Finite Group Databasebeta

← C2×#10596696 #11919269

Subgroups — C2×#10596696 #11919269

Order 1152.

12309 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64367C211yesmaximal, characteristic, complemented
2C2×C3×#1009C211yesmaximal, characteristic, complemented
3C2×C3×D3×#41C211yesmaximal, characteristic, complemented
4#10596696C2132yesmaximal, direct product factor
5C2×#64319C212yesmaximal, complemented
6C2×#64315C212yesmaximal, complemented
7C2×#64313C216yesmaximal, complemented
8C2×D3×#237C216yesmaximal, complemented
9C2×#64307C213yesmaximal, complemented
10C2×D3×#235C213yesmaximal, complemented
11C2×#64298C213yesmaximal, complemented
12C22×#3795C213yesmaximal, complemented
13C2×#5966—31nomaximal
14C2×#5964—31nomaximal
15C2×C32×#41C2211yescharacteristic, complemented
16#64367C22116yescomplemented
17C2×Q8×C3⋊D3C2212yescomplemented
18C2×#3830C2216yescomplemented
19C2×#3828C2213yescomplemented
20C22×#634C2213yescomplemented
21C3×#1009C22116yescomplemented
22C3×D3×#41C22116yescomplemented
23C2×C3×#239C2212yescomplemented
24C2×C3×#239C2211yescharacteristic, complemented
25C2×C3×D3×Q8C2211yescharacteristic, complemented
26C2×C3×#237C2213yescomplemented
27C2×C3×D3×D4C2216yescomplemented
28C2×C3×D3×D4C2213yescomplemented
29C2×C3×#235C2213yescomplemented
30C2×C3×#235C2213yescomplemented
31C22×C3×D12C2213yescomplemented
32C22×C3×C4×D3C2213yescomplemented
33C2×D3×#67C2216yescomplemented
34C2×D3×#67C22112yescomplemented
35C22×#625C2216yescomplemented
36C2×#3805C22112yescomplemented
37C2×#3804C2216yescomplemented
38C22×D3×Dic3C2216yescomplemented
39#64319C22132yescomplemented
40#64315C22132yescomplemented
41#64313C22196yescomplemented
42D3×#237C22196yescomplemented
43#64307C22148yescomplemented
44D3×#235C22148yescomplemented
45C2×#3802C2216yescomplemented
46C2×D3×D12C2213yescomplemented
47C2×C4×D32C2216yescomplemented
48C2×#3799C2211yescharacteristic, complemented
49C2×#3798C2216yescomplemented
50#64298C22148yescomplemented
51C2×#3796C2216yescomplemented
52C2×#3795C2213yescomplemented
53C2×#3795C2216yescomplemented
54C2×#3795C2216yescomplemented
55C2×#3795C2216yescomplemented
56C2×#3795C2216yescomplemented
57C2×#3795C22148yescomplemented
58C2×D3×Dic6C2213yescomplemented
59C2×D3×Dic6C2216yescomplemented
60C2×C3×H(5,𝔽2)—31no—
61C22×C3×#41—31no—
62#5966—332no—
63#5964—332no—
64C2×#1010—31no—
65C2×#1010—31no—
66C2×#1010—32no—
67C2×#1010—33no—
68C2×#1010—33no—
69C2×#1010—61no—
70C2×#1009—33no—
71C2×#1009D311yescharacteristic, complemented
72C2×D3×#41—32no—
73C2×D3×#41—32no—
74C2×D3×#41—36no—
75C2×D3×#41—33no—
76C2×D3×#41D311yescharacteristic, complemented
77C2×#1007—32no—
