Finite Group Databasebeta

← #11867177

Subgroups — #11867177

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#10595995C211yesmaximal, characteristic, complemented
2C2×#63916C211yesmaximal, characteristic, complemented
3C2×#63830C211yesmaximal, characteristic, complemented
4C2×#63818C211yesmaximal, characteristic, complemented
5C3×#5001C211yesmaximal, characteristic, complemented
6C3×#4995C211yesmaximal, characteristic, complemented
7#10591106C211yesmaximal, characteristic, complemented
8#10590509C212yesmaximal, complemented
9#10590508C212yesmaximal, complemented
10#10590507C212yesmaximal, complemented
11#10590506C212yesmaximal, complemented
12#79211—31nomaximal
13#78930—31nomaximal
14C2×#3828C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×C3×D12C2211yescharacteristic
17C22×#626—21no—
18C32×#117C2211yescharacteristic
19#64106C2211yescharacteristic, complemented
20#64106C2211yescharacteristic, complemented
21#64104C2211yescharacteristic, complemented
22#64104C2211yescharacteristic, complemented
23#64095—21no—
24#64091—21no—
25C4×C4⋊(C3⋊D3)—21no—
26C4×C4⋊(C3⋊D3)—21no—
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×#208C2211yescharacteristic
29C2×C3×#208C2211yescharacteristic
30C2×(C2×D3)⋊Dic3—21no—
31#63916—21no—
32#63916—21no—
33#63916C2212yes—
34#63916C2212yes—
35#63830—24no—
36C2×#3716C2212yescomplemented
37C2×#3714C2212yescomplemented
38C2×#3712C2212yescomplemented
39#63818—24no—
40C2×#3710C2212yescomplemented
41C3×#809C2212yescomplemented
42C3×#809C2212yescomplemented
43C3×#808C2212yescomplemented
44C3×#807C2212yescomplemented
45#63567C2212yescomplemented
46#63564C2212yescomplemented
47C2×#938—31no—
48C2×#932—31no—
49C2×#908—31no—
50C2×D3×M16—31no—
51C2×D3×M16—31no—
52#5524—31no—
53#5524—31no—
54#5524—61no—
55C2×#895—31no—
56C3×#428—31no—
57C3×#418—31no—
58#5133—31no—
59#5001D311yescharacteristic, complemented
60#4995D311yescharacteristic, complemented
61#4966—31no—
62#4886—32no—
63#4883—32no—
64#4865—32no—
65#4864—32no—
66#4782—32no—
67#4780—32no—
68#4778—32no—
69#4775—32no—
70C23×C3⋊D3D411yescharacteristic
71C23×C3×D3—21no—
72C22×C32×C4C2311yescharacteristic
73C2×#638—21no—
74C22×C3⋊Dic3D411yescharacteristic
75#3828—22no—
76#3828—22no—
77C2×C4⋊(C3⋊D3)—21no—
78C2×C4⋊(C3⋊D3)—21no—
79C2×C4⋊(C3⋊D3)C2311yescharacteristic
80C2×C4×C3⋊D3—22no—
81C2×C4×C3⋊D3—22no—
82C2×C4×C3⋊D3—21no—
83C2×C4×C3⋊D3D411yescharacteristic
84C2×C4×C3⋊D3D411yescharacteristic
85C2×C4×C3⋊D3C2311yescharacteristic
86C2×C4×C3⋊D3C2311yescharacteristic
87C2×#634C2311yescharacteristic
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—
96C32×C4⋊C4C2311yescharacteristic
