Finite Group Databasebeta

← #11904791

Subgroups — #11904791

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
1C2×#41×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#64297C211yesmaximal, characteristic, complemented
3C3×#5833C211yesmaximal, characteristic, complemented
4C3×#5825C211yesmaximal, characteristic, complemented
5#10595361C212yesmaximal, complemented
6#10595341C212yesmaximal, complemented
7#10595243C212yesmaximal, complemented
8#10595163C214yesmaximal, complemented
9#10595162C214yesmaximal, complemented
10#10595161C212yesmaximal, complemented
11#10595034C211yesmaximal, characteristic, complemented
12#10594990C211yesmaximal, characteristic, complemented
13#10594925C212yesmaximal, complemented
14#10594923C212yesmaximal, complemented
15#10594922C212yesmaximal, complemented
16C2×#63871C211yesmaximal, characteristic, complemented
17#10594805C212yesmaximal, complemented
18#86380—31nomaximal
19#86356—31nomaximal
20C2×C32×#41C2211yescharacteristic
21#41×C3⋊D3—28no—
22C2×#3832C2211yescharacteristic
23C2×Q8×C3⋊D3C2211yescharacteristic
24C2×#3830C2211yescharacteristic
25C2×#3830C2212yes—
26C2×D4×C3⋊D3C2212yes—
27C2×D4×C3⋊D3C2211yescharacteristic
28C2×#3828C2212yes—
29C2×#3828C2211yescharacteristic
30C22×C4×C3⋊D3C2211yescharacteristic
31C22×C4×C3⋊D3C2212yes—
32C2×C3×#235C2211yescharacteristic, complemented
33C22×C3×Dic6C2211yescharacteristic, complemented
34C2×#3804C2214yescomplemented
35C2×#3799C2212yescomplemented
36C2×#3797C2212yescomplemented
37#64297—28no—
38C2×#3796C2212yescomplemented
39C2×D3×Dic6C2212yescomplemented
40C3×#946C2212yescomplemented
41C3×#944C2212yescomplemented
42C3×#939C2214yescomplemented
43C3×#938C2212yescomplemented
44C3×#936C2212yescomplemented
45C3×#935C2214yescomplemented
46C3×#930C2212yescomplemented
47C3×#926C2211yescharacteristic, complemented
48C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
49C3×#924C2212yescomplemented
50C3×#924C2212yescomplemented
51C3×#924C2212yescomplemented
52#63982C2214yescomplemented
53#63981C2212yes—
54#63981C2214yes—
55#63975C2214yescomplemented
56#63974C2214yes—
57#67⋊Dic3C2214yescomplemented
58#63971C2214yescomplemented
59C2×Dic3⋊Dic3C2212yescomplemented
60C2×#3722C2212yes—
61#63962C2212yescomplemented
62#63958C2214yescomplemented
63#63953C2214yescomplemented
64#63952C2214yescomplemented
65#63916C2211yescharacteristic
66#63916C2211yescharacteristic, complemented
67#63910C2214yescomplemented
68C4×#626C2212yes—
69C4×#626C2212yescomplemented
70#63900C2212yescomplemented
71#63897C2214yescomplemented
72#63896C2214yescomplemented
73#63894C2212yescomplemented
74#63883C2214yescomplemented
75#63881C2214yes—
76#63871C2212yes—
77#63871C2212yes—
78#63871C2211yescharacteristic
79#63871C2212yescomplemented
80#63871C2212yescomplemented
81#63871C2211yescharacteristic, complemented
82#63865C2214yes—
83#63853C2214yescomplemented
84#63849C2212yescomplemented
85#63844C2212yescomplemented
86#63840C2214yescomplemented
87C2×#1010—31no—
88C2×D3×#41—31no—
89C2×D3×#41—31no—
90C2×D3×#41—61no—
91C2×#1007—31no—
92C3×#537—31no—
93C3×#536—31no—