78C2×#1004—36no—
79C2×#1004—36no—
80C2×#1004—33no—
81C22×#237—36no—
82C22×#237—33no—
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—
93C22×C3⋊Dic3C2316yes—
94Q8×C3⋊D3C23116yescomplemented
95#3830C23148yescomplemented
96#3828C23124yescomplemented
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3C2316yes—
99C2×#634C2313yes—
100C2×#634C2316yes—
101C2×#634C23124yescomplemented
102C2×C3×#67C2316yes—
103C2×C3×#67C2316yes—
104C22×C3×Dic3C2313yes—
105C3×#239C23116yescomplemented
106C3×#239C2318yescomplemented
107C3×D3×Q8C2318yescomplemented
108C3×#237C23124yescomplemented
109C3×D3×D4C23148yescomplemented
110C3×D3×D4C23124yescomplemented
111C3×#235C23124yescomplemented
112C3×#235C23124yescomplemented
113C2×C3×D12C2313yes—
114C2×C3×D12C2316yes—
115C2×C3×D12C2313yes—
116C2×C3×D12C23124yescomplemented
117C2×C3×C4×D3C2313yes—
118C2×C3×C4×D3C2316yes—
119C2×C3×C4×D3C2311yescharacteristic
120C2×C3×C4×D3C2313yes—
121C2×C3×C4×D3C2313yes—
122C2×C3×C4×D3C23124yescomplemented
123C2×C3×Dic6C2311yescharacteristic
124C2×C3×Dic6C2313yes—
125D3×#67C23148yescomplemented
126D3×#67C23196yescomplemented
127C2×#627C2316yes—
128C2×#626C2316yes—
129C2×#626C2312yes—
130C2×#625C2316yes—
131C2×#625C23112yes—
132C2×#625C23148yescomplemented
133C2×#624C2312yes—
134#3805C23196yescomplemented
135#3804C23148yescomplemented
136C2×D3×Dic3C23112yes—
137C2×D3×Dic3C2316yes—
138C2×D3×Dic3C2316yes—
139C2×D3×Dic3C23148yescomplemented
140#3802C23148yescomplemented
141D3×D12C23124yescomplemented
142C4×D32C23148yescomplemented
143#3799C2318yescomplemented
144#3798C23148yescomplemented
145#3796C23148yescomplemented
146#3795C23124yescomplemented
147#3795C23148yescomplemented
148#3795C23148yescomplemented
149#3795C23148yescomplemented
150#3795C23148yescomplemented
151D3×Dic6C23124yescomplemented
152D3×Dic6C23148yescomplemented
153C2×#585—91noSylow
154C3×H(5,𝔽2)—316no—
155C2×C3×#41—21no—
156C2×C3×#41—316no—
157C2×C3×#41—31no—
158C2×C3×#41—32no—
159C2×C3×#41—33no—
160C2×C3×#41—33no—
161C2×C3×#41—33no—
162C2×C3×#41C2×D311yescharacteristic, complemented
163C2×C3×#41C2×D311yescharacteristic, complemented
164C22×C3×Q8—31no—
165C22×C3×D4—36no—
166C22×C3×D4—33no—
167C22×C3×D4—33no—
168C23×C3×C4—33no—
169C22×#67—36no—
170C22×#67—36no—
171C22×#67—36no—
172C22×#67—312no—
173C23×Dic3—36no—
174#1010—316no—
175#1010—316no—
176#1010—332no—
177#1010—348no—
178#1010—348no—
179#1010—616no—
180#1009—348no—
181#1009C2×D3116yescomplemented
182D3×#41—332no—
183D3×#41—332no—
184D3×#41—396no—
185D3×#41—348no—
186D3×#41C2×D3116yescomplemented
187#1007—332no—
188C2×#239—36no—
189C2×#239—31no—
190C2×#239C2×D312yescomplemented
