Finite Group Databasebeta

← C2×#86745 #11703587

Subgroups — C2×#86745 #11703587

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×#1007C211yesmaximal, characteristic, complemented
2C23×#239C211yesmaximal, characteristic, complemented
3C2×C3×D4×Q8C211yesmaximal, characteristic, complemented
4C2×#5817C211yesmaximal, characteristic, complemented
5C2×Q8×#67C211yesmaximal, characteristic, complemented
6#86745C2132yesmaximal, direct product factor
7C2×#5726C213yesmaximal, complemented
8C2×#5724C213yesmaximal, complemented
9C2×#5631C213yesmaximal, complemented
10C2×#5630C213yesmaximal, complemented
11C2×#5629C213yesmaximal, complemented
12C2×D3×C22⋊Q8C213yesmaximal, complemented
13C2×#5576C211yesmaximal, characteristic, complemented
14C2×#5574C211yesmaximal, characteristic, complemented
15C2×#5550C213yesmaximal, complemented
16C2×#5547C213yesmaximal, complemented
17C2×#3489—31nomaximal, Sylow
18C23×C3×Q8C2211yescharacteristic
19C23×C3×Q8C2211yescharacteristic, complemented
20C2×#1007—216no—
21C2×#1007C22116yescomplemented
22C22×#239—216no—
23C22×#239C2211yescharacteristic
24C22×#239C2213yes—
25C22×#239C2213yes—
26C22×#239C2211yescharacteristic
27C22×#239C22116yescomplemented
28C22×#239C2213yescomplemented
29C22×D3×Q8C2211yescharacteristic, complemented
30C22×D3×Q8C2213yescomplemented
31C22×#235C2213yescomplemented
32C22×#235C2213yescomplemented
33C23×D12C2213yes—
34C23×C4×D3C2213yes—
35C3×D4×Q8C22116yescomplemented
36C2×C3×C4⋊Q8C2213yescomplemented
37C2×C3×C22⋊Q8C2213yes—
38C2×C3×C22⋊Q8C2213yescomplemented
39C2×C3×C4×Q8C2211yescharacteristic, complemented
40C2×C3×C4×D4C2213yes—
41#5817C22116yescomplemented
42Q8×#67C22116yescomplemented
43C2×#947C2213yescomplemented
44C2×#946C2213yescomplemented
45C2×#946C2213yescomplemented
46C2×Q8×Dic3C2211yescharacteristic, complemented
47C2×#944C2213yescomplemented
48C2×#939C2211yescharacteristic
49C2×#937C2213yes—
50C2×#930C2213yescomplemented
51C2×C4×#67C2213yes—
52C2×C4×#67C2213yescomplemented
53C2×#924C2213yes—
54#5726C22148yescomplemented
55#5724C22148yescomplemented
56#5631C22148yescomplemented
57#5630C22148yescomplemented
58#5629C22148yescomplemented
59D3×C22⋊Q8C22148yescomplemented
60#5576C22116yescomplemented
61#5574C22116yescomplemented
62#5550C22148yescomplemented
63#5547C22148yescomplemented
64C2×#897C2213yescomplemented
65C2×#896C2213yescomplemented
66C2×#896C2216yescomplemented
67C2×#895C2213yescomplemented
68C2×#895C2216yescomplemented
69C2×#894C2213yescomplemented
70C2×#894C2216yescomplemented
71C2×#894C2216yescomplemented