94#5833D311yescharacteristic, complemented
95#5828—31no—
96#5825D311yescharacteristic, complemented
97C2×#946—31no—
98#5727—32no—
99#5726—32no—
100#5677—32no—
101#5676—32no—
102#5655—34no—
103#5654—34no—
104#5632—32no—
105#5631—32no—
106#5629—32no—
107#5628—32no—
108#5628—32no—
109#5627—32no—
110D3×C22⋊Q8—32no—
111D3×C22⋊Q8—32no—
112#5612—32no—
113#5611—34no—
114#5610—34no—
115#5608—32no—
116#5606—32no—
117#5598—32no—
118#5524—31no—
119#5523—31no—
120C2×#897—31no—
121#5504—31no—
122C23×C3⋊D3C2311yescharacteristic
123C23×C3⋊D3C2312yes—
124C32×#41—24no—
125C2×C32×Q8C2311yescharacteristic
126C2×C32×D4C2312yes—
127C2×C32×D4C2311yescharacteristic
128C22×C32×C4C2312yes—
129C22×C32×C4C2311yescharacteristic
130C2×#638C2312yes—
131C2×#638C2312yes—
132C2×#638C2312yes—
133C22×C3⋊Dic3C2311yescharacteristic
134C22×C3⋊Dic3C2312yes—
135#3832—24no—
136Q8×C3⋊D3—24no—
137#3830—28no—
138#3830—24no—
139D4×C3⋊D3—28no—
140D4×C3⋊D3—24no—
141#3828—28no—
142#3828D418yescomplemented
143C2×C4⋊(C3⋊D3)C2312yes—
144C2×C4⋊(C3⋊D3)C2311yescharacteristic
145C2×C4×C3⋊D3—24no—
146C2×C4×C3⋊D3—28no—
147C2×C4×C3⋊D3C2311yescharacteristic
148C2×C4×C3⋊D3C2311yescharacteristic
149C2×C4×C3⋊D3C2312yes—
150C2×C4×C3⋊D3C2311yescharacteristic
151C2×C4×C3⋊D3C2312yes—
152C2×C4×C3⋊D3C2311yescharacteristic
153C2×C4×C3⋊D3C2312yes—
154C2×#634C2312yes—
155C2×#634C2311yescharacteristic
156C2×C3×#67C2312yes—
157C2×C3×#67C2314yes—
158C22×C3×Dic3C2312yes—
159C22×C3×Dic3C2312yes—
160C3×#235—24no—
161C2×C3×D12C2311yescharacteristic
162C2×C3×C4×D3C2312yes—
163C2×C3×Dic6—24no—
164C2×C3×Dic6C2312yes—
165C2×C3×Dic6C2312yes—
166C2×C3×Dic6C2311yescharacteristic
167C2×#627C2314yes—
168C2×#626C2314yes—
169C2×#626C2312yes—
170C2×#626C2312yes—
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×#217C2314yes—
181C3×#217C2314yes—
182C3×#217C2312yes—
183C3×(C2×D3)⋊C4C2314yes—
184C3×C4⋊Dic3C2311yescharacteristic
185C3×C4⋊Dic3C2311yescharacteristic
186C3×C4⋊Dic3C2312yes—
187C3×C4⋊Dic3C2312yes—
188C3×Dic3⋊C4C2314yes—
189C3×Dic3⋊C4C2314yes—
190C3×Dic3⋊C4C2314yes—
191C3×C4×Dic3C2312yes—
192#3724C2314yes—
193Dic3⋊Dic3C2312yes—
194Dic3⋊Dic3C2314yes—
195Dic3⋊Dic3C2314yes—
196Dic3⋊Dic3C2312yes—
197#3722C2314yes—
198#3722C2312yes—
199#3722C2314yes—
200#3722C2314yes—
201#3722C2312yes—
202(C2×D3)⋊Dic3C2312yes—
203(C2×D3)⋊Dic3C2312yes—
204Dic32C2314yes—
205#3489—91noSylow
206C2×C3×#41—21no—
207C2×C3×#41—31no—
208C2×C3×#41C2×D311yescharacteristic
209C2×C3×#41C2×D311yescharacteristic
210C22×C3×Q8—31no—
211#1010—68no—
212D3×#41—68no—
213D3×#41—68no—
214D3×#41—616no—
215#1007—68no—
216C2×#239—31no—
217C2×#239—31no—
218C2×#239—32no—
219C2×#239—32no—
220C2×#239—61no—
221C2×D3×Q8—31no—
222C2×D3×Q8—31no—
223C2×D3×Q8—32no—
224C2×D3×Q8—32no—
225C2×D3×Q8—32no—
226C2×D3×Q8—61no—
227C2×#237—32no—
228C2×#237—31no—
229C2×#237—31no—
230C2×#237—32no—
231C2×#237—34no—
232C2×#237—32no—
233C2×#237—62no—
234C2×#237—61no—
235C2×D3×D4—32no—
236C2×D3×D4—31no—
237C2×D3×D4—32no—
238C2×D3×D4—31no—
239C2×D3×D4—62no—
240C2×D3×D4—61no—
241C2×#235—31no—
242C2×#235—31no—
243C2×#235—32no—
244C2×#235—32no—
245C2×#235—34no—
