Finite Group Databasebeta

← C2×#86714 #11703592

Subgroups — C2×#86714 #11703592

Order 768.

11438 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×#41C211yesmaximal, characteristic, complemented
2C22×#1007C211yesmaximal, characteristic, complemented
3C2×C3×#548C211yesmaximal, characteristic, complemented
4C2×#5831C211yesmaximal, characteristic, complemented
5C2×Q8×#67C211yesmaximal, characteristic, complemented
6#86714C2132yesmaximal, direct product factor
7C2×#5676C213yesmaximal, complemented
8C2×#5675C213yesmaximal, complemented
9C2×#5631C213yesmaximal, complemented
10C2×D3×C22⋊Q8C213yesmaximal, complemented
11C2×#5612C213yesmaximal, complemented
12C2×#5608C213yesmaximal, complemented
13C2×Q8×D12C211yesmaximal, characteristic, complemented
14C2×#5574C211yesmaximal, characteristic, complemented
15C2×#5551C213yesmaximal, complemented
16C2×#5547C213yesmaximal, complemented
17C2×#3489—31nomaximal, Sylow
18C22×C3×#41C2211yescharacteristic
19C23×C3×Q8C2211yescharacteristic, complemented
20C2×D3×#41—216no—
21C2×D3×#41C22116yescomplemented
22C2×#1007—216no—
23C2×#1007C22116yescomplemented
24C22×#239C2211yescharacteristic
25C22×#239C2213yescomplemented
26C22×D3×Q8C2211yescharacteristic
27C22×D3×Q8C2211yescharacteristic, complemented
28C22×D3×Q8C2213yescomplemented
29C22×#237C2213yes—
30C22×D3×D4C2213yes—
31C22×#235C2213yes—
32C22×#235C2213yescomplemented
33C22×#235C2213yescomplemented
34C23×C4×D3C2213yes—
35C3×#548C22116yescomplemented
36C2×C3×#124C2213yescomplemented
37C2×C3×C22⋊Q8C2213yescomplemented
38C2×C3×#121C2213yescomplemented
39C2×C3×C4×Q8C2211yescharacteristic, complemented
40C2×C3×C4×D4C2213yescomplemented
41#5831C22116yescomplemented
42Q8×#67C22116yescomplemented
43C2×#946C2213yes—
44C2×Q8×Dic3C2211yescharacteristic, complemented
45C2×#944C2213yescomplemented
46C2×#939C2213yescomplemented
47C2×#938C2216yescomplemented
48C2×#938C2213yescomplemented
49C2×#937C2213yes—
50C2×#936C2213yescomplemented
51C2×C4×#67C2213yes—
52C2×C4×#67C2213yescomplemented
53C2×#924C2213yescomplemented
54C2×#924C2213yescomplemented
55#5676C22148yescomplemented
56#5675C22148yescomplemented
57#5631C22148yescomplemented
58D3×C22⋊Q8C22148yescomplemented
59#5612C22148yescomplemented
60#5608C22148yescomplemented
61Q8×D12C22116yescomplemented
62#5574C22116yescomplemented
63#5551C22148yescomplemented
64#5547C22148yescomplemented
65C2×#897C2213yes—
66C2×#897C2213yescomplemented
67C2×#896C2213yes—
68C2×#894C2213yescomplemented
69C2×#893C2213yescomplemented
70C2×D3×C4⋊C4C2216yescomplemented
71C2×D3×C4⋊C4C2213yescomplemented
72C2×#884C2211yescharacteristic
73C2×#884C2216yescomplemented
