Finite Group Databasebeta

← #11864201

Subgroups — #11864201

Order 1152.

1669 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3796C211yesmaximal, characteristic
2C3⋊D3×C22⋊Q8C211yesmaximal, characteristic, complemented
3C2×#63951C212yesmaximal, complemented
4C3×#5050C211yesmaximal, characteristic, complemented
5C3×#5046C211yesmaximal, characteristic, complemented
6#10591656C212yesmaximal, complemented
7#10591186C211yesmaximal, characteristic, complemented
8#10591172C211yesmaximal, characteristic, complemented
9#10591159C211yesmaximal, characteristic, complemented
10#10590618C212yesmaximal, complemented
11#10590612C212yesmaximal, complemented
12#80184—31nomaximal
13#80147—31nomaximal
14C2×Q8×C3⋊D3C2211yescharacteristic, complemented
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×C3×D12C2211yescharacteristic
17C22×C3×Dic6C2211yescharacteristic
18C22×#626—21no—
19C22×D3×Dic3—21no—
20C2×#3796—21no—
21C2×#3796—21no—
22C2×#3796—28no—
23C2×#3796C2212yes—
24C2×#3796C2212yes—
25C32×C22⋊Q8C2211yescharacteristic
26#64155C2211yescharacteristic, complemented
27#64133C2211yescharacteristic
28#64106C2211yescharacteristic, complemented
29#64105—21no—
30C4⋊C4×C3⋊D3—21no—
31C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
32C22⋊C4×C3⋊D3—21no—
33#64087—21no—
34C2×C3×#216C2212yescomplemented
35C2×C3×#215C2212yescomplemented
36#63951—28no—
37C2×#3719C2212yescomplemented
38C2×#3716C2212yescomplemented
39C2×#3712C2212yescomplemented
40C3×#830C2211yescharacteristic
41C3×#830C2211yescharacteristic
42C3×#810C2212yescomplemented
43C3×#809C2212yescomplemented
44#63566C2212yescomplemented
45#63563C2212yescomplemented
46#63557C2212yescomplemented
47C22×#239—31no—
48C22×#237—31no—
49C2×#918—32no—
50C2×#915—32no—
51D3×C22⋊Q8—31no—
52D3×C22⋊Q8—31no—
53D3×C22⋊Q8—61no—
54C3×#451—31no—
55C3×#450—31no—
56#5228—31no—
57#5218—31no—
58#5187—32no—
59#5173—32no—
60#5050D311yescharacteristic, complemented
61#5046D311yescharacteristic, complemented
62#4808—32no—
63#4803—32no—
64#4783—32no—
65#4771—32no—
66#4739—31no—
67#4731—31no—
68#4726—31no—
69#4726—31no—
70C23×C3⋊D3D411yescharacteristic
71C23×C3×D3—21no—
72C2×C32×Q8C2311yescharacteristic
73C22×C32×C4C2311yescharacteristic
74C22×C3⋊Dic3D411yescharacteristic
75Q8×C3⋊D3—24no—
76C2×C4×C3⋊D3—24no—
77C2×C4×C3⋊D3—21no—
78C2×C4×C3⋊D3—21no—
79C2×C4×C3⋊D3D411yescharacteristic
80C2×C4×C3⋊D3D411yescharacteristic
81C2×C4×C3⋊D3C2311yescharacteristic
82C2×C4×C3⋊D3C2311yescharacteristic
83C2×#634—21no—
84C2×#634C2311yescharacteristic
85C22×C3×Dic3—21no—
86C2×C3×D12—21no—
87C2×C3×D12—24no—
88C2×C3×D12C2312yes—
89C2×C3×Dic6—21no—
90C2×C3×Dic6—24no—
91C2×C3×Dic6C2312yes—
92C2×#626—28no—
93C2×#626—22no—
94C2×#626—22no—
95C2×D3×Dic3—28no—
96C2×D3×Dic3—22no—
97C2×D3×Dic3—22no—
98#3796—28no—
99#3796—28no—
100#3796—24no—
101#3796—24no—
102#3796—24no—