191C2×#239C2×D311yescharacteristic, complemented
192C2×D3×Q8—32no—
193C2×D3×Q8—32no—
194C2×D3×Q8—36no—
195C2×D3×Q8—33no—
196C2×D3×Q8—62no—
197C2×D3×Q8C2×D311yescharacteristic, complemented
198#1004—396no—
199#1004—396no—
200#1004—348no—
201C2×#237—36no—
202C2×#237—36no—
203C2×#237—312no—
204C2×#237—312no—
205C2×#237—36no—
206C2×#237—396no—
207C2×#237—36no—
208C2×#237—33no—
209C2×#237—36no—
210C2×#237—36no—
211C2×#237—36no—
212C2×#237—348no—
213C2×#237—36no—
214C2×#237—66no—
215C2×#237C2×D313yescomplemented
216C2×D3×D4—36no—
217C2×D3×D4—312no—
218C2×D3×D4—36no—
219C2×D3×D4—36no—
220C2×D3×D4—33no—
221C2×D3×D4C2×D313yescomplemented
222C2×D3×D4C2×D316yescomplemented
223C2×#235—33no—
224C2×#235—33no—
225C2×#235—36no—
226C2×#235—348no—
227C2×#235—33no—
228C2×#235—36no—
229C2×#235—36no—
230C2×#235—36no—
231C2×#235—36no—
232C2×#235—348no—
233C2×#235—36no—
234C2×#235—36no—
235C2×#235—31no—
236C2×#235—63no—
237C2×#235C2×D313yescomplemented
238C2×#235C2×D313yescomplemented
239C22×D12—33no—
240C22×D12C2×D313yescomplemented
241C22×C4×D3—36no—
242C22×C4×D3—36no—
243C22×C4×D3—36no—
244C22×C4×D3C2×D313yescomplemented
245C22×Dic6—33no—
246C22×Dic6—33no—
247C22×Dic6—33no—
248C22×Dic6—36no—
249C22×Dic6—63no—
250C23×C32C2413yes—
251C22×C3⋊D3C2412yes—
252C22×C3×D3—46no—
253C22×C3×D3—412no—
254C22×C3×D3C2413yes—
255C22×C3×D3C2416yes—
256C22×C3×D3C2411yescharacteristic
257C22×C3×D3C24124yes—
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⋊Dic3C2416yes—
268C2×C3⋊Dic3C24124yes—
269C4⋊(C3⋊D3)C2414yes—
270C4×C3⋊D3C24124yes—
271#634C24112yes—
272#634C24124yes—
273C3×#67C24124yes—
274C3×#67C24124yes—
275C2×C3×Dic3C2411yescharacteristic
276C2×C3×Dic3C2413yes—
277C2×C3×Dic3C2412yes—
278C2×C3×Dic3C24112yes—
279C3×D12C24112yes—
280C3×D12C24124yes—
281C3×D12C24112yes—
282C3×C4×D3C24112yes—
283C3×C4×D3C24124yes—
284C3×C4×D3C2414yes—
285C3×C4×D3C24112yes—
286C3×C4×D3C24112yes—
287C3×Dic6C2414yes—
288C3×Dic6C24112yes—
289#627C24124yes—
290#626C24124yes—
291#626C2418yes—
292#625C24124yes—
293#625C24148yes—
294#624C2418yes—
295D3×Dic3C24148yes—
296D3×Dic3C24124yes—
297D3×Dic3C24124yes—
298#585—932no—
299C2×2−1+4—92no—
300C2×2−1+4—93no—
301C2×2−1+4—91no—
302C2×H(5,𝔽2)—31no—
303C2×H(5,𝔽2)—96no—
304C2×H(5,𝔽2)—93no—
305C22×#41—31no—
306C22×#41—93no—
307C22×#41—93no—
308C22×#41—96no—
309C22×#41—92no—
310C24×C3—36no—
311C24×C3—33no—
312C23×D3—36no—
313C23×D3—36no—
314C23×D3C22×D316yes—
315C23×D3C22×D313yes—
316C3×#41—28no—
317C3×#41—38no—
318C3×#41—316no—
319C3×#41—324no—
320C3×#41—324no—
321C3×#41—324no—
322C3×#41C22×D318yescomplemented
323C3×#41C22×D318yescomplemented
324C2×C3×Q8—21no—
325C2×C3×Q8—38no—
326C2×C3×Q8—31no—
327C2×C3×Q8—33no—
