Finite Group Databasebeta

← #11904457

Subgroups — #11904457

Order 1152.

3293 conjugacy classes of subgroups.

The subgroup lattice has 1341 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64312C211yesmaximal, characteristic, complemented
2C2×#64308C211yesmaximal, characteristic, complemented
3#10596124C211yesmaximal, characteristic, complemented
4C3×#5655C212yesmaximal, complemented
5#10595308C211yesmaximal, characteristic, complemented
6#10595305C212yesmaximal, complemented
7C2×#63897C211yesmaximal, characteristic, complemented
8#10594885C212yesmaximal, complemented
9#10594620C212yesmaximal, complemented
10D3×#894C212yesmaximal, complemented
11#10594517C212yesmaximal, complemented
12#10594328C212yesmaximal, complemented
13#10594295C211yesmaximal, characteristic, complemented
14#10594293C212yesmaximal, complemented
15#10594283C212yesmaximal, complemented
16#10594264C212yesmaximal, complemented
17#10594256C211yesmaximal, characteristic, complemented
18#10594066C212yesmaximal, complemented
19#10594064C212yesmaximal, complemented
20#86700—32nomaximal
21C2×D4×C3⋊D3C2211yescharacteristic, complemented
22C22×C4⋊(C3⋊D3)C2211yescharacteristic
23C2×C3×#237C2212yescomplemented
24C2×C3×#235C2212yescomplemented
25C2×#3811C2211yescharacteristic
26C2×#3811C2211yescharacteristic
27C2×#3811C2212yescomplemented
28C2×#3811C2211yescharacteristic, complemented
29C22×#624C2211yescharacteristic, complemented
30C22×#624C2211yescharacteristic, complemented
31C2×#3804C2212yescomplemented
32C2×#3804C2212yescomplemented
33#64312—28no—
34#64308—28no—
35C2×D3×D12C2212yes—
36C2×D3×D12C2212yescomplemented
37C2×C4×D32C2211yescharacteristic, complemented
38C2×#3799C2212yes—
39C2×#3799C2212yescomplemented
40C2×#3799C2212yescomplemented
41C2×#3797C2211yescharacteristic, complemented
42C32×#123C2211yescharacteristic, complemented
43#64146C2211yescharacteristic, complemented
44#64138C2211yescharacteristic, complemented
45#64104C2212yescomplemented
46#64103C2212yescomplemented
47#64093C2212yescomplemented
48#64091C2212yescomplemented
49#64091C2211yescharacteristic, complemented
50C22⋊C4×C3⋊D3C2211yescharacteristic, complemented
51C3×#939C2212yescomplemented
52C2×C3×Dic3⋊C4C2212yescomplemented
53C3×#896C2212yescomplemented
54C3×#894C2212yescomplemented
55C3×D3×C4⋊C4C2212yescomplemented
56C3×#888C2212yescomplemented
57C3×#886C2212yescomplemented
58C3×#884C2212yescomplemented
59C3×#883C2212yescomplemented
60C3×#67⋊C4C2212yescomplemented
61C3×#67⋊C4C2212yescomplemented
62C3×#878C2212yescomplemented
63#63983C2212yescomplemented
64#63983C2211yescharacteristic, complemented
65#63981C2212yescomplemented
66#63978C2212yescomplemented
67#63978C2212yescomplemented
68#63975C2211yescharacteristic, complemented
69Dic3×#67C2212yescomplemented
70#63971C2212yescomplemented
71C2×#3722C2211yescharacteristic, complemented
72C2×#3722C2212yescomplemented
73#63961C2212yescomplemented
74#63952C2212yescomplemented
75#63923C2211yescharacteristic, complemented
76#63923C2212yescomplemented
77#63921C2212yescomplemented
78D3×(C2×D3)⋊C4C2212yescomplemented
79D3×(C2×D3)⋊C4C2212yescomplemented
80D3×(C2×D3)⋊C4C2212yescomplemented
81#63910C2212yescomplemented
82#63909C2212yescomplemented
83#63907C2212yescomplemented
84#63904C2212yescomplemented
85C4×#626C2212yescomplemented
86#63900C2212yescomplemented
87#63897C2212yescomplemented
88#63897C2212yescomplemented
89#63897C2212yescomplemented
90#63897C2212yescomplemented
91#63897C2211yescharacteristic, complemented
92#63895C2212yescomplemented
93#63894C2212yescomplemented
94#63890C2212yescomplemented
95#63888C2212yescomplemented
96#63888C2212yescomplemented