72C2×#893C2213yescomplemented
73C2×D3×C4⋊C4C2213yescomplemented
74C2×D3×C4⋊C4C2216yescomplemented
75C2×#884C2213yescomplemented
76C2×#884C2216yescomplemented
77C2×#883C2213yescomplemented
78C2×#882C2213yes—
79C2×D3×C22⋊C4C2216yes—
80C2×#878C2213yes—
81C2×#875C2213yescomplemented
82C2×C4×D12C2213yescomplemented
83C2×C4×D12C2213yescomplemented
84C2×#872C2213yescomplemented
85C22×2−1+4—31no—
86C23×#41—31no—
87#3489—332no—
88C2×D4×Q8—31no—
89C2×D4×Q8D311yescharacteristic, complemented
90C2×#548—31no—
91C2×#548—31no—
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—
102C22×C3×Q8—28no—
103C22×C3×Q8—28no—
104C22×C3×Q8C2313yes—
105C22×C3×Q8C2313yes—
106C22×C3×Q8C2318yes—
107C22×C3×Q8C2311yescharacteristic
108C22×C3×Q8C2318yescomplemented
109C22×C3×D4C2311yescharacteristic
110C23×C3×C4C2313yes—
111C23×C3×C4C2313yes—
112C22×#67C2313yes—
113C22×#67C2311yescharacteristic
114C22×#67C2311yescharacteristic
115C22×#67C2313yes—
116C23×Dic3C2311yescharacteristic
117#1007—2128no—
118C2×#239—28no—
119C2×#239—2128no—
120C2×#239—224no—
121C2×#239—224no—
122C2×#239—224no—
123C2×#239D4116yescomplemented
124C2×#239C23124yes—
125C2×#239C23124yes—
126C2×#239C2318yes—
127C2×#239C2318yes—
128C2×#239C23124yescomplemented
129C2×D3×Q8—28no—
130C2×D3×Q8—224no—
131C2×D3×Q8C23124yescomplemented
132C2×D3×Q8C2318yescomplemented
133C2×#235—224no—
134C2×#235—224no—
135C2×#235C23124yescomplemented
136C2×#235C23124yescomplemented
137C22×D12—224no—
138C22×D12C2313yes—
139C22×D12C2316yes—
140C22×D12C23124yes—
141C22×D12C2313yes—
142C22×D12C2313yes—
143C22×D12C2313yes—
144C22×C4×D3—224no—
145C22×C4×D3C2313yes—
146C22×C4×D3C2313yes—
147C22×C4×D3C2313yes—
148C22×C4×D3C23124yes—
149C22×C4×D3C2313yes—
150C22×C4×D3C2316yes—
151C22×C4×D3C2316yes—
152C22×C4×D3C2313yes—
153C22×Dic6C2313yes—
154C22×Dic6C2313yes—
155C3×C4⋊Q8C23124yescomplemented
156C3×C22⋊Q8C23124yes—
157C3×C22⋊Q8C23124yescomplemented
158C3×C4×Q8C2318yescomplemented
159C3×C4×D4C23124yes—
160C2×C3×C4⋊C4C2313yes—
161C2×C3×C4⋊C4C2316yes—
162C2×C3×C4⋊C4C2313yes—
163C2×C3×C22⋊C4C2313yes—
164C2×C3×C22⋊C4C2313yes—
165C2×C3×C42C2313yes—
166C2×#217C2313yes—
167C2×#217C2311yescharacteristic
168#947C23124yescomplemented
169#946C23124yescomplemented
170#946C23124yescomplemented
171Q8×Dic3C2318yescomplemented
172#944C23124yescomplemented
173#939C2318yes—
174#937C23124yes—
175#930C23124yescomplemented
176C4×#67C23124yes—
177C4×#67C23124yescomplemented
178C2×(C2×D3)⋊C4C2313yes—
179C2×(C2×D3)⋊C4C2313yes—
180C2×(C2×D3)⋊C4C2311yescharacteristic