328C2×C3×Q8C22×D311yescharacteristic
329C2×C3×Q8C22×D311yescharacteristic
330C2×C3×D4—23no—
331C2×C3×D4—36no—
332C2×C3×D4—36no—
333C2×C3×D4—348no—
334C2×C3×D4—324no—
335C2×C3×D4—33no—
336C2×C3×D4—33no—
337C2×C3×D4—36no—
338C2×C3×D4—324no—
339C2×C3×D4C22×D313yes—
340C2×C3×D4C22×D313yes—
341C22×C3×C4—23no—
342C22×C3×C4—33no—
343C22×C3×C4—36no—
344C22×C3×C4—33no—
345C22×C3×C4—33no—
346C22×C3×C4—31no—
347C22×C3×C4—33no—
348C22×C3×C4—324no—
349C22×C3×C4C22×D313yes—
350C22×C3×C4C22×D313yes—
351C2×#67—36no—
352C2×#67—36no—
353C2×#67—36no—
354C2×#67—312no—
355C2×#67—312no—
356C2×#67—36no—
357C2×#67—348no—
358C2×#67—348no—
359C2×#67—348no—
360C2×#67—396no—
361C2×#67—32no—
362C2×#67—36no—
363C2×#67—66no—
364C2×#67C22×D316yes—
365C2×#67C22×D316yes—
366C22×Dic3—36no—
367C22×Dic3—36no—
368C22×Dic3—36no—
369C22×Dic3—312no—
370C22×Dic3—36no—
371C22×Dic3—348no—
372C22×Dic3—66no—
373C22×Dic3C22×D313yes—
374#239—348no—
375#239—38no—
376#239C22×D3116yescomplemented
377#239C22×D318yescomplemented
378D3×Q8—316no—
379D3×Q8—316no—
380D3×Q8—348no—
381D3×Q8—324no—
382D3×Q8—616no—
383D3×Q8C22×D318yescomplemented
384#237—348no—
385#237—348no—
386#237—396no—
387#237—396no—
388#237—348no—
389#237—348no—
390#237—324no—
391#237—348no—
392#237—348no—
393#237—348no—
394#237—348no—
395#237—648no—
396#237C22×D3124yescomplemented
397D3×D4—348no—
398D3×D4—396no—
399D3×D4—348no—
400D3×D4—348no—
401D3×D4—324no—
402D3×D4C22×D3124yescomplemented
403D3×D4C22×D3148yescomplemented
404#235—324no—
405#235—324no—
406#235—348no—
407#235—324no—
408#235—348no—
409#235—348no—
410#235—348no—
411#235—348no—
412#235—348no—
413#235—348no—
414#235—38no—
415#235—624no—
416#235C22×D3124yescomplemented
417#235C22×D3124yescomplemented
418C2×D12—36no—
419C2×D12—32no—
420C2×D12—31no—
421C2×D12—31no—
422C2×D12—324no—
423C2×D12—61no—
424C2×D12C22×D313yes—
425C2×D12C22×D316yes—
426C2×D12C22×D313yes—
427C2×D12C22×D3124yescomplemented
428C2×C4×D3—36no—
429C2×C4×D3—36no—
430C2×C4×D3—312no—
431C2×C4×D3—348no—
432C2×C4×D3—36no—
433C2×C4×D3—36no—
434C2×C4×D3—32no—
435C2×C4×D3—32no—
436C2×C4×D3—348no—
437C2×C4×D3—348no—
438C2×C4×D3—66no—
439C2×C4×D3C22×D313yes—
440C2×C4×D3C22×D316yes—
441C2×C4×D3C22×D311yescharacteristic
442C2×C4×D3C22×D313yes—
443C2×C4×D3C22×D313yes—
444C2×C4×D3C22×D3124yescomplemented
445C2×Dic6—33no—
446C2×Dic6—33no—
447C2×Dic6—36no—
448C2×Dic6—36no—
449C2×Dic6—324no—
450C2×Dic6—324no—
451C2×Dic6—36no—
452C2×Dic6—36no—
453C2×Dic6—324no—
454C2×Dic6—348no—
455C2×Dic6—63no—
456C2×Dic6—66no—
457C2×Dic6—624no—
458C2×Dic6C22×D311yescharacteristic
459C2×Dic6C22×D313yes—
460C22×C32—26no—
461C22×C32C2516yes—
