Finite Group Databasebeta

← C2×#86783 #11703428

Subgroups — C2×#86783 #11703428

Order 768.

11510 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×#41C211yesmaximal, characteristic, complemented
2C22×#1010C211yesmaximal, characteristic, complemented
3C2×C3×#550C211yesmaximal, characteristic, complemented
4C2×#5834C211yesmaximal, characteristic, complemented
5C2×#5831C211yesmaximal, characteristic, complemented
6#86783C2132yesmaximal, direct product factor
7C2×#5715C213yesmaximal, complemented
8C2×#5718C213yesmaximal, complemented
9C2×#5607C213yesmaximal, complemented
10C2×#5599C213yesmaximal, complemented
11C2×#5598C213yesmaximal, complemented
12C2×#5606C213yesmaximal, complemented
13C2×#5576C211yesmaximal, characteristic, complemented
14C2×#5572C211yesmaximal, characteristic, complemented
15C2×#5547C213yesmaximal, complemented
16C2×#5552C213yesmaximal, complemented
17C2×#3487—31nomaximal, Sylow
18C22×C3×#41C2211yescharacteristic
19C22×C3×#41C2211yescharacteristic, complemented
20C2×#1010—216no—
21C2×#1010C22116yescomplemented
22C2×D3×#41—216no—
23C2×D3×#41C22116yescomplemented
24C22×#239C2211yescharacteristic
25C22×D3×Q8C2211yescharacteristic
26C22×D3×Q8C2211yescharacteristic, complemented
27C22×#237C2213yes—
28C22×#237C2213yes—
29C22×#237C2213yescomplemented
30C22×D3×D4C2213yes—
31C22×#235C2213yes—
32C22×#235C2213yes—
33C23×C4×D3C2213yes—
34C23×Dic6C2213yescomplemented
35C3×#550C22116yescomplemented
36C2×C3×#127C2213yescomplemented
37C2×C3×#121C2213yescomplemented
38C2×C3×#121C2213yescomplemented
39C2×C3×C4×Q8C2211yescharacteristic, complemented
40C2×C3×C4×D4C2213yescomplemented
41#5834C22116yescomplemented
42#5831C22116yescomplemented
43C2×Q8×Dic3C2211yescharacteristic, complemented
44C2×#940C2216yescomplemented
45C2×#940C2213yescomplemented
46C2×#939C2213yescomplemented
47C2×#939C2216yescomplemented
48C2×#939C2216yescomplemented
49C2×#938C2213yescomplemented
50C2×#938C2213yescomplemented
51C2×#937C2213yes—
52C2×#937C2216yes—
53C2×#936C2213yescomplemented
54C2×D4×Dic3C2216yescomplemented
55C2×#930C2213yescomplemented
56C2×C4×#67C2213yescomplemented
57C2×C4×#67C2213yescomplemented
58C2×#924C2213yescomplemented
59#5718C22148yescomplemented
60#5715C22148yescomplemented
61#5607C22148yescomplemented
62#5606C22148yescomplemented
63#5599C22148yescomplemented
64#5598C22148yescomplemented
65#5576C22116yescomplemented
66#5572C22116yescomplemented
67#5552C22148yescomplemented
68#5547C22148yescomplemented
69C2×#897C2213yescomplemented
70C2×#896C2213yescomplemented
71C2×#895C2213yescomplemented
72C2×#894C2211yescharacteristic
73C2×#892C2213yes—