97#63886C2212yescomplemented
98#63884C2212yescomplemented
99#63881C2212yescomplemented
100D3×Dic3⋊C4C2212yescomplemented
101#63854C2212yescomplemented
102#63854C2212yescomplemented
103#63853C2212yescomplemented
104#63852C2212yescomplemented
105#63851C2212yescomplemented
106#63850C2212yescomplemented
107#63850C2212yescomplemented
108#63839C2212yescomplemented
109#63836C2212yescomplemented
110C2×#1009—32no—
111C2×D3×#41—32no—
112C3×#547—32no—
113#5829—32no—
114#5824—32no—
115#5726—32no—
116#5724—32no—
117#5655—32no—
118#5655D312yescomplemented
119#5654—32no—
120#5654—32no—
121#5653—32no—
122#5653—32no—
123#5653—61no—
124D3×#123—32no—
125D3×#123—32no—
126#5631—32no—
127#5630—32no—
128#5628—32no—
129#5627—32no—
130#5610—32no—
131#5610—32no—
132#5605—32no—
133#5605—32no—
134#5554—32no—
135#5550—32no—
136#5547—32no—
137#5545—32no—
138#5507—32no—
139#5507—32no—
140C2×#894—32no—
141C2×#894—32no—
142C23×C3⋊D3C2311yescharacteristic
143C23×C3⋊D3C2311yescharacteristic
144C23×C3⋊D3C2311yescharacteristic
145C22×D32C2312yes—
146C22×D32C2311yescharacteristic
147C22×D32C2311yescharacteristic
148C2×C32×D4C2311yescharacteristic
149C22×C32×C4C2311yescharacteristic
150C2×#638C2311yescharacteristic
151C2×#638C2311yescharacteristic
152C2×#638C2312yes—
153D4×C3⋊D3—24no—
154C2×C4⋊(C3⋊D3)—24no—
155C2×C4⋊(C3⋊D3)C2312yes—
156C2×C4⋊(C3⋊D3)C2311yescharacteristic
157C2×C4⋊(C3⋊D3)C2312yes—
158C2×C4⋊(C3⋊D3)C2312yes—
159C2×C4×C3⋊D3C2311yescharacteristic
160C2×C4×C3⋊D3C2312yes—
161C2×C3×#67C2312yes—
162C2×C3×#67C2312yes—
163C2×C3×#67C2312yes—
164C2×C3×#67C2312yes—
165C22×C3×Dic3C2312yes—
166C22×C3×Dic3C2312yes—
167C22×C3×Dic3C2312yes—
168C3×#237—28no—
169C3×#235—28no—
170C2×C3×D12C2312yes—
171C2×C3×C4×D3C2312yes—
172C2×C3×C4×D3C2312yes—
173C2×C3×C4×D3C2312yes—
174C2×C3×C4×D3C2312yes—
175C2×C3×Dic6C2312yes—
176C2×C3×Dic6C2312yes—
177#3811—24no—
178#3811—24no—
179#3811—28no—
180#3811D418yescomplemented
181C2×#627C2312yes—
182C2×#626C2312yes—
183C2×#626C2312yes—
184C2×#626C2312yes—
185C2×#626C2312yes—
186C2×#626C2312yes—
187C2×#626C2312yes—
188C2×#624—24no—
189C2×#624—24no—
190C2×#624C2311yescharacteristic
191C2×#624C2312yes—
192C2×#624C2311yescharacteristic
193C2×#624C2312yes—
194C2×#624C2312yes—
195C2×#624C2311yescharacteristic
196C2×#624C2311yescharacteristic
197#3804—28no—
198#3804—28no—
199C2×D3×Dic3C2312yes—
200C2×D3×Dic3C2312yes—
201D3×D12—28no—
202D3×D12—28no—
203C4×D32—24no—
204#3799—28no—
205#3799—28no—
206#3799—28no—
207#3797—24no—
208C32×C4⋊C4C2312yes—
209C32×C22⋊C4C2312yes—
210C32×C22⋊C4C2311yescharacteristic
211#3757C2311yescharacteristic
212#3752C2312yes—
213#3752C2312yes—
214#3752C2312yes—
215#3752C2312yes—
216#3750C2312yes—
217C3×#217C2312yes—
218C3×(C2×D3)⋊C4C2312yes—
219C3×(C2×D3)⋊C4C2312yes—
220C3×(C2×D3)⋊C4C2312yes—
221C3×(C2×D3)⋊C4C2312yes—
222C3×C4⋊Dic3C2312yes—
223C3×C4⋊Dic3C2312yes—
224C3×Dic3⋊C4C2312yes—
225C3×Dic3⋊C4C2312yes—
226C3×Dic3⋊C4C2312yes—
227C3×Dic3⋊C4C2312yes—
228C3×Dic3⋊C4C2312yes—
229C3×Dic3⋊C4C2312yes—
230C3×C4×Dic3C2312yes—
231#3724C2312yes—
232#3724C2312yes—
233Dic3⋊Dic3C2312yes—
234Dic3⋊Dic3C2312yes—
235#3722C2312yes—
236#3722C2312yes—
237#3722C2312yes—
238#3722C2312yes—
239#3722C2311yescharacteristic
240#3722C2312yes—
241#3722C2312yes—
242#3722C2311yescharacteristic
243(C2×D3)⋊Dic3C2312yes—
244(C2×D3)⋊Dic3C2312yes—
245(C2×D3)⋊Dic3C2312yes—
246(C2×D3)⋊Dic3C2312yes—
247Dic32C2312yes—
248#3485—91noSylow
249C2×C3×#41—32no—
250C2×C3×#41—32no—
251#1009—616no—
252D3×#41—616no—
253C2×#239—32no—
254C2×#239—32no—
255C2×#239—32no—
256C2×D3×Q8—32no—
257C2×#237—32no—
258C2×#237—32no—
259C2×#237C2×D312yescomplemented
260C2×D3×D4—32no—
