Finite Group Databasebeta

← #11904661

Subgroups — #11904661

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
1C22×#3828C211yesmaximal, characteristic, complemented
2C2×#64307C211yesmaximal, characteristic, complemented
3C3×#5791C211yesmaximal, characteristic, complemented
4C2×C3×#930C211yesmaximal, characteristic, complemented
5#10595526C214yesmaximal, complemented
6#10595082C212yesmaximal, complemented
7#10595081C212yesmaximal, complemented
8#10595078C212yesmaximal, complemented
9#10595077C214yesmaximal, complemented
10#10595074C212yesmaximal, complemented
11#10595043C211yesmaximal, characteristic, complemented
12#10595042C211yesmaximal, characteristic, complemented
13#10594990C211yesmaximal, characteristic, complemented
14#10594923C212yesmaximal, complemented
15#10594922C212yesmaximal, complemented
16#10594919C212yesmaximal, complemented
17#10594918C212yesmaximal, complemented
18#86041—31nomaximal
19#85949—31nomaximal
20C23×C32×C4C2211yescharacteristic, complemented
21C22×#638C2212yescomplemented
22C2×#3828—28no—
23C2×#3828C2211yescharacteristic
24C2×#3828C2212yescomplemented
25C2×#3828C2211yescharacteristic, complemented
26C2×#3828C2212yescomplemented
27C2×#3828C2211yescharacteristic, complemented
28C2×#3828C2211yescharacteristic, complemented
29C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
30C22×C4×C3⋊D3C2212yescomplemented
31C22×#634C2211yescharacteristic, complemented
32C22×C3×#67C2212yescomplemented
33C2×C3×#235C2211yescharacteristic, complemented
34C22×C3×D12C2211yescharacteristic, complemented
35C2×#3811C2214yescomplemented
36C2×D3×#67C2214yescomplemented
37#64307—28no—
38C2×#3802C2212yescomplemented
39C2×D3×D12C2212yescomplemented
40C2×#3796C2212yescomplemented
41C2×#3795C2212yescomplemented
42C3×#953C2212yescomplemented
43C3×#930C2212yescomplemented
44C3×#930C2212yescomplemented
45C3×#930C2211yescharacteristic, complemented
46C3×#930C2212yescomplemented
47C3×#930C2211yescharacteristic, complemented
48C3×#930C2212yescomplemented
49C3×#929C2212yescomplemented
50C3×C4×#67C2212yescomplemented
51C3×C4×#67C2212yescomplemented
52C2×C3×(C2×D3)⋊C4C2212yescomplemented
53C3×#926C2211yescharacteristic, complemented
54C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
55C3×#924C2211yescharacteristic, complemented
56C3×#924C2211yescharacteristic, complemented
57#63983C2214yescomplemented
58#63981C2214yescomplemented
59#63980C2214yescomplemented
60#63979C2214yescomplemented
61#63978C2214yescomplemented
62#63977C2214yescomplemented
63#67⋊Dic3C2214yescomplemented
64#63971C2214yescomplemented
65#63958C2214yescomplemented
66#63952C2214yescomplemented
67#63923C2214yescomplemented
68#63921C2214yescomplemented
69#63916C2212yescomplemented
70#63916C2212yescomplemented
71#63916C2212yescomplemented
72#63913C2214yescomplemented
73#63912C2214yescomplemented
74#63911C2212yescomplemented
75#63910C2214yescomplemented
76#63909C2212yescomplemented
77#63900C2212yescomplemented
78#63896C2214yescomplemented
79#63894C2212yescomplemented
80#63881C2214yescomplemented
81#63871C2212yescomplemented
82#63860C2212yescomplemented
83#63857C2212yescomplemented
84#63853C2214yescomplemented
85#63849C2212yescomplemented
86#63844C2212yescomplemented
87C2×#1009—31no—
88C2×#1004—31no—
89C22×#235—31no—
90C22×#235—31no—
91C22×#235—61no—
92C3×#525—31no—
93C2×C3×#121—31no—
94#5833—31no—
95#5805—31no—
96D4×#67—34no—
97#5791D311yescharacteristic, complemented
98C2×#930D311yescharacteristic, complemented
99#5654—34no—
100#5629—32no—
101#5627—32no—
