Finite Group Databasebeta

← #10955167

Subgroups — #10955167

Order 768.

2564 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5585C211yesmaximal, characteristic
2C3×#2355C211yesmaximal, characteristic, complemented
3C4×Q8×Dic3C211yesmaximal, characteristic, complemented
4#76493C212yesmaximal, complemented
5#76480C212yesmaximal, complemented
6#74975C214yesmaximal, complemented
7#74940C214yesmaximal, complemented
8#74325C211yesmaximal, characteristic, complemented
9#74319C211yesmaximal, characteristic
10#74160C212yesmaximal, complemented
11#74149C212yesmaximal, complemented
12#73654C212yesmaximal, complemented
13#73653C211yesmaximal, characteristic
14#73646C212yesmaximal, complemented
15C4×#887C211yesmaximal, characteristic, complemented
16C4×#893C212yesmaximal, complemented
17C4×#893C212yesmaximal, complemented
18C4×#559—31nomaximal, Sylow
19C2×C3×C4×Q8C2211yescharacteristic
20C2×#947C2212yes—
21C2×Q8×Dic3C2211yescharacteristic
22C2×Q8×Dic3C2211yescharacteristic
23#5585C4116yescomplemented
24C2×#894C2214yes—
25C2×#893C2212yes—
26C2×#893C2212yes—
27C2×#893C2212yes—
28C2×#893C2212yes—
29C2×#893C2212yes—
30C2×#887C2211yescharacteristic
31C2×#887C2211yescharacteristic
32C2×#875C2212yes—
33C2×#874C2211yescharacteristic
34C2×C4×D12C2212yes—
35C2×C4×D12C2212yes—
36C2×C42×D3C2214yes—
37C2×C4×Dic6C2211yescharacteristic
38C3×#391C2212yes—
39C3×#387C2214yes—
40C3×#384C2211yescharacteristic
41C3×#382C2212yes—
42C3×C4×C4⋊C4C2212yes—
43C3×C4×C4⋊C4C2212yes—
44C3×C4×C4⋊C4C2211yescharacteristic
45#4988C2212yes—
46#4988C2212yes—
47#4988C2212yes—
48#4988C2212yes—
49#4978C2214yes—
50#4977C2212yes—
51Dic3×C4⋊C4C2211yescharacteristic
52Dic3×C4⋊C4C2211yescharacteristic
53Dic3×C4⋊C4C2212yes—
54Dic3×C4⋊C4C2212yes—
55Dic3×C4⋊C4C2212yes—
56Dic3×C4⋊C4C2212yes—
57Dic3×C4⋊C4C2211yescharacteristic
58Dic3×C4⋊C4C2211yescharacteristic
59#4973C2212yes—
60#4940C2214yes—
61#4939C2212yes—
62C4×(C2×D3)⋊C4C2214yes—
63C4×(C2×D3)⋊C4C2214yes—
64C4×C4⋊Dic3C2211yescharacteristic
65C4×C4⋊Dic3C2212yes—
66C4×Dic3⋊C4C2212yes—
67C42×Dic3C2211yescharacteristic
68C42×Dic3C2212yes—
69C42×Dic3C2212yes—
70#4670C2214yes—
71#4670C2214yes—
72#4670C2214yes—
73#4669C2214yes—
74#4669C2214yes—
75#4668C2214yes—
76#4666C2214yes—
77#4666C2214yes—
78#4666C2214yes—
79#4666C2214yes—
80#4666C2214yes—
81#4665C2214yes—
82#4664C2214yes—
83#4649C2212yes—
84#4649C2212yes—
85C2×#559—31no—
86#2374—34no—
87#2367—32no—
88#2367—32no—
89#2366—31no—
90#2357—32no—
91#2357—32no—
92#2355—31no—
93#2355D311yescharacteristic, complemented
94C4×#127—31no—
95C4×#124—32no—
96C4×#124—32no—
97C4×#123—34no—
98C42×Q8—31no—
99C42×Q8—31no—
100C42×D4—32no—