103#3796D418yes—
104C32×C4⋊C4—21no—
105C32×C4⋊C4C2311yescharacteristic
106C32×C22⋊C4—21no—
107#3757—21no—
108#3752—21no—
109#3752—21no—
110C4⋊(C3⋊Dic3)—21no—
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112#3750—21no—
113#3750—21no—
114#3750—21no—
115C3×#216—24no—
116C3×#215—24no—
117C2×C3×C3⋊C8C2312yes—
118C2×C3×C3⋊C8C2312yes—
119#3719—24no—
120#3716—24no—
121#3712—24no—
122#3007—91noSylow
123C22×C3×Q8—31no—
124C22×C3×D4—31no—
125C22×#67—61no—
126C23×Dic3—61no—
127C2×#239—32no—
128C2×#239—32no—
129C2×#239—61no—
130C2×#239—61no—
131C2×#239—68no—
132C2×D3×Q8—31no—
133C2×D3×Q8—31no—
134C2×D3×Q8—61no—
135C2×#237—32no—
136C2×#237—32no—
137C2×#237—61no—
138C2×#237—61no—
139C2×#237—68no—
140C22×D12—61no—
141C22×D12C2×D311yescharacteristic
142C22×C4×D3—31no—
143C22×C4×D3—31no—
144C22×C4×D3—61no—
145C22×C4×D3—61no—
146C22×Dic6C2×D311yescharacteristic
147C2×C3×Q16—32no—
148C2×C3×SD16—32no—
149C3×C22⋊Q8—21no—
150C3×C22⋊Q8C2×D311yescharacteristic
151C3×C22⋊Q8C2×D311yescharacteristic
152#946—31no—
153#946—31no—
154#946—61no—
155C2×#216—32no—
156C2×#216C2×D312yescomplemented
157C2×#215C2×D312yescomplemented
158C2×#214—32no—
159#924—31no—
160#924—31no—
161#924—61no—
162#918—68no—
163#915—68no—
164C2×Dic12—32no—
165C2×#204—32no—
166C2×ΓL(1,𝔽25)—32no—
167C2×ΓL(1,𝔽25)—32no—
168#897—31no—
169#897—31no—
170#897—61no—
171#896—61no—
172#896—61no—
173#896—62no—
174D3×C4⋊C4—31no—
175D3×C4⋊C4—31no—
176D3×C4⋊C4—61no—
177D3×C4⋊C4—61no—
178D3×C4⋊C4—61no—
179D3×C4⋊C4—62no—
180D3×C22⋊C4—61no—
181D3×C22⋊C4—61no—
182D3×C22⋊C4—62no—
183#878—61no—
184#878—61no—
185#878—62no—
186C3×#103—32no—
187C3×#102—32no—
188C3×C22⋊C8—31no—
189C3×C22⋊C8—31no—
190#835—32no—
191#832—32no—
192#830C2×D311yescharacteristic
193#830C2×D311yescharacteristic
194#821—32no—
195(C2×D3)⋊C8—32no—
196(C2×D3)⋊C8—32no—
197#816—32no—
198#810C2×D312yescomplemented
199#809C2×D312yescomplemented
200C23×C32C2×D411yescharacteristic
201C22×C3⋊D3—22no—
202C22×C3⋊D3—22no—
203C22×C3⋊D3—41no—
204C22×C3⋊D3C2×D411yescharacteristic
205C22×C3⋊D3C2×D411yescharacteristic
206C22×C3×D3—24no—
207C22×C3×D3—22no—
208C22×C3×D3—42no—
209C22×C3×D3—42no—
210C32×Q8—22no—
211C2×C32×C4—21no—
212C2×C32×C4—21no—
213C2×C32×C4—22no—
214C2×C32×C4C2×D411yescharacteristic
215C2×C32×C4C2411yescharacteristic
216C2×C3⋊Dic3—21no—
217C2×C3⋊Dic3—21no—
218C2×C3⋊Dic3—22no—
219C2×C3⋊Dic3C2×D411yescharacteristic
220C2×C3⋊Dic3C2×D411yescharacteristic
221C4×C3⋊D3—22no—
222C4×C3⋊D3—22no—
223C4×C3⋊D3—22no—
224C4×C3⋊D3—42no—
225C4×C3⋊D3—42no—
226C4×C3⋊D3C2×D414yes—
227#634—22no—
228#634—42no—
229C2×C3×Dic3—24no—
230C2×C3×Dic3—22no—
231C3×D12—24no—
232C3×D12—22no—
233C3×D12C2×D414yes—
234C3×Dic6—24no—
235C3×Dic6—22no—
236C3×Dic6C2×D414yes—
237#626—28no—
238#626—28no—
239D3×Dic3—28no—
240D3×Dic3—28no—
241C3×C3⋊C8—22no—
242C3×C3⋊C8—22no—
243C22×#41—91no—
