Finite Group Databasebeta

← #10909523

Subgroups — #10909523

Order 768.

960 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#451C211yesmaximal, characteristic, complemented
2#84068C211yesmaximal, characteristic
3C2×#5189C211yesmaximal, characteristic, complemented
4#82777C211yesmaximal, characteristic
5#72132C211yesmaximal, characteristic, complemented
6#72071C211yesmaximal, characteristic, complemented
7#72065C211yesmaximal, characteristic, complemented
8#72065C211yesmaximal, characteristic, complemented
9#71695C211yesmaximal, characteristic, complemented
10#70275C211yesmaximal, characteristic, complemented
11#70271C211yesmaximal, characteristic, complemented
12#70252C211yesmaximal, characteristic, complemented
13#70234C211yesmaximal, characteristic, complemented
14#69958C211yesmaximal, characteristic
15#69940C211yesmaximal, characteristic, complemented
16#30427—31nomaximal, Sylow
17C23×C3×Q8C2211yescharacteristic
18C22×C3×Q16C2211yescharacteristic
19C22×C3×Q16C2211yescharacteristic
20C2×C3×C22⋊Q8C2211yescharacteristic
21C2×#946C2211yescharacteristic
22C2×#946C2211yescharacteristic
23C2×#946C2211yescharacteristic
24C2×Q8×Dic3C2211yescharacteristic
25C2×C4×#67C2211yescharacteristic
26C22×ΓL(1,𝔽25)C2211yescharacteristic
27C3×#451—24no—
28C2×C3×#103C2211yescharacteristic
29C2×C3×#103C2211yescharacteristic
30C2×C3×C22⋊C8C2211yescharacteristic
31#5231—21no—
32#5230—21no—
33#5229C2211yescharacteristic
34#5229C2211yescharacteristic
35C2×#835C2211yescharacteristic
36C2×#835C2211yescharacteristic
37C2×#835C2211yescharacteristic
38C2×#835C2211yescharacteristic
39C2×#835C2211yescharacteristic
40C2×#835C2211yescharacteristic
41#5213—21no—
42#5212C2211yescharacteristic
43#5212C2211yescharacteristic
44#5210—21no—
45C2×#830C2211yescharacteristic
46#5189—24no—
47C2×(C2×D3)⋊C8C2211yescharacteristic
48C2×#817C2211yescharacteristic
49#4990—21no—
50#4987C2211yescharacteristic
51#4982—21no—
52#4977C2211yescharacteristic
53C2×#807C2211yescharacteristic
54#4961—21no—
55#4945—21no—
56#4551C2211yescharacteristic
57#4551C2211yescharacteristic
58#4551C2211yescharacteristic
59#4550C2211yescharacteristic
60#4550C2211yescharacteristic
61#4529C2211yescharacteristic
62C2×#470—31no—
63C2×#451D311yescharacteristic, complemented
64#2536—31no—
65#2409—31no—
66#2097—31no—
67#2077—31no—
68#2074—31no—
69#2036—31no—
70#2036—31no—
71#2001—31no—
72#1894—31no—
73#1878—31no—
74#1878—31no—
75#1870—31no—
76#1787—31no—
77C22×C3×Q8—21no—
78C22×C3×Q8—22no—
79C22×C3×Q8—22no—
80C22×C3×Q8—41no—
81C22×C3×Q8—41no—
82C22×C3×Q8—41no—
83C22×C3×Q8—41no—
84C22×C3×Q8C2311yescharacteristic
85C22×C3×Q8C2311yescharacteristic
86C22×C3×Q8C2311yescharacteristic
87C23×C3×C4—21no—
88C23×C3×C4C2311yescharacteristic
89C22×#67D411yescharacteristic
90C22×C4×D3C2311yescharacteristic
91C2×C3×Q16—22no—
92C2×C3×Q16—22no—
93C2×C3×Q16—41no—
94C2×C3×Q16—41no—
95C2×C3×Q16—41no—
96C2×C3×Q16D414yescomplemented
97C22×C3×C8C2311yescharacteristic
