Finite Group Databasebeta

← #10972904

Subgroups — #10972904

Order 768.

2654 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D3×Q8C211yesmaximal, characteristic, complemented
2C2×#5548C211yesmaximal, characteristic
3C3×#2580C211yesmaximal, characteristic, complemented
4#82501C211yesmaximal, characteristic, complemented
5#82388C211yesmaximal, characteristic, complemented
6#78050C212yesmaximal, complemented
7#78030C212yesmaximal, complemented
8#76812C212yesmaximal, complemented
9#76781C212yesmaximal, complemented
10#76475C212yesmaximal, complemented
11#76353C212yesmaximal, complemented
12#76286C212yesmaximal, complemented
13#76071C212yesmaximal, complemented
14#74600C214yesmaximal, complemented
15#74386C214yesmaximal, complemented
16#74190C211yesmaximal, characteristic, complemented
17#74147C211yesmaximal, characteristic, complemented
18#35249—31nomaximal, Sylow
19C22×D3×Q8C2211yescharacteristic
20C22×#235C2212yes—
21C2×C3×C4×Q8C2211yescharacteristic
22C2×C3×C4×D4C2211yescharacteristic
23C2×Q8×Dic3C2211yescharacteristic
24C2×#940C2211yescharacteristic
25C2×#938C2211yescharacteristic
26C2×C4×#67C2212yes—
27C4×D3×Q8—28no—
28#5548—28no—
29C2×#895C2211yescharacteristic
30C2×#894C2214yes—
31C2×D3×C4⋊C4C2212yes—
32C2×D3×C4⋊C4C2211yescharacteristic
33C2×#888C2211yescharacteristic
34C2×#887C2212yes—
35C2×#887C2211yescharacteristic
36C2×#885C2212yes—
37C2×#885C2214yes—
38C2×#884C2212yes—
39C2×#883C2214yes—
40C2×C4×D12C2211yescharacteristic
41C2×C42×D3C2212yes—
42C2×C42×D3C2211yescharacteristic
43C2×C4×Dic6C2212yes—
44C2×C4×Dic6C2211yescharacteristic
45C3×#399C2212yes—
46C3×#393C2212yes—
47C3×#390C2212yes—
48C3×#389C2212yes—
49C3×#385C2214yes—
50C3×#382C2211yescharacteristic
51#5231C2212yes—
52#5221C2212yes—
53#5210C2214yes—
54#4993C2212yes—
55#4990C2214yes—
56#4989C2214yes—
57#4988C2212yes—
58#4987C2212yes—
59#4984C2212yes—
60#4979C2214yes—
61#4975C2214yes—
62Dic3×C4⋊C4C2212yes—
63#4972C2212yes—
64#4961C2214yes—
65#4959C2214yes—
66#4957C2214yes—
67#4956C2214yes—
68#4951C2214yes—
69#4949C2212yes—
70#4947C2212yes—
71#4945C2214yes—
72#4939C2212yes—
73#4936C2211yescharacteristic
74#4928C2212yes—
75#4677C2212yes—
76#4673C2212yes—
77#4669C2214yes—
78#4668C2214yes—
79#4666C2212yes—
80#4665C2214yes—
81#4664C2212yes—
82#4656C2214yes—
83#4651C2212yes—
84#4648C2212yes—
85#4646C2214yes—
86C2×#532—31no—
87C22×C4×Q8—31no—
88#2854—32no—
89#2854—32no—
90#2632—32no—
91#2632—32no—
92#2580—31no—
93#2580—31no—
94#2580—31no—
95#2580D311yescharacteristic, complemented
96#2567—32no—
97#2548—32no—
98#2501—32no—
99#2436—32no—
100#2406—34no—
101#2326—34no—
