Finite Group Databasebeta

← C2×#10596697 #11919267

Subgroups — C2×#10596697 #11919267

Order 1152.

12361 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64366C211yesmaximal, characteristic, complemented
2C2×C3×#1010C211yesmaximal, characteristic, complemented
3C2×C3×D3×#41C211yesmaximal, characteristic, complemented
4#10596697C2132yesmaximal, direct product factor
5C2×D3×#239C212yesmaximal, complemented
6C2×#64316C212yesmaximal, complemented
7C2×#64314C216yesmaximal, complemented
8C2×#64312C216yesmaximal, complemented
9C2×#64308C213yesmaximal, complemented
10C2×D3×#235C213yesmaximal, complemented
11C22×#3799C213yesmaximal, complemented
12C2×#64297C213yesmaximal, complemented
13C2×#5968—31nomaximal
14C2×#5964—31nomaximal
15C2×C32×#41C2211yescharacteristic, complemented
16#64366C22116yescomplemented
17C2×#3832C2212yescomplemented
18C2×D4×C3⋊D3C2216yescomplemented
19C2×#3828C2213yescomplemented
20C22×C4⋊(C3⋊D3)C2213yescomplemented
21C3×#1010C22116yescomplemented
22C3×D3×#41C22116yescomplemented
23C2×C3×#239C2211yescharacteristic, complemented
24C2×C3×D3×Q8C2211yescharacteristic, complemented
25C2×C3×D3×Q8C2212yescomplemented
26C2×C3×#237C2213yescomplemented
27C2×C3×#237C2216yescomplemented
28C2×C3×D3×D4C2213yescomplemented
29C2×C3×#235C2213yescomplemented
30C2×C3×#235C2213yescomplemented
31C22×C3×C4×D3C2213yescomplemented
32C22×C3×Dic6C2213yescomplemented
33C2×#3811C22112yescomplemented
34C2×D3×#67C2216yescomplemented
35C22×#626C2216yescomplemented
36C22×#624C2216yescomplemented
37C2×#3804C22112yescomplemented
38C2×#3804C2216yescomplemented
39D3×#239C22132yescomplemented
40#64316C22132yescomplemented
41#64314C22196yescomplemented
42#64312C22196yescomplemented
43#64308C22148yescomplemented
44D3×#235C22148yescomplemented
45C2×D3×D12C2213yescomplemented
46C2×D3×D12C2216yescomplemented
47C2×C4×D32C2216yescomplemented
48C2×#3799C2216yescomplemented
49C2×#3799C2213yescomplemented
50C2×#3799C2216yescomplemented
51C2×#3799C2216yescomplemented
52C2×#3799C2216yescomplemented
53C2×#3799C22148yescomplemented
54C2×#3798C2216yescomplemented
55C2×#3797C2216yescomplemented
56#64297C22148yescomplemented
57C2×#3796C2216yescomplemented
58C2×#3795C2211yescharacteristic, complemented
59C2×D3×Dic6C2213yescomplemented
60C2×C3×2−1+4—31no—
61C22×C3×#41—31no—
62#5968—332no—
63#5964—332no—
64C2×#1010—33no—
65C2×#1010D311yescharacteristic, complemented
66C2×#1009—31no—
67C2×#1009—31no—
68C2×#1009—36no—
69C2×#1009—33no—
70C2×#1009—33no—
71C2×#1009—61no—
72C2×D3×#41—32no—
73C2×D3×#41—36no—
74C2×D3×#41—36no—
75C2×D3×#41—33no—
76C2×D3×#41D311yescharacteristic, complemented
77C2×#1007—32no—
78C2×#1007—32no—
79C2×#1007—33no—
