Finite Group Databasebeta

← #11904405

Subgroups — #11904405

Order 1152.

3569 conjugacy classes of subgroups.

The subgroup lattice has 1033 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64361C211yesmaximal, characteristic, complemented
2C2×#64312C211yesmaximal, characteristic, complemented
3C3×#5806C212yesmaximal, complemented
4#10595528C212yesmaximal, complemented
5C2×#63975C212yesmaximal, complemented
6#10595500C214yesmaximal, complemented
7#10595308C212yesmaximal, complemented
8#10595306C211yesmaximal, characteristic, complemented
9#10595248C212yesmaximal, complemented
10#10595243C212yesmaximal, complemented
11#10595223C211yesmaximal, characteristic, complemented
12#10595171C211yesmaximal, characteristic, complemented
13#10595169C212yesmaximal, complemented
14#10595162C214yesmaximal, complemented
15#10595076C211yesmaximal, characteristic, complemented
16#10594834C212yesmaximal, complemented
17#10594805C211yesmaximal, characteristic, complemented
18#86663—32nomaximal
19C22×C32×D4C2211yescharacteristic, complemented
20C22×#638C2212yes—
21C22×#638C2212yescomplemented
22#64361—28no—
23C2×#3830C2211yescharacteristic
24C2×#3830C2212yescomplemented
25C2×#3830C2211yescharacteristic, complemented
26C2×D4×C3⋊D3C2212yes—
27C2×D4×C3⋊D3C2211yescharacteristic
28C2×D4×C3⋊D3C2211yescharacteristic, complemented
29C2×#3828C2211yescharacteristic
30C2×#3828C2211yescharacteristic, complemented
31C2×C3×#237C2212yescomplemented
32C2×#3811C2212yescomplemented
33C22×#624C2212yescomplemented
34C2×#3804C2214yescomplemented
35#64312—28no—
36C2×C4×D32C2211yescharacteristic, complemented
37C2×#3799C2212yescomplemented
38C2×#3797C2211yescharacteristic, complemented
39C3×#953C2214yescomplemented
40C2×C3×#217C2214yescomplemented
41C3×#939C2214yescomplemented
42C3×#938C2212yescomplemented
43C3×#936C2212yescomplemented
44C3×#935C2214yescomplemented
45C3×D4×Dic3C2212yescomplemented
46C3×C4×#67C2212yescomplemented
47C3×#924C2212yescomplemented
48#63983C2211yescharacteristic, complemented
49#63983C2212yescomplemented
50#63982C2214yescomplemented
51#63981C2214yescomplemented
52#63978C2214yescomplemented
53#63975C2211yescharacteristic, complemented
54#63975C2214yescomplemented
55#63975C2214yescomplemented
56#63975C2212yescomplemented
57#63975C2212yescomplemented
58#63975C2212yescomplemented
59#63975C2212yescomplemented
60#63974C2212yescomplemented
61#63974C2214yescomplemented
62#67⋊Dic3C2214yescomplemented
63#63971C2212yescomplemented
64#63966C2214yescomplemented
65C2×Dic3⋊Dic3C2214yescomplemented
66C2×#3722C2212yescomplemented
67#63962C2214yescomplemented
68#63958C2214yescomplemented
69#63958C2214yescomplemented
70#63953C2212yescomplemented
71#63952C2214yescomplemented
72#63923C2211yescharacteristic, complemented