102#2283—31no—
103C22×C3×Q8C2311yescharacteristic
104C22×C3×D4C2311yescharacteristic
105C23×C3×C4C2312yes—
106C22×#67C2312yes—
107C22×#67C2312yes—
108C22×#67C2312yes—
109C2×D3×Q8—24no—
110C2×D3×Q8—28no—
111C2×#235—28no—
112C2×#235—48no—
113C22×D12C2312yes—
114C22×D12C2311yescharacteristic
115C22×C4×D3C2312yes—
116C22×C4×D3C2312yes—
117C22×C4×D3C2311yescharacteristic
118C22×C4×D3C2311yescharacteristic
119C22×C4×D3C2311yescharacteristic
120C22×C4×D3C2312yes—
121C22×Dic6C2311yescharacteristic
122C22×Dic6C2312yes—
123C22×Dic6C2312yes—
124C3×C4×Q8—24no—
125C3×C4×D4—24no—
126C2×C3×C4⋊C4C2311yescharacteristic
127C2×C3×C4⋊C4C2312yes—
128C2×C3×C4⋊C4C2312yes—
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C4⋊C4C2314yes—
131C2×C3×C22⋊C4C2312yes—
132C2×C3×C22⋊C4C2314yes—
133C2×C3×C22⋊C4C2314yes—
134C2×C3×C42C2312yes—
135C2×C3×C42C2311yescharacteristic
136C2×#217C2312yes—
137C2×#217C2314yes—
138C2×#217C2314yes—
139Q8×Dic3—24no—
140#940—24no—
141#938—24no—
142C4×#67—28no—
143C2×(C2×D3)⋊C4C2314yes—
144C2×(C2×D3)⋊C4C2314yes—
145C2×(C2×D3)⋊C4C2314yes—
146C2×(C2×D3)⋊C4C2312yes—
147C2×(C2×D3)⋊C4C2312yes—
148C2×(C2×D3)⋊C4C2314yes—
149C2×(C2×D3)⋊C4C2314yes—
150C2×C4⋊Dic3C2312yes—
151C2×C4⋊Dic3C2311yescharacteristic
152C2×C4⋊Dic3C2312yes—
153C2×C4⋊Dic3C2311yescharacteristic
154C2×C4⋊Dic3C2314yes—
155C2×Dic3⋊C4C2312yes—
156C2×Dic3⋊C4C2312yes—
157C2×Dic3⋊C4C2312yes—
158C2×Dic3⋊C4C2312yes—
159C2×Dic3⋊C4C2314yes—
160C2×Dic3⋊C4C2314yes—
161C2×C4×Dic3C2314yes—
162C2×C4×Dic3C2312yes—
163C2×C4×Dic3C2312yes—
164C2×C4×Dic3C2312yes—
165C2×C4×Dic3C2311yescharacteristic
166C2×C4×Dic3C2311yescharacteristic
167C2×C4×Dic3C2311yescharacteristic
168#895—24no—
169#894—48no—
170D3×C4⋊C4—28no—
171D3×C4⋊C4—24no—
172#888—24no—
173#887—24no—
174#887—28no—
175#885—216no—
176#885—28no—
177#884—28no—
178#883—48no—
179C4×D12—24no—
180C42×D3—28no—
181C42×D3D418yes—
182C4×Dic6—24no—
183C4×Dic6—28no—
184C3×#95C2314yes—
185C3×#95C2312yes—
186C3×#95C2312yes—
187C3⋊#95C2314yes—
188C3⋊#95C2314yes—
189C3⋊#95C2314yes—
190C3⋊#95C2314yes—
191C3⋊#95C2312yes—
192C3⋊#95C2314yes—
193C3⋊#95C2312yes—
194C22×#41—32no—
195C23×Q8—31no—
196#532—68no—
197C2×C4⋊Q8—31no—
198C2×#127—31no—
199C2×#124—34no—
200C2×#124—32no—
201C2×#123—34no—
202C2×#123—34no—
203C2×#121—31no—
204C2×#121—31no—
205C2×#121—32no—
206C2×C4×Q8—31no—
207C2×C4×Q8—32no—
208C2×C4×Q8—31no—
209C2×C4×Q8—32no—
210C2×C4×Q8—31no—
211C2×C4×Q8—68no—
212C2×C4×Q8C2×D311yescharacteristic
213C2×C4×D4—32no—
214C2×C4×D4—31no—
215C2×C4×D4C2×D311yescharacteristic
216C22×C4⋊C4—32no—
217C22×C4⋊C4—31no—
218C22×C42—31no—
219C22×C42—32no—