80C22×#239—32no—
81C22×#239—33no—
82C2×#1004—36no—
83C22×#235—33no—
84C22×#235—33no—
85C23×C3⋊D3C2316yes—
86C23×C3×D3C2313yes—
87C22×D32C2316yes—
88C32×#41C2318yescomplemented
89C2×C32×Q8C2311yescharacteristic
90C2×C32×D4C2313yes—
91C22×C32×C4C2313yes—
92C2×#638C2316yes—
93#3832C23116yescomplemented
94D4×C3⋊D3C23148yescomplemented
95#3828C23124yescomplemented
96C2×C4⋊(C3⋊D3)C2313yes—
97C2×C4⋊(C3⋊D3)C2316yes—
98C2×C4⋊(C3⋊D3)C23124yescomplemented
99C2×C4×C3⋊D3C2316yes—
100C2×#634C2311yescharacteristic
101C2×C3×#67C2316yes—
102C2×C3×#67C2316yes—
103C22×C3×Dic3C2313yes—
104C22×C3×Dic3C2316yes—
105C3×#239C2318yescomplemented
106C3×D3×Q8C2318yescomplemented
107C3×D3×Q8C23116yescomplemented
108C3×#237C23124yescomplemented
109C3×#237C23148yescomplemented
110C3×D3×D4C23124yescomplemented
111C3×#235C23124yescomplemented
112C3×#235C23124yescomplemented
113C2×C3×D12C2311yescharacteristic
114C2×C3×D12C2313yes—
115C2×C3×C4×D3C2313yes—
116C2×C3×C4×D3C2311yescharacteristic
117C2×C3×C4×D3C2313yes—
118C2×C3×C4×D3C2316yes—
119C2×C3×C4×D3C2313yes—
120C2×C3×C4×D3C23124yescomplemented
121C2×C3×Dic6C2313yes—
122C2×C3×Dic6C2316yes—
123C2×C3×Dic6C2313yes—
124C2×C3×Dic6C23124yescomplemented
125#3811C23196yescomplemented
126D3×#67C23148yescomplemented
127C2×#627C2316yes—
128C2×#626C23112yes—
129C2×#626C2316yes—
130C2×#626C2316yes—
131C2×#626C23148yescomplemented
132C2×#625C2312yes—
133C2×#624C23112yes—
134C2×#624C2316yes—
135C2×#624C23148yescomplemented
136#3804C23196yescomplemented
137#3804C23148yescomplemented
138C2×D3×Dic3C2316yes—
139C2×D3×Dic3C2312yes—
140D3×D12C23124yescomplemented
141D3×D12C23148yescomplemented
142C4×D32C23148yescomplemented
143#3799C23148yescomplemented
144#3799C23124yescomplemented
145#3799C23148yescomplemented
146#3799C23148yescomplemented
147#3799C23148yescomplemented
148#3798C23148yescomplemented
149#3797C23148yescomplemented
150#3796C23148yescomplemented
151#3795C2318yescomplemented
152D3×Dic6C23124yescomplemented
153C2×#585—91noSylow
154C3×2−1+4—316no—
155C2×C3×#41—21no—
156C2×C3×#41—316no—
157C2×C3×#41—31no—
158C2×C3×#41—33no—
159C2×C3×#41—36no—
160C2×C3×#41—33no—
161C2×C3×#41—33no—
162C2×C3×#41C2×D311yescharacteristic, complemented
163C2×C3×#41C2×D311yescharacteristic, complemented
164C22×C3×Q8—32no—
165C22×C3×Q8—31no—
166C22×C3×Q8—33no—
167C22×C3×D4—33no—
168C23×C3×C4—33no—
169C22×#67—36no—
170C22×#67—36no—
171#1010—348no—
172#1010C2×D3116yescomplemented
173#1009—316no—
174#1009—316no—
175#1009—396no—
176#1009—348no—
177#1009—348no—
178#1009—616no—
179D3×#41—332no—
180D3×#41—396no—
181D3×#41—396no—
182D3×#41—348no—
183D3×#41C2×D3116yescomplemented
184#1007—332no—
185#1007—332no—
186#1007—348no—
