Finite Group Databasebeta

← #11903523

Subgroups — #11903523

Order 1152.

2477 conjugacy classes of subgroups.

The subgroup lattice has 1294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64090C211yesmaximal, characteristic, complemented
2C3×#5495C212yesmaximal, complemented
3#10595501C211yesmaximal, characteristic, complemented
4#10595500C212yesmaximal, complemented
5C2×#63957C211yesmaximal, characteristic, complemented
6#10595035C212yesmaximal, complemented
7#10594969C211yesmaximal, characteristic, complemented
8#10594960C212yesmaximal, complemented
9#10594920C211yesmaximal, characteristic, complemented
10C4×#3805C211yesmaximal, characteristic, complemented
11#10594810C211yesmaximal, characteristic, complemented
12#10594250C211yesmaximal, characteristic, complemented
13#10594231C211yesmaximal, characteristic, complemented
14#10594229C211yesmaximal, characteristic, complemented
15#10594168C211yesmaximal, characteristic, complemented
16#10594155C211yesmaximal, characteristic, complemented
17#10594150C211yesmaximal, characteristic, complemented
18#10594144C212yesmaximal, complemented
19#10594137C212yesmaximal, complemented
20#10594130C212yesmaximal, complemented
21#10594083C211yesmaximal, characteristic, complemented
22#10594048C212yesmaximal, complemented
23#10594046C211yesmaximal, characteristic, complemented
24#86790—32nomaximal
25C22×#638C2211yescharacteristic
26C23×C3⋊Dic3C2211yescharacteristic
27C22×C4×C3⋊D3C2211yescharacteristic
28C2×#3805C2211yescharacteristic
29C2×#3804C2212yes—
30C2×C32×C22⋊C4C2211yescharacteristic
31C2×#3752C2211yescharacteristic
32C2×#3750C2211yescharacteristic
33C2×C4×C3⋊Dic3C2211yescharacteristic
34#64090C2211yescharacteristic
35#64090C2211yescharacteristic
36#64090C2211yescharacteristic
37#64090C2211yescharacteristic
38#64090C2211yescharacteristic
39#64090C2211yescharacteristic
40#64090C2211yescharacteristic
41#64090C2211yescharacteristic
42C3×#953C2212yes—
43C2×C3×#217C2212yes—
44C3×#929C2212yes—
45C3×C4×#67C2212yes—
46C3×#926C2212yes—
47C3×#924C2212yes—
48C3×#886C2212yescomplemented
49C3×#885C2212yescomplemented
50C3×#883C2212yescomplemented
51C3×#67⋊C4C2212yescomplemented
52C3×#879C2212yescomplemented
53C3×#879C2212yescomplemented
54C3×#878C2212yescomplemented
55C3×#877C2212yescomplemented
56#63982C2212yes—
57#63982C2211yescharacteristic, complemented
58#63982C2211yescharacteristic, complemented
59#63981C2212yes—
60#63980C2211yescharacteristic, complemented
61#63980C2211yescharacteristic, complemented
62#63978C2212yes—
63#63975C2212yes—
64#63974C2212yes—
65#67⋊Dic3C2212yes—
66#67⋊Dic3C2212yescomplemented
67#67⋊Dic3C2212yescomplemented
68#63971C2212yes—
69C2×#3724C2211yescharacteristic, complemented
70C2×#3724C2211yescharacteristic, complemented
71#63966C2212yes—
72#63962C2212yes—
73#63958C2212yes—
74#63957C2211yescharacteristic
75#63957C2211yescharacteristic
76#63957C2212yes—
77#63957C2211yescharacteristic
78#63957C2212yescomplemented
79#63957C2211yescharacteristic, complemented
80#63957C2211yescharacteristic, complemented
81C2×Dic32C2212yescomplemented
82#63953C2212yes—
83#63952C2212yes—
84#63919C2211yescharacteristic, complemented
85C4×#627C2211yescharacteristic, complemented
86#63912C2211yescharacteristic, complemented
87#63912C2211yescharacteristic, complemented
88#63907C2212yescomplemented
89#63904C2212yescomplemented
90#63902C2211yescharacteristic, complemented
91C4×#625C2211yescharacteristic, complemented
92#63900C2211yescharacteristic, complemented
93#63900C2211yescharacteristic, complemented
94#63899C2212yescomplemented
95#63888C2212yescomplemented
