Finite Group Databasebeta

← #11904784

Subgroups — #11904784

Order 1152.

3489 conjugacy classes of subgroups.

The subgroup lattice has 1198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3828C211yesmaximal, characteristic, complemented
2C2×#64297C211yesmaximal, characteristic, complemented
3C3×#5791C211yesmaximal, characteristic, complemented
4C2×C3×#924C211yesmaximal, characteristic, complemented
5#10595500C214yesmaximal, complemented
6#10595043C211yesmaximal, characteristic, complemented
7#10595018C212yesmaximal, complemented
8#10594990C211yesmaximal, characteristic, complemented
9#10594925C212yesmaximal, complemented
10#10594923C212yesmaximal, complemented
11#10594922C212yesmaximal, complemented
12#10594917C214yesmaximal, complemented
13#10594916C212yesmaximal, complemented
14#10594915C212yesmaximal, complemented
15#10594866C211yesmaximal, characteristic, complemented
16#10594834C212yesmaximal, complemented
17#10594805C212yesmaximal, complemented
18#86042—31nomaximal
19#85985—31nomaximal
20C23×C32×C4C2211yescharacteristic
21C22×#638C2212yes—
22C2×#3828—28no—
23C2×#3828C2211yescharacteristic
24C2×#3828C2211yescharacteristic
25C2×#3828C2211yescharacteristic
26C2×#3828C2212yes—
27C2×#3828C2212yes—
28C2×#3828C2211yescharacteristic
29C22×C4⋊(C3⋊D3)C2211yescharacteristic
30C22×C4×C3⋊D3C2212yes—
31C22×#634C2211yescharacteristic
32C2×C3×#235C2211yescharacteristic, complemented
33C22×C3×Dic6C2211yescharacteristic, complemented
34C2×#3804C2214yescomplemented
35C2×#3799C2212yescomplemented
36C2×#3797C2212yescomplemented
37#64297—28no—
38C2×#3796C2212yescomplemented
39C2×D3×Dic6C2212yescomplemented
40C3×#953C2212yes—
41C2×C3×#217C2212yes—
42C3×#930C2211yescharacteristic
43C3×#930C2211yescharacteristic, complemented
44C3×#929C2212yescomplemented
45C3×C4×#67C2212yes—
46C3×C4×#67C2212yescomplemented
47C3×#926C2211yescharacteristic, complemented
48C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
49C3×#924C2212yes—
50C3×#924C2212yes—
51C3×#924C2211yescharacteristic
52C3×#924C2212yescomplemented
53C3×#924C2212yescomplemented
54C3×#924C2211yescharacteristic, complemented
55C2×C3×Dic3⋊C4C2212yescomplemented
56#63982C2214yes—
57#63981C2214yes—
58#63978C2214yescomplemented
59#63975C2214yescomplemented
60#63974C2214yes—
61#67⋊Dic3C2214yes—
62#63971C2214yescomplemented
63#63966C2214yescomplemented
64#63958C2214yescomplemented
65#63953C2214yescomplemented
66#63952C2214yescomplemented
67#63916C2212yescomplemented
68#63910C2214yescomplemented
69#63909C2212yescomplemented
70#63900C2212yescomplemented
71#63897C2214yescomplemented
72#63896C2214yescomplemented
73#63894C2212yescomplemented
74#63883C2214yescomplemented
75#63881C2214yescomplemented
76#63871C2212yescomplemented
77#63871C2212yescomplemented
78#63871C2212yescomplemented
79#63866C2212yescomplemented
80#63865C2214yescomplemented
81#63864C2212yescomplemented
82#63857C2212yescomplemented
83#63853C2214yescomplemented
84#63849C2212yescomplemented
85#63844C2212yescomplemented
86#63840C2214yescomplemented
87C2×#1010—31no—
88C2×#1007—31no—
89C22×#235—31no—
90C22×#235—31no—
91C22×#235—61no—
92C3×#525—31no—
93C2×C3×C22⋊Q8—31no—
94#5833—31no—
95#5816—31no—
96#5791D311yescharacteristic, complemented
97C2×#924D311yescharacteristic, complemented
98#5655—34no—
99#5633—32no—