246C2×#235—32no—
247C2×#235—61no—
248C2×#235—62no—
249C2×#235C2×D311yescharacteristic, complemented
250C22×C4×D3—31no—
251C22×C4×D3—31no—
252C22×C4×D3—32no—
253C22×C4×D3—32no—
254C22×C4×D3—61no—
255C22×C4×D3—62no—
256C22×Dic6—32no—
257C22×Dic6C2×D311yescharacteristic, complemented
258C3×C4⋊Q8—32no—
259C3×#124—32no—
260C3×#123—34no—
261C3×C22⋊Q8—32no—
262C3×C22⋊Q8—32no—
263C3×C22⋊Q8—32no—
264C3×C22⋊Q8—32no—
265C3×#121—32no—
266C3×#121—34no—
267C3×#121—32no—
268C3×#117—31no—
269C2×C3×C4⋊C4—31no—
270#946—32no—
271#946—32no—
272#946—32no—
273#946—31no—
274#946—32no—
275#946—31no—
276#946C2×D312yescomplemented
277#944C2×D312yescomplemented
278#939—34no—
279#939C2×D314yescomplemented
280#938—34no—
281#938—31no—
282#938—31no—
283#938C2×D312yescomplemented
284#937—32no—
285#937—34no—
286#936C2×D312yescomplemented
287#935—32no—
288#935C2×D314yescomplemented
289D4×Dic3—34no—
290#930C2×D312yescomplemented
291C4×#67—34no—
292C4×#67—32no—
293C4×#67—32no—
294C2×(C2×D3)⋊C4—32no—
295C2×(C2×D3)⋊C4—32no—
296#926C2×D311yescharacteristic, complemented
297C2×C4⋊Dic3—32no—
298C2×C4⋊Dic3C2×D311yescharacteristic, complemented
299#924C2×D312yescomplemented
300#924C2×D312yescomplemented
301#924C2×D312yescomplemented
302C2×Dic3⋊C4—32no—
303#897—32no—
304#897—32no—
305#897—31no—
306#897—32no—
307#897—32no—
308#897—31no—
309#896—34no—
310#896—34no—
311#896—34no—
312#895—31no—
313#895—31no—
314#895—34no—
315#894—34no—
316#894—34no—
317#894—34no—
318#893—34no—
319#893—32no—
320#892—32no—
321#892—32no—
322D3×C4⋊C4—32no—
323D3×C4⋊C4—32no—
324D3×C4⋊C4—34no—
325D3×C4⋊C4—34no—
326#888—34no—
327#888—34no—
328#887—32no—
329#886—32no—
330#885—34no—
331#885—34no—
332#884—34no—
333#884—34no—
334#884—34no—
335#883—34no—
336#883—34no—
337#883—34no—
338#882—32no—
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—
348C4×D12—32no—
349C4×D12—32no—
350C4×D12—32no—
351C4×Dic6—32no—
352C23×C32C2412yes—
353C23×C32C2411yescharacteristic
354C22×C3⋊D3—22no—
355C22×C3⋊D3—24no—
356C22×C3⋊D3—24no—
357C22×C3⋊D3—22no—
358C22×C3⋊D3—42no—
359C22×C3⋊D3—41no—
360C22×C3⋊D3C2411yescharacteristic
361C22×C3⋊D3C2412yes—
362C22×C3⋊D3C2411yescharacteristic
363C22×C3×D3C2412yes—
364C32×Q8—22no—
365C32×D4—24no—
366C32×D4—22no—
367C2×C32×C4—24no—
368C2×C32×C4C2×D414yes—
369C2×C32×C4C2412yes—
370C2×C32×C4C2411yescharacteristic
371C2×C32×C4C2411yescharacteristic
372#638—24no—
373#638—24no—
374#638C2×D418yes—
375C2×C3⋊Dic3—22no—
376C2×C3⋊Dic3—24no—
377C2×C3⋊Dic3C2411yescharacteristic
378C2×C3⋊Dic3C2411yescharacteristic
379C2×C3⋊Dic3C2412yes—
380C4⋊(C3⋊D3)—24no—
381C4⋊(C3⋊D3)C2×D414yes—
382C4×C3⋊D3—24no—
383C4×C3⋊D3—22no—
384C4×C3⋊D3—22no—
385C4×C3⋊D3—22no—
386C4×C3⋊D3—22no—
387C4×C3⋊D3—24no—
388C4×C3⋊D3C2×D418yes—
389#634—24no—
390#634C2×D414yes—
391C3×#67—24no—
392C3×#67—44no—
393C2×C3×Dic3—24no—
394C2×C3×Dic3—42no—
395C2×C3×Dic3C2412yes—
396C2×C3×Dic3C2414yes—
397C2×C3×Dic3C2412yes—
398C2×C3×Dic3C2414yes—
399C2×C3×Dic3C2412yes—
400C3×D12—22no—
401C3×C4×D3—24no—
402C3×Dic6—24no—
403C3×Dic6—24no—
404C3×Dic6—22no—
405#627—28no—
406#626—28no—
407#626—24no—