96C4×#624C2212yescomplemented
97#63881C2212yescomplemented
98#63881C2212yescomplemented
99#63878C2212yescomplemented
100#63877C2212yescomplemented
101C4×D3×Dic3C2212yescomplemented
102#63874C2211yescharacteristic, complemented
103#63874C2211yescharacteristic, complemented
104#63873C2211yescharacteristic, complemented
105#63870C2211yescharacteristic, complemented
106#63870C2211yescharacteristic, complemented
107#63868C2212yescomplemented
108#63867C2212yescomplemented
109#63865C2211yescharacteristic, complemented
110#63865C2211yescharacteristic, complemented
111#63859C2212yescomplemented
112#63858C2212yescomplemented
113#63854C2212yescomplemented
114#63850C2212yescomplemented
115#63849C2212yescomplemented
116#63848C2212yescomplemented
117#63847C2212yescomplemented
118#63846C2212yescomplemented
119#63843C2212yescomplemented
120#63838C2212yescomplemented
121#63838C2211yescharacteristic, complemented
122#63837C2212yescomplemented
123#63836C2212yescomplemented
124C3×#551—32no—
125#5708—32no—
126#5706—32no—
127#5706—32no—
128#5702—32no—
129#5680—32no—
130#5670—32no—
131#5661—32no—
132#5656—32no—
133#5655—32no—
134#5650—32no—
135#5649—32no—
136#5649—32no—
137#5637—32no—
138#5636—32no—
139#5624—32no—
140#5622—32no—
141#5591—32no—
142#5586—32no—
143#5556—32no—
144#5540—32no—
145C4×#237—32no—
146C4×#237—32no—
147#5531—32no—
148#5531—32no—
149#5522—32no—
150D3×#117—32no—
151#5495D312yescomplemented
152#5490—32no—
153C2×#67⋊C4—32no—
154C2×#67⋊C4—61no—
155C2×#877—32no—
156C24×C32C2311yescharacteristic
157C23×C3⋊D3C2311yescharacteristic
158C22×C32×C4C2311yescharacteristic
159C22×C32×C4C2311yescharacteristic
160C2×#638—24no—
161C2×#638C2311yescharacteristic
162C2×#638C2311yescharacteristic
163C2×#638C2311yescharacteristic
164C2×#638C2311yescharacteristic
165C22×C3⋊Dic3—24no—
166C22×C3⋊Dic3C2311yescharacteristic
167C22×C3⋊Dic3C2311yescharacteristic
168C22×C3⋊Dic3C2311yescharacteristic
169C22×C3⋊Dic3C2311yescharacteristic
170C22×C3⋊Dic3C2311yescharacteristic
171C22×C3⋊Dic3C2311yescharacteristic
172C22×C3⋊Dic3C2311yescharacteristic
173C2×C4×C3⋊D3—24no—
174C2×C4×C3⋊D3C2311yescharacteristic
175C2×C4×C3⋊D3C2311yescharacteristic
176C2×C4×C3⋊D3C2311yescharacteristic
177C2×C4×C3⋊D3C2311yescharacteristic
178C2×C3×#67C2312yes—
179C2×C3×#67C2312yes—
180C2×C3×#67C2312yes—
181C22×C3×Dic3C2312yes—
182C22×C3×Dic3C2312yes—
183C2×C3×C4×D3C2312yes—
184C2×C3×Dic6C2312yes—
185C2×#627C2312yes—
186C2×#627C2311yescharacteristic
187C2×#626C2312yes—
188C2×#626C2312yes—
189C2×#625C2311yescharacteristic
190C2×#624C2312yes—
191C2×#624C2312yes—
192#3805—24no—
193#3804—28no—
194C2×D3×Dic3C2312yes—
195C2×D3×Dic3C2312yes—
196C32×C22⋊C4C2311yescharacteristic
197C32×C22⋊C4C2311yescharacteristic
198C32×C22⋊C4C2311yescharacteristic
199C32×C22⋊C4C2311yescharacteristic
200#3752C2311yescharacteristic
201#3752C2311yescharacteristic
202#3752C2311yescharacteristic
203#3752C2311yescharacteristic
204#3750C2311yescharacteristic
205#3750C2311yescharacteristic
206#3750C2311yescharacteristic
207#3750C2311yescharacteristic
208C4×C3⋊Dic3C2311yescharacteristic
209C4×C3⋊Dic3C2311yescharacteristic
210C4×C3⋊Dic3C2311yescharacteristic
211C4×C3⋊Dic3C2311yescharacteristic
212C3×#217C2312yes—
213C3×#217C2312yes—
214C3×#217C2312yes—
215C3×#217C2312yes—
216C3×#217C2312yes—
217C3×#217C2312yes—
218C3×#217C2312yes—
219C3×(C2×D3)⋊C4C2312yes—
220C3×(C2×D3)⋊C4C2312yes—
221C3×(C2×D3)⋊C4C2312yes—
222C3×C4⋊Dic3C2312yes—
223C3×C4⋊Dic3C2312yes—
224C3×C4⋊Dic3C2312yes—
225C3×Dic3⋊C4C2312yes—
226C3×Dic3⋊C4C2312yes—
227C3×Dic3⋊C4C2312yes—
228C3×Dic3⋊C4C2312yes—
229C3×Dic3⋊C4C2312yes—
230C3×C4×Dic3C2312yes—
