Finite Group Databasebeta

← #11901013

Subgroups — #11901013

Order 1152.

4123 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3811C211yesmaximal, characteristic, complemented
2C2×#64312C211yesmaximal, characteristic, complemented
3C3⋊D3×#120C211yesmaximal, characteristic, complemented
4C3×#5592C212yesmaximal, complemented
5#10595527C211yesmaximal, characteristic, complemented
6#10595513C212yesmaximal, complemented
7#10595300C212yesmaximal, complemented
8#10595299C214yesmaximal, complemented
9#10595298C212yesmaximal, complemented
10#10595278C211yesmaximal, characteristic, complemented
11#10595238C212yesmaximal, complemented
12#10594288C212yesmaximal, complemented
13#10594287C214yesmaximal, complemented
14#10594265C212yesmaximal, complemented
15#10594258C211yesmaximal, characteristic, complemented
16#10594080C212yesmaximal, complemented
17#10594052C211yesmaximal, characteristic, complemented
18D3×#535—32nomaximal
19C24×C3⋊D3C2211yescharacteristic
20C23×D32C2211yescharacteristic
21C2×D4×C3⋊D3C2211yescharacteristic
22C2×D4×C3⋊D3C2212yescomplemented
23C22×C3×#67C2212yescomplemented
24C2×C3×#237C2212yescomplemented
25C2×#3811—28no—
26C2×#3811C2211yescharacteristic
27C2×#3811C2212yes—
28C2×#3811C2212yes—
29C2×#3811C2214yescomplemented
30C2×#3811C2211yescharacteristic, complemented
31C2×#3811C2212yescomplemented
32C2×#3811C2212yescomplemented
33C22×#626C2212yescomplemented
34C22×#624C2211yescharacteristic
35C22×#624C2211yescharacteristic, complemented
36C2×#3804C2212yescomplemented
37C2×#3804C2212yescomplemented
38#64312—28no—
39C2×#3802C2212yescomplemented
40C2×C4×D32C2211yescharacteristic, complemented
41C2×#3799C2212yescomplemented
42C2×#3797C2211yescharacteristic, complemented
43C32×#120C2211yescharacteristic, complemented
44#64162C2211yescharacteristic, complemented
45#64146C2212yescomplemented
46#64146C2211yescharacteristic, complemented
47#64091C2212yescomplemented
48#64091C2211yescharacteristic, complemented
49C22⋊C4×C3⋊D3C2211yescharacteristic
50C22⋊C4×C3⋊D3C2212yescomplemented
51C3×#953C2212yescomplemented
52C3×#940C2214yescomplemented
53C3×#939C2214yescomplemented
54C3×#937C2212yescomplemented
55C3×#885C2214yescomplemented
56C3×#884C2214yescomplemented
57C3×#882C2212yescomplemented
58C3×#877C2212yescomplemented
59#63983C2212yescomplemented
60#63981C2214yescomplemented
61#63981C2212yescomplemented
62#63979C2214yescomplemented
63#63979C2214yescomplemented
64#63978C2214yescomplemented
65#63977C2212yescomplemented
66#63976C2212yescomplemented
67#63974C2211yescharacteristic
68#63974C2212yescomplemented
69#63970C2214yescomplemented
70#63959C2214yescomplemented
71#63958C2214yescomplemented
72#63955C2212yescomplemented
73#63923C2212yescomplemented
74#63922C2214yescomplemented
75#63921C2212yescomplemented
76#63921C2212yescomplemented
77#63911C2214yescomplemented
78#63910C2214yescomplemented
79#63907C2214yescomplemented
80#63906C2214yescomplemented
81#63886C2214yescomplemented
82#63883C2212yescomplemented
83C4×#624C2212yescomplemented
84#63852C2214yescomplemented
85#63836C2214yescomplemented
86C2×D3×#41—32no—
87C22×D3×D4—32no—
88C3×#535—32no—
89#5830—32no—
90#5805—32no—
91#5715—34no—
92D3×#127—34no—
93#5674—34no—
94D3×#124—34no—
95#5607—34no—
96#5607—34no—
97D3×#121—34no—
98D3×#121—34no—
99#5592—32no—