98C22×C3×C8C2311yescharacteristic
99C3×C22⋊Q8—22no—
100C3×C22⋊Q8—41no—
101C2×C3×C4⋊C4—21no—
102C2×C3×C4⋊C4C2311yescharacteristic
103C2×C3×C22⋊C4—21no—
104C2×#217—21no—
105C2×#217—21no—
106C2×#217D411yescharacteristic
107#946—22no—
108#946—22no—
109#946—22no—
110#946—41no—
111#946—41no—
112#946—41no—
113Q8×Dic3—41no—
114Q8×Dic3—41no—
115C4×#67—41no—
116C4×#67—41no—
117C2×(C2×D3)⋊C4—21no—
118C2×(C2×D3)⋊C4—21no—
119C2×(C2×D3)⋊C4—21no—
120C2×(C2×D3)⋊C4—21no—
121C2×(C2×D3)⋊C4D411yescharacteristic
122C2×C4⋊Dic3—21no—
123C2×C4⋊Dic3C2311yescharacteristic
124C2×C4⋊Dic3C2311yescharacteristic
125C2×C4⋊Dic3C2311yescharacteristic
126C2×C4⋊Dic3C2311yescharacteristic
127C2×Dic3⋊C4—21no—
128C2×Dic3⋊C4—21no—
129C2×Dic3⋊C4—21no—
130C2×Dic3⋊C4D411yescharacteristic
131C2×C4×Dic3—21no—
132C2×C4×Dic3C2311yescharacteristic
133C22×C3⋊C8C2311yescharacteristic
134C22×C3⋊C8C2311yescharacteristic
135C2×ΓL(1,𝔽25)—22no—
136C2×ΓL(1,𝔽25)—41no—
137C2×ΓL(1,𝔽25)—41no—
138C3×#103—22no—
139C3×#103—22no—
140C3×C22⋊C8—22no—
141#835—22no—
142#835—22no—
143#835—41no—
144#835—41no—
145#835—41no—
146#835—41no—
147C3⋊#95—21no—
148C3⋊#95—21no—
149C3⋊#95—21no—
150C3⋊#95—21no—
151C3⋊#95—21no—
152C3⋊#95—21no—
153C3⋊#95—21no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156#830—41no—
157(C2×D3)⋊C8—41no—
158#817—22no—
159#807—41no—
160C23×Q8C2×D311yescharacteristic
161C22×Q16C2×D311yescharacteristic
162C22×Q16C2×D311yescharacteristic
163C22×M16—31no—
164C2×C22⋊Q8—31no—
165C2×C22⋊Q8—31no—
166C2×C22⋊Q8—31no—
167C2×C22⋊Q8C2×D311yescharacteristic
168C2×C4×Q8—31no—
169C2×C4×D4—31no—
170#470—64no—
171#451—24no—
172C2×#107—31no—
173C2×#106—31no—
174C2×#103—31no—
175C2×#103—31no—
176C2×#103—31no—
177C2×#103—31no—
178C2×#103—31no—
179C2×#103—31no—
180C2×#103C2×D311yescharacteristic
181C2×#103C2×D311yescharacteristic
182C2×C22⋊C8—31no—
183C2×C22⋊C8—31no—
184C2×C22⋊C8C2×D311yescharacteristic
185#398—61no—
186#395—61no—
187#394—61no—
188#393—61no—
189#391—31no—
190#391—31no—
191#388—61no—
192#388—61no—
193#386—61no—
194#385—61no—
195#382—31no—
196#380—31no—
197#380—31no—
198#380—31no—
199#340—31no—
200#340—31no—
201#340—31no—
202#340—31no—
203#336—31no—
204#336—31no—
205C24×C3C2×D411yescharacteristic
206C23×D3C2×D411yescharacteristic
207C2×C3×Q8—21no—
208C2×C3×Q8—21no—
209C2×C3×Q8—21no—
210C2×C3×Q8—21no—
211C2×C3×Q8—21no—
212C2×C3×Q8—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—42no—
223C2×C3×Q8—42no—
224C2×C3×Q8—42no—
225C2×C3×Q8—44no—
226C2×C3×Q8—44no—
227C2×C3×Q8—44no—
228C2×C3×Q8—44no—
229C2×C3×Q8C2×D412yes—
230C2×C3×Q8C2×D412yes—
231C2×C3×Q8#4112yes—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—42no—
243C22×C3×C4—42no—
244C22×C3×C4—42no—
245C22×C3×C4C2×D411yescharacteristic
246C22×C3×C4C2411yescharacteristic
247C2×#67—22no—
248C2×#67—41no—
249C2×#67—41no—
250C22×Dic3—21no—
251C22×Dic3—21no—
252C22×Dic3—21no—
253C22×Dic3—21no—
254C22×Dic3C2×D411yescharacteristic
255C22×Dic3C2×D411yescharacteristic
256C22×Dic3C2×D411yescharacteristic