231C3×C4×Dic3C2312yes—
232C3×C4×Dic3C2312yes—
233#3724C2312yes—
234#3724C2311yescharacteristic
235#3724C2312yes—
236#3724C2312yes—
237#3724C2311yescharacteristic
238#3724C2311yescharacteristic
239#3724C2311yescharacteristic
240#3724C2311yescharacteristic
241#3724C2311yescharacteristic
242Dic3⋊Dic3C2312yes—
243Dic3⋊Dic3C2312yes—
244Dic3⋊Dic3C2312yes—
245Dic3⋊Dic3C2312yes—
246Dic3⋊Dic3C2312yes—
247#3722C2312yes—
248#3722C2312yes—
249#3722C2312yes—
250#3722C2312yes—
251(C2×D3)⋊Dic3C2312yes—
252(C2×D3)⋊Dic3C2312yes—
253(C2×D3)⋊Dic3C2312yes—
254Dic32C2312yes—
255Dic32C2312yes—
256Dic32C2312yes—
257Dic32C2312yes—
258Dic32C2312yes—
259Dic32C2312yes—
260#3475—91noSylow
261C22×#67—32no—
262C22×#67—61no—
263C23×Dic3—32no—
264C23×Dic3—61no—
265C2×#237—32no—
266C2×#237—32no—
267C2×#235—32no—
268C22×C4×D3—32no—
269C22×C4×D3—61no—
270C3×#126—32no—
271C3×#126—32no—
272C3×#124—32no—
273C3×#123—32no—
274C3×#123—32no—
275C3×#123—32no—
276C3×C22⋊Q8—32no—
277C3×C22⋊Q8—32no—
278C3×#120—32no—
279C3×C4×D4—32no—
280C3×C4×D4—32no—
281C3×#117—32no—
282C3×#117—32no—
283C2×C3×C22⋊C4—21no—
284C2×C3×C22⋊C4—32no—
285C2×C3×C22⋊C4C2×D312yes—
286#953C2×D312yes—
287C2×#217C2×D312yes—
288#947—32no—
289#946—32no—
290Q8×Dic3—32no—
291#944—32no—
292#939—32no—
293#939—32no—
294#939—32no—
295#939—32no—
296#938—32no—
297#937—32no—
298#935—32no—
299D4×Dic3—32no—
300D4×Dic3—32no—
301D4×Dic3—32no—
302#930—32no—
303#929—32no—
304#929—32no—
305#929C2×D312yes—
306C4×#67—32no—
307C4×#67—32no—
308C4×#67—32no—
309C4×#67C2×D312yes—
310C2×(C2×D3)⋊C4—32no—
311C2×(C2×D3)⋊C4—61no—
312#926C2×D312yes—
313#924C2×D312yes—
314C2×Dic3⋊C4—32no—
315C2×Dic3⋊C4—32no—
316C2×Dic3⋊C4—32no—
317C2×Dic3⋊C4—61no—
318C2×C4×Dic3—32no—
319C2×C4×Dic3—32no—
320C2×C4×Dic3—32no—
321C2×C4×Dic3—32no—
322C2×C4×Dic3—61no—
323#898—32no—
324#898—32no—
325#898—32no—
326#898—32no—
327#896—32no—
328#896—32no—
329#896—32no—
330#896—32no—
331#894—32no—
332#894—32no—
333#893—32no—
334#893—32no—
335#893—32no—
336#892—32no—
337#892—32no—
338#892—32no—
339#892—32no—
340D3×C4⋊C4—32no—
341D3×C4⋊C4—32no—
342#890—32no—
343#889—32no—
344#889—32no—
345#889—32no—
346#889—32no—
347#889—32no—
348#889—32no—
349#888—32no—
350#887—32no—
351#887—32no—
352#887—32no—
353#887—32no—
354#887—32no—
355#886—32no—
356#886—32no—
357#886C2×D312yescomplemented
358#885—32no—
359#885—32no—
360#885—32no—
361#885C2×D312yescomplemented
362#884—32no—
363#884—32no—
364#884—32no—
365#884—32no—
366#883—32no—
367#883—32no—
368#883—32no—
369#883C2×D312yescomplemented
370#882—32no—
371#67⋊C4—32no—
372#67⋊C4—32no—
373#67⋊C4—32no—
374#67⋊C4—32no—
375#67⋊C4—32no—
376#67⋊C4—32no—
377#67⋊C4—32no—
378#67⋊C4—32no—
379#67⋊C4—32no—
380#67⋊C4—32no—
381#67⋊C4—32no—
382#67⋊C4—32no—
383#67⋊C4—32no—
384#67⋊C4—32no—
385#67⋊C4—32no—
386#67⋊C4—61no—
387#67⋊C4—61no—
388#67⋊C4—61no—
389#67⋊C4—61no—
390#67⋊C4—61no—
391#67⋊C4—61no—
392#67⋊C4—61no—
393#67⋊C4—61no—
394#67⋊C4C2×D312yescomplemented
395D3×C22⋊C4—32no—
396D3×C22⋊C4—32no—
397#879—32no—
398#879—32no—
399#879C2×D312yescomplemented
400#879C2×D312yescomplemented
401#878—32no—
402#878—32no—
403#878—32no—
404#878—32no—
405#878—32no—
406#878C2×D312yescomplemented
407#877—32no—
408#877—32no—
409#877—32no—
410#877—32no—
411#877—32no—
412#877—32no—
413#877—32no—
414#877—32no—
415#877—32no—
416#877—32no—
417#877—32no—
418#877C2×D312yescomplemented
419#876—32no—
420#876—32no—
421#872—32no—
422#872—32no—
423#872—32no—
424#872—32no—
425C42×D3—32no—
426C42×D3—32no—
427C42×D3—32no—
428#870—32no—
429C4×Dic6—32no—
430C4×Dic6—32no—
431C23×C32—22no—
432C23×C32—22no—
433C23×C32—41no—
434C23×C32C2411yescharacteristic