187C2×#239—32no—
188C2×#239—32no—
189C2×#239—332no—
190C2×#239—36no—
191C2×#239—36no—
192C2×#239—33no—
193C2×#239—36no—
194C2×#239—36no—
195C2×#239—36no—
196C2×#239—348no—
197C2×#239—62no—
198C2×#239C2×D311yescharacteristic, complemented
199C2×D3×Q8—33no—
200C2×D3×Q8—36no—
201C2×D3×Q8—36no—
202C2×D3×Q8C2×D311yescharacteristic, complemented
203C2×D3×Q8C2×D312yescomplemented
204#1004—396no—
205C2×#237—312no—
206C2×#237—36no—
207C2×#237—31no—
208C2×#237—36no—
209C2×#237C2×D316yescomplemented
210C2×#237C2×D313yescomplemented
211C2×D3×D4—36no—
212C2×D3×D4—36no—
213C2×D3×D4—36no—
214C2×D3×D4—312no—
215C2×D3×D4—312no—
216C2×D3×D4—36no—
217C2×D3×D4—33no—
218C2×D3×D4—66no—
219C2×D3×D4C2×D313yescomplemented
220C2×#235—33no—
221C2×#235—33no—
222C2×#235—36no—
223C2×#235—312no—
224C2×#235—348no—
225C2×#235—31no—
226C2×#235—36no—
227C2×#235—36no—
228C2×#235—33no—
229C2×#235—36no—
230C2×#235—36no—
231C2×#235—36no—
232C2×#235—36no—
233C2×#235—348no—
234C2×#235—63no—
235C2×#235C2×D313yescomplemented
236C2×#235C2×D313yescomplemented
237C22×D12—36no—
238C22×D12—33no—
239C22×D12—33no—
240C22×D12—33no—
241C22×D12—36no—
242C22×D12—63no—
243C22×C4×D3—36no—
244C22×C4×D3—36no—
245C22×C4×D3—36no—
246C22×C4×D3—36no—
247C22×C4×D3C2×D313yescomplemented
248C22×Dic6—33no—
249C22×Dic6C2×D313yescomplemented
250C23×C32C2413yes—
251C22×C3⋊D3—412no—
252C22×C3⋊D3C2416yes—
253C22×C3⋊D3C24124yes—
254C22×C3×D3—46no—
255C22×C3×D3C2412yes—
256C22×C3×D3C2413yes—
257C22×C3×D3C2411yescharacteristic
258C22×C3×D3C24112yes—
259C2×D32—412no—
260C2×D32C24124yes—
261C32×Q8C2414yes—
262C32×D4C24112yes—
263C2×C32×C4C2411yescharacteristic
264C2×C32×C4C2413yes—
265C2×C32×C4C24112yes—
266#638C24124yes—
267C2×C3⋊Dic3C2412yes—
268C4⋊(C3⋊D3)C24112yes—
269C4⋊(C3⋊D3)C24124yes—
270C4×C3⋊D3C24124yes—
271#634C2414yes—
272C3×#67C24124yes—
273C3×#67C24124yes—
274C2×C3×Dic3C2411yescharacteristic
275C2×C3×Dic3C2416yes—
276C2×C3×Dic3C24112yes—
277C2×C3×Dic3C24124yes—
278C2×C3×Dic3C2413yes—
279C3×D12C2414yes—
280C3×D12C24112yes—
281C3×C4×D3C24112yes—
282C3×C4×D3C2414yes—
283C3×C4×D3C24112yes—
284C3×C4×D3C24124yes—
285C3×C4×D3C24112yes—
286C3×Dic6C24112yes—
287C3×Dic6C24124yes—
288C3×Dic6C24112yes—
289#627C24124yes—
290#626C24148yes—
291#626C24124yes—
292#626C24124yes—
293#625C2418yes—
294#624C24148yes—
295#624C24124yes—
296D3×Dic3C24124yes—
297D3×Dic3C2418yes—
298#585—932no—
299C2×2−1+4—31no—
300C2×2−1+4—92no—
301C2×2−1+4—93no—
302C2×H(5,𝔽2)—96no—
303C2×H(5,𝔽2)—93no—
304C2×H(5,𝔽2)—91no—
305C22×#41—31no—
306C22×#41—93no—
307C22×#41—93no—
308C22×#41—92no—
309C22×#41—96no—
310C24×C3—33no—
311C23×D3—36no—
312C23×D3—36no—
313C23×D3—36no—
314C23×D3—36no—
315C23×D3—66no—
316C23×D3C22×D313yes—
