Finite Group Databasebeta

← #11904643

Subgroups — #11904643

Order 1152.

3761 conjugacy classes of subgroups.

The subgroup lattice has 1087 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#64313C211yesmaximal, characteristic, complemented
3C3×#5829C212yesmaximal, complemented
4#10595433C211yesmaximal, characteristic, complemented
5#10595404C211yesmaximal, characteristic, complemented
6#10595362C212yesmaximal, complemented
7#10595292C214yesmaximal, complemented
8#10595239C212yesmaximal, complemented
9D4×#626C212yesmaximal, complemented
10#10595219C211yesmaximal, characteristic, complemented
11#10595166C212yesmaximal, complemented
12#10595081C211yesmaximal, characteristic, complemented
13#10595077C214yesmaximal, complemented
14#10595016C211yesmaximal, characteristic, complemented
15C2×#63912C212yesmaximal, complemented
16#10594920C212yesmaximal, complemented
17#10594919C212yesmaximal, complemented
18#86629—32nomaximal
19C2×C32×#41C2211yescharacteristic, complemented
20#41×C3⋊D3—28no—
21C2×#3832C2211yescharacteristic, complemented
22C2×Q8×C3⋊D3C2211yescharacteristic, complemented
23C2×#3830C2211yescharacteristic
24C2×#3830C2212yescomplemented
25C2×D4×C3⋊D3C2211yescharacteristic, complemented
26C2×D4×C3⋊D3C2212yescomplemented
27C2×#3828C2212yescomplemented
28C2×#3828C2211yescharacteristic, complemented
29C22×C4×C3⋊D3C2211yescharacteristic, complemented
30C22×C4×C3⋊D3C2212yescomplemented
31C2×C3×D3×D4C2212yescomplemented
32C2×#3811C2212yescomplemented
33C2×D3×#67C2214yescomplemented
34C22×#626C2214yescomplemented
35C22×#625C2212yescomplemented
36C2×#3805C2212yescomplemented
37#64313—28no—
38C2×#3802C2211yescharacteristic, complemented
39C2×#3798C2211yescharacteristic, complemented
40C2×#3795C2212yescomplemented
41C3×#947C2212yescomplemented
42C3×#946C2212yescomplemented
43C3×#939C2214yescomplemented
44C3×#937C2214yescomplemented
45C3×D4×Dic3C2212yescomplemented
46C3×#930C2212yescomplemented
47C3×#929C2214yescomplemented
48C3×C4×#67C2212yescomplemented
49C2×C3×(C2×D3)⋊C4C2214yescomplemented
50#63982C2211yescharacteristic, complemented
51#63981C2214yescomplemented
52#63981C2212yescomplemented
53#63980C2212yescomplemented
54#63980C2211yescharacteristic, complemented
55#63979C2214yescomplemented
56#63978C2214yescomplemented
57#63977C2214yescomplemented
58#63971C2214yescomplemented
59C2×#3724C2212yescomplemented
60#63957C2212yescomplemented
61#63952C2214yescomplemented
62#63923C2214yescomplemented
63#63921C2212yescomplemented
64#63916C2212yescomplemented
65#63913C2214yescomplemented
66#63912C2214yescomplemented
67#63912C2212yescomplemented
68#63912C2214yescomplemented
69#63912C2212yescomplemented
70#63912C2212yescomplemented
71#63912C2212yescomplemented
72#63912C2211yescharacteristic, complemented
73#63911C2212yescomplemented
74#63910C2214yescomplemented
75#63909C2212yescomplemented
76C4×#626C2212yescomplemented
77#63900C2211yescharacteristic, complemented
78#63896C2214yescomplemented
79#63881C2214yescomplemented