102#5612—32no—
103#5609—32no—
104#5608—32no—
105#5607—32no—
106#5607—32no—
107#5606—32no—
108D3×#121—32no—
109D3×#121—32no—
110#5599—32no—
111#5598—32no—
112#5590—34no—
113#5553—32no—
114#5552—32no—
115#5550—32no—
116D4×D12—32no—
117#5525—31no—
118#5523—31no—
119#5510—31no—
120#5504—31no—
121#5490—34no—
122C24×C32C2311yescharacteristic
123C23×C3⋊D3C2312yes—
124C23×C3×D3C2312yes—
125C22×D32C2314yes—
126C22×C32×C4—24no—
127C22×C32×C4C2311yescharacteristic
128C22×C32×C4C2311yescharacteristic
129C22×C32×C4C2311yescharacteristic
130C22×C32×C4C2311yescharacteristic
131C22×C32×C4C2311yescharacteristic
132C22×C32×C4C2311yescharacteristic
133C2×#638—28no—
134C2×#638C2312yes—
135C2×#638C2312yes—
136C2×#638C2312yes—
137C2×#638C2312yes—
138C22×C3⋊Dic3C2312yes—
139#3828—24no—
140#3828—28no—
141#3828—24no—
142#3828—28no—
143#3828—24no—
144#3828D418yescomplemented
145C2×C4⋊(C3⋊D3)—24no—
146C2×C4⋊(C3⋊D3)C2311yescharacteristic
147C2×C4⋊(C3⋊D3)C2312yes—
148C2×C4⋊(C3⋊D3)C2311yescharacteristic
149C2×C4×C3⋊D3—28no—
150C2×C4×C3⋊D3C2312yes—
151C2×C4×C3⋊D3C2312yes—
152C2×C4×C3⋊D3C2312yes—
153C2×C4×C3⋊D3C2312yes—
154C2×#634—24no—
155C2×#634C2311yescharacteristic
156C2×#634C2312yes—
157C2×#634C2311yescharacteristic
158C2×C3×#67—44no—
159C2×C3×#67C2312yes—
160C2×C3×#67C2312yes—
161C2×C3×#67C2314yes—
162C2×C3×#67C2312yes—
163C2×C3×#67C2314yes—
164C22×C3×Dic3C2312yes—
165C3×#235—24no—
166C2×C3×D12—24no—
167C2×C3×D12C2312yes—
168C2×C3×D12C2312yes—
169C2×C3×D12C2311yescharacteristic
170C2×C3×C4×D3C2312yes—
171C2×C3×Dic6C2311yescharacteristic
172#3811—48no—
173D3×#67—216no—
174C2×#626C2314yes—
175C2×#626C2314yes—
176C2×#626C2314yes—
177C2×#626C2314yes—
178C2×#625C2314yes—
179C2×#624C2314yes—
180C2×D3×Dic3C2314yes—
181#3802—28no—
182D3×D12—28no—
183#3796—28no—
184#3795—28no—
185C3×#217C2312yes—
186C3×#217C2312yes—
187C3×#217C2312yes—
188C3×(C2×D3)⋊C4C2314yes—
189C3×(C2×D3)⋊C4C2314yes—
190C3×(C2×D3)⋊C4C2312yes—
191C3×(C2×D3)⋊C4C2312yes—
192C3×C4⋊Dic3C2311yescharacteristic
193C3×C4⋊Dic3C2311yescharacteristic
194C3×C4⋊Dic3C2312yes—
195C3×C4⋊Dic3C2312yes—
196C3×Dic3⋊C4C2312yes—
197C3×Dic3⋊C4C2312yes—
198C3×C4×Dic3C2312yes—
199#3724C2314yes—
200Dic3⋊Dic3C2314yes—
201#3722C2314yes—
202#3722C2314yes—
203(C2×D3)⋊Dic3C2314yes—
204(C2×D3)⋊Dic3C2314yes—
205(C2×D3)⋊Dic3C2314yes—
206Dic32C2314yes—
207#3488—91noSylow
208C2×C3×#41—31no—
209C22×C3×D4—32no—
210C22×C3×D4—31no—
211C23×C3×C4—21no—
212C23×C3×C4C2×D311yescharacteristic, complemented
213C23×C3×C4C2×D311yescharacteristic, complemented
214C22×#67—32no—
215C22×#67—32no—
216C22×#67—34no—
217C22×#67—62no—
218C22×#67C2×D312yescomplemented
219#1009—68no—
220C2×#239—32no—
221#1004—68no—
222C2×#237—32no—
223C2×#237—32no—
224C2×D3×D4—34no—
225C2×D3×D4—34no—
226C2×D3×D4—34no—
227C2×D3×D4—32no—
228C2×D3×D4—32no—
229C2×D3×D4—32no—
230C2×#235—31no—
231C2×#235—31no—
232C2×#235—32no—
233C2×#235—32no—
234C2×#235—31no—
235C2×#235—31no—
236C2×#235—31no—
237C2×#235—31no—
238C2×#235—31no—
239C2×#235—32no—
240C2×#235—32no—
241C2×#235—31no—
242C2×#235—32no—
243C2×#235—61no—
244C2×#235—62no—
245C2×#235—61no—
246C2×#235—62no—
247C2×#235—61no—
248C2×#235—61no—
249C2×#235—68no—
250C2×#235—68no—
251C2×#235—616no—
252C2×#235C2×D311yescharacteristic, complemented
253C22×D12—31no—
254C22×D12—31no—
255C22×D12—32no—
256C22×D12—61no—
257C22×D12C2×D311yescharacteristic, complemented
258C22×C4×D3—32no—
259C22×C4×D3—32no—
260C22×C4×D3—62no—
261C22×Dic6—31no—
262C22×Dic6—31no—
263C22×Dic6—61no—
264C3×#123—32no—
265C3×C22⋊Q8—31no—
266C3×C22⋊Q8—31no—
