Finite Group Databasebeta

← #11867168

Subgroups — #11867168

Order 1152.

1261 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596299C211yesmaximal, characteristic, complemented
2C2×C3×#949C211yesmaximal, characteristic, complemented
3C2×#63916C211yesmaximal, characteristic, complemented
4C2×#63818C211yesmaximal, characteristic, complemented
5C3×#5232C211yesmaximal, characteristic, complemented
6#10591591C212yesmaximal, complemented
7#10591590C212yesmaximal, complemented
8#10591455C212yesmaximal, complemented
9#10591454C212yesmaximal, complemented
10#10591130C211yesmaximal, characteristic, complemented
11#10591086C211yesmaximal, characteristic, complemented
12#83950—31nomaximal
13#78888—31nomaximal
14C2×C32×#41C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×C3×D12C2211yescharacteristic
17C22×#626—21no—
18#64155C2211yescharacteristic, complemented
19#64155C2211yescharacteristic, complemented
20#64147C2211yescharacteristic, complemented
21#64147C2211yescharacteristic, complemented
22#64146—21no—
23#64144—21no—
24C4×#638—21no—
25C4×#638—21no—
26#64135C2211yescharacteristic
27C3×#949—24no—
28C2×C3×#215C2212yescomplemented
29C2×C3×#213C2212yescomplemented
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×C3×#208C2211yescharacteristic
32C2×C3×#208C2211yescharacteristic
33C2×(C2×D3)⋊Dic3—21no—
34#63916—21no—
35#63916—21no—
36#63916C2212yes—
37#63916C2212yes—
38C2×#3712C2212yescomplemented
39#63818—24no—
40C2×#3710C2212yescomplemented
41C3×#835C2212yescomplemented
42C3×#832C2212yescomplemented
43#63575C2212yescomplemented
44#63573C2212yescomplemented
45#63563C2212yescomplemented
46#63563C2212yescomplemented
47C2×C3×AGL(1,ℤ/8)—31no—
48#5828—31no—
49#5828—31no—
50#5828—61no—
51C2×#949D311yescharacteristic, complemented
52C2×#938—31no—
53C2×D3×M16—31no—
54C2×D3×M16—31no—
55C2×#895—31no—
56C3×#417—31no—
57#5232D311yescharacteristic, complemented
58#5215—31no—
59#5174—32no—
60#5171—32no—
61#5159—32no—
62#5157—32no—
63#5131—31no—
64#5121—31no—
65#4964—31no—
66#4812—32no—
67#4807—32no—
68#4782—32no—
69#4775—32no—
70C23×C3⋊D3D411yescharacteristic
71C23×C3×D3—21no—
72C32×#41—22no—
73C32×#41—22no—
74C2×C32×Q8C2311yescharacteristic
75C2×C32×D4—21no—
76C2×C32×D4C2311yescharacteristic
77C22×C32×C4—21no—
78C22×C32×C4C2311yescharacteristic
79C2×#638—21no—
80C2×#638—21no—
81C22×C3⋊Dic3D411yescharacteristic
82C2×C4×C3⋊D3—22no—
83C2×C4×C3⋊D3—22no—
84C2×C4×C3⋊D3D411yescharacteristic
85C2×C4×C3⋊D3D411yescharacteristic
86C2×C4×C3⋊D3C2311yescharacteristic
87C2×C4×C3⋊D3C2311yescharacteristic
88C22×C3×Dic3—21no—
89C2×C3×D12—22no—
90C2×C3×D12—22no—
91C2×C3×D12—21no—
92C2×C3×D12C2312yes—
93C2×#626—22no—
94C2×#626—22no—
95C2×#626—44no—
96#3757—21no—
97#3757—21no—
98#3757—21no—
99#3752—21no—
100#3752—21no—