220#399—32no—
221#399—32no—
222#399—32no—
223#399C2×D312yes—
224#395—34no—
225#395—34no—
226#394—34no—
227#394—34no—
228#393—32no—
229#393—32no—
230#393—32no—
231#393C2×D312yes—
232#391—34no—
233#390—32no—
234#390—32no—
235#390—34no—
236#390—32no—
237#390C2×D312yes—
238#389—32no—
239#389—32no—
240#389—32no—
241#389C2×D312yes—
242#388—34no—
243#388—34no—
244#388—34no—
245#388—34no—
246#386—34no—
247#386—34no—
248#385—34no—
249#385—34no—
250#385—34no—
251#385C2×D314yes—
252#384—34no—
253#383—32no—
254#382—31no—
255#382C2×D311yescharacteristic
256#381—32no—
257#380—32no—
258C4×C4⋊C4—32no—
259C4×C22⋊C4—32no—
260#376—32no—
261C24×C3C2412yes—
262C23×D3C2412yes—
263C23×D3C2411yescharacteristic
264C2×C3×Q8—22no—
265C2×C3×Q8—24no—
266C2×C3×D4—22no—
267C2×C3×D4—22no—
268C2×C3×D4—22no—
269C22×C3×C4—24no—
270C22×C3×C4—44no—
271C22×C3×C4C2414yes—
272C22×C3×C4C2412yes—
273C22×C3×C4C2412yes—
274C22×C3×C4C2411yescharacteristic
275C22×C3×C4C2411yescharacteristic
276C22×C3×C4C2412yes—
277C22×C3×C4C2411yescharacteristic
278C2×#67—24no—
279C2×#67—28no—
280C2×#67—24no—
281C2×#67—24no—
282C2×#67—28no—
283C2×#67—44no—
284C22×Dic3C2414yes—
285C22×Dic3C2412yes—
286C22×Dic3C2412yes—
287C22×Dic3C2411yescharacteristic
288C22×Dic3C2411yescharacteristic
289C22×Dic3C2412yes—
290C22×Dic3C2411yescharacteristic
291D3×Q8—232no—
292#235—432no—
293C2×D12—24no—
294C2×D12—28no—
295C2×D12—22no—
296C2×D12—22no—
297C2×D12—22no—
298C2×C4×D3—24no—
299C2×C4×D3—24no—
300C2×C4×D3—24no—
301C2×C4×D3—22no—
302C2×C4×D3—22no—
303C2×C4×D3—24no—
304C2×C4×D3—24no—
305C2×C4×D3—24no—
306C2×C4×D3—24no—
307C2×C4×D3—24no—
308C2×C4×D3—24no—
309C2×C4×D3—44no—
310C2×C4×D3C2×D414yes—
311C2×C4×D3C2×D414yes—
312C2×C4×D3C2×D414yes—
313C2×Dic6—22no—
314C2×Dic6—24no—
315C2×Dic6—24no—
316C2×Dic6—24no—
317C2×Dic6—24no—
318C2×Dic6—44no—
319C2×Dic6#4118yescomplemented
320C3×C4⋊C4—24no—
321C3×C4⋊C4—22no—
322C3×C4⋊C4—22no—
323C3×C4⋊C4—24no—
324C3×C4⋊C4—44no—
325C3×C22⋊C4—24no—
326C3×C22⋊C4—28no—
327C3×C22⋊C4—44no—
328C3×C42—24no—
329C3×C42C2×D414yes—
330#217—24no—
331#217—28no—
332#217—44no—
333(C2×D3)⋊C4—28no—
334(C2×D3)⋊C4—24no—
335(C2×D3)⋊C4—28no—
336(C2×D3)⋊C4—24no—
337(C2×D3)⋊C4—28no—
338(C2×D3)⋊C4—44no—
339(C2×D3)⋊C4—44no—
340C4⋊Dic3—22no—
341C4⋊Dic3—22no—
342C4⋊Dic3—24no—
343C4⋊Dic3—24no—
344C4⋊Dic3—44no—
345Dic3⋊C4—24no—
346Dic3⋊C4—24no—
347Dic3⋊C4—24no—
348Dic3⋊C4—24no—
349Dic3⋊C4—44no—
350Dic3⋊C4—44no—
351C4×Dic3—24no—
352C4×Dic3—24no—
353C4×Dic3—24no—
354C4×Dic3—28no—
355C4×Dic3C2×D414yes—
356C4×Dic3C2×D414yes—
357C4×Dic3C2×D414yes—
358C2×#41—68no—
359C2×#41—128no—
360C22×Q8—32no—
361C22×Q8—31no—