181C2×(C2×D3)⋊C4C2313yes—
182C2×(C2×D3)⋊C4C2316yes—
183C2×(C2×D3)⋊C4C2316yes—
184C2×(C2×D3)⋊C4C2313yes—
185C2×(C2×D3)⋊C4C2313yes—
186C2×C4⋊Dic3C2313yes—
187C2×C4⋊Dic3C2313yes—
188#924C23124yes—
189C2×Dic3⋊C4C2311yescharacteristic
190C2×Dic3⋊C4C2313yes—
191C2×Dic3⋊C4C2313yes—
192C2×Dic3⋊C4C2313yes—
193C2×Dic3⋊C4C2316yes—
194C2×C4×Dic3C2313yes—
195#897C23124yescomplemented
196#896C23124yescomplemented
197#896C23148yescomplemented
198#895C23148yescomplemented
199#895C23124yescomplemented
200#894C23148yescomplemented
201#894C23148yescomplemented
202#894C23124yescomplemented
203#893C23124yescomplemented
204D3×C4⋊C4C23148yescomplemented
205D3×C4⋊C4C23124yescomplemented
206#884C23124yescomplemented
207#884C23148yescomplemented
208#883C23124yescomplemented
209#882C23124yes—
210D3×C22⋊C4C23148yes—
211#878C23124yes—
212#875C23124yescomplemented
213C4×D12C23124yescomplemented
214C4×D12C23124yescomplemented
215#872C23124yescomplemented
216C2×2−1+4—316no—
217C2×2−1+4—616no—
218C22×#41—31no—
219C22×#41—33no—
220C22×#41—33no—
221C22×#41—31no—
222C22×#41—316no—
223C22×#41—33no—
224C22×#41—33no—
225C22×#41—33no—
226C22×#41—616no—
227C23×Q8—33no—
228C23×Q8—31no—
229C23×Q8C2×D311yescharacteristic
230C23×Q8C2×D311yescharacteristic, complemented
231C23×D4—33no—
232C24×C4—33no—
233D4×Q8—316no—
234D4×Q8C2×D3116yescomplemented
235#548—316no—
236#548—316no—
237#547—348no—
238#547—348no—
239#546—348no—
240#546—348no—
241#537—348no—
242#536—348no—
243C2×C4⋊Q8—33no—
244C2×C4⋊Q8C2×D313yescomplemented
245C2×#124—33no—
246C2×#124—33no—
247#525—348no—
248C2×#123—33no—
249C2×#123—36no—
250C2×#123—36no—
251C2×#123—33no—
252C2×C22⋊Q8—33no—
253C2×C22⋊Q8—33no—
254C2×C22⋊Q8—33no—
255C2×C22⋊Q8—348no—
256C2×C22⋊Q8—36no—
257C2×C22⋊Q8—33no—
258C2×C22⋊Q8—33no—
259C2×C22⋊Q8—33no—
260C2×C22⋊Q8C2×D313yes—
261C2×C22⋊Q8C2×D313yescomplemented
262C2×#121—31no—
263C2×#121—33no—
264C2×#121—36no—
265C2×#121—33no—
266C2×#121—33no—
267C2×#121—36no—
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×D313yes—
279C2×#117—33no—
280C22×C4⋊C4—33no—
281C22×C4⋊C4—36no—
282C22×C22⋊C4—36no—
283C24×C3C2411yescharacteristic
284C24×C3C2411yescharacteristic
285C23×D3—212no—
286C23×D3—212no—
287C23×D3—46no—
288C23×D3C2413yes—
289C23×D3C2411yescharacteristic
290C23×D3C24112yes—
291C23×D3C2413yes—
292C2×C3×Q8—232no—
293C2×C3×Q8—232no—
294C2×C3×Q8—212no—
295C2×C3×Q8—212no—
296C2×C3×Q8C2×D418yes—
297C2×C3×Q8C24112yes—
298C2×C3×Q8C24112yes—
299C2×C3×Q8C2414yes—
300C2×C3×D4—24no—
301C2×C3×D4C2414yes—
302C22×C3×C4—212no—
303C22×C3×C4—212no—