101C42×D4—32no—
102C22×C3×Q8C2311yescharacteristic
103C22×D12C2312yes—
104C22×D12C2312yes—
105C22×D12C2312yes—
106C22×C4×D3C2314yes—
107C22×C4×D3C2314yes—
108C22×C4×D3C2314yes—
109C22×Dic6C2311yescharacteristic
110C3×C4×Q8C2×C418yescomplemented
111C2×C3×C4⋊C4C2312yes—
112C2×C3×C4⋊C4C2312yes—
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C4⋊C4C2312yes—
115C2×C3×C4⋊C4C2311yescharacteristic
116C2×C3×C4⋊C4C2312yes—
117C2×C3×C4⋊C4C2311yescharacteristic
118C2×C3×C42C2312yes—
119C2×C3×C42C2314yes—
120C2×C3×C42C2311yescharacteristic
121C2×C3×C42C2312yes—
122#947C2×C4116yescomplemented
123Q8×Dic3—24no—
124Q8×Dic3—24no—
125C2×(C2×D3)⋊C4C2314yes—
126C2×(C2×D3)⋊C4C2314yes—
127C2×(C2×D3)⋊C4C2314yes—
128C2×(C2×D3)⋊C4C2314yes—
129C2×(C2×D3)⋊C4C2314yes—
130C2×(C2×D3)⋊C4C2314yes—
131C2×(C2×D3)⋊C4C2314yes—
132C2×(C2×D3)⋊C4C2314yes—
133C2×(C2×D3)⋊C4C2314yes—
134C2×C4⋊Dic3C2312yes—
135C2×C4⋊Dic3C2312yes—
136C2×C4⋊Dic3C2311yescharacteristic
137C2×C4⋊Dic3C2311yescharacteristic
138C2×C4⋊Dic3C2311yescharacteristic
139C2×Dic3⋊C4C2312yes—
140C2×Dic3⋊C4C2312yes—
141C2×Dic3⋊C4C2312yes—
142C2×C4×Dic3C2311yescharacteristic
143C2×C4×Dic3C2312yes—
144C2×C4×Dic3C2312yes—
145C2×C4×Dic3C2312yes—
146C2×C4×Dic3C2312yes—
147C2×C4×Dic3C2312yes—
148C2×C4×Dic3C2312yes—
149C2×C4×Dic3C2311yescharacteristic
150C2×C4×Dic3C2312yes—
151C2×C4×Dic3C2311yescharacteristic
152C2×C4×Dic3C2311yescharacteristic
153C2×C4×Dic3C2312yes—
154C2×C4×Dic3C2314yes—
155C2×C4×Dic3C2312yes—
156C2×C4×Dic3C2312yes—
157C2×C4×Dic3C2311yescharacteristic
158C2×C4×Dic3C2311yescharacteristic
159#894C2×C4132yescomplemented
160#893—28no—
161#893—28no—
162#893—28no—
163#893—44no—
164#893C2×C4116yescomplemented
165#887—24no—
166#887—24no—
167#875C2×C4116yescomplemented
168#874C2×C418yes—
169C4×D12—28no—
170C4×D12C2×C4116yescomplemented
171C42×D3—48no—
172C4×Dic6C2×C418yescomplemented
173C3×#95C2312yes—
174C3×#95C2314yes—
175C3×#95C2314yes—
176C3×#95C2314yes—
177C3⋊#95C2312yes—
178C3⋊#95C2312yes—
179C3⋊#95C2312yes—
180C3⋊#95C2314yes—
181C3⋊#95C2312yes—
182C3⋊#95C2312yes—
183C3⋊#95C2314yes—
184C3⋊#95C2314yes—
185#559—316no—
186C2×#127—31no—
187C2×#124—32no—
188C2×#124—32no—
189C2×#123—34no—
190C2×C4×Q8—31no—
191C2×C4×Q8—31no—
192C2×C4×Q8—31no—
193C2×C4×Q8—31no—
194C2×C4×Q8—31no—
195C2×C4×Q8C2×D311yescharacteristic
196C2×C4×D4—32no—
197C2×C4×D4—32no—
198C2×C4×D4—32no—
199C2×C4×D4—32no—
200C2×C4×D4—32no—
201C2×C4×D4—32no—
202C2×C4×D4—32no—
203C22×C42—34no—
204#391—32no—
205#391C2×D312yes—
206#390—32no—
207#390—32no—
208#390—32no—
209#390—32no—
210#390—32no—
211#388—34no—
212#388—34no—
213#388—34no—
214#388—34no—
215#388—34no—