80#63881C2214yescomplemented
81#63874C2211yescharacteristic, complemented
82#63865C2212yescomplemented
83#63865C2211yescharacteristic, complemented
84#63853C2212yescomplemented
85#63844C2212yescomplemented
86C2×D3×#41—32no—
87C2×D3×#41—61no—
88C2×#1004—32no—
89C3×#546—32no—
90#5829D312yescomplemented
91D4×#67—32no—
92#5677—32no—
93#5674—32no—
94#5656—34no—
95#5654—34no—
96#5633—32no—
97#5629—32no—
98#5609—34no—
99D3×#121—32no—
100#5599—32no—
101#5597—34no—
102#5592—34no—
103#5590—34no—
104#5553—32no—
105D4×D12—32no—
106#5547—32no—
107#5546—32no—
108#5490—34no—
109C2×#884—34no—
110C23×C3⋊D3C2312yes—
111C23×C3⋊D3C2311yescharacteristic
112C23×C3×D3C2314yes—
113C22×D32C2312yes—
114C32×#41—24no—
115C2×C32×Q8C2311yescharacteristic
116C2×C32×D4C2312yes—
117C2×C32×D4C2311yescharacteristic
118C22×C32×C4C2312yes—
119C22×C32×C4C2311yescharacteristic
120C2×#638C2312yes—
121C2×#638C2312yes—
122C2×#638C2312yes—
123C22×C3⋊Dic3C2311yescharacteristic
124C22×C3⋊Dic3C2312yes—
125#3832—24no—
126Q8×C3⋊D3—24no—
127#3830—28no—
128#3830D418yescomplemented
129D4×C3⋊D3—24no—
130D4×C3⋊D3—28no—
131#3828—28no—
132#3828—24no—
133C2×C4⋊(C3⋊D3)C2311yescharacteristic
134C2×C4⋊(C3⋊D3)C2312yes—
135C2×C4×C3⋊D3—28no—
136C2×C4×C3⋊D3—24no—
137C2×C4×C3⋊D3C2311yescharacteristic
138C2×C4×C3⋊D3C2311yescharacteristic
139C2×C4×C3⋊D3C2312yes—
140C2×C4×C3⋊D3C2312yes—
141C2×C4×C3⋊D3C2311yescharacteristic
142C2×C4×C3⋊D3C2312yes—
143C2×C4×C3⋊D3C2311yescharacteristic
144C2×#634C2312yes—
145C2×#634C2311yescharacteristic
146C2×C3×#67C2314yes—
147C2×C3×#67C2312yes—
148C2×C3×#67C2314yes—
149C22×C3×Dic3C2314yes—
150C3×D3×D4—28no—
151C2×C3×D12C2312yes—
152C2×C3×C4×D3C2312yes—
153#3811—44no—
154D3×#67—216no—
155C2×#627C2311yescharacteristic
156C2×#626—48no—
157C2×#626C2312yes—
158C2×#626C2312yes—
159C2×#626C2314yes—
160C2×#626C2314yes—
161C2×#626C2314yes—
162C2×#626C2314yes—
163C2×#625—28no—
164C2×#625C2314yes—
165C2×#625C2311yescharacteristic
166C2×#625C2312yes—
167C2×#624C2312yes—
168#3805—28no—
169C2×D3×Dic3C2314yes—
170#3802—24no—
171#3798—24no—
172#3795—28no—
173C3×#217C2312yes—
174C3×#217C2314yes—
175C3×(C2×D3)⋊C4C2312yes—
176C3×(C2×D3)⋊C4C2314yes—
177C3×(C2×D3)⋊C4C2314yes—
178C3×(C2×D3)⋊C4C2314yes—
179C3×(C2×D3)⋊C4C2314yes—
180C3×C4⋊Dic3C2312yes—
181C3×Dic3⋊C4C2312yes—
182C3×Dic3⋊C4C2314yes—
183C3×C4×Dic3C2312yes—
184#3724C2314yes—
185#3724C2311yescharacteristic
186#3724C2312yes—
187#3724C2311yescharacteristic
188Dic3⋊Dic3C2312yes—
189#3722C2312yes—
190#3722C2312yes—
191#3722C2314yes—
192(C2×D3)⋊Dic3C2312yes—
193(C2×D3)⋊Dic3C2314yes—
194Dic32C2314yes—
195#3488—91noSylow
196C2×C3×#41—21no—
197C2×C3×#41C2×D312yescomplemented
198C22×C3×D4—32no—
199C22×#67—34no—
200C22×#67—34no—
201C22×#67—34no—
202D3×#41—616no—
203D3×#41—616no—
204C2×#239—32no—
205C2×#239—61no—
206C2×D3×Q8—32no—
207C2×D3×Q8—61no—
208#1004—616no—
209C2×#237—32no—
210C2×#237—34no—
211C2×#237—34no—
212C2×#237—32no—
213C2×#237—61no—
214C2×#237—62no—
215C2×D3×D4—34no—
216C2×D3×D4—32no—
217C2×D3×D4—34no—
218C2×D3×D4—34no—
