Finite Group Databasebeta

← #11904394

Subgroups — #11904394

Order 1152.

3291 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64330C211yesmaximal, characteristic, complemented
2C2×#64306C211yesmaximal, characteristic, complemented
3C2×#64092C211yesmaximal, characteristic, complemented
4C3×#5490C212yesmaximal, complemented
5#10595528C211yesmaximal, characteristic, complemented
6#10595494C212yesmaximal, complemented
7#10595084C211yesmaximal, characteristic, complemented
8#10595079C211yesmaximal, characteristic, complemented
9#10595058C211yesmaximal, characteristic, complemented
10#10594907C212yesmaximal, complemented
11#10594888C212yesmaximal, complemented
12#10594286C212yesmaximal, complemented
13#10594281C212yesmaximal, complemented
14#10594278C212yesmaximal, complemented
15#10594263C212yesmaximal, complemented
16D3×#883C212yesmaximal, complemented
17#10594188C212yesmaximal, complemented
18#10594070C212yesmaximal, complemented
19#10594065C212yesmaximal, complemented
20#86663—32nomaximal
21C22×#638C2211yescharacteristic
22C22×C4×C3⋊D3C2211yescharacteristic, complemented
23C22×C3×#67C2212yescomplemented
24C2×C3×#235C2212yescomplemented
25#64330—28no—
26C2×#3811C2211yescharacteristic
27C2×#3811C2211yescharacteristic
28C2×#3811C2211yescharacteristic, complemented
29C2×D3×#67C2212yes—
30C2×D3×#67C2212yescomplemented
31C2×#3805C2212yescomplemented
32C2×#3805C2212yescomplemented
33C2×#3804C2212yes—
34C2×#3804C2212yescomplemented
35#64306—28no—
36C2×#3802C2211yescharacteristic, complemented
37C2×C4×D32C2211yescharacteristic, complemented
38C2×C4×D32C2211yescharacteristic, complemented
39C2×#3798C2212yescomplemented
40C2×#3797C2211yescharacteristic, complemented
41C2×#3796C2212yescomplemented
42C2×C32×C22⋊C4C2211yescharacteristic, complemented
43C2×#3757C2211yescharacteristic, complemented
44C2×#3752C2211yescharacteristic, complemented
45C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
46C2×#3750C2211yescharacteristic, complemented
47#64092C2212yescomplemented
48#64092C2212yescomplemented
49#64092C2212yescomplemented
50#64092C2212yescomplemented
51C3×#953C2212yescomplemented
52C3×#930C2212yescomplemented
53C3×#929C2212yescomplemented
54C3×C4×#67C2212yescomplemented
55C3×#885C2212yescomplemented
56C3×#884C2212yescomplemented
57C3×#884C2212yescomplemented
58C3×#883C2212yescomplemented
59C3×#882C2212yescomplemented
60C3×#67⋊C4C2212yescomplemented
61C3×D3×C22⋊C4C2212yescomplemented
62C3×#878C2212yescomplemented
63#63983C2212yescomplemented
64#63980C2212yescomplemented
65#63976C2212yescomplemented
66#63975C2212yescomplemented
67#63974C2211yescharacteristic, complemented
68#67⋊Dic3C2212yescomplemented
69Dic3×#67C2212yescomplemented
70#63970C2212yescomplemented
71#63970C2212yescomplemented
72#63969C2212yescomplemented
73D3×#217C2212yescomplemented
74#63964C2212yescomplemented
75#63962C2212yescomplemented
76#63962C2212yescomplemented
77#63959C2212yescomplemented
78#63958C2212yescomplemented
79#63958C2212yescomplemented
80#63922C2212yescomplemented
81#63922C2212yescomplemented
82#63921C2211yescharacteristic, complemented
83#63921C2211yescharacteristic, complemented
84D3×(C2×D3)⋊C4C2212yescomplemented
85#63918C2212yescomplemented
86#63908C2212yescomplemented
87#63905C2212yescomplemented
88#63904C2212yescomplemented
89#63893C2212yescomplemented
90#63893C2212yescomplemented
91Dic3×D12C2212yescomplemented
92#63891C2212yescomplemented
93#63891C2212yescomplemented
94D3×C4⋊Dic3C2212yescomplemented
95#63887C2212yescomplemented
96#63885C2212yescomplemented
97#63884C2212yescomplemented
98#63883C2211yescharacteristic, complemented
99#63883C2211yescharacteristic, complemented
100#63880C2212yescomplemented
101#63879C2212yescomplemented