304C22×C3×C4C2413yes—
305C22×C3×C4C2413yes—
306C22×C3×C4C2411yescharacteristic
307C22×C3×C4C2413yes—
308C22×C3×C4C24112yes—
309C22×C3×C4C24112yes—
310C22×C3×C4C2413yes—
311C2×#67—24no—
312C2×#67—212no—
313C2×#67—24no—
314C2×#67—46no—
315C2×#67C2414yes—
316C2×#67C24112yes—
317C2×#67C2414yes—
318C2×#67C24112yes—
319C22×Dic3—24no—
320C22×Dic3C2414yes—
321C22×Dic3C2411yescharacteristic
322C22×Dic3C2413yes—
323C22×Dic3C2411yescharacteristic
324C22×Dic3C2413yes—
325C22×Dic3C2411yescharacteristic
326#239—232no—
327#239—296no—
328#239—296no—
329#239—296no—
330#239C2×D4164yescomplemented
331D3×Q8—232no—
332D3×Q8—296no—
333#235—296no—
334#235—296no—
335C2×D12—224no—
336C2×D12—212no—
337C2×D12—212no—
338C2×D12—296no—
339C2×D12—46no—
340C2×D12C2×D4124yes—
341C2×D12C24112yes—
342C2×D12C24112yes—
343C2×D12C24124yes—
344C2×D12C24112yes—
345C2×D12C24112yes—
346C2×C4×D3—212no—
347C2×C4×D3—224no—
348C2×C4×D3—212no—
349C2×C4×D3—212no—
350C2×C4×D3—212no—
351C2×C4×D3—296no—
352C2×C4×D3—412no—
353C2×C4×D3C2×D4124yes—
354C2×C4×D3C24112yes—
355C2×C4×D3C24112yes—
356C2×C4×D3C24124yes—
357C2×C4×D3C24112yes—
358C2×C4×D3C24112yes—
359C2×C4×D3C24124yes—
360C2×C4×D3C24112yes—
361C2×Dic6—212no—
362C2×Dic6—212no—
363C2×Dic6C24112yes—
364C2×Dic6C24112yes—
365C3×C4⋊C4C24112yes—
366C3×C4⋊C4C24124yes—
367C3×C4⋊C4C24112yes—
368C3×C22⋊C4C24112yes—
369C3×C22⋊C4C24112yes—
370C3×C42C24112yes—
371#217C24112yes—
372#217C2414yes—
373(C2×D3)⋊C4C24112yes—
374(C2×D3)⋊C4C24112yes—
375(C2×D3)⋊C4C2414yes—
376(C2×D3)⋊C4C24112yes—
377(C2×D3)⋊C4C24124yes—
378(C2×D3)⋊C4C24124yes—
379(C2×D3)⋊C4C24112yes—
380(C2×D3)⋊C4C24112yes—
381C4⋊Dic3C24112yes—
382C4⋊Dic3C24112yes—
383Dic3⋊C4C2414yes—
384Dic3⋊C4C24112yes—
385Dic3⋊C4C24112yes—
386Dic3⋊C4C24112yes—
387Dic3⋊C4C24124yes—
388C4×Dic3C24112yes—
389C25—33no—
3902−1+4—6128no—
391C2×#41—316no—
392C2×#41—38no—
393C2×#41—324no—
394C2×#41—324no—
395C2×#41—324no—
396C2×#41—38no—
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×#41—68no—
406C22×Q8—28no—
407C22×Q8—28no—
408C22×Q8—324no—
409C22×Q8—38no—
410C22×Q8—33no—
411C22×Q8—33no—
412C22×Q8—624no—
413C22×Q8—68no—
414C22×Q8C22×D313yes—
415C22×Q8C22×D313yes—
416C22×Q8C22×D318yes—
417C22×Q8C22×D311yescharacteristic
418C22×Q8C22×D318yescomplemented
419C22×D4—31no—
420C22×D4—33no—
421C22×D4—31no—
422C22×D4—33no—
423C22×D4—33no—
424C22×D4—33no—
425C22×D4—36no—
426C22×D4—33no—
427C22×D4—324no—
428C22×D4—33no—
429C22×D4—624no—
430C22×D4C22×D311yescharacteristic
431C23×C4—33no—
432C23×C4—31no—
433C23×C4—36no—
434C23×C4—33no—
