Finite Group Databasebeta

← #10815461

Subgroups — #10815461

Order 768.

1170 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
2C2×#4806C211yesmaximal, characteristic
3C2×D3×#103C211yesmaximal, characteristic, complemented
4C2×#4817C211yesmaximal, characteristic, complemented
5#73774C211yesmaximal, characteristic
6C3×#1763C211yesmaximal, characteristic, complemented
7#71633C211yesmaximal, characteristic, complemented
8#70236C211yesmaximal, characteristic, complemented
9#69831C211yesmaximal, characteristic, complemented
10#69826C211yesmaximal, characteristic, complemented
11#69465C211yesmaximal, characteristic, complemented
12#68896C211yesmaximal, characteristic, complemented
13#68883C211yesmaximal, characteristic
14#68874C211yesmaximal, characteristic, complemented
15#68855C211yesmaximal, characteristic, complemented
16#22855—31nomaximal, Sylow
17C22×D3×Q8C2211yescharacteristic
18C2×C3×C4×Q8C2211yescharacteristic
19C2×Q8×Dic3C2211yescharacteristic
20C22×#215C2211yescharacteristic
21C22×#204C2211yescharacteristic
22C22×D3×C8C2211yescharacteristic
23C2×#895C2211yescharacteristic
24C2×#893C2211yescharacteristic
25C2×D3×C4⋊C4C2211yescharacteristic
26C2×C4×D12—21no—
27C2×C3×#103C2211yescharacteristic
28C2×C3×#103C2211yescharacteristic
29C2×C3×#97C2211yescharacteristic
30C3×C4×C4⋊C4C2211yescharacteristic
31C2×#835C2211yescharacteristic
32C2×#821C2211yescharacteristic
33C2×(C2×D3)⋊C8C2211yescharacteristic
34C2×#818C2211yescharacteristic
35C2×#816C2211yescharacteristic
36C2×#815C2211yescharacteristic
37#4987—21no—
38#4987C2211yescharacteristic
39#4984C2211yescharacteristic
40#4973—21no—
41#4973C2211yescharacteristic
42C2×#810C2211yescharacteristic
43C2×#810C2211yescharacteristic
44C2×#809C2211yescharacteristic
45C2×#807C2211yescharacteristic
46#4940—21no—
47#4939C2211yescharacteristic
48C4×(C2×D3)⋊C4—21no—
49C4×(C2×D3)⋊C4C2211yescharacteristic
50#4929—21no—
51#4929C2211yescharacteristic
52#4817—24no—
53#4806C418yescomplemented
54D3×#103—24no—
55#4668—21no—
56#4665—21no—
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59#4550C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4524C2211yescharacteristic
63C2×#448—31no—
64C2×#440—31no—
65C22×#103—31no—
66#2361—31no—
67Q8×C22⋊C4—31no—
68#1973—31no—
69#1935—31no—
70#1928—31no—
71#1893—31no—
72#1880—31no—
73#1877—31no—
74#1863—31no—
75#1852—31no—
76#1763D311yescharacteristic, complemented
77#1752—31no—
78C22×C3×Q8C2311yescharacteristic
79C2×D3×Q8—22no—
80C2×D3×Q8—22no—
81C2×D3×Q8—22no—
82C2×D3×Q8—41no—
83C2×D3×Q8—41no—
84C2×D3×Q8C2×C414yescomplemented
85C22×D12—21no—
86C22×D12C2311yescharacteristic
87C22×C4×D3—21no—
88C22×C4×D3—21no—
89C22×C4×D3—21no—