74C2×#887C2213yescomplemented
75C2×#885C2216yescomplemented
76C2×#884C2213yescomplemented
77C2×#883C2213yes—
78C2×#882C2213yes—
79C2×#67⋊C4C2216yescomplemented
80C2×#878C2213yescomplemented
81C2×#875C2213yescomplemented
82C2×C4×D12C2213yescomplemented
83C2×#872C2213yes—
84C2×C4×Dic6C2213yescomplemented
85C22×2−1+4—31no—
86C23×#41—31no—
87#3487—332no—
88C2×#550—31no—
89C2×#550—33no—
90C2×#550—33no—
91C2×#550D311yescharacteristic, complemented
92C2×#548—31no—
93C2×#548—33no—
94C2×#548—31no—
95C2×#548—33no—
96C2×#535—33no—
97C2×#535—33no—
98C2×#525—33no—
99C2×#525—33no—
100C2×#519—31no—
101C24×D3C2313yes—
102C2×C3×#41—28no—
103C2×C3×#41—28no—
104C2×C3×#41C2318yes—
105C2×C3×#41C2318yescomplemented
106C22×C3×Q8C2311yescharacteristic
107C22×C3×D4C2313yes—
108C22×C3×D4C2313yes—
109C22×C3×D4C2316yes—
110C22×C3×D4C2313yes—
111C23×C3×C4C2313yes—
112C23×C3×C4C2313yes—
113C22×#67C2316yes—
114C22×#67C2313yes—
115C22×#67C2313yes—
116C22×#67C2316yes—
117C22×#67C2313yes—
118C22×#67C2313yes—
119C23×Dic3C2316yes—
120C23×Dic3C2313yes—
121#1010—2128no—
122D3×#41—2128no—
123C2×#239—28no—
124C2×#239C2318yes—
125C2×D3×Q8—28no—
126C2×D3×Q8D4116yescomplemented
127C2×D3×Q8C2318yes—
128C2×D3×Q8C2318yescomplemented
129C2×#237—224no—
130C2×#237—224no—
131C2×#237—224no—
132C2×#237C23124yes—
133C2×#237C23124yes—
134C2×#237C23124yescomplemented
135C2×D3×D4—224no—
136C2×D3×D4C23124yes—
137C2×#235—224no—
138C2×#235—224no—
139C2×#235C23124yes—
140C2×#235C23124yes—
141C22×D12C2311yescharacteristic
142C22×D12C2313yes—
143C22×D12C2313yes—
144C22×C4×D3—224no—
145C22×C4×D3C2311yescharacteristic
146C22×C4×D3C2313yes—
147C22×C4×D3C2313yes—
148C22×C4×D3C23124yes—
149C22×C4×D3C2313yes—
150C22×C4×D3C2313yes—
151C22×Dic6—224no—
152C22×Dic6C2313yes—
153C22×Dic6C2313yes—
154C22×Dic6C2313yes—
155C22×Dic6C23124yescomplemented
156C3×#127C23124yescomplemented
157C3×#121C23124yescomplemented
158C3×#121C23124yescomplemented
159C3×C4×Q8C2318yescomplemented
160C3×C4×D4C23124yescomplemented
161C2×C3×C4⋊C4C2313yes—
162C2×C3×C4⋊C4C2311yescharacteristic
163C2×C3×C22⋊C4C2313yes—
164C2×C3×C22⋊C4C2313yes—
165C2×C3×C42C2313yes—
166C2×#217C2313yes—
167C2×#217C2313yes—
168C2×#217C2316yes—
169Q8×Dic3C2318yescomplemented
170#940C23124yescomplemented
171#940C23148yescomplemented
172#939C23148yescomplemented
173#939C23148yescomplemented
174#939C23124yescomplemented
175#938C23124yescomplemented
176#938C23124yescomplemented
177#937C23124yes—
178#937C23148yes—
179#936C23124yescomplemented
180D4×Dic3C23148yescomplemented
181#930C23124yescomplemented
182C4×#67C23124yescomplemented
183C4×#67C23124yescomplemented