435C23×C4—33no—
436C23×C4—33no—
437C23×C4—33no—
438C23×C4—324no—
439C23×C4—36no—
440C23×C4—624no—
441C23×C4C22×D313yes—
442C23×C4C22×D313yes—
443C4⋊Q8—324no—
444C4⋊Q8C22×D3124yescomplemented
445#124—324no—
446#124—324no—
447#123—324no—
448#123—348no—
449#123—348no—
450#123—324no—
451C22⋊Q8—324no—
452C22⋊Q8—324no—
453C22⋊Q8—324no—
454C22⋊Q8—348no—
455C22⋊Q8—324no—
456C22⋊Q8—324no—
457C22⋊Q8—324no—
458C22⋊Q8C22×D3124yes—
459C22⋊Q8C22×D3124yescomplemented
460#121—38no—
461#121—324no—
462#121—348no—
463#121—324no—
464#121—324no—
465#121—348no—
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×D3124yes—
476#117—324no—
477C2×C4⋊C4—33no—
478C2×C4⋊C4—33no—
479C2×C4⋊C4—33no—
480C2×C4⋊C4—33no—
481C2×C4⋊C4—36no—
482C2×C4⋊C4—31no—
483C2×C4⋊C4—33no—
484C2×C4⋊C4—324no—
485C2×C4⋊C4—348no—
486C2×C4⋊C4C22×D313yes—
487C2×C4⋊C4C22×D316yes—
488C2×C4⋊C4C22×D313yes—
489C2×C22⋊C4—33no—
490C2×C22⋊C4—31no—
491C2×C22⋊C4—36no—
492C2×C22⋊C4—36no—
493C2×C22⋊C4—33no—
494C2×C22⋊C4—33no—
495C2×C22⋊C4—31no—
496C2×C22⋊C4—33no—
497C2×C22⋊C4—33no—
498C2×C22⋊C4—33no—
499C2×C22⋊C4—348no—
500C2×C22⋊C4C22×D313yes—
501C2×C22⋊C4C22×D313yes—
502C2×C42—33no—
503C2×C42C22×D313yes—
504C23×C3—22no—
505C23×C3—22no—
506C23×C3—22no—
507C23×C3—22no—
508C23×C3—22no—
509C23×C32−1+414yescomplemented
510C23×C3C2512yes—
511C23×C3C2512yes—
512C23×C3C2511yescharacteristic
513C22×D3—26no—
514C22×D3—26no—
515C22×D3—22no—
516C22×D3—26no—
517C22×D3—22no—
518C22×D3—26no—
519C22×D3—224no—
520C22×D3—22no—
521C22×D3—26no—
522C22×D3—224no—
523C22×D3—412no—
524C22×D3—448no—
525C22×D3C22×D4112yes—
526C22×D3C2516yes—
527C22×D3C2512yes—
528C22×D3C2516yes—
529C3×Q8—224no—
530C3×Q8—224no—
531C3×Q8C22×D4116yes—
532C3×D4—28no—
533C2×C3×C4—26no—
534C2×C3×C4—26no—
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×C4C2516yes—
542C2×C3×C4C2512yes—
543C2×C3×C4C2516yes—
544C2×C3×C4C2516yes—
545#67—28no—
546#67—224no—
547#67—28no—
548#67—412no—
549C2×Dic3—26no—
550C2×Dic3—22no—
551C2×Dic3—22no—
552C2×Dic3—26no—
553C2×Dic3—28no—
554C2×Dic3C22×D414yes—
555C2×Dic3C2512yes—
556C2×Dic3C2516yes—
557C2×Dic3C2512yes—
558C2×Dic3C2516yes—
559C2×Dic3C2512yes—
560D12—248no—
561D12—224no—
562D12—224no—
563D12—412no—
564D12C22×D4148yes—
565C4×D3—224no—
566C4×D3—248no—
567C4×D3—224no—
568C4×D3—224no—
569C4×D3—224no—
570C4×D3—424no—
571C4×D3C22×D4148yes—
572Dic6—224no—
573Dic6—224no—
574C24—33no—
575C24—33no—
576C24—31no—
577C24—312no—
578C24—612no—
579C24—612no—
580C24—126no—
581C24C23×D311yescharacteristic
582C24C23×D311yescharacteristic
583#41—364no—