257C2×C4×D3—21no—
258C2×C4×D3—21no—
259C2×C4×D3—21no—
260C2×C4×D3—21no—
261C2×C4×D3—21no—
262C2×C4×D3—21no—
263C3×Q16—44no—
264C3×Q16—44no—
265C2×C3×C8—21no—
266C2×C3×C8—21no—
267C2×C3×C8—21no—
268C2×C3×C8—21no—
269C2×C3×C8—21no—
270C2×C3×C8C2×D412yes—
271C3×C4⋊C4—21no—
272C3×C4⋊C4—21no—
273C3×C4⋊C4—42no—
274C3×C22⋊C4—42no—
275#217—41no—
276#217—42no—
277#217—42no—
278(C2×D3)⋊C4—41no—
279(C2×D3)⋊C4—42no—
280(C2×D3)⋊C4—42no—
281(C2×D3)⋊C4—42no—
282(C2×D3)⋊C4—42no—
283C4⋊Dic3—21no—
284C4⋊Dic3—21no—
285C4⋊Dic3—21no—
286C4⋊Dic3—21no—
287C4⋊Dic3—21no—
288C4⋊Dic3—21no—
289C4⋊Dic3—21no—
290C4⋊Dic3—21no—
291C4⋊Dic3—42no—
292Dic3⋊C4—41no—
293Dic3⋊C4—42no—
294Dic3⋊C4—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⋊C8—21no—
305ΓL(1,𝔽25)—44no—
306C22×Q8—21no—
307C22×Q8—22no—
308C22×Q8—22no—
309C22×Q8—41no—
310C22×Q8—41no—
311C22×Q8—41no—
312C22×Q8—41no—
313C22×Q8C22×D311yescharacteristic
314C22×Q8C22×D311yescharacteristic
315C22×Q8C22×D311yescharacteristic
316C22×D4—31no—
317C23×C4—21no—
318C23×C4—31no—
319C23×C4C22×D311yescharacteristic
320C2×Q16—22no—
321C2×Q16—22no—
322C2×Q16—41no—
323C2×Q16—41no—
324C2×Q16—41no—
325C2×Q16#6714yescomplemented
326C2×M16—62no—
327C2×M16—121no—
328C2×M16—121no—
329C22×C8—31no—
330C22×C8—31no—
331C22×C8C22×D311yescharacteristic
332C22×C8C22×D311yescharacteristic
333C22⋊Q8—22no—
334C22⋊Q8—41no—
335C22⋊Q8—62no—
336C22⋊Q8—62no—
337C22⋊Q8—62no—
338C22⋊Q8—121no—
339C22⋊Q8—121no—
340C22⋊Q8—121no—
341C4×Q8—121no—
342C4×Q8—121no—
343C4×D4—121no—
344C4×D4—121no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—31no—
347C2×C4⋊C4—31no—
348C2×C4⋊C4—31no—
349C2×C4⋊C4—31no—
350C2×C4⋊C4—31no—
351C2×C4⋊C4—61no—
352C2×C4⋊C4—61no—
353C2×C4⋊C4—61no—
354C2×C4⋊C4—61no—
355C2×C4⋊C4C22×D311yescharacteristic
356C2×C22⋊C4—21no—
357C2×C22⋊C4—31no—
358C2×C22⋊C4—31no—
359C2×C22⋊C4—61no—
360C2×C22⋊C4—61no—
361C2×C22⋊C4—61no—
362C2×C22⋊C4—61no—
363C2×C22⋊C4—61no—
364C2×C22⋊C4—61no—
365C2×C42—31no—
366C2×C42—61no—
367#107—121no—
368#106—62no—
369#103—22no—
370#103—22no—
371#103—62no—
372#103—62no—
373#103—121no—
374#103—121no—
375#103—121no—
376#103—121no—
377C22⋊C8—22no—
378C22⋊C8—121no—
379C22⋊C8—121no—
380#95—61no—
381#95—61no—
382#95—61no—
383#95—61no—
384#95—61no—
385#95—61no—
386#95—61no—
387#95—61no—
388#95—61no—
389C23×C3—21no—
390C23×C3—21no—
391C23×C3—21no—
392C23×C3—21no—
393C23×C3—21no—
394C23×C3—21no—
395C23×C3#13712yes—
396C23×C3C22×D411yescharacteristic
397C22×D3—21no—
398C22×D3—21no—
399C22×D3—21no—
400C22×D3—21no—
401C22×D3—21no—
402C22×D3—21no—
403C22×D3—21no—
404C3×Q8—22no—
405C3×Q8—22no—
406C3×Q8—22no—
407C3×Q8—22no—
408C3×Q8—22no—
409C3×Q8—22no—
410C3×Q8—48no—
411C3×Q8—41no—
412C3×Q8—41no—
413C3×Q8—41no—
414C3×Q8—41no—
415C3×Q8—41no—
416C3×Q8—41no—
417C2×C3×C4—21no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—21no—
421C2×C3×C4—22no—
422C2×C3×C4—21no—
423C2×C3×C4—48no—
424C2×C3×C4—41no—
425C2×C3×C4—41no—
426C2×C3×C4—41no—
427C2×C3×C4—41no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4—41no—
