Finite Group Databasebeta

← #10823555

Subgroups — #10823555

Order 768.

1114 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#541C211yesmaximal, characteristic, complemented
2C2×#5026C211yesmaximal, characteristic, complemented
3C2×C4×#215C211yesmaximal, characteristic, complemented
4#82236C211yesmaximal, characteristic
5#71791C211yesmaximal, characteristic, complemented
6#71781C211yesmaximal, characteristic, complemented
7#71743C211yesmaximal, characteristic, complemented
8#71739C211yesmaximal, characteristic, complemented
9#71699C211yesmaximal, characteristic
10#71699C211yesmaximal, characteristic
11#71695C211yesmaximal, characteristic, complemented
12#71694C211yesmaximal, characteristic, complemented
13#71631C211yesmaximal, characteristic, complemented
14C4×#835C211yesmaximal, characteristic, complemented
15#71582C211yesmaximal, characteristic, complemented
16#23584—31nomaximal, Sylow
17C3×#541—24no—
18C3×#541—24no—
19C2×C3×C4⋊Q8C2211yescharacteristic
20C2×C3×#126—21no—
21C2×C3×#126—21no—
22C2×C3×#125—21no—
23C2×C3×#125—21no—
24C2×C3×#125C2211yescharacteristic
25C2×C3×C22⋊Q8C2211yescharacteristic
26C2×C3×C22⋊Q8C2211yescharacteristic
27C2×C3×C4×Q8C2211yescharacteristic
28C2×C3×C4×Q8C2211yescharacteristic
29C2×C3×#117C2211yescharacteristic
30C22×#215C2211yescharacteristic
31C22×#215C2211yescharacteristic
32C2×#930C2211yescharacteristic
33C2×C4×D12C2211yescharacteristic
34C2×#835C2211yescharacteristic
35C2×#835C2211yescharacteristic
36C2×#835C2211yescharacteristic
37C2×#835C2211yescharacteristic
38C2×#835C2211yescharacteristic
39C2×#835C2211yescharacteristic
40#5212C2211yescharacteristic
41C2×#830C2211yescharacteristic
42C2×#830C2211yescharacteristic
43#5026—24no—
44C4×#215—24no—
45#4990—21no—
46#4989—21no—
47C2×#809C2211yescharacteristic
48C2×#809C2211yescharacteristic
49C2×#808C2211yescharacteristic
50C2×#807C2211yescharacteristic
51#4957—21no—
52#4956—21no—
53#4939C2211yescharacteristic
54C4×C4⋊Dic3C2211yescharacteristic
55#4928C2211yescharacteristic
56C2×#803C2211yescharacteristic
57C2×C4×C3⋊C8C2211yescharacteristic
58#4529C2211yescharacteristic
59#4529C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4524C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#541D311yescharacteristic, complemented
65C2×#440—31no—
66C2×C4×SD16—31no—
67#2324—31no—
68#2059—31no—
69#2043—31no—
70#2036—31no—
71#2035—31no—
72#2025—31no—
73#2013—31no—
74#2000—31no—
75#2000—31no—
76#1763—31no—
77C4×#103—31no—
78#1750—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×Q8C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C22×#67—21no—
83C22×D12C2311yescharacteristic
84C22×C4×D3—21no—
85C3×C4⋊Q8—22no—
86C3×C4⋊Q8—22no—
87C3×#126—28no—
88C3×#126—28no—
89C3×#125—28no—
90C3×#125—28no—
91C3×#125—22no—
92C3×#125—22no—
93C3×C22⋊Q8—22no—
94C3×C22⋊Q8—22no—
95C3×C22⋊Q8—22no—
96C3×C22⋊Q8—22no—
97C3×C4×Q8—22no—
98C3×C4×Q8—22no—
