Finite Group Databasebeta

← C2×#10596698 #11919268

Subgroups — C2×#10596698 #11919268

Order 1152.

12357 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C3×#1010C211yesmaximal, characteristic, complemented
3C2×C3×#1009C211yesmaximal, characteristic, complemented
4#10596698C2132yesmaximal, direct product factor
5C2×D3×#239C212yesmaximal, complemented
6C2×#64315C212yesmaximal, complemented
7C2×#64314C216yesmaximal, complemented
8C2×D3×#237C216yesmaximal, complemented
9C2×#64307C213yesmaximal, complemented
10C2×#64306C213yesmaximal, complemented
11C2×#64297C213yesmaximal, complemented
12C22×#3796C213yesmaximal, complemented
13C2×#5968—31nomaximal
14C2×#5966—31nomaximal
15C2×C32×#41C2211yescharacteristic, complemented
16#41×C3⋊D3C22116yescomplemented
17C2×#3832C2211yescharacteristic, complemented
18C2×Q8×C3⋊D3C2211yescharacteristic, complemented
19C2×#3830C2213yescomplemented
20C2×D4×C3⋊D3C2213yescomplemented
21C2×#3828C2213yescomplemented
22C22×C4×C3⋊D3C2213yescomplemented
23C3×#1010C22116yescomplemented
24C3×#1009C22116yescomplemented
25C2×C3×#239C2212yescomplemented
26C2×C3×D3×Q8C2212yescomplemented
27C2×C3×#237C2216yescomplemented
28C2×C3×D3×D4C2216yescomplemented
29C2×C3×#235C2213yescomplemented
30C2×C3×#235C2213yescomplemented
31C22×C3×D12C2213yescomplemented
32C22×C3×Dic6C2213yescomplemented
33C2×#3811C2216yescomplemented
34C2×D3×#67C22112yescomplemented
35C22×#626C2216yescomplemented
36C2×#3805C2216yescomplemented
37C2×#3804C22112yescomplemented
38C22×D3×Dic3C2216yescomplemented
39D3×#239C22132yescomplemented
40#64315C22132yescomplemented
41#64314C22196yescomplemented
42D3×#237C22196yescomplemented
43#64307C22148yescomplemented
44#64306C22148yescomplemented
45C2×#3802C2213yescomplemented
46C2×D3×D12C2216yescomplemented
47C2×C4×D32C2216yescomplemented
48C2×#3799C2216yescomplemented
49C2×#3798C2216yescomplemented
50C2×#3797C2213yescomplemented
51#64297C22148yescomplemented
52C2×#3796C2213yescomplemented
53C2×#3796C2216yescomplemented
54C2×#3796C2216yescomplemented
55C2×#3796C2216yescomplemented
56C2×#3796C2211yescharacteristic, complemented
57C2×#3796C22148yescomplemented
58C2×#3795C2216yescomplemented
59C2×D3×Dic6C2216yescomplemented
60C2×C3×2−1+4—31no—
61C2×C3×H(5,𝔽2)—31no—
62#5968—332no—
63#5966—332no—
64C2×#1010—32no—
65C2×#1010—33no—
66C2×#1010D311yescharacteristic, complemented
67C2×#1009—36no—
68C2×#1009—33no—
69C2×#1009D311yescharacteristic, complemented
70C2×D3×#41—31no—
71C2×D3×#41—31no—
72C2×D3×#41—32no—
73C2×D3×#41—36no—
74C2×D3×#41—33no—
75C2×D3×#41—33no—
76C2×D3×#41—61no—
77C2×#1007—32no—
78C2×#1007—33no—
79C22×#239—32no—
80C22×#239—33no—
81C2×#1004—36no—
82C2×#1004—33no—
83C22×#237—36no—