100#5592—32no—
101#5592—32no—
102#5592D312yescomplemented
103D3×#120—32no—
104D3×#120—32no—
105D3×#120—32no—
106D3×#120—32no—
107D3×#120—61no—
108#5525—32no—
109D3×#117—32no—
110C24×C32C2311yescharacteristic
111C23×C3⋊D3—24no—
112C23×C3⋊D3—44no—
113C23×C3⋊D3C2311yescharacteristic
114C23×C3⋊D3C2312yes—
115C23×C3⋊D3C2311yescharacteristic
116C23×C3⋊D3C2311yescharacteristic
117C23×C3⋊D3C2312yes—
118C23×C3×D3C2312yes—
119C22×D32—24no—
120C22×D32—44no—
121C22×D32C2311yescharacteristic
122C22×D32C2312yes—
123C22×D32C2312yes—
124C2×C32×D4C2311yescharacteristic
125C2×C32×D4C2312yescomplemented
126C2×#638C2311yescharacteristic
127C2×#638C2311yescharacteristic
128C2×#638C2312yescomplemented
129C2×#638C2312yescomplemented
130D4×C3⋊D3—24no—
131D4×C3⋊D3—44no—
132C2×C4⋊(C3⋊D3)C2311yescharacteristic
133C2×C4⋊(C3⋊D3)C2312yescomplemented
134C2×C4×C3⋊D3C2311yescharacteristic
135C2×C4×C3⋊D3C2312yes—
136C2×C3×#67—28no—
137C2×C3×#67C2312yes—
138C2×C3×#67C2314yes—
139C2×C3×#67C2314yes—
140C2×C3×#67C2312yescomplemented
141C2×C3×#67C2314yescomplemented
142C2×C3×#67C2314yescomplemented
143C22×C3×Dic3C2312yes—
144C22×C3×Dic3C2312yescomplemented
145C3×#237—28no—
146C2×C3×D12C2314yescomplemented
147C2×C3×C4×D3C2312yescomplemented
148C2×C3×Dic6C2312yescomplemented
149#3811—24no—
150#3811—24no—
151#3811—28no—
152#3811—28no—
153#3811—216no—
154#3811—44no—
155#3811—44no—
156C2×#627C2312yescomplemented
157C2×#626—28no—
158C2×#626C2312yes—
159C2×#626C2314yes—
160C2×#626C2314yes—
161C2×#626C2312yescomplemented
162C2×#626C2314yescomplemented
163C2×#626C2314yescomplemented
164C2×#625C2314yescomplemented
165C2×#624—24no—
166C2×#624D418yescomplemented
167C2×#624C2311yescharacteristic
168C2×#624C2312yes—
169C2×#624C2311yescharacteristic
170C2×#624C2311yescharacteristic
171C2×#624C2312yes—
172C2×#624C2312yescomplemented
173#3804—28no—
174#3804—28no—
175C2×D3×Dic3C2312yescomplemented
176#3802—44no—
177C4×D32—24no—
178#3799—28no—
179#3797—24no—
180C32×C22⋊C4C2311yescharacteristic
181C32×C22⋊C4C2312yescomplemented
182#3757C2311yescharacteristic
183#3757C2312yescomplemented
184#3752C2312yes—
185#3752C2312yescomplemented
186#3752C2312yescomplemented
187C3×#217C2312yes—
188C3×#217C2314yescomplemented
189C3×(C2×D3)⋊C4C2314yescomplemented
190C3×(C2×D3)⋊C4C2314yescomplemented
191C3×Dic3⋊C4C2314yescomplemented
192C3×C4×Dic3C2314yescomplemented
193Dic3⋊Dic3C2314yescomplemented
194#3722C2312yes—
195#3722C2314yescomplemented
196(C2×D3)⋊Dic3C2314yescomplemented
197(C2×D3)⋊Dic3C2314yescomplemented
198Dic32C2314yescomplemented
199C2×#535—91noSylow
200C24×D3—32no—
201C24×D3—32no—
202C24×D3—61no—
203C2×C3×#41—32no—
204C22×C3×D4—32no—
205C22×#67—32no—
206C22×#67C2×D312yescomplemented
207D3×#41—616no—
208C2×#239—32no—
209C2×D3×Q8—32no—
210C2×#237—32no—
211C2×#237—32no—
212C2×#237C2×D312yescomplemented
213C2×D3×D4—32no—
214C2×D3×D4—34no—
215C2×D3×D4—34no—
216C2×D3×D4—34no—
217C2×D3×D4—34no—
218C2×D3×D4—32no—
219C2×D3×D4—32no—
220C2×D3×D4—34no—
221C2×D3×D4—34no—
222C2×D3×D4—34no—
223C2×D3×D4—34no—
224C2×D3×D4—61no—
225C2×D3×D4—62no—
226C2×D3×D4—616no—
227C2×#235—32no—
228C2×#235—32no—
229C2×#235—32no—
230C22×D12—32no—
231C22×C4×D3—32no—
232C22×C4×D3—32no—
233C22×C4×D3—32no—
234C3×#127—34no—
235C3×#124—34no—
236C3×#121—34no—
237C3×#121—34no—
238C3×#120—21no—
