Finite Group Databasebeta

← #11904756

Subgroups — #11904756

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
1C22×#3830C211yesmaximal, characteristic, complemented
2C2×#64309C211yesmaximal, characteristic, complemented
3C3×#5806C212yesmaximal, complemented
4C2×#63982C212yesmaximal, complemented
5#10595501C212yesmaximal, complemented
6#10595500C214yesmaximal, complemented
7#10595271C212yesmaximal, complemented
8#10595248C212yesmaximal, complemented
9#10595240C211yesmaximal, characteristic, complemented
10#10595219C211yesmaximal, characteristic, complemented
11#10595171C211yesmaximal, characteristic, complemented
12#10595166C212yesmaximal, complemented
13#10595162C214yesmaximal, complemented
14#10595161C212yesmaximal, complemented
15#10595016C211yesmaximal, characteristic, complemented
16#10594925C211yesmaximal, characteristic, complemented
17#10594915C212yesmaximal, complemented
18#86630—32nomaximal
19C22×C32×D4C2211yescharacteristic
20C22×#638C2212yes—
21C23×C3⋊Dic3C2212yes—
22C2×#3830—28no—
23C2×#3830C2211yescharacteristic
24C2×#3830C2212yes—
25C2×#3830C2212yes—
26C2×#3830C2211yescharacteristic
27C2×#3830C2211yescharacteristic
28C2×#3830C2211yescharacteristic
29C22×C4×C3⋊D3C2211yescharacteristic
30C22×#634C2211yescharacteristic
31C2×C3×#237C2212yescomplemented
32C22×#627C2212yescomplemented
33C2×#3805C2212yescomplemented
34C2×#3804C2214yescomplemented
35#64309—28no—
36C2×#3798C2211yescharacteristic, complemented
37C2×#3797C2211yescharacteristic, complemented
38C2×D3×Dic6C2212yescomplemented
39C3×#953C2214yes—
40C2×C3×#217C2214yes—
41C3×#939C2214yescomplemented
42C3×#938C2212yescomplemented
43C3×#936C2212yescomplemented
44C3×#935C2214yescomplemented
45C3×D4×Dic3C2212yescomplemented
46C3×C4×#67C2212yes—
47C3×#924C2212yes—
48#63982C2214yes—
49#63982C2212yes—
50#63982C2211yescharacteristic
51#63982C2214yescomplemented
52#63982C2212yescomplemented
53#63982C2212yescomplemented
54#63982C2212yescomplemented
55#63981C2212yes—
56#63980C2211yescharacteristic
57#63980C2212yescomplemented
58#63978C2214yescomplemented
59#63975C2214yescomplemented
60#63974C2212yes—
61#67⋊Dic3C2214yes—
62#67⋊Dic3C2214yescomplemented
63#63971C2214yescomplemented
64C2×#3724C2212yescomplemented
65#63966C2214yescomplemented
66C2×Dic3⋊Dic3C2214yescomplemented
67#63962C2214yescomplemented
68#63958C2214yescomplemented
69#63957C2212yescomplemented
70#63953C2214yescomplemented
71#63952C2214yescomplemented
72#63912C2211yescharacteristic, complemented
73C4×#626C2212yescomplemented
74#63900C2211yescharacteristic, complemented
75#63896C2214yescomplemented
76#63883C2212yescomplemented