216#388—34no—
217#387—34no—
218#387C2×D314yes—
219#386—34no—
220#385—34no—
221#384C2×D311yescharacteristic
222#382—32no—
223#382C2×D312yes—
224#381—34no—
225C4×C4⋊C4—32no—
226C4×C4⋊C4—32no—
227C4×C4⋊C4—31no—
228C4×C4⋊C4—31no—
229C4×C4⋊C4—32no—
230C4×C4⋊C4—31no—
231C4×C4⋊C4—31no—
232C4×C4⋊C4—32no—
233C4×C4⋊C4—31no—
234C4×C4⋊C4—32no—
235C4×C4⋊C4—32no—
236C4×C4⋊C4—32no—
237C4×C4⋊C4—32no—
238C4×C4⋊C4C2×D312yes—
239C4×C4⋊C4C2×D311yescharacteristic
240C4×C4⋊C4C2×D312yes—
241C4×C22⋊C4—34no—
242C4×C22⋊C4—34no—
243C4×C22⋊C4—34no—
244C4×C22⋊C4—34no—
245C4×C22⋊C4—34no—
246C4×C22⋊C4—34no—
247C4×C22⋊C4—34no—
248C43—31no—
249C43—32no—
250C43—32no—
251C23×D3C2414yes—
252C2×C3×Q8—22no—
253C2×C3×Q8—22no—
254C2×C3×Q8C22×C414yes—
255C22×C3×C4C2414yes—
256C22×C3×C4C2412yes—
257C22×C3×C4C2411yescharacteristic
258C22×C3×C4C2412yes—
259C22×C3×C4C2412yes—
260C22×C3×C4C2412yes—
261C22×C3×C4C2411yescharacteristic
262C22×C3×C4C2411yescharacteristic
263C22×Dic3C2412yes—
264C22×Dic3C2411yescharacteristic
265C22×Dic3C2412yes—
266C22×Dic3C2412yes—
267C22×Dic3C2412yes—
268C22×Dic3C2411yescharacteristic
269C22×Dic3C2411yescharacteristic
270C22×Dic3C2411yescharacteristic
271C2×D12—24no—
272C2×D12—24no—
273C2×D12—24no—
274C2×D12—24no—
275C2×D12—42no—
276C2×D12—42no—
277C2×D12C22×C418yes—
278C2×D12C22×C418yes—
279C2×D12C22×C418yes—
280C2×C4×D3—28no—
281C2×C4×D3—28no—
282C2×C4×D3—28no—
283C2×C4×D3—28no—
284C2×C4×D3—28no—
285C2×C4×D3—44no—
286C2×C4×D3—44no—
287C2×C4×D3—44no—
288C2×C4×D3C22×C4116yes—
289C2×Dic6—22no—
290C2×Dic6—22no—
291C2×Dic6C22×C414yes—
292C3×C4⋊C4—22no—
293C3×C4⋊C4—24no—
294C3×C4⋊C4—24no—
295C3×C4⋊C4—42no—
296C3×C4⋊C4C22×C414yes—
297C3×C4⋊C4C22×C418yes—
298C3×C4⋊C4#4114yes—
299C3×C42—24no—
300C3×C42—44no—
301C3×C42C22×C414yes—
302C3×C42C22×C418yes—
303(C2×D3)⋊C4—28no—
304(C2×D3)⋊C4—28no—
305(C2×D3)⋊C4—28no—
306(C2×D3)⋊C4—28no—
307(C2×D3)⋊C4—44no—
308(C2×D3)⋊C4—44no—
309(C2×D3)⋊C4C22×C4116yes—
310(C2×D3)⋊C4C22×C4116yes—
311(C2×D3)⋊C4C22×C4116yes—
312C4⋊Dic3—22no—
313C4⋊Dic3—24no—
314C4⋊Dic3—24no—
315C4⋊Dic3C22×C414yes—
316C4⋊Dic3#4114yes—
317Dic3⋊C4—24no—
318Dic3⋊C4—24no—
319Dic3⋊C4C22×C418yes—
320C4×Dic3—24no—
321C4×Dic3—22no—
322C4×Dic3—24no—
323C4×Dic3—22no—
324C4×Dic3—24no—
325C4×Dic3—24no—
326C4×Dic3—24no—
327C4×Dic3—24no—
328C4×Dic3—24no—
329C4×Dic3—22no—
330C4×Dic3—44no—
331C4×Dic3—41no—
332C4×Dic3—42no—
333C4×Dic3—42no—
334C4×Dic3C22×C418yes—
335C4×Dic3#4114yes—
336C4×Dic3#4114yes—
337C22×Q8—31no—
338C22×Q8C22×D311yescharacteristic
339C22×D4—32no—
340C22×D4—32no—
341C22×D4—32no—
342C23×C4—34no—
343C23×C4—34no—
344C23×C4—34no—
345#127—38no—
346#124—316no—
347#124—316no—
348#123—332no—