408#626—42no—
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—31no—
421#537—92no—
422#536—31no—
423#536—92no—
424#525—91no—
425#525—92no—
426C2×C22⋊Q8—91no—
427C2×C22⋊Q8—92no—
428#520—91no—
429C23×D3—32no—
430C23×D3—32no—
431C23×D3—31no—
432C23×D3—31no—
433C23×D3—61no—
434C23×D3—62no—
435C3×#41—28no—
436C3×#41—24no—
437C3×#41—24no—
438C3×#41—64no—
439C2×C3×Q8—21no—
440C2×C3×Q8—31no—
441C2×C3×Q8—32no—
442C2×C3×Q8—32no—
443C2×C3×Q8—64no—
444C2×C3×Q8C22×D311yescharacteristic
445C2×C3×Q8C22×D311yescharacteristic
446C2×C3×D4—22no—
447C2×C3×D4—21no—
448C2×C3×D4—32no—
449C2×C3×D4—34no—
450C2×C3×D4—31no—
451C2×C3×D4C22×D312yes—
452C2×C3×D4C22×D311yescharacteristic
453C2×C3×D4C22×D311yescharacteristic
454C2×C3×D4C22×D312yes—
455C22×C3×C4—22no—
456C22×C3×C4—21no—
457C22×C3×C4—32no—
458C22×C3×C4—32no—
459C22×C3×C4—32no—
460C22×C3×C4C22×D312yes—
461C22×C3×C4C22×D312yes—
462C22×C3×C4C22×D311yescharacteristic
463C22×C3×C4C22×D311yescharacteristic
464C2×#67—32no—
465C2×#67—32no—
466C2×#67—32no—
467C2×#67—32no—
468C2×#67—32no—
469C2×#67—32no—
470C2×#67—32no—
471C2×#67—34no—
472C2×#67—32no—
473C2×#67—62no—
474C2×#67—62no—
475C2×#67—62no—
476C2×#67C22×D312yes—
477C2×#67C22×D314yes—
478C22×Dic3—32no—
479C22×Dic3—32no—
480C22×Dic3—31no—
481C22×Dic3—31no—
482C22×Dic3—34no—
483C22×Dic3—61no—
484C22×Dic3—62no—
485C22×Dic3C22×D312yes—
486C22×Dic3C22×D312yes—
487#239—68no—
488#239—68no—
489#239—64no—
490#239—64no—
491#239—68no—
492D3×Q8—68no—
493D3×Q8—68no—
494D3×Q8—68no—
495D3×Q8—64no—
496D3×Q8—64no—
497D3×Q8—68no—
498#237—68no—
499#237—64no—
500#237—64no—
501#237—616no—
502#237—68no—
503#237—68no—
504#237—616no—
505#237—68no—
506D3×D4—64no—
507D3×D4—64no—
508D3×D4—68no—
509D3×D4—68no—
510D3×D4—68no—
511D3×D4—616no—
512#235—24no—
513#235—38no—
514#235—38no—
515#235—68no—
516#235—68no—
517#235—68no—
518#235—68no—
519#235—616no—
520#235—616no—
521C2×D12—31no—
522C2×D12—31no—
523C2×D12—32no—
524C2×D12—34no—
525C2×D12—32no—
526C2×D12—32no—
527C2×D12—32no—
528C2×D12—61no—
529C2×D12—62no—
530C2×D12C22×D311yescharacteristic
531C2×C4×D3—32no—
532C2×C4×D3—32no—
533C2×C4×D3—34no—
534C2×C4×D3—31no—
535C2×C4×D3—31no—
536C2×C4×D3—32no—
537C2×C4×D3—32no—
538C2×C4×D3—32no—
539C2×C4×D3—32no—
540C2×C4×D3—31no—
541C2×C4×D3—31no—
542C2×C4×D3—31no—
543C2×C4×D3—31no—
544C2×C4×D3—31no—
545C2×C4×D3—31no—
546C2×C4×D3—34no—
547C2×C4×D3—34no—
548C2×C4×D3—34no—
549C2×C4×D3—34no—
550C2×C4×D3—61no—
551C2×C4×D3—62no—
552C2×C4×D3—61no—
553C2×C4×D3—62no—
554C2×C4×D3—61no—
555C2×C4×D3—62no—
556C2×C4×D3—61no—
557C2×C4×D3—68no—
558C2×C4×D3—68no—
559C2×C4×D3—616no—
560C2×C4×D3—68no—
561C2×C4×D3—64no—
562C2×C4×D3—64no—
563C2×C4×D3C22×D312yes—
564C2×Dic6—24no—
565C2×Dic6—31no—
566C2×Dic6—31no—
567C2×Dic6—32no—
568C2×Dic6—32no—
569C2×Dic6—34no—
570C2×Dic6—34no—
571C2×Dic6—61no—
572C2×Dic6—62no—
573C2×Dic6—68no—
574C2×Dic6C22×D312yes—
575C2×Dic6C22×D311yescharacteristic
576C2×Dic6C22×D312yes—
577C3×C4⋊C4—32no—
578C3×C4⋊C4—34no—
579C3×C4⋊C4—34no—
580C3×C4⋊C4—31no—
581C3×C4⋊C4—32no—
582C3×C4⋊C4—34no—
583C3×C4⋊C4—31no—
584C3×C22⋊C4—34no—
585C3×C22⋊C4—34no—