101C4⋊(C3⋊Dic3)C2311yescharacteristic
102C4⋊(C3⋊Dic3)C2311yescharacteristic
103#3750—21no—
104#3750—21no—
105C4×C3⋊Dic3—21no—
106C3×#215—24no—
107C3×#213—24no—
108C3×C4⋊Dic3—21no—
109C3×C4⋊Dic3C2312yes—
110C3×#208—22no—
111C3×#208D414yescomplemented
112C2×C3×C3⋊C8C2312yes—
113C2×C3×C3⋊C8C2312yes—
114(C2×D3)⋊Dic3—22no—
115(C2×D3)⋊Dic3—22no—
116#3712—24no—
117#3710—24no—
118#3055—91noSylow
119C2×C3×#41—21no—
120C2×C3×#41C2×D311yescharacteristic
121C2×C3×#41C2×D311yescharacteristic
122C22×C3×D4—31no—
123C22×#67—61no—
124C22×D12—61no—
125C22×D12C2×D311yescharacteristic
126C22×C4×D3—31no—
127C22×C4×D3—31no—
128C22×C4×D3—61no—
129C3×AGL(1,ℤ/8)—64no—
130C2×C3×SD16—32no—
131C2×C3×D8—32no—
132C2×C3×M16—31no—
133C2×C3×M16—31no—
134C2×C3×C4⋊C4—31no—
135C2×#217—61no—
136#949—24no—
137#946—31no—
138#946—31no—
139#946—31no—
140#946—31no—
141#946—61no—
142#946—61no—
143C2×#215C2×D312yescomplemented
144#938—31no—
145#938—31no—
146#938—31no—
147#938—31no—
148#938—32no—
149#938—32no—
150#938—61no—
151#938—61no—
152#938—61no—
153#938—61no—
154#937—61no—
155#937—61no—
156#937—62no—
157#935—61no—
158#935—61no—
159#935—62no—
160C2×#213C2×D312yescomplemented
161C4×#67—61no—
162C4×#67—61no—
163C4×#67—61no—
164C4×#67—61no—
165C4×#67—62no—
166C4×#67—62no—
167C2×(C2×D3)⋊C4—61no—
168#926—31no—
169#926—31no—
170#926—61no—
171C2×C4⋊Dic3C2×D311yescharacteristic
172C2×#208C2×D311yescharacteristic
173C2×#208C2×D311yescharacteristic
174D3×M16—64no—
175D3×M16—64no—
176C2×ΓL(1,𝔽25)—32no—
177C2×ΓL(1,𝔽25)—32no—
178C2×D3×C8—32no—
179C2×D3×C8—32no—
180#895—32no—
181#895—32no—
182#895—61no—
183#895—61no—
184C3×#103—32no—
185C3×#102—32no—
186#835C2×D312yescomplemented
187#832—32no—
188#832—32no—
189#832C2×D312yescomplemented
190#821—32no—
191#821—32no—
192#818—32no—
193#817—32no—
194#808—32no—
195#807—32no—
196C23×C32—21no—
197C23×C32C2×D411yescharacteristic
198C22×C3⋊D3—22no—
199C22×C3⋊D3—22no—
200C22×C3⋊D3—41no—
201C22×C3⋊D3C2×D411yescharacteristic
202C22×C3⋊D3C2×D411yescharacteristic
203C22×C3×D3—22no—
204C22×C3×D3—42no—
205C22×C3×D3—42no—
206C22×C3×D3—42no—
207C32×Q8—21no—
208C32×Q8—21no—
209C32×D4—21no—
210C32×D4—21no—
211C32×D4—42no—
212C2×C32×C4—21no—
213C2×C32×C4—42no—
214C2×C32×C4C2×D411yescharacteristic
215C2×C32×C4C2×D412yes—
216C2×C32×C4#4112yes—
217C2×C32×C4C2411yescharacteristic
218#638—42no—
219#638—42no—
220C2×C3⋊Dic3—21no—
221C2×C3⋊Dic3—21no—
222C2×C3⋊Dic3—22no—
223C2×C3⋊Dic3C2×D411yescharacteristic
224C2×C3⋊Dic3C2×D411yescharacteristic
225C4×C3⋊D3—22no—
226C4×C3⋊D3—22no—
227C4×C3⋊D3—21no—
228C4×C3⋊D3—21no—
229C4×C3⋊D3—21no—
230C4×C3⋊D3—21no—
231C2×C3×Dic3—22no—
232C2×C3×Dic3—42no—
233C3×D12—22no—
234C3×D12—22no—
235C3×D12—42no—
236#626—44no—
237#626—44no—
238C3×C3⋊C8—22no—
239C3×C3⋊C8C2×D414yescomplemented