77#63874C2211yescharacteristic, complemented
78#63871C2212yescomplemented
79#63866C2212yescomplemented
80#63865C2212yescomplemented
81#63865C2211yescharacteristic, complemented
82#63857C2212yescomplemented
83#63853C2212yescomplemented
84#63844C2212yescomplemented
85#63840C2214yescomplemented
86C2×#1010—32no—
87C22×#237—32no—
88C22×#237—61no—
89C3×#546—32no—
90#5824—32no—
91#5806D312yescomplemented
92#5677—32no—
93#5675—32no—
94#5655—34no—
95#5648—34no—
96#5632—32no—
97D3×C22⋊Q8—32no—
98#5611—34no—
99#5608—32no—
100#5598—32no—
101#5597—34no—
102#5591—34no—
103#5586—34no—
104#5555—32no—
105#5547—32no—
106#5546—32no—
107D4×Dic6—32no—
108#5490—34no—
109C2×#878—34no—
110C24×C32C2312yes—
111C23×C3⋊D3C2311yescharacteristic
112C2×C32×D4—24no—
113C2×C32×D4C2312yes—
114C2×C32×D4C2311yescharacteristic
115C2×C32×D4C2311yescharacteristic
116C22×C32×C4C2311yescharacteristic
117C2×#638—28no—
118C2×#638C2312yes—
119C2×#638C2312yes—
120C2×#638C2312yes—
121C2×#638C2312yes—
122C22×C3⋊Dic3—28no—
123C22×C3⋊Dic3C2312yes—
124C22×C3⋊Dic3C2311yescharacteristic
125C22×C3⋊Dic3C2312yes—
126C22×C3⋊Dic3C2312yes—
127C22×C3⋊Dic3C2312yes—
128C22×C3⋊Dic3C2312yes—
129#3830—24no—
130#3830—28no—
131#3830—28no—
132#3830—24no—
133#3830—24no—
134#3830D418yescomplemented
135C2×C4×C3⋊D3—24no—
136C2×C4×C3⋊D3C2311yescharacteristic
137C2×C4×C3⋊D3C2311yescharacteristic
138C2×C4×C3⋊D3C2311yescharacteristic
139C2×C4×C3⋊D3C2311yescharacteristic
140C2×#634—24no—
141C2×#634C2312yes—
142C2×#634C2311yescharacteristic
143C2×#634C2311yescharacteristic
144C2×C3×#67C2312yes—
145C2×C3×#67C2314yes—
146C2×C3×#67C2314yes—
147C22×C3×Dic3C2314yes—
148C22×C3×Dic3C2314yes—
149C3×#237—28no—
150C2×C3×C4×D3C2312yes—
151C2×C3×Dic6C2312yes—
152C2×#627—28no—
153C2×#627C2314yes—
154C2×#627C2312yes—
155C2×#627C2311yescharacteristic
156C2×#626C2312yes—
157C2×#626C2312yes—
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×#217C2314yes—
171C3×#217C2314yes—
172C3×#217C2314yes—
173C3×(C2×D3)⋊C4C2312yes—
174C3×C4⋊Dic3C2312yes—
175C3×Dic3⋊C4C2314yes—
176C3×Dic3⋊C4C2312yes—
177C3×C4×Dic3C2312yes—
178#3724C2314yes—
179#3724C2311yescharacteristic
180#3724C2312yes—
181#3724C2311yescharacteristic
182Dic3⋊Dic3C2314yes—
183Dic3⋊Dic3C2314yes—
184Dic3⋊Dic3C2312yes—
185Dic3⋊Dic3C2314yes—
186Dic3⋊Dic3C2314yes—
187#3722C2312yes—
188#3722C2314yes—
189#3722C2312yes—
190(C2×D3)⋊Dic3C2312yes—
191(C2×D3)⋊Dic3C2314yes—
192Dic32C2314yes—
193#3489—91noSylow
194C2×C3×#41—32no—
195C22×C3×D4—21no—
196C22×C3×D4C2×D312yes—
197C22×#67—34no—
198C22×#67—62no—
199C23×Dic3—34no—
200C23×Dic3—62no—
201#1010—616no—
202C2×D3×Q8—32no—
203C2×D3×Q8—32no—
204C2×#237—32no—
205C2×#237—34no—