100#5632—32no—
101#5631—32no—
102#5630—32no—
103#5629—32no—
104#5628—32no—
105#5628—32no—
106#5627—32no—
107D3×C22⋊Q8—32no—
108D3×C22⋊Q8—32no—
109#5608—32no—
110#5606—32no—
111#5591—34no—
112#5552—32no—
113#5551—32no—
114#5550—32no—
115D4×Dic6—32no—
116#5526—31no—
117#5523—31no—
118#5510—31no—
119#5507—34no—
120#5504—31no—
121#5490—34no—
122C24×C32C2311yescharacteristic
123C23×C3⋊D3C2312yes—
124C22×C32×C4—24no—
125C22×C32×C4C2311yescharacteristic
126C22×C32×C4C2311yescharacteristic
127C22×C32×C4C2311yescharacteristic
128C22×C32×C4C2311yescharacteristic
129C22×C32×C4C2311yescharacteristic
130C22×C32×C4C2311yescharacteristic
131C2×#638—28no—
132C2×#638C2312yes—
133C2×#638C2312yes—
134C2×#638C2312yes—
135C2×#638C2312yes—
136C22×C3⋊Dic3C2312yes—
137#3828—24no—
138#3828—28no—
139#3828—24no—
140#3828—28no—
141#3828—24no—
142#3828D418yescomplemented
143C2×C4⋊(C3⋊D3)—24no—
144C2×C4⋊(C3⋊D3)C2311yescharacteristic
145C2×C4⋊(C3⋊D3)C2312yes—
146C2×C4⋊(C3⋊D3)C2311yescharacteristic
147C2×C4×C3⋊D3—28no—
148C2×C4×C3⋊D3C2312yes—
149C2×C4×C3⋊D3C2312yes—
150C2×C4×C3⋊D3C2312yes—
151C2×C4×C3⋊D3C2312yes—
152C2×#634—24no—
153C2×#634C2312yes—
154C2×#634C2311yescharacteristic
155C2×#634C2311yescharacteristic
156C2×C3×#67C2312yes—
157C2×C3×#67C2312yes—
158C2×C3×#67C2312yes—
159C22×C3×Dic3C2312yes—
160C22×C3×Dic3C2312yes—
161C3×#235—24no—
162C2×C3×D12C2311yescharacteristic
163C2×C3×C4×D3C2312yes—
164C2×C3×Dic6—24no—
165C2×C3×Dic6C2312yes—
166C2×C3×Dic6C2312yes—
167C2×C3×Dic6C2311yescharacteristic
168C2×#627C2314yes—
169C2×#626C2314yes—
170C2×#626C2314yes—
171C2×#624C2314yes—
172C2×#624C2314yes—
173#3804—216no—
174C2×D3×Dic3C2314yes—
175#3799—28no—
176#3797—28no—
177#3796—28no—
178D3×Dic6—28no—
179C3×#217C2314yes—
180C3×#217C2312yes—
181C3×#217C2314yes—
182C3×#217C2312yes—
183C3×#217C2312yes—
184C3×(C2×D3)⋊C4C2312yes—
185C3×(C2×D3)⋊C4C2312yes—
186C3×C4⋊Dic3C2312yes—
187C3×C4⋊Dic3C2312yes—
188C3×C4⋊Dic3C2311yescharacteristic
189C3×C4⋊Dic3C2311yescharacteristic
190C3×Dic3⋊C4C2314yes—
191C3×Dic3⋊C4C2314yes—
192C3×Dic3⋊C4C2312yes—
193C3×Dic3⋊C4C2312yes—
194C3×C4×Dic3C2312yes—
195#3724C2314yes—
196Dic3⋊Dic3C2314yes—
197Dic3⋊Dic3C2314yes—
198Dic3⋊Dic3C2314yes—
199#3722C2314yes—
200#3722C2314yes—
201#3722C2314yes—
202#3722C2314yes—
203(C2×D3)⋊Dic3C2314yes—
204Dic32C2314yes—
205#3489—91noSylow
206C2×C3×#41—31no—
207C22×C3×Q8—31no—
208C23×C3×C4—21no—
209C23×C3×C4C2×D311yescharacteristic
210C23×C3×C4C2×D311yescharacteristic
211C22×#67—32no—
212C22×#67—32no—
213C22×#67—62no—
214#1010—68no—
215#1007—68no—
216C2×#239—32no—
217C2×#239—32no—
218C2×D3×Q8—32no—
219C2×D3×Q8—32no—
220C2×D3×Q8—32no—
221C2×#237—34no—
222C2×#237—32no—
223C2×#235—31no—
224C2×#235—31no—
225C2×#235—31no—
226C2×#235—32no—
227C2×#235—32no—
228C2×#235—31no—
229C2×#235—31no—
230C2×#235—31no—
231C2×#235—31no—
232C2×#235—32no—
233C2×#235—32no—
234C2×#235—31no—
235C2×#235—34no—
236C2×#235—32no—
237C2×#235—61no—
238C2×#235—61no—
239C2×#235—62no—
240C2×#235—61no—
241C2×#235—62no—
242C2×#235—61no—
243C2×#235—68no—
244C2×#235—68no—
245C2×#235—616no—
246C2×#235C2×D311yescharacteristic, complemented
247C22×D12—31no—
248C22×D12—31no—
249C22×D12—61no—
250C22×C4×D3—32no—
251C22×C4×D3—32no—
252C22×C4×D3—62no—
253C22×Dic6—31no—
254C22×Dic6—31no—
255C22×Dic6—32no—
256C22×Dic6—61no—