90C22×C4×D3C2311yescharacteristic
91C22×Dic6—21no—
92C22×Dic6C2311yescharacteristic
93C22×C3×C8C2311yescharacteristic
94C22×C3×C8C2311yescharacteristic
95C3×C4×Q8—22no—
96C3×C4×Q8—41no—
97C2×C3×C4⋊C4—21no—
98C2×C3×C4⋊C4C2311yescharacteristic
99C2×C3×C4⋊C4C2311yescharacteristic
100C2×C3×C4⋊C4C2311yescharacteristic
101C2×C3×C42—21no—
102C2×C3×C42—21no—
103C2×C3×C42C2311yescharacteristic
104Q8×Dic3—22no—
105Q8×Dic3—41no—
106C2×#215—22no—
107C2×#215—22no—
108C2×#215C2×C414yescomplemented
109C2×(C2×D3)⋊C4—21no—
110C2×(C2×D3)⋊C4—21no—
111C2×(C2×D3)⋊C4—21no—
112C2×(C2×D3)⋊C4—21no—
113C2×(C2×D3)⋊C4—21no—
114C2×(C2×D3)⋊C4D411yescharacteristic
115C2×(C2×D3)⋊C4D411yescharacteristic
116C2×C4⋊Dic3—21no—
117C2×C4⋊Dic3—21no—
118C2×C4⋊Dic3C2311yescharacteristic
119C2×C4⋊Dic3C2311yescharacteristic
120C2×Dic3⋊C4—21no—
121C2×C4×Dic3—21no—
122C2×C4×Dic3C2311yescharacteristic
123C22×C3⋊C8C2311yescharacteristic
124C22×C3⋊C8C2311yescharacteristic
125C2×#204—41no—
126C2×#204—41no—
127C2×#204C2×C414yescomplemented
128C2×D3×C8—22no—
129C2×D3×C8—22no—
130C2×D3×C8—41no—
131#895—22no—
132#895C2×C414yes—
133#893—22no—
134#893—41no—
135D3×C4⋊C4—22no—
136D3×C4⋊C4—41no—
137C4×D12—44no—
138C3×#103C2×C414yescomplemented
139C3×#103D414yescomplemented
140C3×#97—41no—
141C3×#95—21no—
142#835—22no—
143C3⋊#95—21no—
144C3⋊#95—21no—
145C3⋊#95—21no—
146C3⋊#95—21no—
147C3⋊#95—21no—
148C3⋊#95—21no—
149C3⋊#95D411yescharacteristic
150C3⋊#95D411yescharacteristic
151#821—22no—
152(C2×D3)⋊C8C2×C414yescomplemented
153#818—41no—
154#816—22no—
155#815—22no—
156#810—22no—
157#810C2×C414yescomplemented
158#809—41no—
159#807—22no—
160C23×Q8—31no—
161C22×SD16—31no—
162C22×SD16—31no—
163C23×C8—31no—
164C2×#121—31no—
165C2×C4×Q8—31no—
166C2×C4×Q8C2×D311yescharacteristic
167C2×C4×D4—31no—
168C2×C4×D4—61no—
169C22×C4⋊C4—31no—
170#448—38no—
171#440—64no—
172C2×#107—31no—
173C2×#107—31no—
174C2×#103—31no—
175C2×#103—31no—
176C2×#103—31no—
177C2×#103—31no—
178C2×#103—64no—
179C2×#103C2×D311yescharacteristic
180C2×#103C2×D311yescharacteristic
181C2×#102—31no—
182C2×#102—31no—
183C2×C22⋊C8—31no—
184C2×#97—31no—
185C2×#97C2×D311yescharacteristic
186#391—31no—
187#391—31no—
188#391—61no—
189#391—61no—
190#390—31no—
191#389—31no—
192#388—61no—
193#386—61no—
194#385—61no—
195#380—31no—
196#380—61no—
197C4×C4⋊C4C2×D311yescharacteristic
198C4×C22⋊C4—31no—
199C4×C22⋊C4—61no—
200#340—31no—
201#340—31no—
202#340C2×D311yescharacteristic
203#340C2×D311yescharacteristic
204#336—31no—
205#336—31no—
206C23×D3—21no—
207C23×D3C2×D411yescharacteristic
208C2×C3×Q8—21no—
209C2×C3×Q8—21no—
210C2×C3×Q8—21no—
211C2×C3×Q8C22×C412yes—
212C2×C3×Q8C2×D412yes—
