Finite Group Databasebeta

← C2×#86722 #11703395

Subgroups — C2×#86722 #11703395

Order 768.

7758 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#548C211yesmaximal, characteristic, complemented
2C2×#5834C211yesmaximal, characteristic, complemented
3C2×#5827C211yesmaximal, characteristic, complemented
4C2×#5817C211yesmaximal, characteristic, complemented
5C22×Q8×Dic3C211yesmaximal, characteristic, complemented
6#86722C2132yesmaximal, direct product factor
7C2×#5682C213yesmaximal, complemented
8C2×#5681C213yesmaximal, complemented
9C2×#5635C213yesmaximal, complemented
10C2×#5643C213yesmaximal, complemented
11C2×#5611C213yesmaximal, complemented
12C2×#5596C213yesmaximal, complemented
13C2×Q8×Dic6C211yesmaximal, characteristic, complemented
14C2×#5574C211yesmaximal, characteristic, complemented
15C2×#5555C213yesmaximal, complemented
16C2×#5538C213yesmaximal, complemented
17C2×#3522—31nomaximal, Sylow
18C22×C3×#41C2211yescharacteristic
19C23×C3×Q8C2211yescharacteristic
20C22×#239C2211yescharacteristic
21C22×#237C2216yes—
22C3×#548C22116yescomplemented
23C2×C3×#124C2213yes—
24C2×C3×C22⋊Q8C2213yes—
25C2×C3×#121C2213yes—
26C2×C3×C4×Q8C2211yescharacteristic
27C2×C3×C4×D4C2213yes—
28#5834C22116yescomplemented
29#5827C22116yescomplemented
30#5817C22116yescomplemented
31C2×#947C2213yes—
32C2×#946C2213yes—
33C2×Q8×Dic3C2211yescharacteristic
34C2×Q8×Dic3C2211yescharacteristic
35C2×Q8×Dic3C2211yescharacteristic
36C2×Q8×Dic3C2213yes—
37C2×Q8×Dic3C2213yes—
38C2×Q8×Dic3C22116yescomplemented
39C2×#940C2213yes—
40C2×#939C2213yes—
41C2×#938C2213yes—
42C2×#935C2213yes—
43C2×D4×Dic3C2213yes—
44C2×D4×Dic3C2213yes—
45C2×#930C2213yes—
46C2×#930C2213yes—
47C2×C4×#67C2213yes—
48C2×C4×#67C2213yes—
49C2×#926C2213yes—
50C22×C4⋊Dic3C2213yes—
51C22×C4⋊Dic3C2213yes—
52C22×C4×Dic3C2213yes—
53#5682C22148yescomplemented
54#5681C22148yescomplemented
55#5643C22148yescomplemented
56#5635C22148yescomplemented
57#5611C22148yescomplemented
58#5596C22148yescomplemented
59#5574C22116yescomplemented
60Q8×Dic6C22116yescomplemented
61#5555C22148yescomplemented
62#5538C22148yescomplemented
63C2×#898C2213yes—
64C2×#897C2216yes—
65C2×#893C2213yes—
66C2×D3×C4⋊C4C2213yes—
67C2×#889C2213yes—
68C2×#888C2213yes—
69C2×#888C2213yes—
70C2×#886C2216yes—
71C2×#886C2213yes—
72C2×#885C2213yes—
73C2×#885C2216yes—