586C3×C22⋊C4—32no—
587C3×C22⋊C4—34no—
588C3×C22⋊C4—34no—
589C3×C42—32no—
590#217—32no—
591#217—32no—
592#217C22×D314yes—
593#217C22×D314yes—
594#217C22×D314yes—
595#217C22×D312yes—
596(C2×D3)⋊C4—32no—
597(C2×D3)⋊C4—32no—
598(C2×D3)⋊C4—32no—
599(C2×D3)⋊C4—34no—
600(C2×D3)⋊C4—32no—
601(C2×D3)⋊C4—32no—
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—32no—
608(C2×D3)⋊C4C22×D314yes—
609C4⋊Dic3—32no—
610C4⋊Dic3—32no—
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—32no—
620Dic3⋊C4—34no—
621Dic3⋊C4—32no—
622Dic3⋊C4—34no—
623Dic3⋊C4C22×D314yes—
624Dic3⋊C4C22×D314yes—
625Dic3⋊C4C22×D314yes—
626C4×Dic3—34no—
627C4×Dic3—34no—
628C4×Dic3C22×D312yes—
629C22×C32—22no—
630C22×C32—21no—
631C22×C32—21no—
632C22×C32—22no—
633C22×C32—22no—
634C22×C32C22×D412yes—
635C22×C32C2511yescharacteristic
636C2×C3⋊D3—21no—
637C2×C3⋊D3—21no—
638C2×C3⋊D3—21no—
639C2×C3⋊D3—22no—
640C2×C3⋊D3—22no—
641C2×C3⋊D3—21no—
642C2×C3⋊D3—21no—
643C2×C3⋊D3—48no—
644C2×C3⋊D3—44no—
645C2×C3⋊D3C22×D414yes—
646C2×C3⋊D32−1+412yescomplemented
647C2×C3×D3—22no—
648C2×C3×D3—22no—
649C2×C3×D3—22no—
650C32×C4—22no—
651C32×C4C22×D412yes—
652C32×C4C22×D412yes—
653C3⋊Dic3—21no—
654C3⋊Dic3—21no—
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—188no—
672C2×#41D3211yescharacteristic
673C22×Q8—31no—
674C22×Q8—92no—
675C22×Q8—92no—
676C22×Q8—91no—
677C22×D4—92no—
678C22×D4—91no—
679C23×C4—92no—
680C23×C4—91no—
681C4⋊Q8—32no—
682C4⋊Q8—94no—
683#124—32no—
684#124—94no—
685#123—34no—
686#123—94no—
687#123—94no—
688#123—92no—
689#123—94no—
690C22⋊Q8—32no—
691C22⋊Q8—32no—
692C22⋊Q8—32no—
693C22⋊Q8—32no—
694C22⋊Q8—94no—
695C22⋊Q8—94no—
696C22⋊Q8—94no—
697C22⋊Q8—92no—
698C22⋊Q8—91no—
699C22⋊Q8—92no—
700C22⋊Q8—92no—
701C22⋊Q8—92no—
702C22⋊Q8—91no—
703#121—34no—
704#121—32no—
705#121—32no—
706#121—94no—
707#121—94no—
708#121—94no—
709#121—91no—
710#121—91no—
711#120—92no—
712#120—94no—
713C4×Q8—92no—
714C4×D4—92no—
715C4×D4—92no—
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—92no—
724C2×C4⋊C4—94no—
725C2×C4⋊C4—92no—
726C2×C22⋊C4—94no—
727C2×C22⋊C4—92no—
728C23×C3—22no—
729C23×C3—21no—
730C23×C3—32no—
731C23×C3C23×D312yes—
732C23×C3C23×D312yes—
733C23×C3C23×D311yescharacteristic
734C23×C3C23×D311yescharacteristic
735C22×D3—31no—
736C22×D3—31no—
737C22×D3—32no—
738C22×D3—32no—
739C22×D3—31no—
740C22×D3—31no—
741C22×D3—61no—
742C22×D3—62no—
743C22×D3—61no—
744C22×D3—64no—
745C22×D3—64no—
746C22×D3—64no—
747C22×D3—62no—
748C22×D3—64no—
749C22×D3—62no—
750C22×D3—68no—
751C22×D3—64no—
752C22×D3—62no—
753C22×D3—62no—
754C22×D3—122no—
755C22×D3—124no—
756C22×D3—122no—
757C22×D3—121no—
758C22×D3—122no—
759C22×D3—121no—
760C22×D3—122no—
761C22×D3—124no—
762C22×D3C23×D312yes—
763C3×Q8—24no—
764C3×Q8—22no—
765C3×Q8—22no—
766C3×Q8—62no—
767C3×Q8—64no—
768C3×Q8—64no—
769C3×D4—28no—
770C3×D4—24no—
771C3×D4—24no—
772C3×D4—24no—
773C3×D4—22no—
774C3×D4—22no—
775C3×D4—64no—
776C3×D4—62no—
777C3×D4—124no—
778C2×C3×C4—28no—
779C2×C3×C4—24no—
780C2×C3×C4—24no—
781C2×C3×C4—22no—
782C2×C3×C4—21no—
783C2×C3×C4—21no—
784C2×C3×C4—24no—
785C2×C3×C4—32no—
786C2×C3×C4—34no—