184C2×(C2×D3)⋊C4C2311yescharacteristic
185C2×(C2×D3)⋊C4C2313yes—
186C2×(C2×D3)⋊C4C2311yescharacteristic
187C2×(C2×D3)⋊C4C2313yes—
188C2×(C2×D3)⋊C4C2316yes—
189C2×(C2×D3)⋊C4C2313yes—
190C2×(C2×D3)⋊C4C2311yescharacteristic
191C2×C4⋊Dic3C2313yes—
192C2×C4⋊Dic3C2313yes—
193#924C23124yescomplemented
194C2×Dic3⋊C4C2313yes—
195C2×Dic3⋊C4C2313yes—
196C2×Dic3⋊C4C2311yescharacteristic
197C2×Dic3⋊C4C2313yes—
198C2×C4×Dic3C2316yes—
199C2×C4×Dic3C2313yes—
200#897C23124yescomplemented
201#896C23124yescomplemented
202#895C23124yescomplemented
203#894C2318yes—
204#892C23124yes—
205#887C23124yescomplemented
206#885C23148yescomplemented
207#884C23124yescomplemented
208#883C23124yes—
209#882C23124yes—
210#67⋊C4C23148yescomplemented
211#878C23124yescomplemented
212#875C23124yescomplemented
213C4×D12C23124yescomplemented
214#872C23124yes—
215C4×Dic6C23124yescomplemented
216C2×2−1+4—316no—
217C2×2−1+4—616no—
218C22×#41—316no—
219C22×#41—31no—
220C22×#41—33no—
221C22×#41—33no—
222C22×#41—33no—
223C22×#41—33no—
224C22×#41—33no—
225C22×#41—616no—
226C22×#41C2×D311yescharacteristic
227C22×#41C2×D311yescharacteristic, complemented
228C23×Q8—31no—
229C23×Q8—31no—
230C23×Q8—33no—
231C23×D4—33no—
232C24×C4—33no—
233#550—316no—
234#550—348no—
235#550—348no—
236#550C2×D3116yescomplemented
237#548—316no—
238#548—348no—
239#548—316no—
240#548—348no—
241#535—348no—
242#535—348no—
243C2×#127—36no—
244C2×#127—33no—
245C2×#127C2×D313yescomplemented
246C2×#124—33no—
247C2×#124—36no—
248C2×#124—33no—
249#525—348no—
250#525—348no—
251C2×#123—31no—
252C2×#123—33no—
253C2×C22⋊Q8—33no—
254C2×C22⋊Q8—33no—
255C2×C22⋊Q8—33no—
256C2×C22⋊Q8—33no—
257C2×#121—33no—
258C2×#121—33no—
259C2×#121—33no—
260C2×#121—36no—
261C2×#121—36no—
262C2×#121—33no—
263C2×#121—33no—
264C2×#121—33no—
265C2×#121C2×D313yescomplemented
266C2×#121C2×D313yescomplemented
267C2×#120—36no—
268C2×#120—33no—
269C2×#120—33no—
270#519—316no—
271C2×C4×Q8—31no—
272C2×C4×Q8—33no—
273C2×C4×Q8—33no—
274C2×C4×Q8C2×D311yescharacteristic, complemented
275C2×C4×D4—36no—
276C2×C4×D4—33no—
277C2×C4×D4—33no—
278C2×C4×D4—36no—
279C2×C4×D4—33no—
280C2×C4×D4C2×D313yescomplemented
281C2×#117—33no—
282C2×#117—33no—
283C24×C3C2413yes—
284C24×C3C2413yes—
285C23×D3—212no—
286C23×D3—46no—
287C23×D3—46no—
288C23×D3C2413yes—
289C23×D3C2411yescharacteristic
290C23×D3C2411yescharacteristic
291C23×D3C24112yes—
292C3×#41—232no—
293C3×#41—232no—
294C2×C3×Q8C2×D418yes—
295C2×C3×Q8C2414yes—
296C2×C3×D4—212no—
297C2×C3×D4—212no—
298C2×C3×D4—412no—
299C2×C3×D4—46no—
300C2×C3×D4C24112yes—
301C2×C3×D4C24112yes—
302C2×C3×D4C24124yes—
303C2×C3×D4C24112yes—
304C22×C3×C4—212no—