435C23×C32C2411yescharacteristic
436C23×C32C2411yescharacteristic
437C22×C3⋊D3—22no—
438C22×C3⋊D3—22no—
439C22×C3⋊D3—41no—
440C22×C3⋊D3C2411yescharacteristic
441C22×C3⋊D3C2411yescharacteristic
442C22×C3×D3C2412yes—
443C2×C32×C4—22no—
444C2×C32×C4—41no—
445C2×C32×C4C2411yescharacteristic
446C2×C32×C4C2411yescharacteristic
447C2×C32×C4C2411yescharacteristic
448C2×C32×C4C2411yescharacteristic
449#638—22no—
450#638—22no—
451#638—22no—
452#638#4114yescomplemented
453C2×C3⋊Dic3—22no—
454C2×C3⋊Dic3—22no—
455C2×C3⋊Dic3—22no—
456C2×C3⋊Dic3—22no—
457C2×C3⋊Dic3—22no—
458C2×C3⋊Dic3—22no—
459C2×C3⋊Dic3#4114yescomplemented
460C2×C3⋊Dic3C2411yescharacteristic
461C2×C3⋊Dic3C2411yescharacteristic
462C2×C3⋊Dic3C2411yescharacteristic
463C2×C3⋊Dic3C2411yescharacteristic
464C2×C3⋊Dic3C2411yescharacteristic
465C2×C3⋊Dic3C2411yescharacteristic
466C4×C3⋊D3—22no—
467C4×C3⋊D3—22no—
468C4×C3⋊D3—22no—
469C4×C3⋊D3—22no—
470C3×#67—24no—
471C3×#67—24no—
472C3×#67—42no—
473C2×C3×Dic3—24no—
474C2×C3×Dic3—42no—
475C2×C3×Dic3C2412yes—
476C2×C3×Dic3C2412yes—
477C2×C3×Dic3C2412yes—
478C2×C3×Dic3C2412yes—
479C2×C3×Dic3C2412yes—
480C2×C3×Dic3C2412yes—
481C2×C3×Dic3C2412yes—
482C3×C4×D3—42no—
483C3×Dic6—42no—
484#627—24no—
485#627—22no—
486#626—24no—
487#626—42no—
488#625—22no—
489#624—24no—
490#624—42no—
491D3×Dic3—24no—
492D3×Dic3—24no—
493#556—91no—
494#555—91no—
495#554—91no—
496#553—91no—
497#553—91no—
498#552—91no—
499#552—92no—
500#552—91no—
501#551—32no—
502#551—92no—
503#547—91no—
504#546—92no—
505#533—91no—
506#529—92no—
507#529—92no—
508#529—92no—
509#525—91no—
510#525—91no—
511C4×#41—92no—
512C4×#41—91no—
513C2×C4×D4—91no—
514C2×#117—91no—
515C2×#117—91no—
516C24×C3—21no—
517C24×C3C22×D312yes—
518C23×D3—32no—
519C23×D3—61no—
520C2×C3×Q8—32no—
521C2×C3×D4—32no—
522C2×C3×D4—32no—
523C2×C3×D4—32no—
524C22×C3×C4—21no—
525C22×C3×C4—21no—
526C22×C3×C4—32no—
527C22×C3×C4—32no—
528C22×C3×C4—32no—
529C22×C3×C4C22×D312yes—
530C22×C3×C4C22×D312yes—
531C2×#67—32no—
532C2×#67—32no—
533C2×#67—32no—
534C2×#67—32no—
535C2×#67—32no—
536C2×#67—32no—
537C2×#67—32no—
538C2×#67—61no—
539C2×#67—61no—
540C2×#67—61no—
541C2×#67—61no—
542C2×#67—68no—
543C2×#67—68no—
544C2×#67C22×D312yes—
545C2×#67C22×D312yes—
546C2×#67C22×D312yes—
547C22×Dic3—32no—
548C22×Dic3—32no—
549C22×Dic3—32no—
550C22×Dic3—32no—
551C22×Dic3—32no—
552C22×Dic3—32no—
553C22×Dic3—32no—
554C22×Dic3—32no—
555C22×Dic3—32no—
556C22×Dic3—61no—
557C22×Dic3—61no—
558C22×Dic3—61no—
559C22×Dic3—61no—
560C22×Dic3—61no—
561C22×Dic3—61no—
562C22×Dic3—61no—
563C22×Dic3—68no—
564C22×Dic3—124no—
565C22×Dic3C22×D312yes—
566C22×Dic3C22×D312yes—
567#237—68no—
568#237—68no—
569#235—68no—
570C2×D12—32no—
571C2×D12—32no—
572C2×C4×D3—32no—
573C2×C4×D3—32no—
574C2×C4×D3—32no—
575C2×C4×D3—32no—
576C2×C4×D3—32no—
577C2×C4×D3—32no—
578C2×C4×D3—32no—
579C2×C4×D3—32no—
580C2×C4×D3—32no—
581C2×C4×D3—32no—
582C2×C4×D3—61no—
583C2×C4×D3—61no—
584C2×C4×D3—61no—
585C2×C4×D3—61no—
586C2×C4×D3—68no—
587C2×C4×D3—124no—
588C2×C4×D3C22×D312yes—
589C2×Dic6—32no—
590C2×Dic6—32no—
591C2×Dic6—32no—
592C2×Dic6C22×D312yes—
593C3×C4⋊C4—32no—
594C3×C4⋊C4—32no—
595C3×C4⋊C4—32no—
596C3×C4⋊C4—32no—
597C3×C4⋊C4—32no—
598C3×C4⋊C4—32no—
599C3×C4⋊C4—32no—
600C3×C4⋊C4—32no—
601C3×C22⋊C4—21no—
602C3×C22⋊C4—21no—
603C3×C22⋊C4—21no—
604C3×C22⋊C4—21no—
605C3×C22⋊C4—32no—
606C3×C22⋊C4—32no—
607C3×C22⋊C4—32no—
608C3×C22⋊C4—32no—
609C3×C22⋊C4—32no—
610C3×C22⋊C4—32no—
611C3×C22⋊C4—32no—
612C3×C22⋊C4—32no—
613C3×C22⋊C4—32no—
614C3×C22⋊C4—32no—
615C3×C22⋊C4C22×D312yes—
616C3×C22⋊C4C22×D312yes—
617C3×C22⋊C4C22×D312yes—
618C3×C22⋊C4C22×D312yes—
619C3×C42—32no—