74C2×#883C2213yescomplemented
75C2×#883C2216yescomplemented
76C2×#883C2216yescomplemented
77C2×#882C2213yes—
78C2×D3×C22⋊C4C2216yes—
79C2×#878C2213yescomplemented
80C2×#878C2216yescomplemented
81C2×C4×D12C2213yes—
82C2×C4×D12C2213yescomplemented
83C2×#872C2213yescomplemented
84C2×#869C2213yescomplemented
85C22×2−1+4—31no—
86C23×#41—31no—
87#3489—332no—
88C2×D4×Q8—31no—
89C2×D4×Q8—31no—
90C2×#548—31no—
91C2×#548D311yescharacteristic, complemented
92C2×#547—33no—
93C2×#547—33no—
94C2×#546—33no—
95C2×#546—33no—
96C2×#537—33no—
97C2×#536—33no—
98C2×#525—33no—
99C22×C22⋊Q8—33no—
100C2×#520—31no—
101C24×D3C2313yes—
102C2×C3×#41—28no—
103C2×C3×#41C2318yes—
104C22×C3×Q8—28no—
105C22×C3×Q8C2313yes—
106C22×C3×Q8C2311yescharacteristic
107C22×C3×Q8C2318yescomplemented
108C22×C3×D4C2313yes—
109C22×C3×D4C2313yes—
110C23×C3×C4C2313yes—
111C23×C3×C4C2313yes—
112C22×#67C2316yes—
113C22×#67C2313yes—
114C22×#67C2311yescharacteristic
115C22×#67C2311yescharacteristic
116C22×#67C2313yes—
117C23×Dic3C2313yes—
118D3×#41—2128no—
119#1007—2128no—
120C2×#239—224no—
121C2×#239D4116yescomplemented
122C2×#239C2318yes—
123C2×#239C23124yescomplemented
124C2×D3×Q8—28no—
125C2×D3×Q8—28no—
126C2×D3×Q8—224no—
127C2×D3×Q8C2318yes—
128C2×D3×Q8C23124yescomplemented
129C2×D3×Q8C2318yescomplemented
130C2×#237—224no—
131C2×#237C23124yes—
132C2×D3×D4—224no—
133C2×D3×D4C23124yes—
134C2×#235—224no—
135C2×#235—224no—
136C2×#235—224no—
137C2×#235C23124yes—
138C2×#235C23124yescomplemented
139C2×#235C23124yescomplemented
140C22×D12C2313yes—
141C22×D12C2311yescharacteristic
142C22×D12C2313yes—
143C22×C4×D3—224no—
144C22×C4×D3C2311yescharacteristic
145C22×C4×D3C2313yes—
146C22×C4×D3C2313yes—
147C22×C4×D3C23124yes—
148C22×C4×D3C2313yes—
149C22×C4×D3C2316yes—
150C22×C4×D3C2316yes—
151C22×C4×D3C2313yes—
152C22×Dic6C2313yes—
153C22×Dic6C2313yes—
154C22×Dic6C2313yes—
155C3×#124C23124yescomplemented
156C3×C22⋊Q8C23124yescomplemented
157C3×#121C23124yescomplemented
158C3×C4×Q8C2318yescomplemented
159C3×C4×D4C23124yescomplemented
160C2×C3×C4⋊C4C2313yes—
161C2×C3×C4⋊C4C2313yes—
162C2×C3×C22⋊C4C2316yes—
163C2×C3×C22⋊C4C2313yes—
164C2×C3×C22⋊C4C2311yescharacteristic
165C2×C3×C42C2313yes—
166C2×#217C2316yes—
167C2×#217C2313yes—
168C2×#217C2313yes—
169#946C23124yes—
170Q8×Dic3C2318yescomplemented
171#944C23124yescomplemented
172#939C23124yescomplemented
173#938C23124yescomplemented
174#938C23148yescomplemented
175#937C23124yes—
176#936C23124yescomplemented
177C4×#67C23124yes—
178C4×#67C23124yescomplemented
179C2×(C2×D3)⋊C4C2313yes—
180C2×(C2×D3)⋊C4C2313yes—
181C2×(C2×D3)⋊C4C2313yes—
182C2×(C2×D3)⋊C4C2313yes—