219C2×D3×D4—32no—
220C2×D3×D4—61no—
221C2×D3×D4—62no—
222C2×D3×D4C2×D312yescomplemented
223C2×#235—34no—
224C2×#235—32no—
225C2×#235—32no—
226C2×#235—32no—
227C2×#235—62no—
228C2×#235—61no—
229C22×D12—34no—
230C22×C4×D3—34no—
231C22×C4×D3—32no—
232C22×C4×D3—61no—
233C22×C4×D3—62no—
234C3×#124—32no—
235C3×#123—34no—
236C3×C22⋊Q8—32no—
237C3×#121—34no—
238C3×#121—32no—
239C3×#120—34no—
240C3×C4×D4—32no—
241C3×C4×D4—32no—
242C2×C3×C22⋊C4—34no—
243#953—34no—
244#947C2×D312yescomplemented
245#946C2×D312yescomplemented
246#940—34no—
247#940—34no—
248#940—32no—
249#939—32no—
250#939—34no—
251#939—34no—
252#939—34no—
253#939C2×D314yescomplemented
254#938—32no—
255#937—34no—
256#937—32no—
257#937C2×D314yescomplemented
258D4×Dic3C2×D312yescomplemented
259#930—34no—
260#930—32no—
261#930C2×D312yescomplemented
262#929C2×D314yescomplemented
263C4×#67—34no—
264C4×#67—32no—
265C4×#67C2×D312yescomplemented
266C2×(C2×D3)⋊C4C2×D314yescomplemented
267C2×Dic3⋊C4—34no—
268#896—34no—
269#896—32no—
270#896—34no—
271#895—32no—
272#895—32no—
273#895—34no—
274#894—32no—
275#893—34no—
276#893—34no—
277D3×C4⋊C4—32no—
278#887—32no—
279#885—34no—
280#885—34no—
281#884—34no—
282#884—34no—
283#884—34no—
284#884—34no—
285#884—34no—
286#884—34no—
287#884—34no—
288#884—32no—
289#884—34no—
290#884—34no—
291#884—34no—
292#883—32no—
293#882—34no—
294#882—34no—
295#882—32no—
296#882—34no—
297#882—34no—
298#67⋊C4—34no—
299#67⋊C4—34no—
300#67⋊C4—34no—
301D3×C22⋊C4—34no—
302#878—32no—
303#878—34no—
304#877—34no—
305#874—32no—
306C4×D12—32no—
307#872—32no—
308C4×Dic6—32no—
309C23×C32C2411yescharacteristic
310C23×C32C2412yes—
311C22×C3⋊D3—24no—
312C22×C3⋊D3—22no—
313C22×C3⋊D3—24no—
314C22×C3⋊D3—22no—
315C22×C3⋊D3—41no—
316C22×C3⋊D3—42no—
317C22×C3⋊D3C2412yes—
318C22×C3⋊D3C2411yescharacteristic
319C22×C3⋊D3C2411yescharacteristic
320C22×C3×D3—28no—
321C22×C3×D3—44no—
322C22×C3×D3—44no—
323C22×C3×D3C2414yes—
324C22×C3×D3C2412yes—
325C2×D32—24no—
326C2×D32—42no—
327C2×D32—42no—
328C32×Q8—22no—
329C32×D4—24no—
330C32×D4C2×D414yescomplemented
331C2×C32×C4—24no—
332C2×C32×C4—22no—
333C2×C32×C4C2412yes—
334C2×C32×C4C2411yescharacteristic
335C2×C32×C4C2411yescharacteristic
336#638—24no—
337#638—24no—
338#638C2×D418yescomplemented
339C2×C3⋊Dic3—22no—
340C2×C3⋊Dic3C2×D418yescomplemented
341C2×C3⋊Dic3C2411yescharacteristic
342C2×C3⋊Dic3C2412yes—
343C2×C3⋊Dic3C2411yescharacteristic
344C4⋊(C3⋊D3)—24no—
345C4⋊(C3⋊D3)—22no—
346C4×C3⋊D3—22no—
347C4×C3⋊D3—22no—
348C4×C3⋊D3—22no—
349C4×C3⋊D3—24no—
350C4×C3⋊D3—24no—
351C4×C3⋊D3—24no—
352C4×C3⋊D3C2×D414yescomplemented
353#634—24no—
354#634C2×D414yescomplemented
355C3×#67—28no—
356C3×#67—44no—
357C3×#67—42no—
358C2×C3×Dic3—44no—
359C2×C3×Dic3C2412yes—
360C2×C3×Dic3C2414yes—
361C2×C3×Dic3C2412yes—
362C2×C3×Dic3C2412yes—
363C3×D12—24no—
364C3×C4×D3—24no—
365#627—22no—
366#626—24no—
367#626—24no—
368#626—28no—
369#626—44no—
370#626—44no—
371#626—44no—
372#625—28no—
373#625—22no—
374#625—24no—
375#624—42no—
376D3×Dic3—28no—
377C2×H(5,𝔽2)—91no—