433C2×C3×C4—41no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4C22×D411yescharacteristic
438C2×C3×C4C2×#4111yescharacteristic
439C2×C3×C4H(5,𝔽2)11yescharacteristic
440C2×C3×C4H(5,𝔽2)11yescharacteristic
441C2×C3×C4H(5,𝔽2)11yescharacteristic
442C2×C3×C4H(5,𝔽2)11yescharacteristic
443#67—44no—
444C2×Dic3—21no—
445C2×Dic3—21no—
446C2×Dic3—21no—
447C2×Dic3—21no—
448C2×Dic3—21no—
449C2×Dic3—21no—
450C2×Dic3—21no—
451C2×Dic3—21no—
452C2×Dic3—21no—
453C2×Dic3—41no—
454C2×Dic3—41no—
455C2×Dic3—41no—
456C2×Dic3—41no—
457C2×Dic3—41no—
458C2×Dic3—41no—
459C2×Dic3—41no—
460C2×Dic3—41no—
461C2×Dic3—41no—
462C2×Dic3—41no—
463C2×Dic3—41no—
464C2×Dic3—41no—
465C4×D3—41no—
466C4×D3—41no—
467C4×D3—41no—
468C4×D3—41no—
469C3×C8—22no—
470C3×C8—41no—
471C3⋊C8—41no—
472C3⋊C8—41no—
473C24—31no—
474C24D3×D411yescharacteristic
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×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—42no—
491C2×Q8—42no—
492C2×Q8—42no—
493C2×Q8—44no—
494C2×Q8—44no—
495C2×Q8—44no—
496C2×Q8—44no—
497C2×Q8#23712yes—
498C2×Q8C2×#6712yes—
499C2×Q8C2×#6712yes—
500C2×D4—62no—
501C2×D4—121no—
502C2×D4—121no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—31no—
514C22×C4—31no—
515C22×C4—31no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—61no—
520C22×C4—61no—
521C22×C4—61no—
522C22×C4—61no—
523C22×C4—61no—
524C22×C4—61no—
525C22×C4—61no—
526C22×C4—61no—
527C22×C4—61no—
528C22×C4—61no—
529C22×C4D3×D411yescharacteristic
530C22×C4C23×D311yescharacteristic
531Q16—44no—
532Q16—44no—
533M16—124no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—61no—
540C2×C8—61no—
541C2×C8—61no—
542C2×C8—61no—
543C2×C8—61no—
544C2×C8—61no—
545C2×C8C2×#6712yes—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—42no—
549C4⋊C4—61no—
550C4⋊C4—61no—
551C4⋊C4—61no—
552C4⋊C4—61no—
553C4⋊C4—61no—
554C4⋊C4—61no—
555C4⋊C4—61no—
556C4⋊C4—61no—
557C4⋊C4—121no—
558C4⋊C4—122no—
559C4⋊C4—122no—
560C4⋊C4—122no—
561C4⋊C4—122no—
562C22⋊C4—42no—
563C22⋊C4—121no—
564C22⋊C4—122no—
565C22⋊C4—122no—
566C22⋊C4—122no—
567C22⋊C4—122no—
568C22⋊C4—121no—
569C22⋊C4—122no—
570C22⋊C4—122no—
571C42—61no—
572C42—61no—
573C42—122no—
574C22×C3—22no—
575C22×C3—22no—
576C22×C3—22no—
577C22×C3—41no—
578C22×C3—41no—
579C22×C3—41no—
580C22×C3—41no—
581C22×C3#53411yescharacteristic
582C22×C3D4211yescharacteristic
583C22×C3#54611yescharacteristic
584C22×C3C2×#13711yescharacteristic
585C22×C3#57511yescharacteristic
586C22×C3#57811yescharacteristic
587C22×C3#57811yescharacteristic
588C2×D3—41no—
589C2×D3—41no—
590C2×D3—41no—
591C2×D3—41no—
592C2×D3—41no—
593C2×D3—41no—
594C2×D3—41no—
595C3×C4—41no—
596C3×C4—42no—
597C3×C4—42no—
598C3×C4—42no—
599C3×C4—81no—
600C3×C4#53411yescharacteristic
601C3×C4#53811yescharacteristic
602C3×C4#54611yescharacteristic
603C3×C4#56011yescharacteristic
604Dic3—41no—
605Dic3—41no—
606Dic3—41no—
607Dic3—81no—
608Dic3—81no—
609Dic3—81no—
610Dic3—81no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—61no—