240C2×AGL(1,ℤ/8)—31no—
241C22×M16—91no—
242#525—91no—
243C2×#121—91no—
244#469—92no—
245#468—92no—
246#466—92no—
247#465—92no—
248#428—91no—
249#418—91no—
250#417—31no—
251C24×C3—61no—
252C23×D3—21no—
253C23×D3—31no—
254C23×D3—31no—
255C23×D3—61no—
256C3×#41—22no—
257C3×#41—22no—
258C3×#41—22no—
259C3×#41—22no—
260C3×#41—42no—
261C3×#41—42no—
262C2×C3×Q8—21no—
263C2×C3×Q8C22×D311yescharacteristic
264C2×C3×Q8C22×D311yescharacteristic
265C2×C3×D4—22no—
266C2×C3×D4—21no—
267C2×C3×D4—21no—
268C2×C3×D4—21no—
269C2×C3×D4—32no—
270C2×C3×D4—62no—
271C2×C3×D4—62no—
272C2×C3×D4—61no—
273C2×C3×D4C22×D311yescharacteristic
274C2×C3×D4C22×D311yescharacteristic
275C22×C3×C4—22no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—61no—
280C22×C3×C4C22×D311yescharacteristic
281C22×C3×C4C22×D311yescharacteristic
282C2×#67—62no—
283C2×#67—62no—
284C2×#67—61no—
285C2×#67—61no—
286C2×#67—61no—
287C2×#67—61no—
288C2×#67—62no—
289C2×#67—62no—
290C2×#67—124no—
291C22×Dic3—21no—
292C22×Dic3—31no—
293C22×Dic3—31no—
294C22×Dic3—61no—
295C2×D12—22no—
296C2×D12—22no—
297C2×D12—21no—
298C2×D12—62no—
299C2×D12—62no—
300C2×D12—124no—
301C2×D12C22×D312yes—
302C2×C4×D3—31no—
303C2×C4×D3—31no—
304C2×C4×D3—31no—
305C2×C4×D3—31no—
306C2×C4×D3—31no—
307C2×C4×D3—31no—
308C2×C4×D3—31no—
309C2×C4×D3—31no—
310C2×C4×D3—61no—
311C2×C4×D3—61no—
312C2×C4×D3—61no—
313C2×C4×D3—61no—
314C2×C4×D3—62no—
315C2×C4×D3—62no—
316C2×C4×D3—62no—
317C2×C4×D3—62no—
318C2×C4×D3—122no—
319C2×C4×D3—122no—
320C3×SD16—64no—
321C3×D8—64no—
322C3×M16—34no—
323C3×M16—62no—
324C2×C3×C8—32no—
325C2×C3×C8—32no—
326C3×C4⋊C4—32no—
327C3×C4⋊C4—61no—
328#217—62no—
329#217—62no—
330#217—61no—
331#217—61no—
332#217—61no—
333#217—61no—
334#217—62no—
335#217—62no—
336#217—62no—
337#217—61no—
338#217—61no—
339#215—24no—
340#213—24no—
341(C2×D3)⋊C4—62no—
342(C2×D3)⋊C4—62no—
343(C2×D3)⋊C4—61no—
344(C2×D3)⋊C4—61no—
345(C2×D3)⋊C4—61no—
346(C2×D3)⋊C4—61no—
347(C2×D3)⋊C4—62no—
348(C2×D3)⋊C4—62no—
349C4⋊Dic3—21no—
350C4⋊Dic3—31no—
351C4⋊Dic3—31no—
352C4⋊Dic3—31no—
353C4⋊Dic3—31no—
354C4⋊Dic3—61no—
355C4⋊Dic3—61no—
356C4⋊Dic3C22×D312yes—
357Dic3⋊C4—61no—
358Dic3⋊C4—61no—
359Dic3⋊C4—61no—
360Dic3⋊C4—61no—
361Dic3⋊C4—62no—
362Dic3⋊C4—62no—
363C4×Dic3—62no—
364C4×Dic3—61no—
365C4×Dic3—61no—
366#208—22no—
367#208#6714yescomplemented
368C2×C3⋊C8C22×D312yes—
369C2×C3⋊C8C22×D312yes—
370ΓL(1,𝔽25)—64no—
371ΓL(1,𝔽25)—64no—
372D3×C8—64no—
373D3×C8—64no—
374C22×C32—21no—
375C22×C32—21no—
376C22×C32—41no—
377C22×C32—41no—
378C22×C32—41no—
379C22×C32#12112yes—
380C22×C32C22×D411yescharacteristic
381C2×C3⋊D3—21no—
382C2×C3⋊D3—21no—
383C2×C3⋊D3—21no—
384C2×C3⋊D3—21no—
385C2×C3⋊D3—21no—
386C2×C3⋊D3—44no—
387C2×C3⋊D3AGL(1,ℤ/8)12yescomplemented
388C2×C3×D3—42no—
389C2×C3×D3—42no—
390C2×C3×D3—42no—