378C22×#41—91no—
379#550—92no—
380#548—92no—
381#546—32no—
382#546—94no—
383D42—92no—
384D42—94no—
385#537—92no—
386#537—91no—
387#535—92no—
388#535—91no—
389#525—91no—
390#525—92no—
391C2×#121—92no—
392C2×#121—91no—
393#520—91no—
394C24×C3—34no—
395C23×D3—34no—
396C23×D3—32no—
397C23×D3—34no—
398C23×D3—62no—
399C23×D3—61no—
400C23×D3C22×D314yes—
401C3×#41—28no—
402C3×#41—28no—
403C2×C3×Q8—21no—
404C2×C3×Q8C22×D312yes—
405C2×C3×D4—22no—
406C2×C3×D4—21no—
407C2×C3×D4—34no—
408C2×C3×D4—32no—
409C2×C3×D4—34no—
410C2×C3×D4—32no—
411C2×C3×D4—68no—
412C2×C3×D4C22×D314yes—
413C2×C3×D4C22×D312yes—
414C22×C3×C4—22no—
415C22×C3×C4—21no—
416C22×C3×C4—34no—
417C22×C3×C4—32no—
418C22×C3×C4C22×D314yes—
419C22×C3×C4C22×D312yes—
420C2×#67—34no—
421C2×#67—34no—
422C2×#67—34no—
423C2×#67—32no—
424C2×#67—34no—
425C2×#67—34no—
426C2×#67—34no—
427C2×#67—34no—
428C2×#67—32no—
429C2×#67—32no—
430C2×#67—34no—
431C2×#67—34no—
432C2×#67—34no—
433C2×#67—62no—
434C2×#67—62no—
435C2×#67—62no—
436C2×#67—616no—
437C2×#67—616no—
438C2×#67—128no—
439C2×#67C22×D314yes—
440C2×#67C22×D312yes—
441C2×#67C22×D314yes—
442C22×Dic3—34no—
443C22×Dic3—32no—
444C22×Dic3—34no—
445C22×Dic3—62no—
446C22×Dic3—61no—
447C22×Dic3C22×D314yes—
448#239—68no—
449#239—68no—
450D3×Q8—68no—
451D3×Q8—68no—
452#237—316no—
453#237—68no—
454#237—68no—
455#237—616no—
456#237—616no—
457#237—616no—
458D3×D4—28no—
459D3×D4—68no—
460D3×D4—616no—
461D3×D4—616no—
462D3×D4—616no—
463D3×D4—68no—
464D3×D4—68no—
465D3×D4—128no—
466#235—68no—
467#235—68no—
468#235—68no—
469#235—616no—
470#235—616no—
471#235—68no—
472C2×D12—32no—
473C2×D12—34no—
474C2×D12—32no—
475C2×D12—32no—
476C2×D12—34no—
477C2×D12—34no—
478C2×D12—34no—
479C2×D12—34no—
480C2×D12—62no—
481C2×D12—61no—
482C2×D12—128no—
483C2×D12C22×D312yes—
484C2×C4×D3—32no—
485C2×C4×D3—34no—
486C2×C4×D3—32no—
487C2×C4×D3—32no—
488C2×C4×D3—34no—
489C2×C4×D3—34no—
490C2×C4×D3—32no—
491C2×C4×D3—34no—
492C2×C4×D3—34no—
493C2×C4×D3—61no—
494C2×C4×D3—61no—
495C2×C4×D3—62no—
496C2×C4×D3—62no—
497C2×C4×D3—61no—
498C2×C4×D3—61no—
499C2×C4×D3—62no—
500C2×C4×D3—68no—
501C2×C4×D3—616no—
502C2×C4×D3—68no—
503C2×C4×D3—616no—
504C2×C4×D3C22×D312yes—
505C2×Dic6—32no—
506C2×Dic6—34no—
507C2×Dic6—32no—
508C2×Dic6—61no—
509C2×Dic6—62no—
510C3×C4⋊C4—32no—
511C3×C4⋊C4—32no—
512C3×C4⋊C4—34no—
513C3×C22⋊C4—34no—
514C3×C22⋊C4—32no—
515C3×C22⋊C4—34no—
516C3×C22⋊C4—34no—
517C3×C22⋊C4—34no—
518C3×C22⋊C4—32no—
519C3×C22⋊C4—34no—
520C3×C42—32no—
521#217—34no—
522#217—32no—
523#217C22×D314yes—
524#217C22×D312yes—
525(C2×D3)⋊C4—32no—
526(C2×D3)⋊C4—34no—
527(C2×D3)⋊C4—32no—
528(C2×D3)⋊C4—32no—
529(C2×D3)⋊C4—32no—
530(C2×D3)⋊C4—34no—
531(C2×D3)⋊C4—32no—
532(C2×D3)⋊C4—34no—
533(C2×D3)⋊C4C22×D314yes—
534(C2×D3)⋊C4C22×D314yes—
535(C2×D3)⋊C4C22×D314yes—
536(C2×D3)⋊C4C22×D312yes—
537(C2×D3)⋊C4C22×D314yes—
538C4⋊Dic3—32no—
539C4⋊Dic3C22×D312yes—
540Dic3⋊C4—34no—
541Dic3⋊C4—32no—
542Dic3⋊C4—32no—
543Dic3⋊C4—34no—
544Dic3⋊C4—32no—
545Dic3⋊C4—34no—
546Dic3⋊C4C22×D314yes—