618C23—61no—
619C23—61no—
620C23—61no—
621C23—61no—
622C23—61no—
623C23—61no—
624C23#91812yes—
625C23C2×D3×D411yescharacteristic
626Q8—22no—
627Q8—22no—
628Q8—22no—
629Q8—22no—
630Q8—22no—
631Q8—22no—
632Q8—48no—
633Q8—41no—
634Q8—41no—
635Q8—41no—
636Q8—41no—
637Q8—41no—
638Q8—41no—
639D4—124no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—21no—
646C2×C4—48no—
647C2×C4—41no—
648C2×C4—41no—
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—61no—
661C2×C4—61no—
662C2×C4—61no—
663C2×C4—61no—
664C2×C4—61no—
665C2×C4—61no—
666C2×C4—61no—
667C2×C4—61no—
668C2×C4—61no—
669C2×C4—121no—
670C2×C4—121no—
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—121no—
680C2×C4—121no—
681C2×C4—121no—
682C2×C4—121no—
683C2×C4—121no—
684C2×C4—121no—
685C2×C4C2×#23711yescharacteristic
686C2×C4#100411yescharacteristic
687C2×C4#100411yescharacteristic
688C2×C4#100411yescharacteristic
689C2×C4#100411yescharacteristic
690C2×C4C22×#6711yescharacteristic
691C8—22no—
692C8—41no—
693C8—121no—
694C8—121no—
695C2×C3—42no—
696C2×C3#266811yescharacteristic
697C2×C3#319611yescharacteristic
698C2×C3#320211yescharacteristic
699C2×C3#327011yescharacteristic
700C2×C3#327711yescharacteristic
701C2×C3#331211yescharacteristic
702C2×C3#332711yescharacteristic
703D3—81no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—121no—
712C22—121no—
713C22—121no—
714C22—121no—
715C22—121no—
716C22—121no—
717C22—121no—
718C22#558911yescharacteristic
719C22#559111yescharacteristic
720C22C2×#91811yescharacteristic
721C22#576611yescharacteristic
722C22#577711yescharacteristic
723C22#577911yescharacteristic
724C22D4×#6711yescharacteristic
725C4—41no—
726C4—42no—
727C4—42no—
728C4—42no—
729C4—81no—
730C4—121no—
731C4—121no—
732C4—121no—
733C4—241no—
734C4—241no—
735C4—241no—
736C4—241no—
737C4#559311yescharacteristic
738C4#559511yescharacteristic
739C4#580411yescharacteristic
740C4#580611yescharacteristic
741C3#3042711yescharacteristic, complemented, Sylow
742C2—42no—
743C2—241no—
744C2#8019011yescharacteristic
745C2#8019211yescharacteristic
746C2#8019511yescharacteristic
747C2#8019911yescharacteristic
748C2#8260811yescharacteristic
749C2#8388811yescharacteristic
750C2#8399411yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#451C2
socleC23×C3C22×D4
prime radicalC22×#67D4
hypercenterC2×#451D3
hypocenterC3#30427
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
1. C2×C3×#451C2semidirect
3. C2×#5189C2semidirect
5. #72132C2semidirect
6. #72071C2semidirect
7. #72065C2semidirect
8. #72065C2semidirect
9. #71695C2semidirect
10. #70275C2semidirect
11. #70271C2semidirect
12. #70252C2semidirect
13. #70234C2semidirect
15. #69940C2semidirect
63. C2×#451D3semidirect
96. C2×C3×Q16D4semidirect
325. C2×Q16#67semidirect
741. C3#30427semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#4512
#840682
C2×#51892
#827772
#721322
#720712
#720652
#716952
#702752
#702712
#702522
#702342
#699582
#699402
#304273