73C4×#626C2212yescomplemented
74#63897C2211yescharacteristic, complemented
75#63897C2212yescomplemented
76#63896C2212yescomplemented
77#63894C2212yescomplemented
78#63883C2214yescomplemented
79#63874C2211yescharacteristic, complemented
80#63871C2212yescomplemented
81#63866C2212yescomplemented
82#63857C2212yescomplemented
83#63853C2214yescomplemented
84#63849C2211yescharacteristic, complemented
85#63840C2212yescomplemented
86C2×D3×#41—32no—
87C2×#1004—32no—
88C2×#1004—61no—
89C3×#546—32no—
90#5824—32no—
91#5806D312yescomplemented
92#5676—32no—
93#5675—32no—
94#5655—34no—
95D3×#123—34no—
96#5631—32no—
97#5628—32no—
98#5612—32no—
99#5611—34no—
100#5606—32no—
101#5605—34no—
102#5591—34no—
103#5589—34no—
104#5555—32no—
105#5551—32no—
106#5547—32no—
107#5545—32no—
108#5490—34no—
109C2×#883—34no—
110C24×C32C2312yes—
111C23×C3⋊D3C2312yes—
112C23×C3⋊D3C2312yes—
113C22×D32C2311yescharacteristic
114C2×C32×D4—24no—
115C2×C32×D4C2312yes—
116C2×C32×D4C2311yescharacteristic
117C2×C32×D4C2311yescharacteristic
118C22×C32×C4C2311yescharacteristic
119C2×#638—28no—
120C2×#638—28no—
121C2×#638C2311yescharacteristic
122C2×#638C2311yescharacteristic
123C2×#638C2312yes—
124C2×#638C2312yes—
125C2×#638C2312yes—
126C2×#638C2312yes—
127C2×#638C2312yes—
128C22×C3⋊Dic3C2312yes—
129C22×C3⋊Dic3C2312yes—
130#3830—24no—
131#3830—28no—
132#3830—24no—
133D4×C3⋊D3—28no—
134D4×C3⋊D3—24no—
135D4×C3⋊D3D418yescomplemented
136#3828—24no—
137#3828—24no—
138C2×C4⋊(C3⋊D3)C2311yescharacteristic
139C2×C4⋊(C3⋊D3)C2311yescharacteristic
140C2×C4×C3⋊D3C2311yescharacteristic
141C2×C4×C3⋊D3C2312yes—
142C2×C4×C3⋊D3C2311yescharacteristic
143C2×#634C2311yescharacteristic
144C2×#634C2311yescharacteristic
145C2×C3×#67C2314yes—
146C2×C3×#67C2312yes—
147C2×C3×#67C2314yes—
148C22×C3×Dic3C2314yes—
149C22×C3×Dic3C2314yes—
150C3×#237—28no—
151C2×C3×C4×D3C2312yes—
152C2×C3×Dic6C2312yes—
153#3811—28no—
154C2×#627C2312yes—
155C2×#626C2314yes—
156C2×#626C2312yes—
157C2×#624—28no—
158C2×#624C2312yes—
159C2×#624C2314yes—
160C2×#624C2311yescharacteristic
161C2×#624C2314yes—
162#3804—216no—
163C2×D3×Dic3C2312yes—
164C4×D32—24no—
165#3799—28no—
166#3797—24no—
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#3724C2312yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2314yes—
181Dic3⋊Dic3C2314yes—
182Dic3⋊Dic3C2314yes—
183Dic3⋊Dic3C2312yes—
184#3722C2312yes—
185#3722C2314yes—
186#3722C2314yes—
187#3722C2311yescharacteristic
188#3722C2311yescharacteristic
189#3722C2312yes—
190(C2×D3)⋊Dic3C2314yes—
191(C2×D3)⋊Dic3C2312yes—
192Dic32C2312yes—
193#3485—91noSylow
194C2×C3×#41—32no—
195C22×C3×D4—21no—
196C22×C3×D4C2×D312yescomplemented
197C22×#67—34no—
198C22×#67—34no—
199C22×#67—62no—
200C22×#67—62no—
201D3×#41—616no—
202C2×#239—32no—
203C2×D3×Q8—32no—
204#1004—616no—