620C3×C42—32no—
621C3×C42—32no—
622#217—32no—
623#217—32no—
624#217—32no—
625#217C22×D312yes—
626#217C22×D312yes—
627#217C22×D312yes—
628#217C22×D312yes—
629#217C22×D312yes—
630#217C22×D312yes—
631#217C22×D312yes—
632(C2×D3)⋊C4—32no—
633(C2×D3)⋊C4—32no—
634(C2×D3)⋊C4—32no—
635(C2×D3)⋊C4—32no—
636(C2×D3)⋊C4—32no—
637(C2×D3)⋊C4—32no—
638(C2×D3)⋊C4—32no—
639(C2×D3)⋊C4—32no—
640(C2×D3)⋊C4—32no—
641(C2×D3)⋊C4—32no—
642(C2×D3)⋊C4—32no—
643(C2×D3)⋊C4—32no—
644(C2×D3)⋊C4—32no—
645(C2×D3)⋊C4—32no—
646(C2×D3)⋊C4—32no—
647(C2×D3)⋊C4—61no—
648(C2×D3)⋊C4—61no—
649(C2×D3)⋊C4—61no—
650(C2×D3)⋊C4—61no—
651(C2×D3)⋊C4C22×D312yes—
652(C2×D3)⋊C4C22×D312yes—
653(C2×D3)⋊C4C22×D312yes—
654C4⋊Dic3—32no—
655C4⋊Dic3—32no—
656C4⋊Dic3—32no—
657C4⋊Dic3—32no—
658C4⋊Dic3—32no—
659C4⋊Dic3C22×D312yes—
660C4⋊Dic3C22×D312yes—
661C4⋊Dic3C22×D312yes—
662Dic3⋊C4—32no—
663Dic3⋊C4—32no—
664Dic3⋊C4—32no—
665Dic3⋊C4—32no—
666Dic3⋊C4—32no—
667Dic3⋊C4—32no—
668Dic3⋊C4—32no—
669Dic3⋊C4—32no—
670Dic3⋊C4—32no—
671Dic3⋊C4—32no—
672Dic3⋊C4—32no—
673Dic3⋊C4—32no—
674Dic3⋊C4—32no—
675Dic3⋊C4—32no—
676Dic3⋊C4—32no—
677Dic3⋊C4—32no—
678Dic3⋊C4—32no—
679Dic3⋊C4—32no—
680Dic3⋊C4—32no—
681Dic3⋊C4—32no—
682Dic3⋊C4—32no—
683Dic3⋊C4—61no—
684Dic3⋊C4—61no—
685Dic3⋊C4—61no—
686Dic3⋊C4—61no—
687Dic3⋊C4C22×D312yes—
688Dic3⋊C4C22×D312yes—
689Dic3⋊C4C22×D312yes—
690Dic3⋊C4C22×D312yes—
691Dic3⋊C4C22×D312yes—
692C4×Dic3—32no—
693C4×Dic3—32no—
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—32no—
704C4×Dic3—32no—
705C4×Dic3—32no—
706C4×Dic3—32no—
707C4×Dic3—32no—
708C4×Dic3—61no—
709C4×Dic3—61no—
710C4×Dic3—61no—
711C4×Dic3—61no—
712C4×Dic3C22×D312yes—
713C4×Dic3C22×D312yes—
714C4×Dic3C22×D312yes—
715C22×C32—21no—
716C22×C32—21no—
717C22×C32—21no—
718C22×C32—21no—
719C22×C32—21no—
720C22×C32—21no—
721C22×C32—21no—
722C22×C32—44no—
723C22×C32C2×#4112yes—
724C22×C32C2×#4112yes—
725C22×C32C2511yescharacteristic
726C2×C3⋊D3—21no—
727C2×C3⋊D3—21no—
728C2×C3⋊D3—21no—
729C2×C3⋊D3—21no—
730C2×C3⋊D3—21no—
731C2×C3⋊D3—44no—
732C2×C3⋊D3C2×#4112yes—
733C2×C3×D3—22no—
734C2×C3×D3—22no—
735C2×C3×D3—22no—
736C32×C4—21no—
737C32×C4—21no—
738C32×C4—21no—
739C32×C4—21no—
740C3⋊Dic3—21no—
741C3⋊Dic3—21no—
742C3⋊Dic3—21no—
743C3⋊Dic3C2×#4112yes—
744C3⋊Dic3C2×#4112yes—
745C3⋊Dic3C2×#4112yes—
746C3×Dic3—22no—
747C3×Dic3—22no—
748C3×Dic3—22no—
749C3×Dic3—22no—
750C3×Dic3—22no—
751C3×Dic3—22no—
752C3×Dic3—22no—
753C2×#41—92no—
754C2×#41—91no—
755C22×D4—91no—
756C23×C4—91no—
757C23×C4—91no—
758C4⋊Q8—91no—
759C4⋊Q8—91no—
760#126—32no—
761#126—32no—
762#126—92no—
763#126—92no—
764#126—92no—
765#126—92no—
766#125—92no—
767#125—92no—
768#125—92no—
769#125—91no—
770#125—91no—
771#124—32no—
772#124—92no—
773#124—92no—
774#123—32no—
775#123—32no—
776#123—32no—
777#123—92no—
778#123—92no—
779#123—92no—
780#123—92no—
781#123—92no—
782C22⋊Q8—32no—
783C22⋊Q8—32no—
784C22⋊Q8—91no—
785C22⋊Q8—91no—
786C22⋊Q8—92no—
787C22⋊Q8—92no—
788C22⋊Q8—91no—
789C22⋊Q8—91no—
790C22⋊Q8—92no—
791#121—91no—
792#121—91no—
793#121—92no—
794#121—92no—
795#121—92no—
796#121—91no—
797#121—91no—
798#120—32no—
799#120—92no—
800C4×Q8—91no—
801C4×Q8—92no—
802C4×Q8—92no—
803C4×Q8—91no—
804C4×Q8—92no—
805C4×D4—32no—
806C4×D4—32no—
807C4×D4—91no—
808C4×D4—92no—
809C4×D4—92no—
810C4×D4—92no—
811C4×D4—92no—
812C4×D4—92no—
813C4×D4—92no—
814C4×D4—92no—
815C4×D4—91no—
816C4×D4—91no—
817C4×D4—91no—
818C4×D4—91no—
819C4×D4—91no—
820C4×D4—91no—
821C4×D4—91no—
822C4×D4—91no—
823C4×D4—91no—
824#117—32no—
825#117—32no—
826#117—91no—
827#117—91no—
828#117—92no—
829#117—92no—
830#117—91no—
831#117—91no—
832#117—91no—
833#117—92no—
834#117—92no—
835#117—91no—