244C2×#137—92no—
245C2×C22⋊Q8—91no—
246#452—92no—
247#452—92no—
248#451—31no—
249#451—91no—
250#450—31no—
251#450—91no—
252#417—92no—
253#407—91no—
254C24×C3—61no—
255C23×D3—21no—
256C23×D3—31no—
257C23×D3—31no—
258C23×D3—61no—
259C2×C3×Q8—21no—
260C2×C3×Q8—32no—
261C2×C3×Q8—64no—
262C2×C3×Q8—61no—
263C2×C3×Q8C22×D311yescharacteristic
264C2×C3×Q8C22×D311yescharacteristic
265C2×C3×D4—32no—
266C2×C3×D4—64no—
267C2×C3×D4—61no—
268C22×C3×C4—21no—
269C22×C3×C4—61no—
270C22×C3×C4C22×D311yescharacteristic
271C22×C3×C4C22×D311yescharacteristic
272C2×#67—62no—
273C2×#67—62no—
274C2×#67—68no—
275C22×Dic3—21no—
276C22×Dic3—31no—
277C22×Dic3—31no—
278C22×Dic3—61no—
279C22×Dic3—62no—
280C22×Dic3—62no—
281C22×Dic3—68no—
282#239—38no—
283#239—64no—
284#239—64no—
285#239—68no—
286#239—68no—
287#239—64no—
288D3×Q8—64no—
289D3×Q8—64no—
290D3×Q8—124no—
291#237—38no—
292#237—64no—
293#237—64no—
294#237—68no—
295#237—68no—
296#237—64no—
297C2×D12—21no—
298C2×D12—24no—
299C2×D12—62no—
300C2×D12—62no—
301C2×D12—68no—
302C2×D12C22×D312yes—
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—31no—
311C2×C4×D3—61no—
312C2×C4×D3—61no—
313C2×C4×D3—61no—
314C2×C4×D3—61no—
315C2×C4×D3—64no—
316C2×C4×D3—64no—
317C2×C4×D3—62no—
318C2×C4×D3—62no—
319C2×C4×D3—68no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—62no—
325C2×C4×D3—62no—
326C2×C4×D3—124no—
327C2×Dic6—21no—
328C2×Dic6—24no—
329C2×Dic6—31no—
330C2×Dic6—31no—
331C2×Dic6—61no—
332C2×Dic6—61no—
333C2×Dic6—61no—
334C2×Dic6—62no—
335C2×Dic6C22×D312yes—
336C3×Q16—64no—
337C3×SD16—64no—
338C2×C3×C8—32no—
339C2×C3×C8—32no—
340C3×C4⋊C4—22no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C22⋊C4—22no—
347C3×C22⋊C4—21no—
348C3×C22⋊C4—21no—
349#217—62no—
350#217—61no—
351#217—61no—
352#216—24no—
353#216—64no—
354#215—24no—
355#214—64no—
356(C2×D3)⋊C4—61no—
357(C2×D3)⋊C4—61no—
358(C2×D3)⋊C4—61no—
359(C2×D3)⋊C4—61no—
360(C2×D3)⋊C4—62no—
361(C2×D3)⋊C4—62no—
362C4⋊Dic3—31no—
363C4⋊Dic3—31no—
364C4⋊Dic3—61no—
365C4⋊Dic3—61no—
366C4⋊Dic3—61no—
367C4⋊Dic3—62no—
368Dic3⋊C4—61no—
369Dic3⋊C4—61no—
370Dic3⋊C4—61no—
371Dic3⋊C4—61no—
372Dic3⋊C4—62no—
373Dic3⋊C4—62no—
374Dic3⋊C4—62no—
375Dic3⋊C4—61no—
376Dic3⋊C4—61no—
377C2×C3⋊C8C22×D312yes—
378C2×C3⋊C8C22×D312yes—
379Dic12—64no—
380#204—64no—
381ΓL(1,𝔽25)—64no—
382ΓL(1,𝔽25)—64no—
383C22×C32—21no—
384C22×C32—21no—
385C22×C32#13712yescomplemented
386C22×C32C22×D411yescharacteristic
387C2×C3⋊D3—21no—
388C2×C3⋊D3—21no—
389C2×C3⋊D3—21no—
390C2×C3⋊D3—21no—
391C2×C3⋊D3—21no—
392C2×C3⋊D3—44no—
393C2×C3⋊D3#12012yes—
394C2×C3×D3—24no—
395C2×C3×D3—48no—
396C2×C3×D3—42no—
397C2×C3×D3—42no—
398C32×C4—21no—
399C32×C4—41no—
400C32×C4—41no—
401C32×C4C22×D412yes—
402C3⋊Dic3—21no—
403C3⋊Dic3—41no—
404C3⋊Dic3—41no—
405C3⋊Dic3#12012yes—
406C3×Dic3—24no—
407C2×#41—92no—
408C2×#41—92no—
409C2×#41—181no—