239C3×#120—32no—
240C3×#120—32no—
241C3×#120—32no—
242C3×#120C2×D312yescomplemented
243C3×#117—32no—
244#953—32no—
245#953—32no—
246#953—32no—
247#953—61no—
248#953C2×D312yescomplemented
249#947—34no—
250#940—34no—
251#940—34no—
252#940—34no—
253#940—34no—
254#940—34no—
255#940C2×D314yescomplemented
256#939—34no—
257#939—34no—
258#939—34no—
259#939C2×D314yescomplemented
260#938—34no—
261#938—34no—
262#937—32no—
263#937—32no—
264#937—34no—
265#937—34no—
266#937—32no—
267#937—34no—
268#937—34no—
269#937—61no—
270#937—62no—
271#937C2×D312yescomplemented
272#936—34no—
273#930—34no—
274#930—34no—
275#926—32no—
276#895—34no—
277#895—34no—
278#892—34no—
279D3×C4⋊C4—34no—
280#885—34no—
281#885—34no—
282#885—34no—
283#885C2×D314yescomplemented
284#884—34no—
285#884—34no—
286#884—34no—
287#884C2×D314yescomplemented
288#882—32no—
289#882—32no—
290#882—34no—
291#882—34no—
292#882—32no—
293#882—34no—
294#882—34no—
295#882—61no—
296#882—62no—
297#882C2×D312yescomplemented
298D3×C22⋊C4—32no—
299D3×C22⋊C4—34no—
300D3×C22⋊C4—32no—
301D3×C22⋊C4—34no—
302D3×C22⋊C4—34no—
303D3×C22⋊C4—34no—
304D3×C22⋊C4—61no—
305D3×C22⋊C4—62no—
306#877—32no—
307#877C2×D312yescomplemented
308#875—34no—
309#874—34no—
310#872—34no—
311C42×D3—34no—
312C23×C32—22no—
313C23×C32—42no—
314C23×C32C2412yes—
315C23×C32C2411yescharacteristic
316C23×C32C2411yescharacteristic
317C22×C3⋊D3—24no—
318C22×C3⋊D3—24no—
319C22×C3⋊D3—22no—
320C22×C3⋊D3—24no—
321C22×C3⋊D3—24no—
322C22×C3⋊D3—22no—
323C22×C3⋊D3—24no—
324C22×C3⋊D3—24no—
325C22×C3⋊D3—42no—
326C22×C3⋊D3—42no—
327C22×C3⋊D3—42no—
328C22×C3⋊D3—416no—
329C22×C3⋊D3C2×D414yes—
330C22×C3⋊D3C2412yes—
331C22×C3⋊D3C2411yescharacteristic
332C22×C3⋊D3C2411yescharacteristic
333C22×C3⋊D3C2411yescharacteristic
334C22×C3×D3—24no—
335C22×C3×D3—44no—
336C22×C3×D3C2414yes—
337C22×C3×D3C2412yes—
338C2×D32—24no—
339C2×D32—24no—
340C2×D32—22no—
341C2×D32—24no—
342C2×D32—24no—
343C2×D32—24no—
344C2×D32—44no—
345C2×D32—416no—
346C32×D4—22no—
347C32×D4—42no—
348C2×C32×C4C2412yes—
349C2×C32×C4C2411yescharacteristic
350#638—22no—
351#638—22no—
352#638—42no—
353#638—42no—
354C2×C3⋊Dic3C2412yes—
355C2×C3⋊Dic3C2411yescharacteristic
356C4⋊(C3⋊D3)—22no—
357C4⋊(C3⋊D3)—42no—
358C4×C3⋊D3—22no—
359C4×C3⋊D3—24no—
360C3×#67—24no—
361C3×#67—24no—
362C3×#67—28no—
363C3×#67—28no—
364C3×#67—44no—
365C3×#67—44no—
366C2×C3×Dic3—24no—
367C2×C3×Dic3C2×D418yescomplemented
368C2×C3×Dic3C2414yes—
369C2×C3×Dic3C2412yes—
370C2×C3×Dic3C2412yes—
371C2×C3×Dic3C2412yes—
372C3×D12—44no—
373C3×C4×D3—24no—
374C3×Dic6—24no—
375#627—24no—
376#626—24no—
377#626—24no—
378#626—28no—
379#626—28no—
380#626—44no—
381#626—44no—
382#625—44no—
383#624—22no—
384#624—24no—
385#624—24no—
386#624C2×D414yes—
387#624C2×D414yes—
388#624C2×D418yescomplemented
389D3×Dic3—24no—
390C22×#41—91no—
391C23×D4—91no—
392#535—32no—
393#535—92no—
394#535—92no—
395#535—92no—
396#535—94no—
397#535—94no—
398C2×#127—92no—
399C2×#124—92no—
400C2×#121—92no—
401C2×#121—92no—
402C2×#120—91no—
403C2×#120—91no—
404C2×#120—91no—
405C2×#120—91no—
406C2×#117—91no—
407C24×C3—21no—
408C24×C3—32no—
409C24×C3C22×D312yes—
410C23×D3—32no—
411C23×D3—34no—
412C23×D3—32no—
413C23×D3—32no—
414C23×D3—34no—
415C23×D3—34no—
416C23×D3—32no—
417C23×D3—34no—
418C23×D3—61no—
419C23×D3—62no—
420C23×D3—62no—