391C2×C3×D3—84no—
392C32×C4—41no—
393C32×C4#12112yes—
394C32×C4C22×D411yescharacteristic
395C32×C4C2×#4111yescharacteristic
396C3⋊Dic3—21no—
397C3⋊Dic3—21no—
398C3⋊Dic3—41no—
399C3⋊Dic3—41no—
400C3×Dic3—42no—
401C2×#41D3211yescharacteristic
402C22×D4—31no—
403C22×D4—181no—
404C23×C4—91no—
405AGL(1,ℤ/8)—64no—
406C2×SD16—32no—
407C2×D8—32no—
408C2×M16—31no—
409C2×M16—31no—
410C2×M16—92no—
411C2×M16—184no—
412C22×C8—92no—
413#123—181no—
414C22⋊Q8—91no—
415C22⋊Q8—91no—
416#121—92no—
417#121—92no—
418#121—91no—
419#121—91no—
420#121—181no—
421#121—181no—
422#120—181no—
423C4×D4—181no—
424C4×D4—181no—
425#117—91no—
426C2×C4⋊C4—31no—
427C2×C22⋊C4—181no—
428#107—92no—
429#106—92no—
430#103—32no—
431#102—32no—
432#102—92no—
433#102—92no—
434C23×C3—22no—
435C23×C3—21no—
436C23×C3—21no—
437C23×C3—21no—
438C23×C3—62no—
439C23×C3—122no—
440C23×C3—122no—
441C23×C3—122no—
442C23×C3D3×D411yescharacteristic
443C23×C3D3×D411yescharacteristic
444C22×D3—22no—
445C22×D3—31no—
446C22×D3—31no—
447C22×D3—31no—
448C22×D3—31no—
449C22×D3—42no—
450C22×D3—42no—
451C22×D3—42no—
452C22×D3—61no—
453C22×D3—61no—
454C22×D3—62no—
455C22×D3—62no—
456C22×D3—62no—
457C22×D3—62no—
458C22×D3—122no—
459C22×D3—122no—
460C22×D3—121no—
461C22×D3—121no—
462C22×D3—122no—
463C3×Q8—21no—
464C3×Q8—21no—
465C3×Q8—21no—
466C3×Q8—21no—
467C3×Q8—41no—
468C3×Q8—41no—
469C3×D4—21no—
470C3×D4—21no—
471C3×D4—21no—
472C3×D4—21no—
473C3×D4—41no—
474C3×D4—41no—
475C3×D4—44no—
476C3×D4—42no—
477C3×D4—42no—
478C3×D4—62no—
479C3×D4—62no—
480C3×D4—122no—
481C2×C3×C4—22no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—21no—
488C2×C3×C4—44no—
489C2×C3×C4—42no—
490C2×C3×C4—42no—
491C2×C3×C4—62no—
492C2×C3×C4—122no—
493C2×C3×C4#23512yes—
494C2×C3×C4D3×D412yes—
495C2×C3×C4D3×D411yescharacteristic
496C2×C3×C4D3×D411yescharacteristic
497C2×C3×C4#23712yes—
498C2×C3×C4C2×#6712yes—
499C2×C3×C4C23×D311yescharacteristic
500C2×C3×C4C23×D311yescharacteristic
501#67—124no—
502#67—124no—
503#67—122no—
504#67—122no—
505#67—124no—
506#67—124no—
507#67—122no—
508#67—122no—
509C2×Dic3—22no—
510C2×Dic3—31no—
511C2×Dic3—31no—
512C2×Dic3—31no—
513C2×Dic3—31no—
514C2×Dic3—42no—
515C2×Dic3—61no—
516C2×Dic3—61no—
517C2×Dic3—62no—
518C2×Dic3—62no—
519C2×Dic3—62no—
520C2×Dic3—62no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—122no—
526D12—22no—
527D12—22no—
528D12—42no—
529D12—124no—
530D12—124no—
531C4×D3—62no—
532C4×D3—62no—
533C4×D3—62no—
534C4×D3—62no—
535C4×D3—61no—
536C4×D3—61no—
537C4×D3—61no—
538C4×D3—61no—
539C4×D3—61no—
540C4×D3—61no—
541C4×D3—61no—
542C4×D3—61no—
543C4×D3—121no—
544C4×D3—121no—
545C4×D3—121no—
546C4×D3—121no—
547C4×D3—122no—
548C4×D3—122no—
549C3×C8—34no—
550C3×C8—62no—
551C3⋊C8—22no—
552C3⋊C8C2×#6714yescomplemented
553C2×C32—22no—