584#41—696no—
585#41—696no—
586#41—696no—
587#41—696no—
588#41—696no—
589#41—632no—
590C2×Q8—232no—
591C2×Q8—232no—
592C2×Q8—212no—
593C2×Q8—212no—
594C2×Q8—312no—
595C2×Q8—312no—
596C2×Q8—612no—
597C2×Q8—696no—
598C2×Q8—632no—
599C2×Q8—612no—
600C2×Q8D3×D418yes—
601C2×Q8C23×D3112yes—
602C2×Q8C23×D3112yes—
603C2×Q8C23×D314yes—
604C2×D4—24no—
605C2×D4—34no—
606C2×D4—312no—
607C2×D4—34no—
608C2×D4—312no—
609C2×D4—324no—
610C2×D4—312no—
611C2×D4—312no—
612C2×D4—324no—
613C2×D4—312no—
614C2×D4—312no—
615C2×D4—696no—
616C2×D4—624no—
617C2×D4—612no—
618C2×D4—64no—
619C2×D4—612no—
620C2×D4—64no—
621C2×D4—612no—
622C2×D4—126no—
623C2×D4—126no—
624C2×D4C23×D314yes—
625C22×C4—212no—
626C22×C4—212no—
627C22×C4—31no—
628C22×C4—324no—
629C22×C4—312no—
630C22×C4—34no—
631C22×C4—31no—
632C22×C4—33no—
633C22×C4—33no—
634C22×C4—31no—
635C22×C4—324no—
636C22×C4—312no—
637C22×C4—312no—
638C22×C4—312no—
639C22×C4—312no—
640C22×C4—324no—
641C22×C4—612no—
642C22×C4—696no—
643C22×C4—612no—
644C22×C4—624no—
645C22×C4—64no—
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×D313yes—
655C22×C4C23×D313yes—
656C4⋊C4—312no—
657C4⋊C4—312no—
658C4⋊C4—312no—
659C4⋊C4—312no—
660C4⋊C4—324no—
661C4⋊C4—34no—
662C4⋊C4—312no—
663C4⋊C4C23×D3112yes—
664C4⋊C4C23×D3124yes—
665C4⋊C4C23×D3112yes—
666C22⋊C4—312no—
667C22⋊C4—34no—
668C22⋊C4—324no—
669C22⋊C4—324no—
670C22⋊C4—312no—
671C22⋊C4—312no—
672C22⋊C4—34no—
673C22⋊C4—312no—
674C22⋊C4—312no—
675C22⋊C4—312no—
676C22⋊C4C23×D3112yes—
677C22⋊C4C23×D3112yes—
678C42—312no—
679C42C23×D3112yes—
680C22×C3—22no—
681C22×C3—22no—
682C22×C3—28no—
683C22×C3—22no—
684C22×C3—22no—
685C22×C3—22no—
686C22×C3—44no—
687C22×C3C23×D412yes—
688C22×C3C2×2−1+412yes—
689C22×C3C2×2−1+414yescomplemented
690C22×C3#58512yes—
691C22×C3C2611yescharacteristic
692C2×D3—26no—
693C2×D3—26no—
694C2×D3—224no—
695C2×D3—22no—
696C2×D3—26no—
697C2×D3—22no—
698C2×D3—26no—
699C2×D3—22no—
700C2×D3—26no—
701C2×D3—448no—
702C2×D3—44no—
703C2×D3—412no—
704C2×D3C23×D4112yes—
705C3×C4—26no—
706C3×C4—26no—
707C3×C4—22no—
708C3×C4—26no—
709C3×C4C23×D4112yes—
710Dic3—26no—
711Dic3—22no—
712Dic3—22no—
713Dic3—26no—
714Dic3C23×D414yes—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—312no—
721C23—36no—
722C23—36no—
723C23—32no—
724C23—624no—
725C23—66no—
726C23—66no—
727C23—62no—
728C23—66no—
729C23—62no—
730C23—66no—
731C23—624no—
732C23—62no—
733C23—66no—
734C23—1212no—
735C23—1248no—
736C23#100714yescomplemented
737C23C24×D312yes—
738C23C24×D312yes—
739C23C24×D311yescharacteristic
740Q8—224no—