205#1004—616no—
206C2×#237—34no—
207C2×#237—32no—
208C2×#237—32no—
209C2×#237—34no—
210C2×#237—61no—
211C2×#237—62no—
212C2×#237—61no—
213C2×#237C2×D312yescomplemented
214C2×D3×D4—32no—
215C2×D3×D4—34no—
216C2×D3×D4—32no—
217C2×D3×D4—34no—
218C2×D3×D4—61no—
219C2×D3×D4—62no—
220C2×D3×D4—61no—
221C2×#235—32no—
222C2×#235—32no—
223C2×#235—34no—
224C2×#235—32no—
225C2×#235—61no—
226C2×#235—61no—
227C22×C4×D3—34no—
228C22×C4×D3—32no—
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×D314yescomplemented
239C2×#217C2×D314yescomplemented
240#946—32no—
241#944—32no—
242#939—34no—
243#939—32no—
244#939C2×D314yescomplemented
245#938—34no—
246#938—34no—
247#938C2×D312yescomplemented
248#937—32no—
249#937—34no—
250#937—34no—
251#936C2×D312yescomplemented
252#935—34no—
253#935C2×D314yescomplemented
254D4×Dic3—34no—
255D4×Dic3C2×D312yescomplemented
256#930—34no—
257#929—34no—
258C4×#67—34no—
259C4×#67—32no—
260C4×#67C2×D312yescomplemented
261C2×(C2×D3)⋊C4—34no—
262C2×C4⋊Dic3—34no—
263#924—32no—
264#924C2×D312yescomplemented
265C2×Dic3⋊C4—34no—
266#897—32no—
267#897—32no—
268#896—32no—
269#894—34no—
270#894—32no—
271#894—34no—
272#893—32no—
273#892—32no—
274D3×C4⋊C4—34no—
275D3×C4⋊C4—34no—
276#888—34no—
277#886—34no—
278#886—34no—
279#885—34no—
280#884—34no—
281#884—32no—
282#884—34no—
283#883—34no—
284#883—34no—
285#883—34no—
286#883—34no—
287#883—34no—
288#883—32no—
289#883—34no—
290#883—34no—
291#883—34no—
292#883—34no—
293#882—34no—
294#882—32no—
295#67⋊C4—34no—
296#67⋊C4—34no—
297D3×C22⋊C4—34no—
298D3×C22⋊C4—34no—
299D3×C22⋊C4—34no—
300#878—34no—
301#878—34no—
302#878—32no—
303C4×D12—32no—
304C4×D12—32no—
305#872—32no—
306#869—32no—
307C23×C32—24no—
308C23×C32—44no—
309C23×C32C2412yes—
310C23×C32C2411yescharacteristic
311C23×C32C2412yes—
312C22×C3⋊D3—24no—
313C22×C3⋊D3—44no—
314C22×C3⋊D3—44no—
315C22×C3⋊D3C2×D418yes—
316C22×C3⋊D3C2411yescharacteristic
317C22×C3⋊D3C2411yescharacteristic
318C22×C3⋊D3C2412yes—
319C22×C3×D3C2412yes—
320C2×D32—22no—
321C2×D32—42no—
322C32×D4—24no—
323C32×D4—22no—
324C32×D4C2×D414yes—
325C2×C32×C4—22no—
326C2×C32×C4C2411yescharacteristic
327C2×C32×C4C2411yescharacteristic
328#638—24no—
329#638—22no—
330#638—24no—
331#638—24no—
332#638—24no—
333#638—22no—
334#638C2×D418yes—
335C2×C3⋊Dic3—24no—
336C2×C3⋊Dic3—24no—
337C2×C3⋊Dic3C2412yes—
338C2×C3⋊Dic3C2411yescharacteristic
339C2×C3⋊Dic3C2411yescharacteristic
340C4⋊(C3⋊D3)—22no—
341C4⋊(C3⋊D3)C2×D414yes—
342C4×C3⋊D3—24no—
343C4×C3⋊D3—22no—
344C4×C3⋊D3C2×D414yes—
345#634—22no—
346#634—22no—
347C3×#67—28no—
348C3×#67—42no—
349C3×#67—44no—
350C2×C3×Dic3—28no—
351C2×C3×Dic3—44no—
352C2×C3×Dic3C2414yes—
353C2×C3×Dic3C2412yes—
354C2×C3×Dic3C2412yes—
355C2×C3×Dic3C2412yes—
356C2×C3×Dic3C2414yes—
357C3×C4×D3—24no—
358C3×Dic6—24no—
359#627—24no—