257C22×Dic6C2×D311yescharacteristic, complemented
258C3×#123—32no—
259C3×C22⋊Q8—32no—
260C3×C22⋊Q8—32no—
261C3×C22⋊Q8—32no—
262C3×C22⋊Q8—31no—
263C3×C22⋊Q8—32no—
264C3×C22⋊Q8—31no—
265C3×#121—31no—
266C3×#121—31no—
267C3×#120—32no—
268C3×C4×D4—32no—
269C3×C4×D4—32no—
270C3×#117—31no—
271C2×C3×C4⋊C4—32no—
272C2×C3×C4⋊C4—31no—
273C2×C3×C22⋊C4—32no—
274#953C2×D312yes—
275C2×#217C2×D312yes—
276#947—32no—
277#946—32no—
278#946—32no—
279#946—32no—
280#944—32no—
281#939—34no—
282#939—34no—
283#938—34no—
284#938—32no—
285#937—34no—
286D4×Dic3—34no—
287#930—34no—
288#930—32no—
289#930C2×D311yescharacteristic
290#930C2×D311yescharacteristic, complemented
291#929—34no—
292#929C2×D312yescomplemented
293C4×#67—34no—
294C4×#67C2×D312yes—
295C4×#67C2×D312yescomplemented
296#926C2×D311yescharacteristic, complemented
297C2×C4⋊Dic3C2×D311yescharacteristic, complemented
298#924—32no—
299#924C2×D312yes—
300#924C2×D312yes—
301#924C2×D311yescharacteristic
302#924C2×D312yescomplemented
303#924C2×D312yescomplemented
304#924C2×D311yescharacteristic, complemented
305C2×Dic3⋊C4C2×D312yescomplemented
306#897—32no—
307#897—32no—
308#897—32no—
309#897—32no—
310#896—34no—
311#896—34no—
312#896—34no—
313#895—32no—
314#895—32no—
315#895—34no—
316#894—34no—
317#894—34no—
318#894—34no—
319#893—34no—
320#893—32no—
321#892—32no—
322#892—32no—
323D3×C4⋊C4—32no—
324D3×C4⋊C4—32no—
325D3×C4⋊C4—34no—
326D3×C4⋊C4—34no—
327#888—34no—
328#888—34no—
329#887—32no—
330#886—34no—
331#885—34no—
332#885—34no—
333#884—34no—
334#884—34no—
335#884—34no—
336#883—34no—
337#883—34no—
338#883—34no—
339#882—34no—
340#67⋊C4—34no—
341#67⋊C4—34no—
342#67⋊C4—34no—
343D3×C22⋊C4—34no—
344D3×C22⋊C4—34no—
345#878—34no—
346#878—34no—
347#878—34no—
348#875—32no—
349C4×D12—32no—
350#869—32no—
351C4×Dic6—32no—
352C23×C32—22no—
353C23×C32—22no—
354C23×C32—41no—
355C23×C32C2411yescharacteristic
356C23×C32C2411yescharacteristic
357C23×C32C2411yescharacteristic
358C22×C3⋊D3—24no—
359C22×C3⋊D3—24no—
360C22×C3⋊D3—42no—
361C22×C3⋊D3C2412yes—
362C22×C3⋊D3C2412yes—
363C22×C3×D3C2412yes—
364C2×C32×C4—22no—
365C2×C32×C4—22no—
366C2×C32×C4—22no—
367C2×C32×C4—22no—
368C2×C32×C4—22no—
369C2×C32×C4C2×D414yes—
370C2×C32×C4C2411yescharacteristic
371C2×C32×C4C2411yescharacteristic
372C2×C32×C4C2411yescharacteristic
373C2×C32×C4C2411yescharacteristic
374#638—24no—
375#638—24no—
376#638—24no—
377#638C2×D418yes—
378C2×C3⋊Dic3—24no—
379C2×C3⋊Dic3C2412yes—
380C2×C3⋊Dic3C2412yes—
381C4⋊(C3⋊D3)—24no—
382C4⋊(C3⋊D3)—22no—
383C4⋊(C3⋊D3)C2×D414yes—
384C4×C3⋊D3—24no—
385C4×C3⋊D3—24no—
386C4×C3⋊D3—24no—
387C4×C3⋊D3C2×D418yes—
388#634—22no—
389#634—24no—
390#634C2×D414yes—
391C3×#67—24no—
392C3×#67—24no—
393C3×#67—42no—
394C2×C3×Dic3—24no—
395C2×C3×Dic3—42no—
396C2×C3×Dic3C2412yes—
397C2×C3×Dic3C2414yes—
398C2×C3×Dic3C2412yes—
399C2×C3×Dic3C2414yes—
400C2×C3×Dic3C2412yes—
401C3×D12—22no—
402C3×C4×D3—24no—
403C3×Dic6—24no—
404C3×Dic6—24no—
405C3×Dic6—22no—
406#627—28no—
407#626—28no—
408#626—44no—
409#624—28no—
410#624—44no—
411D3×Dic3—28no—
412C2×2−1+4—91no—
413C22×#41—91no—
414D4×Q8—92no—
415#548—92no—
416#547—94no—
417#547—92no—
418#546—94no—
419#546—92no—
420#537—91no—
421#537—92no—
422#536—91no—
423#536—92no—
424#525—31no—
425#525—92no—
426C2×C22⋊Q8—31no—
427C2×C22⋊Q8—92no—
428#520—91no—
429C24×C3—21no—