213C2×C3×Q8#4112yes—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4C2×D411yescharacteristic
219C22×C3×C4C2×D411yescharacteristic
220C22×C3×C4C2411yescharacteristic
221C22×Dic3—21no—
222C22×Dic3—21no—
223C22×Dic3—21no—
224C22×Dic3C2×D411yescharacteristic
225C22×Dic3C2×D411yescharacteristic
226C22×Dic3C2×D411yescharacteristic
227D3×Q8—28no—
228D3×Q8—44no—
229D3×Q8—44no—
230D3×Q8—44no—
231C2×D12—21no—
232C2×D12—21no—
233C2×D12—21no—
234C2×D12—21no—
235C2×D12—24no—
236C2×D12—21no—
237C2×D12—42no—
238C2×D12—42no—
239C2×D12C22×C412yes—
240C2×C4×D3—21no—
241C2×C4×D3—21no—
242C2×C4×D3—21no—
243C2×C4×D3—21no—
244C2×C4×D3—24no—
245C2×C4×D3—42no—
246C2×C4×D3—42no—
247C2×C4×D3—42no—
248C2×C4×D3—42no—
249C2×C4×D3—42no—
250C2×C4×D3—42no—
251C2×C4×D3—81no—
252C2×C4×D3—81no—
253C2×C4×D3C22×C412yes—
254C2×C4×D3#4112yes—
255C2×Dic6—21no—
256C2×Dic6—21no—
257C2×Dic6—21no—
258C2×Dic6—21no—
259C2×Dic6—21no—
260C2×Dic6—24no—
261C2×Dic6—42no—
262C2×Dic6—42no—
263C2×Dic6C22×C412yes—
264C2×C3×C8—21no—
265C2×C3×C8—21no—
266C2×C3×C8—21no—
267C2×C3×C8—21no—
268C2×C3×C8C22×C412yes—
269C2×C3×C8C2×D412yes—
270C3×C4⋊C4—21no—
271C3×C4⋊C4—21no—
272C3×C4⋊C4—21no—
273C3×C4⋊C4—21no—
274C3×C4⋊C4—42no—
275C3×C4⋊C4C22×C412yes—
276C3×C4⋊C4C2×D412yes—
277C3×C42—21no—
278C3×C42—21no—
279C3×C42—42no—
280C3×C42—42no—
281#215—28no—
282(C2×D3)⋊C4—22no—
283(C2×D3)⋊C4—22no—
284(C2×D3)⋊C4—24no—
285(C2×D3)⋊C4—42no—
286(C2×D3)⋊C4—42no—
287(C2×D3)⋊C4—42no—
288(C2×D3)⋊C4—81no—
289C4⋊Dic3—21no—
290C4⋊Dic3—21no—
291C4⋊Dic3—21no—
292C4⋊Dic3—21no—
293C4⋊Dic3—42no—
294C4⋊Dic3—42no—
295Dic3⋊C4—42no—
296C4×Dic3—21no—
297C4×Dic3—21no—
298C4×Dic3—42no—
299C2×C3⋊C8—21no—
300C2×C3⋊C8—21no—
301C2×C3⋊C8—21no—
302C2×C3⋊C8—21no—
303C2×C3⋊C8—21no—
304C2×C3⋊C8C22×C412yes—
305#204—44no—
306D3×C8—44no—
307C22×Q8—34no—
308C22×Q8—31no—
309C22×Q8—61no—
310C22×Q8—62no—
311C22×Q8—62no—
312C22×Q8—62no—
313C22×Q8—121no—
314C22×Q8—121no—
315C22×Q8C22×D311yescharacteristic
316C22×D4—31no—
317C22×D4—61no—
318C23×C4—31no—
319C23×C4—61no—
320C23×C4—61no—
321C23×C4—61no—
322C2×SD16—34no—
323C2×SD16—34no—
324C2×SD16—62no—
325C2×SD16—62no—
326C2×SD16—121no—
327C2×SD16—121no—
328C22×C8—31no—
329C22×C8—31no—
330C22×C8—62no—
331C22×C8—62no—
332C22×C8—121no—
333C22×C8C22×D311yescharacteristic
334C22×C8C22×D311yescharacteristic
335#121—34no—
336#121—62no—
337C4×Q8—22no—
338C4×Q8—41no—
339C4×Q8—62no—
340C4×Q8—121no—
341C4×D4—62no—
342C4×D4—124no—
343C4×D4—121no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—31no—
346C2×C4⋊C4—31no—
347C2×C4⋊C4—62no—
348C2×C4⋊C4—61no—
349C2×C4⋊C4—61no—
350C2×C4⋊C4—61no—
351C2×C4⋊C4—121no—
352C2×C4⋊C4C22×D311yescharacteristic
353C2×C4⋊C4C22×D311yescharacteristic
