Finite Group Databasebeta

← C2×D3×#1010 #11919238

Subgroups — C2×D3×#1010 #11919238

Order 1152.

12141 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64367C211yesmaximal, characteristic, complemented
2C2×C3×#1010C211yesmaximal, characteristic, complemented
3C2×C3×D3×#41C211yesmaximal, characteristic, complemented
4D3×#1010C2132yesmaximal, direct product factor
5C2×D32×Q8C212yesmaximal, complemented
6C2×#64315C212yesmaximal, complemented
7C2×D3×#237C216yesmaximal, complemented
8C2×#64309C216yesmaximal, complemented
9C2×D3×#235C213yesmaximal, complemented
10C2×#64298C213yesmaximal, complemented
11C2×#64297C213yesmaximal, complemented
12C22×D3×Dic6C213yesmaximal, complemented
13C2×D3×2−1+4—31nomaximal
14C22×#1010—31nomaximal
15C2×C32×#41C2211yescharacteristic, complemented
16#64367C22116yescomplemented
17C2×Q8×C3⋊D3C2212yescomplemented
18C2×#3830C2216yescomplemented
19C2×#3828C2213yescomplemented
20C22×#634C2213yescomplemented
21C3×#1010C22116yescomplemented
22C3×D3×#41C22116yescomplemented
23C2×C3×#239C2211yescharacteristic, complemented
24C2×C3×D3×Q8C2211yescharacteristic
25C2×C3×D3×Q8C2212yescomplemented
26C2×C3×#237C2213yescomplemented
27C2×C3×#237C2216yescomplemented
28C2×C3×D3×D4C2213yes—
29C2×C3×#235C2213yescomplemented
30C2×C3×#235C2213yescomplemented
31C22×C3×C4×D3C2213yes—
32C22×C3×Dic6C2213yescomplemented
33C2×D3×#67C2216yes—
34C22×#627C2216yescomplemented
35C2×#3805C22112yescomplemented
36C2×#3804C22112yescomplemented
37C2×#3804C2216yescomplemented
38C22×D3×Dic3C2216yes—
39D32×Q8C22132yescomplemented
40#64315C22132yescomplemented
41D3×#237C22196yescomplemented
42#64309C22196yescomplemented
43D3×#235C22148yescomplemented
44C2×D3×D12C2211yescharacteristic
45C2×C4×D32C2216yes—
46C2×#3799C2213yescomplemented
47C2×#3798C2216yescomplemented
48C2×#3797C2216yescomplemented
49#64298C22148yescomplemented
50#64297C22148yescomplemented
51C2×#3796C2216yescomplemented
52C2×#3795C2213yescomplemented
53C2×#3795C2216yescomplemented
54C2×D3×Dic6C2213yes—
55C2×D3×Dic6C2216yes—
56C2×D3×Dic6C22148yescomplemented
57C2×D3×Dic6C2216yescomplemented
58C2×D3×Dic6C2216yescomplemented
59C2×D3×Dic6C2216yescomplemented
60C2×C3×2−1+4—31no—
61C22×C3×#41—31no—
62D3×2−1+4—332no—
63C2×#1010—31no—
64C2×#1010—31no—
65C2×#1010—332no—
66C2×#1010—32no—
67C2×#1010—36no—
68C2×#1010—36no—
69C2×#1010—33no—
70C2×#1010—33no—
71C2×#1010—33no—
72C2×#1010—61no—
73C2×#1010D311yescharacteristic, direct product factor
74C2×D3×#41—36no—
75C2×D3×#41—33no—
76C2×D3×#41D311yescharacteristic, complemented
77C2×#1007—32no—
78C2×#1007—33no—
79C22×D3×Q8—32no—