74C2×#883C2216yes—
75C2×#67⋊C4C2216yes—
76C2×#879C2213yes—
77C2×#878C2216yes—
78C2×#878C2211yescharacteristic
79C2×C4×D12C2213yes—
80C2×#872C2213yes—
81C2×#869C2213yes—
82C2×C4×Dic6C2213yes—
83#3522—332no—
84C2×#559—33no—
85C2×Q82—31no—
86C2×#554—33no—
87C2×#550—31no—
88C2×#548—31no—
89C2×#548D311yescharacteristic, complemented
90C2×#547—33no—
91C2×#547—33no—
92C2×#542—33no—
93C2×#542—33no—
94C2×#532—33no—
95C2×#529—33no—
96C2×#520—31no—
97C2×#520—31no—
98C22×C4×Q8—31no—
99C2×C3×#41—28no—
100C2×C3×#41C2318yes—
101C22×C3×Q8—28no—
102C22×C3×Q8C2313yes—
103C22×C3×Q8C2318yes—
104C22×C3×Q8C2311yescharacteristic
105C22×C3×D4C2313yes—
106C22×C3×D4C2313yes—
107C23×C3×C4C2313yes—
108C23×C3×C4C2313yes—
109C22×#67C2313yes—
110C22×#67C2313yes—
111C22×#67C2316yes—
112C23×Dic3C2313yes—
113C23×Dic3C2311yescharacteristic
114C23×Dic3C2316yes—
115C2×#239—28no—
116C2×#239C2318yes—
117C2×#237—424no—
118C2×#237C23148yes—
119C22×D12C2313yes—
120C22×C4×D3C2313yes—
121C22×C4×D3C2316yes—
122C22×Dic6C2311yescharacteristic
123C22×Dic6C2316yes—
124C3×#124C23124yes—
125C3×C22⋊Q8C23124yes—
126C3×#121C23124yes—
127C3×C4×Q8C2318yes—
128C3×C4×D4C23124yes—
129C2×C3×C4⋊C4C2313yes—
130C2×C3×C4⋊C4C2313yes—
131C2×C3×C22⋊C4C2316yes—
132C2×C3×C22⋊C4C2311yescharacteristic
133C2×C3×C22⋊C4C2313yes—
134C2×C3×C42C2313yes—
135C2×#217C2313yes—
136C2×#217C2311yescharacteristic
137C2×#217C2313yes—
138C2×#217C2313yes—
139#947C23124yes—
140#946C23124yes—
141Q8×Dic3C23124yes—
142Q8×Dic3C23124yes—
143Q8×Dic3C2318yes—
144Q8×Dic3C2318yes—
145Q8×Dic3C2318yes—
146#940C23124yes—
147#939C23124yes—
148#938C23124yes—
149#935C23124yes—
150D4×Dic3C23124yes—
151D4×Dic3C23124yes—
152#930C23124yes—
153#930C23124yes—
154C4×#67C23124yes—
155C4×#67C23124yes—
156C2×(C2×D3)⋊C4C2313yes—
157C2×(C2×D3)⋊C4C2313yes—
158C2×(C2×D3)⋊C4C2316yes—
159C2×(C2×D3)⋊C4C2313yes—
160C2×(C2×D3)⋊C4C2313yes—
161#926C23124yes—
162C2×C4⋊Dic3C23124yes—
163C2×C4⋊Dic3C2313yes—
164C2×C4⋊Dic3C2313yes—
165C2×C4⋊Dic3C2313yes—
166C2×C4⋊Dic3C2313yes—
167C2×C4⋊Dic3C2316yes—
168C2×C4⋊Dic3C2311yescharacteristic
169C2×C4⋊Dic3C2313yes—
170C2×C4⋊Dic3C23124yes—
171C2×Dic3⋊C4C2313yes—
172C2×Dic3⋊C4C2313yes—
173C2×Dic3⋊C4C2311yescharacteristic
174C2×Dic3⋊C4C2313yes—
175C2×Dic3⋊C4C2313yes—
176C2×Dic3⋊C4C2311yescharacteristic
177C2×C4×Dic3C2313yes—
178C2×C4×Dic3C2313yes—
