Finite Group Databasebeta

← #11904766

Subgroups — #11904766

Order 1152.

3489 conjugacy classes of subgroups.

The subgroup lattice has 1031 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#64309C211yesmaximal, characteristic, complemented
3C3×#5824C212yesmaximal, complemented
4#10595404C211yesmaximal, characteristic, complemented
5#10595361C212yesmaximal, complemented
6#10595350C211yesmaximal, characteristic, complemented
7#10595271C212yesmaximal, complemented
8#10595254C212yesmaximal, complemented
9#10595219C211yesmaximal, characteristic, complemented
10#10595166C212yesmaximal, complemented
11#10595163C214yesmaximal, complemented
12#10595016C211yesmaximal, characteristic, complemented
13#10594925C211yesmaximal, characteristic, complemented
14#10594920C212yesmaximal, complemented
15#10594917C214yesmaximal, complemented
16#10594916C212yesmaximal, complemented
17C2×#63865C212yesmaximal, complemented
18#86677—32nomaximal
19C2×C32×#41C2211yescharacteristic
20#41×C3⋊D3—28no—
21C2×#3832C2211yescharacteristic
22C2×Q8×C3⋊D3C2211yescharacteristic
23C2×#3830C2212yes—
24C2×#3830C2211yescharacteristic
25C2×D4×C3⋊D3C2212yes—
26C2×D4×C3⋊D3C2211yescharacteristic
27C2×#3828C2211yescharacteristic
28C2×#3828C2212yes—
29C22×C4×C3⋊D3C2212yes—
30C22×C4×C3⋊D3C2211yescharacteristic
31C2×C3×#237C2212yescomplemented
32C22×#627C2212yescomplemented
33C2×#3805C2212yescomplemented
34C2×#3804C2214yescomplemented
35#64309—28no—
36C2×#3798C2211yescharacteristic, complemented
37C2×#3797C2211yescharacteristic, complemented
38C2×D3×Dic6C2212yescomplemented
39C3×#946C2212yescomplemented
40C3×#944C2212yescomplemented
41C3×#939C2214yescomplemented
42C3×#935C2214yescomplemented
43C3×D4×Dic3C2212yescomplemented
44C3×#929C2214yescomplemented
45C3×C4×#67C2212yescomplemented
46C3×#924C2212yescomplemented
47C2×C3×Dic3⋊C4C2214yescomplemented
48#63982C2212yescomplemented
49#63982C2211yescharacteristic, complemented
50#63981C2212yes—
51#63981C2214yes—
52#63980C2211yescharacteristic, complemented
53#63978C2214yescomplemented
54#63974C2212yes—
55#63971C2214yescomplemented
56C2×#3724C2212yescomplemented
57#63966C2214yescomplemented
58C2×#3722C2214yes—
59#63957C2212yescomplemented
60#63953C2214yescomplemented
61#63952C2214yescomplemented
62#63912C2211yescharacteristic
63#63912C2212yescomplemented
64#63910C2214yescomplemented
65#63909C2212yescomplemented
66C4×#626C2212yes—
67#63900C2211yescharacteristic, complemented
68#63897C2214yescomplemented
69#63896C2214yescomplemented
70#63883C2212yescomplemented
71#63881C2214yes—
72#63881C2214yescomplemented
73#63874C2211yescharacteristic, complemented
74#63871C2212yes—
75#63865C2214yes—
76#63865C2211yescharacteristic
77#63865C2212yes—
78#63865C2212yescomplemented