554C2×C32—81no—
555C2×C32C2×#12111yescharacteristic
556C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
557C2×C32#57511yescharacteristic
558C3⋊D3—22no—
559C3⋊D3—41no—
560C3×D3—82no—
561C24—61no—
562C24—91no—
563#41—22no—
564#41—22no—
565C2×Q8C2×D3211yescharacteristic
566C2×D4—21no—
567C2×D4—32no—
568C2×D4—62no—
569C2×D4—62no—
570C2×D4—61no—
571C2×D4—182no—
572C2×D4—182no—
573C2×D4—181no—
574C2×D4—181no—
575C2×D4—364no—
576C2×D4C2×D3211yescharacteristic
577C22×C4—21no—
578C22×C4—61no—
579C22×C4—91no—
580C22×C4—91no—
581C22×C4—91no—
582C22×C4—91no—
583C22×C4—91no—
584C22×C4—182no—
585C22×C4—182no—
586C22×C4C2×D3211yescharacteristic
587SD16—64no—
588D8—64no—
589M16—34no—
590M16—62no—
591M16—184no—
592C2×C8—32no—
593C2×C8—32no—
594C2×C8—184no—
595C4⋊C4—32no—
596C4⋊C4—61no—
597C4⋊C4—91no—
598C4⋊C4—91no—
599C4⋊C4—181no—
600C4⋊C4—181no—
601C22⋊C4—181no—
602C22⋊C4—181no—
603C22⋊C4—182no—
604C22⋊C4—182no—
605C22⋊C4—181no—
606C22⋊C4—181no—
607C22⋊C4—181no—
608C42—181no—
609C22×C3—21no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—22no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—42no—
618C22×C3—42no—
619C22×C3—42no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—122no—
627C22×C3—122no—
628C22×C3—122no—
629C22×C3—244no—
630C22×C3#88412yes—
631C22×C3#93812yes—
632C22×C3C2×D3×D411yescharacteristic
633C22×C3C2×D3×D411yescharacteristic
634C2×D3—32no—
635C2×D3—32no—
636C2×D3—42no—
637C2×D3—42no—
638C2×D3—42no—
639C2×D3—62no—
640C2×D3—61no—
641C2×D3—61no—
642C2×D3—61no—
643C2×D3—61no—
644C2×D3—62no—
645C2×D3—61no—
646C2×D3—61no—
647C2×D3—61no—
648C2×D3—61no—
649C2×D3—61no—
650C2×D3—61no—
651C2×D3—84no—
652C2×D3—121no—
653C2×D3—121no—
654C2×D3—121no—
655C2×D3—121no—
656C2×D3—124no—
657C2×D3—124no—
658C2×D3—128no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—22no—
662C3×C4—42no—
663C3×C4—41no—
664C3×C4—41no—
665C3×C4—122no—
666C3×C4#88412yes—
667C3×C4#93812yes—
668C3×C4C2×#23511yescharacteristic
669C3×C4C2×D3×D411yescharacteristic
670C3×C4C2×#23711yescharacteristic
671C3×C4C22×#6711yescharacteristic
672Dic3—42no—
673Dic3—61no—
674Dic3—61no—
675Dic3—61no—
676Dic3—61no—
677Dic3—121no—
678Dic3—121no—
679Dic3—122no—
680Dic3—122no—
681Dic3—121no—
682Dic3—121no—
683Dic3—121no—
684Dic3—121no—
685C32#305511yescharacteristic, complemented, Sylow
686C23—21no—
687C23—62no—
688C23—91no—
689C23—91no—
690C23—122no—
691C23—122no—
692C23—122no—
693C23—182no—
694C23—182no—
695C23—361no—
696C23#381111yescharacteristic
697Q8—21no—
698Q8—21no—
699D4—21no—
700D4—21no—
701D4—42no—
702D4—62no—
703D4—62no—
704D4—122no—
705D4—364no—
706D4—364no—
707D4—362no—
708D4—362no—
709C2×C4—21no—
710C2×C4—42no—
711C2×C4—62no—
712C2×C4—91no—
713C2×C4—91no—
714C2×C4—122no—
715C2×C4—182no—
716C2×C4—181no—
717C2×C4—181no—