741Q8—224no—
742Q8—624no—
743Q8—624no—
744Q8C2×D3×D4116yes—
745D4—28no—
746D4—348no—
747D4—648no—
748D4—624no—
749D4—68no—
750D4—624no—
751D4—68no—
752D4—624no—
753D4—1212no—
754D4—1212no—
755C2×C4—26no—
756C2×C4—26no—
757C2×C4—22no—
758C2×C4—26no—
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—32no—
768C2×C4—624no—
769C2×C4—624no—
770C2×C4—648no—
771C2×C4—68no—
772C2×C4—62no—
773C2×C4—66no—
774C2×C4—62no—
775C2×C4—66no—
776C2×C4—624no—
777C2×C4—624no—
778C2×C4—1224no—
779C2×C4C2×D3×D4112yes—
780C2×C4C24×D312yes—
781C2×C4C24×D316yes—
782C2×C4C24×D316yes—
783C2×C4C24×D316yes—
784C2×C4C24×D316yes—
785C2×C3—24no—
786C2×C3—42no—
787C2×C3#348914yescomplemented
788C2×C3C24×D411yescharacteristic
789C2×C3C22×2−1+411yescharacteristic
790C2×C3C2×#58511yescharacteristic
791D3—212no—
792D3—42no—
793D3—46no—
794C22—22no—
795C22—22no—
796C22—28no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—312no—
801C22—44no—
802C22—66no—
803C22—66no—
804C22—624no—
805C22—62no—
806C22—66no—
807C22—62no—
808C22—66no—
809C22—62no—
810C22—66no—
811C22—1248no—
812C22—1212no—
813C22—124no—
814C22C22×D3×D412yes—
815C22C2×#100712yes—
816C22C2×#100714yescomplemented
817C22#596812yes—
818C22C25×D311yescharacteristic
819C4—26no—
820C4—26no—
821C4—22no—
822C4—26no—
823C4—34no—
824C4—62no—
825C4—66no—
826C4—62no—
827C4—66no—
828C4C22×D3×D4112yes—
829C3C2×#348911yescharacteristic, complemented, Sylow
830C2—24no—
831C2—42no—
832C2—612no—
833C2—126no—
834C2—122no—
835C2#8674514yesdirect product factor
836C2C23×D3×D411yescharacteristic
837C2C22×#100711yescharacteristic
838C2C2×#596811yescharacteristic
subgroupG/H
centerC23C24×D3
commutator, cosocleC22×C3C26
FrattiniC22C25×D3
FittingC2×C3×D4×Q8C2
socleC23×C3C25
hypercenterC2×D4×Q8D3
hypocenterC3C2×#3489
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#1007C2semidirect
2. C23×#239C2semidirect
3. C2×C3×D4×Q8C2semidirect
4. C2×#5817C2semidirect
5. C2×Q8×#67C2semidirect
6. #86745C2direct (N × H)
7. C2×#5726C2semidirect
8. C2×#5724C2semidirect
9. C2×#5631C2semidirect
10. C2×#5630C2semidirect
11. C2×#5629C2semidirect
12. C2×D3×C22⋊Q8C2semidirect
13. C2×#5576C2semidirect
14. C2×#5574C2semidirect
15. C2×#5550C2semidirect
16. C2×#5547C2semidirect
19. C23×C3×Q8C22semidirect
21. C2×#1007C22semidirect
27. C22×#239C22semidirect
28. C22×#239C22semidirect
29. C22×D3×Q8C22semidirect
30. C22×D3×Q8C22semidirect
31. C22×#235C22semidirect
32. C22×#235C22semidirect
35. C3×D4×Q8C22semidirect
36. C2×C3×C4⋊Q8C22semidirect
38. C2×C3×C22⋊Q8C22semidirect