79#63865C2212yescomplemented
80#63865C2212yescomplemented
81#63865C2214yescomplemented
82#63864C2212yescomplemented
83#63853C2212yescomplemented
84#63844C2212yescomplemented
85#63840C2214yescomplemented
86C2×#1010—32no—
87C2×D3×#41—32no—
88C2×D3×#41—61no—
89C3×#547—32no—
90#5829—32no—
91#5824D312yescomplemented
92#5727—32no—
93#5724—32no—
94#5656—34no—
95#5655—34no—
96#5654—34no—
97#5648—34no—
98#5633—32no—
99#5632—32no—
100#5629—32no—
101D3×C22⋊Q8—32no—
102#5610—34no—
103#5597—34no—
104#5554—32no—
105#5552—32no—
106#5547—32no—
107#5546—32no—
108C2×#896—34no—
109#5507—34no—
110C23×C3⋊D3C2312yes—
111C23×C3⋊D3C2311yescharacteristic
112C32×#41—24no—
113C2×C32×Q8C2311yescharacteristic
114C2×C32×D4C2312yes—
115C2×C32×D4C2311yescharacteristic
116C22×C32×C4C2312yes—
117C22×C32×C4C2311yescharacteristic
118C2×#638C2312yes—
119C2×#638C2312yes—
120C2×#638C2312yes—
121C22×C3⋊Dic3C2311yescharacteristic
122C22×C3⋊Dic3C2312yes—
123#3832—24no—
124Q8×C3⋊D3—24no—
125#3830—28no—
126#3830D418yescomplemented
127D4×C3⋊D3—24no—
128D4×C3⋊D3—28no—
129#3828—28no—
130#3828—24no—
131C2×C4⋊(C3⋊D3)C2311yescharacteristic
132C2×C4⋊(C3⋊D3)C2312yes—
133C2×C4×C3⋊D3—28no—
134C2×C4×C3⋊D3—24no—
135C2×C4×C3⋊D3C2311yescharacteristic
136C2×C4×C3⋊D3C2311yescharacteristic
137C2×C4×C3⋊D3C2312yes—
138C2×C4×C3⋊D3C2312yes—
139C2×C4×C3⋊D3C2311yescharacteristic
140C2×C4×C3⋊D3C2312yes—
141C2×C4×C3⋊D3C2311yescharacteristic
142C2×#634C2312yes—
143C2×#634C2311yescharacteristic
144C2×C3×#67C2314yes—
145C2×C3×#67C2312yes—
146C22×C3×Dic3C2314yes—
147C22×C3×Dic3C2314yes—
148C3×#237—28no—
149C2×C3×C4×D3C2312yes—
150C2×C3×Dic6C2312yes—
151C2×#627—28no—
152C2×#627C2314yes—
153C2×#627C2312yes—
154C2×#627C2311yescharacteristic
155C2×#626C2312yes—
156C2×#626C2312yes—
157C2×#626C2314yes—
158C2×#625C2311yescharacteristic
159C2×#624C2312yes—
160C2×#624C2312yes—
161#3805—28no—
162#3804—216no—
163C2×D3×Dic3C2314yes—
164#3798—24no—
165#3797—24no—
166D3×Dic6—28no—
167C3×#217C2314yes—
168C3×#217C2312yes—
169C3×#217C2314yes—
170C3×(C2×D3)⋊C4C2312yes—
171C3×(C2×D3)⋊C4C2314yes—
172C3×C4⋊Dic3C2312yes—
173C3×Dic3⋊C4C2312yes—
174C3×Dic3⋊C4C2314yes—
175C3×Dic3⋊C4C2314yes—
176C3×Dic3⋊C4C2314yes—
177C3×Dic3⋊C4C2314yes—
178C3×C4×Dic3C2312yes—
179#3724C2314yes—
180#3724C2311yescharacteristic
181#3724C2312yes—
182#3724C2311yescharacteristic
183Dic3⋊Dic3C2312yes—
184Dic3⋊Dic3C2314yes—
185#3722C2312yes—
186#3722C2314yes—
187#3722C2314yes—
188#3722C2312yes—
189#3722C2314yes—
190#3722C2314yes—
191(C2×D3)⋊Dic3C2312yes—
192Dic32C2314yes—
193#3489—91noSylow
194C2×C3×#41—21no—
195C2×C3×#41—32no—
196C2×C3×#41C2×D312yes—
197#1010—616no—
198D3×#41—616no—
199D3×#41—616no—
200C2×#239—32no—
201C2×#239—61no—
202C2×D3×Q8—32no—
203C2×D3×Q8—32no—
204C2×D3×Q8—32no—