80C22×D3×Q8—32no—
81C22×D3×Q8—33no—
82C22×#237—36no—
83C22×#235—33no—
84C23×Dic6—33no—
85C23×C3×D3C2313yes—
86C22×D32C2312yes—
87C32×#41C2318yescomplemented
88C2×C32×Q8C2311yescharacteristic
89C2×C32×D4C2313yes—
90C22×C32×C4C2313yes—
91C2×#638C2316yes—
92C22×C3⋊Dic3C2316yes—
93Q8×C3⋊D3C23116yescomplemented
94#3830C23148yescomplemented
95#3828C23124yescomplemented
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4×C3⋊D3C2316yes—
98C2×#634C2313yes—
99C2×#634C2316yes—
100C2×#634C23124yescomplemented
101C2×C3×#67C2316yes—
102C2×C3×#67C2316yes—
103C22×C3×Dic3C2316yes—
104C22×C3×Dic3C2313yes—
105C3×#239C2318yescomplemented
106C3×D3×Q8C2318yes—
107C3×D3×Q8C23116yescomplemented
108C3×#237C23124yescomplemented
109C3×#237C23148yescomplemented
110C3×D3×D4C23124yes—
111C3×#235C23124yescomplemented
112C3×#235C23124yescomplemented
113C2×C3×D12C2311yescharacteristic
114C2×C3×D12C2313yes—
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×C4×D3C2313yes—
117C2×C3×C4×D3C2313yes—
118C2×C3×C4×D3C2313yes—
119C2×C3×C4×D3C23124yes—
120C2×C3×C4×D3C2316yes—
121C2×C3×Dic6C2313yes—
122C2×C3×Dic6C2316yes—
123C2×C3×Dic6C2313yes—
124C2×C3×Dic6C23124yescomplemented
125D3×#67C23148yes—
126C2×#627C23112yes—
127C2×#627C2316yes—
128C2×#627C23148yescomplemented
129C2×#626C2316yes—
130C2×#626C2312yes—
131C2×#625C2316yes—
132C2×#624C2316yes—
133#3805C23196yescomplemented
134#3804C23196yescomplemented
135#3804C23148yescomplemented
136C2×D3×Dic3C2316yes—
137C2×D3×Dic3C23112yes—
138C2×D3×Dic3C2316yes—
139C2×D3×Dic3C23148yes—
140D3×D12C2318yes—
141C4×D32C23148yes—
142#3799C23124yescomplemented
143#3798C23148yescomplemented
144#3797C23148yescomplemented
145#3796C23148yescomplemented
146#3795C23124yescomplemented
147#3795C23148yescomplemented
148D3×Dic6C23124yes—
149D3×Dic6C23148yes—
150D3×Dic6C23148yescomplemented
151D3×Dic6C23148yescomplemented
152D3×Dic6C23148yescomplemented
153C22×2−1+4—91noSylow
154C3×2−1+4—316no—
155C2×C3×#41—21no—
156C2×C3×#41—316no—
157C2×C3×#41—31no—
158C2×C3×#41—36no—
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×Q8—32no—
166C22×C3×Q8—33no—
167C22×C3×D4—33no—
168C23×C3×C4—33no—
169C22×#67—36no—
170C23×Dic3—36no—
171#1010—316no—
172#1010—316no—
173#1010—332no—
174#1010—396no—
175#1010—396no—
176#1010—348no—
177#1010—348no—
178#1010—348no—
179#1010—616no—
180#1010C2×D3116yesdirect product factor
181D3×#41—396no—
182D3×#41—348no—
183D3×#41C2×D3116yescomplemented
184#1007—332no—
185#1007—348no—
186C2×#239—36no—
187C2×#239—33no—
188C2×#239C2×D311yescharacteristic, complemented
189C2×D3×Q8—32no—
190C2×D3×Q8—32no—
191C2×D3×Q8—332no—