84C22×#237—33no—
85C23×C3⋊D3C2313yes—
86C23×C3×D3C2316yes—
87C22×D32C2316yes—
88C32×#41C2318yescomplemented
89C2×C32×Q8C2311yescharacteristic
90C2×C32×D4C2313yes—
91C22×C32×C4C2313yes—
92C2×#638C2316yes—
93C22×C3⋊Dic3C2313yes—
94#3832C2318yescomplemented
95Q8×C3⋊D3C2318yescomplemented
96#3830C23124yescomplemented
97D4×C3⋊D3C23124yescomplemented
98#3828C23124yescomplemented
99C2×C4⋊(C3⋊D3)C2313yes—
100C2×C4×C3⋊D3C2311yescharacteristic
101C2×C4×C3⋊D3C2313yes—
102C2×C4×C3⋊D3C2313yes—
103C2×C4×C3⋊D3C2313yes—
104C2×C4×C3⋊D3C23124yescomplemented
105C2×#634C2313yes—
106C2×C3×#67C2316yes—
107C2×C3×#67C2316yes—
108C22×C3×Dic3C2316yes—
109C3×#239C23116yescomplemented
110C3×D3×Q8C23116yescomplemented
111C3×#237C23148yescomplemented
112C3×D3×D4C23148yescomplemented
113C3×#235C23124yescomplemented
114C3×#235C23124yescomplemented
115C2×C3×D12C2316yes—
116C2×C3×D12C2313yes—
117C2×C3×D12C2311yescharacteristic
118C2×C3×D12C23124yescomplemented
119C2×C3×C4×D3C2316yes—
120C2×C3×C4×D3C2316yes—
121C2×C3×Dic6C2316yes—
122C2×C3×Dic6C2313yes—
123C2×C3×Dic6C2311yescharacteristic
124C2×C3×Dic6C23124yescomplemented
125#3811C23148yescomplemented
126D3×#67C23196yescomplemented
127C2×#627C2316yes—
128C2×#626C2316yes—
129C2×#626C23112yes—
130C2×#626C2312yes—
131C2×#626C23148yescomplemented
132C2×#625C2316yes—
133C2×#624C2316yes—
134#3805C23148yescomplemented
135#3804C23196yescomplemented
136C2×D3×Dic3C23112yes—
137C2×D3×Dic3C2316yes—
138C2×D3×Dic3C2312yes—
139C2×D3×Dic3C23148yescomplemented
140#3802C23124yescomplemented
141D3×D12C23148yescomplemented
142C4×D32C23148yescomplemented
143#3799C23148yescomplemented
144#3798C23148yescomplemented
145#3797C23124yescomplemented
146#3796C23124yescomplemented
147#3796C23148yescomplemented
148#3796C23148yescomplemented
149#3796C23148yescomplemented
150#3796C2318yescomplemented
151#3795C23148yescomplemented
152D3×Dic6C23148yescomplemented
153C2×#585—91noSylow
154C3×2−1+4—316no—
155C3×H(5,𝔽2)—316no—
156C2×C3×#41—21no—
157C2×C3×#41—32no—
158C2×C3×#41—36no—
159C2×C3×#41—33no—
160C2×C3×#41—33no—
161C2×C3×#41C2×D311yescharacteristic, complemented
162C2×C3×#41C2×D311yescharacteristic, complemented
163C22×C3×Q8—32no—
164C22×C3×Q8—33no—
165C22×C3×D4—36no—
166C22×C3×D4—33no—
167C22×#67—312no—
168C22×#67—36no—
169C23×Dic3—36no—
170#1010—332no—
171#1010—348no—
172#1010C2×D3116yescomplemented
173#1009—396no—
174#1009—348no—
175#1009C2×D3116yescomplemented
176D3×#41—316no—
177D3×#41—316no—
178D3×#41—332no—
179D3×#41—396no—
180D3×#41—348no—
181D3×#41—348no—
182D3×#41—616no—
183#1007—332no—
184#1007—348no—
185C2×#239—31no—
186C2×#239—31no—
187C2×#239—332no—
188C2×#239—36no—
189C2×#239—33no—
190C2×#239—36no—
191C2×#239—36no—
192C2×#239—31no—