547Dic3⋊C4C22×D312yes—
548C4×Dic3—34no—
549C4×Dic3—34no—
550C4×Dic3C22×D312yes—
551C22×C32—21no—
552C22×C32—22no—
553C22×C32—22no—
554C22×C32—21no—
555C22×C32—21no—
556C22×C32C22×D414yes—
557C22×C32C2511yescharacteristic
558C2×C3⋊D3—21no—
559C2×C3⋊D3—21no—
560C2×C3⋊D3—22no—
561C2×C3⋊D3—21no—
562C2×C3⋊D3—21no—
563C2×C3⋊D3—22no—
564C2×C3⋊D3—22no—
565C2×C3⋊D3—44no—
566C2×C3⋊D3—48no—
567C2×C3⋊D3C22×D412yes—
568C2×C3⋊D3H(5,𝔽2)12yescomplemented
569C2×C3×D3—24no—
570C2×C3×D3—22no—
571C2×C3×D3—22no—
572C2×C3×D3—24no—
573C2×C3×D3—24no—
574C2×C3×D3—22no—
575C2×C3×D3—88no—
576D32—84no—
577C32×C4—22no—
578C32×C4—21no—
579C32×C4C22×D412yes—
580C3⋊Dic3—21no—
581C3⋊Dic3C22×D414yes—
582C3⋊Dic3C22×D412yes—
583C3×Dic3—22no—
584C3×Dic3—24no—
585C3×Dic3—22no—
586C3×Dic3—22no—
587H(5,𝔽2)—188no—
588C2×#41—91no—
589C2×#41—92no—
590C2×#41—92no—
591C2×#41—91no—
592C2×#41—91no—
593C2×#41—92no—
594C2×#41—92no—
595C2×#41—91no—
596C2×#41—188no—
597C2×#41D3211yescharacteristic, complemented
598C22×Q8—91no—
599C22×D4—32no—
600C22×D4—94no—
601C22×D4—91no—
602C22×D4—92no—
603C22×D4—94no—
604C22×D4—92no—
605C22×D4—92no—
606C22×D4—91no—
607C23×C4—92no—
608C23×C4—91no—
609#127—92no—
610#127—94no—
611#124—32no—
612#124—94no—
613#123—34no—
614#123—92no—
615C22⋊Q8—32no—
616C22⋊Q8—91no—
617C22⋊Q8—94no—
618C22⋊Q8—91no—
619C22⋊Q8—92no—
620#121—34no—
621#121—32no—
622#121—91no—
623#121—92no—
624#121—92no—
625#121—92no—
626#121—94no—
627#121—94no—
628#121—92no—
629#121—94no—
630#121—94no—
631#121—92no—
632#121—92no—
633#121—94no—
634#121—92no—
635#121—91no—
636#120—34no—
637#120—94no—
638#120—94no—
639#120—92no—
640#120—94no—
641C4×Q8—92no—
642C4×D4—32no—
643C4×D4—32no—
644C4×D4—92no—
645C4×D4—94no—
646C4×D4—94no—
647C4×D4—94no—
648#117—91no—
649#117—92no—
650C2×C4⋊C4—91no—
651C2×C4⋊C4—92no—
652C2×C22⋊C4—34no—
653C2×C22⋊C4—92no—
654C23×C3—21no—
655C23×C3—22no—
656C23×C3—34no—
657C23×C3—32no—
658C23×C3—68no—
659C23×C3—124no—
660C23×C3—124no—
661C23×C3C23×D312yes—
662C23×C3C23×D314yes—
663C22×D3—28no—
664C22×D3—32no—
665C22×D3—32no—
666C22×D3—34no—
667C22×D3—44no—
668C22×D3—44no—
669C22×D3—61no—
670C22×D3—61no—
671C22×D3—62no—
672C22×D3—68no—
673C22×D3—64no—
674C22×D3—68no—
675C22×D3—64no—
676C22×D3—64no—
677C22×D3—68no—
678C22×D3—68no—
679C22×D3—124no—
680C22×D3—122no—
681C22×D3—124no—
682C22×D3—124no—
683C22×D3—122no—
684C22×D3—124no—
685C22×D3—124no—
686C22×D3—122no—
687C22×D3C23×D314yes—
688C22×D3C23×D312yes—
689C3×Q8—24no—
690C3×Q8—24no—
691C3×D4—28no—
692C3×D4—28no—
693C3×D4—24no—
694C3×D4—68no—
695C3×D4—64no—
696C3×D4—124no—
697C3×D4—122no—
698C3×D4D3×D418yescomplemented
699C2×C3×C4—28no—
700C2×C3×C4—24no—
701C2×C3×C4—28no—
702C2×C3×C4—24no—
703C2×C3×C4—22no—
704C2×C3×C4—21no—
705C2×C3×C4—21no—
706C2×C3×C4—32no—
707C2×C3×C4—34no—
708C2×C3×C4—32no—
709C2×C3×C4—32no—
710C2×C3×C4—64no—
711C2×C3×C4—124no—
712C2×C3×C4C23×D314yes—
713C2×C3×C4C23×D312yes—
714C2×C3×C4C23×D312yes—
715#67—28no—
716#67—316no—
717#67—44no—
718#67—42no—
719#67—68no—
720#67—64no—
721#67—68no—
722#67—64no—