192C2×D3×Q8—332no—
193C2×D3×Q8—36no—
194C2×D3×Q8—33no—
195C2×D3×Q8—36no—
196C2×D3×Q8—36no—
197C2×D3×Q8—36no—
198C2×D3×Q8—348no—
199C2×D3×Q8—36no—
200C2×D3×Q8—36no—
201C2×D3×Q8—62no—
202C2×D3×Q8C2×D311yescharacteristic
203C2×D3×Q8C2×D312yescomplemented
204C2×#237—36no—
205C2×#237—36no—
206C2×#237—312no—
207C2×#237—312no—
208C2×#237—312no—
209C2×#237—36no—
210C2×#237—396no—
211C2×#237—36no—
212C2×#237—33no—
213C2×#237—36no—
214C2×#237—66no—
215C2×#237C2×D316yescomplemented
216C2×#237C2×D313yescomplemented
217C2×D3×D4—36no—
218C2×D3×D4—31no—
219C2×D3×D4C2×D313yes—
220C2×#235—33no—
221C2×#235—33no—
222C2×#235—36no—
223C2×#235—312no—
224C2×#235—348no—
225C2×#235—33no—
226C2×#235—36no—
227C2×#235—36no—
228C2×#235—36no—
229C2×#235—33no—
230C2×#235—63no—
231C2×#235C2×D313yescomplemented
232C2×#235C2×D313yescomplemented
233C22×D12—31no—
234C22×C4×D3—36no—
235C22×C4×D3—36no—
236C22×C4×D3—36no—
237C22×C4×D3C2×D313yes—
238C22×Dic6—33no—
239C22×Dic6—33no—
240C22×Dic6—36no—
241C22×Dic6—36no—
242C22×Dic6—33no—
243C22×Dic6—36no—
244C22×Dic6—36no—
245C22×Dic6—36no—
246C22×Dic6—36no—
247C22×Dic6—348no—
248C22×Dic6—63no—
249C22×Dic6C2×D313yescomplemented
250C23×C32C2413yes—
251C22×C3⋊D3C2412yes—
252C22×C3×D3—212no—
253C22×C3×D3C2412yes—
254C22×C3×D3C2413yes—
255C22×C3×D3C24112yes—
256C22×C3×D3C2411yescharacteristic
257C2×D32—28no—
258C2×D32C2418yes—
259C32×Q8C2414yes—
260C32×D4C24112yes—
261C2×C32×C4C2411yescharacteristic
262C2×C32×C4C2413yes—
263C2×C32×C4C24112yes—
264#638C24124yes—
265C2×C3⋊Dic3C2416yes—
266C2×C3⋊Dic3C24124yes—
267C4⋊(C3⋊D3)C2414yes—
268C4×C3⋊D3C24124yes—
269#634C24112yes—
270#634C24124yes—
271C3×#67C24124yes—
272C3×#67C24124yes—
273C2×C3×Dic3C2416yes—
274C2×C3×Dic3C24124yes—
275C2×C3×Dic3C2413yes—
276C2×C3×Dic3C24112yes—
277C2×C3×Dic3C2411yescharacteristic
278C3×D12C2414yes—
279C3×D12C24112yes—
280C3×C4×D3C2414yes—
281C3×C4×D3C24112yes—
282C3×C4×D3C24112yes—
283C3×C4×D3C24112yes—
284C3×C4×D3C24124yes—
285C3×Dic6C24112yes—
286C3×Dic6C24124yes—
287C3×Dic6C24112yes—
288#627C24148yes—
289#627C24124yes—
290#626C24124yes—
291#626C2418yes—
292#625C24124yes—
293#624C24124yes—
294D3×Dic3C24124yes—
295D3×Dic3C24148yes—
296D3×Dic3C24124yes—
297C2×2−1+4—31no—
298C2×2−1+4—92no—
299C2×2−1+4—93no—
300C2×2−1+4—96no—
301C2×2−1+4—93no—
302C2×2−1+4—932no—
303C2×2−1+4—91no—
304C22×#41—31no—
305C22×#41—93no—
306C22×#41—96no—
307C23×Q8—93no—
308C23×Q8—92no—
309C24×C3—33no—
310C23×D3—32no—
311C23×D3—32no—
312C23×D3C22×D313yes—
313C3×#41—28no—
314C3×#41—38no—
315C3×#41—348no—
316C3×#41—324no—
317C3×#41—324no—
318C3×#41—324no—
319C3×#41C22×D318yescomplemented