421C23×D3—61no—
422C23×D3—61no—
423C23×D3—68no—
424C23×D3—68no—
425C23×D3—124no—
426C23×D3—128no—
427C23×D3—128no—
428C23×D3—128no—
429C23×D3C22×D312yes—
430C3×#41—68no—
431C2×C3×Q8—32no—
432C2×C3×D4—21no—
433C2×C3×D4—22no—
434C2×C3×D4—34no—
435C2×C3×D4—32no—
436C2×C3×D4—34no—
437C2×C3×D4—32no—
438C2×C3×D4—34no—
439C2×C3×D4—34no—
440C2×C3×D4—34no—
441C2×C3×D4—68no—
442C2×C3×D4C22×D312yes—
443C2×C3×D4C22×D314yescomplemented
444C22×C3×C4—32no—
445C22×C3×C4—32no—
446C22×C3×C4—32no—
447C2×#67—28no—
448C2×#67—32no—
449C2×#67—32no—
450C2×#67—34no—
451C2×#67—34no—
452C2×#67—34no—
453C2×#67—34no—
454C2×#67—34no—
455C2×#67—34no—
456C2×#67—32no—
457C2×#67—32no—
458C2×#67—34no—
459C2×#67—34no—
460C2×#67—61no—
461C2×#67—62no—
462C2×#67—61no—
463C2×#67—62no—
464C2×#67—68no—
465C2×#67C22×D312yes—
466C2×#67C22×D314yes—
467C2×#67C22×D314yes—
468C2×#67C22×D312yescomplemented
469C2×#67C22×D314yescomplemented
470C2×#67C22×D314yescomplemented
471C22×Dic3—32no—
472C22×Dic3C22×D312yes—
473C22×Dic3C22×D312yescomplemented
474#239—68no—
475D3×Q8—68no—
476#237—28no—
477#237—68no—
478#237—68no—
479D3×D4—616no—
480D3×D4—616no—
481D3×D4—616no—
482D3×D4—616no—
483D3×D4—68no—
484D3×D4—68no—
485D3×D4—68no—
486D3×D4—124no—
487D3×D4—128no—
488D3×D4—128no—
489D3×D4—128no—
490D3×D4—128no—
491D3×D4—128no—
492#235—68no—
493#235—68no—
494#235—68no—
495C2×D12—32no—
496C2×D12—34no—
497C2×D12—32no—
498C2×D12—34no—
499C2×D12—32no—
500C2×D12—34no—
501C2×D12—34no—
502C2×D12—34no—
503C2×D12—61no—
504C2×D12—62no—
505C2×D12—68no—
506C2×D12C22×D314yescomplemented
507C2×C4×D3—316no—
508C2×C4×D3—32no—
509C2×C4×D3—32no—
510C2×C4×D3—32no—
511C2×C4×D3—32no—
512C2×C4×D3—32no—
513C2×C4×D3—34no—
514C2×C4×D3—32no—
515C2×C4×D3—34no—
516C2×C4×D3—32no—
517C2×C4×D3—32no—
518C2×C4×D3—32no—
519C2×C4×D3—62no—
520C2×C4×D3—61no—
521C2×C4×D3—68no—
522C2×C4×D3—68no—
523C2×C4×D3C22×D312yescomplemented
524C2×Dic6—32no—
525C2×Dic6—32no—
526C2×Dic6C22×D312yescomplemented
527C3×C4⋊C4—34no—
528C3×C22⋊C4—21no—
529C3×C22⋊C4—22no—
530C3×C22⋊C4—32no—
531C3×C22⋊C4—34no—
532C3×C22⋊C4—34no—
533C3×C22⋊C4—34no—
534C3×C22⋊C4C22×D312yes—
535C3×C22⋊C4C22×D314yescomplemented
536C3×C42—34no—
537#217—32no—
538#217—34no—
539#217—34no—
540#217—34no—
541#217—61no—
542#217—62no—
543#217C22×D312yes—
544#217C22×D314yescomplemented
545(C2×D3)⋊C4—34no—
546(C2×D3)⋊C4—34no—
547(C2×D3)⋊C4—34no—
548(C2×D3)⋊C4—34no—
549(C2×D3)⋊C4—34no—
550(C2×D3)⋊C4—34no—
551(C2×D3)⋊C4—34no—
552(C2×D3)⋊C4—34no—
553(C2×D3)⋊C4—62no—
554(C2×D3)⋊C4—62no—
555(C2×D3)⋊C4—62no—
556(C2×D3)⋊C4C22×D314yescomplemented
557(C2×D3)⋊C4C22×D314yescomplemented
558C4⋊Dic3—34no—
559Dic3⋊C4—34no—
560Dic3⋊C4C22×D314yescomplemented
561C4×Dic3—34no—
562C4×Dic3—34no—
563C4×Dic3C22×D314yescomplemented
564C22×C32—22no—
565C22×C32—22no—
566C22×C32—21no—
567C22×C32—22no—
568C22×C32—22no—
569C22×C32—22no—
570C22×C32—44no—
571C22×C32C22×D412yes—
572C22×C32C2511yescharacteristic
573C2×C3⋊D3—22no—
574C2×C3⋊D3—22no—
575C2×C3⋊D3—28no—
576C2×C3⋊D3—21no—
577C2×C3⋊D3—22no—
578C2×C3⋊D3—22no—
579C2×C3⋊D3—22no—
580C2×C3⋊D3—48no—
581C2×C3⋊D3—44no—
582C2×C3⋊D3—48no—
583C2×C3⋊D3—44no—
584C2×C3⋊D3C22×D412yes—
585C2×C3⋊D3C22×D412yes—
586C2×C3⋊D3H(5,𝔽2)14yes—
587C2×C3×D3—22no—
588C2×C3×D3—24no—
589C2×C3×D3—24no—
590C2×C3×D3—24no—
591C2×C3×D3—24no—
592C2×C3×D3—48no—