360#626—28no—
361#626—42no—
362#624—24no—
363#624—28no—
364#624—22no—
365#624—44no—
366D3×Dic3—24no—
367C2×H(5,𝔽2)—91no—
368C22×#41—91no—
369#547—92no—
370#547—92no—
371#547—94no—
372#546—32no—
373#546—94no—
374#546—92no—
375#536—91no—
376#536—91no—
377#534—92no—
378#534—92no—
379#525—91no—
380#525—91no—
381C2×#123—92no—
382C2×#123—92no—
383#518—91no—
384C24×C3—22no—
385C24×C3C22×D314yes—
386C23×D3—34no—
387C23×D3—34no—
388C23×D3—32no—
389C23×D3—62no—
390C23×D3—62no—
391C3×#41—68no—
392C2×C3×Q8—32no—
393C2×C3×D4—28no—
394C2×C3×D4—28no—
395C2×C3×D4—22no—
396C2×C3×D4—21no—
397C2×C3×D4—21no—
398C2×C3×D4—34no—
399C2×C3×D4—34no—
400C2×C3×D4—32no—
401C2×C3×D4C22×D314yes—
402C2×C3×D4C22×D312yes—
403C2×C3×D4C22×D312yes—
404C22×C3×C4—21no—
405C22×C3×C4—34no—
406C22×C3×C4—34no—
407C22×C3×C4—32no—
408C22×C3×C4C22×D312yes—
409C2×#67—34no—
410C2×#67—32no—
411C2×#67—34no—
412C2×#67—34no—
413C2×#67—34no—
414C2×#67—32no—
415C2×#67—34no—
416C2×#67—34no—
417C2×#67—32no—
418C2×#67—61no—
419C2×#67—62no—
420C2×#67—61no—
421C2×#67—62no—
422C2×#67—62no—
423C2×#67—62no—
424C2×#67—62no—
425C2×#67—616no—
426C2×#67—616no—
427C2×#67—616no—
428C2×#67—616no—
429C2×#67C22×D314yes—
430C2×#67C22×D314yes—
431C2×#67C22×D312yes—
432C22×Dic3—34no—
433C22×Dic3—34no—
434C22×Dic3—32no—
435C22×Dic3—62no—
436C22×Dic3—62no—
437C22×Dic3C22×D314yes—
438C22×Dic3C22×D314yes—
439#239—68no—
440D3×Q8—68no—
441#237—28no—
442#237—68no—
443#237—616no—
444#237—616no—
445#237—68no—
446#237—616no—
447#237—68no—
448#237—68no—
449D3×D4—316no—
450D3×D4—68no—
451D3×D4—68no—
452D3×D4—616no—
453D3×D4—616no—
454D3×D4—68no—
455D3×D4—616no—
456#235—68no—
457#235—68no—
458#235—68no—
459#235—616no—
460#235—68no—
461#235—68no—
462C2×D12—32no—
463C2×D12—34no—
464C2×D12—32no—
465C2×D12—32no—
466C2×D12—61no—
467C2×D12—61no—
468C2×C4×D3—32no—
469C2×C4×D3—32no—
470C2×C4×D3—32no—
471C2×C4×D3—34no—
472C2×C4×D3—34no—
473C2×C4×D3—34no—
474C2×C4×D3—32no—
475C2×C4×D3—34no—
476C2×C4×D3—34no—
477C2×C4×D3—34no—
478C2×C4×D3—61no—
479C2×C4×D3—62no—
480C2×C4×D3—61no—
481C2×C4×D3—68no—
482C2×C4×D3—616no—
483C2×C4×D3C22×D312yes—
484C2×Dic6—32no—
485C2×Dic6—32no—
486C2×Dic6—34no—
487C2×Dic6—61no—
488C2×Dic6—61no—
489C2×Dic6C22×D312yes—
490C3×C4⋊C4—34no—
491C3×C4⋊C4—32no—
492C3×C4⋊C4—32no—
493C3×C22⋊C4—34no—
494C3×C22⋊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#217—34no—
503#217C22×D314yes—
504#217C22×D314yes—
505#217C22×D314yes—
506#217C22×D314yes—
507#217C22×D312yes—
508#217C22×D314yes—
509(C2×D3)⋊C4—32no—
510(C2×D3)⋊C4—34no—
511(C2×D3)⋊C4—32no—
512(C2×D3)⋊C4—32no—
513(C2×D3)⋊C4—32no—
514(C2×D3)⋊C4—34no—
515(C2×D3)⋊C4—32no—
516(C2×D3)⋊C4—34no—
517(C2×D3)⋊C4—34no—
518(C2×D3)⋊C4—34no—
519(C2×D3)⋊C4—34no—
520(C2×D3)⋊C4C22×D312yes—
521C4⋊Dic3—34no—
522C4⋊Dic3—34no—
523C4⋊Dic3—32no—