305C22×C3×C4—212no—
306C22×C3×C4C2413yes—
307C22×C3×C4C2411yescharacteristic
308C22×C3×C4C2411yescharacteristic
309C22×C3×C4C2411yescharacteristic
310C22×C3×C4C24112yes—
311C22×C3×C4C24112yes—
312C22×C3×C4C2413yes—
313C2×#67—212no—
314C2×#67—224no—
315C2×#67—212no—
316C2×#67—46no—
317C2×#67—46no—
318C2×#67—412no—
319C2×#67C24112yes—
320C2×#67C24112yes—
321C2×#67C24124yes—
322C2×#67C24124yes—
323C2×#67C24112yes—
324C2×#67C24112yes—
325C22×Dic3—224no—
326C22×Dic3—212no—
327C22×Dic3C24112yes—
328C22×Dic3C24124yes—
329C22×Dic3C2411yescharacteristic
330C22×Dic3C2413yes—
331C22×Dic3C2411yescharacteristic
332C22×Dic3C2413yes—
333C22×Dic3C2413yes—
334#239—232no—
335D3×Q8—232no—
336D3×Q8C2×D4164yescomplemented
337#237—296no—
338#237—296no—
339#237—296no—
340D3×D4—296no—
341#235—296no—
342#235—296no—
343C2×D12—24no—
344C2×D12—212no—
345C2×D12—46no—
346C2×D12C24112yes—
347C2×D12C2414yes—
348C2×D12C24112yes—
349C2×C4×D3—24no—
350C2×C4×D3—212no—
351C2×C4×D3—212no—
352C2×C4×D3—212no—
353C2×C4×D3—296no—
354C2×C4×D3C2×D4124yes—
355C2×C4×D3C24112yes—
356C2×C4×D3C24112yes—
357C2×C4×D3C24112yes—
358C2×C4×D3C2414yes—
359C2×C4×D3C24112yes—
360C2×Dic6—212no—
361C2×Dic6—212no—
362C2×Dic6—296no—
363C2×Dic6C2×D4124yes—
364C2×Dic6C24112yes—
365C2×Dic6C24112yes—
366C2×Dic6C24112yes—
367C3×C4⋊C4C24112yes—
368C3×C4⋊C4C2414yes—
369C3×C22⋊C4C24112yes—
370C3×C22⋊C4C24112yes—
371C3×C42C24112yes—
372#217C24112yes—
373#217C24112yes—
374#217C24124yes—
375(C2×D3)⋊C4C2414yes—
376(C2×D3)⋊C4C24112yes—
377(C2×D3)⋊C4C2414yes—
378(C2×D3)⋊C4C24112yes—
379(C2×D3)⋊C4C24124yes—
380(C2×D3)⋊C4C24112yes—
381(C2×D3)⋊C4C2414yes—
382C4⋊Dic3C24112yes—
383C4⋊Dic3C24112yes—
384Dic3⋊C4C24112yes—
385Dic3⋊C4C24112yes—
386Dic3⋊C4C2414yes—
387Dic3⋊C4C24112yes—
388C4×Dic3C24124yes—
389C4×Dic3C24112yes—
390C25—33no—
3912−1+4—6128no—
392C2×#41—28no—
393C2×#41—28no—
394C2×#41—38no—
395C2×#41—324no—
396C2×#41—324no—
397C2×#41—324no—
398C2×#41—324no—
399C2×#41—324no—
400C2×#41—624no—
401C2×#41—624no—
402C2×#41—624no—
403C2×#41—624no—
404C2×#41—624no—
405C2×#41—6128no—
406C2×#41—68no—
407C2×#41C22×D318yes—
408C2×#41C22×D318yescomplemented
409C22×Q8—316no—
410C22×Q8—38no—
411C22×Q8—38no—
412C22×Q8—33no—
413C22×Q8—33no—
414C22×Q8—33no—
415C22×Q8—324no—
416C22×Q8—624no—
417C22×Q8—68no—
418C22×Q8C22×D311yescharacteristic
419C22×D4—33no—
420C22×D4—36no—
421C22×D4—33no—
422C22×D4—33no—
423C22×D4—36no—
424C22×D4—33no—
425C22×D4—324no—
426C22×D4—31no—
427C22×D4—33no—
428C22×D4—33no—
429C22×D4—624no—
430C22×D4C22×D313yes—
431C22×D4C22×D313yes—
432C22×D4C22×D316yes—
433C22×D4C22×D313yes—
434C23×C4—33no—
435C23×C4—36no—
436C23×C4—33no—