593D32—48no—
594D32—44no—
595D32—48no—
596C32×C4—21no—
597C32×C4—22no—
598C3⋊Dic3—21no—
599C3⋊Dic3—22no—
600C3×Dic3—22no—
601C3×Dic3—24no—
602C3×Dic3C22×D414yes—
603C3×Dic3C22×D414yes—
604C25—91no—
605C25—91no—
606C2×#41—32no—
607C2×#41—92no—
608C2×#41—92no—
609C2×#41—92no—
610C2×#41—188no—
611C22×Q8—91no—
612C22×D4—32no—
613C22×D4—92no—
614C22×D4—91no—
615C22×D4—92no—
616C22×D4—92no—
617C22×D4—91no—
618C22×D4—94no—
619C22×D4—92no—
620C22×D4—92no—
621C22×D4—92no—
622C22×D4—91no—
623C22×D4—92no—
624C22×D4—188no—
625C23×C4—91no—
626C23×C4—91no—
627C23×C4—91no—
628#127—34no—
629#127—94no—
630#127—94no—
631#127—94no—
632#124—34no—
633#124—94no—
634#124—94no—
635#124—94no—
636#121—34no—
637#121—34no—
638#121—94no—
639#121—94no—
640#121—94no—
641#121—94no—
642#121—94no—
643#121—94no—
644#120—32no—
645#120—32no—
646#120—32no—
647#120—92no—
648#120—92no—
649#120—94no—
650#120—94no—
651#120—92no—
652#120—92no—
653#120—92no—
654#120—91no—
655#120—91no—
656#120—92no—
657#120—91no—
658#120—92no—
659#120D3211yescharacteristic, complemented
660#117—32no—
661#117—94no—
662#117—92no—
663C2×C4⋊C4—92no—
664C2×C22⋊C4—91no—
665C2×C22⋊C4—92no—
666C2×C22⋊C4—92no—
667C2×C22⋊C4—92no—
668C2×C22⋊C4—91no—
669C2×C22⋊C4—92no—
670C2×C42—92no—
671C23×C3—24no—
672C23×C3—22no—
673C23×C3—21no—
674C23×C3—21no—
675C23×C3—34no—
676C23×C3—32no—
677C23×C3—42no—
678C23×C3—44no—
679C23×C3—44no—
680C23×C3—64no—
681C23×C3—124no—
682C23×C3C23×D314yes—
683C23×C3C23×D312yes—
684C23×C3C23×D312yes—
685C22×D3—24no—
686C22×D3—32no—
687C22×D3—38no—
688C22×D3—32no—
689C22×D3—34no—
690C22×D3—32no—
691C22×D3—44no—
692C22×D3—61no—
693C22×D3—64no—
694C22×D3—61no—
695C22×D3—62no—
696C22×D3—61no—
697C22×D3—64no—
698C22×D3—68no—
699C22×D3—68no—
700C22×D3—68no—
701C22×D3—68no—
702C22×D3—68no—
703C22×D3—68no—
704C22×D3—64no—
705C22×D3—68no—
706C22×D3—68no—
707C22×D3—68no—
708C22×D3—68no—
709C22×D3—68no—
710C22×D3—68no—
711C22×D3—64no—
712C22×D3—124no—
713C22×D3—124no—
714C22×D3—124no—
715C22×D3—124no—
716C22×D3—122no—
717C22×D3—124no—
718C22×D3—122no—
719C22×D3—124no—
720C22×D3—124no—
721C22×D3—1232no—
722C22×D3—124no—
723C22×D3—124no—
724C22×D3—124no—
725C22×D3—124no—
726C22×D3—124no—
727C22×D3—1232no—
728C22×D3—124no—
729C22×D3—1232no—
730C22×D3C23×D314yes—
731C22×D3C23×D312yes—
732C3×Q8—64no—
733C3×D4—24no—
734C3×D4—42no—
735C3×D4—44no—
736C3×D4—44no—
737C3×D4—68no—
738C3×D4—68no—
739C3×D4—64no—
740C3×D4—64no—
741C3×D4—124no—
742C3×D4—124no—
743C3×D4—124no—
744C2×C3×C4—22no—
745C2×C3×C4—21no—
746C2×C3×C4—38no—
747C2×C3×C4—32no—
748C2×C3×C4—32no—
749C2×C3×C4—34no—
750C2×C3×C4—32no—
751C2×C3×C4—64no—
752C2×C3×C4—64no—
753C2×C3×C4C23×D314yes—
754C2×C3×C4C23×D312yes—
755#67—24no—
756#67—24no—
757#67—28no—
758#67—28no—
759#67—44no—
760#67—44no—
761#67—64no—
762#67—64no—
763#67—64no—
764#67—64no—
765#67—68no—
766#67—68no—
767#67—122no—
768#67—122no—
769#67—124no—
770#67—124no—
771#67—124no—
772#67—124no—
773#67—124no—
774#67—124no—
775#67—124no—
776#67—124no—
777C2×Dic3—24no—
778C2×Dic3—34no—
779C2×Dic3—32no—
780C2×Dic3—62no—
781C2×Dic3—61no—
782C2×Dic3—64no—
783C2×Dic3D3×D418yescomplemented
784C2×Dic3C23×D314yes—
785C2×Dic3C23×D312yes—
786C2×Dic3C23×D312yes—
787C2×Dic3C23×D312yes—
788D12—44no—
789D12—64no—
790D12—68no—
791D12—68no—
792D12—64no—
793D12—64no—