524C4⋊Dic3—34no—
525C4⋊Dic3—34no—
526C4⋊Dic3C22×D312yes—
527Dic3⋊C4—32no—
528Dic3⋊C4—32no—
529Dic3⋊C4—34no—
530Dic3⋊C4—34no—
531Dic3⋊C4—34no—
532Dic3⋊C4—32no—
533Dic3⋊C4—34no—
534Dic3⋊C4C22×D312yes—
535Dic3⋊C4C22×D314yes—
536C4×Dic3—34no—
537C4×Dic3C22×D312yes—
538C22×C32—22no—
539C22×C32—21no—
540C22×C32—24no—
541C22×C32—24no—
542C22×C32—22no—
543C22×C32—84no—
544C22×C32C22×D414yes—
545C22×C32C2511yescharacteristic
546C2×C3⋊D3—21no—
547C2×C3⋊D3—24no—
548C2×C3⋊D3—22no—
549C2×C3⋊D3—22no—
550C2×C3⋊D3—48no—
551C2×C3⋊D3—84no—
552C2×C3⋊D3C22×D412yes—
553C2×C3⋊D3C22×D414yes—
554C2×C3×D3—22no—
555C2×C3×D3—22no—
556C2×C3×D3—22no—
557D32—44no—
558C32×C4—21no—
559C32×C4C22×D412yes—
560C3⋊Dic3—22no—
561C3⋊Dic3—21no—
562C3⋊Dic3C22×D412yes—
563C3×Dic3—22no—
564C3×Dic3—24no—
565C3×Dic3—22no—
566C3×Dic3—24no—
567C3×Dic3—22no—
568H(5,𝔽2)—188no—
569C2×#41—32no—
570C2×#41—94no—
571C2×#41—92no—
572C2×#41—91no—
573C2×#41—91no—
574C2×#41—92no—
575C2×#41—91no—
576C2×#41—91no—
577C2×#41—188no—
578C22×Q8—91no—
579C22×D4—92no—
580C22×D4—91no—
581C22×D4—92no—
582C22×D4—92no—
583C22×D4—92no—
584C22×D4—91no—
585C22×D4D3211yescharacteristic, complemented
586C23×C4—92no—
587C23×C4—91no—
588C4⋊Q8—92no—
589C4⋊Q8—92no—
590#124—32no—
591#124—92no—
592#123—34no—
593#123—91no—
594#123—92no—
595#123—92no—
596#123—92no—
597#123—92no—
598#123—94no—
599#123—94no—
600#123—94no—
601#123—94no—
602#123—94no—
603#123—91no—
604#123—92no—
605C22⋊Q8—32no—
606C22⋊Q8—94no—
607C22⋊Q8—92no—
608C22⋊Q8—92no—
609C22⋊Q8—92no—
610#121—32no—
611#121—34no—
612#121—92no—
613#121—94no—
614#121—94no—
615#121—94no—
616#120—34no—
617#120—91no—
618#120—94no—
619#120—91no—
620#120—92no—
621C4×D4—32no—
622C4×D4—32no—
623C4×D4—92no—
624C4×D4—92no—
625C4×D4—94no—
626C4×D4—94no—
627#117—91no—
628#117—91no—
629C2×C4⋊C4—94no—
630C2×C4⋊C4—94no—
631C2×C22⋊C4—34no—
632C2×C22⋊C4—92no—
633C2×C22⋊C4—94no—
634C2×C22⋊C4—92no—
635C23×C3—28no—
636C23×C3—28no—
637C23×C3—22no—
638C23×C3—22no—
639C23×C3—21no—
640C23×C3—32no—
641C23×C3—44no—
642C23×C3—44no—
643C23×C3—84no—
644C23×C3C23×D314yes—
645C23×C3C23×D312yes—
646C23×C3C23×D314yes—
647C22×D3—32no—
648C22×D3—34no—
649C22×D3—316no—
650C22×D3—32no—
651C22×D3—61no—
652C22×D3—62no—
653C22×D3—61no—
654C22×D3—68no—
655C22×D3—64no—
656C22×D3—68no—
657C22×D3—68no—
658C22×D3—122no—
659C22×D3—122no—
660C22×D3—124no—
661C22×D3—124no—
662C22×D3—124no—
663C22×D3—124no—
664C22×D3—244no—
665C22×D3—244no—
666C22×D3C23×D312yes—
667C3×Q8—64no—
668C3×D4—28no—
669C3×D4—24no—
670C3×D4—28no—
671C3×D4—24no—
672C3×D4—24no—
673C3×D4—68no—
674C3×D4—124no—
675C3×D4—122no—
676C3×D4D3×D418yes—
677C2×C3×C4—24no—
678C2×C3×C4—24no—
679C2×C3×C4—21no—
680C2×C3×C4—21no—
681C2×C3×C4—34no—
682C2×C3×C4—34no—
683C2×C3×C4—32no—
684C2×C3×C4—32no—
685C2×C3×C4—32no—