97C32×C4⋊C4C2311yescharacteristic
98C32×C22⋊C4—21no—
99C32×C42—21no—
100#3752—21no—
101#3752—21no—
102#3752—21no—
103#3752—21no—
104C4⋊(C3⋊Dic3)—21no—
105C4⋊(C3⋊Dic3)—21no—
106C3×C4⋊Dic3—21no—
107C3×C4⋊Dic3C2312yes—
108C3×#208—22no—
109C3×#208D414yescomplemented
110C2×C3×C3⋊C8C2312yes—
111C2×C3×C3⋊C8C2312yes—
112(C2×D3)⋊Dic3—22no—
113(C2×D3)⋊Dic3—22no—
114#3716—24no—
115#3714—24no—
116#3712—24no—
117#3710—24no—
118#3055—91noSylow
119C22×C3×D4—31no—
120C22×#67—61no—
121C2×#235—31no—
122C2×#235—31no—
123C2×#235—61no—
124C22×D12—61no—
125C22×D12C2×D311yescharacteristic
126C22×C4×D3—31no—
127C22×C4×D3—31no—
128C22×C4×D3—61no—
129C2×C3×M16—31no—
130C2×C3×M16—31no—
131C3×#117—21no—
132C3×#117C2×D311yescharacteristic
133C3×#117C2×D311yescharacteristic
134C2×C3×C4⋊C4—31no—
135C2×#217—61no—
136#938—32no—
137#938—32no—
138#938—61no—
139#938—61no—
140C2×#214—32no—
141#932—64no—
142C2×#213—32no—
143C2×(C2×D3)⋊C4—61no—
144C2×C4⋊Dic3C2×D311yescharacteristic
145C2×#208C2×D311yescharacteristic
146C2×#208C2×D311yescharacteristic
147#908—64no—
148D3×M16—64no—
149D3×M16—64no—
150C2×D24—32no—
151C2×#204—32no—
152C2×ΓL(1,𝔽25)—32no—
153C2×ΓL(1,𝔽25)—32no—
154C2×D3×C8—32no—
155C2×D3×C8—32no—
156#897—31no—
157#897—31no—
158#897—31no—
159#897—31no—
160#897—61no—
161#897—61no—
162#895—32no—
163#895—32no—
164#895—31no—
165#895—31no—
166#895—31no—
167#895—31no—
168#895—61no—
169#895—61no—
170#895—61no—
171#895—61no—
172#886—61no—
173#886—61no—
174#886—62no—
175#882—61no—
176#882—61no—
177#882—62no—
178C4×D12—61no—
179C4×D12—61no—
180C4×D12—61no—
181C4×D12—61no—
182C4×D12—62no—
183C4×D12—62no—
184C3×#107—32no—
185C3×#106—32no—
186C3×#102—32no—
187C3×#102—32no—
188#821—32no—
189#816—32no—
190#810—32no—
191#809—32no—
192#809C2×D312yescomplemented
193#809C2×D312yescomplemented
194#808C2×D312yescomplemented
195#807C2×D312yescomplemented
196C23×C32C2×D411yescharacteristic
197C22×C3⋊D3—21no—
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—
207C2×C32×C4—21no—
208C2×C32×C4—21no—
209C2×C32×C4C2×D412yes—
210C2×C32×C4C2×D411yescharacteristic
211C2×C32×C4#4112yes—
212C2×C32×C4C2411yescharacteristic
213#638—42no—
214C2×C3⋊Dic3—21no—
215C2×C3⋊Dic3—22no—
216C2×C3⋊Dic3C2×D411yescharacteristic
217C2×C3⋊Dic3C2×D411yescharacteristic
218C4⋊(C3⋊D3)—21no—
219C4⋊(C3⋊D3)—21no—
220C4⋊(C3⋊D3)—42no—
221C4⋊(C3⋊D3)—42no—
222C4×C3⋊D3—22no—
223C4×C3⋊D3—22no—
224C4×C3⋊D3—21no—
225C4×C3⋊D3—21no—
226C4×C3⋊D3—21no—
227C4×C3⋊D3—21no—
228C4×C3⋊D3—42no—
229#634—21no—
230#634—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)—91no—
241C22×M16—91no—
242#525—91no—
243C2×#121—91no—
244#469—92no—
