3⋊D3C22semidirect
24. C2×#3830C22semidirect
25. C2×#3830C22semidirect
26. C2×D4×C3⋊D3C22semidirect
27. C2×D4×C3⋊D3C22semidirect
29. C2×#3828C22semidirect
30. C22×C4×C3⋊D3C22semidirect
31. C22×C4×C3⋊D3C22semidirect
32. C2×C3×#235C22semidirect
33. C22×C3×D12C22semidirect
34. C2×#3811C22semidirect
35. C2×D3×#67C22semidirect
36. C22×#626C22semidirect
38. C2×#3802C22semidirect
39. C2×D3×D12C22semidirect
40. C2×#3796C22semidirect
41. C2×#3795C22semidirect
42. C3×#947C22semidirect
43. C3×#946C22semidirect
44. C3×#940C22semidirect
45. C3×#939C22semidirect
46. C3×#938C22semidirect
47. C3×#937C22semidirect
48. C3×#930C22semidirect
49. C3×#930C22semidirect
50. C3×#930C22semidirect
51. C3×#926C22semidirect
52. C2×C3×C4⋊Dic3C22semidirect
53. C3×#924C22semidirect
54. #63983C22semidirect
55. #63981C22semidirect
56. #63981C22semidirect
57. #63980C22semidirect
58. #63979C22semidirect
59. #67⋊Dic3C22semidirect
60. #63971C22semidirect
61. #63962C22semidirect
62. C2×(C2×D3)⋊Dic3C22semidirect
63. #63958C22semidirect
64. #63952C22semidirect
65. #63923C22semidirect
66. #63921C22semidirect
67. #63916C22semidirect
68. #63916C22semidirect
69. #63916C22semidirect
70. #63916C22semidirect
71. #63916C22semidirect
72. #63916C22semidirect
73. #63913C22semidirect
74. #63912C22semidirect
75. #63910C22semidirect
76. C4×#626C22semidirect
77. C4×#626C22semidirect
78. #63900C22semidirect
79. #63896C22semidirect
80. #63894C22semidirect
81. #63881C22semidirect
82. #63871C22semidirect
83. #63871C22semidirect
84. #63853C22semidirect
85. #63849C22semidirect
86. #63844C22semidirect
94. #5833D3semidirect
95. #5830D3semidirect
144. #3828D4semidirect
210. C2×C3×#41C2×D3semidirect
211. C2×C3×#41C2×D3semidirect
254. C2×#235C2×D3semidirect
257. C22×D12C2×D3semidirect
277. #947C2×D3semidirect
280. #946C2×D3semidirect
283. #940C2×D3semidirect
287. #939C2×D3semidirect
295. #938C2×D3semidirect
300. #937C2×D3semidirect
303. #930C2×D3semidirect
304. #930C2×D3semidirect
305. #930C2×D3semidirect
310. #926C2×D3semidirect
311. C2×C4⋊Dic3C2×D3semidirect
312. #924C2×D3semidirect
377. C2×C32×C4C2×D4semidirect
383. #638C2×D4semidirect
390. C4⋊(C3⋊D3)C2×D4semidirect
397. C4×C3⋊D3C2×D4semidirect
399. #634C2×D4semidirect
660. C2×C3⋊D3H(5,𝔽2)semidirect
689. C2×#41D32semidirect
825. C2×C3×C4D3×D4semidirect
826. C2×C3×C4D3×D4semidirect
1111. C32#3488semidirect
1176. C2×C4#3811semidirect
1245. C3#86331semidirect
1246. C3#86379semidirect

Maximal subgroups

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

subgroupindex
C2×#41×C3⋊D32
C2×#643072
C3×#58332
C3×#58302
#105954312
#105953622
#105953072
#105952972
#105952922
#105951642
#105950822
#105950812
#105950342
C2×#639162
#105949902
#105949232
#105949222
#863793
#863313