193C2×#239—348no—
194C2×#239—36no—
195C2×#239—61no—
196C2×#239C2×D312yescomplemented
197C2×D3×Q8—31no—
198C2×D3×Q8—31no—
199C2×D3×Q8—36no—
200C2×D3×Q8—33no—
201C2×D3×Q8—33no—
202C2×D3×Q8—61no—
203C2×D3×Q8C2×D312yescomplemented
204#1004—396no—
205#1004—348no—
206C2×#237—33no—
207C2×#237—33no—
208C2×#237—36no—
209C2×#237—36no—
210C2×#237—312no—
211C2×#237—396no—
212C2×#237—36no—
213C2×#237—36no—
214C2×#237—33no—
215C2×#237—36no—
216C2×#237—36no—
217C2×#237—31no—
218C2×#237—348no—
219C2×#237—63no—
220C2×#237C2×D316yescomplemented
221C2×D3×D4—312no—
222C2×D3×D4—33no—
223C2×D3×D4—33no—
224C2×D3×D4—36no—
225C2×D3×D4—36no—
226C2×D3×D4—33no—
227C2×D3×D4—33no—
228C2×D3×D4—36no—
229C2×D3×D4—63no—
230C2×D3×D4C2×D316yescomplemented
231C2×#235—33no—
232C2×#235—33no—
233C2×#235—312no—
234C2×#235—36no—
235C2×#235—36no—
236C2×#235—36no—
237C2×#235—36no—
238C2×#235—63no—
239C2×#235C2×D313yescomplemented
240C2×#235C2×D313yescomplemented
241C22×D12—36no—
242C22×D12—36no—
243C22×D12C2×D313yescomplemented
244C22×C4×D3—36no—
245C22×C4×D3—33no—
246C22×C4×D3—33no—
247C22×C4×D3—36no—
248C22×C4×D3—36no—
249C22×C4×D3—63no—
250C22×Dic6—36no—
251C22×Dic6C2×D313yescomplemented
252C23×C32C2413yes—
253C22×C3⋊D3—46no—
254C22×C3⋊D3C2413yes—
255C22×C3⋊D3C2411yescharacteristic
256C22×C3⋊D3C24112yes—
257C22×C3×D3—412no—
258C22×C3×D3C2412yes—
259C22×C3×D3C2416yes—
260C22×C3×D3C24124yes—
261C2×D32—412no—
262C2×D32C24124yes—
263C32×Q8C2414yes—
264C32×D4C24112yes—
265C2×C32×C4C2411yescharacteristic
266C2×C32×C4C2413yes—
267C2×C32×C4C24112yes—
268#638C24124yes—
269C2×C3⋊Dic3C2411yescharacteristic
270C2×C3⋊Dic3C2413yes—
271C2×C3⋊Dic3C24112yes—
272C4⋊(C3⋊D3)C24112yes—
273C4×C3⋊D3C2414yes—
274C4×C3⋊D3C24112yes—
275C4×C3⋊D3C24112yes—
276C4×C3⋊D3C24112yes—
277#634C24112yes—
278C3×#67C24124yes—
279C3×#67C24124yes—
280C2×C3×Dic3C2416yes—
281C2×C3×Dic3C2412yes—
282C2×C3×Dic3C24124yes—
283C3×D12C24124yes—
284C3×D12C24112yes—
285C3×D12C2414yes—
286C3×C4×D3C24124yes—
287C3×C4×D3C24124yes—
288C3×Dic6C24124yes—
289C3×Dic6C24112yes—
290C3×Dic6C2414yes—
291#627C24124yes—
292#626C24124yes—
293#626C24148yes—
294#626C2418yes—
295#625C24124yes—
296#624C24124yes—
297D3×Dic3C24148yes—
298D3×Dic3C24124yes—
299D3×Dic3C2418yes—
300#585—932no—
301C2×2−1+4—31no—
302C2×2−1+4—92no—
303C2×2−1+4—93no—
304C2×H(5,𝔽2)—31no—
305C2×H(5,𝔽2)—96no—
306C2×H(5,𝔽2)—93no—
307C22×#41—93no—
308C22×#41—96no—
309C22×#41—92no—
310C22×#41—93no—
311C22×#41—91no—
312C24×C3—36no—
313C23×D3—33no—
314C23×D3—33no—
315C23×D3—36no—
316C23×D3—36no—
317C23×D3—63no—
318C23×D3C22×D316yes—
319C3×#41—28no—
320C3×#41—316no—
321C3×#41—348no—
322C3×#41—324no—
323C3×#41—324no—
324C3×#41C22×D318yescomplemented