794D12—122no—
795D12—124no—
796D12—124no—
797D12—124no—
798D12—124no—
799C4×D3—24no—
800C4×D3—38no—
801C4×D3—38no—
802C4×D3—38no—
803C4×D3—38no—
804C4×D3—64no—
805C4×D3—64no—
806C4×D3—68no—
807C4×D3—64no—
808C4×D3—68no—
809C4×D3—64no—
810C4×D3—64no—
811C4×D3—122no—
812C4×D3—124no—
813Dic6—24no—
814Dic6—64no—
815Dic6—64no—
816C2×C32—22no—
817C2×C32—42no—
818C2×C32—41no—
819C2×C32C23×D411yescharacteristic
820C2×C32C2×H(5,𝔽2)12yes—
821C3⋊D3—22no—
822C3⋊D3—42no—
823C3⋊D3—41no—
824C3⋊D3#53514yescomplemented
825C3×D3—44no—
826C3×D3—42no—
827C24—32no—
828C24—92no—
829C24—91no—
830C24—92no—
831C24—91no—
832C24—92no—
833C24—91no—
834C24—92no—
835C24—91no—
836C24—184no—
837C24—184no—
838C24—364no—
839C24—364no—
840C24C2×D3211yescharacteristic
841#41—68no—
842#41—188no—
843#41—188no—
844#41—188no—
845C2×Q8—32no—
846C2×Q8—92no—
847C2×Q8—184no—
848C2×D4—32no—
849C2×D4—34no—
850C2×D4—34no—
851C2×D4—32no—
852C2×D4—34no—
853C2×D4—34no—
854C2×D4—34no—
855C2×D4—68no—
856C2×D4—92no—
857C2×D4—94no—
858C2×D4—94no—
859C2×D4—92no—
860C2×D4—94no—
861C2×D4—94no—
862C2×D4—91no—
863C2×D4—91no—
864C2×D4—94no—
865C2×D4—92no—
866C2×D4—92no—
867C2×D4—91no—
868C2×D4—92no—
869C2×D4—188no—
870C2×D4—188no—
871C2×D4—188no—
872C2×D4—1816no—
873C2×D4—184no—
874C2×D4—184no—
875C2×D4—184no—
876C2×D4—364no—
877C2×D4—364no—
878C2×D4—364no—
879C2×D4—364no—
880C2×D4C2×D3211yescharacteristic
881C2×D4C2×D3212yescomplemented
882C22×C4—32no—
883C22×C4—32no—
884C22×C4—32no—
885C22×C4—91no—
886C22×C4—91no—
887C22×C4—92no—
888C22×C4—98no—
889C22×C4—92no—
890C22×C4—91no—
891C22×C4—92no—
892C22×C4—92no—
893C22×C4—92no—
894C22×C4—91no—
895C22×C4—184no—
896C22×C4—184no—
897C4⋊C4—34no—
898C4⋊C4—94no—
899C22⋊C4—32no—
900C22⋊C4—34no—
901C22⋊C4—34no—
902C22⋊C4—34no—
903C22⋊C4—92no—
904C22⋊C4—94no—
905C22⋊C4—94no—
906C22⋊C4—94no—
907C22⋊C4—91no—
908C22⋊C4—92no—
909C22⋊C4—92no—
910C22⋊C4—92no—
911C22⋊C4—92no—
912C22⋊C4C2×D3211yescharacteristic
913C22⋊C4C2×D3212yescomplemented
914C42—34no—
915C42—94no—
916C22×C3—24no—
917C22×C3—24no—
918C22×C3—22no—
919C22×C3—24no—
920C22×C3—24no—
921C22×C3—24no—
922C22×C3—24no—
923C22×C3—22no—
924C22×C3—21no—
925C22×C3—42no—
926C22×C3—42no—
927C22×C3—42no—
928C22×C3—41no—
929C22×C3—42no—
930C22×C3—48no—
931C22×C3—48no—
932C22×C3—62no—
933C22×C3—64no—
934C22×C3—64no—
935C22×C3—64no—
936C22×C3—64no—
937C22×C3—128no—
938C22×C3C2×D3×D414yes—
939C22×C3C24×D312yes—
940C2×D3—22no—
941C2×D3—24no—
942C2×D3—24no—
943C2×D3—24no—
944C2×D3—24no—
945C2×D3—34no—
946C2×D3—38no—
947C2×D3—34no—
948C2×D3—48no—
949C2×D3—62no—
950C2×D3—64no—
951C2×D3—62no—
952C2×D3—616no—
953C2×D3—64no—
954C2×D3—64no—
955C2×D3—62no—
956C2×D3—64no—
957C2×D3—64no—
958C2×D3—64no—
959C2×D3—64no—
960C2×D3—128no—
961C2×D3—122no—
962C2×D3—122no—
963C2×D3—122no—
964C2×D3—121no—
965C2×D3—122no—
966C2×D3—1216no—
967C2×D3—128no—
968C2×D3—1216no—
969C2×D3—128no—
970C2×D3—1216no—
971C2×D3—1216no—
972C2×D3—1216no—
973C2×D3—128no—
974C2×D3—128no—
975C2×D3—1216no—
976C2×D3—244no—
977C3×C4—22no—
978C3×C4—24no—
979C3×C4—34no—
980C3×C4—34no—
981C3×C4—41no—
982C3×C4—42no—
983C3×C4—62no—
984C3×C4—64no—
985Dic3—22no—
986Dic3—24no—
987Dic3—62no—
988Dic3—64no—
989Dic3—121no—
990Dic3—122no—
991Dic3C2×D3×D414yes—
992Dic3C2×D3×D414yes—
993C32C2×#53511yescharacteristic, complemented, Sylow