245#468—92no—
246#466—92no—
247#465—92no—
248#428—31no—
249#418—31no—
250#417—91no—
251C24×C3—61no—
252C23×D3—21no—
253C23×D3—31no—
254C23×D3—31no—
255C23×D3—61no—
256C2×C3×D4—32no—
257C2×C3×D4—62no—
258C2×C3×D4—61no—
259C2×C3×D4—62no—
260C22×C3×C4—21no—
261C22×C3×C4—61no—
262C22×C3×C4C22×D311yescharacteristic
263C22×C3×C4C22×D311yescharacteristic
264C2×#67—62no—
265C2×#67—62no—
266C2×#67—62no—
267C2×#67—61no—
268C2×#67—61no—
269C2×#67—124no—
270C22×Dic3—21no—
271C22×Dic3—31no—
272C22×Dic3—31no—
273C22×Dic3—61no—
274#235—62no—
275#235—62no—
276#235—62no—
277#235—62no—
278#235—122no—
279#235—122no—
280C2×D12—22no—
281C2×D12—22no—
282C2×D12—21no—
283C2×D12—31no—
284C2×D12—31no—
285C2×D12—61no—
286C2×D12—61no—
287C2×D12—61no—
288C2×D12—61no—
289C2×D12—61no—
290C2×D12—62no—
291C2×D12—62no—
292C2×D12—62no—
293C2×D12—62no—
294C2×D12—124no—
295C2×D12C22×D312yes—
296C2×C4×D3—31no—
297C2×C4×D3—31no—
298C2×C4×D3—31no—
299C2×C4×D3—31no—
300C2×C4×D3—31no—
301C2×C4×D3—31no—
302C2×C4×D3—31no—
303C2×C4×D3—31no—
304C2×C4×D3—61no—
305C2×C4×D3—61no—
306C2×C4×D3—61no—
307C2×C4×D3—61no—
308C2×C4×D3—62no—
309C2×C4×D3—62no—
310C2×C4×D3—62no—
311C2×C4×D3—62no—
312C2×C4×D3—62no—
313C2×C4×D3—61no—
314C2×C4×D3—61no—
315C2×C4×D3—122no—
316C2×C4×D3—122no—
317C2×Dic6—31no—
318C2×Dic6—31no—
319C2×Dic6—61no—
320C3×M16—34no—
321C3×M16—62no—
322C2×C3×C8—32no—
323C2×C3×C8—32no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—21no—
326C3×C4⋊C4—32no—
327C3×C4⋊C4—61no—
328C3×C4⋊C4C22×D311yescharacteristic
329C3×C4⋊C4C22×D311yescharacteristic
330C3×C4⋊C4C22×D311yescharacteristic
331C3×C4⋊C4C22×D311yescharacteristic
332C3×C22⋊C4—22no—
333C3×C22⋊C4—21no—
334C3×C22⋊C4—21no—
335C3×C42—22no—
336C3×C42—21no—
337C3×C42—21no—
338#217—62no—
339#217—62no—
340#214—64no—
341#213—64no—
342(C2×D3)⋊C4—61no—
343(C2×D3)⋊C4—61no—
344(C2×D3)⋊C4—61no—
345(C2×D3)⋊C4—61no—
346(C2×D3)⋊C4—62no—
347(C2×D3)⋊C4—62no—
348(C2×D3)⋊C4—61no—
349(C2×D3)⋊C4—61no—
350(C2×D3)⋊C4—61no—
351(C2×D3)⋊C4—61no—
352(C2×D3)⋊C4—62no—
353(C2×D3)⋊C4—62no—
354(C2×D3)⋊C4—62no—
355(C2×D3)⋊C4—62no—
356C4⋊Dic3—21no—
357C4⋊Dic3—61no—
358C4⋊Dic3—61no—
359C4⋊Dic3—61no—
360C4⋊Dic3—61no—
361C4⋊Dic3—62no—
362C4⋊Dic3—62no—
363C4⋊Dic3C22×D312yes—
364#208—22no—
365#208D1214yescomplemented
366C2×C3⋊C8C22×D312yes—
367C2×C3⋊C8C22×D312yes—
368D24—64no—
369#204—64no—
370ΓL(1,𝔽25)—64no—
371ΓL(1,𝔽25)—64no—
372D3×C8—64no—
373D3×C8—64no—
374C22×C32—21no—
375C22×C32—21no—
376C22×C32#12112yes—
377C22×C32C22×D411yescharacteristic
378C2×C3⋊D3—21no—
379C2×C3⋊D3—21no—
380C2×C3⋊D3—21no—
381C2×C3⋊D3—21no—
382C2×C3⋊D3—21no—
383C2×C3⋊D3—44no—
384C2×C3⋊D3—41no—