430C24×C3C22×D311yescharacteristic
431C24×C3C22×D311yescharacteristic
432C23×D3—32no—
433C23×D3—32no—
434C23×D3—62no—
435C3×#41—64no—
436C2×C3×Q8—32no—
437C2×C3×Q8—31no—
438C2×C3×Q8—32no—
439C2×C3×Q8—64no—
440C2×C3×D4—32no—
441C2×C3×D4—32no—
442C2×C3×D4—32no—
443C2×C3×D4—31no—
444C22×C3×C4—28no—
445C22×C3×C4—24no—
446C22×C3×C4—24no—
447C22×C3×C4—21no—
448C22×C3×C4—21no—
449C22×C3×C4—21no—
450C22×C3×C4—21no—
451C22×C3×C4—21no—
452C22×C3×C4—21no—
453C22×C3×C4—32no—
454C22×C3×C4—32no—
455C22×C3×C4—32no—
456C22×C3×C4C22×D311yescharacteristic
457C22×C3×C4C22×D311yescharacteristic
458C22×C3×C4C22×D311yescharacteristic
459C22×C3×C4C22×D311yescharacteristic
460C22×C3×C4C22×D311yescharacteristic
461C22×C3×C4C22×D311yescharacteristic
462C22×C3×C4C22×D311yescharacteristic
463C22×C3×C4C22×D311yescharacteristic
464C22×C3×C4C22×D311yescharacteristic
465C22×C3×C4C22×D311yescharacteristic
466C22×C3×C4C22×D311yescharacteristic
467C22×C3×C4C22×D311yescharacteristic
468C2×#67—32no—
469C2×#67—32no—
470C2×#67—32no—
471C2×#67—32no—
472C2×#67—32no—
473C2×#67—32no—
474C2×#67—32no—
475C2×#67—32no—
476C2×#67—34no—
477C2×#67—34no—
478C2×#67—62no—
479C2×#67—62no—
480C2×#67—62no—
481C2×#67—62no—
482C2×#67—68no—
483C2×#67—68no—
484C2×#67—616no—
485C2×#67C22×D312yes—
486C2×#67C22×D312yes—
487C2×#67C22×D312yes—
488C22×Dic3—32no—
489C22×Dic3—32no—
490C22×Dic3—34no—
491C22×Dic3—62no—
492C22×Dic3C22×D312yes—
493C22×Dic3C22×D312yes—
494#239—68no—
495#239—68no—
496D3×Q8—68no—
497D3×Q8—68no—
498D3×Q8—68no—
499#237—68no—
500#237—616no—
501#235—24no—
502#235—38no—
503#235—38no—
504#235—68no—
505#235—68no—
506#235—64no—
507#235—64no—
508#235—68no—
509#235—68no—
510#235—64no—
511#235—64no—
512#235—616no—
513#235—68no—
514#235—68no—
515#235—616no—
516#235—68no—
517#235—616no—
518#235—68no—
519#235—68no—
520#235—64no—
521#235—64no—
522C2×D12—31no—
523C2×D12—31no—
524C2×D12—34no—
525C2×D12—31no—
526C2×D12—32no—
527C2×D12—32no—
528C2×D12—31no—
529C2×D12—34no—
530C2×D12—61no—
531C2×D12—62no—
532C2×D12—61no—
533C2×D12—64no—
534C2×D12—64no—
535C2×D12—68no—
536C2×D12C22×D311yescharacteristic
537C2×C4×D3—32no—
538C2×C4×D3—32no—
539C2×C4×D3—34no—
540C2×C4×D3—32no—
541C2×C4×D3—32no—
542C2×C4×D3—32no—
543C2×C4×D3—32no—
544C2×C4×D3—32no—
545C2×C4×D3—32no—
546C2×C4×D3—34no—
547C2×C4×D3—34no—
548C2×C4×D3—34no—
549C2×C4×D3—34no—
550C2×C4×D3—62no—
551C2×C4×D3—62no—
552C2×C4×D3—62no—
553C2×C4×D3—62no—
554C2×C4×D3—68no—
555C2×C4×D3—68no—
556C2×C4×D3—616no—
557C2×C4×D3C22×D312yes—
558C2×Dic6—24no—
559C2×Dic6—31no—
560C2×Dic6—31no—
561C2×Dic6—31no—
562C2×Dic6—32no—
563C2×Dic6—32no—
564C2×Dic6—31no—
565C2×Dic6—34no—
566C2×Dic6—34no—
567C2×Dic6—61no—
568C2×Dic6—62no—
569C2×Dic6—61no—
570C2×Dic6—68no—
571C2×Dic6—64no—
572C2×Dic6—64no—
573C2×Dic6—68no—
574C2×Dic6C22×D312yes—
575C2×Dic6C22×D312yes—
576C2×Dic6C22×D311yescharacteristic
577C3×C4⋊C4—32no—
578C3×C4⋊C4—32no—
579C3×C4⋊C4—34no—
580C3×C4⋊C4—32no—
581C3×C4⋊C4—31no—
582C3×C4⋊C4—32no—
583C3×C4⋊C4—34no—
584C3×C4⋊C4—31no—
585C3×C22⋊C4—32no—
586C3×C22⋊C4—34no—
587C3×C22⋊C4—32no—
588C3×C22⋊C4—32no—
589C3×C22⋊C4—34no—
590C3×C22⋊C4—32no—
591C3×C22⋊C4—32no—
592C3×C42—32no—
593#217—34no—
594#217C22×D312yes—
595#217C22×D314yes—
596#217C22×D312yes—
597#217C22×D314yes—
598#217C22×D312yes—
599(C2×D3)⋊C4—34no—
600(C2×D3)⋊C4—34no—