179C2×C4×Dic3C2313yes—
180C2×C4×Dic3C2313yes—
181C2×C4×Dic3C2313yes—
182C2×C4×Dic3C23124yes—
183#898C23124yes—
184#897C23148yes—
185#893C23124yes—
186D3×C4⋊C4C23124yes—
187#889C23124yes—
188#888C23124yes—
189#888C23124yes—
190#886C23148yes—
191#886C23124yes—
192#885C23148yes—
193#885C23124yes—
194#883C23148yes—
195#67⋊C4C23148yes—
196#879C23124yes—
197#878C23148yes—
198#878C2318yes—
199C4×D12C23124yes—
200#872C23124yes—
201#869C23124yes—
202C4×Dic6C23124yes—
203C22×#41—31no—
204C22×#41—36no—
205C22×#41C2×D311yescharacteristic
206C23×Q8C2×D311yescharacteristic
207#559—348no—
208Q82—316no—
209#554—348no—
210#550—316no—
211#548—316no—
212#548C2×D3116yescomplemented
213#547—348no—
214#547—348no—
215#542—348no—
216#542—348no—
217#532—348no—
218C2×C4⋊Q8—33no—
219C2×C4⋊Q8—33no—
220C2×C4⋊Q8—33no—
221C2×#127—33no—
222#529—348no—
223C2×#126—33no—
224C2×#126—33no—
225C2×#125—33no—
226C2×#124—33no—
227C2×#124—33no—
228C2×#124—36no—
229C2×#124C2×D313yes—
230C2×#123—33no—
231C2×#123—33no—
232C2×#123—36no—
233C2×#123—36no—
234C2×C22⋊Q8—33no—
235C2×C22⋊Q8—36no—
236C2×C22⋊Q8—31no—
237C2×C22⋊Q8—36no—
238C2×C22⋊Q8C2×D313yes—
239C2×#121—33no—
240C2×#121—33no—
241C2×#121—33no—
242C2×#121—33no—
243C2×#121C2×D313yes—
244#520—316no—
245#520—316no—
246C2×C4×Q8—31no—
247C2×C4×Q8—33no—
248C2×C4×Q8—31no—
249C2×C4×Q8—33no—
250C2×C4×Q8—316no—
251C2×C4×Q8—31no—
252C2×C4×Q8—33no—
253C2×C4×Q8C2×D311yescharacteristic
254C2×C4×D4—33no—
255C2×C4×D4—33no—
256C2×C4×D4—33no—
257C2×C4×D4—33no—
258C2×C4×D4—33no—
259C2×C4×D4—36no—
260C2×C4×D4—33no—
261C2×C4×D4C2×D313yes—
262C2×#117—33no—
263C2×#117—33no—
264C22×C4⋊C4—33no—
265C22×C4⋊C4—33no—
266C22×C4⋊C4—33no—
267C22×C42—33no—
268C24×C3C2413yes—
269C24×C3C2411yescharacteristic
270C23×D3C2413yes—
271C3×#41—232no—
272C2×C3×Q8—232no—
273C2×C3×Q8—212no—
274C2×C3×Q8#4118yescomplemented
275C2×C3×Q8C24112yes—
276C2×C3×Q8C2414yes—
277C2×C3×D4—212no—
278C2×C3×D4—212no—
279C2×C3×D4C24112yes—
280C2×C3×D4C24112yes—
281C22×C3×C4—212no—
282C22×C3×C4—212no—
283C22×C3×C4C2413yes—
284C22×C3×C4C24112yes—
285C22×C3×C4C2413yes—
286C22×C3×C4C2411yescharacteristic
287C22×C3×C4C2411yescharacteristic
288C22×C3×C4C24112yes—
289C22×C3×C4C2413yes—
290C2×#67—212no—
291C2×#67—212no—
292C2×#67—412no—
293C2×#67C24112yes—
294C2×#67C24112yes—
295C2×#67C24124yes—
296C22×Dic3—212no—