102D3×Dic3⋊C4C2212yescomplemented
103#63854C2212yescomplemented
104#63854C2212yescomplemented
105#63853C2212yescomplemented
106#63853C2212yescomplemented
107#63851C2212yescomplemented
108#63839C2212yescomplemented
109#63836C2212yescomplemented
110C2×D3×#41—32no—
111C2×#1004—32no—
112C3×#546—32no—
113#5824—32no—
114#5806—32no—
115#5676—32no—
116#5675—32no—
117#5655—32no—
118#5655—32no—
119D3×#123—32no—
120D3×#123—32no—
121#5631—32no—
122#5628—32no—
123#5612—32no—
124#5611—32no—
125#5611—32no—
126#5606—32no—
127#5605—32no—
128#5605—32no—
129#5591—32no—
130#5591—32no—
131#5589—32no—
132#5589—32no—
133#5555—32no—
134#5551—32no—
135#5547—32no—
136#5545—32no—
137#5490—32no—
138#5490D312yescomplemented
139C2×#883—32no—
140C2×#883—32no—
141C2×#883—61no—
142C24×C32C2311yescharacteristic
143C23×C3⋊D3C2311yescharacteristic
144C23×C3×D3C2312yes—
145C22×D32C2311yescharacteristic
146C22×D32C2311yescharacteristic
147C22×D32C2311yescharacteristic
148C22×C32×C4C2311yescharacteristic
149C22×C32×C4C2311yescharacteristic
150C2×#638—24no—
151C2×#638C2312yes—
152C2×#638C2312yes—
153C22×C3⋊Dic3C2311yescharacteristic
154C22×C3⋊Dic3C2311yescharacteristic
155C22×C3⋊Dic3C2311yescharacteristic
156C2×C4×C3⋊D3—24no—
157C2×C4×C3⋊D3C2311yescharacteristic
158C2×C4×C3⋊D3C2311yescharacteristic
159C2×C4×C3⋊D3C2311yescharacteristic
160C2×C4×C3⋊D3C2311yescharacteristic
161C2×C3×#67—28no—
162C2×C3×#67C2312yes—
163C2×C3×#67C2312yes—
164C2×C3×#67C2312yes—
165C2×C3×#67C2312yes—
166C2×C3×#67C2312yes—
167C2×C3×#67C2312yes—
168C2×C3×#67C2312yes—
169C22×C3×Dic3C2312yes—
170C3×#235—28no—
171C2×C3×D12C2312yes—
172C2×C3×D12C2312yes—
173C2×C3×C4×D3C2312yes—
174C2×C3×C4×D3C2312yes—
175C2×C3×C4×D3C2312yes—
176C2×C3×Dic6C2312yes—
177#3811—24no—
178#3811—24no—
179#3811D418yescomplemented
180D3×#67—28no—
181D3×#67—28no—
182C2×#627C2312yes—
183C2×#627C2312yes—
184C2×#626C2312yes—
185C2×#626C2312yes—
186C2×#626C2312yes—
187C2×#625C2312yes—
188C2×#625C2312yes—
189C2×#625C2312yes—
190C2×#624C2311yescharacteristic
191C2×#624C2311yescharacteristic
192C2×#624C2311yescharacteristic
193C2×#624C2311yescharacteristic
194C2×#624C2311yescharacteristic
195#3805—28no—
196#3805—28no—
197#3804—28no—
198#3804—28no—
199C2×D3×Dic3C2312yes—
200C2×D3×Dic3C2312yes—
201C2×D3×Dic3C2312yes—
202C2×D3×Dic3C2312yes—
203C2×D3×Dic3C2312yes—
204#3802—24no—
205C4×D32—24no—
206C4×D32—24no—
207#3798—28no—
208#3797—24no—
209#3796—28no—
210C32×C22⋊C4C2312yes—
211C32×C22⋊C4C2312yes—
212#3757C2312yes—
213#3757C2312yes—
214#3752C2312yes—
215#3752C2312yes—
216C4⋊(C3⋊Dic3)C2312yes—
217C4⋊(C3⋊Dic3)C2312yes—
218#3750C2312yes—
219#3750C2312yes—
220C3×#217C2312yes—
221C3×#217C2312yes—
222C3×#217C2312yes—
223C3×(C2×D3)⋊C4C2312yes—
224C3×(C2×D3)⋊C4C2312yes—
225C3×(C2×D3)⋊C4C2312yes—
226C3×(C2×D3)⋊C4C2312yes—
227C3×(C2×D3)⋊C4C2312yes—
228C3×C4⋊Dic3C2312yes—
229C3×Dic3⋊C4C2312yes—
230C3×Dic3⋊C4C2312yes—
231C3×Dic3⋊C4C2312yes—
232C3×C4×Dic3C2312yes—
233#3724C2312yes—
234Dic3⋊Dic3C2312yes—
235Dic3⋊Dic3C2312yes—
236Dic3⋊Dic3C2312yes—
237Dic3⋊Dic3C2312yes—
238Dic3⋊Dic3C2312yes—
239#3722C2312yes—
240(C2×D3)⋊Dic3C2312yes—
241(C2×D3)⋊Dic3C2312yes—
242(C2×D3)⋊Dic3C2312yes—
243(C2×D3)⋊Dic3C2312yes—
244(C2×D3)⋊Dic3C2312yes—
245(C2×D3)⋊Dic3C2312yes—
246(C2×D3)⋊Dic3C2312yes—
247Dic32C2312yes—
248#3485—91noSylow
249C2×C3×#41—32no—
250C22×C3×D4—32no—
251C22×#67—32no—
252C22×#67—32no—
253C22×#67—32no—
254C22×#67—61no—
255C22×#67C2×D312yescomplemented
256D3×#41—616no—
257C2×#239—32no—
258C2×D3×Q8—32no—
259#1004—616no—
260C2×#237—32no—
261C2×#237—32no—
262C2×#237—32no—
263C2×#237—32no—
264C2×#237—32no—
265C2×#237—32no—
266C2×#237—32no—
267C2×D3×D4—32no—
268C2×D3×D4—32no—
269C2×D3×D4—32no—
270C2×D3×D4—32no—
271C2×D3×D4—32no—
272C2×D3×D4—32no—
273C2×#235—32no—