994C23—22no—
995C23—34no—
996C23—32no—
997C23—42no—
998C23—64no—
999C23—91no—
1000C23—94no—
1001C23—91no—
1002C23—92no—
1003C23—91no—
1004C23—124no—
1005C23—184no—
1006C23—182no—
1007C23—184no—
1008C23—184no—
1009C23—184no—
1010C23—184no—
1011C23—184no—
1012C23—182no—
1013C23—184no—
1014C23—184no—
1015C23—184no—
1016C23—184no—
1017C23—184no—
1018C23—182no—
1019C23—362no—
1020C23—362no—
1021C23—362no—
1022C23—3616no—
1023C23—364no—
1024C23—3616no—
1025C23C22×D3212yes—
1026C23C22×D3211yescharacteristic
1027C23C22×D3211yescharacteristic
1028Q8—64no—
1029Q8—184no—
1030D4—22no—
1031D4—42no—
1032D4—68no—
1033D4—68no—
1034D4—64no—
1035D4—64no—
1036D4—124no—
1037D4—124no—
1038D4—124no—
1039D4—182no—
1040D4—188no—
1041D4—188no—
1042D4—184no—
1043D4—184no—
1044D4—182no—
1045D4—182no—
1046D4—362no—
1047D4—364no—
1048D4—364no—
1049D4—362no—
1050D4—362no—
1051D4—364no—
1052C2×C4—38no—
1053C2×C4—32no—
1054C2×C4—32no—
1055C2×C4—34no—
1056C2×C4—32no—
1057C2×C4—64no—
1058C2×C4—64no—
1059C2×C4—94no—
1060C2×C4—94no—
1061C2×C4—98no—
1062C2×C4—92no—
1063C2×C4—91no—
1064C2×C4—182no—
1065C2×C4—184no—
1066C2×C4—184no—
1067C2×C4—184no—
1068C2×C4—182no—
1069C2×C4—184no—
1070C2×C4C22×D3212yes—
1071C2×C4C22×D3211yescharacteristic
1072C2×C3—24no—
1073C2×C3—21no—
1074C2×C3—22no—
1075C2×C3—42no—
1076C2×C3—44no—
1077C2×C3—44no—
1078C2×C3—42no—
1079C2×C3—81no—
1080C2×C3—124no—
1081C2×C3—122no—
1082C2×C3C22×D3×D412yes—
1083C2×C3D3×H(5,𝔽2)14yes—
1084D3—38no—
1085D3—44no—
1086D3—42no—
1087D3—64no—
1088D3—64no—
1089D3—122no—
1090D3—124no—
1091D3—124no—
1092D3—122no—
1093D3—241no—
1094C22—22no—
1095C22—21no—
1096C22—22no—
1097C22—22no—
1098C22—22no—
1099C22—22no—
1100C22—44no—
1101C22—62no—
1102C22—64no—
1103C22—64no—
1104C22—64no—
1105C22—64no—
1106C22—92no—
1107C22—94no—
1108C22—92no—
1109C22—128no—
1110C22—188no—
1111C22—182no—
1112C22—181no—
1113C22—182no—
1114C22—182no—
1115C22—182no—
1116C22—182no—
1117C22—364no—
1118C22—368no—
1119C22—364no—
1120C22—368no—
1121C22—368no—
1122C22—364no—
1123C22—368no—
1124C22D32×D412yes—
1125C22C23×D3211yescharacteristic
1126C4—21no—
1127C4—22no—
1128C4—34no—
1129C4—34no—
1130C4—62no—
1131C4—64no—
1132C4—181no—
1133C4—182no—
1134C3—21no—
1135C3D3×#53512yescomplemented
1136C2—22no—
1137C2—42no—
1138C2—41no—
1139C2—94no—
1140C2—124no—
1141C2—122no—
1142C2—182no—
1143C2—362no—
1144C2—361no—
1145C2C2×D32×D411yescharacteristic
1146C2#1059667512yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#120C22
hypercenter#120D32
hypocenterC32C2×#535
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C22×#3811C2semidirect
2. C2×#64312C2semidirect
3. C3⋊D3×#120C2semidirect
4. C3×#5592C2semidirect
5. #10595527C2semidirect
6. #10595513C2semidirect
7. #10595300C2semidirect
8. #10595299C2semidirect
9. #10595298C2semidirect
10. #10595278C2semidirect
11. #10595238C2semidirect
12. #10594288C2semidirect
13. #10594287C2semidirect
14. #10594265C2semidirect
15. #10594258C2semidirect
16. #10594080C2semidirect
17. #10594052C2semidirect
22. C2×D4×C3⋊D3C22semidirect
23. C22×C3×#67C22semidirect
24. C2×C3×#237C22semidirect
29. C2×#3811C22semidirect
30. C2×#3811C22semidirect
31. C2×#3811C22semidirect
32. C2×#3811C22semidirect
33. C22×#626C22semidirect
35. C22×#624C22semidirect
36. C2×#3804C22semidirect
37. C2×#3804C22semidirect