99C3×C4×Q8D414yescomplemented
100C3×C4×Q8D414yescomplemented
101C3×#117—22no—
102C3×#117—22no—
103C2×C3×C4⋊C4—21no—
104C2×C3×C4⋊C4—21no—
105C2×C3×C4⋊C4—21no—
106C2×C3×C4⋊C4—21no—
107C2×C3×C4⋊C4—21no—
108C2×C3×C4⋊C4—21no—
109C2×C3×C4⋊C4—21no—
110C2×C3×C4⋊C4—21no—
111C2×C3×C4⋊C4D411yescharacteristic
112C2×C3×C4⋊C4D411yescharacteristic
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C4⋊C4C2311yescharacteristic
115C2×C3×C22⋊C4—21no—
116C2×C3×C22⋊C4—21no—
117C2×C3×C22⋊C4D411yescharacteristic
118C2×C3×C22⋊C4D411yescharacteristic
119C2×C3×C42—21no—
120C2×C3×C42—21no—
121C2×C3×C42C2311yescharacteristic
122C2×C3×C42C2311yescharacteristic
123C2×#217—21no—
124C2×#215—22no—
125C2×#215—22no—
126C2×#215—22no—
127C2×#215—22no—
128C2×#215—22no—
129C2×#215—22no—
130#930—22no—
131#930—22no—
132C2×(C2×D3)⋊C4—21no—
133C2×(C2×D3)⋊C4—21no—
134C2×(C2×D3)⋊C4—21no—
135C2×(C2×D3)⋊C4—21no—
136C2×C4⋊Dic3C2311yescharacteristic
137C2×C4⋊Dic3C2311yescharacteristic
138C2×C4⋊Dic3C2311yescharacteristic
139C2×Dic3⋊C4—21no—
140C2×C4×Dic3—21no—
141C22×C3⋊C8C2311yescharacteristic
142C22×C3⋊C8C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145C4×D12—22no—
146C4×D12—22no—
147#835—22no—
148#835—22no—
149#835—22no—
150#835—22no—
151#835—22no—
152#835—22no—
153C3⋊#95—21no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156#830—22no—
157#830—22no—
158#809—22no—
159#809—22no—
160#808—22no—
161#807—22no—
162#803—22no—
163C4×C3⋊C8—22no—
164C22×SD16—31no—
165C22×SD16—31no—
166#541—24no—
167#541—24no—
168C2×C4⋊Q8C2×D311yescharacteristic
169C2×#126—21no—
170C2×#126—21no—
171C2×#125—21no—
172C2×#125—21no—
173C2×#125C2×D311yescharacteristic
174C2×C22⋊Q8C2×D311yescharacteristic
175C2×C22⋊Q8C2×D311yescharacteristic
176C2×#121—31no—
177C2×C4×Q8C2×D311yescharacteristic
178C2×C4×Q8C2×D311yescharacteristic
179C2×C4×D4—31no—
180C2×#117C2×D311yescharacteristic
181#440—64no—
182C4×SD16—64no—
183C2×#107—31no—
184C2×#106—31no—
185C2×#103—31no—
186C2×#103—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#103—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×C22⋊C8—31no—
194C2×C22⋊C8—31no—
195C2×#97—31no—
196C2×C4×C8—31no—
197#390—31no—
198#390—61no—
199#389—31no—
200#388—61no—
201#386—61no—
202#385—61no—
203#380—31no—
204C4×C4⋊C4—31no—
205#340—31no—
206#340—31no—
207#340—31no—
208#340—31no—
209#336—31no—
210#336—31no—
211C24×C3C2×D411yescharacteristic
212C23×D3—21no—
213C2×C3×Q8—21no—
214C2×C3×Q8—21no—
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8C2×D412yes—
224C2×C3×Q8C2×D412yes—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4C2×D411yescharacteristic
236C22×C3×C4C2×D411yescharacteristic
237C22×C3×C4C2×D411yescharacteristic
238C22×C3×C4C2×D411yescharacteristic
239C22×C3×C4C2×D411yescharacteristic
240C22×C3×C4C2411yescharacteristic
241C2×#67—24no—
242C2×#67—81no—
243C2×#67—81no—
244C22×Dic3—21no—
245C22×Dic3—21no—
246C22×Dic3—21no—