274C2×#235—32no—
275C2×#235—32no—
276C2×#235—32no—
277C2×#235C2×D312yescomplemented
278C22×C4×D3—32no—
279C22×C4×D3—32no—
280C22×C4×D3—32no—
281C22×C4×D3—61no—
282C3×#124—32no—
283C3×#123—32no—
284C3×#123—32no—
285C3×C22⋊Q8—32no—
286C3×#121—32no—
287C3×#121—32no—
288C3×#121—32no—
289C3×#120—32no—
290C3×#120—32no—
291C3×C4×D4—32no—
292C3×C4×D4—32no—
293C2×C3×C22⋊C4—21no—
294C2×C3×C22⋊C4—32no—
295C2×C3×C22⋊C4C2×D312yescomplemented
296#953—32no—
297#953C2×D312yescomplemented
298C2×#217—32no—
299C2×#217—32no—
300C2×#217—61no—
301#946—32no—
302#944—32no—
303#939—32no—
304#939—32no—
305#939—32no—
306#939—32no—
307#939—32no—
308#938—32no—
309#938—32no—
310#938—32no—
311#938—32no—
312#938—32no—
313#937—32no—
314#937—32no—
315#937—32no—
316#937—32no—
317#937—32no—
318#936—32no—
319#935—32no—
320#935—32no—
321#935—32no—
322#935—32no—
323D4×Dic3—32no—
324D4×Dic3—32no—
325D4×Dic3—32no—
326#930—32no—
327#930C2×D312yescomplemented
328#929—32no—
329#929C2×D312yescomplemented
330C4×#67—32no—
331C4×#67—32no—
332C4×#67—32no—
333C4×#67C2×D312yescomplemented
334C2×(C2×D3)⋊C4—32no—
335C2×(C2×D3)⋊C4—32no—
336C2×(C2×D3)⋊C4—61no—
337C2×C4⋊Dic3—32no—
338C2×C4⋊Dic3—32no—
339C2×C4⋊Dic3—61no—
340#924—32no—
341#924—32no—
342C2×Dic3⋊C4—32no—
343C2×Dic3⋊C4—32no—
344C2×Dic3⋊C4—61no—
345#897—32no—
346#897—32no—
347#896—32no—
348#894—32no—
349#894—32no—
350#894—32no—
351#894—32no—
352#894—32no—
353#893—32no—
354#892—32no—
355D3×C4⋊C4—32no—
356D3×C4⋊C4—32no—
357D3×C4⋊C4—32no—
358D3×C4⋊C4—32no—
359#888—32no—
360#888—32no—
361#886—32no—
362#886—32no—
363#886—32no—
364#886—32no—
365#885—32no—
366#885C2×D312yescomplemented
367#884—32no—
368#884—32no—
369#884—32no—
370#884C2×D312yescomplemented
371#884C2×D312yescomplemented
372#883—32no—
373#883—32no—
374#883—32no—
375#883—32no—
376#883—32no—
377#883—32no—
378#883—32no—
379#883—32no—
380#883—32no—
381#883—32no—
382#883—32no—
383#883—32no—
384#883—32no—
385#883—32no—
386#883—32no—
387#883—32no—
388#883—32no—
389#883—32no—
390#883—62no—
391#883—62no—
392#883—62no—
393#883—62no—
394#883C2×D312yescomplemented
395#882—32no—
396#882—32no—
397#882C2×D312yescomplemented
398#67⋊C4—32no—
399#67⋊C4—32no—
400#67⋊C4—32no—
401#67⋊C4C2×D312yescomplemented
402D3×C22⋊C4—32no—
403D3×C22⋊C4—32no—
404D3×C22⋊C4—32no—
405D3×C22⋊C4—32no—
406D3×C22⋊C4—32no—
407D3×C22⋊C4C2×D312yescomplemented
408#878—32no—
409#878—32no—
410#878—32no—
411#878—32no—
412#878C2×D312yescomplemented
413C4×D12—32no—
414C4×D12—32no—
415#872—32no—
416#869—32no—
417C23×C32—22no—
418C23×C32—41no—
419C23×C32—41no—
420C23×C32C2412yes—
421C23×C32C2411yescharacteristic
422C22×C3⋊D3—41no—
423C22×C3⋊D3—41no—
424C22×C3⋊D3C2×D414yes—
425C22×C3⋊D3C2411yescharacteristic
426C22×C3⋊D3C2411yescharacteristic
427C22×C3×D3—24no—
428C22×C3×D3—42no—
429C22×C3×D3—42no—
430C22×C3×D3C2412yes—
431C22×C3×D3C2412yes—
432C22×C3×D3C2412yes—
433C2×D32—22no—
434C2×D32—22no—
435C2×D32—41no—
436C2×D32—41no—
437C2×D32—41no—
438C2×D32—41no—
439C2×D32—41no—
440C2×D32—41no—
441C2×D32C2×D414yes—
442C2×C32×C4—22no—
443C2×C32×C4—41no—
444C2×C32×C4C2412yes—
445C2×C32×C4C2411yescharacteristic
446C2×C32×C4C2411yescharacteristic
447#638—24no—
448#638—24no—
449C2×C3⋊Dic3—22no—
450C2×C3⋊Dic3—22no—
451C2×C3⋊Dic3—41no—
452C2×C3⋊Dic3C2412yes—
453C2×C3⋊Dic3C2412yes—
454C2×C3⋊Dic3C2411yescharacteristic
455C2×C3⋊Dic3C2411yescharacteristic
456C4×C3⋊D3—22no—
457C4×C3⋊D3—22no—
458C4×C3⋊D3—22no—
459C4×C3⋊D3—22no—
460C3×#67—24no—
461C3×#67—24no—
462C3×#67—24no—
463C3×#67—24no—
464C3×#67—42no—
465C3×#67—42no—
466C3×#67C2×D418yes—
467C2×C3×Dic3—24no—
468C2×C3×Dic3C2412yes—
469C2×C3×Dic3C2412yes—
470C2×C3×Dic3C2412yes—
471C2×C3×Dic3C2412yes—
472C2×C3×Dic3C2412yes—
473C3×D12—24no—
474C3×D12—42no—
475C3×C4×D3—24no—