723#67—68no—
724#67—64no—
725#67—68no—
726#67—68no—
727#67—68no—
728#67—68no—
729#67—68no—
730#67—68no—
731#67—124no—
732#67—124no—
733#67—124no—
734C2×Dic3—316no—
735C2×Dic3—34no—
736C2×Dic3—32no—
737C2×Dic3—32no—
738C2×Dic3—44no—
739C2×Dic3—68no—
740C2×Dic3—62no—
741C2×Dic3—61no—
742C2×Dic3—61no—
743C2×Dic3—68no—
744C2×Dic3—64no—
745C2×Dic3—64no—
746C2×Dic3C23×D312yes—
747C2×Dic3C23×D314yes—
748C2×Dic3C23×D312yes—
749C2×Dic3C23×D312yes—
750D12—24no—
751D12—68no—
752D12—68no—
753D12—64no—
754D12—64no—
755D12—68no—
756D12—64no—
757D12—64no—
758D12—124no—
759D12—124no—
760D12—124no—
761C4×D3—24no—
762C4×D3—38no—
763C4×D3—64no—
764C4×D3—64no—
765C4×D3—68no—
766C4×D3—68no—
767C4×D3—68no—
768C4×D3—68no—
769C4×D3—64no—
770C4×D3—64no—
771C4×D3—68no—
772C4×D3—64no—
773C4×D3—68no—
774C4×D3—64no—
775C4×D3—68no—
776C4×D3—64no—
777C4×D3—124no—
778Dic6—38no—
779Dic6—64no—
780Dic6—64no—
781Dic6—68no—
782Dic6—68no—
783C2×C32—24no—
784C2×C32—41no—
785C2×C32C23×D411yescharacteristic
786C2×C32C2×H(5,𝔽2)11yescharacteristic
787C2×C32#58511yescharacteristic
788C3⋊D3—22no—
789C3⋊D3—22no—
790C3⋊D3—42no—
791C3×D3—44no—
792C3×D3—42no—
793C24—34no—
794C24—92no—
795C24—91no—
796C24—92no—
797#41—24no—
798#41—98no—
799#41—188no—
800#41—184no—
801#41—184no—
802#41—188no—
803#41—188no—
804#41—188no—
805#41—184no—
806C2×Q8—91no—
807C2×Q8—91no—
808C2×Q8—92no—
809C2×Q8—184no—
810C2×Q8C2×D3211yescharacteristic
811C2×D4—34no—
812C2×D4—32no—
813C2×D4—34no—
814C2×D4—32no—
815C2×D4—68no—
816C2×D4—92no—
817C2×D4—94no—
818C2×D4—92no—
819C2×D4—94no—
820C2×D4—94no—
821C2×D4—94no—
822C2×D4—92no—
823C2×D4—91no—
824C2×D4—92no—
825C2×D4—94no—
826C2×D4—92no—
827C2×D4—92no—
828C2×D4—92no—
829C2×D4—91no—
830C2×D4—184no—
831C2×D4—188no—
832C2×D4—188no—
833C2×D4—1816no—
834C2×D4—184no—
835C2×D4—368no—
836C2×D4—364no—
837C2×D4C2×D3212yes—
838C2×D4C2×D3211yescharacteristic
839C22×C4—34no—
840C22×C4—32no—
841C22×C4—92no—
842C22×C4—94no—
843C22×C4—92no—
844C22×C4—91no—
845C22×C4—91no—
846C22×C4—91no—
847C22×C4—92no—
848C22×C4—91no—
849C22×C4—92no—
850C22×C4—91no—
851C22×C4—92no—
852C22×C4—188no—
853C22×C4—184no—
854C22×C4C2×D3212yes—
855C22×C4C2×D3211yescharacteristic
856C4⋊C4—32no—
857C4⋊C4—32no—
858C4⋊C4—34no—
859C4⋊C4—91no—
860C4⋊C4—92no—
861C4⋊C4—94no—
862C4⋊C4—91no—
863C4⋊C4—92no—
864C22⋊C4—34no—
865C22⋊C4—32no—
866C22⋊C4—32no—
867C22⋊C4—34no—
868C22⋊C4—34no—
869C22⋊C4—34no—
870C22⋊C4—34no—
871C22⋊C4—92no—
872C22⋊C4—92no—
873C22⋊C4—94no—
874C22⋊C4—94no—
875C22⋊C4—92no—
876C42—32no—
877C42—94no—
878C22×C3—24no—
879C22×C3—24no—
880C22×C3—22no—
881C22×C3—22no—
882C22×C3—22no—
883C22×C3—22no—
884C22×C3—24no—
885C22×C3—21no—
886C22×C3—42no—
887C22×C3—42no—
888C22×C3—41no—
889C22×C3—41no—
890C22×C3—64no—
891C22×C3—62no—
892C22×C3—64no—
893C22×C3—62no—
894C22×C3—62no—
895C22×C3—64no—
896C22×C3—248no—
897C22×C3C2×D3×D418yes—
898C22×C3C24×D312yes—
899C2×D3—22no—
900C2×D3—24no—
901C2×D3—24no—
902C2×D3—22no—
903C2×D3—22no—
904C2×D3—24no—
905C2×D3—34no—
906C2×D3—34no—
907C2×D3—62no—