205C2×D3×Q8—61no—
206C2×#237—32no—
207C2×#237—34no—
208C2×#237—34no—
209C2×#237—34no—
210C2×#237—61no—
211C2×#237—62no—
212C2×#237C2×D312yescomplemented
213C2×D3×D4—34no—
214C2×D3×D4—32no—
215C2×D3×D4—62no—
216C2×D3×D4—61no—
217C2×#235—32no—
218C2×#235—34no—
219C2×#235—34no—
220C2×#235—32no—
221C2×#235—62no—
222C2×#235—61no—
223C22×C4×D3—34no—
224C22×C4×D3—32no—
225C22×C4×D3—62no—
226C22×C4×D3—61no—
227C22×Dic6—34no—
228C22×Dic6—32no—
229C3×C4⋊Q8—32no—
230C3×#123—34no—
231C3×#123—34no—
232C3×C22⋊Q8—32no—
233C3×C22⋊Q8—32no—
234C3×#121—34no—
235C3×C4×D4—32no—
236C3×C4×D4—32no—
237C2×C3×C4⋊C4—34no—
238#947—32no—
239#946—32no—
240#946C2×D312yescomplemented
241#944C2×D312yescomplemented
242#939—32no—
243#939—34no—
244#939—34no—
245#939C2×D314yescomplemented
246#937—34no—
247#937—32no—
248#935C2×D314yescomplemented
249D4×Dic3C2×D312yescomplemented
250#930—34no—
251#930—32no—
252#929—34no—
253#929C2×D314yescomplemented
254C4×#67—34no—
255C4×#67—32no—
256C4×#67C2×D312yescomplemented
257C2×(C2×D3)⋊C4—34no—
258C2×(C2×D3)⋊C4—34no—
259#924C2×D312yescomplemented
260C2×Dic3⋊C4—34no—
261C2×Dic3⋊C4C2×D314yescomplemented
262#897—32no—
263#896—34no—
264#896—34no—
265#896—34no—
266#896—34no—
267#896—34no—
268#896—34no—
269#896—34no—
270#896—34no—
271#896—32no—
272#896—34no—
273#895—32no—
274#895—34no—
275#894—32no—
276#894—34no—
277#894—34no—
278#893—34no—
279#893—34no—
280D3×C4⋊C4—32no—
281D3×C4⋊C4—34no—
282#888—34no—
283#888—34no—
284#887—32no—
285#886—34no—
286#885—34no—
287#885—34no—
288#884—34no—
289#884—32no—
290#884—34no—
291#884—34no—
292#883—32no—
293#882—32no—
294#882—34no—
295#67⋊C4—34no—
296#67⋊C4—34no—
297#67⋊C4—34no—
298D3×C22⋊C4—34no—
299#878—32no—
300#878—34no—
301#878—34no—
302#877—34no—
303#875—32no—
304C4×D12—32no—
305#872—32no—
306C4×Dic6—32no—
307C23×C32C2411yescharacteristic
308C23×C32C2412yes—
309C22×C3⋊D3—24no—
310C22×C3⋊D3—22no—
311C22×C3⋊D3—22no—
312C22×C3⋊D3—24no—
313C22×C3⋊D3—41no—
314C22×C3⋊D3—42no—
315C22×C3⋊D3C2412yes—
316C22×C3⋊D3C2411yescharacteristic
317C22×C3⋊D3C2411yescharacteristic
318C22×C3×D3C2412yes—
319C32×Q8—22no—
320C32×D4—24no—
321C32×D4C2×D414yes—
322C2×C32×C4—24no—
323C2×C32×C4—22no—
324C2×C32×C4C2412yes—
325C2×C32×C4C2411yescharacteristic
326C2×C32×C4C2411yescharacteristic
327#638—24no—
328#638—24no—
329#638C2×D418yes—
330C2×C3⋊Dic3—22no—
331C2×C3⋊Dic3C2×D418yes—
332C2×C3⋊Dic3C2411yescharacteristic
333C2×C3⋊Dic3C2412yes—
334C2×C3⋊Dic3C2411yescharacteristic
335C4⋊(C3⋊D3)—24no—
336C4⋊(C3⋊D3)—22no—
337C4×C3⋊D3—22no—
338C4×C3⋊D3—22no—
339C4×C3⋊D3—22no—
340C4×C3⋊D3—24no—
341C4×C3⋊D3—24no—
342C4×C3⋊D3—24no—
343C4×C3⋊D3C2×D414yes—
344#634—24no—
345#634C2×D414yes—
346C3×#67—28no—
347C3×#67—42no—
348C2×C3×Dic3—28no—
349C2×C3×Dic3—44no—
350C2×C3×Dic3C2412yes—