476C3×C4×D3—24no—
477C3×C4×D3—42no—
478C3×Dic6—24no—
479#627—24no—
480#627—24no—
481#626—24no—
482#626—24no—
483#626C2×D418yes—
484#625—24no—
485#625—24no—
486#625—42no—
487#624—22no—
488#624—22no—
489#624—41no—
490#624—41no—
491#624C2×D414yes—
492D3×Dic3—24no—
493D3×Dic3—24no—
494D3×Dic3—24no—
495D3×Dic3—24no—
496D3×Dic3—42no—
497C2×H(5,𝔽2)—91no—
498C22×#41—91no—
499#547—92no—
500#547—92no—
501#547—92no—
502#547—92no—
503#546—32no—
504#546—92no—
505#546—92no—
506#546—92no—
507#536—92no—
508#534—91no—
509#534—92no—
510#534—91no—
511#525—92no—
512C2×#123—92no—
513C2×#123—91no—
514C2×#123—91no—
515#518—91no—
516C24×C3—21no—
517C24×C3—32no—
518C24×C3C22×D312yes—
519C23×D3—32no—
520C23×D3—32no—
521C23×D3—32no—
522C23×D3—32no—
523C23×D3—61no—
524C23×D3C22×D312yes—
525C3×#41—68no—
526C2×C3×Q8—32no—
527C2×C3×D4—32no—
528C2×C3×D4—32no—
529C2×C3×D4—32no—
530C2×C3×D4—32no—
531C2×C3×D4—32no—
532C2×C3×D4—32no—
533C2×C3×D4—32no—
534C2×C3×D4—32no—
535C2×C3×D4—32no—
536C2×C3×D4—68no—
537C22×C3×C4—21no—
538C22×C3×C4—21no—
539C22×C3×C4—32no—
540C22×C3×C4—32no—
541C22×C3×C4—32no—
542C22×C3×C4—32no—
543C22×C3×C4C22×D312yes—
544C22×C3×C4C22×D312yes—
545C2×#67—28no—
546C2×#67—32no—
547C2×#67—32no—
548C2×#67—32no—
549C2×#67—32no—
550C2×#67—32no—
551C2×#67—32no—
552C2×#67—32no—
553C2×#67—32no—
554C2×#67—32no—
555C2×#67—32no—
556C2×#67—32no—
557C2×#67—32no—
558C2×#67—32no—
559C2×#67—62no—
560C2×#67—62no—
561C2×#67—68no—
562C2×#67—68no—
563C2×#67—68no—
564C2×#67—124no—
565C2×#67C22×D312yes—
566C2×#67C22×D312yes—
567C2×#67C22×D312yes—
568C2×#67C22×D312yes—
569C2×#67C22×D312yes—
570C2×#67C22×D312yes—
571C2×#67C22×D312yes—
572C22×Dic3—32no—
573C22×Dic3—32no—
574C22×Dic3—32no—
575C22×Dic3—32no—
576C22×Dic3—32no—
577C22×Dic3—32no—
578C22×Dic3—32no—
579C22×Dic3—32no—
580C22×Dic3—61no—
581C22×Dic3—61no—
582C22×Dic3—61no—
583C22×Dic3C22×D312yes—
584#239—68no—
585D3×Q8—68no—
586#237—68no—
587#237—68no—
588#237—68no—
589#237—68no—
590#237—68no—
591#237—68no—
592#237—68no—
593D3×D4—316no—
594D3×D4—68no—
595D3×D4—68no—
596D3×D4—68no—
597D3×D4—68no—
598D3×D4—68no—
599#235—28no—
600#235—68no—
601#235—68no—
602#235—68no—
603#235—68no—
604C2×D12—32no—
605C2×D12—32no—
606C2×D12—32no—
607C2×D12C22×D312yes—
608C2×D12C22×D312yes—
609C2×C4×D3—32no—
610C2×C4×D3—32no—
611C2×C4×D3—32no—
612C2×C4×D3—32no—
613C2×C4×D3—32no—
614C2×C4×D3—32no—
615C2×C4×D3—32no—
616C2×C4×D3—32no—
617C2×C4×D3—32no—
618C2×C4×D3—32no—
619C2×C4×D3—32no—
620C2×C4×D3—32no—
621C2×C4×D3—32no—
622C2×C4×D3—32no—
623C2×C4×D3—61no—
624C2×C4×D3—61no—
625C2×C4×D3—61no—
626C2×C4×D3—61no—
627C2×C4×D3—68no—
628C2×C4×D3—68no—
629C2×C4×D3—68no—
630C2×C4×D3—124no—
631C2×C4×D3C22×D312yes—
632C2×C4×D3C22×D312yes—
633C2×C4×D3C22×D312yes—
634C2×Dic6—32no—
635C2×Dic6—32no—
636C2×Dic6—32no—
637C2×Dic6—32no—
638C2×Dic6C22×D312yes—
639C3×C4⋊C4—32no—
640C3×C4⋊C4—32no—
641C3×C4⋊C4—32no—
642C3×C4⋊C4—32no—
643C3×C22⋊C4—22no—
644C3×C22⋊C4—22no—
645C3×C22⋊C4—32no—
646C3×C22⋊C4—32no—
647C3×C22⋊C4—32no—
648C3×C22⋊C4—32no—
649C3×C22⋊C4—32no—
650C3×C22⋊C4—32no—
651C3×C22⋊C4—32no—
652C3×C22⋊C4—32no—
653C3×C22⋊C4C22×D312yes—
654C3×C22⋊C4C22×D312yes—
655C3×C22⋊C4C22×D312yes—
656C3×C22⋊C4C22×D312yes—
657C3×C42—32no—
658#217—32no—
659#217—32no—
660#217—32no—
661#217—32no—
662#217—32no—
663#217—32no—
664#217—32no—
665#217—32no—
666#217—32no—
667#217—32no—
668#217—32no—
669#217—62no—
670#217—62no—
671#217C22×D312yes—
672#217C22×D312yes—
673#217C22×D312yes—
674(C2×D3)⋊C4—32no—
675(C2×D3)⋊C4—32no—
676(C2×D3)⋊C4—32no—
677(C2×D3)⋊C4—32no—
678(C2×D3)⋊C4—32no—
679(C2×D3)⋊C4—32no—
680(C2×D3)⋊C4—32no—
681(C2×D3)⋊C4—32no—
682(C2×D3)⋊C4—32no—
683(C2×D3)⋊C4—32no—
684(C2×D3)⋊C4—32no—
685(C2×D3)⋊C4—32no—
686(C2×D3)⋊C4—32no—
687(C2×D3)⋊C4—62no—
688(C2×D3)⋊C4—62no—