437C23×C4—33no—
438C23×C4—33no—
439C23×C4—33no—
440C23×C4—31no—
441C23×C4—324no—
442C23×C4—624no—
443C23×C4C22×D313yes—
444C23×C4C22×D313yes—
445#127—348no—
446#127—324no—
447#127C22×D3124yescomplemented
448#124—324no—
449#124—348no—
450#124—324no—
451#123—38no—
452#123—324no—
453C22⋊Q8—324no—
454C22⋊Q8—324no—
455C22⋊Q8—324no—
456C22⋊Q8—324no—
457#121—324no—
458#121—324no—
459#121—324no—
460#121—348no—
461#121—348no—
462#121—324no—
463#121—324no—
464#121—324no—
465#121C22×D3124yescomplemented
466#121C22×D3124yescomplemented
467#120—348no—
468#120—324no—
469#120—324no—
470C4×Q8—38no—
471C4×Q8—324no—
472C4×Q8—324no—
473C4×Q8C22×D318yescomplemented
474C4×D4—348no—
475C4×D4—324no—
476C4×D4—324no—
477C4×D4—348no—
478C4×D4—324no—
479C4×D4C22×D3124yescomplemented
480#117—324no—
481#117—324no—
482C2×C4⋊C4—33no—
483C2×C4⋊C4—33no—
484C2×C4⋊C4—33no—
485C2×C4⋊C4—33no—
486C2×C4⋊C4—31no—
487C2×C4⋊C4—33no—
488C2×C4⋊C4C22×D313yes—
489C2×C4⋊C4C22×D311yescharacteristic
490C2×C22⋊C4—33no—
491C2×C22⋊C4—36no—
492C2×C22⋊C4—33no—
493C2×C22⋊C4—33no—
494C2×C22⋊C4—31no—
495C2×C22⋊C4—31no—
496C2×C22⋊C4—31no—
497C2×C22⋊C4—33no—
498C2×C22⋊C4—36no—
499C2×C22⋊C4—33no—
500C2×C22⋊C4C22×D313yes—
501C2×C22⋊C4C22×D313yes—
502C2×C42—36no—
503C2×C42—33no—
504C2×C42C22×D313yes—
505C23×C3—26no—
506C23×C3—26no—
507C23×C3—26no—
508C23×C3—26no—
509C23×C3—26no—
510C23×C3—26no—
511C23×C3C2516yes—
512C23×C3C2516yes—
513C23×C3C2511yescharacteristic
514C22×D3—22no—
515C22×D3—22no—
516C22×D3—22no—
517C22×D3—26no—
518C22×D3—22no—
519C22×D3—26no—
520C22×D3—22no—
521C22×D3—26no—
522C22×D3—224no—
523C22×D3—412no—
524C22×D3—412no—
525C22×D3—448no—
526C22×D3C22×D414yes—
527C22×D3C2516yes—
528C22×D3C2512yes—
529C22×D3C2512yes—
530C3×Q8C22×D4116yes—
531C3×D4—224no—
532C3×D4—224no—
533C3×D4—424no—
534C3×D4—412no—
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—26no—
538C2×C3×C4—22no—
539C2×C3×C4—224no—
540C2×C3×C4—224no—
541C2×C3×C4C22×D4112yes—
542C2×C3×C4C2516yes—
543C2×C3×C4C2512yes—
544C2×C3×C4C2512yes—
545C2×C3×C4C2512yes—
546C2×C3×C4C2516yes—
547#67—224no—
548#67—248no—
549#67—224no—
550#67—412no—
551#67—412no—
552#67—424no—
553C2×Dic3—26no—
554C2×Dic3—22no—
555C2×Dic3—26no—
556C2×Dic3—22no—
557C2×Dic3—248no—
558C2×Dic3—224no—
559C2×Dic3C22×D4112yes—
560C2×Dic3C2512yes—
561C2×Dic3C2516yes—
562C2×Dic3C2512yes—
563C2×Dic3C2516yes—
564C2×Dic3C2516yes—
565D12—28no—
566D12—224no—
567D12—412no—
568C4×D3—28no—
569C4×D3—224no—
570C4×D3—224no—
571C4×D3—224no—
572C4×D3C22×D4148yes—
573Dic6—224no—
574Dic6—224no—
575Dic6C22×D4148yes—
576C24—31no—
577C24—33no—
578C24—31no—
579C24—312no—
580C24—612no—