247C2×D12—21no—
248C2×D12—21no—
249C2×D12—21no—
250C2×D12—21no—
251C2×D12—21no—
252C2×D12#4112yes—
253C2×C4×D3—42no—
254C2×C4×D3—81no—
255C2×C4×D3—81no—
256C3×C4⋊C4—24no—
257C3×C4⋊C4—24no—
258C3×C4⋊C4—24no—
259C3×C4⋊C4—24no—
260C3×C4⋊C4—24no—
261C3×C4⋊C4—24no—
262C3×C4⋊C4—24no—
263C3×C4⋊C4—24no—
264C3×C4⋊C4—22no—
265C3×C4⋊C4—22no—
266C3×C4⋊C4—21no—
267C3×C4⋊C4—21no—
268C3×C4⋊C4C2×D412yes—
269C3×C4⋊C4C2×D412yes—
270C3×C22⋊C4—24no—
271C3×C22⋊C4—24no—
272C3×C22⋊C4—22no—
273C3×C22⋊C4—22no—
274C3×C42—24no—
275C3×C42—24no—
276C3×C42—21no—
277C3×C42—21no—
278C3×C42C2×D412yes—
279C3×C42C2×D412yes—
280#217—81no—
281#215—28no—
282#215—28no—
283(C2×D3)⋊C4—24no—
284(C2×D3)⋊C4—42no—
285(C2×D3)⋊C4—81no—
286(C2×D3)⋊C4—81no—
287C4⋊Dic3—21no—
288C4⋊Dic3—21no—
289C4⋊Dic3—21no—
290C4⋊Dic3—21no—
291C4⋊Dic3—21no—
292C4⋊Dic3#4112yes—
293Dic3⋊C4—81no—
294C4×Dic3—81no—
295C2×C3⋊C8—21no—
296C2×C3⋊C8—21no—
297C2×C3⋊C8—21no—
298C2×C3⋊C8—21no—
299C2×C3⋊C8—21no—
300C2×C3⋊C8—21no—
301C2×C3⋊C8—21no—
302C2×C3⋊C8—21no—
303C2×C3⋊C8—21no—
304C2×C3⋊C8—21no—
305C2×C3⋊C8#4112yes—
306C2×C3⋊C8#4112yes—
307C22×Q8C22×D311yescharacteristic
308C22×Q8C22×D311yescharacteristic
309C22×D4—31no—
310C22×D4—61no—
311C23×C4—61no—
312C23×C4C22×D311yescharacteristic
313C2×SD16—62no—
314C2×SD16—62no—
315C2×SD16—62no—
316C2×SD16—62no—
317C2×SD16—62no—
318C2×SD16—62no—
319C22×C8—31no—
320C22×C8—31no—
321C22×C8—31no—
322C22×C8—31no—
323C4⋊Q8—22no—
324C4⋊Q8—22no—
325#126—28no—
326#126—28no—
327#125—28no—
328#125—28no—
329#125—22no—
330#125—22no—
331C22⋊Q8—22no—
332C22⋊Q8—22no—
333C22⋊Q8—22no—
334C22⋊Q8—22no—
335#121—62no—
336#121—62no—
337C4×Q8—22no—
338C4×Q8—22no—
339C4×Q8#6714yescomplemented
340C4×Q8#6714yescomplemented
341C4×D4—62no—
342C4×D4—62no—
343#117—22no—
344#117—22no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—31no—
354C2×C4⋊C4—31no—
355C2×C4⋊C4—31no—
356C2×C4⋊C4—61no—
357C2×C4⋊C4#6711yescharacteristic
358C2×C4⋊C4#6711yescharacteristic
359C2×C4⋊C4C22×D311yescharacteristic
360C2×C4⋊C4C22×D311yescharacteristic
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—61no—
364C2×C22⋊C4—61no—
365C2×C22⋊C4—61no—
366C2×C22⋊C4—61no—
367C2×C22⋊C4—61no—
368C2×C22⋊C4#6711yescharacteristic
369C2×C22⋊C4#6711yescharacteristic
370C2×C42—21no—
371C2×C42—21no—
372C2×C42—61no—
373C2×C42C22×D311yescharacteristic
374C2×C42C22×D311yescharacteristic
375#107—62no—
376#106—62no—
377#103—62no—
378#103—62no—
379#103—62no—
380#103—62no—
381#103—62no—
382#103—62no—
383#102—62no—
384#102—62no—
385C22⋊C8—62no—
386C22⋊C8—62no—
387#97—62no—
388C4×C8—62no—
389#95—61no—
390#95—61no—
391#95—61no—
392C23×C3—21no—
393C23×C3—21no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3—21no—
399C23×C3C22×D411yescharacteristic
400C22×D3—22no—
401C22×D3—41no—
402C22×D3—41no—
403C22×D3—41no—
404C22×D3—41no—
405C22×D3—41no—
406C22×D3—41no—
407C3×Q8—22no—
408C3×Q8—22no—
409C3×Q8—22no—
410C3×Q8—22no—