689(C2×D3)⋊C4C22×D312yes—
690(C2×D3)⋊C4C22×D312yes—
691(C2×D3)⋊C4C22×D312yes—
692(C2×D3)⋊C4C22×D312yes—
693(C2×D3)⋊C4C22×D312yes—
694C4⋊Dic3—32no—
695C4⋊Dic3—32no—
696C4⋊Dic3—32no—
697C4⋊Dic3—32no—
698C4⋊Dic3—32no—
699C4⋊Dic3—32no—
700C4⋊Dic3—32no—
701C4⋊Dic3—32no—
702C4⋊Dic3—32no—
703C4⋊Dic3—62no—
704C4⋊Dic3—62no—
705C4⋊Dic3C22×D312yes—
706Dic3⋊C4—32no—
707Dic3⋊C4—32no—
708Dic3⋊C4—32no—
709Dic3⋊C4—32no—
710Dic3⋊C4—32no—
711Dic3⋊C4—32no—
712Dic3⋊C4—32no—
713Dic3⋊C4—32no—
714Dic3⋊C4—32no—
715Dic3⋊C4—32no—
716Dic3⋊C4—32no—
717Dic3⋊C4—62no—
718Dic3⋊C4—62no—
719Dic3⋊C4C22×D312yes—
720Dic3⋊C4C22×D312yes—
721Dic3⋊C4C22×D312yes—
722C4×Dic3—32no—
723C4×Dic3—32no—
724C4×Dic3C22×D312yes—
725C22×C32—21no—
726C22×C32—21no—
727C22×C32—22no—
728C22×C32—22no—
729C22×C32—22no—
730C22×C32—82no—
731C22×C32C22×D412yes—
732C22×C32C2511yescharacteristic
733C2×C3⋊D3—21no—
734C2×C3⋊D3—21no—
735C2×C3⋊D3—21no—
736C2×C3⋊D3—21no—
737C2×C3⋊D3—44no—
738C2×C3⋊D3C22×D412yes—
739C2×C3⋊D3C22×D412yes—
740C2×C3×D3—22no—
741C2×C3×D3—22no—
742C2×C3×D3—22no—
743C2×C3×D3—22no—
744C2×C3×D3—22no—
745C2×C3×D3—22no—
746C2×C3×D3—22no—
747C2×C3×D3—22no—
748C2×C3×D3—84no—
749C2×C3×D3C22×D414yes—
750D32—44no—
751D32—44no—
752D32—82no—
753C32×C4—21no—
754C32×C4—21no—
755C32×C4—22no—
756C3⋊Dic3—21no—
757C3⋊Dic3—22no—
758C3⋊Dic3—21no—
759C3⋊Dic3—22no—
760C3×Dic3—22no—
761C3×Dic3—22no—
762C3×Dic3—22no—
763C3×Dic3—22no—
764C3×Dic3C22×D414yes—
765H(5,𝔽2)—188no—
766C2×#41—32no—
767C2×#41—92no—
768C2×#41—92no—
769C2×#41—92no—
770C2×#41—92no—
771C2×#41—92no—
772C2×#41—92no—
773C2×#41—188no—
774C22×Q8—91no—
775C22×D4—32no—
776C22×D4—91no—
777C22×D4—91no—
778C22×D4—91no—
779C22×D4—91no—
780C22×D4—92no—
781C22×D4—92no—
782C22×D4—91no—
783C23×C4—91no—
784C23×C4—91no—
785C23×C4—91no—
786C4⋊Q8—92no—
787C4⋊Q8—92no—
788#124—32no—
789#124—92no—
790#123—32no—
791#123—32no—
792#123—92no—
793#123—92no—
794#123—92no—
795#123—92no—
796#123—92no—
797#123—92no—
798#123—92no—
799#123—92no—
800#123—92no—
801#123—92no—
802#123—92no—
803#123—92no—
804#123—92no—
805#123—92no—
806#123—92no—
807#123—92no—
808C22⋊Q8—32no—
809C22⋊Q8—92no—
810C22⋊Q8—92no—
811C22⋊Q8—92no—
812C22⋊Q8—92no—
813C22⋊Q8—92no—
814#121—32no—
815#121—32no—
816#121—32no—
817#121—92no—
818#121—92no—
819#121—92no—
820#121—92no—
821#121—92no—
822#121—92no—
823#121—92no—
824#120—32no—
825#120—32no—
826#120—92no—
827#120—92no—
828#120—92no—
829#120—92no—
830C4×D4—32no—
831C4×D4—32no—
832C4×D4—92no—
833C4×D4—92no—
834C4×D4—92no—
835C4×D4—92no—
836C4×D4—92no—
837C4×D4—92no—
838#117—92no—
839C2×C4⋊C4—91no—
840C2×C4⋊C4—91no—
841C2×C4⋊C4—92no—
842C2×C4⋊C4—92no—
843C2×C4⋊C4—91no—
844C2×C4⋊C4—91no—
845C2×C22⋊C4—32no—
846C2×C22⋊C4—91no—
847C2×C22⋊C4—91no—
848C2×C22⋊C4—91no—
849C2×C22⋊C4—92no—
850C2×C22⋊C4—92no—
851C2×C22⋊C4—91no—
852C2×C22⋊C4—91no—
853C2×C22⋊C4D3211yescharacteristic, complemented
854C23×C3—24no—
855C23×C3—21no—
856C23×C3—22no—
857C23×C3—32no—
858C23×C3—32no—
859C23×C3—32no—
860C23×C3—42no—
861C23×C3—42no—
862C23×C3—42no—
863C23×C3—42no—
864C23×C3—42no—
865C23×C3—64no—
866C23×C3—122no—
867C23×C3—122no—
868C23×C3C23×D312yes—
869C23×C3C23×D312yes—
870C23×C3C23×D312yes—
871C22×D3—24no—
872C22×D3—32no—
873C22×D3—32no—
874C22×D3—38no—
875C22×D3—38no—
876C22×D3—42no—
877C22×D3—42no—
878C22×D3—64no—
879C22×D3—61no—
880C22×D3—61no—
881C22×D3—64no—
882C22×D3—64no—
883C22×D3—122no—
884C22×D3—122no—
885C22×D3—122no—
886C22×D3—122no—
887C22×D3—122no—
888C22×D3—122no—
889C22×D3—122no—
890C22×D3—122no—
891C22×D3—122no—
892C22×D3—122no—
893C22×D3C23×D312yes—
894C22×D3C23×D312yes—
895C22×D3C23×D312yes—
896C3×Q8—64no—
897C3×D4—38no—
898C3×D4—64no—
899C3×D4—64no—
900C3×D4—64no—
901C3×D4—64no—
902C3×D4—64no—
903C3×D4—122no—
904C3×D4—122no—