581C24—126no—
582C24—126no—
583C24C23×D313yes—
584C24C23×D313yes—
585#41—232no—
586#41—232no—
587#41—696no—
588#41—696no—
589#41—696no—
590#41—696no—
591#41—696no—
592#41—632no—
593C2×Q8—364no—
594C2×Q8—324no—
595C2×Q8—312no—
596C2×Q8—312no—
597C2×Q8—312no—
598C2×Q8—612no—
599C2×Q8—696no—
600C2×Q8—632no—
601C2×Q8—612no—
602C2×Q8D3×D418yes—
603C2×Q8C23×D314yes—
604C2×D4—212no—
605C2×D4—212no—
606C2×D4—312no—
607C2×D4—324no—
608C2×D4—312no—
609C2×D4—312no—
610C2×D4—324no—
611C2×D4—312no—
612C2×D4—34no—
613C2×D4—312no—
614C2×D4—312no—
615C2×D4—46no—
616C2×D4—412no—
617C2×D4—64no—
618C2×D4—696no—
619C2×D4—624no—
620C2×D4—612no—
621C2×D4—612no—
622C2×D4—612no—
623C2×D4—126no—
624C2×D4—1212no—
625C2×D4—126no—
626C2×D4—126no—
627C2×D4C23×D3112yes—
628C2×D4C23×D3112yes—
629C2×D4C23×D3124yes—
630C2×D4C23×D3112yes—
631C22×C4—212no—
632C22×C4—212no—
633C22×C4—33no—
634C22×C4—324no—
635C22×C4—312no—
636C22×C4—324no—
637C22×C4—312no—
638C22×C4—33no—
639C22×C4—31no—
640C22×C4—33no—
641C22×C4—31no—
642C22×C4—312no—
643C22×C4—312no—
644C22×C4—312no—
645C22×C4—34no—
646C22×C4—612no—
647C22×C4—696no—
648C22×C4—64no—
649C22×C4—612no—
650C22×C4—624no—
651C22×C4—612no—
652C22×C4—612no—
653C22×C4C23×D3112yes—
654C22×C4C23×D3112yes—
655C22×C4C23×D313yes—
656C22×C4C23×D311yescharacteristic
657C22×C4C23×D311yescharacteristic
658C22×C4C23×D311yescharacteristic
659C22×C4C23×D313yes—
660C4⋊C4—312no—
661C4⋊C4—312no—
662C4⋊C4—312no—
663C4⋊C4—312no—
664C4⋊C4—34no—
665C4⋊C4—312no—
666C4⋊C4C23×D3112yes—
667C4⋊C4C23×D314yes—
668C22⋊C4—312no—
669C22⋊C4—324no—
670C22⋊C4—312no—
671C22⋊C4—312no—
672C22⋊C4—34no—
673C22⋊C4—34no—
674C22⋊C4—34no—
675C22⋊C4—312no—
676C22⋊C4—324no—
677C22⋊C4—312no—
678C22⋊C4C23×D3112yes—
679C22⋊C4C23×D3112yes—
680C42—324no—
681C42—312no—
682C42C23×D3112yes—
683C22×C3—26no—
684C22×C3—26no—
685C22×C3—26no—
686C22×C3—26no—
687C22×C3—26no—
688C22×C3—26no—
689C22×C3—412no—
690C22×C3—412no—
691C22×C3C23×D412yes—
692C22×C3#58512yes—
693C22×C3#58512yes—
694C22×C3C2611yescharacteristic
695C2×D3—22no—
696C2×D3—22no—
697C2×D3—28no—
698C2×D3—22no—
699C2×D3—26no—
700C2×D3—22no—
701C2×D3—26no—
702C2×D3—22no—
703C2×D3—26no—
704C2×D3—448no—
705C2×D3—44no—
706C2×D3—412no—
707C2×D3C23×D414yes—
708C3×C4—22no—
709C3×C4—22no—
710C3×C4—26no—
711C3×C4—22no—
712C3×C4C23×D4112yes—
713Dic3—26no—
714Dic3—22no—
715Dic3—26no—
716Dic3—22no—
717Dic3C23×D4112yes—
718C23—26no—
719C23—26no—
720C23—26no—
721C23—26no—
722C23—26no—
723C23—26no—
724C23—34no—
725C23—32no—
726C23—36no—
727C23—32no—
728C23—624no—
729C23—62no—
730C23—62no—
731C23—62no—
732C23—66no—
733C23—62no—
734C23—66no—
735C23—62no—