183C2×(C2×D3)⋊C4C2313yes—
184C2×(C2×D3)⋊C4C2311yescharacteristic
185C2×C4⋊Dic3C2313yes—
186C2×C4⋊Dic3C2316yes—
187C2×C4⋊Dic3C2313yes—
188#924C23124yescomplemented
189#924C23124yescomplemented
190C2×Dic3⋊C4C2311yescharacteristic
191C2×Dic3⋊C4C2313yes—
192C2×Dic3⋊C4C2313yes—
193C2×Dic3⋊C4C2316yes—
194C2×Dic3⋊C4C2313yes—
195C2×C4×Dic3C2313yes—
196#897C23124yes—
197#897C23124yescomplemented
198#896C23124yes—
199#894C23124yescomplemented
200#893C23124yescomplemented
201D3×C4⋊C4C23148yescomplemented
202D3×C4⋊C4C23124yescomplemented
203#884C2318yes—
204#884C23148yescomplemented
205#883C23148yescomplemented
206#883C23148yescomplemented
207#883C23124yescomplemented
208#882C23124yes—
209D3×C22⋊C4C23148yes—
210#878C23124yescomplemented
211#878C23148yescomplemented
212C4×D12C23124yes—
213C4×D12C23124yescomplemented
214#872C23124yescomplemented
215#869C23124yescomplemented
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
227C23×Q8—31no—
228C23×Q8—33no—
229C23×Q8—31no—
230C23×Q8C2×D311yescharacteristic, complemented
231C23×D4—33no—
232C24×C4—33no—
233D4×Q8—316no—
234D4×Q8—316no—
235#548—316no—
236#548C2×D3116yescomplemented
237#547—348no—
238#547—348no—
239#546—348no—
240#546—348no—
241#537—348no—
242#536—348no—
243C2×C4⋊Q8—33no—
244C2×C4⋊Q8—33no—
245C2×#124—33no—
246C2×#124C2×D313yescomplemented
247#525—348no—
248C2×#123—33no—
249C2×#123—33no—
250C2×#123—36no—
251C2×#123—36no—
252C2×C22⋊Q8—33no—
253C2×C22⋊Q8—33no—
254C2×C22⋊Q8—33no—
255C2×C22⋊Q8—348no—
256C2×C22⋊Q8—33no—
257C2×C22⋊Q8—33no—
258C2×C22⋊Q8—33no—
259C2×C22⋊Q8—36no—
260C2×C22⋊Q8—33no—
261C2×C22⋊Q8C2×D313yescomplemented
262C2×#121—33no—
263C2×#121—36no—
264C2×#121—33no—
265C2×#121—31no—
266C2×#121—36no—
267C2×#121C2×D313yescomplemented
268C2×#120—33no—
269C2×#120—33no—
270#520—316no—
271C2×C4×Q8—31no—
272C2×C4×Q8C2×D311yescharacteristic, complemented
273C2×C4×D4—33no—
274C2×C4×D4—33no—
275C2×C4×D4—33no—
276C2×C4×D4—33no—
277C2×C4×D4—33no—
278C2×C4×D4C2×D313yescomplemented
279C2×#117—33no—
280C22×C4⋊C4—33no—
281C22×C4⋊C4—36no—
282C22×C22⋊C4—36no—
283C24×C3C2413yes—
284C24×C3C2411yescharacteristic
285C23×D3—212no—
286C23×D3—212no—
287C23×D3—46no—
288C23×D3C2411yescharacteristic
289C23×D3C24112yes—
290C23×D3C2413yes—
291C23×D3C2411yescharacteristic
292C3×#41—232no—
293C2×C3×Q8—232no—
294C2×C3×Q8—212no—
295C2×C3×Q8C2×D418yes—
296C2×C3×Q8C24112yes—
297C2×C3×Q8C2414yes—
298C2×C3×D4—212no—
299C2×C3×D4—46no—
300C2×C3×D4C24112yes—
301C2×C3×D4C24112yes—
302C22×C3×C4—212no—
303C22×C3×C4—212no—
304C22×C3×C4C2413yes—
305C22×C3×C4C2411yescharacteristic
306C22×C3×C4C2411yescharacteristic
307C22×C3×C4C2413yes—