317C3×#41—28no—
318C3×#41—38no—
319C3×#41—324no—
320C3×#41—348no—
321C3×#41—324no—
322C3×#41—324no—
323C3×#41C22×D318yescomplemented
324C3×#41C22×D318yescomplemented
325C2×C3×Q8—21no—
326C2×C3×Q8—316no—
327C2×C3×Q8—38no—
328C2×C3×Q8—33no—
329C2×C3×Q8—33no—
330C2×C3×Q8—36no—
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—324no—
338C2×C3×D4—31no—
339C2×C3×D4—33no—
340C2×C3×D4C22×D313yes—
341C2×C3×D4C22×D313yes—
342C22×C3×C4—23no—
343C22×C3×C4—33no—
344C22×C3×C4—36no—
345C22×C3×C4—33no—
346C22×C3×C4—33no—
347C22×C3×C4—36no—
348C22×C3×C4—31no—
349C22×C3×C4—33no—
350C22×C3×C4—324no—
351C22×C3×C4C22×D313yes—
352C22×C3×C4C22×D313yes—
353C2×#67—36no—
354C2×#67—36no—
355C2×#67—32no—
356C2×#67—32no—
357C2×#67—348no—
358C2×#67—36no—
359C2×#67—36no—
360C2×#67—312no—
361C2×#67—348no—
362C2×#67—66no—
363C2×#67C22×D316yes—
364C2×#67C22×D316yes—
365C22×Dic3—36no—
366C22×Dic3—32no—
367C22×Dic3C22×D316yes—
368C22×Dic3C22×D313yes—
369#239—316no—
370#239—316no—
371#239—348no—
372#239—348no—
373#239—324no—
374#239—348no—
375#239—348no—
376#239—348no—
377#239—616no—
378#239C22×D318yescomplemented
379D3×Q8—324no—
380D3×Q8—348no—
381D3×Q8—348no—
382D3×Q8C22×D318yescomplemented
383D3×Q8C22×D3116yescomplemented
384#237—396no—
385#237—348no—
386#237—38no—
387#237—348no—
388#237C22×D3148yescomplemented
389#237C22×D3124yescomplemented
390D3×D4—348no—
391D3×D4—348no—
392D3×D4—348no—
393D3×D4—396no—
394D3×D4—396no—
395D3×D4—348no—
396D3×D4—324no—
397D3×D4—648no—
398D3×D4C22×D3124yescomplemented
399#235—324no—
400#235—324no—
401#235—348no—
402#235—396no—
403#235—38no—
404#235—348no—
405#235—348no—
406#235—324no—
407#235—348no—
408#235—348no—
409#235—348no—
410#235—348no—
411#235—624no—
412#235C22×D3124yescomplemented
413#235C22×D3124yescomplemented
414C2×D12—312no—
415C2×D12—36no—
416C2×D12—36no—
417C2×D12—348no—
418C2×D12—33no—
419C2×D12—33no—
420C2×D12—36no—
421C2×D12—36no—
422C2×D12—324no—
423C2×D12—324no—
424C2×D12—324no—
425C2×D12—348no—
426C2×D12—63no—
427C2×D12—66no—
428C2×D12—624no—
429C2×D12C22×D311yescharacteristic
430C2×D12C22×D313yes—
431C2×C4×D3—32no—
432C2×C4×D3—36no—
433C2×C4×D3—36no—
434C2×C4×D3—36no—
435C2×C4×D3—36no—
436C2×C4×D3—36no—
437C2×C4×D3—312no—
438C2×C4×D3—312no—
439C2×C4×D3—348no—
440C2×C4×D3—348no—
441C2×C4×D3—348no—
442C2×C4×D3—348no—
443C2×C4×D3—66no—
444C2×C4×D3C22×D313yes—
445C2×C4×D3C22×D316yes—
446C2×C4×D3C22×D311yescharacteristic
447C2×C4×D3C22×D313yes—
448C2×C4×D3C22×D313yes—
449C2×C4×D3C22×D3124yescomplemented
450C2×Dic6—31no—
451C2×Dic6—31no—
452C2×Dic6—36no—
453C2×Dic6—36no—
454C2×Dic6—324no—
455C2×Dic6—61no—
456C2×Dic6C22×D313yes—
457C2×Dic6C22×D316yes—
458C2×Dic6C22×D313yes—