261C2×D3×D4—32no—
262C2×D3×D4—32no—
263C2×D3×D4—32no—
264C2×D3×D4—32no—
265C2×D3×D4—32no—
266C2×D3×D4—32no—
267C2×D3×D4—32no—
268C2×D3×D4—61no—
269C2×#235—32no—
270C2×#235—32no—
271C2×#235—32no—
272C2×#235—32no—
273C2×#235—32no—
274C2×#235C2×D312yescomplemented
275C22×D12—32no—
276C22×D12—32no—
277C22×D12—32no—
278C22×D12—61no—
279C22×C4×D3—32no—
280C22×C4×D3—32no—
281C22×C4×D3—32no—
282C3×C4⋊Q8—32no—
283C3×#123—21no—
284C3×#123—32no—
285C3×#123—32no—
286C3×#123—32no—
287C3×#123C2×D312yescomplemented
288C3×C22⋊Q8—32no—
289C3×C22⋊Q8—32no—
290C3×#121—32no—
291C3×#121—32no—
292C3×C4×D4—32no—
293C3×C4×D4—32no—
294C2×C3×C4⋊C4—32no—
295C2×C3×C4⋊C4—32no—
296#947—32no—
297#946—32no—
298#946—32no—
299#944—32no—
300#939—32no—
301#939—32no—
302#939—32no—
303#939—32no—
304#939C2×D312yescomplemented
305#937—32no—
306#937—32no—
307#937—32no—
308#937—32no—
309#937—32no—
310#937—61no—
311#935—32no—
312#935—32no—
313D4×Dic3—32no—
314#930—32no—
315#930—32no—
316#930—32no—
317#929—32no—
318#929—32no—
319#929—32no—
320#929—32no—
321#929—61no—
322C4×#67—32no—
323C4×#67—32no—
324C4×#67—32no—
325C4×#67—32no—
326C2×(C2×D3)⋊C4—32no—
327C2×(C2×D3)⋊C4—32no—
328C2×(C2×D3)⋊C4—32no—
329C2×(C2×D3)⋊C4—32no—
330C2×(C2×D3)⋊C4—32no—
331C2×(C2×D3)⋊C4—32no—
332#924—32no—
333C2×Dic3⋊C4—32no—
334C2×Dic3⋊C4C2×D312yescomplemented
335#897—32no—
336#896—32no—
337#896—32no—
338#896—32no—
339#896—32no—
340#896C2×D312yescomplemented
341#895—32no—
342#895—32no—
343#895—32no—
344#895—32no—
345#895—32no—
346#895—62no—
347#894—32no—
348#894—32no—
349#894—32no—
350#894—32no—
351#894—32no—
352#894—32no—
353#894—32no—
354#894—32no—
355#894—32no—
356#894—32no—
357#894—32no—
358#894—32no—
359#894—32no—
360#894—32no—
361#894—32no—
362#894—32no—
363#894—32no—
364#894—32no—
365#894—62no—
366#894C2×D312yescomplemented
367#893—32no—
368#893—32no—
369#893—32no—
370#892—32no—
371D3×C4⋊C4—32no—
372D3×C4⋊C4—32no—
373D3×C4⋊C4—32no—
374D3×C4⋊C4C2×D312yescomplemented
375#888—32no—
376#888C2×D312yescomplemented
377#886—32no—
378#886C2×D312yescomplemented
379#885—32no—
380#885—32no—
381#884—32no—
382#884—32no—
383#884—32no—
384#884—32no—
385#884—62no—
386#884C2×D312yescomplemented
387#883—32no—
388#883—32no—
389#883—32no—
390#883—32no—
391#883C2×D312yescomplemented
392#882—32no—
393#882—32no—
394#882—32no—
395#882—32no—
396#882—32no—
397#882—32no—
398#882—32no—
399#882—62no—
400#882—61no—
401#67⋊C4—32no—
402#67⋊C4—32no—
403#67⋊C4C2×D312yescomplemented
404#67⋊C4C2×D312yescomplemented
405D3×C22⋊C4—32no—
406D3×C22⋊C4—32no—
407D3×C22⋊C4—32no—
408D3×C22⋊C4—32no—
409D3×C22⋊C4—32no—
410D3×C22⋊C4—32no—
411D3×C22⋊C4—61no—
412#878C2×D312yescomplemented
413#875—32no—
414C4×D12—32no—
415C4×D12—32no—
416#872—32no—
417C23×C32C2411yescharacteristic
418C23×C32C2411yescharacteristic
419C22×C3⋊D3—22no—
420C22×C3⋊D3—22no—
421C22×C3⋊D3—42no—
422C22×C3⋊D3—42no—
423C22×C3⋊D3—42no—
424C22×C3⋊D3C2×D414yes—
425C22×C3⋊D3C2412yes—
426C22×C3⋊D3C2411yescharacteristic
427C22×C3⋊D3C2411yescharacteristic
428C22×C3⋊D3C2411yescharacteristic
429C22×C3×D3C2412yes—
430C22×C3×D3C2412yes—
431C2×D32—22no—
432C2×D32—24no—
433C2×D32—42no—
434C2×D32—42no—
435C2×D32—42no—
436C2×D32—42no—
437C2×D32C2×D414yes—
438C32×D4—22no—
439C2×C32×C4—22no—
440C2×C32×C4C2412yes—
441C2×C32×C4C2412yes—
442C2×C32×C4C2411yescharacteristic
443#638—22no—
444#638—22no—
445#638—42no—
446C2×C3⋊Dic3C2412yes—
447C2×C3⋊Dic3C2411yescharacteristic
448C4⋊(C3⋊D3)—22no—
449C4⋊(C3⋊D3)—24no—
450C4⋊(C3⋊D3)—24no—
451C4⋊(C3⋊D3)—42no—
452C4×C3⋊D3—22no—
453C4×C3⋊D3—42no—
454C3×#67—24no—
455C3×#67—24no—
456C3×#67—42no—
457C3×#67C2×D418yes—
458C2×C3×Dic3—24no—
459C2×C3×Dic3—24no—
460C2×C3×Dic3—42no—