308C22×C3×C4C24112yes—
309C22×C3×C4C24112yes—
310C22×C3×C4C2413yes—
311C2×#67—212no—
312C2×#67—224no—
313C2×#67—24no—
314C2×#67—24no—
315C2×#67—46no—
316C2×#67C24124yes—
317C2×#67C24112yes—
318C2×#67C2414yes—
319C2×#67C2414yes—
320C2×#67C24112yes—
321C22×Dic3—212no—
322C22×Dic3C24112yes—
323C22×Dic3C2411yescharacteristic
324C22×Dic3C2413yes—
325C22×Dic3C2413yes—
326C22×Dic3C2413yes—
327C22×Dic3C2411yescharacteristic
328#239—296no—
329#239C2×D4164yescomplemented
330D3×Q8—232no—
331D3×Q8—232no—
332D3×Q8—296no—
333#237—296no—
334D3×D4—296no—
335#235—296no—
336#235—296no—
337#235—296no—
338C2×D12—212no—
339C2×D12—24no—
340C2×D12C2×D4124yes—
341C2×D12C2414yes—
342C2×D12C24112yes—
343C2×D12C24112yes—
344C2×C4×D3—212no—
345C2×C4×D3—224no—
346C2×C4×D3—212no—
347C2×C4×D3—212no—
348C2×C4×D3—24no—
349C2×C4×D3—296no—
350C2×C4×D3—412no—
351C2×C4×D3C2×D4124yes—
352C2×C4×D3C24112yes—
353C2×C4×D3C24112yes—
354C2×C4×D3C24124yes—
355C2×C4×D3C24112yes—
356C2×C4×D3C2414yes—
357C2×C4×D3C24124yes—
358C2×C4×D3C24112yes—
359C2×Dic6—212no—
360C2×Dic6—212no—
361C2×Dic6—212no—
362C2×Dic6C24112yes—
363C2×Dic6C24112yes—
364C2×Dic6C24112yes—
365C3×C4⋊C4C24112yes—
366C3×C4⋊C4C24112yes—
367C3×C22⋊C4C24124yes—
368C3×C22⋊C4C24112yes—
369C3×C22⋊C4C2414yes—
370C3×C42C24112yes—
371#217C24124yes—
372#217C24112yes—
373#217C24112yes—
374(C2×D3)⋊C4C24112yes—
375(C2×D3)⋊C4C24112yes—
376(C2×D3)⋊C4C24112yes—
377(C2×D3)⋊C4C24112yes—
378(C2×D3)⋊C4C24112yes—
379(C2×D3)⋊C4C2414yes—
380C4⋊Dic3C24112yes—
381C4⋊Dic3C24124yes—
382C4⋊Dic3C24112yes—
383Dic3⋊C4C2414yes—
384Dic3⋊C4C24112yes—
385Dic3⋊C4C24112yes—
386Dic3⋊C4C24124yes—
387Dic3⋊C4C24112yes—
388C4×Dic3C24112yes—
389C25—33no—
3902−1+4—6128no—
391C2×#41—28no—
392C2×#41—316no—
393C2×#41—38no—
394C2×#41—324no—
395C2×#41—324no—
396C2×#41—324no—
397C2×#41—324no—
398C2×#41—324no—
399C2×#41—624no—
400C2×#41—624no—
401C2×#41—624no—
402C2×#41—624no—
403C2×#41—624no—
404C2×#41—6128no—
405C2×#41C22×D318yes—
406C22×Q8—28no—
407C22×Q8—324no—
408C22×Q8—38no—
409C22×Q8—38no—
410C22×Q8—33no—
411C22×Q8—33no—
412C22×Q8—33no—
413C22×Q8—624no—
414C22×Q8—68no—
415C22×Q8—68no—
416C22×Q8C22×D313yes—
417C22×Q8C22×D311yescharacteristic
418C22×Q8C22×D318yescomplemented
419C22×D4—31no—
420C22×D4—33no—
421C22×D4—31no—
422C22×D4—36no—
423C22×D4—33no—
424C22×D4—324no—
425C22×D4—33no—
426C22×D4—31no—
427C22×D4—33no—
428C22×D4—624no—
429C22×D4C22×D313yes—
430C22×D4C22×D313yes—
431C23×C4—33no—
432C23×C4—33no—
433C23×C4—36no—
434C23×C4—33no—
435C23×C4—33no—
436C23×C4—33no—
437C23×C4—31no—
438C23×C4—324no—
439C23×C4—36no—
440C23×C4—624no—
441C23×C4C22×D313yes—