206C2×#237—34no—
207C2×#237—32no—
208C2×#237—32no—
209C2×#237—32no—
210C2×#237—34no—
211C2×#237—34no—
212C2×#237—61no—
213C2×#237—62no—
214C2×#237—61no—
215C2×#237—62no—
216C2×#237—61no—
217C2×#237—61no—
218C2×#237—616no—
219C2×#237—616no—
220C2×#237C2×D312yescomplemented
221C2×#235—34no—
222C2×#235—32no—
223C22×C4×D3—32no—
224C22×C4×D3—61no—
225C22×Dic6—32no—
226C22×Dic6—34no—
227C22×Dic6—32no—
228C22×Dic6—61no—
229C3×#124—32no—
230C3×#123—34no—
231C3×C22⋊Q8—32no—
232C3×#121—32no—
233C3×#121—34no—
234C3×#120—34no—
235C3×C4×D4—32no—
236C3×C4×D4—32no—
237C2×C3×C22⋊C4—34no—
238#953C2×D314yes—
239C2×#217C2×D314yes—
240#946—32no—
241#944—32no—
242#939—32no—
243#939—34no—
244#939—34no—
245#939—34no—
246#939C2×D314yescomplemented
247#938—34no—
248#938C2×D312yescomplemented
249#937—32no—
250#936C2×D312yescomplemented
251#935—34no—
252#935C2×D314yescomplemented
253D4×Dic3—34no—
254D4×Dic3—34no—
255D4×Dic3C2×D312yescomplemented
256#930—34no—
257#929—34no—
258C4×#67—34no—
259C4×#67—32no—
260C4×#67C2×D312yes—
261C2×C4⋊Dic3—34no—
262#924—32no—
263#924C2×D312yes—
264C2×Dic3⋊C4—34no—
265C2×Dic3⋊C4—34no—
266#897—32no—
267#897—32no—
268#896—34no—
269#896—32no—
270#896—34no—
271#894—32no—
272D3×C4⋊C4—32no—
273D3×C4⋊C4—34no—
274#888—34no—
275#888—34no—
276#887—32no—
277#886—34no—
278#886—34no—
279#885—34no—
280#885—34no—
281#884—34no—
282#884—34no—
283#884—32no—
284#883—34no—
285#883—34no—
286#883—32no—
287#882—32no—
288#67⋊C4—34no—
289#67⋊C4—34no—
290#67⋊C4—34no—
291D3×C22⋊C4—34no—
292#878—34no—
293#878—34no—
294#878—34no—
295#878—34no—
296#878—34no—
297#878—34no—
298#878—32no—
299#878—34no—
300#878—34no—
301#878—34no—
302#877—34no—
303C4×D12—32no—
304#872—32no—
305#869—32no—
306C4×Dic6—32no—
307C23×C32—24no—
308C23×C32—24no—
309C23×C32—42no—
310C23×C32C2412yes—
311C23×C32C2412yes—
312C23×C32C2411yescharacteristic
313C22×C3⋊D3—22no—
314C22×C3⋊D3—22no—
315C22×C3⋊D3—41no—
316C22×C3⋊D3C2411yescharacteristic
317C22×C3⋊D3C2411yescharacteristic
318C22×C3×D3C2412yes—
319C32×D4—24no—
320C32×D4—22no—
321C32×D4C2×D414yes—
322C2×C32×C4—22no—
323C2×C32×C4C2411yescharacteristic
324C2×C32×C4C2411yescharacteristic
325#638—24no—
326#638—24no—
327#638—24no—
328#638C2×D418yes—
329C2×C3⋊Dic3—24no—
330C2×C3⋊Dic3—24no—
331C2×C3⋊Dic3—22no—
332C2×C3⋊Dic3—24no—
333C2×C3⋊Dic3—24no—
334C2×C3⋊Dic3C2×D418yes—
335C2×C3⋊Dic3C2412yes—
336C2×C3⋊Dic3C2411yescharacteristic
337C2×C3⋊Dic3C2412yes—
338C2×C3⋊Dic3C2411yescharacteristic
339C4×C3⋊D3—22no—
340C4×C3⋊D3—22no—
341C4×C3⋊D3—22no—
342C4×C3⋊D3C2×D414yes—
343#634—22no—
344#634—24no—
345#634C2×D414yes—
346C3×#67—28no—
347C3×#67—24no—
348C3×#67—44no—
349C2×C3×Dic3—28no—