267C3×#121—32no—
268C3×#121—32no—
269C3×#121—32no—
270C3×#121—32no—
271C3×#121—31no—
272C3×#121—31no—
273C3×#120—32no—
274C3×C4×D4—32no—
275C3×C4×D4—32no—
276C3×#117—31no—
277C2×C3×C4⋊C4—31no—
278C2×C3×C22⋊C4—32no—
279#953—34no—
280#953C2×D312yescomplemented
281#946—32no—
282#940—34no—
283#940—34no—
284#940—32no—
285#939—34no—
286#939—34no—
287#939—34no—
288#939—34no—
289#938—34no—
290#938—32no—
291#938—32no—
292#938—32no—
293#937—34no—
294#937—34no—
295#937—34no—
296#936—32no—
297D4×Dic3—34no—
298#930—34no—
299#930—32no—
300#930C2×D312yescomplemented
301#930C2×D312yescomplemented
302#930C2×D312yescomplemented
303#930C2×D312yescomplemented
304#930C2×D311yescharacteristic, complemented
305#930C2×D311yescharacteristic, complemented
306#929C2×D312yescomplemented
307C4×#67—34no—
308C4×#67C2×D312yescomplemented
309C4×#67C2×D312yescomplemented
310C2×(C2×D3)⋊C4C2×D312yescomplemented
311#926C2×D311yescharacteristic, complemented
312C2×C4⋊Dic3C2×D311yescharacteristic, complemented
313#924—32no—
314#924C2×D311yescharacteristic, complemented
315#924C2×D311yescharacteristic, complemented
316#897—32no—
317#897—32no—
318#896—34no—
319#895—32no—
320#895—32no—
321#895—32no—
322#895—32no—
323#895—34no—
324#894—34no—
325#893—34no—
326#893—32no—
327#892—32no—
328#892—32no—
329D3×C4⋊C4—32no—
330D3×C4⋊C4—32no—
331#887—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—34no—
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—
350#875—32no—
351#874—32no—
352C4×D12—32no—
353C4×Dic6—32no—
354C23×C32—22no—
355C23×C32—22no—
356C23×C32—41no—
357C23×C32C2411yescharacteristic
358C23×C32C2411yescharacteristic
359C23×C32C2411yescharacteristic
360C22×C3⋊D3—24no—
361C22×C3⋊D3—24no—
362C22×C3⋊D3—42no—
363C22×C3⋊D3C2412yes—
364C22×C3⋊D3C2412yes—
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—
373C2×C32×C4—22no—
374C2×C32×C4—22no—
375C2×C32×C4—22no—
376C2×C32×C4—22no—
377C2×C32×C4—22no—
378C2×C32×C4C2×D414yescomplemented
379C2×C32×C4C2411yescharacteristic
380C2×C32×C4C2411yescharacteristic
381C2×C32×C4C2411yescharacteristic
382C2×C32×C4C2411yescharacteristic
383#638—24no—
384#638—24no—
385#638—24no—
386#638C2×D418yescomplemented
387C2×C3⋊Dic3—24no—
388C2×C3⋊Dic3C2412yes—
389C2×C3⋊Dic3C2412yes—
390C4⋊(C3⋊D3)—24no—
391C4⋊(C3⋊D3)—22no—
392C4⋊(C3⋊D3)C2×D414yescomplemented
393C4×C3⋊D3—24no—
394C4×C3⋊D3—24no—
395C4×C3⋊D3—24no—
396C4×C3⋊D3C2×D418yescomplemented
397#634—22no—
398#634—24no—
399#634C2×D414yescomplemented
400C3×#67—24no—
401C3×#67—24no—
402C3×#67—28no—
403C3×#67—44no—
404C3×#67—42no—
405C2×C3×Dic3—42no—
406C2×C3×Dic3C2412yes—
407C2×C3×Dic3C2414yes—
408C2×C3×Dic3C2412yes—
409C2×C3×Dic3C2412yes—
410C3×D12—24no—
411C3×D12—24no—
412C3×D12—22no—
413C3×C4×D3—24no—
414C3×Dic6—22no—
415#626—28no—
416#626—44no—
417#626—44no—
418#626—44no—
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—92no—
429D42—94no—
430#537—91no—
431#537—92no—
432#535—91no—
433#535—92no—
434#525—31no—
435#525—92no—
436C2×#121—31no—
437C2×#121—92no—
438#520—91no—
439C24×C3—21no—
440C24×C3—32no—
441C24×C3C22×D311yescharacteristic
442C24×C3C22×D311yescharacteristic
443C23×D3—32no—
444C23×D3—32no—
445C23×D3—34no—
446C23×D3—34no—
447C23×D3—62no—
448C23×D3C22×D312yes—
449C3×#41—64no—
450C2×C3×Q8—31no—
451C2×C3×D4—34no—
452C2×C3×D4—32no—
453C2×C3×D4—32no—
454C2×C3×D4—32no—
455C2×C3×D4—34no—
456C2×C3×D4—32no—
457C2×C3×D4—31no—
458C2×C3×D4—32no—
459C2×C3×D4—64no—
460C2×C3×D4—124no—
461C22×C3×C4—28no—
462C22×C3×C4—24no—
463C22×C3×C4—24no—
464C22×C3×C4—21no—
465C22×C3×C4—21no—