905C3×D4—122no—
906C2×C3×C4—24no—
907C2×C3×C4—21no—
908C2×C3×C4—21no—
909C2×C3×C4—22no—
910C2×C3×C4—32no—
911C2×C3×C4—32no—
912C2×C3×C4—32no—
913C2×C3×C4—32no—
914C2×C3×C4—32no—
915C2×C3×C4—42no—
916C2×C3×C4—42no—
917C2×C3×C4—42no—
918C2×C3×C4—64no—
919C2×C3×C4—64no—
920C2×C3×C4—64no—
921C2×C3×C4—122no—
922C2×C3×C4C23×D312yes—
923C2×C3×C4C23×D312yes—
924C2×C3×C4C23×D312yes—
925C2×C3×C4C23×D312yes—
926#67—24no—
927#67—24no—
928#67—24no—
929#67—24no—
930#67—38no—
931#67—42no—
932#67—42no—
933#67—64no—
934#67—64no—
935#67—64no—
936#67—64no—
937#67—64no—
938#67—64no—
939#67—64no—
940#67—64no—
941#67—64no—
942#67—64no—
943#67—124no—
944#67—124no—
945#67—122no—
946#67—122no—
947#67D3×D418yes—
948C2×Dic3—24no—
949C2×Dic3—32no—
950C2×Dic3—32no—
951C2×Dic3—32no—
952C2×Dic3—32no—
953C2×Dic3—32no—
954C2×Dic3—32no—
955C2×Dic3—62no—
956C2×Dic3—62no—
957C2×Dic3—61no—
958C2×Dic3—61no—
959C2×Dic3—64no—
960C2×Dic3—64no—
961C2×Dic3—64no—
962C2×Dic3—64no—
963C2×Dic3—64no—
964C2×Dic3—64no—
965C2×Dic3—122no—
966C2×Dic3—122no—
967C2×Dic3—122no—
968C2×Dic3—122no—
969C2×Dic3—122no—
970C2×Dic3C23×D312yes—
971C2×Dic3C23×D312yes—
972C2×Dic3C23×D312yes—
973C2×Dic3C23×D312yes—
974C2×Dic3C23×D312yes—
975D12—24no—
976D12—38no—
977D12—42no—
978D12—64no—
979D12—64no—
980C4×D3—24no—
981C4×D3—24no—
982C4×D3—38no—
983C4×D3—42no—
984C4×D3—64no—
985C4×D3—64no—
986C4×D3—64no—
987C4×D3—64no—
988C4×D3—64no—
989C4×D3—64no—
990C4×D3—64no—
991C4×D3—64no—
992C4×D3—64no—
993C4×D3—64no—
994C4×D3—122no—
995C4×D3—122no—
996C4×D3—122no—
997C4×D3—122no—
998C4×D3—122no—
999C4×D3—122no—
1000C4×D3—122no—
1001Dic6—24no—
1002Dic6—64no—
1003Dic6—64no—
1004Dic6—64no—
1005Dic6—64no—
1006C2×C32—22no—
1007C2×C32—42no—
1008C2×C32C23×D411yescharacteristic
1009C2×C32#58511yescharacteristic
1010C2×C32#58511yescharacteristic
1011C3⋊D3—22no—
1012C3⋊D3—22no—
1013C3×D3—24no—
1014C3×D3—42no—
1015C3×D3—42no—
1016C24—32no—
1017C24—91no—
1018C24—91no—
1019C24—91no—
1020C24—91no—
1021C24C2×D3211yescharacteristic
1022#41—68no—
1023#41—188no—
1024#41—188no—
1025#41—188no—
1026#41—188no—
1027#41—188no—
1028#41—188no—
1029C2×Q8—32no—
1030C2×Q8—92no—
1031C2×Q8—92no—
1032C2×Q8—184no—
1033C2×D4—32no—
1034C2×D4—32no—
1035C2×D4—32no—
1036C2×D4—32no—
1037C2×D4—32no—
1038C2×D4—32no—
1039C2×D4—32no—
1040C2×D4—32no—
1041C2×D4—32no—
1042C2×D4—68no—
1043C2×D4—92no—
1044C2×D4—92no—
1045C2×D4—92no—
1046C2×D4—98no—
1047C2×D4—92no—
1048C2×D4—92no—
1049C2×D4—92no—
1050C2×D4—92no—
1051C2×D4—92no—
1052C2×D4—184no—
1053C2×D4—184no—
1054C2×D4—184no—
1055C2×D4—188no—
1056C2×D4—188no—
1057C2×D4—184no—
1058C22×C4—32no—
1059C22×C4—32no—
1060C22×C4—32no—
1061C22×C4—32no—
1062C22×C4—91no—
1063C22×C4—91no—
1064C22×C4—91no—
1065C22×C4—91no—
1066C22×C4—91no—
1067C22×C4—92no—
1068C22×C4—92no—
1069C22×C4—92no—
1070C22×C4—92no—
1071C22×C4—92no—
1072C22×C4—91no—
1073C22×C4—91no—
1074C22×C4—91no—
1075C22×C4—91no—
1076C22×C4—91no—
1077C22×C4—91no—
1078C22×C4—91no—
1079C22×C4—184no—
1080C22×C4—184no—
1081C22×C4—184no—
1082C22×C4C2×D3211yescharacteristic
1083C22×C4C2×D3211yescharacteristic
1084C4⋊C4—32no—
1085C4⋊C4—32no—
1086C4⋊C4—32no—
1087C4⋊C4—32no—
1088C4⋊C4—92no—
1089C4⋊C4—92no—
1090C4⋊C4—92no—
1091C4⋊C4—92no—
1092C4⋊C4—92no—
1093C4⋊C4—92no—
1094C4⋊C4—92no—
1095C4⋊C4—92no—
1096C4⋊C4—92no—
1097C4⋊C4—92no—
1098C22⋊C4—32no—
1099C22⋊C4—32no—
1100C22⋊C4—32no—
1101C22⋊C4—32no—
1102C22⋊C4—32no—
1103C22⋊C4—32no—
1104C22⋊C4—32no—
1105C22⋊C4—32no—
1106C22⋊C4—92no—
1107C22⋊C4—92no—
1108C22⋊C4—92no—
1109C22⋊C4—92no—
1110C22⋊C4—92no—
1111C22⋊C4—92no—
1112C22⋊C4—92no—
1113C22⋊C4—92no—
1114C22⋊C4—92no—
1115C22⋊C4—92no—
1116C22⋊C4—92no—
1117C22⋊C4—92no—
1118C22⋊C4C2×D3212yes—
1119C22⋊C4C2×D3212yes—
1120C42—32no—
1121C42—92no—
1122C22×C3—22no—
1123C22×C3—22no—