349C4×Q8—38no—
350C4×Q8—64no—
351C4×Q8—64no—
352C4×Q8—64no—
353C4×Q8—64no—
354C4×Q8C4×D318yescomplemented
355C4×D4—316no—
356C4×D4—316no—
357C4×D4—68no—
358C4×D4—68no—
359C4×D4—68no—
360C4×D4—68no—
361C4×D4—124no—
362C2×C4⋊C4—31no—
363C2×C4⋊C4—31no—
364C2×C4⋊C4—32no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—32no—
367C2×C4⋊C4—32no—
368C2×C4⋊C4—32no—
369C2×C4⋊C4—32no—
370C2×C4⋊C4C22×D312yes—
371C2×C4⋊C4C22×D312yes—
372C2×C4⋊C4C22×D311yescharacteristic
373C2×C4⋊C4C22×D312yes—
374C2×C4⋊C4C22×D311yescharacteristic
375C2×C4⋊C4C22×D312yes—
376C2×C4⋊C4C22×D311yescharacteristic
377C2×C22⋊C4—34no—
378C2×C22⋊C4—34no—
379C2×C22⋊C4—34no—
380C2×C22⋊C4—34no—
381C2×C22⋊C4—34no—
382C2×C22⋊C4—34no—
383C2×C22⋊C4—34no—
384C2×C22⋊C4—34no—
385C2×C22⋊C4—34no—
386C2×C42—31no—
387C2×C42—31no—
388C2×C42—32no—
389C2×C42—31no—
390C2×C42—32no—
391C2×C42—32no—
392C2×C42—32no—
393C2×C42—32no—
394C2×C42—32no—
395C2×C42—31no—
396C2×C42—31no—
397C2×C42—32no—
398C2×C42—32no—
399C2×C42—32no—
400C2×C42—32no—
401C2×C42—31no—
402C2×C42—34no—
403C2×C42—128no—
404C2×C42C22×D312yes—
405C2×C42C22×D314yes—
406C2×C42C22×D312yes—
407C2×C42C22×D311yescharacteristic
408#95—32no—
409#95—32no—
410#95—34no—
411#95—34no—
412#95—34no—
413#95—32no—
414#95—32no—
415#95—32no—
416#95C22×D314yes—
417#95C22×D314yes—
418#95C22×D314yes—
419#95C22×D312yes—
420C23×C3C2511yescharacteristic
421C22×D3—24no—
422C22×D3—24no—
423C22×D3—24no—
424C22×D3—24no—
425C22×D3—24no—
426C22×D3—24no—
427C22×D3C23×C418yes—
428C3×Q8—28no—
429C2×C3×C4—22no—
430C2×C3×C4—22no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—21no—
435C2×C3×C4—22no—
436C2×C3×C4—21no—
437C2×C3×C4—22no—
438C2×C3×C4—22no—
439C2×C3×C4—24no—
440C2×C3×C4—24no—
441C2×C3×C4—24no—
442C2×C3×C4—22no—
443C2×C3×C4C23×C412yes—
444C2×C3×C4C23×C414yes—
445C2×C3×C4C23×C414yes—
446C2×C3×C4C23×C412yes—
447C2×C3×C4C23×C412yes—
448C2×C3×C4C2×#4114yes—
449C2×C3×C4C2×#4112yes—
450C2×C3×C4C2×#4112yes—
451C2×C3×C4C2×#4112yes—
452C2×C3×C4C2×#4112yes—
453C2×Dic3—21no—
454C2×Dic3—21no—
455C2×Dic3—22no—
456C2×Dic3—22no—
457C2×Dic3—22no—
458C2×Dic3—22no—
459C2×Dic3—22no—
460C2×Dic3—21no—
461C2×Dic3—21no—
462C2×Dic3—22no—
463C2×Dic3—21no—
464C2×Dic3—22no—
465C2×Dic3—21no—
466C2×Dic3—22no—
467C2×Dic3—21no—
468C2×Dic3—22no—
469C2×Dic3C23×C414yes—
470C2×Dic3C23×C414yes—
471C2×Dic3C2×#4114yes—
472C2×Dic3C2×#4112yes—
473C2×Dic3C2×#4112yes—
474C2×Dic3C2×#4112yes—
475C2×Dic3C2×#4112yes—
476C2×Dic3H(5,𝔽2)12yes—
477D12—216no—
478D12—216no—
479D12—48no—
480C4×D3—416no—
481C4×D3—416no—
482C4×D3—416no—
483Dic6—28no—
484C24—34no—
485C2×Q8—22no—
486C2×Q8—22no—
487C2×Q8—34no—
488C2×Q8—62no—