459C2×Dic6C22×D3124yescomplemented
460C22×C32—26no—
461C22×C32C2516yes—
462C22×C32C2511yescharacteristic
463C2×C3⋊D3—212no—
464C2×C3⋊D3—424no—
465C2×C3⋊D3C25112yes—
466C2×C3×D3—24no—
467C2×C3×D3—26no—
468C2×C3×D3—22no—
469C2×C3×D3—412no—
470C2×C3×D3C2516yes—
471C2×C3×D3C2514yes—
472C2×C3×D3C2512yes—
473D32—424no—
474C32×C4C2512yes—
475C32×C4C2516yes—
476C3⋊Dic3C2514yes—
477C3×Dic3C2512yes—
478C3×Dic3C25112yes—
479C3×Dic3C2516yes—
4802−1+4—316no—
4812−1+4—932no—
4822−1+4—948no—
483H(5,𝔽2)—996no—
484H(5,𝔽2)—948no—
485H(5,𝔽2)—916no—
486C2×#41—316no—
487C2×#41—31no—
488C2×#41—33no—
489C2×#41—36no—
490C2×#41—33no—
491C2×#41—33no—
492C2×#41—96no—
493C2×#41—96no—
494C2×#41—91no—
495C2×#41—912no—
496C2×#41—93no—
497C2×#41—96no—
498C2×#41—96no—
499C2×#41—96no—
500C2×#41—96no—
501C2×#41—948no—
502C2×#41—948no—
503C2×#41—96no—
504C2×#41—932no—
505C2×#41—996no—
506C2×#41—92no—
507C2×#41—93no—
508C2×#41D3211yescharacteristic, complemented
509C22×Q8—31no—
510C22×Q8—32no—
511C22×Q8—33no—
512C22×Q8—93no—
513C22×Q8—96no—
514C22×D4—33no—
515C22×D4—93no—
516C22×D4—96no—
517C22×D4—96no—
518C22×D4—912no—
519C22×D4—96no—
520C22×D4—96no—
521C22×D4—93no—
522C23×C4—33no—
523C23×C4—96no—
524C23×C4—96no—
525C23×C3—23no—
526C23×C3—33no—
527C23×C3—32no—
528C23×C3—31no—
529C23×C3—312no—
530C23×C3—126no—
531C23×C3C23×D313yes—
532C23×C3C23×D313yes—
533C22×D3—36no—
534C22×D3—36no—
535C22×D3—324no—
536C22×D3—324no—
537C22×D3—324no—
538C22×D3—324no—
539C22×D3—46no—
540C22×D3—66no—
541C22×D3—624no—
542C22×D3—1212no—
543C22×D3—1212no—
544C22×D3—1212no—
545C22×D3—1212no—
546C22×D3—2412no—
547C22×D3C23×D313yes—
548C22×D3C23×D312yes—
549C22×D3C23×D311yescharacteristic
550C22×D3C23×D3112yes—
551C3×Q8—24no—
552C3×Q8—312no—
553C3×Q8—312no—
554C3×Q8—324no—
555C3×Q8C23×D314yes—
556C3×Q8C23×D314yes—
557C3×D4—212no—
558C3×D4—324no—
559C3×D4—324no—
560C3×D4—34no—
561C3×D4—312no—
562C3×D4C23×D3112yes—
563C3×D4C23×D3112yes—
564C2×C3×C4—21no—
565C2×C3×C4—23no—
566C2×C3×C4—212no—
567C2×C3×C4—33no—
568C2×C3×C4—36no—
569C2×C3×C4—31no—
570C2×C3×C4—312no—
571C2×C3×C4—324no—
572C2×C3×C4—312no—
573C2×C3×C4—312no—
574C2×C3×C4—324no—
575C2×C3×C4—34no—
576C2×C3×C4—312no—
577C2×C3×C4C23×D311yescharacteristic
578C2×C3×C4C23×D311yescharacteristic
579C2×C3×C4C23×D313yes—
580C2×C3×C4C23×D313yes—
581C2×C3×C4C23×D3112yes—
582C2×C3×C4C23×D3112yes—
583#67—324no—
584#67—324no—
585#67—38no—
586#67—38no—
587#67—324no—
588#67—324no—
589#67—348no—
590#67—624no—
591#67C23×D3124yes—
592#67C23×D3124yes—
593C2×Dic3—32no—
594C2×Dic3—32no—
595C2×Dic3—324no—
596C2×Dic3—38no—
597C2×Dic3—62no—
598C2×Dic3C23×D313yes—
599C2×Dic3C23×D316yes—
600C2×Dic3C23×D3124yes—
601C2×Dic3C23×D311yescharacteristic