350C2×C3×Dic3—44no—
351C2×C3×Dic3C2412yes—
352C2×C3×Dic3C2414yes—
353C2×C3×Dic3C2412yes—
354C2×C3×Dic3C2414yes—
355C2×C3×Dic3C2412yes—
356C3×C4×D3—24no—
357C3×Dic6—24no—
358#627—28no—
359#627—24no—
360#627—22no—
361#626—24no—
362#626—42no—
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—92no—
372#547—94no—
373#546—32no—
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—
384C24×C3—22no—
385C24×C3C22×D314yes—
386C23×D3—32no—
387C23×D3—61no—
388C3×#41—68no—
389C2×C3×Q8—32no—
390C2×C3×D4—28no—
391C2×C3×D4—28no—
392C2×C3×D4—22no—
393C2×C3×D4—21no—
394C2×C3×D4—21no—
395C2×C3×D4—32no—
396C2×C3×D4—34no—
397C2×C3×D4—34no—
398C2×C3×D4C22×D314yes—
399C2×C3×D4C22×D312yes—
400C2×C3×D4C22×D312yes—
401C22×C3×C4—21no—
402C22×C3×C4—34no—
403C22×C3×C4—34no—
404C22×C3×C4—32no—
405C22×C3×C4C22×D312yes—
406C2×#67—34no—
407C2×#67—34no—
408C2×#67—34no—
409C2×#67—34no—
410C2×#67—32no—
411C2×#67—32no—
412C2×#67—32no—
413C2×#67—62no—
414C2×#67—62no—
415C2×#67—62no—
416C2×#67—62no—
417C2×#67—616no—
418C2×#67—616no—
419C2×#67C22×D312yes—
420C2×#67C22×D314yes—
421C2×#67C22×D314yes—
422C22×Dic3—34no—
423C22×Dic3—32no—
424C22×Dic3—34no—
425C22×Dic3—34no—
426C22×Dic3—34no—
427C22×Dic3—34no—
428C22×Dic3—34no—
429C22×Dic3—62no—
430C22×Dic3—61no—
431C22×Dic3—62no—
432C22×Dic3—62no—
433C22×Dic3—62no—
434C22×Dic3—62no—
435C22×Dic3—616no—
436C22×Dic3—616no—
437C22×Dic3C22×D314yes—
438C22×Dic3C22×D314yes—
439D3×Q8—68no—
440D3×Q8—68no—
441#237—28no—
442#237—316no—
443#237—68no—
444#237—68no—
445#237—68no—
446#237—616no—
447#237—616no—
448#237—616no—
449#237—616no—
450#237—68no—
451#237—616no—
452#237—616no—
453#237—68no—
454#237—68no—
455#237—68no—
456#235—68no—
457#235—616no—
458C2×D12—32no—
459C2×D12—32no—
460C2×C4×D3—32no—
461C2×C4×D3—34no—
462C2×C4×D3—32no—
463C2×C4×D3—32no—
464C2×C4×D3—32no—
465C2×C4×D3—34no—
466C2×C4×D3—34no—
467C2×C4×D3—61no—
468C2×C4×D3—61no—
469C2×C4×D3—61no—
470C2×C4×D3—61no—
471C2×C4×D3—68no—
472C2×C4×D3—68no—
473C2×C4×D3C22×D312yes—
474C2×Dic6—32no—
475C2×Dic6—32no—
476C2×Dic6—34no—
477C2×Dic6—32no—
478C2×Dic6—34no—
479C2×Dic6—34no—
480C2×Dic6—34no—
481C2×Dic6—61no—
482C2×Dic6—62no—
483C2×Dic6—61no—
484C2×Dic6—68no—
485C2×Dic6—68no—
486C2×Dic6—616no—
487C2×Dic6—68no—
488C2×Dic6C22×D312yes—
489C3×C4⋊C4—32no—
490C3×C4⋊C4—32no—
491C3×C4⋊C4—34no—
492C3×C22⋊C4—34no—
493C3×C22⋊C4—32no—
494C3×C22⋊C4—34no—
495C3×C22⋊C4—34no—
496C3×C22⋊C4—34no—
497C3×C22⋊C4—34no—
498C3×C22⋊C4—32no—
499C3×C42—32no—
500#217—34no—
501#217—32no—
502#217C22×D314yes—
503#217C22×D312yes—
504#217C22×D314yes—
505#217C22×D314yes—
506#217C22×D314yes—
507#217C22×D314yes—
508(C2×D3)⋊C4—32no—