385C2×C3⋊D3—41no—
386C2×C3⋊D3—41no—
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—41no—
394C32×C4#12112yes—
395C32×C4C22×D411yescharacteristic
396C32×C4C2×#4111yescharacteristic
397C3⋊Dic3—21no—
398C3⋊Dic3—21no—
399C3⋊Dic3—41no—
400C3×Dic3—42no—
401C2×#41—91no—
402C22×D4—31no—
403C22×D4—181no—
404C23×C4—91no—
405AGL(1,ℤ/8)—184no—
406C2×SD16—92no—
407C2×D8—92no—
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#117D3211yescharacteristic
426C2×C4⋊C4—31no—
427C2×C22⋊C4—181no—
428#107—32no—
429#106—32no—
430#103—92no—
431#102—32no—
432#102—32no—
433#102—92no—
434C23×C3—21no—
435C23×C3—62no—
436C23×C3—122no—
437C23×C3—122no—
438C23×C3—122no—
439C23×C3D3×D411yescharacteristic
440C23×C3D3×D411yescharacteristic
441C22×D3—22no—
442C22×D3—31no—
443C22×D3—31no—
444C22×D3—31no—
445C22×D3—31no—
446C22×D3—42no—
447C22×D3—42no—
448C22×D3—42no—
449C22×D3—61no—
450C22×D3—61no—
451C22×D3—62no—
452C22×D3—62no—
453C22×D3—62no—
454C22×D3—62no—
455C22×D3—62no—
456C22×D3—61no—
457C22×D3—61no—
458C22×D3—122no—
459C22×D3—122no—
460C22×D3—121no—
461C22×D3—121no—
462C22×D3—122no—
463C3×D4—62no—
464C3×D4—62no—
465C3×D4—122no—
466C2×C3×C4—22no—
467C2×C3×C4—22no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—22no—
474C2×C3×C4—22no—
475C2×C3×C4—21no—
476C2×C3×C4—62no—
477C2×C3×C4—122no—
478C2×C3×C4C2×D1212yes—
479C2×C3×C4#23512yes—
480C2×C3×C4D3×D412yes—
481C2×C3×C4D3×D411yescharacteristic
482C2×C3×C4D3×D411yescharacteristic
483C2×C3×C4#23912yes—
484C2×C3×C4C23×D311yescharacteristic
485C2×C3×C4C23×D311yescharacteristic
486#67—124no—
487#67—124no—
488#67—124no—
489#67—122no—
490#67—122no—
491C2×Dic3—22no—
492C2×Dic3—31no—
493C2×Dic3—31no—
494C2×Dic3—31no—
495C2×Dic3—31no—
496C2×Dic3—42no—
497C2×Dic3—61no—
498C2×Dic3—61no—
499C2×Dic3—62no—
500C2×Dic3—62no—
501C2×Dic3—62no—
502C2×Dic3—61no—
503C2×Dic3—61no—
504C2×Dic3—122no—
505D12—22no—
506D12—22no—
507D12—42no—
508D12—61no—
509D12—61no—
510D12—61no—
511D12—61no—
512D12—121no—
513D12—121no—
514D12—122no—
515D12—122no—
516D12—124no—
517D12—124no—
518D12—122no—
519D12—122no—
520D12—124no—
521D12—124no—
522C4×D3—62no—
523C4×D3—62no—
524C4×D3—62no—
525C4×D3—62no—
526C4×D3—61no—
527C4×D3—61no—
528C4×D3—61no—
529C4×D3—61no—
530C4×D3—61no—
531C4×D3—61no—
532C4×D3—61no—
533C4×D3—61no—
534C4×D3—121no—
535C4×D3—121no—
536C4×D3—121no—
537C4×D3—121no—
538C4×D3—122no—
539C4×D3—122no—
540C4×D3—124no—
541C4×D3—122no—
542C4×D3—122no—
543Dic6—61no—
544Dic6—61no—
545Dic6—61no—
546Dic6—61no—
547Dic6—121no—
548Dic6—121no—
549C3×C8—34no—
550C3×C8—62no—
551C3⋊C8—22no—
552C3⋊C8C2×D1214yescomplemented
553C2×C32—22no—
554C2×C32C2×#12111yescharacteristic