461C2×C3×Dic3C2412yes—
462C2×C3×Dic3C2412yes—
463C2×C3×Dic3C2412yes—
464C2×C3×Dic3C2412yes—
465C2×C3×Dic3C2412yes—
466C2×C3×Dic3C2412yes—
467C3×D12—24no—
468C3×C4×D3—24no—
469C3×C4×D3—24no—
470C3×C4×D3—24no—
471C3×C4×D3—42no—
472C3×Dic6—24no—
473C3×Dic6—24no—
474#627—24no—
475#626—24no—
476#626—24no—
477#626—24no—
478#626—24no—
479#626—42no—
480#626C2×D418yes—
481#624—22no—
482#624—22no—
483#624—24no—
484#624—22no—
485#624—24no—
486#624—24no—
487#624C2×D414yes—
488D3×Dic3—24no—
489D3×Dic3—42no—
490C2×H(5,𝔽2)—91no—
491C22×#41—91no—
492#547—32no—
493#547—92no—
494#547—92no—
495#547—92no—
496#546—92no—
497#546—92no—
498#546—92no—
499#546—92no—
500#536—92no—
501#534—91no—
502#534—92no—
503#534—91no—
504#525—92no—
505C2×#123—91no—
506C2×#123—92no—
507C2×#123—91no—
508#518—91no—
509C23×D3—32no—
510C23×D3—32no—
511C23×D3—32no—
512C23×D3—32no—
513C23×D3—32no—
514C23×D3—32no—
515C23×D3—32no—
516C23×D3—61no—
517C23×D3—61no—
518C23×D3—61no—
519C3×#41—68no—
520C3×#41—68no—
521C2×C3×Q8—32no—
522C2×C3×Q8—32no—
523C2×C3×D4—21no—
524C2×C3×D4—32no—
525C2×C3×D4—32no—
526C2×C3×D4—32no—
527C2×C3×D4—32no—
528C2×C3×D4—32no—
529C2×C3×D4C22×D312yes—
530C22×C3×C4—21no—
531C22×C3×C4—32no—
532C22×C3×C4—32no—
533C22×C3×C4—32no—
534C22×C3×C4—32no—
535C22×C3×C4—32no—
536C22×C3×C4—32no—
537C22×C3×C4—32no—
538C22×C3×C4C22×D312yes—
539C2×#67—32no—
540C2×#67—32no—
541C2×#67—32no—
542C2×#67—32no—
543C2×#67—32no—
544C2×#67—32no—
545C2×#67—32no—
546C2×#67—32no—
547C2×#67—32no—
548C2×#67—32no—
549C2×#67—61no—
550C2×#67—61no—
551C2×#67—62no—
552C2×#67C22×D312yes—
553C2×#67C22×D312yes—
554C2×#67C22×D312yes—
555C2×#67C22×D312yes—
556C22×Dic3—32no—
557C22×Dic3—32no—
558C22×Dic3C22×D312yes—
559C22×Dic3C22×D312yes—
560C22×Dic3C22×D312yes—
561#239—68no—
562#239—68no—
563#239—68no—
564D3×Q8—68no—
565#237—28no—
566#237—68no—
567#237—68no—
568D3×D4—316no—
569D3×D4—68no—
570D3×D4—68no—
571D3×D4—68no—
572D3×D4—68no—
573D3×D4—68no—
574D3×D4—68no—
575D3×D4—68no—
576D3×D4—124no—
577#235—28no—
578#235—68no—
579#235—68no—
580#235—68no—
581#235—68no—
582#235—68no—
583C2×D12—32no—
584C2×D12—32no—
585C2×D12—32no—
586C2×D12—32no—
587C2×D12—32no—
588C2×D12—32no—
589C2×D12—32no—
590C2×D12—32no—
591C2×D12—32no—
592C2×D12—32no—
593C2×D12—32no—
594C2×D12—32no—
595C2×D12—32no—
596C2×D12—62no—
597C2×D12—62no—
598C2×D12—61no—
599C2×D12—62no—
600C2×D12—68no—
601C2×D12—68no—
602C2×D12—68no—
603C2×D12—124no—
604C2×D12C22×D312yes—
605C2×C4×D3—32no—
606C2×C4×D3—32no—
607C2×C4×D3—32no—
608C2×C4×D3—32no—
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—61no—
621C2×C4×D3—62no—
622C2×C4×D3—68no—
623C2×C4×D3—68no—
624C2×C4×D3—68no—
625C2×C4×D3C22×D312yes—
626C2×C4×D3C22×D312yes—
627C2×C4×D3C22×D312yes—
628C2×C4×D3C22×D312yes—
629C2×Dic6—32no—
630C2×Dic6—32no—
631C2×Dic6C22×D312yes—
632C2×Dic6C22×D312yes—
633C3×C4⋊C4—22no—
634C3×C4⋊C4—32no—
635C3×C4⋊C4—32no—
636C3×C4⋊C4—32no—
637C3×C4⋊C4—32no—
638C3×C4⋊C4—32no—
639C3×C4⋊C4—32no—
640C3×C4⋊C4—32no—
641C3×C4⋊C4—32no—
642C3×C4⋊C4C22×D312yes—
643C3×C4⋊C4C22×D312yes—
644C3×C22⋊C4—21no—
645C3×C22⋊C4—22no—
646C3×C22⋊C4—32no—
647C3×C22⋊C4—32no—
648C3×C22⋊C4—32no—
649C3×C22⋊C4—32no—
650C3×C22⋊C4—32no—
651C3×C22⋊C4C22×D312yes—
652C3×C22⋊C4C22×D312yes—
653C3×C22⋊C4C22×D312yes—
654C3×C42—32no—
655#217—32no—
656#217—32no—
657#217—32no—
658#217—32no—
659#217—32no—
660#217—61no—
661#217C22×D312yes—
662(C2×D3)⋊C4—32no—
663(C2×D3)⋊C4—32no—
664(C2×D3)⋊C4—32no—
665(C2×D3)⋊C4—32no—
666(C2×D3)⋊C4—32no—
667(C2×D3)⋊C4—32no—
668(C2×D3)⋊C4—32no—
669(C2×D3)⋊C4—32no—
670(C2×D3)⋊C4—32no—
671(C2×D3)⋊C4—32no—
672(C2×D3)⋊C4—32no—
673(C2×D3)⋊C4—32no—
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—32no—