466C22×C3×C4—21no—
467C22×C3×C4—21no—
468C22×C3×C4—21no—
469C22×C3×C4—21no—
470C22×C3×C4—32no—
471C22×C3×C4—32no—
472C22×C3×C4C22×D311yescharacteristic
473C22×C3×C4C22×D311yescharacteristic
474C22×C3×C4C22×D311yescharacteristic
475C22×C3×C4C22×D311yescharacteristic
476C22×C3×C4C22×D311yescharacteristic
477C22×C3×C4C22×D311yescharacteristic
478C22×C3×C4C22×D311yescharacteristic
479C22×C3×C4C22×D311yescharacteristic
480C22×C3×C4C22×D311yescharacteristic
481C22×C3×C4C22×D311yescharacteristic
482C22×C3×C4C22×D311yescharacteristic
483C22×C3×C4C22×D311yescharacteristic
484C2×#67—32no—
485C2×#67—32no—
486C2×#67—32no—
487C2×#67—32no—
488C2×#67—32no—
489C2×#67—32no—
490C2×#67—32no—
491C2×#67—32no—
492C2×#67—34no—
493C2×#67—34no—
494C2×#67—34no—
495C2×#67—34no—
496C2×#67—34no—
497C2×#67—34no—
498C2×#67—44no—
499C2×#67—62no—
500C2×#67—62no—
501C2×#67—62no—
502C2×#67—62no—
503C2×#67—616no—
504C2×#67—68no—
505C2×#67—68no—
506C2×#67—616no—
507C2×#67C22×D314yes—
508C2×#67C22×D312yes—
509C2×#67C22×D312yes—
510C2×#67C22×D314yes—
511C2×#67C22×D312yes—
512C22×Dic3—32no—
513C22×Dic3—32no—
514C22×Dic3—34no—
515C22×Dic3—62no—
516C22×Dic3C22×D312yes—
517#239—68no—
518#237—68no—
519#237—68no—
520D3×D4—68no—
521D3×D4—68no—
522D3×D4—68no—
523D3×D4—616no—
524D3×D4—128no—
525D3×D4—128no—
526#235—24no—
527#235—38no—
528#235—38no—
529#235—68no—
530#235—68no—
531#235—64no—
532#235—64no—
533#235—68no—
534#235—68no—
535#235—64no—
536#235—64no—
537#235—68no—
538#235—68no—
539#235—616no—
540#235—68no—
541#235—616no—
542#235—68no—
543#235—68no—
544#235—64no—
545#235—64no—
546C2×D12—24no—
547C2×D12—31no—
548C2×D12—31no—
549C2×D12—34no—
550C2×D12—31no—
551C2×D12—32no—
552C2×D12—32no—
553C2×D12—31no—
554C2×D12—34no—
555C2×D12—34no—
556C2×D12—34no—
557C2×D12—61no—
558C2×D12—62no—
559C2×D12—61no—
560C2×D12—68no—
561C2×D12—64no—
562C2×D12—64no—
563C2×D12—68no—
564C2×D12C22×D312yes—
565C2×D12C22×D312yes—
566C2×D12C22×D311yescharacteristic
567C2×C4×D3—32no—
568C2×C4×D3—32no—
569C2×C4×D3—34no—
570C2×C4×D3—32no—
571C2×C4×D3—32no—
572C2×C4×D3—32no—
573C2×C4×D3—32no—
574C2×C4×D3—32no—
575C2×C4×D3—32no—
576C2×C4×D3—34no—
577C2×C4×D3—34no—
578C2×C4×D3—62no—
579C2×C4×D3—62no—
580C2×C4×D3—62no—
581C2×C4×D3—62no—
582C2×C4×D3—68no—
583C2×C4×D3—68no—
584C2×C4×D3—616no—
585C2×C4×D3C22×D312yes—
586C2×Dic6—31no—
587C2×Dic6—31no—
588C2×Dic6—31no—
589C2×Dic6—32no—
590C2×Dic6—32no—
591C2×Dic6—31no—
592C2×Dic6—61no—
593C2×Dic6—61no—
594C2×Dic6—62no—
595C2×Dic6—64no—
596C2×Dic6—64no—
597C2×Dic6—68no—
598C2×Dic6C22×D311yescharacteristic
599C3×C4⋊C4—32no—
600C3×C4⋊C4—31no—
601C3×C4⋊C4—32no—
602C3×C4⋊C4—31no—
603C3×C4⋊C4—32no—
604C3×C4⋊C4—32no—
605C3×C22⋊C4—32no—
606C3×C22⋊C4—32no—
607C3×C22⋊C4—32no—
608C3×C22⋊C4—34no—
609C3×C22⋊C4—32no—
610C3×C22⋊C4—34no—
611C3×C22⋊C4—32no—
612C3×C42—32no—
613#217—34no—
614#217—34no—
615#217—34no—
616#217C22×D312yes—
617#217C22×D312yes—
618#217C22×D312yes—
619(C2×D3)⋊C4—34no—
620(C2×D3)⋊C4—34no—
621(C2×D3)⋊C4—34no—
622(C2×D3)⋊C4—34no—
623(C2×D3)⋊C4—34no—
624(C2×D3)⋊C4—34no—
625(C2×D3)⋊C4—34no—
626(C2×D3)⋊C4C22×D312yes—
627(C2×D3)⋊C4C22×D314yes—
628(C2×D3)⋊C4C22×D312yes—
629(C2×D3)⋊C4C22×D314yes—
630C4⋊Dic3—34no—
631C4⋊Dic3C22×D312yes—
632C4⋊Dic3C22×D311yescharacteristic
633C4⋊Dic3C22×D312yes—
634C4⋊Dic3C22×D311yescharacteristic
635Dic3⋊C4—34no—
636Dic3⋊C4—34no—
637Dic3⋊C4—34no—
638Dic3⋊C4C22×D312yes—
639Dic3⋊C4C22×D312yes—
640C4×Dic3—34no—
641C4×Dic3—34no—
642C4×Dic3C22×D312yes—
643C22×C32—21no—
644C22×C32—21no—
645C22×C32—21no—
646C22×C32—21no—