602C2×Dic3C23×D3112yes—
603D12—348no—
604D12—324no—
605D12—324no—
606D12—312no—
607D12—312no—
608D12—324no—
609D12—324no—
610D12—612no—
611D12—624no—
612D12C23×D314yes—
613D12C23×D3112yes—
614C4×D3—38no—
615C4×D3—324no—
616C4×D3—324no—
617C4×D3—324no—
618C4×D3—324no—
619C4×D3—324no—
620C4×D3—348no—
621C4×D3—348no—
622C4×D3—624no—
623C4×D3C23×D3112yes—
624C4×D3C23×D3124yes—
625C4×D3C23×D314yes—
626C4×D3C23×D3112yes—
627C4×D3C23×D3112yes—
628Dic6—34no—
629Dic6—34no—
630Dic6—324no—
631Dic6—324no—
632Dic6—64no—
633Dic6C23×D3112yes—
634Dic6C23×D3124yes—
635Dic6C23×D3112yes—
636C2×C32—26no—
637C2×C32#58512yescomplemented
638C2×C32C2611yescharacteristic
639C3⋊D3—212no—
640C3×D3—24no—
641C3×D3—26no—
642C3×D3—22no—
643C24—33no—
644C24—96no—
645C24—96no—
646#41—38no—
647#41—324no—
648#41—348no—
649#41—324no—
650#41—324no—
651#41—948no—
652#41—948no—
653#41—98no—
654#41—996no—
655#41—924no—
656#41—948no—
657#41—948no—
658#41—948no—
659#41—948no—
660#41—948no—
661#41—916no—
662#41—924no—
663#41C2×D3218yescomplemented
664C2×Q8—38no—
665C2×Q8—316no—
666C2×Q8—36no—
667C2×Q8—33no—
668C2×Q8—33no—
669C2×Q8—324no—
670C2×Q8—96no—
671C2×Q8—924no—
672C2×Q8—948no—
673C2×Q8—91no—
674C2×Q8C2×D3211yescharacteristic
675C2×D4—36no—
676C2×D4—36no—
677C2×D4—324no—
678C2×D4—33no—
679C2×D4—31no—
680C2×D4—924no—
681C2×D4—948no—
682C2×D4—96no—
683C2×D4—96no—
684C2×D4—912no—
685C2×D4—948no—
686C2×D4—996no—
687C2×D4—948no—
688C2×D4—92no—
689C2×D4—96no—
690C2×D4—948no—
691C2×D4—96no—
692C2×D4—93no—
693C2×D4—924no—
694C2×D4C2×D3213yes—
695C22×C4—33no—
696C22×C4—36no—
697C22×C4—31no—
698C22×C4—33no—
699C22×C4—33no—
700C22×C4—33no—
701C22×C4—324no—
702C22×C4—36no—
703C22×C4—96no—
704C22×C4—912no—
705C22×C4—948no—
706C22×C4—948no—
707C22×C4—92no—
708C22×C4—96no—
709C22×C4—96no—
710C22×C4C2×D3213yes—
711C22×C3—26no—
712C22×C3—26no—
713C22×C3—26no—
714C22×C3—21no—
715C22×C3—36no—
716C22×C3—34no—
717C22×C3—32no—
718C22×C3—46no—
719C22×C3—64no—
720C22×C3—66no—
721C22×C3—62no—
722C22×C3—1212no—
723C22×C3C24×D316yes—
724C22×C3C24×D316yes—
725C22×C3C24×D311yescharacteristic
726C22×C3C24×D311yescharacteristic
727C2×D3—22no—
728C2×D3—26no—
729C2×D3—24no—
730C2×D3—312no—
731C2×D3—312no—
732C2×D3—412no—
733C2×D3—612no—
734C2×D3—612no—
735C2×D3—612no—
736C2×D3—1212no—
737C2×D3—1224no—
738C2×D3—1224no—
739C2×D3—1224no—
740C2×D3—1224no—
741C2×D3—2424no—
742C2×D3C24×D316yes—
743C2×D3C24×D314yes—
744C2×D3C24×D312yes—
745C3×C4—22no—
746C3×C4—26no—
747C3×C4—36no—
748C3×C4—312no—
749C3×C4—32no—
750C3×C4C24×D312yes—
751C3×C4C24×D312yes—
752C3×C4C24×D316yes—
753C3×C4C24×D316yes—
754Dic3—34no—
755Dic3—34no—
756Dic3—64no—
757Dic3C24×D316yes—
758Dic3C24×D3112yes—