442C23×C4C22×D313yes—
443C4⋊Q8—324no—
444C4⋊Q8—324no—
445#124—324no—
446#124C22×D3124yescomplemented
447#123—324no—
448#123—324no—
449#123—348no—
450#123—348no—
451C22⋊Q8—324no—
452C22⋊Q8—324no—
453C22⋊Q8—324no—
454C22⋊Q8—324no—
455C22⋊Q8—324no—
456C22⋊Q8—324no—
457C22⋊Q8—348no—
458C22⋊Q8—324no—
459C22⋊Q8C22×D3124yescomplemented
460#121—324no—
461#121—348no—
462#121—324no—
463#121—38no—
464#121—348no—
465#121C22×D3124yescomplemented
466#120—324no—
467#120—324no—
468C4×Q8—38no—
469C4×Q8C22×D318yescomplemented
470C4×D4—324no—
471C4×D4—324no—
472C4×D4—324no—
473C4×D4—324no—
474C4×D4—324no—
475C4×D4C22×D3124yescomplemented
476#117—324no—
477C2×C4⋊C4—33no—
478C2×C4⋊C4—33no—
479C2×C4⋊C4—33no—
480C2×C4⋊C4—36no—
481C2×C4⋊C4—36no—
482C2×C4⋊C4—31no—
483C2×C4⋊C4—33no—
484C2×C4⋊C4—33no—
485C2×C4⋊C4—324no—
486C2×C4⋊C4—348no—
487C2×C4⋊C4C22×D313yes—
488C2×C4⋊C4C22×D313yes—
489C2×C22⋊C4—36no—
490C2×C22⋊C4—33no—
491C2×C22⋊C4—33no—
492C2×C22⋊C4—33no—
493C2×C22⋊C4—33no—
494C2×C22⋊C4—33no—
495C2×C22⋊C4—33no—
496C2×C22⋊C4—31no—
497C2×C22⋊C4—33no—
498C2×C22⋊C4—348no—
499C2×C22⋊C4C22×D316yes—
500C2×C22⋊C4C22×D311yescharacteristic
501C2×C22⋊C4C22×D313yes—
502C2×C42—33no—
503C2×C42C22×D313yes—
504C23×C3—26no—
505C23×C3—22no—
506C23×C3—22no—
507C23×C3—26no—
508C23×C3—26no—
509C23×C3—22no—
510C23×C3C2516yes—
511C23×C3C2512yes—
512C23×C3C2511yescharacteristic
513C22×D3—22no—
514C22×D3—26no—
515C22×D3—26no—
516C22×D3—22no—
517C22×D3—22no—
518C22×D3—22no—
519C22×D3—22no—
520C22×D3—224no—
521C22×D3—224no—
522C22×D3—412no—
523C22×D3—448no—
524C22×D3C22×D4112yes—
525C22×D32−1+414yescomplemented
526C22×D3C2512yes—
527C22×D3C2516yes—
528C22×D3C2512yes—
529C3×Q8—224no—
530C3×Q8C22×D4116yes—
531C3×D4—224no—
532C3×D4—412no—
533C2×C3×C4—26no—
534C2×C3×C4—22no—
535C2×C3×C4—22no—
536C2×C3×C4—26no—
537C2×C3×C4—224no—
538C2×C3×C4—224no—
539C2×C3×C4C22×D4112yes—
540C2×C3×C4C2516yes—
541C2×C3×C4C2512yes—
542C2×C3×C4C2512yes—
543C2×C3×C4C2516yes—
544C2×C3×C4C2516yes—
545#67—224no—
546#67—248no—
547#67—28no—
548#67—28no—
549#67—412no—
550C2×Dic3—26no—
551C2×Dic3—26no—
552C2×Dic3—22no—
553C2×Dic3—26no—
554C2×Dic3—224no—
555C2×Dic3C22×D414yes—
556C2×Dic3C2512yes—
557C2×Dic3C2516yes—
558C2×Dic3C2516yes—
559C2×Dic3C2516yes—
560C2×Dic3C2512yes—
561D12—224no—
562D12—28no—
563D12C22×D4148yes—
564C4×D3—224no—
565C4×D3—248no—
566C4×D3—224no—
567C4×D3—224no—
568C4×D3—28no—
569C4×D3—424no—
570C4×D3C22×D4148yes—
571Dic6—224no—
572Dic6—224no—
573Dic6—224no—
574C24—31no—
575C24—33no—
576C24—31no—
577C24—312no—
578C24—612no—
579C24—612no—
580C24—126no—
581C24C23×D313yes—
582C24C23×D311yescharacteristic
583#41—232no—