647C22×C32—21no—
648C22×C32—21no—
649C22×C32—21no—
650C22×C32—44no—
651C22×C32C22×D412yes—
652C22×C32H(5,𝔽2)12yescomplemented
653C22×C32C2511yescharacteristic
654C2×C3⋊D3—22no—
655C2×C3⋊D3—22no—
656C2×C3⋊D3—22no—
657C2×C3⋊D3—22no—
658C2×C3⋊D3—22no—
659C2×C3⋊D3—48no—
660C2×C3⋊D3C22×D414yes—
661C2×C3×D3—24no—
662C2×C3×D3—22no—
663C2×C3×D3—22no—
664C2×C3×D3—24no—
665C2×C3×D3—24no—
666C2×C3×D3—22no—
667C2×C3×D3—84no—
668D32—88no—
669C32×C4—21no—
670C32×C4—21no—
671C32×C4C22×D412yes—
672C32×C4C22×D412yes—
673C3⋊Dic3—22no—
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—91no—
689C2×#41—188no—
690C22×Q8—91no—
691C22×D4—32no—
692C22×D4—31no—
693C22×D4—92no—
694C22×D4—92no—
695C22×D4—94no—
696C22×D4—94no—
697C22×D4—92no—
698C22×D4—91no—
699C23×C4—92no—
700C23×C4D3211yescharacteristic, complemented
701#127—92no—
702#127—94no—
703#124—92no—
704#124—94no—
705#123—32no—
706#123—94no—
707C22⋊Q8—31no—
708C22⋊Q8—31no—
709C22⋊Q8—94no—
710C22⋊Q8—92no—
711C22⋊Q8—92no—
712#121—32no—
713#121—32no—
714#121—32no—
715#121—32no—
716#121—31no—
717#121—31no—
718#121—94no—
719#121—94no—
720#121—94no—
721#121—94no—
722#121—92no—
723#121—92no—
724#121—92no—
725#121—92no—
726#121—94no—
727#121—94no—
728#120—32no—
729#120—94no—
730#120—94no—
731#120—94no—
732#120—94no—
733C4×Q8—92no—
734C4×D4—32no—
735C4×D4—32no—
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—32no—
745C2×C22⋊C4—94no—
746C23×C3—24no—
747C23×C3—22no—
748C23×C3—22no—
749C23×C3—22no—
750C23×C3—22no—
751C23×C3—21no—
752C23×C3—21no—
753C23×C3—21no—
754C23×C3—34no—
755C23×C3—32no—
756C23×C3—42no—
757C23×C3—41no—
758C23×C3—41no—
759C23×C3—42no—
760C23×C3—64no—
761C23×C3—122no—
762C23×C3—122no—
763C23×C3C23×D311yescharacteristic
764C23×C3C23×D311yescharacteristic
765C23×C3C23×D311yescharacteristic
766C23×C3C23×D311yescharacteristic
767C23×C3C23×D311yescharacteristic
768C23×C3C23×D311yescharacteristic
769C22×D3—24no—
770C22×D3—32no—
771C22×D3—32no—
772C22×D3—32no—
773C22×D3—32no—
774C22×D3—42no—
775C22×D3—42no—
776C22×D3—62no—
777C22×D3—62no—
778C22×D3—68no—
779C22×D3—68no—
780C22×D3—64no—
781C22×D3—64no—
782C22×D3—68no—
783C22×D3—64no—
784C22×D3—64no—
785C22×D3—124no—
786C22×D3—124no—
787C22×D3—124no—
788C22×D3—124no—
789C22×D3—124no—
790C22×D3—122no—
791C22×D3—122no—
792C22×D3—124no—
793C22×D3C23×D314yes—
794C22×D3C23×D312yes—
795C3×Q8—62no—
796C3×D4—64no—
797C3×D4—64no—
798C3×D4—68no—
799C3×D4—62no—
800C3×D4—64no—
801C3×D4—64no—
802C3×D4—122no—
803C3×D4—124no—
804C2×C3×C4—24no—
805C2×C3×C4—24no—
806C2×C3×C4—24no—
807C2×C3×C4—24no—
808C2×C3×C4—24no—
809C2×C3×C4—22no—
810C2×C3×C4—22no—
811C2×C3×C4—22no—
812C2×C3×C4—22no—
813C2×C3×C4—22no—
814C2×C3×C4—22no—
815C2×C3×C4—22no—
816C2×C3×C4—22no—
817C2×C3×C4—22no—
818C2×C3×C4—22no—
819C2×C3×C4—21no—
820C2×C3×C4—21no—
821C2×C3×C4—21no—
822C2×C3×C4—21no—
823C2×C3×C4—24no—
824C2×C3×C4—32no—
825C2×C3×C4—34no—
826C2×C3×C4—32no—
827C2×C3×C4—32no—
828C2×C3×C4—64no—
829C2×C3×C4—122no—
830C2×C3×C4D3×D414yescomplemented
831C2×C3×C4D3×D414yescomplemented
832C2×C3×C4C23×D311yescharacteristic
833C2×C3×C4C23×D311yescharacteristic
834C2×C3×C4C23×D311yescharacteristic
835C2×C3×C4C23×D311yescharacteristic
836C2×C3×C4C23×D311yescharacteristic
837C2×C3×C4C23×D311yescharacteristic
838C2×C3×C4C23×D311yescharacteristic
839C2×C3×C4C23×D311yescharacteristic
840#67—24no—
841#67—28no—
842#67—24no—
843#67—38no—
844#67—38no—
845#67—44no—
846#67—42no—
847#67—68no—
848#67—68no—
849#67—68no—
850#67—68no—
851#67—64no—
852#67—64no—
853#67—64no—
854#67—64no—
855#67—68no—