354C2×C4⋊C4C22×D311yescharacteristic
355C2×C22⋊C4—31no—
356C2×C22⋊C4—31no—
357C2×C22⋊C4—61no—
358C2×C22⋊C4—61no—
359C2×C22⋊C4—61no—
360C2×C22⋊C4—61no—
361C2×C22⋊C4—61no—
362C2×C42—21no—
363C2×C42—21no—
364C2×C42—31no—
365C2×C42—61no—
366C2×C42C22×D311yescharacteristic
367#107—62no—
368#107—121no—
369#103—34no—
370#103—62no—
371#103—62no—
372#103—62no—
373#103C4×D314yescomplemented
374#103D1214yescomplemented
375#102—62no—
376#102—121no—
377C22⋊C8—34no—
378#97—41no—
379#97—62no—
380#95—21no—
381#95—31no—
382#95—31no—
383#95—61no—
384#95—61no—
385#95—61no—
386#95—61no—
387#95—61no—
388#95—61no—
389C23×C3C22×D411yescharacteristic
390C22×D3—21no—
391C22×D3—21no—
392C22×D3—21no—
393C22×D3—21no—
394C22×D3—22no—
395C22×D3—41no—
396C22×D3—41no—
397C22×D3—41no—
398C22×D3—41no—
399C22×D3—41no—
400C22×D3—41no—
401C22×D3C4×D412yes—
402C22×D3AGL(1,ℤ/8)12yes—
403C22×D3#13712yes—
404C3×Q8—22no—
405C3×Q8—22no—
406C3×Q8—22no—
407C3×Q8C4×D414yescomplemented
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—41no—
420C2×C3×C4—41no—
421C2×C3×C4—41no—
422C2×C3×C4—41no—
423C2×C3×C4—41no—
424C2×C3×C4—41no—
425C2×C3×C4—41no—
426C2×C3×C4C23×C411yescharacteristic
427C2×C3×C4C22×D411yescharacteristic
428C2×C3×C4C2×#4111yescharacteristic
429C2×C3×C4C2×#4111yescharacteristic
430C2×C3×C4H(5,𝔽2)11yescharacteristic
431C2×C3×C4H(5,𝔽2)11yescharacteristic
432C2×Dic3—21no—
433C2×Dic3—21no—
434C2×Dic3—22no—
435C2×Dic3—21no—
436C2×Dic3—21no—
437C2×Dic3—21no—
438C2×Dic3—21no—
439C2×Dic3—21no—
440C2×Dic3—21no—
441C2×Dic3—41no—
442C2×Dic3—41no—
443C2×Dic3—41no—
444C2×Dic3—41no—
445C2×Dic3—41no—
446C2×Dic3—41no—
447C2×Dic3—41no—
448C2×Dic3—41no—
449C2×Dic3C4×D412yes—
450D12—22no—
451D12—22no—
452D12—48no—
453D12—41no—
454D12—41no—
455C4×D3—22no—
456C4×D3—22no—
457C4×D3—22no—
458C4×D3—22no—
459C4×D3—48no—
460C4×D3—84no—
461C4×D3—84no—
462Dic6—22no—
463Dic6—22no—
464Dic6—48no—
465Dic6—41no—
466Dic6—41no—
467C3×C8—22no—
468C3×C8—22no—
469C3⋊C8—22no—
470C3⋊C8—41no—
471C24—31no—
472C24—61no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—32no—
477C2×Q8—64no—
478C2×Q8—61no—
479C2×Q8—68no—
480C2×Q8—61no—
481C2×Q8—61no—
482C2×Q8—61no—
483C2×Q8—61no—
484C2×Q8—122no—
485C2×Q8—122no—
486C2×Q8—124no—
487C2×Q8—124no—
488C2×Q8—124no—
489C2×Q8C2×C4×D312yes—
490C2×Q8C2×D1212yes—
491C2×Q8#23512yes—
492C2×D4—32no—
493C2×D4—64no—
494C2×D4—61no—
495C2×D4—61no—
496C2×D4—61no—
497C2×D4—61no—
498C2×D4—61no—
499C2×D4—122no—
500C2×D4—122no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—31no—
506C22×C4—32no—
507C22×C4—32no—
508C22×C4—31no—
509C22×C4—31no—
510C22×C4—64no—
511C22×C4—61no—
512C22×C4—61no—
513C22×C4—61no—
514C22×C4—61no—
515C22×C4—61no—