787C2×C3×C4—32no—
788C2×C3×C4—32no—
789C2×C3×C4—34no—
790C2×C3×C4—64no—
791C2×C3×C4—64no—
792C2×C3×C4—122no—
793C2×C3×C4D3×D414yes—
794C2×C3×C4D3×D414yes—
795C2×C3×C4C23×D312yes—
796C2×C3×C4C23×D312yes—
797C2×C3×C4C23×D311yescharacteristic
798C2×C3×C4C23×D311yescharacteristic
799C2×C3×C4C23×D311yescharacteristic
800C2×C3×C4C23×D311yescharacteristic
801#67—24no—
802#67—38no—
803#67—38no—
804#67—44no—
805#67—68no—
806#67—68no—
807#67—64no—
808#67—64no—
809#67—64no—
810#67—64no—
811#67—64no—
812#67—68no—
813#67—68no—
814#67—122no—
815C2×Dic3—24no—
816C2×Dic3—32no—
817C2×Dic3—32no—
818C2×Dic3—31no—
819C2×Dic3—31no—
820C2×Dic3—31no—
821C2×Dic3—31no—
822C2×Dic3—42no—
823C2×Dic3—62no—
824C2×Dic3—61no—
825C2×Dic3—61no—
826C2×Dic3—68no—
827C2×Dic3—64no—
828C2×Dic3—64no—
829C2×Dic3—68no—
830C2×Dic3—64no—
831C2×Dic3—62no—
832C2×Dic3—62no—
833C2×Dic3C23×D312yes—
834C2×Dic3C23×D314yes—
835C2×Dic3C23×D312yes—
836C2×Dic3C23×D312yes—
837C2×Dic3C23×D314yes—
838D12—22no—
839D12—34no—
840D12—34no—
841D12—64no—
842D12—64no—
843D12—64no—
844D12—68no—
845D12—64no—
846D12—68no—
847D12—122no—
848C4×D3—24no—
849C4×D3—38no—
850C4×D3—38no—
851C4×D3—68no—
852C4×D3—68no—
853C4×D3—68no—
854C4×D3—64no—
855C4×D3—64no—
856C4×D3—68no—
857C4×D3—64no—
858C4×D3—64no—
859C4×D3—64no—
860C4×D3—64no—
861C4×D3—68no—
862C4×D3—64no—
863C4×D3—68no—
864C4×D3—64no—
865C4×D3—62no—
866C4×D3—62no—
867C4×D3—62no—
868C4×D3—62no—
869C4×D3—62no—
870C4×D3—62no—
871C4×D3—62no—
872C4×D3—62no—
873C4×D3—124no—
874C4×D3—124no—
875Dic6—24no—
876Dic6—24no—
877Dic6—22no—
878Dic6—34no—
879Dic6—34no—
880Dic6—64no—
881Dic6—68no—
882Dic6—68no—
883Dic6—64no—
884Dic6—64no—
885Dic6—68no—
886C2×C32—22no—
887C2×C32—42no—
888C2×C32C23×D411yescharacteristic
889C2×C32C2×2−1+411yescharacteristic
890C2×C32#58511yescharacteristic
891C3⋊D3—22no—
892C3⋊D3—24no—
893C3⋊D3—41no—
894C3×D3—42no—
895C24—92no—
896C24—91no—
897#41—24no—
898#41—64no—
899#41—98no—
900#41—188no—
901#41—1816no—
902#41—188no—
903#41—188no—
904#41—188no—
905#41—184no—
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—188no—
915C2×Q8—188no—
916C2×Q8—184no—
917C2×Q8C2×D3211yescharacteristic
918C2×D4—32no—
919C2×D4—34no—
920C2×D4—31no—
921C2×D4—92no—
922C2×D4—94no—
923C2×D4—92no—
924C2×D4—92no—
925C2×D4—92no—
926C2×D4—92no—
927C2×D4—91no—
928C2×D4—92no—
929C2×D4—188no—
930C2×D4—184no—
931C2×D4C2×D3212yes—
932C2×D4C2×D3211yescharacteristic
933C22×C4—32no—
934C22×C4—32no—
935C22×C4—32no—
936C22×C4—94no—
937C22×C4—94no—
938C22×C4—94no—
939C22×C4—92no—
940C22×C4—91no—
941C22×C4—92no—
942C22×C4—92no—
943C22×C4—92no—
944C22×C4—91no—
945C22×C4—91no—
946C22×C4—91no—
947C22×C4—91no—
948C22×C4—188no—
949C22×C4—184no—
950C22×C4C2×D3212yes—
951C22×C4C2×D3211yescharacteristic
952C4⋊C4—32no—
953C4⋊C4—32no—
954C4⋊C4—31no—
955C4⋊C4—34no—
956C4⋊C4—34no—
957C4⋊C4—31no—
958C4⋊C4—34no—
959C4⋊C4—92no—
960C4⋊C4—94no—
961C4⋊C4—94no—
962C4⋊C4—94no—
963C4⋊C4—92no—
964C22⋊C4—34no—
965C22⋊C4—34no—
966C22⋊C4—32no—
967C22⋊C4—34no—
968C22⋊C4—34no—
969C22⋊C4—92no—
970C22⋊C4—94no—
971C22⋊C4—94no—
972C22⋊C4—94no—
973C22⋊C4—92no—
974C22⋊C4—92no—