362C22×Q8—32no—
363C22×Q8—64no—
364C22×Q8—68no—
365C22×Q8C22×D311yescharacteristic
366C22×D4—32no—
367C22×D4—32no—
368C22×D4—32no—
369C22×D4—31no—
370C22×D4—32no—
371C22×D4C22×D311yescharacteristic
372C23×C4—31no—
373C23×C4—31no—
374C23×C4—31no—
375C23×C4—32no—
376C23×C4—32no—
377C23×C4—32no—
378C23×C4C22×D312yes—
379C4⋊Q8—64no—
380#127—64no—
381#124—68no—
382#124—616no—
383#123—128no—
384#123—128no—
385#121—68no—
386#121—64no—
387#121—64no—
388C4×Q8—24no—
389C4×Q8—68no—
390C4×Q8—68no—
391C4×Q8—64no—
392C4×Q8—64no—
393C4×Q8—64no—
394C4×D4—24no—
395C4×D4—68no—
396C4×D4—64no—
397C2×C4⋊C4—32no—
398C2×C4⋊C4—32no—
399C2×C4⋊C4—32no—
400C2×C4⋊C4—32no—
401C2×C4⋊C4—31no—
402C2×C4⋊C4—32no—
403C2×C4⋊C4—31no—
404C2×C4⋊C4—32no—
405C2×C4⋊C4—34no—
406C2×C4⋊C4—34no—
407C2×C4⋊C4—34no—
408C2×C4⋊C4—64no—
409C2×C4⋊C4—68no—
410C2×C4⋊C4C22×D312yes—
411C2×C4⋊C4C22×D311yescharacteristic
412C2×C4⋊C4C22×D311yescharacteristic
413C2×C4⋊C4C22×D312yes—
414C2×C4⋊C4C22×D314yes—
415C2×C22⋊C4—32no—
416C2×C22⋊C4—34no—
417C2×C22⋊C4—32no—
418C2×C22⋊C4—32no—
419C2×C22⋊C4—34no—
420C2×C22⋊C4—34no—
421C2×C22⋊C4—34no—
422C2×C22⋊C4—34no—
423C2×C22⋊C4—34no—
424C2×C22⋊C4—34no—
425C2×C22⋊C4C22×D312yes—
426C2×C22⋊C4C22×D314yes—
427C2×C22⋊C4C22×D314yes—
428C2×C42—31no—
429C2×C42—31no—
430C2×C42—31no—
431C2×C42—38no—
432C2×C42—32no—
433C2×C42—32no—
434C2×C42—32no—
435C2×C42—34no—
436C2×C42—68no—
437C2×C42C22×D312yes—
438C2×C42C22×D311yescharacteristic
439#95—34no—
440#95—32no—
441#95—32no—
442#95—34no—
443#95—34no—
444#95—34no—
445#95—34no—
446#95C22×D312yes—
447#95C22×D312yes—
448#95C22×D314yes—
449C23×C3—22no—
450C23×C3—24no—
451C23×C3—24no—
452C23×C3—22no—
453C23×C3—22no—
454C23×C3C2511yescharacteristic
455C22×D3—22no—
456C22×D3—21no—
457C22×D3—21no—
458C22×D3—22no—
459C22×D3—24no—
460C22×D3—24no—
461C22×D3—22no—
462C22×D3—22no—
463C22×D3C22×D412yes—
464C22×D3H(5,𝔽2)14yes—
465C3×Q8—28no—
466C3×D4—44no—
467C2×C3×C4—22no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—22no—
473C2×C3×C4—24no—
474C2×C3×C4—22no—
475C2×C3×C4—24no—
476C2×C3×C4—24no—
477C2×C3×C4—22no—
478C2×C3×C4—24no—
479C2×C3×C4—48no—
480C2×C3×C4C22×D412yes—
481C2×C3×C4C22×D412yes—
482C2×C3×C4C22×D412yes—
483C2×C3×C4C2×#4114yes—
484C2×C3×C42−1+412yes—
485C2×C3×C42−1+412yes—
486#67—48no—
487#67—48no—
488#67—48no—
489C2×Dic3—22no—
490C2×Dic3—22no—
491C2×Dic3—22no—
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3—22no—
495C2×Dic3—22no—
496C2×Dic3—24no—
497C2×Dic3—24no—
498C2×Dic3—22no—
499C2×Dic3—24no—
500C2×Dic3—22no—
501C2×Dic3—24no—
502C2×Dic3C22×D412yes—
503C2×Dic3C22×D412yes—
504C2×Dic3C22×D412yes—