555C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
556C2×C32#57511yescharacteristic
557C3⋊D3—22no—
558C3⋊D3—41no—
559C3⋊D3—81no—
560C3×D3—82no—
561C24—61no—
562C24—91no—
563#41—182no—
564#41—182no—
565C2×Q8—91no—
566C2×D4—32no—
567C2×D4—62no—
568C2×D4—62no—
569C2×D4—61no—
570C2×D4—91no—
571C2×D4—181no—
572C2×D4—181no—
573C2×D4—182no—
574C2×D4—182no—
575C2×D4—181no—
576C2×D4—364no—
577C22×C4—61no—
578C22×C4—91no—
579C22×C4—91no—
580C22×C4—91no—
581C22×C4—91no—
582C22×C4—91no—
583C22×C4—182no—
584C22×C4—182no—
585C22×C4—181no—
586C22×C4C2×D3211yescharacteristic
587SD16—184no—
588D8—184no—
589M16—34no—
590M16—62no—
591M16—184no—
592C2×C8—32no—
593C2×C8—32no—
594C2×C8—184no—
595C4⋊C4—32no—
596C4⋊C4—61no—
597C4⋊C4—181no—
598C4⋊C4—181no—
599C4⋊C4C2×D3211yescharacteristic
600C4⋊C4C2×D3211yescharacteristic
601C22⋊C4—21no—
602C22⋊C4—181no—
603C22⋊C4—181no—
604C22⋊C4—181no—
605C22⋊C4—181no—
606C22⋊C4—182no—
607C22⋊C4—182no—
608C42—21no—
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—122no—
618C22×C3—122no—
619C22×C3—122no—
620C22×C3—244no—
621C22×C3#88412yes—
622C22×C3#89512yes—
623C22×C3C2×D3×D411yescharacteristic
624C22×C3C2×D3×D411yescharacteristic
625C2×D3—32no—
626C2×D3—32no—
627C2×D3—42no—
628C2×D3—42no—
629C2×D3—42no—
630C2×D3—62no—
631C2×D3—61no—
632C2×D3—61no—
633C2×D3—61no—
634C2×D3—61no—
635C2×D3—62no—
636C2×D3—61no—
637C2×D3—61no—
638C2×D3—61no—
639C2×D3—61no—
640C2×D3—61no—
641C2×D3—61no—
642C2×D3—84no—
643C2×D3—121no—
644C2×D3—121no—
645C2×D3—121no—
646C2×D3—121no—
647C2×D3—124no—
648C2×D3—124no—
649C2×D3—128no—
650C2×D3—122no—
651C2×D3—122no—
652C2×D3—122no—
653C2×D3—121no—
654C2×D3—121no—
655C2×D3—121no—
656C2×D3—121no—
657C2×D3—121no—
658C2×D3—121no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—22no—
662C3×C4—42no—
663C3×C4—42no—
664C3×C4—41no—
665C3×C4—41no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—122no—
669C3×C4#88412yes—
670C3×C4#89512yes—
671C3×C4C22×D1211yescharacteristic
672C3×C4C2×#23511yescharacteristic
673C3×C4C2×D3×D411yescharacteristic
674C3×C4C2×#23911yescharacteristic
675Dic3—42no—
676Dic3—61no—
677Dic3—61no—
678Dic3—61no—
679Dic3—61no—
680Dic3—121no—
681Dic3—121no—
682Dic3—122no—
683Dic3—121no—
684Dic3—121no—
685C32#305511yescharacteristic, complemented, Sylow
686C23—62no—
687C23—91no—
688C23—91no—
689C23—122no—
690C23—122no—
691C23—122no—
692C23—182no—
693C23—182no—
694C23—181no—
695C23—361no—
696C23#381111yescharacteristic
697Q8—181no—
698Q8—181no—
699D4—62no—
700D4—62no—
701D4—122no—
702D4—181no—
703D4—181no—
704D4—362no—
705D4—362no—
706D4—364no—
707D4—364no—
708D4—362no—