351C2×C3×Dic3C2414yes—
352C2×C3×Dic3C2412yes—
353C2×C3×Dic3C2414yes—
354C2×C3×Dic3C2412yes—
355C3×C4×D3—24no—
356C3×Dic6—24no—
357#627—28no—
358#627—24no—
359#627—22no—
360#626—24no—
361#626—24no—
362#626—44no—
363#625—22no—
364#624—24no—
365#624—42no—
366D3×Dic3—28no—
367C2×2−1+4—91no—
368C22×#41—91no—
369D4×Q8—92no—
370#548—92no—
371#547—32no—
372#547—94no—
373#546—92no—
374#546—94no—
375#537—92no—
376#537—91no—
377#536—92no—
378#536—91no—
379#525—91no—
380#525—92no—
381C2×C22⋊Q8—92no—
382C2×C22⋊Q8—91no—
383#520—91no—
384C23×D3—32no—
385C23×D3—34no—
386C23×D3—62no—
387C23×D3—61no—
388C3×#41—28no—
389C3×#41—28no—
390C3×#41—68no—
391C2×C3×Q8—21no—
392C2×C3×Q8—32no—
393C2×C3×Q8C22×D312yes—
394C2×C3×D4—22no—
395C2×C3×D4—21no—
396C2×C3×D4—34no—
397C2×C3×D4—32no—
398C2×C3×D4C22×D314yes—
399C2×C3×D4C22×D312yes—
400C22×C3×C4—22no—
401C22×C3×C4—21no—
402C22×C3×C4—34no—
403C22×C3×C4—34no—
404C22×C3×C4—32no—
405C22×C3×C4C22×D314yes—
406C22×C3×C4C22×D312yes—
407C2×#67—34no—
408C2×#67—34no—
409C2×#67—34no—
410C2×#67—32no—
411C2×#67—32no—
412C2×#67—32no—
413C2×#67—34no—
414C2×#67—62no—
415C2×#67—62no—
416C2×#67—62no—
417C2×#67C22×D314yes—
418C2×#67C22×D312yes—
419C22×Dic3—34no—
420C22×Dic3—32no—
421C22×Dic3—34no—
422C22×Dic3—62no—
423C22×Dic3—61no—
424C22×Dic3C22×D314yes—
425C22×Dic3C22×D314yes—
426#239—68no—
427#239—68no—
428D3×Q8—68no—
429D3×Q8—68no—
430D3×Q8—68no—
431D3×Q8—68no—
432#237—28no—
433#237—316no—
434#237—68no—
435#237—616no—
436#237—616no—
437#237—616no—
438#237—616no—
439D3×D4—616no—
440D3×D4—616no—
441D3×D4—68no—
442D3×D4—68no—
443#235—68no—
444#235—68no—
445#235—616no—
446#235—616no—
447#235—616no—
448#235—68no—
449C2×D12—32no—
450C2×D12—32no—
451C2×D12—32no—
452C2×D12—34no—
453C2×D12—34no—
454C2×D12—62no—
455C2×D12—61no—
456C2×C4×D3—32no—
457C2×C4×D3—34no—
458C2×C4×D3—32no—
459C2×C4×D3—34no—
460C2×C4×D3—34no—
461C2×C4×D3—32no—
462C2×C4×D3—32no—
463C2×C4×D3—34no—
464C2×C4×D3—34no—
465C2×C4×D3—34no—
466C2×C4×D3—61no—
467C2×C4×D3—61no—
468C2×C4×D3—62no—
469C2×C4×D3—62no—
470C2×C4×D3—61no—
471C2×C4×D3—61no—
472C2×C4×D3—62no—
473C2×C4×D3—68no—
474C2×C4×D3—616no—
475C2×C4×D3—68no—
476C2×C4×D3—616no—
477C2×C4×D3C22×D312yes—
478C2×Dic6—32no—
479C2×Dic6—34no—
480C2×Dic6—32no—
481C2×Dic6—34no—
482C2×Dic6—34no—
483C2×Dic6—34no—
484C2×Dic6—61no—
485C2×Dic6—62no—
486C2×Dic6—68no—
487C2×Dic6—616no—
488C2×Dic6C22×D312yes—
489C3×C4⋊C4—32no—
490C3×C4⋊C4—34no—
491C3×C4⋊C4—34no—
492C3×C4⋊C4—34no—
493C3×C4⋊C4—32no—
494C3×C4⋊C4—34no—
495C3×C22⋊C4—34no—
496C3×C22⋊C4—34no—
497C3×C22⋊C4—32no—
498C3×C22⋊C4—34no—
499C3×C22⋊C4—32no—
500C3×C42—32no—
501#217—32no—
502#217C22×D314yes—
503#217C22×D314yes—
504#217C22×D312yes—
505(C2×D3)⋊C4—32no—
506(C2×D3)⋊C4—32no—
507(C2×D3)⋊C4—32no—