505C2×Dic3C2×#4114yes—
506C2×Dic3C2×#4114yes—
507D12—48no—
508D12—44no—
509C4×D3—216no—
510C4×D3—28no—
511C4×D3—28no—
512C4×D3—28no—
513C4×D3—48no—
514C4×D3—48no—
515Dic6—28no—
516Dic6—216no—
517Dic6—48no—
518C24—31no—
519C24—32no—
520C24C23×D312yes—
521#41—1232no—
522C2×Q8—22no—
523C2×Q8—24no—
524C2×Q8—38no—
525C2×Q8—64no—
526C2×Q8—64no—
527C2×Q8—64no—
528C2×Q8—64no—
529C2×Q8—632no—
530C2×Q8—62no—
531C2×Q8—124no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—64no—
536C2×D4—68no—
537C2×D4—64no—
538C2×D4—64no—
539C2×D4—68no—
540C2×D4—64no—
541C2×D4—68no—
542C2×D4—62no—
543C2×D4—62no—
544C2×D4—62no—
545C2×D4—124no—
546C22×C4—24no—
547C22×C4—31no—
548C22×C4—31no—
549C22×C4—32no—
550C22×C4—31no—
551C22×C4—34no—
552C22×C4—34no—
553C22×C4—34no—
554C22×C4—34no—
555C22×C4—32no—
556C22×C4—32no—
557C22×C4—44no—
558C22×C4—64no—
559C22×C4—64no—
560C22×C4—64no—
561C22×C4—64no—
562C22×C4—64no—
563C22×C4—64no—
564C22×C4—64no—
565C22×C4—62no—
566C22×C4—64no—
567C22×C4—62no—
568C22×C4—64no—
569C22×C4—124no—
570C22×C4C23×D314yes—
571C22×C4C23×D312yes—
572C22×C4C23×D312yes—
573C22×C4C23×D311yescharacteristic
574C22×C4C23×D311yescharacteristic
575C22×C4C23×D312yes—
576C22×C4C23×D311yescharacteristic
577C4⋊C4—24no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—24no—
581C4⋊C4—44no—
582C4⋊C4—64no—
583C4⋊C4—64no—
584C4⋊C4—64no—
585C4⋊C4—64no—
586C4⋊C4—64no—
587C4⋊C4—62no—
588C4⋊C4—62no—
589C4⋊C4—64no—
590C4⋊C4—124no—
591C4⋊C4—124no—
592C4⋊C4—124no—
593C22⋊C4—24no—
594C22⋊C4—28no—
595C22⋊C4—44no—
596C22⋊C4—64no—
597C22⋊C4—68no—
598C22⋊C4—68no—
599C22⋊C4—64no—
600C22⋊C4—68no—
601C22⋊C4—64no—
602C22⋊C4—68no—
603C22⋊C4—124no—
604C22⋊C4—124no—
605C22⋊C4—124no—
606C42—24no—
607C42—34no—
608C42—34no—
609C42—34no—
610C42—64no—
611C42—64no—
612C42—68no—
613C42—64no—
614C42D3×D414yes—
615C22×C3—42no—
616C22×C3—42no—
617C22×C3—42no—
618C22×C3—44no—
619C22×C3—44no—
620C22×C3C23×D411yescharacteristic
621C22×C3C22×#4112yes—
622C22×C3C2×H(5,𝔽2)12yes—
623C22×C3C2×2−1+411yescharacteristic
624C22×C3C2×2−1+411yescharacteristic
625C2×D3—22no—
626C2×D3—22no—
627C2×D3—24no—
628C2×D3—24no—
629C2×D3—42no—
630C2×D3—42no—
631C2×D3—42no—
632C2×D3—44no—
633C2×D3—44no—
634C2×D3#53514yes—
635C3×C4—22no—
636C3×C4—24no—
637C3×C4—22no—
638C3×C4—42no—
639C3×C4—42no—
640C3×C4—44no—
641C3×C4#53614yes—
642Dic3—24no—
643Dic3—22no—
644Dic3—22no—
645Dic3—42no—
646Dic3—42no—
647Dic3—44no—
648Dic3#52514yes—
649C23—22no—
650C23—22no—
651C23—24no—
652C23—22no—
653C23—24no—
654C23—32no—
655C23—34no—
656C23—61no—
657C23—62no—
658C23—61no—
659C23—62no—
660C23—62no—
661C23—64no—