709C2×C4—21no—
710C2×C4—21no—
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—362no—
724C2×C4#379912yes—
725C2×C4D3×D1212yes—
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—242no—
737C2×C3C2×#88411yescharacteristic
738C2×C3C2×#89511yescharacteristic
739C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
740C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
741C2×C3#577311yescharacteristic
742C2×C3#577711yescharacteristic
743D3—62no—
744D3—62no—
745D3—82no—
746D3—122no—
747D3—122no—
748D3—121no—
749D3—121no—
750D3—242no—
751D3—241no—
752D3—241no—
753C22—21no—
754C22—21no—
755C22—92no—
756C22—122no—
757C22—122no—
758C22—122no—
759C22—181no—
760C22—181no—
761C22—181no—
762C22—181no—
763C22—181no—
764C22—244no—
765C22—364no—
766C22—361no—
767C22—361no—
768C22—361no—
769C22#6391012yes—
770C22C2×#381111yescharacteristic
771C4—41no—
772C4—41no—
773C4—122no—
774C4—181no—
775C4—181no—
776C4—361no—
777C4#6391012yes—
778C4C2×#379911yescharacteristic
779C4C2×D3×D1211yescharacteristic
780C3—21no—
781C3#7893011yescharacteristic, complemented
782C3#7921111yescharacteristic, complemented
783C2—22no—
784C2—182no—
785C2—242no—
786C2—361no—
787C2—721no—
788C2C2×#6391011yescharacteristic
789C2#1059545811yescharacteristic
790C2#1059547111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
hypercenter#117D32
hypocenterC32#3055
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10595995C2semidirect
2. C2×#63916C2semidirect
3. C2×#63830C2semidirect
4. C2×#63818C2semidirect
5. C3×#5001C2semidirect
6. C3×#4995C2semidirect
7. #10591106C2semidirect
8. #10590509C2semidirect
9. #10590508C2semidirect
10. #10590507C2semidirect
11. #10590506C2semidirect
19. #64106C22semidirect
20. #64106C22semidirect
21. #64104C22semidirect
22. #64104C22semidirect
36. C2×#3716C22semidirect
37. C2×#3714C22semidirect
38. C2×#3712C22semidirect
40. C2×#3710C22semidirect
41. C3×#809C22semidirect
42. C3×#809C22semidirect
43. C3×#808C22semidirect
44. C3×#807C22semidirect
45. #63567C22semidirect
46. #63564C22semidirect
59. #5001D3semidirect
60. #4995D3semidirect
109. C3×#208D4semidirect
192. #809C2×D3semidirect
193. #809C2×D3semidirect
194. #808C2×D3semidirect
195. #807C2×D3semidirect
239. C3×C3⋊C8C2×D4semidirect
365. #208D12semidirect
387. C2×C3⋊D3AGL(1,ℤ/8)semidirect
552. C3⋊C8C2×D12semidirect
685. C32#3055semidirect
781. C3#78930semidirect
782. C3#79211semidirect

Maximal subgroups

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

subgroupindex
#105959952
C2×#639162
C2×#638302
C2×#638182
C3×#50012
C3×#49952
#105911062
#105905092
#105905082
#105905072
#105905062
#792113
#789303