736C23—66no—
737C23—1212no—
738C23—1212no—
739C23—1248no—
740C23C24×D316yes—
741C23C24×D316yes—
742C23C24×D311yescharacteristic
743Q8—348no—
744Q8—624no—
745Q8—624no—
746Q8C2×D3×D4116yes—
747D4—224no—
748D4—224no—
749D4—412no—
750D4—424no—
751D4—68no—
752D4—648no—
753D4—624no—
754D4—624no—
755D4—624no—
756D4—1212no—
757D4—1224no—
758D4—1212no—
759D4—1212no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—26no—
764C2×C4—224no—
765C2×C4—224no—
766C2×C4—312no—
767C2×C4—36no—
768C2×C4—348no—
769C2×C4—36no—
770C2×C4—32no—
771C2×C4—36no—
772C2×C4—32no—
773C2×C4—624no—
774C2×C4—68no—
775C2×C4—624no—
776C2×C4—648no—
777C2×C4—62no—
778C2×C4—66no—
779C2×C4—66no—
780C2×C4—62no—
781C2×C4—624no—
782C2×C4—624no—
783C2×C4C2×D3×D4112yes—
784C2×C4C24×D316yes—
785C2×C4C24×D312yes—
786C2×C4C24×D312yes—
787C2×C4C24×D312yes—
788C2×C4C24×D316yes—
789C2×C3—46no—
790C2×C3—46no—
791C2×C3#348714yescomplemented
792C2×C3C24×D411yescharacteristic
793C2×C3C2×#58511yescharacteristic
794C2×C3C2×#58511yescharacteristic
795D3—24no—
796D3—42no—
797D3—46no—
798C22—26no—
799C22—26no—
800C22—26no—
801C22—26no—
802C22—26no—
803C22—26no—
804C22—34no—
805C22—412no—
806C22—412no—
807C22—62no—
808C22—62no—
809C22—68no—
810C22—62no—
811C22—66no—
812C22—62no—
813C22—66no—
814C22—62no—
815C22—66no—
816C22—1248no—
817C22—1212no—
818C22—124no—
819C22C22×D3×D412yes—
820C22#596412yes—
821C22#596612yes—
822C22C25×D311yescharacteristic
823C4—22no—
824C4—22no—
825C4—22no—
826C4—26no—
827C4—312no—
828C4—62no—
829C4—66no—
830C4—66no—
831C4—62no—
832C4C22×D3×D4112yes—
833C3C2×#348711yescharacteristic, complemented, Sylow
834C2—46no—
835C2—46no—
836C2—64no—
837C2—126no—
838C2—122no—
839C2#8678314yesdirect product factor
840C2C23×D3×D411yescharacteristic
841C2C2×#596411yescharacteristic
842C2C2×#596611yescharacteristic
subgroupG/H
centerC23C24×D3
commutator, cosocleC22×C3C26
FrattiniC22C25×D3
FittingC2×C3×#550C2
socleC23×C3C25
hypercenterC2×#550D3
hypocenterC3C2×#3487
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C22×D3×#41C2semidirect
2. C22×#1010C2semidirect
3. C2×C3×#550C2semidirect
4. C2×#5834C2semidirect
5. C2×#5831C2semidirect
6. #86783C2direct (N × H)
7. C2×#5715C2semidirect
8. C2×#5718C2semidirect
9. C2×#5607C2semidirect
10. C2×#5599C2semidirect
11. C2×#5598C2semidirect
12. C2×#5606C2semidirect
13. C2×#5576C2semidirect
14. C2×#5572C2semidirect
15. C2×#5547C2semidirect
16. C2×#5552C2semidirect
19. C22×C3×#41C22semidirect
21. C2×#1010C22semidirect
23. C2×D3×#41C22semidirect
26. C22×D3×Q8C22semidirect
29. C22×#237C22semidirect
34. C23×Dic6C22semidirect
35. C3×#550C22semidirect
36. C2×C3×#127C22semidirect