509(C2×D3)⋊C4—34no—
510(C2×D3)⋊C4—32no—
511(C2×D3)⋊C4—32no—
512(C2×D3)⋊C4—32no—
513(C2×D3)⋊C4—34no—
514(C2×D3)⋊C4—34no—
515(C2×D3)⋊C4—32no—
516(C2×D3)⋊C4C22×D312yes—
517C4⋊Dic3—34no—
518C4⋊Dic3—34no—
519C4⋊Dic3—32no—
520C4⋊Dic3—34no—
521C4⋊Dic3—34no—
522C4⋊Dic3C22×D312yes—
523Dic3⋊C4—34no—
524Dic3⋊C4—32no—
525Dic3⋊C4—32no—
526Dic3⋊C4—34no—
527Dic3⋊C4—32no—
528Dic3⋊C4—34no—
529Dic3⋊C4—34no—
530Dic3⋊C4—34no—
531Dic3⋊C4—34no—
532Dic3⋊C4—34no—
533Dic3⋊C4C22×D314yes—
534Dic3⋊C4C22×D312yes—
535C4×Dic3—34no—
536C4×Dic3—34no—
537C4×Dic3C22×D312yes—
538C22×C32—21no—
539C22×C32—21no—
540C22×C32—22no—
541C22×C32—22no—
542C22×C32—22no—
543C22×C32—22no—
544C22×C32—22no—
545C22×C32—48no—
546C22×C32C22×D414yes—
547C22×C322−1+412yescomplemented
548C22×C32C2511yescharacteristic
549C2×C3⋊D3—21no—
550C2×C3⋊D3—21no—
551C2×C3⋊D3—21no—
552C2×C3⋊D3—21no—
553C2×C3⋊D3—21no—
554C2×C3⋊D3—44no—
555C2×C3⋊D3C22×D412yes—
556C2×C3×D3—22no—
557C2×C3×D3—22no—
558C2×C3×D3—22no—
559C32×C4—21no—
560C32×C4C22×D412yes—
561C3⋊Dic3—22no—
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—92no—
577C2×#41—91no—
578C2×#41—91no—
579C2×#41—92no—
580C2×#41—91no—
581C2×#41—188no—
582C22×Q8—92no—
583C22×Q8—92no—
584C22×Q8—91no—
585C22×Q8—91no—
586C22×D4—92no—
587C22×D4D3211yescharacteristic
588C23×C4—92no—
589C23×C4—91no—
590C4⋊Q8—92no—
591C4⋊Q8—94no—
592#124—32no—
593#124—94no—
594#123—34no—
595#123—94no—
596#123—92no—
597#123—94no—
598#123—94no—
599C22⋊Q8—32no—
600C22⋊Q8—91no—
601C22⋊Q8—92no—
602C22⋊Q8—92no—
603C22⋊Q8—92no—
604C22⋊Q8—94no—
605C22⋊Q8—94no—
606C22⋊Q8—92no—
607C22⋊Q8—94no—
608C22⋊Q8—92no—
609C22⋊Q8—91no—
610C22⋊Q8—92no—
611C22⋊Q8—92no—
612#121—34no—
613#121—32no—
614#121—91no—
615#121—94no—
616#121—94no—
617#121—94no—
618#121—91no—
619#121—92no—
620#120—34no—
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—91no—
632C2×C4⋊C4—92no—
633C2×C4⋊C4—92no—
634C2×C4⋊C4—94no—
635C2×C22⋊C4—34no—
636C2×C22⋊C4—92no—
637C23×C3—28no—
638C23×C3—28no—
639C23×C3—28no—
640C23×C3—21no—
641C23×C3—22no—
642C23×C3—22no—
643C23×C3—32no—
644C23×C3—44no—
645C23×C3—44no—
646C23×C3—44no—
647C23×C3C23×D314yes—
648C23×C3C23×D314yes—
649C23×C3C23×D312yes—
650C22×D3—32no—
651C22×D3—32no—
652C22×D3—61no—
653C22×D3—61no—
654C22×D3—64no—
655C22×D3—64no—
656C22×D3—64no—
657C22×D3—122no—
658C22×D3—122no—
659C22×D3—122no—
660C22×D3C23×D312yes—
661C3×Q8—64no—
662C3×D4—28no—
663C3×D4—24no—
664C3×D4—28no—
665C3×D4—24no—
666C3×D4—24no—
667C3×D4—68no—
668C3×D4—64no—
669C3×D4—124no—
670C3×D4D3×D418yes—
671C2×C3×C4—24no—
672C2×C3×C4—24no—
673C2×C3×C4—21no—
674C2×C3×C4—21no—
675C2×C3×C4—32no—
676C2×C3×C4—34no—
677C2×C3×C4—32no—
678C2×C3×C4—32no—