688(C2×D3)⋊C4—62no—
689(C2×D3)⋊C4—62no—
690(C2×D3)⋊C4—62no—
691(C2×D3)⋊C4—62no—
692(C2×D3)⋊C4C22×D312yes—
693(C2×D3)⋊C4C22×D312yes—
694(C2×D3)⋊C4C22×D312yes—
695(C2×D3)⋊C4C22×D312yes—
696C4⋊Dic3—32no—
697C4⋊Dic3—32no—
698C4⋊Dic3C22×D312yes—
699C4⋊Dic3C22×D312yes—
700Dic3⋊C4—32no—
701Dic3⋊C4—32no—
702Dic3⋊C4—32no—
703Dic3⋊C4—32no—
704Dic3⋊C4—32no—
705Dic3⋊C4—32no—
706Dic3⋊C4—32no—
707Dic3⋊C4—32no—
708Dic3⋊C4—62no—
709Dic3⋊C4C22×D312yes—
710Dic3⋊C4C22×D312yes—
711Dic3⋊C4C22×D312yes—
712Dic3⋊C4C22×D312yes—
713Dic3⋊C4C22×D312yes—
714Dic3⋊C4C22×D312yes—
715C4×Dic3—32no—
716C4×Dic3—32no—
717C4×Dic3C22×D312yes—
718C22×C32—22no—
719C22×C32—21no—
720C22×C32—22no—
721C22×C32C22×D412yes—
722C22×C32C2511yescharacteristic
723C2×C3⋊D3—22no—
724C2×C3⋊D3—22no—
725C2×C3⋊D3—21no—
726C2×C3⋊D3—22no—
727C2×C3⋊D3—22no—
728C2×C3⋊D3—22no—
729C2×C3⋊D3—22no—
730C2×C3⋊D3—44no—
731C2×C3⋊D3—44no—
732C2×C3⋊D3—82no—
733C2×C3⋊D3C22×D412yes—
734C2×C3⋊D3C22×D412yes—
735C2×C3×D3—22no—
736C2×C3×D3—22no—
737C2×C3×D3—22no—
738C2×C3×D3—22no—
739C2×C3×D3—22no—
740C2×C3×D3C22×D414yes—
741D32—44no—
742D32—84no—
743D32—82no—
744C32×C4—21no—
745C32×C4—22no—
746C32×C4—22no—
747C3⋊Dic3—21no—
748C3⋊Dic3—22no—
749C3×Dic3—22no—
750C3×Dic3—22no—
751C3×Dic3—22no—
752C3×Dic3—22no—
753C3×Dic3—22no—
754C3×Dic3C22×D414yes—
755H(5,𝔽2)—188no—
756C2×#41—32no—
757C2×#41—32no—
758C2×#41—92no—
759C2×#41—92no—
760C2×#41—92no—
761C2×#41—92no—
762C2×#41—92no—
763C2×#41—188no—
764C22×Q8—91no—
765C22×D4—92no—
766C22×D4—92no—
767C22×D4—91no—
768C22×D4—91no—
769C22×D4—91no—
770C22×D4—92no—
771C22×D4—91no—
772C22×D4—91no—
773C23×C4—91no—
774C23×C4—91no—
775C23×C4—91no—
776C4⋊Q8—32no—
777C4⋊Q8—92no—
778#124—92no—
779#124—92no—
780#123—32no—
781#123—32no—
782#123—32no—
783#123—91no—
784#123—92no—
785#123—92no—
786#123—92no—
787#123—92no—
788#123—92no—
789#123—92no—
790#123—92no—
791#123—92no—
792#123—91no—
793#123—92no—
794#123—92no—
795#123—92no—
796#123—92no—
797#123—91no—
798#123—92no—
799#123D3211yescharacteristic, complemented
800C22⋊Q8—32no—
801C22⋊Q8—32no—
802C22⋊Q8—92no—
803C22⋊Q8—92no—
804C22⋊Q8—92no—
805C22⋊Q8—92no—
806#121—32no—
807#121—32no—
808#121—92no—
809#121—92no—
810#121—92no—
811#121—92no—
812#121—92no—
813#121—92no—
814#121—92no—
815#121—92no—
816#120—92no—
817#120—91no—
818#120—92no—
819#120—91no—
820#120—92no—
821#120—91no—
822#120—92no—
823#120—91no—
824C4×D4—32no—
825C4×D4—32no—
826C4×D4—92no—
827C4×D4—92no—
828C4×D4—92no—
829C4×D4—92no—
830C4×D4—92no—
831C4×D4—92no—
832#117—92no—
833C2×C4⋊C4—32no—
834C2×C4⋊C4—32no—
835C2×C4⋊C4—92no—
836C2×C4⋊C4—92no—
837C2×C22⋊C4—92no—
838C2×C22⋊C4—92no—
839C2×C22⋊C4—92no—
840C2×C22⋊C4—92no—
841C2×C22⋊C4—91no—
842C2×C22⋊C4—92no—
843C2×C22⋊C4—91no—
844C23×C3—21no—
845C23×C3—21no—
846C23×C3—32no—
847C23×C3—32no—
848C23×C3C23×D312yes—
849C23×C3C23×D312yes—
850C22×D3—32no—
851C22×D3—32no—
852C22×D3—38no—
853C22×D3—38no—
854C22×D3—32no—
855C22×D3—32no—
856C22×D3—32no—
857C22×D3—61no—
858C22×D3—61no—
859C22×D3—64no—
860C22×D3—62no—
861C22×D3—61no—
862C22×D3—64no—
863C22×D3—64no—
864C22×D3—64no—
865C22×D3—64no—
866C22×D3—64no—
867C22×D3—122no—
868C22×D3—122no—
869C22×D3—122no—
870C22×D3—122no—
871C22×D3—122no—
872C22×D3—122no—
873C22×D3—122no—
874C22×D3—122no—
875C22×D3—122no—
876C22×D3—122no—
877C22×D3—122no—
878C22×D3—122no—
879C22×D3—122no—
880C22×D3—122no—
881C22×D3—122no—
882C22×D3—122no—
883C22×D3—242no—
884C22×D3—242no—
885C22×D3—242no—
886C22×D3C23×D312yes—
887C22×D3C23×D312yes—
888C3×Q8—64no—
889C3×Q8—64no—
890C3×D4—24no—
891C3×D4—38no—
892C3×D4—42no—
893C3×D4—64no—
894C3×D4—64no—
895C3×D4—64no—
896C3×D4—122no—
897C2×C3×C4—24no—