325C3×#41C22×D318yescomplemented
326C2×C3×Q8—21no—
327C2×C3×Q8—316no—
328C2×C3×Q8—31no—
329C2×C3×Q8—36no—
330C2×C3×Q8—33no—
331C2×C3×Q8—324no—
332C2×C3×Q8C22×D311yescharacteristic
333C2×C3×Q8C22×D311yescharacteristic
334C2×C3×D4—23no—
335C2×C3×D4—36no—
336C2×C3×D4—36no—
337C2×C3×D4—348no—
338C2×C3×D4—31no—
339C2×C3×D4—36no—
340C2×C3×D4—33no—
341C2×C3×D4—324no—
342C2×C3×D4C22×D313yes—
343C2×C3×D4C22×D313yes—
344C22×C3×C4—23no—
345C22×C3×C4—36no—
346C22×C3×C4—36no—
347C22×C3×C4—36no—
348C22×C3×C4C22×D313yes—
349C22×C3×C4C22×D313yes—
350C2×#67—36no—
351C2×#67—36no—
352C2×#67—36no—
353C2×#67—36no—
354C2×#67—396no—
355C2×#67—32no—
356C2×#67—36no—
357C2×#67—312no—
358C2×#67—348no—
359C2×#67—66no—
360C2×#67C22×D316yes—
361C2×#67C22×D316yes—
362C22×Dic3—33no—
363C22×Dic3—33no—
364C22×Dic3—312no—
365C22×Dic3—32no—
366C22×Dic3—36no—
367C22×Dic3—348no—
368C22×Dic3—63no—
369C22×Dic3C22×D316yes—
370#239—38no—
371#239—38no—
372#239—348no—
373#239—324no—
374#239—348no—
375#239—348no—
376#239—38no—
377#239—348no—
378#239—68no—
379#239C22×D3116yescomplemented
380D3×Q8—38no—
381D3×Q8—38no—
382D3×Q8—348no—
383D3×Q8—324no—
384D3×Q8—324no—
385D3×Q8—68no—
386D3×Q8C22×D3116yescomplemented
387#237—324no—
388#237—324no—
389#237—348no—
390#237—348no—
391#237—396no—
392#237—348no—
393#237—348no—
394#237—324no—
395#237—348no—
396#237—348no—
397#237—38no—
398#237—624no—
399#237C22×D3148yescomplemented
400D3×D4—396no—
401D3×D4—324no—
402D3×D4—324no—
403D3×D4—348no—
404D3×D4—348no—
405D3×D4—324no—
406D3×D4—324no—
407D3×D4—348no—
408D3×D4—624no—
409D3×D4C22×D3148yescomplemented
410#235—324no—
411#235—324no—
412#235—396no—
413#235—348no—
414#235—348no—
415#235—348no—
416#235—348no—
417#235—624no—
418#235C22×D3124yescomplemented
419#235C22×D3124yescomplemented
420C2×D12—36no—
421C2×D12—312no—
422C2×D12—32no—
423C2×D12—348no—
424C2×D12—33no—
425C2×D12—33no—
426C2×D12—348no—
427C2×D12—63no—
428C2×D12C22×D316yes—
429C2×D12C22×D313yes—
430C2×D12C22×D311yescharacteristic
431C2×D12C22×D3124yescomplemented
432C2×C4×D3—32no—
433C2×C4×D3—36no—
434C2×C4×D3—312no—
435C2×C4×D3—348no—
436C2×C4×D3—33no—
437C2×C4×D3—31no—
438C2×C4×D3—33no—
439C2×C4×D3—31no—
440C2×C4×D3—33no—
441C2×C4×D3—33no—
442C2×C4×D3—33no—
443C2×C4×D3—33no—
444C2×C4×D3—324no—
445C2×C4×D3—324no—
446C2×C4×D3—36no—
447C2×C4×D3—36no—
448C2×C4×D3—348no—
449C2×C4×D3—348no—
450C2×C4×D3—61no—
451C2×C4×D3—63no—
452C2×C4×D3—63no—
453C2×C4×D3—63no—
454C2×C4×D3—624no—
455C2×C4×D3C22×D316yes—
456C2×C4×D3C22×D316yes—
457C2×Dic6—33no—
458C2×Dic6—33no—
459C2×Dic6—36no—
460C2×Dic6—36no—
461C2×Dic6—348no—
462C2×Dic6—63no—
463C2×Dic6C22×D316yes—
464C2×Dic6C22×D313yes—
465C2×Dic6C22×D311yescharacteristic
466C2×Dic6C22×D3124yescomplemented