679C2×C3×C4—34no—
680C2×C3×C4—68no—
681C2×C3×C4—64no—
682C2×C3×C4—124no—
683C2×C3×C4C23×D312yes—
684C2×C3×C4C23×D312yes—
685#67—28no—
686#67—24no—
687#67—316no—
688#67—44no—
689#67—68no—
690#67—64no—
691#67—64no—
692#67—68no—
693#67—68no—
694#67—68no—
695#67—68no—
696#67—68no—
697#67—68no—
698#67—122no—
699C2×Dic3—28no—
700C2×Dic3—316no—
701C2×Dic3—34no—
702C2×Dic3—32no—
703C2×Dic3—34no—
704C2×Dic3—32no—
705C2×Dic3—44no—
706C2×Dic3—68no—
707C2×Dic3—62no—
708C2×Dic3—62no—
709C2×Dic3—61no—
710C2×Dic3—61no—
711C2×Dic3—68no—
712C2×Dic3—68no—
713C2×Dic3—64no—
714C2×Dic3—68no—
715C2×Dic3—68no—
716C2×Dic3—68no—
717C2×Dic3—64no—
718C2×Dic3—68no—
719C2×Dic3—68no—
720C2×Dic3—68no—
721C2×Dic3—68no—
722C2×Dic3C23×D312yes—
723C2×Dic3C23×D314yes—
724C2×Dic3C23×D312yes—
725C2×Dic3C23×D312yes—
726C2×Dic3C23×D314yes—
727D12—64no—
728D12—122no—
729C4×D3—24no—
730C4×D3—38no—
731C4×D3—64no—
732C4×D3—68no—
733C4×D3—64no—
734C4×D3—68no—
735C4×D3—64no—
736C4×D3—64no—
737C4×D3—64no—
738C4×D3—64no—
739C4×D3—64no—
740C4×D3—124no—
741Dic6—24no—
742Dic6—38no—
743Dic6—64no—
744Dic6—68no—
745Dic6—64no—
746Dic6—68no—
747Dic6—68no—
748Dic6—68no—
749Dic6—68no—
750Dic6—64no—
751Dic6—64no—
752C2×C32—22no—
753C2×C32—24no—
754C2×C32—42no—
755C2×C32C23×D411yescharacteristic
756C2×C32C2×2−1+411yescharacteristic
757C2×C32#58511yescharacteristic
758C3⋊D3—22no—
759C3⋊D3—41no—
760C3×D3—42no—
761C24—91no—
762C24C2×D3212yes—
763#41—68no—
764#41—98no—
765#41—184no—
766#41—1816no—
767#41—188no—
768#41—184no—
769#41—188no—
770#41—188no—
771#41—184no—
772#41—184no—
773C2×Q8—32no—
774C2×Q8—91no—
775C2×Q8—92no—
776C2×Q8—94no—
777C2×Q8—91no—
778C2×Q8—92no—
779C2×Q8—91no—
780C2×Q8—184no—
781C2×Q8—188no—
782C2×Q8—188no—
783C2×Q8—184no—
784C2×D4—24no—
785C2×D4—32no—
786C2×D4—34no—
787C2×D4—34no—
788C2×D4—92no—
789C2×D4—92no—
790C2×D4—92no—
791C2×D4—91no—
792C2×D4—92no—
793C2×D4—92no—
794C2×D4—92no—
795C2×D4—188no—
796C2×D4C2×D3212yes—
797C2×D4C2×D3211yescharacteristic
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—92no—
808C22×C4—92no—
809C22×C4—92no—
810C22×C4—91no—
811C22×C4—92no—
812C22×C4—91no—
813C22×C4—91no—
814C22×C4—91no—
815C22×C4—184no—
816C22×C4—188no—
817C22×C4C2×D3211yescharacteristic
818C4⋊C4—32no—
819C4⋊C4—34no—
820C4⋊C4—32no—
821C4⋊C4—91no—
822C4⋊C4—92no—
823C4⋊C4—92no—
824C4⋊C4—94no—
825C4⋊C4—94no—
826C4⋊C4—94no—
827C4⋊C4—94no—
828C4⋊C4—91no—
829C4⋊C4—94no—
830C22⋊C4—32no—
831C22⋊C4—34no—
832C22⋊C4—34no—
833C22⋊C4—34no—
834C22⋊C4—34no—
835C22⋊C4—34no—
836C22⋊C4—32no—
837C22⋊C4—94no—
838C22⋊C4—92no—
839C22⋊C4—92no—
840C22⋊C4—92no—
841C22⋊C4—94no—
842C42—32no—
843C42—94no—
844C22×C3—22no—