601(C2×D3)⋊C4—34no—
602(C2×D3)⋊C4—34no—
603(C2×D3)⋊C4—34no—
604(C2×D3)⋊C4—34no—
605(C2×D3)⋊C4—34no—
606(C2×D3)⋊C4—34no—
607(C2×D3)⋊C4—34no—
608(C2×D3)⋊C4C22×D312yes—
609(C2×D3)⋊C4C22×D312yes—
610C4⋊Dic3—34no—
611C4⋊Dic3—34no—
612C4⋊Dic3—34no—
613C4⋊Dic3C22×D312yes—
614C4⋊Dic3C22×D311yescharacteristic
615C4⋊Dic3C22×D312yes—
616C4⋊Dic3C22×D311yescharacteristic
617Dic3⋊C4—34no—
618Dic3⋊C4—34no—
619Dic3⋊C4—34no—
620Dic3⋊C4—34no—
621Dic3⋊C4—34no—
622Dic3⋊C4C22×D314yes—
623Dic3⋊C4C22×D314yes—
624Dic3⋊C4C22×D312yes—
625Dic3⋊C4C22×D312yes—
626C4×Dic3—34no—
627C4×Dic3—34no—
628C4×Dic3C22×D312yes—
629C22×C32—21no—
630C22×C32—21no—
631C22×C32—21no—
632C22×C32—21no—
633C22×C32—21no—
634C22×C32—21no—
635C22×C32—21no—
636C22×C32—44no—
637C22×C32C22×D412yes—
638C22×C322−1+412yescomplemented
639C22×C32C2511yescharacteristic
640C2×C3⋊D3—22no—
641C2×C3⋊D3—22no—
642C2×C3⋊D3—22no—
643C2×C3⋊D3—22no—
644C2×C3⋊D3—22no—
645C2×C3⋊D3—48no—
646C2×C3⋊D3C22×D414yes—
647C2×C3×D3—22no—
648C2×C3×D3—22no—
649C2×C3×D3—22no—
650C32×C4—21no—
651C32×C4—21no—
652C32×C4C22×D412yes—
653C32×C4C22×D412yes—
654C3⋊Dic3—22no—
655C3⋊Dic3C22×D414yes—
656C3×Dic3—24no—
657C3×Dic3—22no—
658C3×Dic3—22no—
659C3×Dic3—22no—
660C3×Dic3—24no—
6612−1+4—188no—
662C2×#41—31no—
663C2×#41—94no—
664C2×#41—92no—
665C2×#41—92no—
666C2×#41—91no—
667C2×#41—92no—
668C2×#41—91no—
669C2×#41—91no—
670C2×#41—92no—
671C2×#41—91no—
672C2×#41—188no—
673C22×Q8—31no—
674C22×Q8—92no—
675C22×Q8—92no—
676C22×Q8—91no—
677C22×D4—92no—
678C22×D4—91no—
679C23×C4—92no—
680C23×C4D3211yescharacteristic
681C4⋊Q8—92no—
682C4⋊Q8—94no—
683#124—92no—
684#124—94no—
685#123—32no—
686#123—94no—
687#123—94no—
688#123—94no—
689#123—94no—
690C22⋊Q8—32no—
691C22⋊Q8—32no—
692C22⋊Q8—32no—
693C22⋊Q8—32no—
694C22⋊Q8—31no—
695C22⋊Q8—31no—
696C22⋊Q8—94no—
697C22⋊Q8—94no—
698C22⋊Q8—94no—
699C22⋊Q8—92no—
700C22⋊Q8—92no—
701C22⋊Q8—92no—
702C22⋊Q8—92no—
703#121—31no—
704#121—31no—
705#121—94no—
706#121—94no—
707#121—94no—
708#121—92no—
709#121—92no—
710#121—94no—
711#120—32no—
712#120—94no—
713C4×Q8—92no—
714C4×D4—32no—
715C4×D4—32no—
716C4×D4—92no—
717C4×D4—94no—
718C4×D4—94no—
719C4×D4—94no—
720#117—31no—
721#117—92no—
722C2×C4⋊C4—31no—
723C2×C4⋊C4—32no—
724C2×C4⋊C4—92no—
725C2×C4⋊C4—94no—
726C2×C22⋊C4—32no—
727C2×C22⋊C4—94no—
728C23×C3—24no—
729C23×C3—22no—
730C23×C3—22no—
731C23×C3—22no—
732C23×C3—22no—
733C23×C3—21no—
734C23×C3—21no—
735C23×C3—21no—
736C23×C3—32no—
737C23×C3—42no—
738C23×C3—41no—
739C23×C3—41no—
740C23×C3—42no—
741C23×C3C23×D311yescharacteristic
742C23×C3C23×D311yescharacteristic
743C23×C3C23×D311yescharacteristic
744C23×C3C23×D311yescharacteristic
745C23×C3C23×D311yescharacteristic
746C23×C3C23×D311yescharacteristic
747C22×D3—32no—
748C22×D3—32no—
749C22×D3—32no—
750C22×D3—32no—
751C22×D3—62no—
752C22×D3—62no—
753C22×D3—64no—
754C22×D3—64no—
755C22×D3—68no—
756C22×D3—64no—
757C22×D3—64no—
758C22×D3—124no—
759C22×D3—122no—
760C22×D3—122no—
761C22×D3—124no—
762C22×D3C23×D312yes—
763C3×Q8—62no—
764C3×Q8—64no—
765C3×Q8—64no—
766C3×D4—64no—
767C3×D4—64no—
768C3×D4—62no—
769C3×D4—122no—
770C2×C3×C4—24no—
771C2×C3×C4—24no—
772C2×C3×C4—24no—
773C2×C3×C4—24no—
774C2×C3×C4—24no—
775C2×C3×C4—22no—
776C2×C3×C4—22no—
777C2×C3×C4—22no—
778C2×C3×C4—22no—
779C2×C3×C4—22no—
780C2×C3×C4—22no—