297C22×Dic3—24no—
298C22×Dic3—412no—
299C22×Dic3C2414yes—
300C22×Dic3C24112yes—
301C22×Dic3C2411yescharacteristic
302C22×Dic3C2411yescharacteristic
303C22×Dic3C2413yes—
304C22×Dic3C2413yes—
305C22×Dic3C2413yes—
306C22×Dic3C2411yescharacteristic
307C22×Dic3C24124yes—
308C22×Dic3C2411yescharacteristic
309#239—232no—
310#237—496no—
311C2×D12—212no—
312C2×D12C24112yes—
313C2×C4×D3—212no—
314C2×C4×D3—412no—
315C2×C4×D3C24112yes—
316C2×C4×D3C24124yes—
317C2×Dic6—24no—
318C2×Dic6—412no—
319C2×Dic6C2414yes—
320C2×Dic6C24124yes—
321C3×C4⋊C4C24112yes—
322C3×C4⋊C4C24112yes—
323C3×C22⋊C4C24124yes—
324C3×C22⋊C4C2414yes—
325C3×C22⋊C4C24112yes—
326C3×C42C24112yes—
327#217C24112yes—
328#217C2414yes—
329#217C24112yes—
330#217C24112yes—
331(C2×D3)⋊C4C24112yes—
332(C2×D3)⋊C4C24112yes—
333(C2×D3)⋊C4C24124yes—
334(C2×D3)⋊C4C24112yes—
335(C2×D3)⋊C4C24112yes—
336C4⋊Dic3C24112yes—
337C4⋊Dic3C24112yes—
338C4⋊Dic3C24112yes—
339C4⋊Dic3C24112yes—
340C4⋊Dic3C24124yes—
341C4⋊Dic3C2414yes—
342C4⋊Dic3C24112yes—
343Dic3⋊C4C24112yes—
344Dic3⋊C4C24112yes—
345Dic3⋊C4C2414yes—
346Dic3⋊C4C24112yes—
347Dic3⋊C4C24112yes—
348Dic3⋊C4C2414yes—
349C4×Dic3C24112yes—
350C4×Dic3C24112yes—
351C4×Dic3C24112yes—
352C4×Dic3C24112yes—
353C4×Dic3C24112yes—
354C2×#41—28no—
355C2×#41—38no—
356C2×#41—348no—
357C2×#41—68no—
358C2×#41—1224no—
359C2×#41C22×D318yes—
360C22×Q8—28no—
361C22×Q8—31no—
362C22×Q8—36no—
363C22×Q8C22×D313yes—
364C22×Q8C22×D318yes—
365C22×Q8C22×D311yescharacteristic
366C22×D4—33no—
367C22×D4—33no—
368C22×D4—36no—
369C22×D4—33no—
370C22×D4C22×D313yes—
371C22×D4C22×D313yes—
372C23×C4—33no—
373C23×C4—31no—
374C23×C4—36no—
375C23×C4—33no—
376C23×C4—36no—
377C23×C4C22×D313yes—
378C23×C4C22×D313yes—
379C4⋊Q8—324no—
380C4⋊Q8—324no—
381C4⋊Q8—324no—
382#127—324no—
383#126—324no—
384#126—324no—
385#125—324no—
386#124—324no—
387#124—324no—
388#124—348no—
389#124C22×D3124yes—
390#123—324no—
391#123—324no—
392#123—348no—
393#123—348no—
394C22⋊Q8—324no—
395C22⋊Q8—348no—
396C22⋊Q8—38no—
397C22⋊Q8—348no—
398C22⋊Q8C22×D3124yes—
399#121—324no—
400#121—324no—
401#121—324no—
402#121—324no—
403#121C22×D3124yes—
404C4×Q8—38no—
405C4×Q8—324no—
406C4×Q8—38no—
407C4×Q8—324no—
408C4×Q8—38no—
409C4×Q8—324no—
410C4×Q8C22×D318yes—
411C4×D4—324no—
412C4×D4—324no—
413C4×D4—324no—
414C4×D4—324no—
415C4×D4—324no—
416C4×D4—348no—