1124C22×C3—22no—
1125C22×C3—22no—
1126C22×C3—22no—
1127C22×C3—22no—
1128C22×C3—22no—
1129C22×C3—22no—
1130C22×C3—22no—
1131C22×C3—22no—
1132C22×C3—22no—
1133C22×C3—21no—
1134C22×C3—34no—
1135C22×C3—42no—
1136C22×C3—42no—
1137C22×C3—42no—
1138C22×C3—62no—
1139C22×C3—62no—
1140C22×C3—62no—
1141C22×C3—62no—
1142C22×C3—62no—
1143C22×C3—62no—
1144C22×C3—62no—
1145C22×C3—62no—
1146C22×C3—84no—
1147C22×C3—84no—
1148C22×C3—244no—
1149C22×C3C2×D3×D414yes—
1150C22×C3C24×D312yes—
1151C2×D3—22no—
1152C2×D3—22no—
1153C2×D3—22no—
1154C2×D3—22no—
1155C2×D3—22no—
1156C2×D3—22no—
1157C2×D3—22no—
1158C2×D3—22no—
1159C2×D3—34no—
1160C2×D3—34no—
1161C2×D3—62no—
1162C2×D3—62no—
1163C2×D3—62no—
1164C2×D3—62no—
1165C2×D3—62no—
1166C2×D3—62no—
1167C2×D3—84no—
1168C2×D3—121no—
1169C2×D3—121no—
1170C2×D3—121no—
1171C2×D3—121no—
1172C2×D3—128no—
1173C2×D3—128no—
1174C2×D3—128no—
1175C2×D3—128no—
1176C2×D3—244no—
1177C2×D3C2×D3×D414yes—
1178C3×C4—22no—
1179C3×C4—22no—
1180C3×C4—22no—
1181C3×C4—22no—
1182C3×C4—34no—
1183C3×C4—41no—
1184C3×C4—41no—
1185C3×C4—42no—
1186C3×C4—62no—
1187C3×C4—62no—
1188C3×C4—62no—
1189C3×C4—62no—
1190Dic3—22no—
1191Dic3—22no—
1192Dic3—22no—
1193Dic3—22no—
1194Dic3—62no—
1195Dic3—62no—
1196Dic3—62no—
1197Dic3—62no—
1198Dic3—62no—
1199Dic3—62no—
1200Dic3—121no—
1201Dic3—121no—
1202Dic3—122no—
1203Dic3—122no—
1204Dic3C2×D3×D414yes—
1205C32#348511yescharacteristic, complemented, Sylow
1206C23—22no—
1207C23—32no—
1208C23—32no—
1209C23—32no—
1210C23—41no—
1211C23—41no—
1212C23—64no—
1213C23—94no—
1214C23—91no—
1215C23—91no—
1216C23—94no—
1217C23—122no—
1218C23—122no—
1219C23—182no—
1220C23—182no—
1221C23—361no—
1222C23—361no—
1223C23—361no—
1224C23—361no—
1225C23—361no—
1226C23—361no—
1227C23—361no—
1228C23—361no—
1229C23C22×D3212yes—
1230C23C22×D3211yescharacteristic
1231Q8—64no—
1232Q8—184no—
1233Q8—184no—
1234D4—38no—
1235D4—64no—
1236D4—64no—
1237D4—64no—
1238D4—64no—
1239D4—64no—
1240D4—98no—
1241D4—122no—
1242D4—122no—
1243D4—122no—
1244D4—184no—
1245D4—184no—
1246D4—184no—
1247D4—184no—
1248D4—184no—
1249D4—184no—
1250D4—362no—
1251C2×C4—22no—
1252C2×C4—32no—
1253C2×C4—32no—
1254C2×C4—32no—
1255C2×C4—32no—
1256C2×C4—32no—
1257C2×C4—41no—
1258C2×C4—64no—
1259C2×C4—64no—
1260C2×C4—64no—
1261C2×C4—94no—
1262C2×C4—92no—
1263C2×C4—91no—
1264C2×C4—91no—
1265C2×C4—92no—
1266C2×C4—122no—
1267C2×C4—182no—
1268C2×C4—182no—
1269C2×C4—182no—
1270C2×C4—182no—
1271C2×C4—184no—
1272C2×C4—184no—
1273C2×C4—182no—
1274C2×C4—182no—
1275C2×C4—184no—
1276C2×C4—184no—
1277C2×C4—182no—
1278C2×C4—182no—
1279C2×C4—361no—
1280C2×C4—361no—
1281C2×C4—362no—
1282C2×C4—361no—
1283C2×C4C22×D3212yes—
1284C2×C4C22×D3211yescharacteristic
1285C2×C4C22×D3211yescharacteristic
1286C2×C3—24no—
1287C2×C3—24no—
1288C2×C3—21no—
1289C2×C3—21no—
1290C2×C3—21no—
1291C2×C3—42no—
1292C2×C3—42no—
1293C2×C3—64no—
1294C2×C3—82no—
1295C2×C3—122no—
1296C2×C3—122no—
1297C2×C3C22×D3×D412yes—
1298C2×C3#596412yes—
1299C2×C3#596612yes—
1300D3—24no—
1301D3—42no—
1302D3—42no—
1303D3—64no—
1304D3—64no—
1305D3—122no—
1306D3—122no—
1307C22—21no—
1308C22—21no—
1309C22—22no—
1310C22—22no—
1311C22—22no—
1312C22—34no—
1313C22—62no—
1314C22—62no—
1315C22—62no—
1316C22—62no—
1317C22—62no—
1318C22—62no—
1319C22—62no—
1320C22—62no—
1321C22—82no—
1322C22—92no—
1323C22—92no—
1324C22—181no—
1325C22—181no—
1326C22—181no—
1327C22—181no—
1328C22—244no—
1329C22—364no—
1330C22—364no—
1331C22—364no—
1332C22—722no—
1333C22D32×D412yes—
1334C22C23×D3211yescharacteristic
1335C4—21no—
1336C4—21no—
1337C4—22no—
1338C4—34no—
1339C4—62no—
1340C4—62no—
1341C4—62no—
1342C4—62no—
1343C4—182no—
1344C4—181no—
1345C4—182no—
1346C4—181no—
1347C3—21no—
1348C3#8666312yescomplemented
1349C2—22no—
1350C2—42no—