781C2×C3×C4—22no—
782C2×C3×C4—22no—
783C2×C3×C4—22no—
784C2×C3×C4—22no—
785C2×C3×C4—21no—
786C2×C3×C4—21no—
787C2×C3×C4—21no—
788C2×C3×C4—21no—
789C2×C3×C4—24no—
790C2×C3×C4—32no—
791C2×C3×C4—34no—
792C2×C3×C4—32no—
793C2×C3×C4—32no—
794C2×C3×C4—34no—
795C2×C3×C4—64no—
796C2×C3×C4—64no—
797C2×C3×C4—122no—
798C2×C3×C4D3×D414yes—
799C2×C3×C4D3×D414yes—
800C2×C3×C4C23×D311yescharacteristic
801C2×C3×C4C23×D311yescharacteristic
802C2×C3×C4C23×D311yescharacteristic
803C2×C3×C4C23×D311yescharacteristic
804C2×C3×C4C23×D311yescharacteristic
805C2×C3×C4C23×D311yescharacteristic
806C2×C3×C4C23×D311yescharacteristic
807C2×C3×C4C23×D311yescharacteristic
808#67—24no—
809#67—24no—
810#67—38no—
811#67—38no—
812#67—42no—
813#67—68no—
814#67—68no—
815#67—64no—
816#67—64no—
817#67—64no—
818#67—64no—
819#67—68no—
820#67—68no—
821#67—68no—
822#67—64no—
823#67—64no—
824#67—124no—
825C2×Dic3—24no—
826C2×Dic3—32no—
827C2×Dic3—32no—
828C2×Dic3—32no—
829C2×Dic3—32no—
830C2×Dic3—42no—
831C2×Dic3—62no—
832C2×Dic3—62no—
833C2×Dic3—68no—
834C2×Dic3—64no—
835C2×Dic3—64no—
836C2×Dic3—68no—
837C2×Dic3C23×D312yes—
838C2×Dic3C23×D314yes—
839C2×Dic3C23×D312yes—
840C2×Dic3C23×D312yes—
841C2×Dic3C23×D314yes—
842D12—22no—
843D12—34no—
844D12—34no—
845D12—64no—
846D12—64no—
847D12—64no—
848D12—68no—
849D12—64no—
850D12—68no—
851D12—62no—
852D12—62no—
853D12—124no—
854C4×D3—24no—
855C4×D3—38no—
856C4×D3—38no—
857C4×D3—68no—
858C4×D3—68no—
859C4×D3—68no—
860C4×D3—64no—
861C4×D3—64no—
862C4×D3—68no—
863C4×D3—64no—
864C4×D3—64no—
865C4×D3—68no—
866C4×D3—68no—
867C4×D3—68no—
868C4×D3—64no—
869C4×D3—64no—
870C4×D3—124no—
871C4×D3—124no—
872Dic6—24no—
873Dic6—24no—
874Dic6—22no—
875Dic6—34no—
876Dic6—34no—
877Dic6—64no—
878Dic6—68no—
879Dic6—68no—
880Dic6—64no—
881Dic6—64no—
882Dic6—68no—
883Dic6—64no—
884Dic6—62no—
885Dic6—62no—
886C2×C32—22no—
887C2×C32—22no—
888C2×C32—41no—
889C2×C32C23×D411yescharacteristic
890C2×C32C2×2−1+411yescharacteristic
891C2×C32#58511yescharacteristic
892C3⋊D3—24no—
893C3⋊D3—42no—
894C3×D3—42no—
895C24—92no—
896C24C2×D3211yescharacteristic
897#41—64no—
898#41—98no—
899#41—188no—
900#41—188no—
901#41—184no—
902#41—184no—
903#41—1816no—
904#41—188no—
905#41—188no—
906#41—184no—
907C2×Q8—32no—
908C2×Q8—31no—
909C2×Q8—32no—
910C2×Q8—64no—
911C2×Q8—94no—
912C2×Q8—91no—
913C2×Q8—92no—
914C2×Q8—91no—
915C2×Q8—184no—
916C2×Q8—188no—
917C2×Q8—188no—
918C2×D4—32no—
919C2×D4—32no—
920C2×D4—32no—
921C2×D4—31no—
922C2×D4—94no—
923C2×D4—94no—
924C2×D4—92no—
925C2×D4—92no—
926C2×D4—92no—
927C2×D4—92no—
928C2×D4—91no—
929C2×D4—92no—
930C2×D4—91no—
931C2×D4—184no—
932C2×D4—188no—
933C22×C4—24no—
934C22×C4—32no—
935C22×C4—32no—
936C22×C4—32no—
937C22×C4—94no—
938C22×C4—94no—
939C22×C4—94no—
940C22×C4—92no—
941C22×C4—92no—
942C22×C4—92no—
943C22×C4—92no—
944C22×C4—92no—
945C22×C4—188no—
946C22×C4C2×D3211yescharacteristic
947C22×C4C2×D3211yescharacteristic
948C22×C4C2×D3211yescharacteristic
949C22×C4C2×D3211yescharacteristic
950C22×C4C2×D3211yescharacteristic
951C22×C4C2×D3211yescharacteristic
952C4⋊C4—32no—
953C4⋊C4—34no—
954C4⋊C4—32no—
955C4⋊C4—34no—
956C4⋊C4—31no—
957C4⋊C4—32no—
958C4⋊C4—31no—
959C4⋊C4—32no—
960C4⋊C4—94no—
961C4⋊C4—94no—
962C4⋊C4—94no—
963C4⋊C4—94no—
964C22⋊C4—34no—
965C22⋊C4—34no—
966C22⋊C4—32no—
967C22⋊C4—32no—