759Dic3C24×D312yes—
760C32C2×#58511yescharacteristic, complemented, Sylow
761C23—31no—
762C23—32no—
763C23—33no—
764C23—312no—
765C23—924no—
766C23—96no—
767C23—924no—
768C23—126no—
769C23—3612no—
770C23—3612no—
771C23C22×D3213yes—
772Q8—324no—
773Q8—312no—
774Q8—312no—
775Q8—924no—
776Q8—94no—
777Q8C22×D3214yes—
778D4—324no—
779D4—324no—
780D4—312no—
781D4—34no—
782D4—924no—
783D4—924no—
784D4—948no—
785D4—98no—
786D4—924no—
787D4—924no—
788D4—912no—
789D4C22×D32112yes—
790C2×C4—312no—
791C2×C4—324no—
792C2×C4—31no—
793C2×C4—33no—
794C2×C4—36no—
795C2×C4—34no—
796C2×C4—312no—
797C2×C4—312no—
798C2×C4—312no—
799C2×C4—324no—
800C2×C4—924no—
801C2×C4—948no—
802C2×C4—98no—
803C2×C4—924no—
804C2×C4—92no—
805C2×C4—924no—
806C2×C4C22×D32112yes—
807C2×C4C22×D3213yes—
808C2×C4C22×D3211yescharacteristic
809C2×C3—26no—
810C2×C3—26no—
811C2×C3—22no—
812C2×C3—21no—
813C2×C3—46no—
814C2×C3—64no—
815C2×C3—66no—
816C2×C3—62no—
817C2×C3#596412yescomplemented
818C2×C3#596812yescomplemented
819C2×C3C25×D311yescharacteristic
820C2×C3C25×D311yescharacteristic
821D3—22no—
822D3—26no—
823D3—24no—
824D3—612no—
825D3—612no—
826D3—1212no—
827C22—26no—
828C22—32no—
829C22—34no—
830C22—36no—
831C22—62no—
832C22—66no—
833C22—64no—
834C22—912no—
835C22—1212no—
836C22—1812no—
837C22—3624no—
838C22—3624no—
839C22C23×D3216yes—
840C22C23×D3211yescharacteristic
841C4—32no—
842C4—36no—
843C4—312no—
844C4—94no—
845C4C23×D3216yes—
846C4C23×D3212yes—
847C3—21no—
848C3C2×#596411yescharacteristic, complemented
849C3C2×#596811yescharacteristic, complemented
850C2—26no—
851C2—62no—
852C2—66no—
853C2—64no—
854C2—1812no—
855C2#1059669712yesdirect product factor
856C2C24×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×#64366C2semidirect
2. C2×C3×#1010C2semidirect
3. C2×C3×D3×#41C2semidirect
4. #10596697C2direct (N × H)
5. C2×D3×#239C2semidirect
6. C2×#64316C2semidirect
7. C2×#64314C2semidirect
8. C2×#64312C2semidirect
9. C2×#64308C2semidirect
10. C2×D3×#235C2semidirect
11. C22×#3799C2semidirect
12. C2×#64297C2semidirect
15. C2×C32×#41C22semidirect
16. #64366C22semidirect
17. C2×#3832C22semidirect
18. C2×D4×C3⋊D3C22semidirect
19. C2×#3828C22semidirect
20. C22×C4⋊(C3⋊D3)C22semidirect
21. C3×#1010C22semidirect
22. C3×D3×#41C22semidirect
23. C2×C3×#239C22semidirect
24. C2×C3×D3×Q8C22semidirect
25. C2×C3×D3×Q8C22semidirect
26. C2×C3×#237C22semidirect
27. C2×C3×#237C22semidirect
28. C2×C3×D3×D4C22semidirect
29. C2×C3×#235C22semidirect
30. C2×C3×#235C22semidirect
31. C22×C3×C4×D3C22semidirect
32. C22×C3×Dic6C22semidirect
33. C2×#3811C22semidirect
34. C2×D3×#67C22semidirect
35. C22×#626C22semidirect
36. C22×#624C22semidirect
37. C2×#3804C22semidirect