908C2×D3—62no—
909C2×D3—62no—
910C2×D3—62no—
911C2×D3—62no—
912C2×D3—62no—
913C2×D3—62no—
914C2×D3—62no—
915C2×D3—64no—
916C2×D3—64no—
917C2×D3—64no—
918C2×D3—64no—
919C2×D3—88no—
920C2×D3—121no—
921C2×D3—121no—
922C2×D3—122no—
923C2×D3—122no—
924C2×D3—128no—
925C2×D3—1216no—
926C2×D3—1216no—
927C2×D3—128no—
928C2×D3—248no—
929C3×C4—24no—
930C3×C4—22no—
931C3×C4—24no—
932C3×C4—22no—
933C3×C4—22no—
934C3×C4—62no—
935C3×C4—62no—
936C3×C4—64no—
937C3×C4—62no—
938C3×C4C2×D3×D414yes—
939Dic3—22no—
940Dic3—22no—
941Dic3—24no—
942Dic3—22no—
943Dic3—38no—
944Dic3—34no—
945Dic3—64no—
946Dic3—62no—
947Dic3—62no—
948Dic3—62no—
949C32#348811yescharacteristic, complemented, Sylow
950C23—32no—
951C23—34no—
952C23—68no—
953C23—91no—
954C23—91no—
955C23—92no—
956C23—124no—
957C23—124no—
958C23—182no—
959C23—184no—
960C23—182no—
961C23—184no—
962C23—184no—
963C23—362no—
964C23—361no—
965C23—362no—
966C23—362no—
967C23C22×D3211yescharacteristic
968C23C22×D3212yes—
969Q8—22no—
970Q8—94no—
971Q8—184no—
972Q8—182no—
973D4—24no—
974D4—68no—
975D4—64no—
976D4—98no—
977D4—124no—
978D4—122no—
979D4—184no—
980D4—184no—
981D4—184no—
982D4—188no—
983D4—184no—
984D4—182no—
985D4—184no—
986D4—188no—
987D4—184no—
988D4—182no—
989D4—364no—
990D4—364no—
991D4—364no—
992D4#381114yescomplemented
993C2×C4—24no—
994C2×C4—22no—
995C2×C4—32no—
996C2×C4—32no—
997C2×C4—34no—
998C2×C4—32no—
999C2×C4—64no—
1000C2×C4—98no—
1001C2×C4—92no—
1002C2×C4—91no—
1003C2×C4—94no—
1004C2×C4—91no—
1005C2×C4—124no—
1006C2×C4—182no—
1007C2×C4—184no—
1008C2×C4—184no—
1009C2×C4—184no—
1010C2×C4—182no—
1011C2×C4—188no—
1012C2×C4—182no—
1013C2×C4—182no—
1014C2×C4—362no—
1015C2×C4C22×D3211yescharacteristic
1016C2×C4C22×D3212yes—
1017C2×C4C22×D3211yescharacteristic
1018C2×C3—28no—
1019C2×C3—21no—
1020C2×C3—21no—
1021C2×C3—21no—
1022C2×C3—44no—
1023C2×C3—42no—
1024C2×C3—42no—
1025C2×C3—124no—
1026C2×C3—122no—
1027C2×C3C22×D3×D412yes—
1028C2×C3#596412yes—
1029C2×C3D3×H(5,𝔽2)12yes—
1030D3—42no—
1031D3—44no—
1032D3—64no—
1033D3—64no—
1034D3—64no—
1035D3—122no—
1036D3—124no—
1037D3—124no—
1038C22—22no—
1039C22—22no—
1040C22—21no—
1041C22—21no—
1042C22—21no—
1043C22—64no—
1044C22—62no—
1045C22—62no—
1046C22—64no—
1047C22—62no—
1048C22—64no—
1049C22—92no—
1050C22—92no—
1051C22—181no—
1052C22—181no—
1053C22—181no—
1054C22—181no—
1055C22—182no—
1056C22—182no—
1057C22—182no—
1058C22—248no—
1059C22—368no—
1060C22—364no—
1061C22—724no—
1062C22C2×#381114yes—
1063C22C23×D3211yescharacteristic
1064C4—21no—
1065C4—22no—
1066C4—62no—
1067C4—64no—
1068C4—62no—
1069C4—62no—
1070C4—92no—
1071C4—94no—
1072C4—181no—
1073C4C2×#381112yes—
1074C3—21no—
1075C3#8662912yescomplemented
1076C2—24no—
1077C2—41no—
1078C2—122no—
1079C2—124no—
1080C2—182no—
1081C2—182no—
1082C2—362no—
1083C2#1059669211yescharacteristic
1084C2#1059669511yescharacteristic
1085C2C22×#381111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×#41C22
hypercenterC2×#41D32
hypocenterC32#3488
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#41×C3⋊D3C2semidirect