462C22×C32C2511yescharacteristic
463C2×C3⋊D3—24no—
464C2×C3⋊D3C2514yes—
465C2×C3×D3—26no—
466C2×C3×D3—212no—
467C2×C3×D3—22no—
468C2×C3×D3—412no—
469C2×C3×D3—424no—
470C2×C3×D3C25112yes—
471C2×C3×D3C2516yes—
472C2×C3×D3C2512yes—
473D32—424no—
474C32×C4C2512yes—
475C32×C4C2516yes—
476C3⋊Dic3C25112yes—
477C3×Dic3C2512yes—
478C3×Dic3C2516yes—
479C3×Dic3C2514yes—
4802−1+4—932no—
4812−1+4—948no—
4822−1+4—916no—
483H(5,𝔽2)—316no—
484H(5,𝔽2)—996no—
485H(5,𝔽2)—948no—
486C2×#41—316no—
487C2×#41—31no—
488C2×#41—32no—
489C2×#41—33no—
490C2×#41—33no—
491C2×#41—33no—
492C2×#41—96no—
493C2×#41—96no—
494C2×#41—93no—
495C2×#41—96no—
496C2×#41—96no—
497C2×#41—96no—
498C2×#41—96no—
499C2×#41—948no—
500C2×#41—91no—
501C2×#41—948no—
502C2×#41—912no—
503C2×#41—96no—
504C2×#41—996no—
505C2×#41—932no—
506C2×#41—96no—
507C2×#41—93no—
508C2×#41D3211yescharacteristic, complemented
509C22×Q8—31no—
510C22×Q8—93no—
511C22×Q8—96no—
512C22×Q8—92no—
513C22×Q8—93no—
514C22×D4—33no—
515C22×D4—36no—
516C22×D4—33no—
517C22×D4—93no—
518C22×D4—96no—
519C22×D4—96no—
520C22×D4—912no—
521C22×D4—96no—
522C23×C4—33no—
523C23×C4—96no—
524C23×C4—96no—
525C23×C3—23no—
526C23×C3—36no—
527C23×C3—33no—
528C23×C3—31no—
529C23×C3—324no—
530C23×C3—312no—
531C23×C3—1212no—
532C23×C3—126no—
533C23×C3C23×D313yes—
534C23×C3C23×D313yes—
535C22×D3—32no—
536C22×D3—32no—
537C22×D3—324no—
538C22×D3—324no—
539C22×D3—46no—
540C22×D3—412no—
541C22×D3—62no—
542C22×D3—1212no—
543C22×D3—1212no—
544C22×D3C23×D316yes—
545C22×D3C23×D313yes—
546C22×D3C23×D311yescharacteristic
547C22×D3C23×D3124yes—
548C22×D3C23×D3112yes—
549C3×Q8—24no—
550C3×Q8—34no—
551C3×Q8—312no—
552C3×Q8C23×D314yes—
553C3×Q8C23×D314yes—
554C3×D4—212no—
555C3×D4—324no—
556C3×D4—324no—
557C3×D4—312no—
558C3×D4—312no—
559C3×D4—324no—
560C3×D4C23×D3112yes—
561C3×D4C23×D3112yes—
562C2×C3×C4—21no—
563C2×C3×C4—23no—
564C2×C3×C4—212no—
565C2×C3×C4—32no—
566C2×C3×C4—33no—
567C2×C3×C4—31no—
568C2×C3×C4—312no—
569C2×C3×C4—324no—
570C2×C3×C4—312no—
571C2×C3×C4—312no—
572C2×C3×C4—34no—
573C2×C3×C4—312no—
574C2×C3×C4C23×D311yescharacteristic
575C2×C3×C4C23×D311yescharacteristic
576C2×C3×C4C23×D313yes—
577C2×C3×C4C23×D313yes—
578C2×C3×C4C23×D3112yes—
579C2×C3×C4C23×D3112yes—
580#67—324no—
581#67—324no—
582#67—324no—
583#67—348no—
584#67—348no—
585#67—324no—
586#67—38no—
587#67—324no—
588#67—624no—
589#67C23×D3124yes—
590#67C23×D3124yes—
591C2×Dic3—36no—
592C2×Dic3—36no—
593C2×Dic3—324no—
594C2×Dic3—324no—
595C2×Dic3—324no—
596C2×Dic3—348no—
597C2×Dic3—324no—
598C2×Dic3—66no—
599C2×Dic3—624no—
600C2×Dic3C23×D312yes—
601C2×Dic3C23×D313yes—
602C2×Dic3C23×D311yescharacteristic
603C2×Dic3C23×D3112yes—