38. C2×#3804C22semidirect
39. D3×#239C22semidirect
40. #64316C22semidirect
41. #64314C22semidirect
42. #64312C22semidirect
43. #64308C22semidirect
44. D3×#235C22semidirect
45. C2×D3×D12C22semidirect
46. C2×D3×D12C22semidirect
47. C2×C4×D32C22semidirect
48. C2×#3799C22semidirect
49. C2×#3799C22semidirect
50. C2×#3799C22semidirect
51. C2×#3799C22semidirect
52. C2×#3799C22semidirect
53. C2×#3799C22semidirect
54. C2×#3798C22semidirect
55. C2×#3797C22semidirect
56. #64297C22semidirect
57. C2×#3796C22semidirect
58. C2×#3795C22semidirect
59. C2×D3×Dic6C22semidirect
65. C2×#1010D3semidirect
76. C2×D3×#41D3semidirect
88. C32×#41C23semidirect
93. #3832C23semidirect
94. D4×C3⋊D3C23semidirect
95. #3828C23semidirect
98. C2×C4⋊(C3⋊D3)C23semidirect
105. C3×#239C23semidirect
106. C3×D3×Q8C23semidirect
107. C3×D3×Q8C23semidirect
108. C3×#237C23semidirect
109. C3×#237C23semidirect
110. C3×D3×D4C23semidirect
111. C3×#235C23semidirect
112. C3×#235C23semidirect
120. C2×C3×C4×D3C23semidirect
124. C2×C3×Dic6C23semidirect
125. #3811C23semidirect
126. D3×#67C23semidirect
131. C2×#626C23semidirect
135. C2×#624C23semidirect
136. #3804C23semidirect
137. #3804C23semidirect
140. D3×D12C23semidirect
141. D3×D12C23semidirect
142. C4×D32C23semidirect
143. #3799C23semidirect
144. #3799C23semidirect
145. #3799C23semidirect
146. #3799C23semidirect
147. #3799C23semidirect
148. #3798C23semidirect
149. #3797C23semidirect
150. #3796C23semidirect
151. #3795C23semidirect
152. D3×Dic6C23semidirect
162. C2×C3×#41C2×D3semidirect
163. C2×C3×#41C2×D3semidirect
172. #1010C2×D3semidirect
183. D3×#41C2×D3semidirect
198. C2×#239C2×D3semidirect
202. C2×D3×Q8C2×D3semidirect
203. C2×D3×Q8C2×D3semidirect
209. C2×#237C2×D3semidirect
210. C2×#237C2×D3semidirect
219. C2×D3×D4C2×D3semidirect
235. C2×#235C2×D3semidirect
236. C2×#235C2×D3semidirect
247. C22×C4×D3C2×D3semidirect
249. C22×Dic6C2×D3semidirect
323. C3×#41C22×D3semidirect
324. C3×#41C22×D3semidirect
378. #239C22×D3semidirect
382. D3×Q8C22×D3semidirect
383. D3×Q8C22×D3semidirect
388. #237C22×D3semidirect
389. #237C22×D3semidirect
398. D3×D4C22×D3semidirect
412. #235C22×D3semidirect
413. #235C22×D3semidirect
449. C2×C4×D3C22×D3semidirect
459. C2×Dic6C22×D3semidirect
508. C2×#41D32semidirect
637. C2×C32#585semidirect
663. #41C2×D32semidirect
760. C32C2×#585semidirect
817. C2×C3#5964semidirect
818. C2×C3#5968semidirect
848. C3C2×#5964semidirect
849. C3C2×#5968semidirect
855. C2#10596697direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643662
C2×C3×#10102
C2×C3×D3×#412
#105966972
C2×D3×#2392
C2×#643162
C2×#643142
C2×#643122
C2×#643082
C2×D3×#2352
C22×#37992
C2×#642972
C2×#59683
C2×#59643