856#67—68no—
857#67—68no—
858#67—64no—
859#67—64no—
860#67—124no—
861#67—124no—
862#67—124no—
863C2×Dic3—32no—
864C2×Dic3—32no—
865C2×Dic3—32no—
866C2×Dic3—32no—
867C2×Dic3—42no—
868C2×Dic3—62no—
869C2×Dic3—62no—
870C2×Dic3—68no—
871C2×Dic3—64no—
872C2×Dic3—64no—
873C2×Dic3—68no—
874C2×Dic3C23×D312yes—
875C2×Dic3C23×D314yes—
876C2×Dic3C23×D312yes—
877C2×Dic3C23×D312yes—
878D12—24no—
879D12—24no—
880D12—22no—
881D12—34no—
882D12—34no—
883D12—64no—
884D12—64no—
885D12—64no—
886D12—68no—
887D12—64no—
888D12—68no—
889D12—62no—
890D12—62no—
891D12—124no—
892D12—124no—
893D12—124no—
894C4×D3—24no—
895C4×D3—38no—
896C4×D3—38no—
897C4×D3—68no—
898C4×D3—64no—
899C4×D3—64no—
900C4×D3—68no—
901C4×D3—64no—
902C4×D3—64no—
903C4×D3—68no—
904C4×D3—68no—
905C4×D3—68no—
906C4×D3—64no—
907C4×D3—64no—
908C4×D3—124no—
909C4×D3—124no—
910Dic6—22no—
911Dic6—34no—
912Dic6—34no—
913Dic6—64no—
914Dic6—64no—
915Dic6—64no—
916Dic6—68no—
917Dic6—64no—
918Dic6—62no—
919Dic6—62no—
920C2×C32—22no—
921C2×C32—22no—
922C2×C32—41no—
923C2×C32C23×D411yescharacteristic
924C2×C32C2×H(5,𝔽2)11yescharacteristic
925C2×C32#58511yescharacteristic
926C3⋊D3—24no—
927C3⋊D3—42no—
928C3×D3—42no—
929C3×D3—44no—
930C24—32no—
931C24—94no—
932C24—92no—
933C24C2×D3211yescharacteristic
934#41—64no—
935#41—98no—
936#41—188no—
937#41—188no—
938#41—184no—
939#41—184no—
940#41—188no—
941#41—188no—
942#41—184no—
943C2×Q8—31no—
944C2×Q8—91no—
945C2×Q8—92no—
946C2×Q8—91no—
947C2×Q8—184no—
948C2×D4—32no—
949C2×D4—34no—
950C2×D4—32no—
951C2×D4—32no—
952C2×D4—34no—
953C2×D4—32no—
954C2×D4—31no—
955C2×D4—32no—
956C2×D4—64no—
957C2×D4—94no—
958C2×D4—94no—
959C2×D4—94no—
960C2×D4—94no—
961C2×D4—92no—
962C2×D4—94no—
963C2×D4—92no—
964C2×D4—92no—
965C2×D4—92no—
966C2×D4—91no—
967C2×D4—92no—
968C2×D4—91no—
969C2×D4—124no—
970C2×D4—184no—
971C2×D4—188no—
972C2×D4—188no—
973C2×D4—1816no—
974C2×D4—188no—
975C2×D4—368no—
976C22×C4—24no—
977C22×C4—32no—
978C22×C4—32no—
979C22×C4—94no—
980C22×C4—94no—
981C22×C4—92no—
982C22×C4—92no—
983C22×C4—92no—
984C22×C4—92no—
985C22×C4—92no—
986C22×C4—188no—
987C22×C4C2×D3211yescharacteristic
988C22×C4C2×D3211yescharacteristic
989C22×C4C2×D3211yescharacteristic
990C22×C4C2×D3211yescharacteristic
991C22×C4C2×D3211yescharacteristic
992C22×C4C2×D3211yescharacteristic
993C4⋊C4—32no—
994C4⋊C4—32no—
995C4⋊C4—31no—
996C4⋊C4—31no—
997C4⋊C4—32no—
998C4⋊C4—32no—
999C4⋊C4—94no—
1000C4⋊C4—94no—
1001C22⋊C4—32no—
1002C22⋊C4—32no—
1003C22⋊C4—32no—
1004C22⋊C4—34no—
1005C22⋊C4—34no—
1006C22⋊C4—32no—
1007C22⋊C4—32no—
1008C22⋊C4—94no—
1009C22⋊C4—94no—
1010C22⋊C4—94no—
1011C22⋊C4—94no—
1012C22⋊C4—94no—
1013C42—32no—
1014C42—94no—
1015C22×C3—22no—
1016C22×C3—22no—
1017C22×C3—21no—
1018C22×C3—21no—
1019C22×C3—21no—
1020C22×C3—21no—
1021C22×C3—21no—
1022C22×C3—21no—
1023C22×C3—21no—
1024C22×C3—21no—
1025C22×C3—22no—
1026C22×C3—21no—
1027C22×C3—21no—
1028C22×C3—21no—
1029C22×C3—21no—
1030C22×C3—21no—
1031C22×C3—21no—
1032C22×C3—22no—
1033C22×C3—22no—
1034C22×C3—21no—
1035C22×C3—41no—
1036C22×C3—41no—
1037C22×C3—41no—
1038C22×C3—41no—
1039C22×C3—44no—
1040C22×C3—44no—
1041C22×C3—48no—
1042C22×C3—64no—
1043C22×C3—62no—
1044C22×C3—62no—
1045C22×C3—64no—
1046C22×C3—64no—
1047C22×C3—62no—
1048C22×C3—244no—
1049C22×C3C2×D3×D412yes—
1050C22×C3C2×D3×D412yes—
1051C22×C3#100412yescomplemented
1052C22×C3#100912yescomplemented
1053C22×C3C24×D311yescharacteristic
1054C22×C3C24×D311yescharacteristic
1055C2×D3—22no—
1056C2×D3—24no—
1057C2×D3—24no—
1058C2×D3—22no—
1059C2×D3—24no—
1060C2×D3—22no—