489C2×Q8—62no—
490C2×Q8C2×C4×D314yes—
491C2×D4—38no—
492C2×D4—38no—
493C2×D4—38no—
494C2×D4—64no—
495C2×D4—64no—
496C2×D4—64no—
497C2×D4—64no—
498C2×D4—122no—
499C2×D4—122no—
500C22×C4—31no—
501C22×C4—32no—
502C22×C4—32no—
503C22×C4—32no—
504C22×C4—31no—
505C22×C4—31no—
506C22×C4—316no—
507C22×C4—32no—
508C22×C4—31no—
509C22×C4—68no—
510C22×C4—68no—
511C22×C4—68no—
512C22×C4—68no—
513C22×C4—68no—
514C22×C4—124no—
515C22×C4—124no—
516C22×C4—124no—
517C22×C4C23×D314yes—
518C22×C4C23×D312yes—
519C22×C4C23×D312yes—
520C22×C4C23×D311yescharacteristic
521C22×C4C23×D312yes—
522C22×C4C23×D312yes—
523C22×C4C23×D311yescharacteristic
524C22×C4C23×D311yescharacteristic
525C4⋊C4—24no—
526C4⋊C4—24no—
527C4⋊C4—22no—
528C4⋊C4—34no—
529C4⋊C4—38no—
530C4⋊C4—34no—
531C4⋊C4—42no—
532C4⋊C4—64no—
533C4⋊C4—64no—
534C4⋊C4—64no—
535C4⋊C4—64no—
536C4⋊C4—62no—
537C4⋊C4C2×C4×D314yes—
538C4⋊C4C2×C4×D318yes—
539C4⋊C4#23914yes—
540C22⋊C4—316no—
541C22⋊C4—316no—
542C22⋊C4—316no—
543C22⋊C4—68no—
544C22⋊C4—68no—
545C22⋊C4—68no—
546C22⋊C4—68no—
547C22⋊C4—124no—
548C22⋊C4—124no—
549C42—24no—
550C42—38no—
551C42—34no—
552C42—34no—
553C42—44no—
554C42—64no—
555C42—64no—
556C42—62no—
557C42—64no—
558C42—64no—
559C42—64no—
560C42—64no—
561C42—64no—
562C42—62no—
563C42—62no—
564C42—124no—
565C42—122no—
566C42—121no—
567C42—122no—
568C42C2×C4×D318yes—
569C42C2×C4×D314yes—
570C22×C3C24×C411yescharacteristic
571C22×C3C22×#4111yescharacteristic
572C22×C3C22×#4111yescharacteristic
573C22×C3C22×#4111yescharacteristic
574C22×C3C22×#4111yescharacteristic
575C22×C3C2×H(5,𝔽2)11yescharacteristic
576C22×C3#58511yescharacteristic
577C2×D3—28no—
578C2×D3—28no—
579C2×D3—28no—
580C2×D3—44no—
581C2×D3—44no—
582C2×D3—44no—
583C2×D3—44no—
584C3×C4—24no—
585C3×C4—24no—
586C3×C4—22no—
587C3×C4—24no—
588C3×C4—44no—
589C3×C4—42no—
590C3×C4C4×#4114yes—
591C3×C4C4×#4114yes—
592Dic3—24no—
593Dic3—24no—
594Dic3—22no—
595Dic3—22no—
596Dic3—24no—
597Dic3—42no—
598Dic3—41no—
599Dic3#55914yescomplemented
600C23—38no—
601C23—64no—
602C23—64no—
603C23—64no—
604C23—64no—
605C23—64no—
606C23—64no—
607C23C24×D311yescharacteristic
608Q8—28no—
609Q8—68no—
610D4—616no—
611D4—616no—
612D4—128no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—21no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—24no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—22no—
627C2×C4—32no—
628C2×C4—32no—
629C2×C4—32no—
630C2×C4—34no—
631C2×C4—34no—
632C2×C4—32no—
633C2×C4—32no—
634C2×C4—34no—
635C2×C4—61no—
636C2×C4—62no—
637C2×C4—62no—
638C2×C4—61no—
639C2×C4—62no—
640C2×C4—62no—
641C2×C4—62no—
642C2×C4—61no—
643C2×C4—61no—
644C2×C4—62no—
645C2×C4—62no—