467C22×C32—26no—
468C22×C32C2516yes—
469C22×C32C2511yescharacteristic
470C2×C3⋊D3—22no—
471C2×C3⋊D3—26no—
472C2×C3⋊D3—412no—
473C2×C3⋊D3C2516yes—
474C2×C3⋊D3C2512yes—
475C2×C3×D3—24no—
476C2×C3×D3—212no—
477C2×C3×D3—424no—
478C2×C3×D3C25112yes—
479C2×C3×D3C2514yes—
480D32—424no—
481C32×C4C2512yes—
482C32×C4C2516yes—
483C3⋊Dic3C2512yes—
484C3⋊Dic3C2516yes—
485C3×Dic3C25112yes—
486C3×Dic3C2514yes—
4872−1+4—316no—
4882−1+4—932no—
4892−1+4—948no—
490H(5,𝔽2)—316no—
491H(5,𝔽2)—996no—
492H(5,𝔽2)—948no—
493C2×#41—32no—
494C2×#41—36no—
495C2×#41—33no—
496C2×#41—33no—
497C2×#41—96no—
498C2×#41—912no—
499C2×#41—96no—
500C2×#41—96no—
501C2×#41—96no—
502C2×#41—93no—
503C2×#41—96no—
504C2×#41—91no—
505C2×#41—96no—
506C2×#41—96no—
507C2×#41—948no—
508C2×#41—996no—
509C2×#41—932no—
510C2×#41—948no—
511C2×#41—916no—
512C2×#41—91no—
513C2×#41—93no—
514C2×#41—93no—
515C2×#41D3211yescharacteristic, complemented
516C22×Q8—32no—
517C22×Q8—33no—
518C22×Q8—96no—
519C22×Q8—93no—
520C22×Q8—91no—
521C22×D4—36no—
522C22×D4—33no—
523C22×D4—96no—
524C22×D4—96no—
525C22×D4—96no—
526C22×D4—93no—
527C22×D4—912no—
528C22×D4—93no—
529C23×C4—96no—
530C23×C4—96no—
531C23×C4—93no—
532C23×C3—23no—
533C23×C3—36no—
534C23×C3—32no—
535C23×C3—324no—
536C23×C3—1212no—
537C23×C3C23×D313yes—
538C23×C3C23×D313yes—
539C22×D3—33no—
540C22×D3—31no—
541C22×D3—33no—
542C22×D3—31no—
543C22×D3—312no—
544C22×D3—312no—
545C22×D3—324no—
546C22×D3—324no—
547C22×D3—412no—
548C22×D3—61no—
549C22×D3—63no—
550C22×D3—612no—
551C22×D3—1212no—
552C22×D3—1212no—
553C22×D3—126no—
554C22×D3—126no—
555C22×D3—1212no—
556C22×D3C23×D316yes—
557C22×D3C23×D312yes—
558C22×D3C23×D3124yes—
559C3×Q8—24no—
560C3×Q8—34no—
561C3×Q8—324no—
562C3×Q8—312no—
563C3×Q8C23×D314yes—
564C3×Q8C23×D314yes—
565C3×D4—212no—
566C3×D4—324no—
567C3×D4—324no—
568C3×D4—34no—
569C3×D4—324no—
570C3×D4—312no—
571C3×D4C23×D3112yes—
572C3×D4C23×D3112yes—
573C2×C3×C4—23no—
574C2×C3×C4—21no—
575C2×C3×C4—212no—
576C2×C3×C4—32no—
577C2×C3×C4—36no—
578C2×C3×C4—324no—
579C2×C3×C4—324no—
580C2×C3×C4—324no—
581C2×C3×C4C23×D313yes—
582C2×C3×C4C23×D313yes—
583C2×C3×C4C23×D311yescharacteristic
584C2×C3×C4C23×D311yescharacteristic
585C2×C3×C4C23×D3112yes—
586C2×C3×C4C23×D3112yes—
587#67—324no—
588#67—324no—
589#67—324no—
590#67—324no—
591#67—38no—
592#67—324no—
593#67—348no—
594#67—624no—
595#67C23×D3124yes—
596#67C23×D3124yes—
597C2×Dic3—33no—
598C2×Dic3—33no—
599C2×Dic3—31no—
600C2×Dic3—312no—
601C2×Dic3—31no—
602C2×Dic3—312no—
603C2×Dic3—348no—
604C2×Dic3—38no—
605C2×Dic3—324no—
606C2×Dic3—63no—
607C2×Dic3—61no—
608C2×Dic3—612no—
609C2×Dic3C23×D312yes—
610C2×Dic3C23×D316yes—
611C2×Dic3C23×D3124yes—
612D12—324no—
613D12—348no—