516C22×C4—61no—
517C22×C4—61no—
518C22×C4—122no—
519C22×C4—122no—
520C22×C4—122no—
521C22×C4—122no—
522C22×C4—122no—
523C22×C4—122no—
524C22×C4—241no—
525C22×C4—241no—
526C22×C4D3×D411yescharacteristic
527C22×C4D3×D411yescharacteristic
528C22×C4C23×D311yescharacteristic
529SD16—68no—
530SD16—124no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—32no—
536C2×C8—61no—
537C2×C8—61no—
538C2×C8—61no—
539C2×C8—61no—
540C2×C8—61no—
541C2×C8—124no—
542C2×C8C2×C4×D312yes—
543C2×C8C2×D1212yes—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—42no—
549C4⋊C4—61no—
550C4⋊C4—61no—
551C4⋊C4—61no—
552C4⋊C4—61no—
553C4⋊C4—122no—
554C4⋊C4—122no—
555C4⋊C4—122no—
556C4⋊C4C2×C4×D312yes—
557C4⋊C4C2×D1212yes—
558C22⋊C4—64no—
559C22⋊C4—62no—
560C22⋊C4—62no—
561C22⋊C4—122no—
562C22⋊C4—122no—
563C22⋊C4—122no—
564C22⋊C4—241no—
565C42—21no—
566C42—21no—
567C42—42no—
568C42—42no—
569C42—61no—
570C42—61no—
571C42—122no—
572C22×C3C2×C4×D411yescharacteristic
573C22×C3D4211yescharacteristic
574C22×C3#54611yescharacteristic
575C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
576C22×C3C2×#13711yescharacteristic
577C22×C3#57711yescharacteristic
578C22×C3#57811yescharacteristic
579C2×D3—22no—
580C2×D3—22no—
581C2×D3—22no—
582C2×D3—22no—
583C2×D3—22no—
584C2×D3—22no—
585C2×D3—42no—
586C2×D3—42no—
587C2×D3—42no—
588C2×D3—81no—
589C2×D3—81no—
590C2×D3—81no—
591C2×D3—81no—
592C2×D3#44014yescomplemented
593C3×C4—24no—
594C3×C4—42no—
595C3×C4—42no—
596C3×C4—41no—
597C3×C4—41no—
598C3×C4—81no—
599C3×C4C2×C4×D411yescharacteristic
600C3×C4#51811yescharacteristic
601C3×C4#54611yescharacteristic
602C3×C4#55111yescharacteristic
603Dic3—22no—
604Dic3—42no—
605Dic3—41no—
606Dic3—41no—
607Dic3—81no—
608Dic3—81no—
609C23—32no—
610C23—32no—
611C23—32no—
612C23—61no—
613C23—61no—
614C23—61no—
615C23—61no—
616C23—62no—
617C23—121no—
618C23—121no—
619C23—121no—
620C23—121no—
621C23—121no—
622C23—121no—
623C23C2×D3×D411yescharacteristic
624Q8—22no—
625Q8—22no—
626Q8—22no—
627Q8—62no—
628Q8—62no—
629Q8—128no—
630Q8—121no—
631Q8—121no—
632Q8C4×D1214yescomplemented
633D4—62no—
634D4—62no—
635D4—128no—
636D4—121no—
637D4—121no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—32no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—61no—
658C2×C4—61no—
659C2×C4—62no—
660C2×C4—62no—
661C2×C4—62no—
662C2×C4—62no—
663C2×C4—61no—
664C2×C4—61no—
665C2×C4—61no—
666C2×C4—61no—
667C2×C4—62no—
668C2×C4—61no—
669C2×C4—61no—
670C2×C4—128no—
671C2×C4—121no—
672C2×C4—121no—
673C2×C4—121no—
674C2×C4—121no—
675C2×C4—121no—
676C2×C4—121no—
677C2×C4—121no—
678C2×C4—121no—
679C2×C4—244no—
680C2×C4—244no—
681C2×C4C22×C4×D311yescharacteristic