320C3×#41C22×D318yescomplemented
321C2×C3×Q8—21no—
322C2×C3×Q8—38no—
323C2×C3×Q8—316no—
324C2×C3×Q8—33no—
325C2×C3×Q8—33no—
326C2×C3×Q8—36no—
327C2×C3×Q8—324no—
328C2×C3×Q8C22×D311yescharacteristic
329C2×C3×Q8C22×D311yescharacteristic
330C2×C3×D4—23no—
331C2×C3×D4—36no—
332C2×C3×D4—36no—
333C2×C3×D4—324no—
334C2×C3×D4—31no—
335C2×C3×D4—33no—
336C2×C3×D4C22×D313yes—
337C2×C3×D4C22×D313yes—
338C22×C3×C4—23no—
339C22×C3×C4—33no—
340C22×C3×C4—36no—
341C22×C3×C4—31no—
342C22×C3×C4—33no—
343C22×C3×C4—33no—
344C22×C3×C4—33no—
345C22×C3×C4—324no—
346C22×C3×C4—36no—
347C22×C3×C4C22×D313yes—
348C22×C3×C4C22×D313yes—
349C2×#67—36no—
350C2×#67—36no—
351C2×#67—36no—
352C2×#67—36no—
353C2×#67—348no—
354C2×#67—32no—
355C2×#67—36no—
356C2×#67—66no—
357C2×#67C22×D316yes—
358C2×#67C22×D316yes—
359C22×Dic3—36no—
360C22×Dic3—36no—
361C22×Dic3—36no—
362C22×Dic3—36no—
363C22×Dic3—312no—
364C22×Dic3—348no—
365C22×Dic3—66no—
366C22×Dic3C22×D313yes—
367C22×Dic3C22×D316yes—
368#239—348no—
369#239—324no—
370#239C22×D318yescomplemented
371D3×Q8—316no—
372D3×Q8—316no—
373D3×Q8—348no—
374D3×Q8—324no—
375D3×Q8—348no—
376D3×Q8—348no—
377D3×Q8—348no—
378D3×Q8—348no—
379D3×Q8—348no—
380D3×Q8—616no—
381D3×Q8C22×D318yes—
382D3×Q8C22×D3116yescomplemented
383#237—348no—
384#237—348no—
385#237—396no—
386#237—396no—
387#237—396no—
388#237—348no—
389#237—348no—
390#237—324no—
391#237—348no—
392#237—648no—
393#237C22×D3148yescomplemented
394#237C22×D3124yescomplemented
395D3×D4—348no—
396D3×D4—38no—
397D3×D4C22×D3124yes—
398#235—324no—
399#235—324no—
400#235—348no—
401#235—396no—
402#235—324no—
403#235—348no—
404#235—348no—
405#235—348no—
406#235—324no—
407#235—624no—
408#235C22×D3124yescomplemented
409#235C22×D3124yescomplemented
410C2×D12—32no—
411C2×D12—36no—
412C2×D12—31no—
413C2×D12—31no—
414C2×D12—38no—
415C2×D12—61no—
416C2×D12C22×D311yescharacteristic
417C2×D12C22×D313yes—
418C2×C4×D3—36no—
419C2×C4×D3—36no—
420C2×C4×D3—312no—
421C2×C4×D3—348no—
422C2×C4×D3—36no—
423C2×C4×D3—36no—
424C2×C4×D3—36no—
425C2×C4×D3—36no—
426C2×C4×D3—348no—
427C2×C4×D3—348no—
428C2×C4×D3—66no—
429C2×C4×D3C22×D313yes—
430C2×C4×D3C22×D316yes—
431C2×C4×D3C22×D311yescharacteristic
432C2×C4×D3C22×D313yes—
433C2×C4×D3C22×D313yes—
434C2×C4×D3C22×D3124yes—
435C2×Dic6—33no—
436C2×Dic6—36no—
437C2×Dic6—324no—
438C2×Dic6—33no—
439C2×Dic6—36no—
440C2×Dic6—324no—
441C2×Dic6—36no—
442C2×Dic6—312no—
443C2×Dic6—36no—
444C2×Dic6—312no—
445C2×Dic6—348no—
446C2×Dic6—348no—
447C2×Dic6—324no—
448C2×Dic6—348no—
449C2×Dic6—348no—
450C2×Dic6—348no—
451C2×Dic6—348no—
452C2×Dic6—63no—
453C2×Dic6—66no—