836#117—91no—
837#117—92no—
838#117—92no—
839C2×C4⋊C4—91no—
840C2×C4⋊C4—91no—
841C2×C4⋊C4—91no—
842C2×C4⋊C4—91no—
843C2×C4⋊C4—91no—
844C2×C22⋊C4—32no—
845C2×C22⋊C4—92no—
846C2×C22⋊C4—91no—
847C2×C22⋊C4D3211yescharacteristic
848C2×C42—92no—
849C2×C42—92no—
850C2×C42—92no—
851C2×C42—91no—
852C23×C3—24no—
853C23×C3—24no—
854C23×C3—24no—
855C23×C3—21no—
856C23×C3—21no—
857C23×C3—21no—
858C23×C3—32no—
859C23×C3—42no—
860C23×C3—42no—
861C23×C3—42no—
862C23×C3C23×D312yes—
863C23×C3C23×D312yes—
864C23×C3C23×D312yes—
865C22×D3—32no—
866C22×D3—32no—
867C22×D3—61no—
868C22×D3—61no—
869C22×D3—64no—
870C22×D3—64no—
871C22×D3—64no—
872C22×D3—122no—
873C22×D3—122no—
874C22×D3—122no—
875C22×D3C23×D312yes—
876C3×Q8—122no—
877C3×D4—64no—
878C3×D4—64no—
879C3×D4—122no—
880C2×C3×C4—24no—
881C2×C3×C4—21no—
882C2×C3×C4—21no—
883C2×C3×C4—21no—
884C2×C3×C4—21no—
885C2×C3×C4—32no—
886C2×C3×C4—32no—
887C2×C3×C4—32no—
888C2×C3×C4—32no—
889C2×C3×C4—32no—
890C2×C3×C4—32no—
891C2×C3×C4—32no—
892C2×C3×C4—42no—
893C2×C3×C4—42no—
894C2×C3×C4—42no—
895C2×C3×C4—64no—
896C2×C3×C4—122no—
897C2×C3×C4—122no—
898C2×C3×C4C23×D312yes—
899C2×C3×C4C23×D312yes—
900C2×C3×C4C23×D312yes—
901C2×C3×C4C23×D312yes—
902#67—24no—
903#67—24no—
904#67—38no—
905#67—42no—
906#67—64no—
907#67—64no—
908#67—64no—
909#67—64no—
910#67—64no—
911#67—64no—
912#67—64no—
913#67—64no—
914#67—64no—
915#67—122no—
916C2×Dic3—24no—
917C2×Dic3—38no—
918C2×Dic3—32no—
919C2×Dic3—32no—
920C2×Dic3—32no—
921C2×Dic3—32no—
922C2×Dic3—32no—
923C2×Dic3—32no—
924C2×Dic3—42no—
925C2×Dic3—64no—
926C2×Dic3—61no—
927C2×Dic3—61no—
928C2×Dic3—61no—
929C2×Dic3—61no—
930C2×Dic3—61no—
931C2×Dic3—61no—
932C2×Dic3—64no—
933C2×Dic3—64no—
934C2×Dic3—64no—
935C2×Dic3—64no—
936C2×Dic3—64no—
937C2×Dic3—64no—
938C2×Dic3—64no—
939C2×Dic3—64no—
940C2×Dic3—64no—
941C2×Dic3—122no—
942C2×Dic3—122no—
943C2×Dic3—122no—
944C2×Dic3—122no—
945C2×Dic3—122no—
946C2×Dic3C23×D312yes—
947C2×Dic3C23×D312yes—
948C2×Dic3C23×D312yes—
949C2×Dic3C23×D312yes—
950C2×Dic3C23×D312yes—
951C2×Dic3C23×D312yes—
952C2×Dic3C23×D312yes—
953D12—64no—
954D12—122no—
955C4×D3—42no—
956C4×D3—64no—
957C4×D3—64no—
958C4×D3—64no—
959C4×D3—64no—
960C4×D3—64no—
961C4×D3—64no—
962C4×D3—64no—
963C4×D3—64no—
964C4×D3—122no—
965C4×D3—122no—
966C4×D3—122no—
967C4×D3—122no—
968C4×D3—122no—
969C4×D3—122no—
970Dic6—42no—
971Dic6—64no—
972Dic6—64no—
973Dic6—64no—
974C2×C32—22no—
975C2×C32—22no—
976C2×C32—41no—
977C2×C32C22×#4111yescharacteristic
978C2×C32C22×#4111yescharacteristic
979C2×C32#58511yescharacteristic
980C3⋊D3—22no—
981C3⋊D3—41no—
982C3×D3—42no—
983C24—91no—
984C24C2×D3211yescharacteristic
985#41—188no—
986#41—184no—
987C2×Q8—32no—
988C2×Q8—91no—
989C2×Q8—92no—
990C2×D4—32no—
991C2×D4—32no—
992C2×D4—32no—
993C2×D4—92no—
994C2×D4—92no—
995C2×D4—91no—
996C2×D4—91no—
997C2×D4—91no—
998C2×D4—91no—
999C2×D4—91no—
1000C2×D4—184no—
1001C22×C4—32no—
1002C22×C4—32no—
1003C22×C4—32no—
1004C22×C4—92no—
1005C22×C4—92no—
1006C22×C4—92no—
1007C22×C4—92no—
1008C22×C4—91no—
1009C22×C4—91no—
1010C22×C4—91no—
1011C22×C4—91no—
1012C22×C4—91no—
1013C22×C4—91no—
1014C22×C4—91no—
1015C22×C4—91no—
1016C22×C4—91no—
1017C22×C4—91no—
1018C22×C4—91no—
1019C22×C4—184no—
1020C22×C4—184no—
1021C22×C4C2×D3211yescharacteristic
1022C22×C4C2×D3211yescharacteristic
1023C4⋊C4—32no—
1024C4⋊C4—32no—
1025C4⋊C4—32no—
1026C4⋊C4—32no—
1027C4⋊C4—32no—
1028C4⋊C4—32no—
1029C4⋊C4—32no—
1030C4⋊C4—32no—
1031C4⋊C4—91no—
1032C4⋊C4—91no—
1033C4⋊C4—91no—
1034C4⋊C4—91no—
1035C4⋊C4—91no—
1036C4⋊C4—91no—
1037C4⋊C4—92no—
1038C4⋊C4—92no—
1039C4⋊C4—92no—
1040C4⋊C4—92no—
1041C4⋊C4—92no—
1042C4⋊C4—92no—