614D12—38no—
615D12—312no—
616D12—312no—
617D12—612no—
618D12C23×D3124yes—
619D12C23×D3112yes—
620D12C23×D314yes—
621C4×D3—38no—
622C4×D3—324no—
623C4×D3—348no—
624C4×D3—312no—
625C4×D3—34no—
626C4×D3—312no—
627C4×D3—34no—
628C4×D3—312no—
629C4×D3—312no—
630C4×D3—312no—
631C4×D3—312no—
632C4×D3—324no—
633C4×D3—324no—
634C4×D3—64no—
635C4×D3—612no—
636C4×D3—612no—
637C4×D3—612no—
638C4×D3C23×D3124yes—
639C4×D3C23×D3124yes—
640Dic6—312no—
641Dic6—312no—
642Dic6—324no—
643Dic6—324no—
644Dic6—612no—
645Dic6C23×D3124yes—
646Dic6C23×D3112yes—
647Dic6C23×D314yes—
648C2×C32—26no—
649C2×C32#58512yescomplemented
650C2×C32C2611yescharacteristic
651C3⋊D3—22no—
652C3⋊D3—26no—
653C3×D3—24no—
654C3×D3—212no—
655C24—36no—
656C24—96no—
657C24—93no—
658#41—316no—
659#41—348no—
660#41—324no—
661#41—324no—
662#41—948no—
663#41—996no—
664#41—948no—
665#41—948no—
666#41—948no—
667#41—924no—
668#41—948no—
669#41—98no—
670#41—948no—
671#41—948no—
672#41—98no—
673#41—924no—
674#41—924no—
675#41C2×D3218yescomplemented
676C2×Q8—316no—
677C2×Q8—36no—
678C2×Q8—33no—
679C2×Q8—324no—
680C2×Q8—31no—
681C2×Q8—96no—
682C2×Q8—948no—
683C2×Q8—924no—
684C2×Q8—98no—
685C2×Q8—93no—
686C2×Q8C2×D3211yescharacteristic
687C2×D4—36no—
688C2×D4—36no—
689C2×D4—348no—
690C2×D4—36no—
691C2×D4—33no—
692C2×D4—324no—
693C2×D4—31no—
694C2×D4—948no—
695C2×D4—92no—
696C2×D4—912no—
697C2×D4—96no—
698C2×D4—948no—
699C2×D4—948no—
700C2×D4—924no—
701C2×D4—996no—
702C2×D4—96no—
703C2×D4—96no—
704C2×D4—924no—
705C2×D4—93no—
706C2×D4C2×D3213yes—
707C22×C4—36no—
708C22×C4—36no—
709C22×C4—36no—
710C22×C4—96no—
711C22×C4—948no—
712C22×C4—92no—
713C22×C4—96no—
714C22×C4—912no—
715C22×C4—948no—
716C22×C4—93no—
717C22×C4—93no—
718C22×C4—91no—
719C22×C4—93no—
720C22×C4—93no—
721C22×C4—924no—
722C22×C4C2×D3213yes—
723C22×C3—26no—
724C22×C3—26no—
725C22×C3—26no—
726C22×C3—21no—
727C22×C3—312no—
728C22×C3—34no—
729C22×C3—46no—
730C22×C3—64no—
731C22×C3—612no—
732C22×C3—1224no—
733C22×C3C24×D316yes—
734C22×C3C24×D316yes—
735C22×C3C24×D311yescharacteristic
736C22×C3C24×D311yescharacteristic
737C2×D3—212no—
738C2×D3—24no—
739C2×D3—32no—
740C2×D3—36no—
741C2×D3—32no—
742C2×D3—36no—
743C2×D3—424no—
744C2×D3—62no—
745C2×D3—66no—
746C2×D3—64no—
747C2×D3—62no—
748C2×D3—66no—
749C2×D3—62no—
750C2×D3—66no—
751C2×D3—126no—
752C2×D3—1224no—
753C2×D3—1224no—
754C2×D3—1212no—
755C2×D3—1212no—
756C2×D3—1224no—
757C2×D3C24×D3112yes—
758C2×D3C24×D314yes—
759C3×C4—26no—
760C3×C4—22no—
761C3×C4—34no—
762C3×C4—312no—
763C3×C4C24×D316yes—
764C3×C4C24×D316yes—
765C3×C4C24×D312yes—
766C3×C4C24×D312yes—
767Dic3—36no—
768Dic3—36no—
769Dic3—32no—
770Dic3—32no—
771Dic3—66no—
772Dic3—62no—
773Dic3C24×D314yes—