584#41—364no—
585#41—696no—
586#41—696no—
587#41—696no—
588#41—696no—
589#41—696no—
590C2×Q8—232no—
591C2×Q8—212no—
592C2×Q8—312no—
593C2×Q8—312no—
594C2×Q8—312no—
595C2×Q8—612no—
596C2×Q8—696no—
597C2×Q8—632no—
598C2×Q8—632no—
599C2×Q8—612no—
600C2×Q8—612no—
601C2×Q8D3×D418yes—
602C2×Q8C23×D3112yes—
603C2×Q8C23×D314yes—
604C2×D4—212no—
605C2×D4—34no—
606C2×D4—312no—
607C2×D4—34no—
608C2×D4—324no—
609C2×D4—312no—
610C2×D4—324no—
611C2×D4—312no—
612C2×D4—34no—
613C2×D4—312no—
614C2×D4—46no—
615C2×D4—612no—
616C2×D4—64no—
617C2×D4—64no—
618C2×D4—696no—
619C2×D4—624no—
620C2×D4—612no—
621C2×D4—64no—
622C2×D4—126no—
623C2×D4C23×D3112yes—
624C2×D4C23×D3112yes—
625C22×C4—212no—
626C22×C4—212no—
627C22×C4—31no—
628C22×C4—324no—
629C22×C4—312no—
630C22×C4—312no—
631C22×C4—31no—
632C22×C4—33no—
633C22×C4—33no—
634C22×C4—33no—
635C22×C4—324no—
636C22×C4—312no—
637C22×C4—312no—
638C22×C4—312no—
639C22×C4—34no—
640C22×C4—324no—
641C22×C4—64no—
642C22×C4—696no—
643C22×C4—612no—
644C22×C4—624no—
645C22×C4—612no—
646C22×C4—612no—
647C22×C4—612no—
648C22×C4—1212no—
649C22×C4C23×D3112yes—
650C22×C4C23×D3112yes—
651C22×C4C23×D311yescharacteristic
652C22×C4C23×D313yes—
653C22×C4C23×D313yes—
654C22×C4C23×D311yescharacteristic
655C22×C4C23×D313yes—
656C4⋊C4—312no—
657C4⋊C4—312no—
658C4⋊C4—312no—
659C4⋊C4—324no—
660C4⋊C4—324no—
661C4⋊C4—34no—
662C4⋊C4—312no—
663C4⋊C4—312no—
664C4⋊C4C23×D3112yes—
665C4⋊C4C23×D3112yes—
666C22⋊C4—324no—
667C22⋊C4—312no—
668C22⋊C4—312no—
669C22⋊C4—312no—
670C22⋊C4—312no—
671C22⋊C4—312no—
672C22⋊C4—312no—
673C22⋊C4—34no—
674C22⋊C4—312no—
675C22⋊C4C23×D3124yes—
676C22⋊C4C23×D314yes—
677C22⋊C4C23×D3112yes—
678C42—312no—
679C42C23×D3112yes—
680C22×C3—26no—
681C22×C3—22no—
682C22×C3—22no—
683C22×C3—26no—
684C22×C3—26no—
685C22×C3—22no—
686C22×C3—412no—
687C22×C3—44no—
688C22×C3C23×D412yes—
689C22×C3C2×2−1+412yes—
690C22×C3#58512yes—
691C22×C3C2611yescharacteristic
692C2×D3—22no—
693C2×D3—26no—
694C2×D3—26no—
695C2×D3—22no—
696C2×D3—28no—
697C2×D3—224no—
698C2×D3—22no—
699C2×D3—22no—
700C2×D3—22no—
701C2×D3—448no—
702C2×D3—44no—
703C2×D3C23×D4112yes—
704C2×D3C2×2−1+414yescomplemented
705C3×C4—26no—
706C3×C4—22no—
707C3×C4—22no—
708C3×C4—26no—
709C3×C4C23×D4112yes—
710Dic3—26no—
711Dic3—26no—
712Dic3—22no—
713Dic3—26no—
714Dic3C23×D414yes—
715C23—22no—
716C23—26no—
717C23—22no—
718C23—26no—
719C23—22no—
720C23—26no—
721C23—312no—
722C23—34no—
723C23—32no—
724C23—36no—
725C23—32no—
726C23—624no—
727C23—624no—
728C23—62no—
729C23—66no—
730C23—62no—
731C23—66no—
732C23—62no—
733C23—62no—
734C23—62no—
735C23—1212no—
736C23—1248no—
737C23C24×D316yes—