662C23—62no—
663C23—64no—
664C23C24×D311yescharacteristic
665Q8—28no—
666Q8—616no—
667Q8—68no—
668Q8—128no—
669D4—44no—
670D4—128no—
671D4—128no—
672D4—128no—
673D4—128no—
674D4—124no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—24no—
687C2×C4—32no—
688C2×C4—34no—
689C2×C4—32no—
690C2×C4—32no—
691C2×C4—34no—
692C2×C4—48no—
693C2×C4—68no—
694C2×C4—68no—
695C2×C4—616no—
696C2×C4—62no—
697C2×C4—61no—
698C2×C4—62no—
699C2×C4—61no—
700C2×C4—62no—
701C2×C4—68no—
702C2×C4—62no—
703C2×C4—62no—
704C2×C4—64no—
705C2×C4—64no—
706C2×C4—64no—
707C2×C4—62no—
708C2×C4—62no—
709C2×C4—64no—
710C2×C4—128no—
711C2×C4—128no—
712C2×C4C2×D3×D412yes—
713C2×C4C2×D3×D412yes—
714C2×C4C2×D3×D412yes—
715C2×C4#100712yes—
716C2×C4D3×#4114yes—
717C2×C4#101012yes—
718C2×C3—82no—
719C2×C3C2×#52511yescharacteristic
720C2×C3C2×#53511yescharacteristic
721C2×C3C2×#53611yescharacteristic
722C2×C3#352212yes—
723C2×C3#352212yes—
724D3—24no—
725D3—82no—
726C22—34no—
727C22—44no—
728C22—42no—
729C22—42no—
730C22—44no—
731C22—42no—
732C22—64no—
733C22—62no—
734C22—64no—
735C22—62no—
736C22—124no—
737C22—122no—
738C22—122no—
739C22—124no—
740C22—122no—
741C22C22×D3×D411yescharacteristic
742C22C2×#100711yescharacteristic
743C22C2×D3×#4112yes—
744C22C2×#101011yescharacteristic
745C22D3×H(5,𝔽2)12yes—
746C4—22no—
747C4—24no—
748C4—22no—
749C4—34no—
750C4—44no—
751C4—42no—
752C4—42no—
753C4—64no—
754C4—62no—
755C4—62no—
756C4—122no—
757C4—122no—
758C4—124no—
759C4#562814yes—
760C3#3524911yescharacteristic, complemented, Sylow
761C2—64no—
762C2—82no—
763C2—242no—
764C2C2×#562811yescharacteristic
765C2D3×#52511yescharacteristic
766C2D3×#53511yescharacteristic
767C2#8693612yes—
768C2#8705512yes—
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2580C2
prime radicalC2×#5548C2
hypercenter#2580D3
hypocenterC3#35249
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2580

Complements

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

NH ≅ G/Ntype
1. C2×C4×D3×Q8C2semidirect
3. C3×#2580C2semidirect
4. #82501C2semidirect
5. #82388C2semidirect
6. #78050C2semidirect
7. #78030C2semidirect
8. #76812C2semidirect
9. #76781C2semidirect
10. #76475C2semidirect
11. #76353C2semidirect
12. #76286C2semidirect
13. #76071C2semidirect
14. #74600C2semidirect
15. #74386C2semidirect
16. #74190C2semidirect
17. #74147C2semidirect
95. #2580D3semidirect
319. C2×Dic6#41semidirect
760. C3#35249semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D3×Q82
C2×#55482
C3×#25802
#825012
#823882
#780502
#780302
#768122
#767812
#764752
#763532
#762862
#760712
#746002
#743862
#741902
#741472
#352493