508(C2×D3)⋊C4—32no—
509(C2×D3)⋊C4—34no—
510(C2×D3)⋊C4—34no—
511(C2×D3)⋊C4—34no—
512(C2×D3)⋊C4—34no—
513(C2×D3)⋊C4—32no—
514(C2×D3)⋊C4—34no—
515(C2×D3)⋊C4—34no—
516(C2×D3)⋊C4—34no—
517(C2×D3)⋊C4—34no—
518(C2×D3)⋊C4C22×D312yes—
519(C2×D3)⋊C4C22×D314yes—
520C4⋊Dic3—32no—
521C4⋊Dic3—34no—
522C4⋊Dic3C22×D312yes—
523Dic3⋊C4—34no—
524Dic3⋊C4—32no—
525Dic3⋊C4—32no—
526Dic3⋊C4—34no—
527Dic3⋊C4—34no—
528Dic3⋊C4—32no—
529Dic3⋊C4—34no—
530Dic3⋊C4C22×D314yes—
531Dic3⋊C4C22×D314yes—
532Dic3⋊C4C22×D314yes—
533Dic3⋊C4C22×D312yes—
534Dic3⋊C4C22×D314yes—
535C4×Dic3—34no—
536C4×Dic3—34no—
537C4×Dic3C22×D312yes—
538C22×C32—21no—
539C22×C32—22no—
540C22×C32—22no—
541C22×C32—21no—
542C22×C32—21no—
543C22×C32C22×D414yes—
544C22×C32C2511yescharacteristic
545C2×C3⋊D3—21no—
546C2×C3⋊D3—21no—
547C2×C3⋊D3—22no—
548C2×C3⋊D3—21no—
549C2×C3⋊D3—21no—
550C2×C3⋊D3—22no—
551C2×C3⋊D3—22no—
552C2×C3⋊D3—44no—
553C2×C3⋊D3—48no—
554C2×C3⋊D3C22×D412yes—
555C2×C3⋊D32−1+412yescomplemented
556C2×C3×D3—22no—
557C2×C3×D3—22no—
558C2×C3×D3—22no—
559C32×C4—22no—
560C32×C4—21no—
561C32×C4C22×D412yes—
562C3⋊Dic3—21no—
563C3⋊Dic3C22×D414yes—
564C3⋊Dic3C22×D412yes—
565C3×Dic3—24no—
566C3×Dic3—22no—
567C3×Dic3—22no—
568C3×Dic3—24no—
569C3×Dic3—22no—
5702−1+4—188no—
571C2×#41—32no—
572C2×#41—91no—
573C2×#41—94no—
574C2×#41—92no—
575C2×#41—91no—
576C2×#41—91no—
577C2×#41—92no—
578C2×#41—92no—
579C2×#41—91no—
580C2×#41—188no—
581C2×#41D3211yescharacteristic
582C22×Q8—92no—
583C22×Q8—92no—
584C22×Q8—91no—
585C22×Q8—91no—
586C22×D4—92no—
587C22×D4—91no—
588C23×C4—92no—
589C23×C4—91no—
590C4⋊Q8—32no—
591C4⋊Q8—94no—
592#124—92no—
593#124—94no—
594#123—34no—
595#123—34no—
596#123—92no—
597#123—94no—
598#123—94no—
599C22⋊Q8—32no—
600C22⋊Q8—32no—
601C22⋊Q8—92no—
602C22⋊Q8—91no—
603C22⋊Q8—94no—
604C22⋊Q8—91no—
605C22⋊Q8—92no—
606C22⋊Q8—92no—
607C22⋊Q8—92no—
608C22⋊Q8—94no—
609C22⋊Q8—94no—
610C22⋊Q8—92no—
611C22⋊Q8—92no—
612#121—34no—
613#121—91no—
614#121—92no—
615#121—94no—
616#121—94no—
617#121—92no—
618#121—94no—
619#121—91no—
620#120—94no—
621#120—92no—
622C4×Q8—92no—
623C4×D4—32no—
624C4×D4—32no—
625C4×D4—92no—
626C4×D4—94no—
627C4×D4—94no—
628C4×D4—94no—
629#117—91no—
630#117—92no—
631C2×C4⋊C4—34no—
632C2×C4⋊C4—91no—
633C2×C4⋊C4—92no—
634C2×C4⋊C4—92no—
635C2×C22⋊C4—92no—
636C2×C22⋊C4—94no—
637C23×C3—21no—
638C23×C3—22no—
639C23×C3—32no—
640C23×C3C23×D312yes—
641C23×C3C23×D314yes—
642C22×D3—32no—
643C22×D3—32no—
644C22×D3—34no—
645C22×D3—61no—
646C22×D3—61no—
647C22×D3—62no—
648C22×D3—64no—
649C22×D3—64no—
650C22×D3—68no—
651C22×D3—64no—
652C22×D3—68no—
653C22×D3—68no—
654C22×D3—124no—
655C22×D3—122no—
656C22×D3—122no—
657C22×D3—124no—
658C22×D3—124no—
659C22×D3—122no—
660C22×D3C23×D312yes—
661C3×Q8—24no—
662C3×Q8—24no—