39. C2×#3802C22semidirect
40. C2×C4×D32C22semidirect
41. C2×#3799C22semidirect
42. C2×#3797C22semidirect
43. C32×#120C22semidirect
44. #64162C22semidirect
45. #64146C22semidirect
46. #64146C22semidirect
47. #64091C22semidirect
48. #64091C22semidirect
50. C22⋊C4×C3⋊D3C22semidirect
51. C3×#953C22semidirect
52. C3×#940C22semidirect
53. C3×#939C22semidirect
54. C3×#937C22semidirect
55. C3×#885C22semidirect
56. C3×#884C22semidirect
57. C3×#882C22semidirect
58. C3×#877C22semidirect
59. #63983C22semidirect
60. #63981C22semidirect
61. #63981C22semidirect
62. #63979C22semidirect
63. #63979C22semidirect
64. #63978C22semidirect
65. #63977C22semidirect
66. #63976C22semidirect
68. #63974C22semidirect
69. #63970C22semidirect
70. #63959C22semidirect
71. #63958C22semidirect
72. #63955C22semidirect
73. #63923C22semidirect
74. #63922C22semidirect
75. #63921C22semidirect
76. #63921C22semidirect
77. #63911C22semidirect
78. #63910C22semidirect
79. #63907C22semidirect
80. #63906C22semidirect
81. #63886C22semidirect
82. #63883C22semidirect
83. C4×#624C22semidirect
84. #63852C22semidirect
85. #63836C22semidirect
102. #5592D3semidirect
125. C2×C32×D4C23semidirect
128. C2×#638C23semidirect
129. C2×#638C23semidirect
133. C2×C4⋊(C3⋊D3)C23semidirect
140. C2×C3×#67C23semidirect
141. C2×C3×#67C23semidirect
142. C2×C3×#67C23semidirect
144. C22×C3×Dic3C23semidirect
146. C2×C3×D12C23semidirect
147. C2×C3×C4×D3C23semidirect
148. C2×C3×Dic6C23semidirect
156. C2×#627C23semidirect
161. C2×#626C23semidirect
162. C2×#626C23semidirect
163. C2×#626C23semidirect
164. C2×#625C23semidirect
166. C2×#624D4semidirect
172. C2×#624C23semidirect
175. C2×D3×Dic3C23semidirect
181. C32×C22⋊C4C23semidirect
183. #3757C23semidirect
185. #3752C23semidirect
186. #3752C23semidirect
188. C3×#217C23semidirect
189. C3×(C2×D3)⋊C4C23semidirect
190. C3×(C2×D3)⋊C4C23semidirect
191. C3×Dic3⋊C4C23semidirect
192. C3×C4×Dic3C23semidirect
193. Dic3⋊Dic3C23semidirect
195. #3722C23semidirect
196. (C2×D3)⋊Dic3C23semidirect
197. (C2×D3)⋊Dic3C23semidirect
198. Dic32C23semidirect
206. C22×#67C2×D3semidirect
212. C2×#237C2×D3semidirect
242. C3×#120C2×D3semidirect
248. #953C2×D3semidirect
255. #940C2×D3semidirect
259. #939C2×D3semidirect
271. #937C2×D3semidirect
283. #885C2×D3semidirect
287. #884C2×D3semidirect
297. #882C2×D3semidirect
307. #877C2×D3semidirect
367. C2×C3×Dic3C2×D4semidirect
388. #624C2×D4semidirect
443. C2×C3×D4C22×D3semidirect
468. C2×#67C22×D3semidirect
469. C2×#67C22×D3semidirect
470. C2×#67C22×D3semidirect
473. C22×Dic3C22×D3semidirect
506. C2×D12C22×D3semidirect
523. C2×C4×D3C22×D3semidirect
526. C2×Dic6C22×D3semidirect
535. C3×C22⋊C4C22×D3semidirect
544. #217C22×D3semidirect
556. (C2×D3)⋊C4C22×D3semidirect
557. (C2×D3)⋊C4C22×D3semidirect
560. Dic3⋊C4C22×D3semidirect
563. C4×Dic3C22×D3semidirect
659. #120D32semidirect
783. C2×Dic3D3×D4semidirect
824. C3⋊D3#535semidirect
881. C2×D4C2×D32semidirect
913. C22⋊C4C2×D32semidirect
993. C32C2×#535semidirect
1135. C3D3×#535semidirect

Maximal subgroups

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

subgroupindex
C22×#38112
C2×#643122
C3⋊D3×#1202
C3×#55922
#105955272
#105955132
#105953002
#105952992
#105952982
#105952782
#105952382
#105942882
#105942872
#105942652
#105942582
#105940802
#105940522
D3×#5353