604D12—324no—
605D12—38no—
606D12—34no—
607D12—34no—
608D12—64no—
609D12C23×D3112yes—
610D12C23×D3124yes—
611D12C23×D3112yes—
612C4×D3—324no—
613C4×D3—324no—
614C4×D3—348no—
615C4×D3—324no—
616C4×D3—324no—
617C4×D3—38no—
618C4×D3—38no—
619C4×D3—624no—
620C4×D3C23×D3112yes—
621C4×D3C23×D3124yes—
622C4×D3C23×D314yes—
623C4×D3C23×D3112yes—
624C4×D3C23×D3112yes—
625Dic6—312no—
626Dic6—312no—
627Dic6—324no—
628Dic6—324no—
629Dic6—324no—
630Dic6—324no—
631Dic6—612no—
632Dic6—624no—
633Dic6C23×D314yes—
634Dic6C23×D3112yes—
635C2×C32—26no—
636C2×C32#58512yescomplemented
637C2×C32C2611yescharacteristic
638C3⋊D3—24no—
639C3×D3—26no—
640C3×D3—212no—
641C3×D3—22no—
642C24—33no—
643C24—36no—
644C24—96no—
645#41—38no—
646#41—316no—
647#41—324no—
648#41—324no—
649#41—324no—
650#41—948no—
651#41—948no—
652#41—924no—
653#41—948no—
654#41—948no—
655#41—948no—
656#41—948no—
657#41—98no—
658#41—996no—
659#41—948no—
660#41—948no—
661#41—924no—
662#41C2×D3218yescomplemented
663C2×Q8—38no—
664C2×Q8—33no—
665C2×Q8—31no—
666C2×Q8—96no—
667C2×Q8—924no—
668C2×Q8—948no—
669C2×Q8—916no—
670C2×Q8—96no—
671C2×Q8—93no—
672C2×Q8—924no—
673C2×Q8C2×D3211yescharacteristic
674C2×D4—36no—
675C2×D4—36no—
676C2×D4—324no—
677C2×D4—348no—
678C2×D4—36no—
679C2×D4—33no—
680C2×D4—33no—
681C2×D4—324no—
682C2×D4—924no—
683C2×D4—92no—
684C2×D4—96no—
685C2×D4—948no—
686C2×D4—948no—
687C2×D4—996no—
688C2×D4—96no—
689C2×D4—912no—
690C2×D4—948no—
691C2×D4—96no—
692C2×D4—91no—
693C2×D4C2×D3213yes—
694C22×C4—33no—
695C22×C4—31no—
696C22×C4—33no—
697C22×C4—33no—
698C22×C4—33no—
699C22×C4—324no—
700C22×C4—36no—
701C22×C4—92no—
702C22×C4—948no—
703C22×C4—96no—
704C22×C4—96no—
705C22×C4—912no—
706C22×C4—948no—
707C22×C4—96no—
708C22×C4—96no—
709C22×C4C2×D3213yes—
710C22×C3—26no—
711C22×C3—26no—
712C22×C3—26no—
713C22×C3—21no—
714C22×C3—312no—
715C22×C3—36no—
716C22×C3—32no—
717C22×C3—46no—
718C22×C3—612no—
719C22×C3—66no—
720C22×C3—62no—
721C22×C3—1224no—
722C22×C3—1212no—
723C22×C3C24×D316yes—
724C22×C3C24×D316yes—
725C22×C3C24×D311yescharacteristic
726C22×C3C24×D311yescharacteristic
727C2×D3—22no—
728C2×D3—26no—
729C2×D3—212no—
730C2×D3—34no—
731C2×D3—34no—
732C2×D3—412no—
733C2×D3—424no—
734C2×D3—64no—
735C2×D3—64no—
736C2×D3—64no—
737C2×D3—124no—
738C2×D3—1224no—
739C2×D3—1224no—
740C2×D3C24×D3112yes—
741C2×D3C24×D316yes—
742C2×D3C24×D312yes—
743C3×C4—22no—
744C3×C4—26no—
745C3×C4—34no—
746C3×C4—36no—
747C3×C4—32no—
748C3×C4C24×D312yes—
749C3×C4C24×D312yes—
750C3×C4C24×D316yes—
751C3×C4C24×D316yes—
752Dic3—312no—
753Dic3—312no—
754Dic3—612no—
755Dic3C24×D314yes—
756Dic3C24×D316yes—
757Dic3C24×D312yes—