774Dic3C24×D3112yes—
775C32C2×#58511yescharacteristic, complemented, Sylow
776C23—32no—
777C23—36no—
778C23—324no—
779C23—924no—
780C23—91no—
781C23—93no—
782C23—912no—
783C23—1212no—
784C23—366no—
785C23—3612no—
786C23C22×D3213yes—
787Q8—324no—
788Q8—312no—
789Q8—34no—
790Q8—924no—
791Q8—912no—
792Q8C22×D3214yes—
793D4—324no—
794D4—324no—
795D4—324no—
796D4—312no—
797D4—34no—
798D4—98no—
799D4—948no—
800D4—924no—
801D4—924no—
802D4—924no—
803D4—912no—
804D4C22×D32112yes—
805C2×C4—324no—
806C2×C4—32no—
807C2×C4—36no—
808C2×C4—324no—
809C2×C4—324no—
810C2×C4—924no—
811C2×C4—98no—
812C2×C4—924no—
813C2×C4—948no—
814C2×C4—912no—
815C2×C4—91no—
816C2×C4—93no—
817C2×C4—912no—
818C2×C4—94no—
819C2×C4—912no—
820C2×C4—912no—
821C2×C4C22×D32112yes—
822C2×C4C22×D3213yes—
823C2×C4C22×D3211yescharacteristic
824C2×C3—26no—
825C2×C3—26no—
826C2×C3—22no—
827C2×C3—21no—
828C2×C3—46no—
829C2×C3—64no—
830C2×C3—612no—
831C2×C3#596612yescomplemented
832C2×C3#596812yescomplemented
833C2×C3C25×D311yescharacteristic
834C2×C3C25×D311yescharacteristic
835D3—212no—
836D3—24no—
837D3—64no—
838D3—62no—
839D3—66no—
840D3—62no—
841D3—66no—
842D3—126no—
843C22—26no—
844C22—34no—
845C22—312no—
846C22—612no—
847C22—64no—
848C22—92no—
849C22—96no—
850C22—1224no—
851C22—182no—
852C22—186no—
853C22—3612no—
854C22—3624no—
855C22C23×D3216yes—
856C22C23×D3211yescharacteristic
857C4—34no—
858C4—312no—
859C4—92no—
860C4—96no—
861C4C23×D3216yes—
862C4C23×D3212yes—
863C3—21no—
864C3C2×#596611yescharacteristic, complemented
865C3C2×#596811yescharacteristic, complemented
866C2—26no—
867C2—612no—
868C2—64no—
869C2—182no—
870C2—186no—
871C2#1059669812yesdirect product factor
872C2C24×D3211yescharacteristic
subgroupG/H
centerC22C23×D32
commutator, cosocleC2×C32C26
FrattiniC2C24×D32
FittingC2×C32×#41C22
socleC22×C32C25
hypercenterC2×#41D32
hypocenterC32C2×#585
LCSG ▷ C2×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×C3×#1010C2semidirect
3. C2×C3×#1009C2semidirect
4. #10596698C2direct (N × H)
5. C2×D3×#239C2semidirect
6. C2×#64315C2semidirect
7. C2×#64314C2semidirect
8. C2×D3×#237C2semidirect
9. C2×#64307C2semidirect
10. C2×#64306C2semidirect
11. C2×#64297C2semidirect
12. C22×#3796C2semidirect
15. C2×C32×#41C22semidirect
16. #41×C3⋊D3C22semidirect
17. C2×#3832C22semidirect
18. C2×Q8×C3⋊D3C22semidirect
19. C2×#3830C22semidirect
20. C2×D4×C3⋊D3C22semidirect
21. C2×#3828C22semidirect
22. C22×C4×C3⋊D3C22semidirect
23. C3×#1010C22semidirect
24. C3×#1009C22semidirect
25. C2×C3×#239C22semidirect
26. C2×C3×D3×Q8C22semidirect
27. C2×C3×#237C22semidirect
28. C2×C3×D3×D4C22semidirect
29. C2×C3×#235C22semidirect
30. C2×C3×#235C22semidirect
31. C22×C3×D12C22semidirect