39. C2×C3×C4×Q8C22semidirect
41. #5817C22semidirect
42. Q8×#67C22semidirect
43. C2×#947C22semidirect
44. C2×#946C22semidirect
45. C2×#946C22semidirect
46. C2×Q8×Dic3C22semidirect
47. C2×#944C22semidirect
50. C2×#930C22semidirect
52. C2×C4×#67C22semidirect
54. #5726C22semidirect
55. #5724C22semidirect
56. #5631C22semidirect
57. #5630C22semidirect
58. #5629C22semidirect
59. D3×C22⋊Q8C22semidirect
60. #5576C22semidirect
61. #5574C22semidirect
62. #5550C22semidirect
63. #5547C22semidirect
64. C2×#897C22semidirect
65. C2×#896C22semidirect
66. C2×#896C22semidirect
67. C2×#895C22semidirect
68. C2×#895C22semidirect
69. C2×#894C22semidirect
70. C2×#894C22semidirect
71. C2×#894C22semidirect
72. C2×#893C22semidirect
73. C2×D3×C4⋊C4C22semidirect
74. C2×D3×C4⋊C4C22semidirect
75. C2×#884C22semidirect
76. C2×#884C22semidirect
77. C2×#883C22semidirect
81. C2×#875C22semidirect
82. C2×C4×D12C22semidirect
83. C2×C4×D12C22semidirect
84. C2×#872C22semidirect
89. C2×D4×Q8D3semidirect
108. C22×C3×Q8C23semidirect
123. C2×#239D4semidirect
128. C2×#239C23semidirect
131. C2×D3×Q8C23semidirect
132. C2×D3×Q8C23semidirect
135. C2×#235C23semidirect
136. C2×#235C23semidirect
155. C3×C4⋊Q8C23semidirect
157. C3×C22⋊Q8C23semidirect
158. C3×C4×Q8C23semidirect
168. #947C23semidirect
169. #946C23semidirect
170. #946C23semidirect
171. Q8×Dic3C23semidirect
172. #944C23semidirect
175. #930C23semidirect
177. C4×#67C23semidirect
195. #897C23semidirect
196. #896C23semidirect
197. #896C23semidirect
198. #895C23semidirect
199. #895C23semidirect
200. #894C23semidirect
201. #894C23semidirect
202. #894C23semidirect
203. #893C23semidirect
204. D3×C4⋊C4C23semidirect
205. D3×C4⋊C4C23semidirect
206. #884C23semidirect
207. #884C23semidirect
208. #883C23semidirect
212. #875C23semidirect
213. C4×D12C23semidirect
214. C4×D12C23semidirect
215. #872C23semidirect
230. C23×Q8C2×D3semidirect
234. D4×Q8C2×D3semidirect
244. C2×C4⋊Q8C2×D3semidirect
261. C2×C22⋊Q8C2×D3semidirect
272. C2×C4×Q8C2×D3semidirect
330. #239C2×D4semidirect
418. C22×Q8C22×D3semidirect
444. C4⋊Q8C22×D3semidirect
459. C22⋊Q8C22×D3semidirect
469. C4×Q8C22×D3semidirect
509. C23×C32−1+4semidirect
689. C22×C3C2×2−1+4semidirect
736. C23#1007semidirect
787. C2×C3#3489semidirect
816. C22C2×#1007semidirect
829. C3C2×#3489semidirect
835. C2#86745direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#10072
C23×#2392
C2×C3×D4×Q82
C2×#58172
C2×Q8×#672
#867452
C2×#57262
C2×#57242
C2×#56312
C2×#56302
C2×#56292
C2×D3×C22⋊Q82
C2×#55762
C2×#55742
C2×#55502
C2×#55472
C2×#34893