738C23C24×D312yes—
739C23C24×D311yescharacteristic
740Q8—224no—
741Q8—624no—
742Q8—624no—
743Q8—624no—
744Q8C2×D3×D4116yes—
745D4—224no—
746D4—348no—
747D4—412no—
748D4—624no—
749D4—68no—
750D4—68no—
751D4—648no—
752D4—624no—
753D4—68no—
754D4—1212no—
755C2×C4—22no—
756C2×C4—26no—
757C2×C4—26no—
758C2×C4—22no—
759C2×C4—224no—
760C2×C4—224no—
761C2×C4—34no—
762C2×C4—32no—
763C2×C4—348no—
764C2×C4—32no—
765C2×C4—36no—
766C2×C4—36no—
767C2×C4—36no—
768C2×C4—68no—
769C2×C4—624no—
770C2×C4—648no—
771C2×C4—624no—
772C2×C4—66no—
773C2×C4—66no—
774C2×C4—66no—
775C2×C4—62no—
776C2×C4—624no—
777C2×C4—624no—
778C2×C4—1224no—
779C2×C4C2×D3×D4112yes—
780C2×C4C24×D312yes—
781C2×C4C24×D316yes—
782C2×C4C24×D316yes—
783C2×C4C24×D312yes—
784C2×C4C24×D316yes—
785C2×C3—46no—
786C2×C3—42no—
787C2×C3#348914yescomplemented
788C2×C3C24×D411yescharacteristic
789C2×C3C22×2−1+411yescharacteristic
790C2×C3C2×#58511yescharacteristic
791D3—24no—
792D3—212no—
793D3—42no—
794C22—22no—
795C22—26no—
796C22—22no—
797C22—26no—
798C22—22no—
799C22—26no—
800C22—312no—
801C22—34no—
802C22—412no—
803C22—44no—
804C22—62no—
805C22—66no—
806C22—62no—
807C22—66no—
808C22—68no—
809C22—624no—
810C22—62no—
811C22—62no—
812C22—62no—
813C22—1248no—
814C22—124no—
815C22C22×D3×D412yes—
816C22#596412yes—
817C22D3×2−1+412yes—
818C22C25×D311yescharacteristic
819C4—22no—
820C4—26no—
821C4—26no—
822C4—22no—
823C4—34no—
824C4—66no—
825C4—66no—
826C4—66no—
827C4—62no—
828C4C22×D3×D4112yes—
829C3C2×#348911yescharacteristic, complemented, Sylow
830C2—46no—
831C2—42no—
832C2—64no—
833C2—612no—
834C2—122no—
835C2#8671414yesdirect product factor
836C2C23×D3×D411yescharacteristic
837C2C2×#596411yescharacteristic
838C2C2×D3×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D3
commutator, cosocleC22×C3C26
FrattiniC22C25×D3
FittingC2×C3×#548C2
socleC23×C3C25
hypercenterC2×#548D3
hypocenterC3C2×#3489
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×D3×#41C2semidirect
2. C22×#1007C2semidirect
3. C2×C3×#548C2semidirect
4. C2×#5831C2semidirect
5. C2×Q8×#67C2semidirect
6. #86714C2direct (N × H)
7. C2×#5676C2semidirect
8. C2×#5675C2semidirect
9. C2×#5631C2semidirect
10. C2×D3×C22⋊Q8C2semidirect
11. C2×#5612C2semidirect
12. C2×#5608C2semidirect
13. C2×Q8×D12C2semidirect
14. C2×#5574C2semidirect
15. C2×#5551C2semidirect
16. C2×#5547C2semidirect
19. C23×C3×Q8C22semidirect
21. C2×D3×#41C22semidirect
23. C2×#1007C22semidirect
25. C22×#239C22semidirect
27. C22×D3×Q8C22semidirect
28. C22×D3×Q8C22semidirect
32. C22×#235C22semidirect
33. C22×#235C22semidirect
35. C3×#548C22semidirect
36. C2×C3×#124C22semidirect