682C2×C4C22×D1211yescharacteristic
683C2×C4C2×#23511yescharacteristic
684C2×C4#100411yescharacteristic
685C2×C4D3×#4111yescharacteristic
686C2×C4#100911yescharacteristic
687C8—22no—
688C8—22no—
689C8—62no—
690C8—121no—
691C2×C3#235811yescharacteristic
692C2×C3C2×#44011yescharacteristic
693C2×C3#294711yescharacteristic
694C2×C3#326511yescharacteristic
695C2×C3#327011yescharacteristic
696C2×C3#330811yescharacteristic
697C2×C3#332011yescharacteristic
698D3—24no—
699D3—82no—
700C22—34no—
701C22—62no—
702C22—62no—
703C22—62no—
704C22—62no—
705C22—62no—
706C22—62no—
707C22—122no—
708C22—122no—
709C22—122no—
710C22—241no—
711C22—241no—
712C22—241no—
713C22—241no—
714C22#549011yescharacteristic
715C22C4×D3×D411yescharacteristic
716C22D4×D1211yescharacteristic
717C22D3×AGL(1,ℤ/8)11yescharacteristic
718C22D3×#13711yescharacteristic
719C22#577811yescharacteristic
720C22#577911yescharacteristic
721C4—24no—
722C4—41no—
723C4—41no—
724C4—42no—
725C4—42no—
726C4—62no—
727C4—81no—
728C4—122no—
729C4—121no—
730C4—121no—
731C4—241no—
732C4—241no—
733C4C2×C4×D1211yescharacteristic
734C4#552711yescharacteristic
735C4#554511yescharacteristic
736C4#555411yescharacteristic
737C3#2285511yescharacteristic, complemented, Sylow
738C2—64no—
739C2—242no—
740C2#7357711yescharacteristic
741C2#7889611yescharacteristic
742C2#7896811yescharacteristic
743C2D3×#44011yescharacteristic
744C2#7979411yescharacteristic
745C2#7983011yescharacteristic
746C2#7983911yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1763C2
socleC23×C3C22×D4
prime radicalC2×#895C22
cosocleC22×C3×C4C24
hypercenter#1763D3
hypocenterC3#22855
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1763

Complements

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

NH ≅ G/Ntype
1. Q8×(C2×D3)⋊C4C2semidirect
3. C2×D3×#103C2semidirect
4. C2×#4817C2semidirect
6. C3×#1763C2semidirect
7. #71633C2semidirect
8. #70236C2semidirect
9. #69831C2semidirect
10. #69826C2semidirect
11. #69465C2semidirect
12. #68896C2semidirect
14. #68874C2semidirect
15. #68855C2semidirect
53. #4806C4semidirect
76. #1763D3semidirect
84. C2×D3×Q8C2×C4semidirect
108. C2×#215C2×C4semidirect
127. C2×#204C2×C4semidirect
138. C3×#103C2×C4semidirect
139. C3×#103D4semidirect
152. (C2×D3)⋊C8C2×C4semidirect
157. #810C2×C4semidirect
373. #103C4×D3semidirect
374. #103D12semidirect
407. C3×Q8C4×D4semidirect
592. C2×D3#440semidirect
632. Q8C4×D12semidirect
737. C3#22855semidirect

Maximal subgroups

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

subgroupindex
Q8×(C2×D3)⋊C42
C2×#48062
C2×D3×#1032
C2×#48172
#737742
C3×#17632
#716332
#702362
#698312
#698262
#694652
#688962
#688832
#688742
#688552
#228553