37. C2×C3×#121C22semidirect
38. C2×C3×#121C22semidirect
39. C2×C3×C4×Q8C22semidirect
40. C2×C3×C4×D4C22semidirect
41. #5834C22semidirect
42. #5831C22semidirect
43. C2×Q8×Dic3C22semidirect
44. C2×#940C22semidirect
45. C2×#940C22semidirect
46. C2×#939C22semidirect
47. C2×#939C22semidirect
48. C2×#939C22semidirect
49. C2×#938C22semidirect
50. C2×#938C22semidirect
53. C2×#936C22semidirect
54. C2×D4×Dic3C22semidirect
55. C2×#930C22semidirect
56. C2×C4×#67C22semidirect
57. C2×C4×#67C22semidirect
58. C2×#924C22semidirect
59. #5718C22semidirect
60. #5715C22semidirect
61. #5607C22semidirect
62. #5606C22semidirect
63. #5599C22semidirect
64. #5598C22semidirect
65. #5576C22semidirect
66. #5572C22semidirect
67. #5552C22semidirect
68. #5547C22semidirect
69. C2×#897C22semidirect
70. C2×#896C22semidirect
71. C2×#895C22semidirect
74. C2×#887C22semidirect
75. C2×#885C22semidirect
76. C2×#884C22semidirect
79. C2×#67⋊C4C22semidirect
80. C2×#878C22semidirect
81. C2×#875C22semidirect
82. C2×C4×D12C22semidirect
84. C2×C4×Dic6C22semidirect
91. C2×#550D3semidirect
105. C2×C3×#41C23semidirect
126. C2×D3×Q8D4semidirect
128. C2×D3×Q8C23semidirect
134. C2×#237C23semidirect
155. C22×Dic6C23semidirect
156. C3×#127C23semidirect
157. C3×#121C23semidirect
158. C3×#121C23semidirect
159. C3×C4×Q8C23semidirect
160. C3×C4×D4C23semidirect
169. Q8×Dic3C23semidirect
170. #940C23semidirect
171. #940C23semidirect
172. #939C23semidirect
173. #939C23semidirect
174. #939C23semidirect
175. #938C23semidirect
176. #938C23semidirect
179. #936C23semidirect
180. D4×Dic3C23semidirect
181. #930C23semidirect
182. C4×#67C23semidirect
183. C4×#67C23semidirect
193. #924C23semidirect
200. #897C23semidirect
201. #896C23semidirect
202. #895C23semidirect
205. #887C23semidirect
206. #885C23semidirect
207. #884C23semidirect
210. #67⋊C4C23semidirect
211. #878C23semidirect
212. #875C23semidirect
213. C4×D12C23semidirect
215. C4×Dic6C23semidirect
227. C22×#41C2×D3semidirect
236. #550C2×D3semidirect
245. C2×#127C2×D3semidirect
265. C2×#121C2×D3semidirect
266. C2×#121C2×D3semidirect
274. C2×C4×Q8C2×D3semidirect
280. C2×C4×D4C2×D3semidirect
336. D3×Q8C2×D4semidirect
408. C2×#41C22×D3semidirect
447. #127C22×D3semidirect
465. #121C22×D3semidirect
466. #121C22×D3semidirect
473. C4×Q8C22×D3semidirect
479. C4×D4C22×D3semidirect
791. C2×C3#3487semidirect
833. C3C2×#3487semidirect
839. C2#86783direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×#412
C22×#10102
C2×C3×#5502
C2×#58342
C2×#58312
#867832
C2×#57152
C2×#57182
C2×#56072
C2×#55992
C2×#55982
C2×#56062
C2×#55762
C2×#55722
C2×#55472
C2×#55522
C2×#34873