898C2×C3×C4—22no—
899C2×C3×C4—22no—
900C2×C3×C4—21no—
901C2×C3×C4—32no—
902C2×C3×C4—32no—
903C2×C3×C4—32no—
904C2×C3×C4—32no—
905C2×C3×C4—32no—
906C2×C3×C4—32no—
907C2×C3×C4—42no—
908C2×C3×C4—64no—
909C2×C3×C4—64no—
910C2×C3×C4—64no—
911C2×C3×C4—64no—
912C2×C3×C4—64no—
913C2×C3×C4—122no—
914C2×C3×C4—122no—
915C2×C3×C4C23×D312yes—
916C2×C3×C4C23×D312yes—
917C2×C3×C4C23×D312yes—
918C2×C3×C4C23×D312yes—
919C2×C3×C4C23×D312yes—
920#67—24no—
921#67—24no—
922#67—38no—
923#67—42no—
924#67—64no—
925#67—64no—
926#67—64no—
927#67—64no—
928#67—64no—
929#67—64no—
930#67—122no—
931#67—122no—
932#67—122no—
933#67—122no—
934#67—122no—
935#67—242no—
936#67D3×D418yes—
937C2×Dic3—24no—
938C2×Dic3—24no—
939C2×Dic3—32no—
940C2×Dic3—32no—
941C2×Dic3—32no—
942C2×Dic3—42no—
943C2×Dic3—61no—
944C2×Dic3—62no—
945C2×Dic3—64no—
946C2×Dic3—122no—
947C2×Dic3C23×D312yes—
948C2×Dic3C23×D312yes—
949C2×Dic3C23×D312yes—
950C2×Dic3C23×D312yes—
951C2×Dic3C23×D312yes—
952C2×Dic3C23×D312yes—
953D12—24no—
954D12—38no—
955D12—64no—
956D12—64no—
957D12—64no—
958D12—64no—
959D12—64no—
960D12—64no—
961D12—64no—
962D12—64no—
963D12—64no—
964D12—124no—
965D12—124no—
966D12—122no—
967D12—122no—
968D12—122no—
969D12—122no—
970D12—242no—
971C4×D3—24no—
972C4×D3—24no—
973C4×D3—24no—
974C4×D3—38no—
975C4×D3—42no—
976C4×D3—64no—
977C4×D3—64no—
978C4×D3—64no—
979C4×D3—64no—
980C4×D3—64no—
981C4×D3—64no—
982C4×D3—64no—
983C4×D3—64no—
984C4×D3—64no—
985C4×D3—64no—
986C4×D3—64no—
987C4×D3—122no—
988C4×D3—122no—
989C4×D3—122no—
990C4×D3—122no—
991C4×D3—242no—
992Dic6—24no—
993Dic6—24no—
994Dic6—64no—
995Dic6—64no—
996C2×C32—22no—
997C2×C32—41no—
998C2×C32C23×D411yescharacteristic
999C2×C32#58512yes—
1000C3⋊D3—22no—
1001C3⋊D3—22no—
1002C3⋊D3—42no—
1003C3⋊D3—41no—
1004C3×D3—24no—
1005C3×D3—42no—
1006C24—91no—
1007C24—92no—
1008C24—91no—
1009C24—91no—
1010C24—91no—
1011C24—91no—
1012#41—68no—
1013#41—68no—
1014#41—188no—
1015#41—188no—
1016#41—188no—
1017#41—188no—
1018#41—188no—
1019C2×Q8—32no—
1020C2×Q8—32no—
1021C2×Q8—92no—
1022C2×Q8—184no—
1023C2×D4—32no—
1024C2×D4—32no—
1025C2×D4—32no—
1026C2×D4—32no—
1027C2×D4—32no—
1028C2×D4—92no—
1029C2×D4—92no—
1030C2×D4—92no—
1031C2×D4—92no—
1032C2×D4—92no—
1033C2×D4—92no—
1034C2×D4—98no—
1035C2×D4—91no—
1036C2×D4—91no—
1037C2×D4—92no—
1038C2×D4—91no—
1039C2×D4—92no—
1040C2×D4—92no—
1041C2×D4—92no—
1042C2×D4—184no—
1043C2×D4—188no—
1044C2×D4—188no—
1045C2×D4—184no—
1046C2×D4—188no—
1047C2×D4—184no—
1048C2×D4—184no—
1049C2×D4C2×D3211yescharacteristic
1050C22×C4—32no—
1051C22×C4—32no—
1052C22×C4—32no—
1053C22×C4—32no—
1054C22×C4—32no—
1055C22×C4—32no—
1056C22×C4—32no—
1057C22×C4—91no—
1058C22×C4—92no—
1059C22×C4—91no—
1060C22×C4—92no—
1061C22×C4—92no—
1062C22×C4—91no—
1063C22×C4—91no—
1064C22×C4—92no—
1065C22×C4—92no—
1066C22×C4—91no—
1067C22×C4—92no—
1068C22×C4—184no—
1069C22×C4—184no—
1070C22×C4—184no—
1071C22×C4C2×D3211yescharacteristic
1072C4⋊C4—32no—
1073C4⋊C4—32no—
1074C4⋊C4—32no—
1075C4⋊C4—32no—
1076C4⋊C4—32no—
1077C4⋊C4—32no—
1078C4⋊C4—32no—
1079C4⋊C4—32no—
1080C4⋊C4—92no—
1081C4⋊C4—92no—
1082C4⋊C4—92no—
1083C4⋊C4—92no—
1084C4⋊C4—92no—
1085C4⋊C4C2×D3212yes—
1086C22⋊C4—32no—
1087C22⋊C4—32no—
1088C22⋊C4—32no—
1089C22⋊C4—32no—
1090C22⋊C4—32no—
1091C22⋊C4—92no—
1092C22⋊C4—92no—
1093C22⋊C4—92no—
1094C22⋊C4—91no—
1095C22⋊C4—91no—
1096C22⋊C4—92no—
1097C22⋊C4—92no—
1098C22⋊C4—92no—
1099C22⋊C4—92no—
1100C22⋊C4—92no—
1101C22⋊C4—92no—
1102C22⋊C4—92no—
1103C22⋊C4—91no—
1104C22⋊C4—92no—
1105C22⋊C4—92no—
1106C22⋊C4—92no—
1107C22⋊C4—92no—
1108C22⋊C4C2×D3211yescharacteristic
1109C22⋊C4C2×D3212yes—
1110C42—32no—
1111C42—92no—
1112C22×C3—22no—
1113C22×C3—22no—