417C4×D4—324no—
418C4×D4C22×D3124yes—
419#117—324no—
420#117—324no—
421C2×C4⋊C4—33no—
422C2×C4⋊C4—33no—
423C2×C4⋊C4—33no—
424C2×C4⋊C4—33no—
425C2×C4⋊C4—33no—
426C2×C4⋊C4—36no—
427C2×C4⋊C4—324no—
428C2×C4⋊C4—324no—
429C2×C4⋊C4—31no—
430C2×C4⋊C4—31no—
431C2×C4⋊C4—31no—
432C2×C4⋊C4—33no—
433C2×C4⋊C4—33no—
434C2×C4⋊C4—33no—
435C2×C4⋊C4—33no—
436C2×C4⋊C4—324no—
437C2×C4⋊C4C22×D313yes—
438C2×C4⋊C4C22×D313yes—
439C2×C22⋊C4—33no—
440C2×C22⋊C4—33no—
441C2×C22⋊C4—31no—
442C2×C22⋊C4—33no—
443C2×C22⋊C4—33no—
444C2×C22⋊C4—33no—
445C2×C22⋊C4—33no—
446C2×C22⋊C4—36no—
447C2×C22⋊C4—33no—
448C2×C22⋊C4C22×D316yes—
449C2×C22⋊C4C22×D311yescharacteristic
450C2×C22⋊C4C22×D313yes—
451C2×C42—33no—
452C2×C42—33no—
453C2×C42—33no—
454C2×C42—33no—
455C2×C42—33no—
456C2×C42—324no—
457C2×C42C22×D313yes—
458C23×C3—22no—
459C23×C3—22no—
460C23×C3—26no—
461C23×C3—26no—
462C23×C3—26no—
463C23×C3H(5,𝔽2)14yes—
464C23×C3C2516yes—
465C23×C3C2512yes—
466C23×C3C2511yescharacteristic
467C22×D3—26no—
468C22×D3—26no—
469C22×D3—26no—
470C22×D3C2516yes—
471C3×Q8—224no—
472C3×Q8C2×#41116yescomplemented
473C3×D4—224no—
474C3×D4—224no—
475C2×C3×C4—22no—
476C2×C3×C4—26no—
477C2×C3×C4—26no—
478C2×C3×C4—22no—
479C2×C3×C4—224no—
480C2×C3×C4—224no—
481C2×C3×C4C2×#41112yes—
482C2×C3×C4C2516yes—
483C2×C3×C4C2516yes—
484C2×C3×C4C2512yes—
485C2×C3×C4C2512yes—
486C2×C3×C4C2516yes—
487#67—224no—
488#67—224no—
489#67—424no—
490C2×Dic3—22no—
491C2×Dic3—26no—
492C2×Dic3—26no—
493C2×Dic3—26no—
494C2×Dic3—224no—
495C2×Dic3—22no—
496C2×Dic3—22no—
497C2×Dic3—28no—
498C2×Dic3—424no—
499C2×Dic32−1+414yes—
500C2×Dic3C2512yes—
501C2×Dic3C2512yes—
502C2×Dic3C2516yes—
503C2×Dic3C2516yes—
504C2×Dic3C2516yes—
505C2×Dic3C2512yes—
506C2×Dic3C2512yes—
507D12—224no—
508C4×D3—224no—
509C4×D3—424no—
510Dic6—28no—
511Dic6—424no—
512C24—33no—
513C24C23×D313yes—
514C24C23×D311yescharacteristic
515#41—232no—
516#41—632no—
517#41—1296no—
518C2×Q8—232no—
519C2×Q8—212no—
520C2×Q8—34no—
521C2×Q8—324no—
522C2×Q8—64no—
523C2×Q8—1212no—
524C2×Q8#23718yescomplemented
525C2×Q8C23×D3112yes—
526C2×Q8C23×D314yes—
527C2×D4—212no—
528C2×D4—212no—
529C2×D4—312no—
530C2×D4—312no—
531C2×D4—324no—
532C2×D4—312no—
533C2×D4—612no—
534C2×D4—612no—
535C2×D4—612no—
536C2×D4—1212no—
537C2×D4C23×D3112yes—
538C2×D4C23×D3112yes—
539C22×C4—212no—
540C22×C4—212no—
541C22×C4—31no—