975C22⋊C4—92no—
976C42—32no—
977C42—94no—
978C22×C3—21no—
979C22×C3—21no—
980C22×C3—21no—
981C22×C3—21no—
982C22×C3—24no—
983C22×C3—22no—
984C22×C3—22no—
985C22×C3—22no—
986C22×C3—22no—
987C22×C3—22no—
988C22×C3—22no—
989C22×C3—22no—
990C22×C3—21no—
991C22×C3—41no—
992C22×C3—41no—
993C22×C3—42no—
994C22×C3—42no—
995C22×C3—62no—
996C22×C3—62no—
997C22×C3—62no—
998C22×C3C2×D3×D412yes—
999C22×C3C2×D3×D412yes—
1000C22×C3C24×D311yescharacteristic
1001C22×C3C24×D311yescharacteristic
1002C2×D3—22no—
1003C2×D3—22no—
1004C2×D3—22no—
1005C2×D3—34no—
1006C2×D3—34no—
1007C2×D3—32no—
1008C2×D3—32no—
1009C2×D3—62no—
1010C2×D3—64no—
1011C2×D3—62no—
1012C2×D3—62no—
1013C2×D3—61no—
1014C2×D3—61no—
1015C2×D3—62no—
1016C2×D3—61no—
1017C2×D3—62no—
1018C2×D3—62no—
1019C2×D3—62no—
1020C2×D3—61no—
1021C2×D3—62no—
1022C2×D3—61no—
1023C2×D3—61no—
1024C2×D3—61no—
1025C2×D3—61no—
1026C2×D3—61no—
1027C2×D3—61no—
1028C2×D3—122no—
1029C2×D3—122no—
1030C2×D3—121no—
1031C2×D3—121no—
1032C2×D3—128no—
1033C2×D3—128no—
1034C2×D3—124no—
1035C2×D3—124no—
1036C2×D3—128no—
1037C2×D3—1216no—
1038C3×C4—24no—
1039C3×C4—22no—
1040C3×C4—22no—
1041C3×C4—22no—
1042C3×C4—22no—
1043C3×C4—62no—
1044C3×C4—64no—
1045C3×C4—62no—
1046C3×C4—62no—
1047C3×C4—64no—
1048C3×C4C2×D3×D412yes—
1049C3×C4C2×D3×D412yes—
1050C3×C4C2×D3×D412yes—
1051C3×C4C2×D3×D412yes—
1052Dic3—24no—
1053Dic3—22no—
1054Dic3—24no—
1055Dic3—22no—
1056Dic3—22no—
1057Dic3—34no—
1058Dic3—34no—
1059Dic3—64no—
1060Dic3—62no—
1061Dic3—62no—
1062Dic3—61no—
1063Dic3—61no—
1064Dic3—61no—
1065Dic3—61no—
1066C32#348911yescharacteristic, complemented, Sylow
1067C23—32no—
1068C23—91no—
1069C23—92no—
1070C23—91no—
1071C23—184no—
1072C23—182no—
1073C23—184no—
1074C23—182no—
1075C23—361no—
1076C23—362no—
1077C23C22×D3212yes—
1078C23C22×D3211yescharacteristic
1079Q8—22no—
1080Q8—64no—
1081Q8—64no—
1082Q8—62no—
1083Q8—94no—
1084Q8—184no—
1085Q8—188no—
1086D4—24no—
1087D4—22no—
1088D4—64no—
1089D4—62no—
1090D4—98no—
1091D4—94no—
1092D4—124no—
1093D4—184no—
1094D4—188no—
1095D4—184no—
1096D4—184no—
1097D4—184no—
1098D4—362no—
1099C2×C4—24no—
1100C2×C4—32no—
1101C2×C4—32no—
1102C2×C4—34no—
1103C2×C4—32no—
1104C2×C4—34no—
1105C2×C4—64no—
1106C2×C4—64no—
1107C2×C4—92no—
1108C2×C4—98no—
1109C2×C4—91no—
1110C2×C4—91no—
1111C2×C4—122no—
1112C2×C4—184no—
1113C2×C4—184no—
1114C2×C4—188no—
1115C2×C4—188no—
1116C2×C4—184no—
1117C2×C4—182no—
1118C2×C4—182no—
1119C2×C4—182no—
1120C2×C4—182no—
1121C2×C4—182no—
1122C2×C4—364no—
1123C2×C4#381114yes—
1124C2×C4C22×D3212yes—
1125C2×C4C22×D3211yescharacteristic
1126C2×C4C22×D3211yescharacteristic
1127C2×C3—22no—
1128C2×C3—22no—
1129C2×C3—21no—
1130C2×C3—21no—
1131C2×C3—21no—
1132C2×C3—42no—
1133C2×C3—44no—
1134C2×C3—42no—
1135C2×C3—42no—
1136C2×C3—122no—
1137C2×C3C22×D3×D411yescharacteristic
1138C2×C3C22×D3×D411yescharacteristic
1139C2×C3#596611yescharacteristic
1140C2×C3D3×2−1+411yescharacteristic
1141C2×C3D3×2−1+411yescharacteristic
1142C2×C3#596811yescharacteristic
1143D3—42no—
1144D3—64no—
1145D3—62no—
1146D3—64no—
1147D3—62no—
1148D3—64no—
1149D3—124no—