968C22⋊C4—32no—
969C22⋊C4—32no—
970C22⋊C4—32no—
971C22⋊C4—94no—
972C22⋊C4—94no—
973C22⋊C4—94no—
974C22⋊C4—94no—
975C22⋊C4—94no—
976C42—32no—
977C42—94no—
978C22×C3—22no—
979C22×C3—22no—
980C22×C3—21no—
981C22×C3—21no—
982C22×C3—21no—
983C22×C3—21no—
984C22×C3—21no—
985C22×C3—21no—
986C22×C3—21no—
987C22×C3—21no—
988C22×C3—22no—
989C22×C3—21no—
990C22×C3—21no—
991C22×C3—21no—
992C22×C3—21no—
993C22×C3—21no—
994C22×C3—21no—
995C22×C3—22no—
996C22×C3—22no—
997C22×C3—21no—
998C22×C3—41no—
999C22×C3—41no—
1000C22×C3—41no—
1001C22×C3—41no—
1002C22×C3—44no—
1003C22×C3—44no—
1004C22×C3—48no—
1005C22×C3—62no—
1006C22×C3—62no—
1007C22×C3—62no—
1008C22×C3C2×D3×D412yes—
1009C22×C3C2×D3×D412yes—
1010C22×C3#100712yescomplemented
1011C22×C3#101012yescomplemented
1012C22×C3C24×D311yescharacteristic
1013C22×C3C24×D311yescharacteristic
1014C2×D3—22no—
1015C2×D3—22no—
1016C2×D3—22no—
1017C2×D3—34no—
1018C2×D3—34no—
1019C2×D3—64no—
1020C2×D3—62no—
1021C2×D3—62no—
1022C2×D3—62no—
1023C2×D3—62no—
1024C2×D3—64no—
1025C2×D3—62no—
1026C2×D3—62no—
1027C2×D3—62no—
1028C2×D3—62no—
1029C2×D3—62no—
1030C2×D3—62no—
1031C2×D3—122no—
1032C2×D3—122no—
1033C2×D3—122no—
1034C2×D3—122no—
1035C2×D3—128no—
1036C2×D3—128no—
1037C2×D3—1216no—
1038C3×C4—22no—
1039C3×C4—22no—
1040C3×C4—21no—
1041C3×C4—21no—
1042C3×C4—21no—
1043C3×C4—21no—
1044C3×C4—22no—
1045C3×C4—22no—
1046C3×C4—62no—
1047C3×C4—64no—
1048C3×C4—62no—
1049C3×C4—62no—
1050C3×C4—64no—
1051C3×C4C2×D3×D412yes—
1052C3×C4C2×D3×D412yes—
1053C3×C4C2×D3×D412yes—
1054C3×C4C2×D3×D412yes—
1055Dic3—24no—
1056Dic3—22no—
1057Dic3—22no—
1058Dic3—22no—
1059Dic3—24no—
1060Dic3—34no—
1061Dic3—34no—
1062Dic3—64no—
1063Dic3—64no—
1064Dic3—62no—
1065Dic3—62no—
1066C32#348911yescharacteristic, complemented, Sylow
1067C23—22no—
1068C23—22no—
1069C23—32no—
1070C23—41no—
1071C23—92no—
1072C23—92no—
1073C23—184no—
1074C23—184no—
1075C23—362no—
1076C23C22×D3211yescharacteristic
1077C23C22×D3211yescharacteristic
1078C23C22×D3211yescharacteristic
1079Q8—64no—
1080Q8—64no—
1081Q8—62no—
1082Q8—94no—
1083Q8—184no—
1084Q8—188no—
1085Q8—182no—
1086D4—64no—
1087D4—64no—
1088D4—62no—
1089D4—98no—
1090D4—94no—
1091D4—122no—
1092D4—184no—
1093D4—188no—
1094D4—184no—
1095D4—184no—
1096D4—184no—
1097D4—182no—
1098D4—364no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—32no—
1105C2×C4—32no—
1106C2×C4—34no—
1107C2×C4—32no—
1108C2×C4—34no—
1109C2×C4—64no—
1110C2×C4—64no—
1111C2×C4—92no—
1112C2×C4—98no—
1113C2×C4—92no—
1114C2×C4—122no—
1115C2×C4—184no—
1116C2×C4—184no—
1117C2×C4—188no—
1118C2×C4—188no—
1119C2×C4—184no—
1120C2×C4—184no—
1121C2×C4—364no—
1122C2×C4#381114yes—
1123C2×C4C22×D3211yescharacteristic
1124C2×C4C22×D3211yescharacteristic
1125C2×C4C22×D3211yescharacteristic
1126C2×C4C22×D3211yescharacteristic
1127C2×C3—24no—
1128C2×C3—22no—
1129C2×C3—22no—
1130C2×C3—22no—
1131C2×C3—22no—
1132C2×C3—21no—
1133C2×C3—21no—
1134C2×C3—21no—
1135C2×C3—42no—
1136C2×C3—42no—
1137C2×C3—41no—
1138C2×C3—41no—
1139C2×C3—122no—
1140C2×C3C22×D3×D411yescharacteristic
1141C2×C3C22×D3×D411yescharacteristic
1142C2×C3C2×#100711yescharacteristic
1143C2×C3C2×#101011yescharacteristic
1144C2×C3#596411yescharacteristic
1145C2×C3#596411yescharacteristic
1146D3—42no—
1147D3—64no—
1148D3—64no—
1149D3—124no—
1150D3—124no—
1151D3—122no—
1152D3—122no—