542C22×C4—34no—
543C22×C4—312no—
544C22×C4—31no—
545C22×C4—31no—
546C22×C4—33no—
547C22×C4—33no—
548C22×C4—33no—
549C22×C4—31no—
550C22×C4—324no—
551C22×C4—312no—
552C22×C4—324no—
553C22×C4—64no—
554C22×C4—612no—
555C22×C4—612no—
556C22×C4—1212no—
557C22×C4—1212no—
558C22×C4C23×D3112yes—
559C22×C4C23×D3112yes—
560C22×C4C23×D313yes—
561C22×C4C23×D311yescharacteristic
562C22×C4C23×D313yes—
563C22×C4C23×D311yescharacteristic
564C22×C4C23×D313yes—
565C4⋊C4—312no—
566C4⋊C4—312no—
567C4⋊C4—312no—
568C4⋊C4—312no—
569C4⋊C4—312no—
570C4⋊C4—324no—
571C4⋊C4—34no—
572C4⋊C4—34no—
573C4⋊C4—34no—
574C4⋊C4—312no—
575C4⋊C4—312no—
576C4⋊C4—312no—
577C4⋊C4—312no—
578C4⋊C4C23×D3112yes—
579C4⋊C4C23×D3112yes—
580C22⋊C4—312no—
581C22⋊C4—312no—
582C22⋊C4—34no—
583C22⋊C4—312no—
584C22⋊C4—312no—
585C22⋊C4—312no—
586C22⋊C4—312no—
587C22⋊C4—324no—
588C22⋊C4—312no—
589C22⋊C4C23×D3124yes—
590C22⋊C4C23×D314yes—
591C22⋊C4C23×D3112yes—
592C42—312no—
593C42—312no—
594C42—312no—
595C42—312no—
596C42—312no—
597C42C23×D3112yes—
598C22×C3—22no—
599C22×C3—22no—
600C22×C3—28no—
601C22×C3—26no—
602C22×C3—26no—
603C22×C3—26no—
604C22×C3—412no—
605C22×C3C22×#4112yes—
606C22×C3C2×H(5,𝔽2)14yes—
607C22×C3C2×H(5,𝔽2)12yes—
608C22×C3C2×2−1+412yes—
609C22×C3C2611yescharacteristic
610C2×D3—26no—
611C2×D3—26no—
612C2×D3—26no—
613C2×D3—412no—
614C3×C4—22no—
615C3×C4—26no—
616C3×C4—26no—
617C3×C4—22no—
618C3×C4C22×#41112yes—
619Dic3—22no—
620Dic3—26no—
621Dic3—26no—
622Dic3—26no—
623Dic3—22no—
624Dic3—22no—
625Dic3C2×2−1+414yes—
626C23—22no—
627C23—22no—
628C23—26no—
629C23—26no—
630C23—26no—
631C23—36no—
632C23—66no—
633C23—66no—
634C23—66no—
635C23#100914yes—
636C23C24×D316yes—
637C23C24×D312yes—
638C23C24×D311yescharacteristic
639Q8—224no—
640Q8—68no—
641Q8—1224no—
642Q8C2×#237116yescomplemented
643D4—224no—
644D4—224no—
645D4—624no—
646D4—624no—
647D4—624no—
648D4—1224no—
649C2×C4—22no—
650C2×C4—26no—
651C2×C4—26no—
652C2×C4—22no—
653C2×C4—224no—
654C2×C4—224no—
655C2×C4—34no—
656C2×C4—32no—
657C2×C4—32no—
658C2×C4—32no—
659C2×C4—36no—
660C2×C4—36no—
661C2×C4—36no—
662C2×C4—32no—
663C2×C4—68no—
664C2×C4—62no—
665C2×C4—66no—
666C2×C4—66no—
667C2×C4—624no—
668C2×C4—66no—
669C2×C4—62no—
670C2×C4—62no—
671C2×C4—624no—
672C2×C4—1224no—
673C2×C4—1224no—
674C2×C4C2×#237112yes—
675C2×C4C24×D316yes—
676C2×C4C24×D312yes—