758C32C2×#58511yescharacteristic, complemented, Sylow
759C23—31no—
760C23—33no—
761C23—36no—
762C23—312no—
763C23—324no—
764C23—924no—
765C23—92no—
766C23—126no—
767C23—1212no—
768C23—3612no—
769C23C22×D3213yes—
770Q8—312no—
771Q8—34no—
772Q8—924no—
773Q8—924no—
774Q8—912no—
775Q8C22×D3214yes—
776D4—324no—
777D4—324no—
778D4—324no—
779D4—312no—
780D4—312no—
781D4—98no—
782D4—924no—
783D4—924no—
784D4—948no—
785D4—924no—
786D4—94no—
787D4C22×D32112yes—
788C2×C4—312no—
789C2×C4—31no—
790C2×C4—32no—
791C2×C4—33no—
792C2×C4—34no—
793C2×C4—312no—
794C2×C4—312no—
795C2×C4—312no—
796C2×C4—324no—
797C2×C4—98no—
798C2×C4—924no—
799C2×C4—924no—
800C2×C4—948no—
801C2×C4—924no—
802C2×C4—96no—
803C2×C4—924no—
804C2×C4C22×D32112yes—
805C2×C4C22×D3213yes—
806C2×C4C22×D3211yescharacteristic
807C2×C3—26no—
808C2×C3—26no—
809C2×C3—22no—
810C2×C3—21no—
811C2×C3—46no—
812C2×C3—612no—
813C2×C3—66no—
814C2×C3—62no—
815C2×C3#596412yescomplemented
816C2×C3#596612yescomplemented
817C2×C3C25×D311yescharacteristic
818C2×C3C25×D311yescharacteristic
819D3—22no—
820D3—26no—
821D3—212no—
822D3—64no—
823D3—64no—
824D3—124no—
825C22—26no—
826C22—32no—
827C22—36no—
828C22—312no—
829C22—62no—
830C22—612no—
831C22—66no—
832C22—94no—
833C22—1212no—
834C22—1224no—
835C22—184no—
836C22—3624no—
837C22C23×D3216yes—
838C22C23×D3211yescharacteristic
839C4—32no—
840C4—34no—
841C4—36no—
842C4—912no—
843C4C23×D3216yes—
844C4C23×D3212yes—
845C3—21no—
846C3C2×#596411yescharacteristic, complemented
847C3C2×#596611yescharacteristic, complemented
848C2—26no—
849C2—62no—
850C2—612no—
851C2—66no—
852C2—184no—
853C2#1059669612yesdirect product factor
854C2C24×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×#64367C2semidirect
2. C2×C3×#1009C2semidirect
3. C2×C3×D3×#41C2semidirect
4. #10596696C2direct (N × H)
5. C2×#64319C2semidirect
6. C2×#64315C2semidirect
7. C2×#64313C2semidirect
8. C2×D3×#237C2semidirect
9. C2×#64307C2semidirect
10. C2×D3×#235C2semidirect
11. C2×#64298C2semidirect
12. C22×#3795C2semidirect
15. C2×C32×#41C22semidirect
16. #64367C22semidirect
17. C2×Q8×C3⋊D3C22semidirect
18. C2×#3830C22semidirect
19. C2×#3828C22semidirect
20. C22×#634C22semidirect
21. C3×#1009C22semidirect
22. C3×D3×#41C22semidirect
23. C2×C3×#239C22semidirect
24. C2×C3×#239C22semidirect
25. C2×C3×D3×Q8C22semidirect
26. C2×C3×#237C22semidirect
27. C2×C3×D3×D4C22semidirect
28. C2×C3×D3×D4C22semidirect
29. C2×C3×#235C22semidirect
30. C2×C3×#235C22semidirect
31. C22×C3×D12C22semidirect
32. C22×C3×C4×D3C22semidirect
33. C2×D3×#67C22semidirect
34. C2×D3×#67C22semidirect
35. C22×#625C22semidirect
36. C2×#3805C22semidirect
37. C2×#3804C22semidirect
38. C22×D3×Dic3C22semidirect