1153C22—21no—
1154C22—21no—
1155C22—21no—
1156C22—21no—
1157C22—21no—
1158C22—21no—
1159C22—21no—
1160C22—44no—
1161C22—62no—
1162C22—62no—
1163C22—62no—
1164C22—94no—
1165C22—182no—
1166C22—182no—
1167C22—182no—
1168C22—182no—
1169C22—182no—
1170C22—368no—
1171C22#6429712yescomplemented
1172C22C2×#381112yes—
1173C22C23×D3211yescharacteristic
1174C4—21no—
1175C4—21no—
1176C4—62no—
1177C4—64no—
1178C4—62no—
1179C4—62no—
1180C4—64no—
1181C4—94no—
1182C4—182no—
1183C4C2×#381112yes—
1184C4C2×#381112yes—
1185C3—21no—
1186C3#8598511yescharacteristic, complemented
1187C3#8604211yescharacteristic, complemented
1188C2—22no—
1189C2—22no—
1190C2—41no—
1191C2—122no—
1192C2—184no—
1193C2—362no—
1194C2C2×#6429711yescharacteristic
1195C2#1059666911yescharacteristic
1196C2C22×#381111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC23×C32×C4C22
hypercenterC23×C4D32
hypocenterC32#3489
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×#64297C2semidirect
3. C3×#5791C2semidirect
4. C2×C3×#924C2semidirect
5. #10595500C2semidirect
6. #10595043C2semidirect
7. #10595018C2semidirect
8. #10594990C2semidirect
9. #10594925C2semidirect
10. #10594923C2semidirect
11. #10594922C2semidirect
12. #10594917C2semidirect
13. #10594916C2semidirect
14. #10594915C2semidirect
15. #10594866C2semidirect
16. #10594834C2semidirect
17. #10594805C2semidirect
32. C2×C3×#235C22semidirect
33. C22×C3×Dic6C22semidirect
34. C2×#3804C22semidirect
35. C2×#3799C22semidirect
36. C2×#3797C22semidirect
38. C2×#3796C22semidirect
39. C2×D3×Dic6C22semidirect
43. C3×#930C22semidirect
44. C3×#929C22semidirect
46. C3×C4×#67C22semidirect
47. C3×#926C22semidirect
48. C2×C3×C4⋊Dic3C22semidirect
52. C3×#924C22semidirect
53. C3×#924C22semidirect
54. C3×#924C22semidirect
55. C2×C3×Dic3⋊C4C22semidirect
58. #63978C22semidirect
59. #63975C22semidirect
62. #63971C22semidirect
63. #63966C22semidirect
64. #63958C22semidirect
65. #63953C22semidirect
66. #63952C22semidirect
67. #63916C22semidirect
68. #63910C22semidirect
69. #63909C22semidirect
70. #63900C22semidirect
71. #63897C22semidirect
72. #63896C22semidirect
73. #63894C22semidirect
74. #63883C22semidirect
75. #63881C22semidirect
76. #63871C22semidirect
77. #63871C22semidirect
78. #63871C22semidirect
79. #63866C22semidirect
80. #63865C22semidirect
81. #63864C22semidirect
82. #63857C22semidirect
83. #63853C22semidirect
84. #63849C22semidirect
85. #63844C22semidirect
86. #63840C22semidirect
96. #5791D3semidirect
97. C2×#924D3semidirect
142. #3828D4semidirect
246. C2×#235C2×D3semidirect
257. C22×Dic6C2×D3semidirect
290. #930C2×D3semidirect
292. #929C2×D3semidirect
295. C4×#67C2×D3semidirect
296. #926C2×D3semidirect
297. C2×C4⋊Dic3C2×D3semidirect
302. #924C2×D3semidirect
303. #924C2×D3semidirect
304. #924C2×D3semidirect
305. C2×Dic3⋊C4C2×D3semidirect
638. C22×C322−1+4semidirect
1010. C22×C3#1007semidirect
1011. C22×C3#1010semidirect
1066. C32#3489semidirect
1171. C22#64297semidirect
1186. C3#85985semidirect
1187. C3#86042semidirect

Maximal subgroups

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

subgroupindex
C22×#38282
C2×#642972
C3×#57912
C2×C3×#9242
#105955002
#105950432
#105950182
#105949902
#105949252
#105949232
#105949222
#105949172
#105949162
#105949152
#105948662
#105948342
#105948052
#860423
#859853