663C3×Q8—64no—
664C3×D4—28no—
665C3×D4—28no—
666C3×D4—24no—
667C3×D4—68no—
668C3×D4—122no—
669C3×D4D3×D418yes—
670C2×C3×C4—28no—
671C2×C3×C4—24no—
672C2×C3×C4—28no—
673C2×C3×C4—24no—
674C2×C3×C4—22no—
675C2×C3×C4—21no—
676C2×C3×C4—21no—
677C2×C3×C4—32no—
678C2×C3×C4—34no—
679C2×C3×C4—32no—
680C2×C3×C4—32no—
681C2×C3×C4—34no—
682C2×C3×C4—68no—
683C2×C3×C4—64no—
684C2×C3×C4—124no—
685C2×C3×C4C23×D314yes—
686C2×C3×C4C23×D312yes—
687C2×C3×C4C23×D312yes—
688#67—28no—
689#67—316no—
690#67—42no—
691#67—68no—
692#67—64no—
693#67—64no—
694#67—64no—
695#67—68no—
696#67—68no—
697#67—68no—
698#67—68no—
699#67—124no—
700C2×Dic3—28no—
701C2×Dic3—316no—
702C2×Dic3—34no—
703C2×Dic3—32no—
704C2×Dic3—32no—
705C2×Dic3—44no—
706C2×Dic3—68no—
707C2×Dic3—62no—
708C2×Dic3—61no—
709C2×Dic3—61no—
710C2×Dic3—68no—
711C2×Dic3—64no—
712C2×Dic3—64no—
713C2×Dic3C23×D312yes—
714C2×Dic3C23×D314yes—
715C2×Dic3C23×D312yes—
716C2×Dic3C23×D312yes—
717C2×Dic3C23×D314yes—
718D12—68no—
719D12—68no—
720D12—64no—
721D12—64no—
722D12—64no—
723D12—64no—
724D12—124no—
725C4×D3—24no—
726C4×D3—38no—
727C4×D3—64no—
728C4×D3—68no—
729C4×D3—64no—
730C4×D3—68no—
731C4×D3—68no—
732C4×D3—68no—
733C4×D3—68no—
734C4×D3—64no—
735C4×D3—64no—
736C4×D3—68no—
737C4×D3—64no—
738C4×D3—68no—
739C4×D3—64no—
740C4×D3—68no—
741C4×D3—64no—
742C4×D3—124no—
743Dic6—24no—
744Dic6—38no—
745Dic6—64no—
746Dic6—68no—
747Dic6—64no—
748Dic6—68no—
749Dic6—68no—
750Dic6—68no—
751Dic6—68no—
752C2×C32—24no—
753C2×C32—41no—
754C2×C32C23×D411yescharacteristic
755C2×C32C2×2−1+411yescharacteristic
756C2×C32#58511yescharacteristic
757C3⋊D3—22no—
758C3⋊D3—22no—
759C3⋊D3—42no—
760C3×D3—42no—
761C24—91no—
762C24—92no—
763#41—24no—
764#41—68no—
765#41—98no—
766#41—188no—
767#41—184no—
768#41—184no—
769#41—1816no—
770#41—188no—
771#41—188no—
772#41—184no—
773C2×Q8—32no—
774C2×Q8—91no—
775C2×Q8—92no—
776C2×Q8—94no—
777C2×Q8—91no—
778C2×Q8—92no—
779C2×Q8—188no—
780C2×Q8—188no—
781C2×Q8—184no—
782C2×Q8—184no—
783C2×Q8C2×D3211yescharacteristic
784C2×D4—34no—
785C2×D4—32no—
786C2×D4—92no—
787C2×D4—92no—
788C2×D4—94no—
789C2×D4—92no—
790C2×D4—91no—
791C2×D4—92no—
792C2×D4—92no—
793C2×D4—92no—
794C2×D4—91no—
795C2×D4—188no—
796C2×D4—184no—
797C2×D4C2×D3212yes—
798C2×D4C2×D3211yescharacteristic
799C22×C4—34no—
800C22×C4—34no—
801C22×C4—32no—
802C22×C4—92no—
803C22×C4—92no—
804C22×C4—94no—
805C22×C4—92no—
806C22×C4—91no—
807C22×C4—91no—
808C22×C4—91no—
809C22×C4—92no—
810C22×C4—91no—
811C22×C4—92no—
812C22×C4—91no—
813C22×C4—92no—
814C22×C4—188no—
815C22×C4—184no—
816C22×C4C2×D3212yes—
817C22×C4C2×D3211yescharacteristic
818C4⋊C4—32no—
819C4⋊C4—34no—
820C4⋊C4—34no—
821C4⋊C4—34no—
822C4⋊C4—32no—
823C4⋊C4—34no—
824C4⋊C4—91no—
825C4⋊C4—92no—
826C4⋊C4—94no—
827C4⋊C4—94no—