1043C4⋊C4—92no—
1044C4⋊C4—92no—
1045C4⋊C4—91no—
1046C4⋊C4—91no—
1047C4⋊C4—91no—
1048C4⋊C4—91no—
1049C22⋊C4—32no—
1050C22⋊C4—32no—
1051C22⋊C4—32no—
1052C22⋊C4—32no—
1053C22⋊C4—32no—
1054C22⋊C4—32no—
1055C22⋊C4—32no—
1056C22⋊C4—32no—
1057C22⋊C4—32no—
1058C22⋊C4—32no—
1059C22⋊C4—92no—
1060C22⋊C4—92no—
1061C22⋊C4—92no—
1062C22⋊C4—92no—
1063C22⋊C4—92no—
1064C22⋊C4—92no—
1065C22⋊C4—92no—
1066C22⋊C4—91no—
1067C22⋊C4—91no—
1068C22⋊C4—91no—
1069C22⋊C4—91no—
1070C22⋊C4C2×D3211yescharacteristic
1071C22⋊C4C2×D3211yescharacteristic
1072C22⋊C4C2×D3211yescharacteristic
1073C22⋊C4C2×D3211yescharacteristic
1074C42—32no—
1075C42—32no—
1076C42—32no—
1077C42—92no—
1078C42—92no—
1079C42—92no—
1080C42—92no—
1081C42—92no—
1082C42—92no—
1083C42—91no—
1084C42—91no—
1085C42—91no—
1086C42—91no—
1087C22×C3—22no—
1088C22×C3—22no—
1089C22×C3—22no—
1090C22×C3—22no—
1091C22×C3—22no—
1092C22×C3—22no—
1093C22×C3—22no—
1094C22×C3—22no—
1095C22×C3—22no—
1096C22×C3—22no—
1097C22×C3—22no—
1098C22×C3—22no—
1099C22×C3—21no—
1100C22×C3—41no—
1101C22×C3—41no—
1102C22×C3—41no—
1103C22×C3—41no—
1104C22×C3—48no—
1105C22×C3—48no—
1106C22×C3—62no—
1107C22×C3—62no—
1108C22×C3—62no—
1109C22×C3D3×#4114yes—
1110C22×C3D3×#4114yes—
1111C22×C3C24×D312yes—
1112C2×D3—22no—
1113C2×D3—22no—
1114C2×D3—22no—
1115C2×D3—34no—
1116C2×D3—62no—
1117C2×D3—62no—
1118C2×D3—62no—
1119C2×D3—62no—
1120C2×D3—62no—
1121C2×D3—62no—
1122C2×D3—62no—
1123C2×D3—121no—
1124C2×D3—121no—
1125C2×D3—121no—
1126C2×D3—121no—
1127C2×D3—128no—
1128C2×D3—128no—
1129C3×C4—22no—
1130C3×C4—22no—
1131C3×C4—22no—
1132C3×C4—22no—
1133C3×C4—41no—
1134C3×C4—41no—
1135C3×C4—41no—
1136C3×C4—41no—
1137C3×C4—62no—
1138C3×C4—62no—
1139C3×C4—62no—
1140C3×C4—62no—
1141C3×C4—62no—
1142C3×C4—62no—
1143C3×C4—62no—
1144Dic3—22no—
1145Dic3—22no—
1146Dic3—22no—
1147Dic3—22no—
1148Dic3—22no—
1149Dic3—22no—
1150Dic3—22no—
1151Dic3—34no—
1152Dic3—34no—
1153Dic3—34no—
1154Dic3—62no—
1155Dic3—62no—
1156Dic3—62no—
1157Dic3—62no—
1158Dic3—62no—
1159Dic3—62no—
1160Dic3—62no—
1161Dic3—121no—
1162Dic3—121no—
1163C32#347511yescharacteristic, complemented, Sylow
1164C23—22no—
1165C23—22no—
1166C23—32no—
1167C23—41no—
1168C23—91no—
1169C23—91no—
1170C23—182no—
1171C23—182no—
1172C23—361no—
1173C23C22×D3211yescharacteristic
1174C23C22×D3211yescharacteristic
1175C23C22×D3211yescharacteristic
1176Q8—122no—
1177Q8—184no—
1178Q8—182no—
1179D4—64no—
1180D4—64no—
1181D4—94no—
1182D4—122no—
1183D4—184no—
1184D4—182no—
1185D4—182no—
1186D4—182no—
1187D4—182no—
1188D4—362no—
1189C2×C4—22no—
1190C2×C4—32no—
1191C2×C4—32no—
1192C2×C4—32no—
1193C2×C4—32no—
1194C2×C4—32no—
1195C2×C4—32no—
1196C2×C4—32no—
1197C2×C4—41no—
1198C2×C4—64no—
1199C2×C4—94no—
1200C2×C4—91no—
1201C2×C4—91no—
1202C2×C4—91no—
1203C2×C4—91no—
1204C2×C4—91no—
1205C2×C4—91no—
1206C2×C4—122no—
1207C2×C4—122no—
1208C2×C4—182no—
1209C2×C4—182no—
1210C2×C4—182no—
1211C2×C4—182no—
1212C2×C4—184no—
1213C2×C4—184no—
1214C2×C4—184no—
1215C2×C4—182no—
1216C2×C4—182no—
1217C2×C4—182no—
1218C2×C4—182no—
1219C2×C4—182no—
1220C2×C4—182no—
1221C2×C4—362no—
1222C2×C4C22×D3211yescharacteristic
1223C2×C4C22×D3211yescharacteristic
1224C2×C4C22×D3211yescharacteristic
1225C2×C4C22×D3211yescharacteristic
1226C2×C3—24no—
1227C2×C3—24no—
1228C2×C3—24no—
1229C2×C3—21no—
1230C2×C3—21no—
1231C2×C3—21no—
1232C2×C3—42no—
1233C2×C3—42no—
1234C2×C3—42no—
1235C2×C3—122no—
1236C2×C3C2×D3×#4112yes—
1237C2×C3C2×D3×#4112yes—
1238C2×C3#596612yes—
1239D3—42no—
1240D3—64no—
1241D3—122no—
1242D3—122no—
1243D3—122no—
1244C22—21no—
1245C22—21no—
1246C22—21no—
1247C22—21no—
1248C22—21no—
1249C22—21no—
1250C22—21no—