454C2×Dic6—624no—
455C2×Dic6C22×D313yes—
456C2×Dic6C22×D316yes—
457C2×Dic6C22×D313yes—
458C2×Dic6C22×D3124yescomplemented
459C22×C32—26no—
460C22×C32C2516yes—
461C22×C32C2511yescharacteristic
462C2×C3⋊D3—24no—
463C2×C3⋊D3C2514yes—
464C2×C3×D3—24no—
465C2×C3×D3—26no—
466C2×C3×D3—224no—
467C2×C3×D32−1+414yescomplemented
468C2×C3×D3C2516yes—
469C2×C3×D3C2514yes—
470C2×C3×D3C2512yes—
471D32—216no—
472C32×C4C2512yes—
473C32×C4C2516yes—
474C3⋊Dic3C25112yes—
475C3×Dic3C25112yes—
476C3×Dic3C2516yes—
477C3×Dic3C2512yes—
4782−1+4—316no—
4792−1+4—932no—
4802−1+4—948no—
4812−1+4—996no—
4822−1+4—948no—
4832−1+4—916no—
484C2×#41—316no—
485C2×#41—31no—
486C2×#41—33no—
487C2×#41—36no—
488C2×#41—33no—
489C2×#41—33no—
490C2×#41—96no—
491C2×#41—96no—
492C2×#41—912no—
493C2×#41—93no—
494C2×#41—96no—
495C2×#41—93no—
496C2×#41—948no—
497C2×#41—912no—
498C2×#41—96no—
499C2×#41—996no—
500C2×#41—96no—
501C2×#41—93no—
502C2×#41D3211yescharacteristic, complemented
503C22×Q8—31no—
504C22×Q8—32no—
505C22×Q8—33no—
506C22×Q8—96no—
507C22×Q8—93no—
508C22×Q8—96no—
509C22×Q8—96no—
510C22×Q8—96no—
511C22×Q8—948no—
512C22×Q8—96no—
513C22×Q8—932no—
514C22×Q8—96no—
515C22×Q8—92no—
516C22×Q8—93no—
517C22×D4—33no—
518C22×D4—91no—
519C22×D4—96no—
520C23×C4—33no—
521C23×C4—96no—
522C23×C4—96no—
523C23×C3—23no—
524C23×C3—31no—
525C23×C3—312no—
526C23×C3—33no—
527C23×C3—32no—
528C23×C3—612no—
529C23×C3C23×D313yes—
530C23×C3C23×D313yes—
531C22×D3—212no—
532C22×D3—32no—
533C22×D3—32no—
534C22×D3—38no—
535C22×D3—38no—
536C22×D3—62no—
537C22×D3—68no—
538C22×D3—68no—
539C22×D3C23×D313yes—
540C22×D3C23×D3112yes—
541C22×D3C23×D312yes—
542C22×D3C23×D311yescharacteristic
543C3×Q8—24no—
544C3×Q8—312no—
545C3×Q8—312no—
546C3×Q8—324no—
547C3×Q8C23×D314yes—
548C3×Q8C23×D314yes—
549C3×D4—212no—
550C3×D4—324no—
551C3×D4—324no—
552C3×D4—34no—
553C3×D4—312no—
554C3×D4C23×D3112yes—
555C3×D4C23×D3112yes—
556C2×C3×C4—21no—
557C2×C3×C4—23no—
558C2×C3×C4—212no—
559C2×C3×C4—31no—
560C2×C3×C4—33no—
561C2×C3×C4—312no—
562C2×C3×C4—36no—
563C2×C3×C4—324no—
564C2×C3×C4—34no—
565C2×C3×C4—312no—
566C2×C3×C4—312no—
567C2×C3×C4—312no—
568C2×C3×C4—324no—
569C2×C3×C4C23×D311yescharacteristic
570C2×C3×C4C23×D311yescharacteristic
571C2×C3×C4C23×D313yes—
572C2×C3×C4C23×D313yes—
573C2×C3×C4C23×D3112yes—
574C2×C3×C4C23×D3112yes—
575#67—324no—
576#67—324no—
577#67—324no—
578#67—324no—
579#67—38no—
580#67—324no—
581#67—624no—
582#67C23×D3124yes—
583#67C23×D3124yes—
584C2×Dic3—36no—
585C2×Dic3—36no—
586C2×Dic3—324no—
587C2×Dic3—324no—
588C2×Dic3—324no—
589C2×Dic3—324no—
590C2×Dic3—348no—
591C2×Dic3—66no—