845C22×C3—22no—
846C22×C3—22no—
847C22×C3—24no—
848C22×C3—24no—
849C22×C3—22no—
850C22×C3—24no—
851C22×C3—24no—
852C22×C3—24no—
853C22×C3—24no—
854C22×C3—22no—
855C22×C3—24no—
856C22×C3—21no—
857C22×C3—42no—
858C22×C3—42no—
859C22×C3—42no—
860C22×C3—42no—
861C22×C3—416no—
862C22×C3—416no—
863C22×C3—62no—
864C22×C3—62no—
865C22×C3—62no—
866C22×C3C2×D3×D418yes—
867C22×C3#101014yescomplemented
868C22×C3C24×D312yes—
869C2×D3—22no—
870C2×D3—22no—
871C2×D3—22no—
872C2×D3—34no—
873C2×D3—62no—
874C2×D3—62no—
875C2×D3—62no—
876C2×D3—62no—
877C2×D3—62no—
878C2×D3—62no—
879C2×D3—62no—
880C2×D3—121no—
881C2×D3—121no—
882C2×D3—121no—
883C2×D3—121no—
884C2×D3—128no—
885C2×D3—128no—
886C3×C4—22no—
887C3×C4—22no—
888C3×C4—22no—
889C3×C4—62no—
890C3×C4—64no—
891C3×C4—62no—
892C3×C4—64no—
893C3×C4—62no—
894C3×C4C2×D3×D414yes—
895Dic3—24no—
896Dic3—22no—
897Dic3—22no—
898Dic3—24no—
899Dic3—22no—
900Dic3—38no—
901Dic3—34no—
902Dic3—64no—
903Dic3—62no—
904Dic3—64no—
905Dic3—62no—
906Dic3—64no—
907Dic3—62no—
908C32#348911yescharacteristic, complemented, Sylow
909C23—24no—
910C23—24no—
911C23—32no—
912C23—42no—
913C23—91no—
914C23—91no—
915C23—182no—
916C23—182no—
917C23—361no—
918C23C22×D3212yes—
919C23C22×D3211yescharacteristic
920C23C22×D3212yes—
921Q8—64no—
922Q8—94no—
923Q8—184no—
924Q8—182no—
925Q8—188no—
926Q8—184no—
927Q8—182no—
928D4—24no—
929D4—22no—
930D4—64no—
931D4—68no—
932D4—98no—
933D4—124no—
934D4—184no—
935D4—184no—
936D4—182no—
937D4—184no—
938D4—184no—
939D4—362no—
940D4#381114yes—
941C2×C4—22no—
942C2×C4—32no—
943C2×C4—32no—
944C2×C4—34no—
945C2×C4—32no—
946C2×C4—34no—
947C2×C4—68no—
948C2×C4—64no—
949C2×C4—98no—
950C2×C4—92no—
951C2×C4—91no—
952C2×C4—94no—
953C2×C4—91no—
954C2×C4—92no—
955C2×C4—124no—
956C2×C4—182no—
957C2×C4—182no—
958C2×C4—184no—
959C2×C4—188no—
960C2×C4—182no—
961C2×C4—184no—
962C2×C4—184no—
963C2×C4—184no—
964C2×C4—184no—
965C2×C4—182no—
966C2×C4—362no—
967C2×C4C22×D3211yescharacteristic
968C2×C4C22×D3211yescharacteristic
969C2×C3—24no—
970C2×C3—24no—
971C2×C3—28no—
972C2×C3—21no—
973C2×C3—21no—
974C2×C3—21no—
975C2×C3—44no—
976C2×C3—44no—
977C2×C3—44no—
978C2×C3—122no—
979C2×C3C22×D3×D412yes—
980C2×C3C2×#101012yes—
981C2×C3#596612yes—
982D3—42no—
983D3—64no—
984D3—122no—
985D3—122no—
986D3—122no—
987C22—22no—
988C22—22no—
989C22—21no—
990C22—21no—
991C22—22no—
992C22—22no—
993C22—22no—
994C22—48no—
995C22—62no—
996C22—62no—
997C22—62no—
998C22—92no—
999C22—181no—
1000C22—181no—
1001C22—181no—
1002C22—181no—
1003C22—181no—
1004C22—364no—
1005C22#6430912yescomplemented
1006C22C2×#381114yes—
1007C22C23×D3211yescharacteristic
1008C4—21no—
1009C4—62no—