1150D3—122no—
1151D3—121no—
1152D3—121no—
1153C22—21no—
1154C22—21no—
1155C22—22no—
1156C22—22no—
1157C22—22no—
1158C22—62no—
1159C22—62no—
1160C22—62no—
1161C22—92no—
1162C22—94no—
1163C22—182no—
1164C22—182no—
1165C22—181no—
1166C22—181no—
1167C22—181no—
1168C22—181no—
1169C22—181no—
1170C22—364no—
1171C22—368no—
1172C22C2×#381112yes—
1173C22C23×D3211yescharacteristic
1174C4—22no—
1175C4—62no—
1176C4—64no—
1177C4—62no—
1178C4—62no—
1179C4—64no—
1180C4—94no—
1181C4—181no—
1182C4—181no—
1183C4C2×#381112yes—
1184C4C2×#381112yes—
1185C3—21no—
1186C3#8635611yescharacteristic, complemented
1187C3#8638011yescharacteristic, complemented
1188C2—22no—
1189C2—42no—
1190C2—122no—
1191C2—182no—
1192C2—184no—
1193C2—361no—
1194C2#1059669411yescharacteristic
1195C2#1059669811yescharacteristic
1196C2C22×#381111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×#41C22
hypercenterC2×#41D32
hypocenterC32#3489
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×#64297C2semidirect
3. C3×#5833C2semidirect
4. C3×#5825C2semidirect
5. #10595361C2semidirect
6. #10595341C2semidirect
7. #10595243C2semidirect
8. #10595163C2semidirect
9. #10595162C2semidirect
10. #10595161C2semidirect
11. #10595034C2semidirect
12. #10594990C2semidirect
13. #10594925C2semidirect
14. #10594923C2semidirect
15. #10594922C2semidirect
16. C2×#63871C2semidirect
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
40. C3×#946C22semidirect
41. C3×#944C22semidirect
42. C3×#939C22semidirect
43. C3×#938C22semidirect
44. C3×#936C22semidirect
45. C3×#935C22semidirect
46. C3×#930C22semidirect
47. C3×#926C22semidirect
48. C2×C3×C4⋊Dic3C22semidirect
49. C3×#924C22semidirect
50. C3×#924C22semidirect
51. C3×#924C22semidirect
52. #63982C22semidirect
55. #63975C22semidirect
57. #67⋊Dic3C22semidirect
58. #63971C22semidirect
59. C2×Dic3⋊Dic3C22semidirect
61. #63962C22semidirect
62. #63958C22semidirect
63. #63953C22semidirect
64. #63952C22semidirect
66. #63916C22semidirect
67. #63910C22semidirect
69. C4×#626C22semidirect
70. #63900C22semidirect
71. #63897C22semidirect
72. #63896C22semidirect
73. #63894C22semidirect
74. #63883C22semidirect
79. #63871C22semidirect
80. #63871C22semidirect
81. #63871C22semidirect
83. #63853C22semidirect
84. #63849C22semidirect
85. #63844C22semidirect
86. #63840C22semidirect
94. #5833D3semidirect
96. #5825D3semidirect
142. #3828D4semidirect
249. C2×#235C2×D3semidirect
257. C22×Dic6C2×D3semidirect
276. #946C2×D3semidirect
277. #944C2×D3semidirect
279. #939C2×D3semidirect
283. #938C2×D3semidirect
286. #936C2×D3semidirect
288. #935C2×D3semidirect
290. #930C2×D3semidirect
296. #926C2×D3semidirect
298. C2×C4⋊Dic3C2×D3semidirect
299. #924C2×D3semidirect
300. #924C2×D3semidirect
301. #924C2×D3semidirect
646. C2×C3⋊D32−1+4semidirect
1066. C32#3489semidirect
1186. C3#86356semidirect
1187. C3#86380semidirect

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×#642972
C3×#58332
C3×#58252
#105953612
#105953412
#105952432
#105951632
#105951622
#105951612
#105950342
#105949902
#105949252
#105949232
#105949222
C2×#638712
#105948052
#863803
#863563