592C2×Dic3—624no—
593C2×Dic3C23×D311yescharacteristic
594C2×Dic3C23×D313yes—
595C2×Dic3C23×D3112yes—
596C2×Dic3C23×D316yes—
597C2×Dic3C23×D3124yes—
598D12—38no—
599D12—324no—
600D12—34no—
601D12—34no—
602D12—64no—
603D12C23×D314yes—
604D12C23×D3112yes—
605C4×D3—324no—
606C4×D3—324no—
607C4×D3—348no—
608C4×D3—324no—
609C4×D3—324no—
610C4×D3—324no—
611C4×D3—324no—
612C4×D3—624no—
613C4×D3C23×D3112yes—
614C4×D3C23×D3124yes—
615C4×D3C23×D314yes—
616C4×D3C23×D3112yes—
617C4×D3C23×D3112yes—
618Dic6—312no—
619Dic6—324no—
620Dic6—312no—
621Dic6—324no—
622Dic6—324no—
623Dic6—348no—
624Dic6—324no—
625Dic6—348no—
626Dic6—612no—
627Dic6—624no—
628Dic6C23×D3112yes—
629Dic6C23×D3124yes—
630Dic6C23×D3112yes—
631C2×C32—26no—
632C2×C32C2×2−1+412yescomplemented
633C2×C32C2611yescharacteristic
634C3⋊D3—24no—
635C3×D3—24no—
636C3×D3—26no—
637C3×D3C2×2−1+414yescomplemented
638C24—33no—
639C24—92no—
640#41—38no—
641#41—324no—
642#41—348no—
643#41—324no—
644#41—324no—
645#41—948no—
646#41—948no—
647#41—996no—
648#41—924no—
649#41—948no—
650#41—924no—
651#41—996no—
652#41—948no—
653#41—948no—
654#41—924no—
655#41C2×D3218yescomplemented
656C2×Q8—38no—
657C2×Q8—316no—
658C2×Q8—36no—
659C2×Q8—33no—
660C2×Q8—33no—
661C2×Q8—324no—
662C2×Q8—96no—
663C2×Q8—912no—
664C2×Q8—948no—
665C2×Q8—924no—
666C2×Q8—948no—
667C2×Q8—948no—
668C2×Q8—948no—
669C2×Q8—948no—
670C2×Q8—948no—
671C2×Q8—916no—
672C2×Q8—96no—
673C2×Q8—93no—
674C2×Q8—924no—
675C2×Q8C2×D3211yescharacteristic
676C2×D4—36no—
677C2×D4—36no—
678C2×D4—324no—
679C2×D4—33no—
680C2×D4—31no—
681C2×D4—98no—
682C2×D4—92no—
683C2×D4—96no—
684C2×D4—948no—
685C2×D4—96no—
686C2×D4—96no—
687C2×D4—91no—
688C2×D4C2×D3213yes—
689C22×C4—33no—
690C22×C4—36no—
691C22×C4—31no—
692C22×C4—33no—
693C22×C4—324no—
694C22×C4—33no—
695C22×C4—33no—
696C22×C4—36no—
697C22×C4—96no—
698C22×C4—948no—
699C22×C4—96no—
700C22×C4—948no—
701C22×C4—96no—
702C22×C4—912no—
703C22×C4—96no—
704C22×C4—96no—
705C22×C4C2×D3213yes—
706C22×C3—26no—
707C22×C3—26no—
708C22×C3—26no—
709C22×C3—21no—
710C22×C3—34no—
711C22×C3—32no—
712C22×C3—36no—
713C22×C3—34no—
714C22×C3—46no—
715C22×C3—624no—
716C22×C3—64no—
717C22×C3—66no—
718C22×C3C24×D316yes—
719C22×C3C24×D316yes—
720C22×C3C24×D311yescharacteristic
721C22×C3C24×D311yescharacteristic
722C2×D3—26no—
723C2×D3—24no—
724C2×D3—224no—
725C2×D3—34no—
726C2×D3—34no—
727C2×D3—64no—
728C2×D3—616no—
729C2×D3—64no—
730C2×D3—64no—
731C2×D3—616no—
732C2×D3—124no—
733C2×D3#101014yesdirect product factor
734C2×D3C24×D316yes—
735C2×D3C24×D314yes—
736C2×D3C24×D312yes—
737C3×C4—22no—
738C3×C4—26no—
739C3×C4—32no—