411C3×Q8—41no—
412C3×Q8—41no—
413C3×Q8—41no—
414C3×Q8—41no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—41no—
433C2×C3×C4—41no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4#12012yes—
445C2×C3×C4#12012yes—
446C2×C3×C4C22×D411yescharacteristic
447C2×C3×C4C22×D411yescharacteristic
448C2×C3×C4C2×#4111yescharacteristic
449C2×C3×C4C2×#4111yescharacteristic
450C2×C3×C4C2×#4111yescharacteristic
451C2×C3×C4C2×#4111yescharacteristic
452#67—84no—
453C2×Dic3—22no—
454C2×Dic3—41no—
455C2×Dic3—41no—
456C2×Dic3—41no—
457C2×Dic3—41no—
458C2×Dic3—41no—
459C2×Dic3—41no—
460C2×Dic3—41no—
461C2×Dic3—41no—
462D12—22no—
463D12—22no—
464D12—41no—
465D12—41no—
466C4×D3—84no—
467C3⋊C8—22no—
468C3⋊C8—22no—
469C3⋊C8—41no—
470C3⋊C8—41no—
471C24—61no—
472C24C2×#6711yescharacteristic
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8C2×#6712yes—
484C2×Q8C2×#6712yes—
485C2×D4—32no—
486C2×D4—64no—
487C2×D4—61no—
488C2×D4—61no—
489C2×D4—61no—
490C2×D4—61no—
491C2×D4—61no—
492C2×D4—241no—
493C2×D4—241no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—61no—
505C22×C4—61no—
506C22×C4—61no—
507C22×C4—122no—
508C22×C4—241no—
509C22×C4—241no—
510C22×C4C2×#6711yescharacteristic
511C22×C4C2×#6711yescharacteristic
512C22×C4C2×#6711yescharacteristic
513C22×C4C2×#6711yescharacteristic
514C22×C4C2×#6711yescharacteristic
515C22×C4C23×D311yescharacteristic
516SD16—68no—
517SD16—68no—
518C2×C8—32no—
519C2×C8—32no—
520C2×C8—61no—
521C2×C8—61no—
522C2×C8—61no—
523C2×C8—61no—
524C2×C8—61no—
525C2×C8—61no—
526C2×C8—61no—
527C2×C8—61no—
528C2×C8—61no—
529C2×C8—61no—
530C4⋊C4—24no—
531C4⋊C4—24no—
532C4⋊C4—24no—
533C4⋊C4—24no—
534C4⋊C4—24no—
535C4⋊C4—24no—
536C4⋊C4—24no—
537C4⋊C4—24no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—32no—
543C4⋊C4—61no—
544C4⋊C4—61no—
545C4⋊C4—61no—
546C4⋊C4—61no—
547C4⋊C4—61no—
548C4⋊C4—241no—
549C4⋊C4C2×#6712yes—
550C4⋊C4C2×#6712yes—
551C22⋊C4—24no—
552C22⋊C4—24no—
553C22⋊C4—22no—
554C22⋊C4—22no—
555C22⋊C4—64no—
556C22⋊C4—122no—
557C22⋊C4—241no—
558C22⋊C4—241no—
559C22⋊C4—241no—
560C42—24no—
561C42—24no—
562C42—21no—
563C42—21no—
564C42—241no—
565C42C2×#6712yes—
566C42C2×#6712yes—
567C22×C3—41no—
568C22×C3—41no—
569C22×C3—41no—
570C22×C3—41no—
571C22×C3—41no—
572C22×C3—41no—
573C22×C3—41no—
574C22×C3C2×#12011yescharacteristic
575C22×C3#52511yescharacteristic
576C22×C3#53211yescharacteristic
577C22×C3#57711yescharacteristic
578C22×C3#57711yescharacteristic
579C22×C3#57711yescharacteristic
580C22×C3#57811yescharacteristic
581C2×D3—42no—
582C2×D3—42no—
583C2×D3—42no—
584C2×D3—81no—
585C2×D3—81no—
586C2×D3—81no—
587C2×D3—81no—
588C3×C4—22no—
589C3×C4—22no—
590C3×C4—41no—
591C3×C4—42no—
592C3×C4—42no—
593C3×C4—41no—
594C3×C4—42no—
595C3×C4—41no—
596C3×C4—42no—
597C3×C4#52511yescharacteristic
598C3×C4#52511yescharacteristic
599C3×C4#53211yescharacteristic
600C3×C4#53211yescharacteristic
601Dic3—42no—
602Dic3—81no—