1114C22×C3—22no—
1115C22×C3—22no—
1116C22×C3—22no—
1117C22×C3—22no—
1118C22×C3—21no—
1119C22×C3—34no—
1120C22×C3—42no—
1121C22×C3—41no—
1122C22×C3—42no—
1123C22×C3—62no—
1124C22×C3—62no—
1125C22×C3—62no—
1126C22×C3—62no—
1127C22×C3—62no—
1128C22×C3C2×D3×D414yes—
1129C22×C3C24×D312yes—
1130C2×D3—22no—
1131C2×D3—22no—
1132C2×D3—22no—
1133C2×D3—22no—
1134C2×D3—22no—
1135C2×D3—34no—
1136C2×D3—34no—
1137C2×D3—62no—
1138C2×D3—62no—
1139C2×D3—62no—
1140C2×D3—62no—
1141C2×D3—62no—
1142C2×D3—62no—
1143C2×D3—62no—
1144C2×D3—62no—
1145C2×D3—62no—
1146C2×D3—62no—
1147C2×D3—62no—
1148C2×D3—62no—
1149C2×D3—62no—
1150C2×D3—62no—
1151C2×D3—62no—
1152C2×D3—122no—
1153C2×D3—122no—
1154C2×D3—122no—
1155C2×D3—121no—
1156C2×D3—122no—
1157C2×D3—122no—
1158C2×D3—122no—
1159C2×D3—128no—
1160C2×D3—128no—
1161C2×D3—128no—
1162C2×D3—244no—
1163C2×D3—244no—
1164C2×D3—244no—
1165C2×D3—244no—
1166C2×D3—244no—
1167C2×D3—244no—
1168C2×D3—244no—
1169C2×D3C2×D3×D414yes—
1170C3×C4—22no—
1171C3×C4—22no—
1172C3×C4—22no—
1173C3×C4—22no—
1174C3×C4—22no—
1175C3×C4—34no—
1176C3×C4—41no—
1177C3×C4—42no—
1178C3×C4—42no—
1179C3×C4—62no—
1180C3×C4—62no—
1181C3×C4—62no—
1182C3×C4—62no—
1183C3×C4—62no—
1184Dic3—22no—
1185Dic3—22no—
1186Dic3—22no—
1187Dic3—22no—
1188Dic3—22no—
1189Dic3—62no—
1190Dic3—62no—
1191Dic3—62no—
1192Dic3—121no—
1193Dic3—122no—
1194Dic3C2×D3×D414yes—
1195C32#348511yescharacteristic, complemented, Sylow
1196C23—32no—
1197C23—32no—
1198C23—94no—
1199C23—91no—
1200C23—91no—
1201C23—94no—
1202C23—92no—
1203C23—91no—
1204C23—182no—
1205C23—184no—
1206C23—182no—
1207C23—182no—
1208C23—362no—
1209C23—362no—
1210C23—362no—
1211C23—362no—
1212C23—362no—
1213C23—362no—
1214C23—362no—
1215C23C22×D3211yescharacteristic
1216C23C22×D3211yescharacteristic
1217Q8—64no—
1218Q8—64no—
1219Q8—184no—
1220D4—22no—
1221D4—38no—
1222D4—64no—
1223D4—64no—
1224D4—64no—
1225D4—98no—
1226D4—122no—
1227D4—184no—
1228D4—184no—
1229D4—182no—
1230D4—184no—
1231D4—184no—
1232D4—184no—
1233D4—184no—
1234D4—182no—
1235D4—182no—
1236D4—362no—
1237D4—362no—
1238D4—362no—
1239C2×C4—22no—
1240C2×C4—32no—
1241C2×C4—32no—
1242C2×C4—32no—
1243C2×C4—32no—
1244C2×C4—32no—
1245C2×C4—32no—
1246C2×C4—64no—
1247C2×C4—64no—
1248C2×C4—64no—
1249C2×C4—64no—
1250C2×C4—64no—
1251C2×C4—94no—
1252C2×C4—92no—
1253C2×C4—91no—
1254C2×C4—122no—
1255C2×C4—122no—
1256C2×C4—182no—
1257C2×C4—184no—
1258C2×C4—184no—
1259C2×C4—182no—
1260C2×C4—182no—
1261C2×C4—184no—
1262C2×C4—182no—
1263C2×C4—184no—
1264C2×C4—362no—
1265C2×C4—362no—
1266C2×C4C22×D3212yes—
1267C2×C4C22×D3211yescharacteristic
1268C2×C4C22×D3212yes—
1269C2×C3—24no—
1270C2×C3—21no—
1271C2×C3—22no—
1272C2×C3—42no—
1273C2×C3—42no—
1274C2×C3—64no—
1275C2×C3—81no—
1276C2×C3—122no—
1277C2×C3C22×D3×D412yes—
1278C2×C3#596412yes—
1279C2×C3#596812yes—
1280D3—24no—
1281D3—42no—
1282D3—64no—
1283D3—64no—
1284D3—122no—
1285D3—122no—
1286D3—122no—
1287D3—122no—
1288D3—122no—
1289D3—241no—
1290D3—242no—
1291C22—22no—
1292C22—21no—
1293C22—22no—
1294C22—34no—
1295C22—62no—
1296C22—62no—
1297C22—62no—
1298C22—62no—
1299C22—62no—
1300C22—92no—
1301C22—92no—
1302C22—182no—
1303C22—182no—
1304C22—181no—
1305C22—182no—
1306C22—182no—
1307C22—182no—
1308C22—182no—
1309C22—364no—
1310C22—364no—
1311C22—364no—
1312C22—722no—
1313C22—724no—
1314C22—722no—
1315C22D32×D412yes—
1316C22C23×D3211yescharacteristic
1317C4—22no—
1318C4—21no—
1319C4—22no—
1320C4—34no—
1321C4—62no—
1322C4—62no—
1323C4—62no—
1324C4—62no—
1325C4—62no—
1326C4—181no—
1327C4—182no—
1328C3—21no—
1329C3#8670012yescomplemented
1330C2—22no—
1331C2—41no—
1332C2—64no—
1333C2—122no—
1334C2—182no—
1335C2—182no—
1336C2—361no—