32. C22×C3×Dic6C22semidirect
33. C2×#3811C22semidirect
34. C2×D3×#67C22semidirect
35. C22×#626C22semidirect
36. C2×#3805C22semidirect
37. C2×#3804C22semidirect
38. C22×D3×Dic3C22semidirect
39. D3×#239C22semidirect
40. #64315C22semidirect
41. #64314C22semidirect
42. D3×#237C22semidirect
43. #64307C22semidirect
44. #64306C22semidirect
45. C2×#3802C22semidirect
46. C2×D3×D12C22semidirect
47. C2×C4×D32C22semidirect
48. C2×#3799C22semidirect
49. C2×#3798C22semidirect
50. C2×#3797C22semidirect
51. #64297C22semidirect
52. C2×#3796C22semidirect
53. C2×#3796C22semidirect
54. C2×#3796C22semidirect
55. C2×#3796C22semidirect
56. C2×#3796C22semidirect
57. C2×#3796C22semidirect
58. C2×#3795C22semidirect
59. C2×D3×Dic6C22semidirect
66. C2×#1010D3semidirect
69. C2×#1009D3semidirect
88. C32×#41C23semidirect
94. #3832C23semidirect
95. Q8×C3⋊D3C23semidirect
96. #3830C23semidirect
97. D4×C3⋊D3C23semidirect
98. #3828C23semidirect
104. C2×C4×C3⋊D3C23semidirect
109. C3×#239C23semidirect
110. C3×D3×Q8C23semidirect
111. C3×#237C23semidirect
112. C3×D3×D4C23semidirect
113. C3×#235C23semidirect
114. C3×#235C23semidirect
118. C2×C3×D12C23semidirect
124. C2×C3×Dic6C23semidirect
125. #3811C23semidirect
126. D3×#67C23semidirect
131. C2×#626C23semidirect
134. #3805C23semidirect
135. #3804C23semidirect
139. C2×D3×Dic3C23semidirect
140. #3802C23semidirect
141. D3×D12C23semidirect
142. C4×D32C23semidirect
143. #3799C23semidirect
144. #3798C23semidirect
145. #3797C23semidirect
146. #3796C23semidirect
147. #3796C23semidirect
148. #3796C23semidirect
149. #3796C23semidirect
150. #3796C23semidirect
151. #3795C23semidirect
152. D3×Dic6C23semidirect
161. C2×C3×#41C2×D3semidirect
162. C2×C3×#41C2×D3semidirect
172. #1010C2×D3semidirect
175. #1009C2×D3semidirect
196. C2×#239C2×D3semidirect
203. C2×D3×Q8C2×D3semidirect
220. C2×#237C2×D3semidirect
230. C2×D3×D4C2×D3semidirect
239. C2×#235C2×D3semidirect
240. C2×#235C2×D3semidirect
243. C22×D12C2×D3semidirect
251. C22×Dic6C2×D3semidirect
324. C3×#41C22×D3semidirect
325. C3×#41C22×D3semidirect
379. #239C22×D3semidirect
386. D3×Q8C22×D3semidirect
399. #237C22×D3semidirect
409. D3×D4C22×D3semidirect
418. #235C22×D3semidirect
419. #235C22×D3semidirect
431. C2×D12C22×D3semidirect
466. C2×Dic6C22×D3semidirect
515. C2×#41D32semidirect
649. C2×C32#585semidirect
675. #41C2×D32semidirect
775. C32C2×#585semidirect
831. C2×C3#5966semidirect
832. C2×C3#5968semidirect
864. C3C2×#5966semidirect
865. C3C2×#5968semidirect
871. C2#10596698direct (N × H)

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×C3×#10102
C2×C3×#10092
#105966982
C2×D3×#2392
C2×#643152
C2×#643142
C2×D3×#2372
C2×#643072
C2×#643062
C2×#642972
C22×#37962
C2×#59683
C2×#59663