740C3×C4—36no—
741C3×C4—312no—
742C3×C4C24×D312yes—
743C3×C4C24×D312yes—
744C3×C4C24×D316yes—
745C3×C4C24×D316yes—
746Dic3—312no—
747Dic3—312no—
748Dic3—612no—
749Dic3C24×D312yes—
750Dic3C24×D316yes—
751Dic3C24×D3112yes—
752C32C22×2−1+411yescharacteristic, complemented, Sylow
753C23—31no—
754C23—312no—
755C23—32no—
756C23—33no—
757C23—612no—
758C23—98no—
759C23—92no—
760C23—188no—
761C23C22×D3213yes—
762Q8—324no—
763Q8—312no—
764Q8—312no—
765Q8—924no—
766Q8—948no—
767Q8—924no—
768Q8—912no—
769Q8C22×D3214yes—
770D4—324no—
771D4—324no—
772D4—312no—
773D4—34no—
774D4—98no—
775D4—924no—
776D4—924no—
777D4—924no—
778D4—94no—
779D4C22×D32112yes—
780C2×C4—312no—
781C2×C4—324no—
782C2×C4—31no—
783C2×C4—33no—
784C2×C4—36no—
785C2×C4—34no—
786C2×C4—312no—
787C2×C4—312no—
788C2×C4—312no—
789C2×C4—324no—
790C2×C4—924no—
791C2×C4—924no—
792C2×C4—924no—
793C2×C4—948no—
794C2×C4—924no—
795C2×C4—96no—
796C2×C4—924no—
797C2×C4C22×D32112yes—
798C2×C4C22×D3213yes—
799C2×C4C22×D3211yescharacteristic
800C2×C3—26no—
801C2×C3—26no—
802C2×C3—22no—
803C2×C3—21no—
804C2×C3—34no—
805C2×C3—46no—
806C2×C3—64no—
807C2×C3—66no—
808C2×C3C2×#101012yescomplemented
809C2×C3D3×2−1+412yescomplemented
810C2×C3C25×D311yescharacteristic
811C2×C3C25×D311yescharacteristic
812D3—26no—
813D3—24no—
814D3—64no—
815D3—64no—
816D3—124no—
817D3C2×#101014yesdirect product factor
818C22—26no—
819C22—34no—
820C22—32no—
821C22—34no—
822C22—36no—
823C22—624no—
824C22—66no—
825C22—64no—
826C22—94no—
827C22—1816no—
828C22—184no—
829C22C23×D3216yes—
830C22C23×D3211yescharacteristic
831C4—32no—
832C4—36no—
833C4—312no—
834C4—912no—
835C4C23×D3216yes—
836C4C23×D3212yes—
837C3—21no—
838C3C22×#101011yescharacteristic, complemented
839C3C2×D3×2−1+411yescharacteristic, complemented
840C2—26no—
841C2—34no—
842C2—66no—
843C2—64no—
844C2—184no—
845C2D3×#101012yesdirect product factor
846C2C24×D3211yescharacteristic
subgroupG/H
centerC22C23×D32
commutator, cosocleC2×C32C26
FrattiniC2C24×D32
FittingC2×C32×#41C22
socleC22×C32C25
hypercenterC2×#41D32
hypocenterC32C22×2−1+4
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×#1010C2semidirect
3. C2×C3×D3×#41C2semidirect
4. D3×#1010C2direct (N × H)
5. C2×D32×Q8C2semidirect
6. C2×#64315C2semidirect
7. C2×D3×#237C2semidirect
8. C2×#64309C2semidirect
9. C2×D3×#235C2semidirect
10. C2×#64298C2semidirect
11. C2×#64297C2semidirect
12. C22×D3×Dic6C2semidirect
15. C2×C32×#41C22semidirect
16. #64367C22semidirect
17. C2×Q8×C3⋊D3C22semidirect
18. C2×#3830C22semidirect
19. C2×#3828C22semidirect
20. C22×#634C22semidirect
21. C3×#1010C22semidirect