1337C2—362no—
1338C2C2×D32×D411yescharacteristic
1339C2#1059669712yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#123C22
hypercenter#123D32
hypocenterC32#3485
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C2×#64312C2semidirect
2. C2×#64308C2semidirect
3. #10596124C2semidirect
4. C3×#5655C2semidirect
5. #10595308C2semidirect
6. #10595305C2semidirect
7. C2×#63897C2semidirect
8. #10594885C2semidirect
9. #10594620C2semidirect
10. D3×#894C2semidirect
11. #10594517C2semidirect
12. #10594328C2semidirect
13. #10594295C2semidirect
14. #10594293C2semidirect
15. #10594283C2semidirect
16. #10594264C2semidirect
17. #10594256C2semidirect
18. #10594066C2semidirect
19. #10594064C2semidirect
21. C2×D4×C3⋊D3C22semidirect
23. C2×C3×#237C22semidirect
24. C2×C3×#235C22semidirect
27. C2×#3811C22semidirect
28. C2×#3811C22semidirect
29. C22×#624C22semidirect
30. C22×#624C22semidirect
31. C2×#3804C22semidirect
32. C2×#3804C22semidirect
36. C2×D3×D12C22semidirect
37. C2×C4×D32C22semidirect
39. C2×#3799C22semidirect
40. C2×#3799C22semidirect
41. C2×#3797C22semidirect
42. C32×#123C22semidirect
43. #64146C22semidirect
44. #64138C22semidirect
45. #64104C22semidirect
46. #64103C22semidirect
47. #64093C22semidirect
48. #64091C22semidirect
49. #64091C22semidirect
50. C22⋊C4×C3⋊D3C22semidirect
51. C3×#939C22semidirect
52. C2×C3×Dic3⋊C4C22semidirect
53. C3×#896C22semidirect
54. C3×#894C22semidirect
55. C3×D3×C4⋊C4C22semidirect
56. C3×#888C22semidirect
57. C3×#886C22semidirect
58. C3×#884C22semidirect
59. C3×#883C22semidirect
60. C3×#67⋊C4C22semidirect
61. C3×#67⋊C4C22semidirect
62. C3×#878C22semidirect
63. #63983C22semidirect
64. #63983C22semidirect
65. #63981C22semidirect
66. #63978C22semidirect
67. #63978C22semidirect
68. #63975C22semidirect
69. Dic3×#67C22semidirect
70. #63971C22semidirect
71. C2×#3722C22semidirect
72. C2×#3722C22semidirect
73. #63961C22semidirect
74. #63952C22semidirect
75. #63923C22semidirect
76. #63923C22semidirect
77. #63921C22semidirect
78. D3×(C2×D3)⋊C4C22semidirect
79. D3×(C2×D3)⋊C4C22semidirect
80. D3×(C2×D3)⋊C4C22semidirect
81. #63910C22semidirect
82. #63909C22semidirect
83. #63907C22semidirect
84. #63904C22semidirect
85. C4×#626C22semidirect
86. #63900C22semidirect
87. #63897C22semidirect
88. #63897C22semidirect
89. #63897C22semidirect
90. #63897C22semidirect
91. #63897C22semidirect
92. #63895C22semidirect
93. #63894C22semidirect
94. #63890C22semidirect
95. #63888C22semidirect
96. #63888C22semidirect
97. #63886C22semidirect
98. #63884C22semidirect
99. #63881C22semidirect
100. D3×Dic3⋊C4C22semidirect
101. #63854C22semidirect
102. #63854C22semidirect
103. #63853C22semidirect
104. #63852C22semidirect
105. #63851C22semidirect
106. #63850C22semidirect
107. #63850C22semidirect
108. #63839C22semidirect
109. #63836C22semidirect
118. #5655D3semidirect
180. #3811D4semidirect
259. C2×#237C2×D3semidirect
274. C2×#235C2×D3semidirect
287. C3×#123C2×D3semidirect
304. #939C2×D3semidirect
334. C2×Dic3⋊C4C2×D3semidirect
340. #896C2×D3semidirect
366. #894C2×D3semidirect
374. D3×C4⋊C4C2×D3semidirect
376. #888C2×D3semidirect
378. #886C2×D3semidirect
386. #884C2×D3semidirect
391. #883C2×D3semidirect
403. #67⋊C4C2×D3semidirect
404. #67⋊C4C2×D3semidirect
412. #878C2×D3semidirect
799. #123D32semidirect
1195. C32#3485semidirect
1329. C3#86700semidirect

Maximal subgroups

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

subgroupindex
C2×#643122
C2×#643082
#105961242
C3×#56552
#105953082
#105953052
C2×#638972
#105948852
#105946202
D3×#8942
#105945172
#105943282
#105942952
#105942932
#105942832
#105942642
#105942562
#105940662
#105940642
#867003