677C2×C4C24×D316yes—
678C2×C4C24×D312yes—
679C2×C4C24×D316yes—
680C2×C3—24no—
681C2×C3—46no—
682C2×C3#352214yescomplemented
683C2×C3C23×#4111yescharacteristic
684C2×C3C22×H(5,𝔽2)11yescharacteristic
685C2×C3C22×2−1+411yescharacteristic
686D3—46no—
687C22—22no—
688C22—22no—
689C22—28no—
690C22—26no—
691C22—26no—
692C22—26no—
693C22—412no—
694C22—66no—
695C22—66no—
696C22—66no—
697C22—1212no—
698C22C22×#23712yes—
699C22C2×#100914yes—
700C22C2×#100912yes—
701C22D3×2−1+412yes—
702C22C25×D311yescharacteristic
703C4—22no—
704C4—26no—
705C4—26no—
706C4—22no—
707C4—34no—
708C4—62no—
709C4—66no—
710C4—66no—
711C4—66no—
712C4—62no—
713C4—62no—
714C4C22×#237112yes—
715C3C2×#352211yescharacteristic, complemented, Sylow
716C2—24no—
717C2—46no—
718C2—126no—
719C2#8672214yesdirect product factor
720C2C23×#23711yescharacteristic
721C2C22×#100911yescharacteristic
722C2C2×D3×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D3
commutator, cosocleC22×C3C26
FrattiniC22C25×D3
FittingC2×C3×#548C2
socleC23×C3C25
hypercenterC2×#548D3
hypocenterC3C2×#3522
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×C3×#548C2semidirect
2. C2×#5834C2semidirect
3. C2×#5827C2semidirect
4. C2×#5817C2semidirect
5. C22×Q8×Dic3C2semidirect
6. #86722C2direct (N × H)
7. C2×#5682C2semidirect
8. C2×#5681C2semidirect
9. C2×#5635C2semidirect
10. C2×#5643C2semidirect
11. C2×#5611C2semidirect
12. C2×#5596C2semidirect
13. C2×Q8×Dic6C2semidirect
14. C2×#5574C2semidirect
15. C2×#5555C2semidirect
16. C2×#5538C2semidirect
22. C3×#548C22semidirect
28. #5834C22semidirect
29. #5827C22semidirect
30. #5817C22semidirect
38. C2×Q8×Dic3C22semidirect
53. #5682C22semidirect
54. #5681C22semidirect
55. #5643C22semidirect
56. #5635C22semidirect
57. #5611C22semidirect
58. #5596C22semidirect
59. #5574C22semidirect
60. Q8×Dic6C22semidirect
61. #5555C22semidirect
62. #5538C22semidirect
89. C2×#548D3semidirect
212. #548C2×D3semidirect
274. C2×C3×Q8#41semidirect
472. C3×Q8C2×#41semidirect
524. C2×Q8#237semidirect
642. Q8C2×#237semidirect
682. C2×C3#3522semidirect
715. C3C2×#3522semidirect
719. C2#86722direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5482
C2×#58342
C2×#58272
C2×#58172
C22×Q8×Dic32
#867222
C2×#56822
C2×#56812
C2×#56352
C2×#56432
C2×#56112
C2×#55962
C2×Q8×Dic62
C2×#55742
C2×#55552
C2×#55382
C2×#35223