686C2×C3×C4—68no—
687C2×C3×C4—64no—
688C2×C3×C4—124no—
689C2×C3×C4C23×D312yes—
690C2×C3×C4C23×D312yes—
691#67—28no—
692#67—316no—
693#67—42no—
694#67—44no—
695#67—68no—
696#67—68no—
697#67—64no—
698#67—64no—
699#67—68no—
700#67—68no—
701#67—68no—
702#67—64no—
703#67—64no—
704#67—68no—
705#67—68no—
706#67—68no—
707#67—68no—
708#67—68no—
709#67—122no—
710C2×Dic3—28no—
711C2×Dic3—32no—
712C2×Dic3—34no—
713C2×Dic3—32no—
714C2×Dic3—44no—
715C2×Dic3—61no—
716C2×Dic3—61no—
717C2×Dic3—62no—
718C2×Dic3—64no—
719C2×Dic3—68no—
720C2×Dic3—68no—
721C2×Dic3—68no—
722C2×Dic3—68no—
723C2×Dic3C23×D314yes—
724C2×Dic3C23×D312yes—
725C2×Dic3C23×D312yes—
726C2×Dic3C23×D314yes—
727C2×Dic3C23×D312yes—
728D12—38no—
729D12—64no—
730D12—64no—
731D12—64no—
732D12—68no—
733D12—122no—
734C4×D3—24no—
735C4×D3—38no—
736C4×D3—64no—
737C4×D3—64no—
738C4×D3—68no—
739C4×D3—68no—
740C4×D3—68no—
741C4×D3—64no—
742C4×D3—68no—
743C4×D3—68no—
744C4×D3—64no—
745C4×D3—64no—
746C4×D3—124no—
747C4×D3—124no—
748Dic6—24no—
749Dic6—68no—
750Dic6—64no—
751Dic6—64no—
752Dic6—64no—
753Dic6—64no—
754C2×C32—24no—
755C2×C32—42no—
756C2×C32—41no—
757C2×C32C23×D411yescharacteristic
758C2×C32#58512yes—
759C3⋊D3—22no—
760C3⋊D3—24no—
761C3⋊D3—41no—
762C3×D3—42no—
763C24—91no—
764C24—92no—
765C24—92no—
766C24C2×D3212yes—
767#41—68no—
768#41—184no—
769#41—184no—
770#41—1816no—
771#41—188no—
772#41—184no—
773#41—188no—
774#41—184no—
775C2×Q8—32no—
776C2×Q8—92no—
777C2×Q8—91no—
778C2×Q8—91no—
779C2×Q8—184no—
780C2×D4—24no—
781C2×D4—34no—
782C2×D4—32no—
783C2×D4—34no—
784C2×D4—94no—
785C2×D4—92no—
786C2×D4—92no—
787C2×D4—98no—
788C2×D4—92no—
789C2×D4—91no—
790C2×D4—92no—
791C2×D4—92no—
792C2×D4—92no—
793C2×D4—91no—
794C2×D4—91no—
795C2×D4—91no—
796C2×D4—184no—
797C2×D4—188no—
798C2×D4—188no—
799C2×D4—188no—
800C2×D4—188no—
801C2×D4C2×D3212yes—
802C2×D4C2×D3211yescharacteristic
803C2×D4C2×D3211yescharacteristic
804C22×C4—34no—
805C22×C4—34no—
806C22×C4—32no—
807C22×C4—94no—
808C22×C4—91no—
809C22×C4—92no—
810C22×C4—94no—
811C22×C4—92no—
812C22×C4—91no—
813C22×C4—92no—
814C22×C4—92no—
815C22×C4—92no—
816C22×C4—91no—
817C22×C4—184no—
818C22×C4—188no—
819C22×C4C2×D3211yescharacteristic
820C4⋊C4—32no—
821C4⋊C4—34no—
822C4⋊C4—32no—
823C4⋊C4—92no—
824C4⋊C4—94no—
825C4⋊C4—94no—
826C4⋊C4—94no—
827C4⋊C4—94no—
828C4⋊C4—92no—
829C22⋊C4—32no—
830C22⋊C4—34no—
831C22⋊C4—34no—
832C22⋊C4—34no—
833C22⋊C4—34no—
834C22⋊C4—34no—
835C22⋊C4—32no—
836C22⋊C4—91no—
837C22⋊C4—91no—
838C22⋊C4—92no—
839C22⋊C4—92no—
840C22⋊C4—94no—
841C22⋊C4—94no—
842C22⋊C4—92no—
843C22⋊C4—94no—
844C42—32no—
845C42—92no—
846C22×C3—24no—
847C22×C3—24no—
848C22×C3—24no—
849C22×C3—22no—
850C22×C3—24no—
851C22×C3—22no—
852C22×C3—22no—
853C22×C3—24no—
854C22×C3—24no—
855C22×C3—22no—
856C22×C3—24no—
857C22×C3—21no—