718C2×C4—181no—
719C2×C4—181no—
720C2×C4—182no—
721C2×C4—182no—
722C2×C4—181no—
723C2×C4—181no—
724C2×C4#380412yes—
725C2×C4D3×#6712yes—
726C2×C4#381111yescharacteristic
727C2×C4C22×D3211yescharacteristic
728C8—34no—
729C8—62no—
730C2×C3—22no—
731C2×C3—22no—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—42no—
736C2×C3—82no—
737C2×C3—81no—
738C2×C3—81no—
739C2×C3—242no—
740C2×C3C2×#88411yescharacteristic
741C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
742C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
743C2×C3#577311yescharacteristic
744C2×C3#577711yescharacteristic
745C2×C3C2×#93811yescharacteristic
746D3—62no—
747D3—62no—
748D3—82no—
749D3—122no—
750D3—122no—
751D3—121no—
752D3—121no—
753C22—21no—
754C22—21no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—92no—
759C22—122no—
760C22—122no—
761C22—122no—
762C22—181no—
763C22—181no—
764C22—181no—
765C22—181no—
766C22—181no—
767C22—244no—
768C22—364no—
769C22#6395812yes—
770C22C2×#381111yescharacteristic
771C4—41no—
772C4—122no—
773C4—181no—
774C4—181no—
775C4—361no—
776C4—361no—
777C4#6395812yes—
778C4C2×#380411yescharacteristic
779C4C2×D3×#6711yescharacteristic
780C3—21no—
781C3#7888811yescharacteristic, complemented
782C3#8395011yescharacteristic, complemented
783C2—22no—
784C2—81no—
785C2—182no—
786C2—242no—
787C2—361no—
788C2#1059545811yescharacteristic
789C2#1059547111yescharacteristic
790C2C2×#6395811yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3055
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #10596299C2semidirect
2. C2×C3×#949C2semidirect
3. C2×#63916C2semidirect
4. C2×#63818C2semidirect
5. C3×#5232C2semidirect
6. #10591591C2semidirect
7. #10591590C2semidirect
8. #10591455C2semidirect
9. #10591454C2semidirect
10. #10591130C2semidirect
11. #10591086C2semidirect
18. #64155C22semidirect
19. #64155C22semidirect
20. #64147C22semidirect
21. #64147C22semidirect
28. C2×C3×#215C22semidirect
29. C2×C3×#213C22semidirect
38. C2×#3712C22semidirect
40. C2×#3710C22semidirect
41. C3×#835C22semidirect
42. C3×#832C22semidirect
43. #63575C22semidirect
44. #63573C22semidirect
45. #63563C22semidirect
46. #63563C22semidirect
51. C2×#949D3semidirect
57. #5232D3semidirect
111. C3×#208D4semidirect
143. C2×#215C2×D3semidirect
160. C2×#213C2×D3semidirect
186. #835C2×D3semidirect
189. #832C2×D3semidirect
239. C3×C3⋊C8C2×D4semidirect
367. #208#67semidirect
387. C2×C3⋊D3AGL(1,ℤ/8)semidirect
552. C3⋊C8C2×#67semidirect
685. C32#3055semidirect
781. C3#78888semidirect
782. C3#83950semidirect

Maximal subgroups

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

subgroupindex
#105962992
C2×C3×#9492
C2×#639162
C2×#638182
C3×#52322
#105915912
#105915902
#105914552
#105914542
#105911302
#105910862
#839503
#788883