603Dic3—81no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—62no—
612C23—121no—
613C23—121no—
614C23—121no—
615C23—121no—
616C23—121no—
617C23—121no—
618C23C22×#6711yescharacteristic
619Q8—22no—
620Q8—22no—
621Q8—22no—
622Q8—22no—
623Q8—41no—
624Q8—41no—
625Q8—41no—
626Q8—41no—
627D4—62no—
628D4—62no—
629D4—121no—
630D4—121no—
631D4—244no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—21no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—62no—
662C2×C4—121no—
663C2×C4—121no—
664C2×C4—121no—
665C2×C4—121no—
666C2×C4—121no—
667C2×C4—121no—
668C2×C4—121no—
669C2×C4—121no—
670C2×C4—244no—
671C2×C4#95312yes—
672C2×C4#95312yes—
673C2×C4D3×#4111yescharacteristic
674C2×C4D3×#4111yescharacteristic
675C2×C4D3×#4111yescharacteristic
676C2×C4D3×#4111yescharacteristic
677C2×C4C22×#6711yescharacteristic
678C2×C4C22×#6711yescharacteristic
679C8—62no—
680C8—62no—
681C8—121no—
682C8—121no—
683C2×C3—81no—
684C2×C3#238811yescharacteristic
685C2×C3#301011yescharacteristic
686C2×C3#301311yescharacteristic
687C2×C3#312011yescharacteristic
688C2×C3#312311yescharacteristic
689C2×C3#317411yescharacteristic
690C2×C3#317811yescharacteristic
691D3—82no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—122no—
700C22—122no—
701C22—122no—
702C22—241no—
703C22—241no—
704C22—241no—
705C22—241no—
706C22#582811yescharacteristic
707C22#583211yescharacteristic
708C22#583711yescharacteristic
709C22#583711yescharacteristic
710C22#583711yescharacteristic
711C22#583811yescharacteristic
712C22C2×#95311yescharacteristic
713C4—22no—
714C4—22no—
715C4—41no—
716C4—42no—
717C4—42no—
718C4—41no—
719C4—42no—
720C4—41no—
721C4—42no—
722C4—122no—
723C4—241no—
724C4—241no—
725C4#582811yescharacteristic
726C4#582811yescharacteristic
727C4#583211yescharacteristic
728C4#583211yescharacteristic
729C3#2358411yescharacteristic, complemented, Sylow
730C2—81no—
731C2—242no—
732C2#8344311yescharacteristic
733C2#8344511yescharacteristic
734C2#8344611yescharacteristic
735C2#8344711yescharacteristic
736C2#8409511yescharacteristic
737C2#8411311yescharacteristic
738C2#8411411yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#541C2
socleC23×C3C22×D4
prime radicalC2×#930C22
hypercenterC2×#541D3
hypocenterC3#23584
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
1. C2×C3×#541C2semidirect
2. C2×#5026C2semidirect
3. C2×C4×#215C2semidirect
5. #71791C2semidirect
6. #71781C2semidirect
7. #71743C2semidirect
8. #71739C2semidirect
11. #71695C2semidirect
12. #71694C2semidirect
13. #71631C2semidirect
14. C4×#835C2semidirect
15. #71582C2semidirect
64. C2×#541D3semidirect
99. C3×C4×Q8D4semidirect
100. C3×C4×Q8D4semidirect
339. C4×Q8#67semidirect
340. C4×Q8#67semidirect
729. C3#23584semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5412
C2×#50262
C2×C4×#2152
#822362
#717912
#717812
#717432
#717392
#716992
#716952
#716942
#716312
C4×#8352
#715822
#235843