1351C2—64no—
1352C2—122no—
1353C2—122no—
1354C2—182no—
1355C2—182no—
1356C2#1059666911yescharacteristic
1357C2C2×D32×D411yescharacteristic
1358C2#1059667911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C22⋊C4C22
hypercenterC2×C22⋊C4D32
hypocenterC32#3485
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64330C2semidirect
2. C2×#64306C2semidirect
3. C2×#64092C2semidirect
4. C3×#5490C2semidirect
5. #10595528C2semidirect
6. #10595494C2semidirect
7. #10595084C2semidirect
8. #10595079C2semidirect
9. #10595058C2semidirect
10. #10594907C2semidirect
11. #10594888C2semidirect
12. #10594286C2semidirect
13. #10594281C2semidirect
14. #10594278C2semidirect
15. #10594263C2semidirect
16. D3×#883C2semidirect
17. #10594188C2semidirect
18. #10594070C2semidirect
19. #10594065C2semidirect
22. C22×C4×C3⋊D3C22semidirect
23. C22×C3×#67C22semidirect
24. C2×C3×#235C22semidirect
28. C2×#3811C22semidirect
30. C2×D3×#67C22semidirect
31. C2×#3805C22semidirect
32. C2×#3805C22semidirect
34. C2×#3804C22semidirect
36. C2×#3802C22semidirect
37. C2×C4×D32C22semidirect
38. C2×C4×D32C22semidirect
39. C2×#3798C22semidirect
40. C2×#3797C22semidirect
41. C2×#3796C22semidirect
42. C2×C32×C22⋊C4C22semidirect
43. C2×#3757C22semidirect
44. C2×#3752C22semidirect
45. C2×C4⋊(C3⋊Dic3)C22semidirect
46. C2×#3750C22semidirect
47. #64092C22semidirect
48. #64092C22semidirect
49. #64092C22semidirect
50. #64092C22semidirect
51. C3×#953C22semidirect
52. C3×#930C22semidirect
53. C3×#929C22semidirect
54. C3×C4×#67C22semidirect
55. C3×#885C22semidirect
56. C3×#884C22semidirect
57. C3×#884C22semidirect
58. C3×#883C22semidirect
59. C3×#882C22semidirect
60. C3×#67⋊C4C22semidirect
61. C3×D3×C22⋊C4C22semidirect
62. C3×#878C22semidirect
63. #63983C22semidirect
64. #63980C22semidirect
65. #63976C22semidirect
66. #63975C22semidirect
67. #63974C22semidirect
68. #67⋊Dic3C22semidirect
69. Dic3×#67C22semidirect
70. #63970C22semidirect
71. #63970C22semidirect
72. #63969C22semidirect
73. D3×#217C22semidirect
74. #63964C22semidirect
75. #63962C22semidirect
76. #63962C22semidirect
77. #63959C22semidirect
78. #63958C22semidirect
79. #63958C22semidirect
80. #63922C22semidirect
81. #63922C22semidirect
82. #63921C22semidirect
83. #63921C22semidirect
84. D3×(C2×D3)⋊C4C22semidirect
85. #63918C22semidirect
86. #63908C22semidirect
87. #63905C22semidirect
88. #63904C22semidirect
89. #63893C22semidirect
90. #63893C22semidirect
91. Dic3×D12C22semidirect
92. #63891C22semidirect
93. #63891C22semidirect
94. D3×C4⋊Dic3C22semidirect
95. #63887C22semidirect
96. #63885C22semidirect
97. #63884C22semidirect
98. #63883C22semidirect
99. #63883C22semidirect
100. #63880C22semidirect
101. #63879C22semidirect
102. D3×Dic3⋊C4C22semidirect
103. #63854C22semidirect
104. #63854C22semidirect
105. #63853C22semidirect
106. #63853C22semidirect
107. #63851C22semidirect
108. #63839C22semidirect
109. #63836C22semidirect
138. #5490D3semidirect
179. #3811D4semidirect
255. C22×#67C2×D3semidirect
277. C2×#235C2×D3semidirect
295. C2×C3×C22⋊C4C2×D3semidirect
297. #953C2×D3semidirect
327. #930C2×D3semidirect
329. #929C2×D3semidirect
333. C4×#67C2×D3semidirect
366. #885C2×D3semidirect
370. #884C2×D3semidirect
371. #884C2×D3semidirect
394. #883C2×D3semidirect
397. #882C2×D3semidirect
401. #67⋊C4C2×D3semidirect
407. D3×C22⋊C4C2×D3semidirect
412. #878C2×D3semidirect
853. C2×C22⋊C4D32semidirect
1205. C32#3485semidirect
1348. C3#86663semidirect

Maximal subgroups

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

subgroupindex
C2×#643302
C2×#643062
C2×#640922
C3×#54902
#105955282
#105954942
#105950842
#105950792
#105950582
#105949072
#105948882
#105942862
#105942812
#105942782
#105942632
D3×#8832
#105941882
#105940702
#105940652
#866633