1251C22—44no—
1252C22—62no—
1253C22—62no—
1254C22—62no—
1255C22—92no—
1256C22—181no—
1257C22—181no—
1258C22—181no—
1259C22—181no—
1260C22—181no—
1261C22—364no—
1262C22#6430612yes—
1263C22#6431212yes—
1264C22C23×D3211yescharacteristic
1265C4—21no—
1266C4—21no—
1267C4—21no—
1268C4—21no—
1269C4—62no—
1270C4—62no—
1271C4—62no—
1272C4—62no—
1273C4—62no—
1274C4—62no—
1275C4—62no—
1276C4—92no—
1277C4—92no—
1278C4—92no—
1279C4—181no—
1280C4—181no—
1281C4—181no—
1282C3—21no—
1283C3#8679012yescomplemented
1284C2—22no—
1285C2—22no—
1286C2—41no—
1287C2—122no—
1288C2—182no—
1289C2—361no—
1290C2C2×#6430611yescharacteristic
1291C2C2×#6431211yescharacteristic
1292C2#1059667911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C22⋊C4C22
hypercenterC2×C22⋊C4D32
hypocenterC32#3475
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×#64090C2semidirect
2. C3×#5495C2semidirect
3. #10595501C2semidirect
4. #10595500C2semidirect
5. C2×#63957C2semidirect
6. #10595035C2semidirect
7. #10594969C2semidirect
8. #10594960C2semidirect
9. #10594920C2semidirect
10. C4×#3805C2semidirect
11. #10594810C2semidirect
12. #10594250C2semidirect
13. #10594231C2semidirect
14. #10594229C2semidirect
15. #10594168C2semidirect
16. #10594155C2semidirect
17. #10594150C2semidirect
18. #10594144C2semidirect
19. #10594137C2semidirect
20. #10594130C2semidirect
21. #10594083C2semidirect
22. #10594048C2semidirect
23. #10594046C2semidirect
48. C3×#886C22semidirect
49. C3×#885C22semidirect
50. C3×#883C22semidirect
51. C3×#67⋊C4C22semidirect
52. C3×#879C22semidirect
53. C3×#879C22semidirect
54. C3×#878C22semidirect
55. C3×#877C22semidirect
57. #63982C22semidirect
58. #63982C22semidirect
60. #63980C22semidirect
61. #63980C22semidirect
66. #67⋊Dic3C22semidirect
67. #67⋊Dic3C22semidirect
69. C2×#3724C22semidirect
70. C2×#3724C22semidirect
78. #63957C22semidirect
79. #63957C22semidirect
80. #63957C22semidirect
81. C2×Dic32C22semidirect
84. #63919C22semidirect
85. C4×#627C22semidirect
86. #63912C22semidirect
87. #63912C22semidirect
88. #63907C22semidirect
89. #63904C22semidirect
90. #63902C22semidirect
91. C4×#625C22semidirect
92. #63900C22semidirect
93. #63900C22semidirect
94. #63899C22semidirect
95. #63888C22semidirect
96. C4×#624C22semidirect
97. #63881C22semidirect
98. #63881C22semidirect
99. #63878C22semidirect
100. #63877C22semidirect
101. C4×D3×Dic3C22semidirect
102. #63874C22semidirect
103. #63874C22semidirect
104. #63873C22semidirect
105. #63870C22semidirect
106. #63870C22semidirect
107. #63868C22semidirect
108. #63867C22semidirect
109. #63865C22semidirect
110. #63865C22semidirect
111. #63859C22semidirect
112. #63858C22semidirect
113. #63854C22semidirect
114. #63850C22semidirect
115. #63849C22semidirect
116. #63848C22semidirect
117. #63847C22semidirect
118. #63846C22semidirect
119. #63843C22semidirect
120. #63838C22semidirect
121. #63838C22semidirect
122. #63837C22semidirect
123. #63836C22semidirect
151. #5495D3semidirect
357. #886C2×D3semidirect
361. #885C2×D3semidirect
369. #883C2×D3semidirect
394. #67⋊C4C2×D3semidirect
399. #879C2×D3semidirect
400. #879C2×D3semidirect
406. #878C2×D3semidirect
418. #877C2×D3semidirect
452. #638#41semidirect
459. C2×C3⋊Dic3#41semidirect
1163. C32#3475semidirect
1283. C3#86790semidirect

Maximal subgroups

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

subgroupindex
C2×#640902
C3×#54952
#105955012
#105955002
C2×#639572
#105950352
#105949692
#105949602
#105949202
C4×#38052
#105948102
#105942502
#105942312
#105942292
#105941682
#105941552
#105941502
#105941442
#105941372
#105941302
#105940832
#105940482
#105940462
#867903