37. C2×C3×C22⋊Q8C22semidirect
38. C2×C3×#121C22semidirect
39. C2×C3×C4×Q8C22semidirect
40. C2×C3×C4×D4C22semidirect
41. #5831C22semidirect
42. Q8×#67C22semidirect
44. C2×Q8×Dic3C22semidirect
45. C2×#944C22semidirect
46. C2×#939C22semidirect
47. C2×#938C22semidirect
48. C2×#938C22semidirect
50. C2×#936C22semidirect
52. C2×C4×#67C22semidirect
53. C2×#924C22semidirect
54. C2×#924C22semidirect
55. #5676C22semidirect
56. #5675C22semidirect
57. #5631C22semidirect
58. D3×C22⋊Q8C22semidirect
59. #5612C22semidirect
60. #5608C22semidirect
61. Q8×D12C22semidirect
62. #5574C22semidirect
63. #5551C22semidirect
64. #5547C22semidirect
66. C2×#897C22semidirect
68. C2×#894C22semidirect
69. C2×#893C22semidirect
70. C2×D3×C4⋊C4C22semidirect
71. C2×D3×C4⋊C4C22semidirect
73. C2×#884C22semidirect
74. C2×#883C22semidirect
75. C2×#883C22semidirect
76. C2×#883C22semidirect
79. C2×#878C22semidirect
80. C2×#878C22semidirect
82. C2×C4×D12C22semidirect
83. C2×#872C22semidirect
84. C2×#869C22semidirect
91. C2×#548D3semidirect
107. C22×C3×Q8C23semidirect
121. C2×#239D4semidirect
123. C2×#239C23semidirect
128. C2×D3×Q8C23semidirect
129. C2×D3×Q8C23semidirect
138. C2×#235C23semidirect
139. C2×#235C23semidirect
155. C3×#124C23semidirect
156. C3×C22⋊Q8C23semidirect
157. C3×#121C23semidirect
158. C3×C4×Q8C23semidirect
159. C3×C4×D4C23semidirect
170. Q8×Dic3C23semidirect
171. #944C23semidirect
172. #939C23semidirect
173. #938C23semidirect
174. #938C23semidirect
176. #936C23semidirect
178. C4×#67C23semidirect
188. #924C23semidirect
189. #924C23semidirect
197. #897C23semidirect
199. #894C23semidirect
200. #893C23semidirect
201. D3×C4⋊C4C23semidirect
202. D3×C4⋊C4C23semidirect
204. #884C23semidirect
205. #883C23semidirect
206. #883C23semidirect
207. #883C23semidirect
210. #878C23semidirect
211. #878C23semidirect
213. C4×D12C23semidirect
214. #872C23semidirect
215. #869C23semidirect
230. C23×Q8C2×D3semidirect
236. #548C2×D3semidirect
246. C2×#124C2×D3semidirect
261. C2×C22⋊Q8C2×D3semidirect
267. C2×#121C2×D3semidirect
272. C2×C4×Q8C2×D3semidirect
278. C2×C4×D4C2×D3semidirect
329. #239C2×D4semidirect
418. C22×Q8C22×D3semidirect
446. #124C22×D3semidirect
459. C22⋊Q8C22×D3semidirect
465. #121C22×D3semidirect
469. C4×Q8C22×D3semidirect
475. C4×D4C22×D3semidirect
525. C22×D32−1+4semidirect
704. C2×D3C2×2−1+4semidirect
787. C2×C3#3489semidirect
829. C3C2×#3489semidirect
835. C2#86714direct (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×#10072
C2×C3×#5482
C2×#58312
C2×Q8×#672
#867142
C2×#56762
C2×#56752
C2×#56312
C2×D3×C22⋊Q82
C2×#56122
C2×#56082
C2×Q8×D122
C2×#55742
C2×#55512
C2×#55472
C2×#34893