858C22×C3—44no—
859C22×C3—44no—
860C22×C3—42no—
861C22×C3—62no—
862C22×C3—62no—
863C22×C3—62no—
864C22×C3—88no—
865C22×C3—88no—
866C22×C3C2×D3×D418yes—
867C22×C3C24×D312yes—
868C2×D3—22no—
869C2×D3—22no—
870C2×D3—22no—
871C2×D3—34no—
872C2×D3—38no—
873C2×D3—62no—
874C2×D3—64no—
875C2×D3—64no—
876C2×D3—62no—
877C2×D3—64no—
878C2×D3—62no—
879C2×D3—62no—
880C2×D3—62no—
881C2×D3—62no—
882C2×D3—62no—
883C2×D3—124no—
884C2×D3—122no—
885C2×D3—122no—
886C2×D3—128no—
887C2×D3—1216no—
888C2×D3—248no—
889C2×D3—248no—
890C2×D3—248no—
891C3×C4—22no—
892C3×C4—22no—
893C3×C4—22no—
894C3×C4—64no—
895C3×C4—62no—
896C3×C4—64no—
897C3×C4—62no—
898C3×C4—62no—
899C3×C4C2×D3×D414yes—
900Dic3—24no—
901Dic3—22no—
902Dic3—22no—
903Dic3—24no—
904Dic3—22no—
905Dic3—34no—
906Dic3—62no—
907Dic3—64no—
908Dic3—62no—
909Dic3—62no—
910Dic3—64no—
911C32#348511yescharacteristic, complemented, Sylow
912C23—24no—
913C23—32no—
914C23—44no—
915C23—91no—
916C23—92no—
917C23—98no—
918C23—91no—
919C23—184no—
920C23—182no—
921C23—364no—
922C23—364no—
923C23—362no—
924C23C22×D3212yes—
925C23C22×D3211yescharacteristic
926C23C22×D3212yes—
927Q8—64no—
928Q8—182no—
929Q8—184no—
930Q8—182no—
931D4—24no—
932D4—22no—
933D4—68no—
934D4—98no—
935D4—94no—
936D4—124no—
937D4—122no—
938D4—182no—
939D4—188no—
940D4—182no—
941D4—182no—
942D4—184no—
943D4—184no—
944D4—184no—
945D4—184no—
946D4—362no—
947D4#381114yes—
948C2×C4—22no—
949C2×C4—32no—
950C2×C4—32no—
951C2×C4—34no—
952C2×C4—32no—
953C2×C4—34no—
954C2×C4—68no—
955C2×C4—64no—
956C2×C4—91no—
957C2×C4—94no—
958C2×C4—91no—
959C2×C4—92no—
960C2×C4—124no—
961C2×C4—184no—
962C2×C4—182no—
963C2×C4—184no—
964C2×C4—188no—
965C2×C4—184no—
966C2×C4—184no—
967C2×C4—184no—
968C2×C4—182no—
969C2×C4—364no—
970C2×C4C22×D3211yescharacteristic
971C2×C4C22×D3211yescharacteristic
972C2×C3—28no—
973C2×C3—22no—
974C2×C3—21no—
975C2×C3—44no—
976C2×C3—44no—
977C2×C3—42no—
978C2×C3—44no—
979C2×C3—42no—
980C2×C3—122no—
981C2×C3C22×D3×D412yes—
982C2×C3#596412yes—
983C2×C3#596612yes—
984D3—42no—
985D3—64no—
986D3—68no—
987D3—122no—
988D3—124no—
989D3—122no—
990D3—122no—
991C22—24no—
992C22—22no—
993C22—24no—
994C22—21no—
995C22—22no—
996C22—62no—
997C22—62no—
998C22—62no—
999C22—84no—
1000C22—92no—
1001C22—94no—
1002C22—184no—
1003C22—182no—
1004C22—182no—
1005C22—181no—
1006C22—368no—
1007C22—364no—
1008C22—724no—
1009C22C2×#381114yes—
1010C22C23×D3211yescharacteristic
1011C4—21no—
1012C4—62no—
1013C4—64no—
1014C4—62no—
1015C4—62no—
1016C4—64no—
1017C4—92no—
1018C4—182no—
1019C4—181no—
1020C4C2×#381112yes—
1021C3—21no—
1022C3#8666312yescomplemented
1023C2—24no—
1024C2—41no—
1025C2—42no—
1026C2—122no—
1027C2—182no—
1028C2—184no—
1029C2—361no—
1030C2#1059667812yes—
1031C2C22×#381111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC22×C32×D4C22