1061C2×D3—34no—
1062C2×D3—34no—
1063C2×D3—64no—
1064C2×D3—62no—
1065C2×D3—62no—
1066C2×D3—62no—
1067C2×D3—62no—
1068C2×D3—64no—
1069C2×D3—62no—
1070C2×D3—62no—
1071C2×D3—62no—
1072C2×D3—62no—
1073C2×D3—62no—
1074C2×D3—62no—
1075C2×D3—84no—
1076C2×D3—122no—
1077C2×D3—122no—
1078C2×D3—122no—
1079C2×D3—122no—
1080C2×D3—128no—
1081C2×D3—128no—
1082C2×D3—1216no—
1083C2×D3—248no—
1084C2×D3—248no—
1085C3×C4—22no—
1086C3×C4—22no—
1087C3×C4—21no—
1088C3×C4—21no—
1089C3×C4—21no—
1090C3×C4—21no—
1091C3×C4—22no—
1092C3×C4—22no—
1093C3×C4—62no—
1094C3×C4—62no—
1095C3×C4—64no—
1096C3×C4—62no—
1097C3×C4C2×D3×D412yes—
1098C3×C4C2×D3×D412yes—
1099C3×C4C2×D3×D412yes—
1100C3×C4C2×D3×D412yes—
1101Dic3—22no—
1102Dic3—24no—
1103Dic3—22no—
1104Dic3—22no—
1105Dic3—34no—
1106Dic3—34no—
1107Dic3—64no—
1108Dic3—64no—
1109Dic3—62no—
1110Dic3—62no—
1111C32#348811yescharacteristic, complemented, Sylow
1112C23—22no—
1113C23—22no—
1114C23—32no—
1115C23—34no—
1116C23—41no—
1117C23—64no—
1118C23—92no—
1119C23—92no—
1120C23—122no—
1121C23—122no—
1122C23—184no—
1123C23—188no—
1124C23—184no—
1125C23—362no—
1126C23—364no—
1127C23—364no—
1128C23C22×D3211yescharacteristic
1129C23C22×D3211yescharacteristic
1130C23C22×D3211yescharacteristic
1131Q8—62no—
1132Q8—94no—
1133Q8—184no—
1134Q8—182no—
1135D4—68no—
1136D4—64no—
1137D4—64no—
1138D4—64no—
1139D4—64no—
1140D4—62no—
1141D4—98no—
1142D4—94no—
1143D4—124no—
1144D4—122no—
1145D4—184no—
1146D4—188no—
1147D4—184no—
1148D4—188no—
1149D4—184no—
1150D4—184no—
1151D4—182no—
1152D4—364no—
1153D4—364no—
1154D4—364no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—32no—
1161C2×C4—32no—
1162C2×C4—34no—
1163C2×C4—32no—
1164C2×C4—64no—
1165C2×C4—92no—
1166C2×C4—98no—
1167C2×C4—92no—
1168C2×C4—122no—
1169C2×C4—184no—
1170C2×C4—184no—
1171C2×C4—188no—
1172C2×C4—184no—
1173C2×C4—184no—
1174C2×C4—364no—
1175C2×C4#381114yescomplemented
1176C2×C4C22×D3211yescharacteristic
1177C2×C4C22×D3211yescharacteristic
1178C2×C4C22×D3211yescharacteristic
1179C2×C4C22×D3211yescharacteristic
1180C2×C3—24no—
1181C2×C3—22no—
1182C2×C3—22no—
1183C2×C3—22no—
1184C2×C3—22no—
1185C2×C3—21no—
1186C2×C3—21no—
1187C2×C3—21no—
1188C2×C3—42no—
1189C2×C3—42no—
1190C2×C3—41no—
1191C2×C3—41no—
1192C2×C3—124no—
1193C2×C3—122no—
1194C2×C3C22×D3×D411yescharacteristic
1195C2×C3C22×D3×D411yescharacteristic
1196C2×C3C2×#100411yescharacteristic
1197C2×C3C2×#100911yescharacteristic
1198C2×C3#596411yescharacteristic
1199C2×C3#596411yescharacteristic
1200D3—42no—
1201D3—44no—
1202D3—64no—
1203D3—64no—
1204D3—124no—
1205D3—124no—
1206D3—122no—
1207D3—122no—
1208C22—21no—
1209C22—21no—
1210C22—21no—
1211C22—21no—
1212C22—21no—
1213C22—21no—
1214C22—21no—
1215C22—44no—
1216C22—64no—
1217C22—62no—
1218C22—62no—
1219C22—64no—
1220C22—62no—
1221C22—64no—
1222C22—94no—
1223C22—182no—
1224C22—182no—
1225C22—182no—
1226C22—182no—
1227C22—182no—
1228C22—244no—
1229C22—368no—
1230C22—728no—
1231C22#6430712yescomplemented
1232C22C2×#381112yes—
1233C22C23×D3211yescharacteristic
1234C4—21no—
1235C4—21no—
1236C4—64no—
1237C4—62no—
1238C4—62no—
1239C4—62no—
1240C4—94no—
1241C4—182no—
1242C4C2×#381112yes—
1243C4C2×#381112yes—
1244C3—21no—
1245C3#8594911yescharacteristic, complemented
1246C3#8604111yescharacteristic, complemented
1247C2—22no—
1248C2—22no—
1249C2—41no—
1250C2—124no—
1251C2—122no—
1252C2—184no—
1253C2—362no—
1254C2C2×#6430711yescharacteristic
1255C2#1059666911yescharacteristic
1256C2C22×#381111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC23×C32×C4C22