828C4⋊C4—91no—
829C4⋊C4—92no—
830C22⋊C4—34no—
831C22⋊C4—34no—
832C22⋊C4—32no—
833C22⋊C4—32no—
834C22⋊C4—34no—
835C22⋊C4—92no—
836C22⋊C4—94no—
837C22⋊C4—94no—
838C22⋊C4—94no—
839C22⋊C4—92no—
840C22⋊C4—94no—
841C22⋊C4—92no—
842C42—32no—
843C42—94no—
844C22×C3—24no—
845C22×C3—24no—
846C22×C3—22no—
847C22×C3—22no—
848C22×C3—22no—
849C22×C3—22no—
850C22×C3—24no—
851C22×C3—21no—
852C22×C3—42no—
853C22×C3—42no—
854C22×C3—41no—
855C22×C3—41no—
856C22×C3—62no—
857C22×C3—62no—
858C22×C3—62no—
859C22×C3C2×D3×D418yes—
860C22×C3C24×D312yes—
861C2×D3—22no—
862C2×D3—22no—
863C2×D3—22no—
864C2×D3—34no—
865C2×D3—34no—
866C2×D3—62no—
867C2×D3—62no—
868C2×D3—62no—
869C2×D3—62no—
870C2×D3—62no—
871C2×D3—62no—
872C2×D3—62no—
873C2×D3—62no—
874C2×D3—64no—
875C2×D3—64no—
876C2×D3—64no—
877C2×D3—64no—
878C2×D3—121no—
879C2×D3—121no—
880C2×D3—122no—
881C2×D3—122no—
882C2×D3—128no—
883C2×D3—1216no—
884C2×D3—1216no—
885C2×D3—128no—
886C3×C4—24no—
887C3×C4—22no—
888C3×C4—24no—
889C3×C4—22no—
890C3×C4—22no—
891C3×C4—62no—
892C3×C4—64no—
893C3×C4—64no—
894C3×C4—62no—
895C3×C4—62no—
896C3×C4C2×D3×D414yes—
897Dic3—24no—
898Dic3—22no—
899Dic3—24no—
900Dic3—22no—
901Dic3—22no—
902Dic3—38no—
903Dic3—34no—
904Dic3—64no—
905Dic3—62no—
906Dic3—62no—
907Dic3—62no—
908C32#348911yescharacteristic, complemented, Sylow
909C23—32no—
910C23—91no—
911C23—91no—
912C23—92no—
913C23—182no—
914C23—184no—
915C23—182no—
916C23—184no—
917C23—362no—
918C23—361no—
919C23C22×D3211yescharacteristic
920C23C22×D3212yes—
921Q8—22no—
922Q8—64no—
923Q8—94no—
924Q8—184no—
925Q8—182no—
926Q8—188no—
927Q8—184no—
928D4—24no—
929D4—68no—
930D4—98no—
931D4—122no—
932D4—184no—
933D4—184no—
934D4—184no—
935D4—184no—
936D4—182no—
937D4—184no—
938D4—182no—
939D4—364no—
940D4#381114yes—
941C2×C4—24no—
942C2×C4—22no—
943C2×C4—32no—
944C2×C4—32no—
945C2×C4—34no—
946C2×C4—32no—
947C2×C4—34no—
948C2×C4—68no—
949C2×C4—64no—
950C2×C4—98no—
951C2×C4—92no—
952C2×C4—91no—
953C2×C4—94no—
954C2×C4—91no—
955C2×C4—124no—
956C2×C4—182no—
957C2×C4—184no—
958C2×C4—184no—
959C2×C4—184no—
960C2×C4—182no—
961C2×C4—184no—
962C2×C4—188no—
963C2×C4—182no—
964C2×C4—182no—
965C2×C4—362no—
966C2×C4C22×D3211yescharacteristic
967C2×C4C22×D3212yes—
968C2×C4C22×D3211yescharacteristic
969C2×C3—28no—
970C2×C3—21no—
971C2×C3—21no—
972C2×C3—21no—
973C2×C3—44no—
974C2×C3—42no—
975C2×C3—42no—
976C2×C3—122no—
977C2×C3C22×D3×D412yes—
978C2×C3#596412yes—
979C2×C3D3×2−1+412yes—
980D3—42no—
981D3—64no—
982D3—64no—
983D3—64no—
984D3—122no—
985D3—124no—
986D3—124no—
987C22—22no—
988C22—22no—
989C22—21no—
990C22—21no—
991C22—21no—
992C22—62no—
993C22—62no—
994C22—62no—
995C22—92no—
996C22—92no—
997C22—181no—
998C22—181no—
999C22—181no—
1000C22—181no—
1001C22—182no—
1002C22—182no—