22. C3×D3×#41C22semidirect
23. C2×C3×#239C22semidirect
25. C2×C3×D3×Q8C22semidirect
26. C2×C3×#237C22semidirect
27. C2×C3×#237C22semidirect
29. C2×C3×#235C22semidirect
30. C2×C3×#235C22semidirect
32. C22×C3×Dic6C22semidirect
34. C22×#627C22semidirect
35. C2×#3805C22semidirect
36. C2×#3804C22semidirect
37. C2×#3804C22semidirect
39. D32×Q8C22semidirect
40. #64315C22semidirect
41. D3×#237C22semidirect
42. #64309C22semidirect
43. D3×#235C22semidirect
46. C2×#3799C22semidirect
47. C2×#3798C22semidirect
48. C2×#3797C22semidirect
49. #64298C22semidirect
50. #64297C22semidirect
51. C2×#3796C22semidirect
52. C2×#3795C22semidirect
53. C2×#3795C22semidirect
56. C2×D3×Dic6C22semidirect
57. C2×D3×Dic6C22semidirect
58. C2×D3×Dic6C22semidirect
59. C2×D3×Dic6C22semidirect
73. C2×#1010D3direct (N × H)
76. C2×D3×#41D3semidirect
87. C32×#41C23semidirect
93. Q8×C3⋊D3C23semidirect
94. #3830C23semidirect
95. #3828C23semidirect
100. C2×#634C23semidirect
105. C3×#239C23semidirect
107. C3×D3×Q8C23semidirect
108. C3×#237C23semidirect
109. C3×#237C23semidirect
111. C3×#235C23semidirect
112. C3×#235C23semidirect
124. C2×C3×Dic6C23semidirect
128. C2×#627C23semidirect
133. #3805C23semidirect
134. #3804C23semidirect
135. #3804C23semidirect
142. #3799C23semidirect
143. #3798C23semidirect
144. #3797C23semidirect
145. #3796C23semidirect
146. #3795C23semidirect
147. #3795C23semidirect
150. D3×Dic6C23semidirect
151. D3×Dic6C23semidirect
152. D3×Dic6C23semidirect
162. C2×C3×#41C2×D3semidirect
163. C2×C3×#41C2×D3semidirect
180. #1010C2×D3direct (N × H)
183. D3×#41C2×D3semidirect
188. C2×#239C2×D3semidirect
203. C2×D3×Q8C2×D3semidirect
215. C2×#237C2×D3semidirect
216. C2×#237C2×D3semidirect
231. C2×#235C2×D3semidirect
232. C2×#235C2×D3semidirect
249. C22×Dic6C2×D3semidirect
319. C3×#41C22×D3semidirect
320. C3×#41C22×D3semidirect
370. #239C22×D3semidirect
382. D3×Q8C22×D3semidirect
393. #237C22×D3semidirect
394. #237C22×D3semidirect
408. #235C22×D3semidirect
409. #235C22×D3semidirect
458. C2×Dic6C22×D3semidirect
467. C2×C3×D32−1+4semidirect
502. C2×#41D32semidirect
632. C2×C32C2×2−1+4semidirect
637. C3×D3C2×2−1+4semidirect
655. #41C2×D32semidirect
733. C2×D3#1010direct (N × H)
752. C32C22×2−1+4semidirect
808. C2×C3C2×#1010semidirect
809. C2×C3D3×2−1+4semidirect
817. D3C2×#1010direct (N × H)
838. C3C22×#1010semidirect
839. C3C2×D3×2−1+4semidirect
845. C2D3×#1010direct (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×#10102
C2×C3×D3×#412
D3×#10102
C2×D32×Q82
C2×#643152
C2×D3×#2372
C2×#643092
C2×D3×#2352
C2×#642982
C2×#642972
C22×D3×Dic62
C2×D3×2−1+43
C22×#10103