hypercenterC23×C4D32
hypocenterC32#3488
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×#3828C2semidirect
2. C2×#64307C2semidirect
3. C3×#5791C2semidirect
4. C2×C3×#930C2semidirect
5. #10595526C2semidirect
6. #10595082C2semidirect
7. #10595081C2semidirect
8. #10595078C2semidirect
9. #10595077C2semidirect
10. #10595074C2semidirect
11. #10595043C2semidirect
12. #10595042C2semidirect
13. #10594990C2semidirect
14. #10594923C2semidirect
15. #10594922C2semidirect
16. #10594919C2semidirect
17. #10594918C2semidirect
20. C23×C32×C4C22semidirect
21. C22×#638C22semidirect
24. C2×#3828C22semidirect
25. C2×#3828C22semidirect
26. C2×#3828C22semidirect
27. C2×#3828C22semidirect
28. C2×#3828C22semidirect
29. C22×C4⋊(C3⋊D3)C22semidirect
30. C22×C4×C3⋊D3C22semidirect
31. C22×#634C22semidirect
32. C22×C3×#67C22semidirect
33. C2×C3×#235C22semidirect
34. C22×C3×D12C22semidirect
35. C2×#3811C22semidirect
36. C2×D3×#67C22semidirect
38. C2×#3802C22semidirect
39. C2×D3×D12C22semidirect
40. C2×#3796C22semidirect
41. C2×#3795C22semidirect
42. C3×#953C22semidirect
43. C3×#930C22semidirect
44. C3×#930C22semidirect
45. C3×#930C22semidirect
46. C3×#930C22semidirect
47. C3×#930C22semidirect
48. C3×#930C22semidirect
49. C3×#929C22semidirect
50. C3×C4×#67C22semidirect
51. C3×C4×#67C22semidirect
52. C2×C3×(C2×D3)⋊C4C22semidirect
53. C3×#926C22semidirect
54. C2×C3×C4⋊Dic3C22semidirect
55. C3×#924C22semidirect
56. C3×#924C22semidirect
57. #63983C22semidirect
58. #63981C22semidirect
59. #63980C22semidirect
60. #63979C22semidirect
61. #63978C22semidirect
62. #63977C22semidirect
63. #67⋊Dic3C22semidirect
64. #63971C22semidirect
65. #63958C22semidirect
66. #63952C22semidirect
67. #63923C22semidirect
68. #63921C22semidirect
69. #63916C22semidirect
70. #63916C22semidirect
71. #63916C22semidirect
72. #63913C22semidirect
73. #63912C22semidirect
74. #63911C22semidirect
75. #63910C22semidirect
76. #63909C22semidirect
77. #63900C22semidirect
78. #63896C22semidirect
79. #63894C22semidirect
80. #63881C22semidirect
81. #63871C22semidirect
82. #63860C22semidirect
83. #63857C22semidirect
84. #63853C22semidirect
85. #63849C22semidirect
86. #63844C22semidirect
97. #5791D3semidirect
98. C2×#930D3semidirect
144. #3828D4semidirect
212. C23×C3×C4C2×D3semidirect
213. C23×C3×C4C2×D3semidirect
218. C22×#67C2×D3semidirect
252. C2×#235C2×D3semidirect
257. C22×D12C2×D3semidirect
280. #953C2×D3semidirect
300. #930C2×D3semidirect
301. #930C2×D3semidirect
302. #930C2×D3semidirect
303. #930C2×D3semidirect
304. #930C2×D3semidirect
305. #930C2×D3semidirect
306. #929C2×D3semidirect
308. C4×#67C2×D3semidirect
309. C4×#67C2×D3semidirect
310. C2×(C2×D3)⋊C4C2×D3semidirect
311. #926C2×D3semidirect
312. C2×C4⋊Dic3C2×D3semidirect
314. #924C2×D3semidirect
315. #924C2×D3semidirect
378. C2×C32×C4C2×D4semidirect
386. #638C2×D4semidirect
392. C4⋊(C3⋊D3)C2×D4semidirect
396. C4×C3⋊D3C2×D4semidirect
399. #634C2×D4semidirect
652. C22×C32H(5,𝔽2)semidirect
700. C23×C4D32semidirect
830. C2×C3×C4D3×D4semidirect
831. C2×C3×C4D3×D4semidirect
1051. C22×C3#1004semidirect
1052. C22×C3#1009semidirect
1111. C32#3488semidirect
1175. C2×C4#3811semidirect
1231. C22#64307semidirect
1245. C3#85949semidirect
1246. C3#86041semidirect

Maximal subgroups

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

subgroupindex
C22×#38282
C2×#643072
C3×#57912
C2×C3×#9302
#105955262
#105950822
#105950812
#105950782
#105950772
#105950742
#105950432
#105950422
#105949902
#105949232
#105949222
#105949192
#105949182
#860413
#859493