39. #64319C22semidirect
40. #64315C22semidirect
41. #64313C22semidirect
42. D3×#237C22semidirect
43. #64307C22semidirect
44. D3×#235C22semidirect
45. C2×#3802C22semidirect
46. C2×D3×D12C22semidirect
47. C2×C4×D32C22semidirect
48. C2×#3799C22semidirect
49. C2×#3798C22semidirect
50. #64298C22semidirect
51. C2×#3796C22semidirect
52. C2×#3795C22semidirect
53. C2×#3795C22semidirect
54. C2×#3795C22semidirect
55. C2×#3795C22semidirect
56. C2×#3795C22semidirect
57. C2×#3795C22semidirect
58. C2×D3×Dic6C22semidirect
59. C2×D3×Dic6C22semidirect
71. C2×#1009D3semidirect
76. C2×D3×#41D3semidirect
88. C32×#41C23semidirect
94. Q8×C3⋊D3C23semidirect
95. #3830C23semidirect
96. #3828C23semidirect
101. C2×#634C23semidirect
105. C3×#239C23semidirect
106. C3×#239C23semidirect
107. C3×D3×Q8C23semidirect
108. C3×#237C23semidirect
109. C3×D3×D4C23semidirect
110. C3×D3×D4C23semidirect
111. C3×#235C23semidirect
112. C3×#235C23semidirect
116. C2×C3×D12C23semidirect
122. C2×C3×C4×D3C23semidirect
125. D3×#67C23semidirect
126. D3×#67C23semidirect
132. C2×#625C23semidirect
134. #3805C23semidirect
135. #3804C23semidirect
139. C2×D3×Dic3C23semidirect
140. #3802C23semidirect
141. D3×D12C23semidirect
142. C4×D32C23semidirect
143. #3799C23semidirect
144. #3798C23semidirect
145. #3796C23semidirect
146. #3795C23semidirect
147. #3795C23semidirect
148. #3795C23semidirect
149. #3795C23semidirect
150. #3795C23semidirect
151. D3×Dic6C23semidirect
152. D3×Dic6C23semidirect
162. C2×C3×#41C2×D3semidirect
163. C2×C3×#41C2×D3semidirect
181. #1009C2×D3semidirect
186. D3×#41C2×D3semidirect
190. C2×#239C2×D3semidirect
191. C2×#239C2×D3semidirect
197. C2×D3×Q8C2×D3semidirect
215. C2×#237C2×D3semidirect
221. C2×D3×D4C2×D3semidirect
222. C2×D3×D4C2×D3semidirect
237. C2×#235C2×D3semidirect
238. C2×#235C2×D3semidirect
240. C22×D12C2×D3semidirect
244. C22×C4×D3C2×D3semidirect
322. C3×#41C22×D3semidirect
323. C3×#41C22×D3semidirect
376. #239C22×D3semidirect
377. #239C22×D3semidirect
383. D3×Q8C22×D3semidirect
396. #237C22×D3semidirect
402. D3×D4C22×D3semidirect
403. D3×D4C22×D3semidirect
416. #235C22×D3semidirect
417. #235C22×D3semidirect
427. C2×D12C22×D3semidirect
444. C2×C4×D3C22×D3semidirect
508. C2×#41D32semidirect
636. C2×C32#585semidirect
662. #41C2×D32semidirect
758. C32C2×#585semidirect
815. C2×C3#5964semidirect
816. C2×C3#5966semidirect
846. C3C2×#5964semidirect
847. C3C2×#5966semidirect
853. C2#10596696direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643672
C2×C3×#10092
C2×C3×D3×#412
#105966962
C2×#643192
C2×#643152
C2×#643132
C2×D3×#2372
C2×#643072
C2×D3×#2352
C2×#642982
C22×#37952
C2×#59663
C2×#59643