646C2×C4—61no—
647C2×C4—61no—
648C2×C4—62no—
649C2×C4—61no—
650C2×C4—62no—
651C2×C4—1216no—
652C2×C4—1216no—
653C2×C4—1216no—
654C2×C4C22×C4×D314yes—
655C2×C4C22×C4×D314yes—
656C2×C4C22×C4×D312yes—
657C2×C4C22×C4×D312yes—
658C2×C4C22×C4×D312yes—
659C2×C4C2×#23914yes—
660C2×C4C2×#23912yes—
661C2×C4D3×#4112yes—
662C2×C4D3×#4112yes—
663C2×C4D3×#4112yes—
664C2×C3C2×C4×#4111yescharacteristic
665C2×C3C2×C4×#4111yescharacteristic
666C2×C3C4×H(5,𝔽2)11yescharacteristic
667C2×C3C2×#55911yescharacteristic
668C2×C3#348011yescharacteristic
669C2×C3#348011yescharacteristic
670C2×C3#348111yescharacteristic
671D3—48no—
672C22—68no—
673C22—68no—
674C22—68no—
675C22—124no—
676C22—124no—
677C22—124no—
678C22—124no—
679C22C23×C4×D311yescharacteristic
680C22C22×#23911yescharacteristic
681C22C2×D3×#4111yescharacteristic
682C22C2×D3×#4111yescharacteristic
683C22C2×D3×#4111yescharacteristic
684C22D3×H(5,𝔽2)11yescharacteristic
685C22#596811yescharacteristic
686C4—24no—
687C4—22no—
688C4—24no—
689C4—24no—
690C4—34no—
691C4—44no—
692C4—42no—
693C4—64no—
694C4—64no—
695C4—64no—
696C4—62no—
697C4—62no—
698C4—121no—
699C4—122no—
700C4#552214yes—
701C4C4×#23914yes—
702C3C4×#55911yescharacteristic, complemented, Sylow
703C2—128no—
704C2C2×#552211yescharacteristic
705C2C2×C4×#23911yescharacteristic
706C2#8588611yescharacteristic
707C2#8692411yescharacteristic
708C2#8698011yescharacteristic
709C2#8701611yescharacteristic
710C2D3×#55911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutatorC22×C3C24×C4
FittingC3×#2355C2
socle, cosocleC23×C3C25
prime radicalC2×#874C22
hypercenter#2355D3
hypocenterC3C4×#559
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2355

Complements

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

NH ≅ G/Ntype
2. C3×#2355C2semidirect
3. C4×Q8×Dic3C2semidirect
4. #76493C2semidirect
5. #76480C2semidirect
6. #74975C2semidirect
7. #74940C2semidirect
8. #74325C2semidirect
10. #74160C2semidirect
11. #74149C2semidirect
12. #73654C2semidirect
14. #73646C2semidirect
15. C4×#887C2semidirect
16. C4×#893C2semidirect
17. C4×#893C2semidirect
23. #5585C4semidirect
93. #2355D3semidirect
110. C3×C4×Q8C2×C4semidirect
122. #947C2×C4semidirect
159. #894C2×C4semidirect
164. #893C2×C4semidirect
167. #875C2×C4semidirect
170. C4×D12C2×C4semidirect
172. C4×Dic6C2×C4semidirect
354. C4×Q8C4×D3semidirect
599. Dic3#559semidirect
702. C3C4×#559semidirect

Maximal subgroups

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

subgroupindex
C2×#55852
C3×#23552
C4×Q8×Dic32
#764932
#764802
#749752
#749402
#743252
#743192
#741602
#741492
#736542
#736532
#736462
C4×#8872
C4×#8932
C4×#5593