hypercenterC22×D4D32
hypocenterC32#3485
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#64361C2semidirect
2. C2×#64312C2semidirect
3. C3×#5806C2semidirect
4. #10595528C2semidirect
5. C2×#63975C2semidirect
6. #10595500C2semidirect
7. #10595308C2semidirect
8. #10595306C2semidirect
9. #10595248C2semidirect
10. #10595243C2semidirect
11. #10595223C2semidirect
12. #10595171C2semidirect
13. #10595169C2semidirect
14. #10595162C2semidirect
15. #10595076C2semidirect
16. #10594834C2semidirect
17. #10594805C2semidirect
19. C22×C32×D4C22semidirect
21. C22×#638C22semidirect
24. C2×#3830C22semidirect
25. C2×#3830C22semidirect
28. C2×D4×C3⋊D3C22semidirect
30. C2×#3828C22semidirect
31. C2×C3×#237C22semidirect
32. C2×#3811C22semidirect
33. C22×#624C22semidirect
34. C2×#3804C22semidirect
36. C2×C4×D32C22semidirect
37. C2×#3799C22semidirect
38. C2×#3797C22semidirect
39. C3×#953C22semidirect
40. C2×C3×#217C22semidirect
41. C3×#939C22semidirect
42. C3×#938C22semidirect
43. C3×#936C22semidirect
44. C3×#935C22semidirect
45. C3×D4×Dic3C22semidirect
46. C3×C4×#67C22semidirect
47. C3×#924C22semidirect
48. #63983C22semidirect
49. #63983C22semidirect
50. #63982C22semidirect
51. #63981C22semidirect
52. #63978C22semidirect
53. #63975C22semidirect
54. #63975C22semidirect
55. #63975C22semidirect
56. #63975C22semidirect
57. #63975C22semidirect
58. #63975C22semidirect
59. #63975C22semidirect
60. #63974C22semidirect
61. #63974C22semidirect
62. #67⋊Dic3C22semidirect
63. #63971C22semidirect
64. #63966C22semidirect
65. C2×Dic3⋊Dic3C22semidirect
66. C2×#3722C22semidirect
67. #63962C22semidirect
68. #63958C22semidirect
69. #63958C22semidirect
70. #63953C22semidirect
71. #63952C22semidirect
72. #63923C22semidirect
73. C4×#626C22semidirect
74. #63897C22semidirect
75. #63897C22semidirect
76. #63896C22semidirect
77. #63894C22semidirect
78. #63883C22semidirect
79. #63874C22semidirect
80. #63871C22semidirect
81. #63866C22semidirect
82. #63857C22semidirect
83. #63853C22semidirect
84. #63849C22semidirect
85. #63840C22semidirect
91. #5806D3semidirect
135. D4×C3⋊D3D4semidirect
196. C22×C3×D4C2×D3semidirect
213. C2×#237C2×D3semidirect
238. #953C2×D3semidirect
239. C2×#217C2×D3semidirect
244. #939C2×D3semidirect
247. #938C2×D3semidirect
251. #936C2×D3semidirect
253. #935C2×D3semidirect
255. D4×Dic3C2×D3semidirect
260. C4×#67C2×D3semidirect
264. #924C2×D3semidirect
585. C22×D4D32semidirect
911. C32#3485semidirect
1022. C3#86663semidirect

Maximal subgroups

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

subgroupindex
C2×#643612
C2×#643122
C3×#58062
#105955282
C2×#639752
#105955002
#105953082
#105953062
#105952482
#105952432
#105952232
#105951712
#105951692
#105951622
#105950762
#105948342
#105948052
#866633