1003C22—182no—
1004C22—368no—
1005C22—364no—
1006C22C2×#381114yes—
1007C22C23×D3211yescharacteristic
1008C4—21no—
1009C4—22no—
1010C4—62no—
1011C4—62no—
1012C4—64no—
1013C4—62no—
1014C4—64no—
1015C4—92no—
1016C4—94no—
1017C4—181no—
1018C4C2×#381112yes—
1019C3—21no—
1020C3#8667712yescomplemented
1021C2—24no—
1022C2—41no—
1023C2—122no—
1024C2—182no—
1025C2—182no—
1026C2—362no—
1027C2#1059669411yescharacteristic
1028C2#1059669511yescharacteristic
1029C2C22×#381111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×#41C22
hypercenterC2×#41D32
hypocenterC32#3489
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×#64309C2semidirect
3. C3×#5824C2semidirect
4. #10595404C2semidirect
5. #10595361C2semidirect
6. #10595350C2semidirect
7. #10595271C2semidirect
8. #10595254C2semidirect
9. #10595219C2semidirect
10. #10595166C2semidirect
11. #10595163C2semidirect
12. #10595016C2semidirect
13. #10594925C2semidirect
14. #10594920C2semidirect
15. #10594917C2semidirect
16. #10594916C2semidirect
17. C2×#63865C2semidirect
31. C2×C3×#237C22semidirect
32. C22×#627C22semidirect
33. C2×#3805C22semidirect
34. C2×#3804C22semidirect
36. C2×#3798C22semidirect
37. C2×#3797C22semidirect
38. C2×D3×Dic6C22semidirect
39. C3×#946C22semidirect
40. C3×#944C22semidirect
41. C3×#939C22semidirect
42. C3×#935C22semidirect
43. C3×D4×Dic3C22semidirect
44. C3×#929C22semidirect
45. C3×C4×#67C22semidirect
46. C3×#924C22semidirect
47. C2×C3×Dic3⋊C4C22semidirect
48. #63982C22semidirect
49. #63982C22semidirect
52. #63980C22semidirect
53. #63978C22semidirect
55. #63971C22semidirect
56. C2×#3724C22semidirect
57. #63966C22semidirect
59. #63957C22semidirect
60. #63953C22semidirect
61. #63952C22semidirect
63. #63912C22semidirect
64. #63910C22semidirect
65. #63909C22semidirect
67. #63900C22semidirect
68. #63897C22semidirect
69. #63896C22semidirect
70. #63883C22semidirect
72. #63881C22semidirect
73. #63874C22semidirect
78. #63865C22semidirect
79. #63865C22semidirect
80. #63865C22semidirect
81. #63865C22semidirect
82. #63864C22semidirect
83. #63853C22semidirect
84. #63844C22semidirect
85. #63840C22semidirect
91. #5824D3semidirect
126. #3830D4semidirect
212. C2×#237C2×D3semidirect
240. #946C2×D3semidirect
241. #944C2×D3semidirect
245. #939C2×D3semidirect
248. #935C2×D3semidirect
249. D4×Dic3C2×D3semidirect
253. #929C2×D3semidirect
256. C4×#67C2×D3semidirect
259. #924C2×D3semidirect
261. C2×Dic3⋊C4C2×D3semidirect
555. C2×C3⋊D32−1+4semidirect
908. C32#3489semidirect
1020. C3#86677semidirect

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×#643092
C3×#58242
#105954042
#105953612
#105953502
#105952712
#105952542
#105952192
#105951662
#105951632
#105950162
#105949252
#105949202
#105949172
#105949162
C2×#638652
#866773