1010C4—62no—
1011C4—64no—
1012C4—62no—
1013C4—64no—
1014C4—92no—
1015C4—94no—
1016C4—181no—
1017C4—182no—
1018C4C2×#381112yes—
1019C3—21no—
1020C3#8663012yescomplemented
1021C2—22no—
1022C2—24no—
1023C2—42no—
1024C2—122no—
1025C2—182no—
1026C2—361no—
1027C2C2×#6430911yescharacteristic
1028C2#1059667911yescharacteristic
1029C2C22×#381111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC22×C32×D4C22
hypercenterC22×D4D32
hypocenterC32#3489
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×#3830C2semidirect
2. C2×#64309C2semidirect
3. C3×#5806C2semidirect
4. C2×#63982C2semidirect
5. #10595501C2semidirect
6. #10595500C2semidirect
7. #10595271C2semidirect
8. #10595248C2semidirect
9. #10595240C2semidirect
10. #10595219C2semidirect
11. #10595171C2semidirect
12. #10595166C2semidirect
13. #10595162C2semidirect
14. #10595161C2semidirect
15. #10595016C2semidirect
16. #10594925C2semidirect
17. #10594915C2semidirect
31. C2×C3×#237C22semidirect
32. C22×#627C22semidirect
33. C2×#3805C22semidirect
34. C2×#3804C22semidirect
36. C2×#3798C22semidirect
37. C2×#3797C22semidirect
38. C2×D3×Dic6C22semidirect
41. C3×#939C22semidirect
42. C3×#938C22semidirect
43. C3×#936C22semidirect
44. C3×#935C22semidirect
45. C3×D4×Dic3C22semidirect
51. #63982C22semidirect
52. #63982C22semidirect
53. #63982C22semidirect
54. #63982C22semidirect
57. #63980C22semidirect
58. #63978C22semidirect
59. #63975C22semidirect
62. #67⋊Dic3C22semidirect
63. #63971C22semidirect
64. C2×#3724C22semidirect
65. #63966C22semidirect
66. C2×Dic3⋊Dic3C22semidirect
67. #63962C22semidirect
68. #63958C22semidirect
69. #63957C22semidirect
70. #63953C22semidirect
71. #63952C22semidirect
72. #63912C22semidirect
73. C4×#626C22semidirect
74. #63900C22semidirect
75. #63896C22semidirect
76. #63883C22semidirect
77. #63874C22semidirect
78. #63871C22semidirect
79. #63866C22semidirect
80. #63865C22semidirect
81. #63865C22semidirect
82. #63857C22semidirect
83. #63853C22semidirect
84. #63844C22semidirect
85. #63840C22semidirect
91. #5806D3semidirect
134. #3830D4semidirect
220. C2×#237C2×D3semidirect
246. #939C2×D3semidirect
248. #938C2×D3semidirect
250. #936C2×D3semidirect
252. #935C2×D3semidirect
255. D4×Dic3C2×D3semidirect
547. C22×C322−1+4semidirect
867. C22×C3#1010semidirect
908. C32#3489semidirect
1005. C22#64309semidirect
1020. C3#86630semidirect

Maximal subgroups

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

subgroupindex
C22×#38302
C2×#643092
C3×#58062
C2×#639822
#105955012
#105955002
#105952712
#105952482
#105952402
#105952192
#105951712
#105951662
#105951622
#105951612
#105950162
#105949252
#105949152
#866303