2. C2×#64313C2semidirect
3. C3×#5829C2semidirect
4. #10595433C2semidirect
5. #10595404C2semidirect
6. #10595362C2semidirect
7. #10595292C2semidirect
8. #10595239C2semidirect
9. D4×#626C2semidirect
10. #10595219C2semidirect
11. #10595166C2semidirect
12. #10595081C2semidirect
13. #10595077C2semidirect
14. #10595016C2semidirect
15. C2×#63912C2semidirect
16. #10594920C2semidirect
17. #10594919C2semidirect
19. C2×C32×#41C22semidirect
21. C2×#3832C22semidirect
22. C2×Q8×C3⋊D3C22semidirect
24. C2×#3830C22semidirect
25. C2×D4×C3⋊D3C22semidirect
26. C2×D4×C3⋊D3C22semidirect
27. C2×#3828C22semidirect
28. C2×#3828C22semidirect
29. C22×C4×C3⋊D3C22semidirect
30. C22×C4×C3⋊D3C22semidirect
31. C2×C3×D3×D4C22semidirect
32. C2×#3811C22semidirect
33. C2×D3×#67C22semidirect
34. C22×#626C22semidirect
35. C22×#625C22semidirect
36. C2×#3805C22semidirect
38. C2×#3802C22semidirect
39. C2×#3798C22semidirect
40. C2×#3795C22semidirect
41. C3×#947C22semidirect
42. C3×#946C22semidirect
43. C3×#939C22semidirect
44. C3×#937C22semidirect
45. C3×D4×Dic3C22semidirect
46. C3×#930C22semidirect
47. C3×#929C22semidirect
48. C3×C4×#67C22semidirect
49. C2×C3×(C2×D3)⋊C4C22semidirect
50. #63982C22semidirect
51. #63981C22semidirect
52. #63981C22semidirect
53. #63980C22semidirect
54. #63980C22semidirect
55. #63979C22semidirect
56. #63978C22semidirect
57. #63977C22semidirect
58. #63971C22semidirect
59. C2×#3724C22semidirect
60. #63957C22semidirect
61. #63952C22semidirect
62. #63923C22semidirect
63. #63921C22semidirect
64. #63916C22semidirect
65. #63913C22semidirect
66. #63912C22semidirect
67. #63912C22semidirect
68. #63912C22semidirect
69. #63912C22semidirect
70. #63912C22semidirect
71. #63912C22semidirect
72. #63912C22semidirect
73. #63911C22semidirect
74. #63910C22semidirect
75. #63909C22semidirect
76. C4×#626C22semidirect
77. #63900C22semidirect
78. #63896C22semidirect
79. #63881C22semidirect
80. #63881C22semidirect
81. #63874C22semidirect
82. #63865C22semidirect
83. #63865C22semidirect
84. #63853C22semidirect
85. #63844C22semidirect
90. #5829D3semidirect
128. #3830D4semidirect
197. C2×C3×#41C2×D3semidirect
222. C2×D3×D4C2×D3semidirect
244. #947C2×D3semidirect
245. #946C2×D3semidirect
253. #939C2×D3semidirect
257. #937C2×D3semidirect
258. D4×Dic3C2×D3semidirect
261. #930C2×D3semidirect
262. #929C2×D3semidirect
265. C4×#67C2×D3semidirect
266. C2×(C2×D3)⋊C4C2×D3semidirect
330. C32×D4C2×D4semidirect
338. #638C2×D4semidirect
340. C2×C3⋊Dic3C2×D4semidirect
352. C4×C3⋊D3C2×D4semidirect
354. #634C2×D4semidirect
568. C2×C3⋊D3H(5,𝔽2)semidirect
597. C2×#41D32semidirect
698. C3×D4D3×D4semidirect
949. C32#3488semidirect
992. D4#3811semidirect
1075. C3#86629semidirect

Maximal subgroups

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

subgroupindex
C2×#41×C3⋊D32
C2×#643132
C3×#58292
#105954332
#105954042
#105953622
#105952922
#105952392
D4×#6262
#105952192
#105951662
#105950812
#105950772
#105950162
C2×#639122
#105949202
#105949192
#866293