410C2×#41—181no—
411C2×#41—188no—
412C22×Q8—31no—
413C22×Q8—91no—
414C22×D4—31no—
415C22×D4—181no—
416C23×C4—91no—
417C23×C4—181no—
418#137—188no—
419C2×Q16—32no—
420C2×Q16—92no—
421C2×SD16—32no—
422C2×SD16—92no—
423C2×M16—92no—
424C22⋊Q8—91no—
425C22⋊Q8—91no—
426C22⋊Q8—91no—
427C22⋊Q8—181no—
428C22⋊Q8—181no—
429C22⋊Q8D3211yescharacteristic
430C2×C4⋊C4—91no—
431C2×C4⋊C4—181no—
432C2×C22⋊C4—181no—
433#103—32no—
434#103—92no—
435#102—32no—
436#102—92no—
437C22⋊C8—31no—
438C22⋊C8—31no—
439C22⋊C8—92no—
440C23×C3—21no—
441C23×C3—64no—
442C23×C3—62no—
443C23×C3—122no—
444C23×C3—122no—
445C23×C3D3×D411yescharacteristic
446C23×C3D3×D411yescharacteristic
447C22×D3—24no—
448C22×D3—22no—
449C22×D3—31no—
450C22×D3—31no—
451C22×D3—31no—
452C22×D3—31no—
453C22×D3—42no—
454C22×D3—42no—
455C22×D3—61no—
456C22×D3—61no—
457C22×D3—62no—
458C22×D3—62no—
459C22×D3—64no—
460C22×D3—62no—
461C22×D3—62no—
462C22×D3—122no—
463C22×D3—121no—
464C22×D3—121no—
465C22×D3—122no—
466C3×Q8—22no—
467C3×Q8—22no—
468C3×Q8—34no—
469C3×Q8—42no—
470C3×Q8—64no—
471C3×Q8—62no—
472C3×D4—34no—
473C3×D4—64no—
474C3×D4—62no—
475C2×C3×C4—22no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—42no—
486C2×C3×C4—64no—
487C2×C3×C4—62no—
488C2×C3×C4D3×D411yescharacteristic
489C2×C3×C4D3×D411yescharacteristic
490C2×C3×C4C23×D311yescharacteristic
491C2×C3×C4C23×D311yescharacteristic
492#67—68no—
493#67—68no—
494C2×Dic3—24no—
495C2×Dic3—22no—
496C2×Dic3—31no—
497C2×Dic3—31no—
498C2×Dic3—31no—
499C2×Dic3—31no—
500C2×Dic3—61no—
501C2×Dic3—61no—
502C2×Dic3—68no—
503C2×Dic3—68no—
504C2×Dic3—62no—
505C2×Dic3—62no—
506C2×Dic3—62no—
507C2×Dic3—62no—
508C2×Dic3—61no—
509C2×Dic3—61no—
510C2×Dic3—61no—
511C2×Dic3—61no—
512C2×Dic3—122no—
513D12—24no—
514D12—22no—
515D12—68no—
516D12—68no—
517D12D3×D414yes—
518C4×D3—34no—
519C4×D3—34no—
520C4×D3—64no—
521C4×D3—62no—
522C4×D3—62no—
523C4×D3—68no—
524C4×D3—62no—
525C4×D3—62no—
526C4×D3—68no—
527C4×D3—62no—
528C4×D3—62no—
529C4×D3—122no—
530C4×D3—122no—
531C4×D3—122no—
532C4×D3—122no—
533C4×D3—122no—
534C4×D3—124no—
535C4×D3—122no—
536C4×D3—122no—
537C4×D3—124no—
538Dic6—24no—
539Dic6—22no—
540Dic6—62no—
541Dic6—62no—
542Dic6—122no—
543Dic6—122no—
544Dic6—122no—
545Dic6—124no—
546Dic6D3×D414yes—
547C3×C8—62no—
548C3×C8—62no—
549C3⋊C8—22no—
550C3⋊C8—22no—
551C2×C32—22no—
552C2×C32C2×#12011yescharacteristic
553C2×C32C2×#13711yescharacteristic
554C2×C32#57511yescharacteristic
555C3⋊D3—22no—
556C3⋊D3—41no—
557C3×D3—44no—
558C24—61no—
559C24—91no—
560#41—98no—
561#41—184no—
562#41—184no—
563#41—184no—
564#41—188no—
565#41—188no—
566C2×Q8—32no—
567C2×Q8—64no—
568C2×Q8—61no—
569C2×Q8—91no—
570C2×Q8—181no—
571C2×Q8—184no—
572C2×Q8C2×D3211yescharacteristic
573C2×D4—32no—
574C2×D4—64no—
575C2×D4—61no—
576C2×D4—182no—
577C2×D4—182no—
578C2×D4—188no—
579C22×C4—61no—
580C22×C4—91no—
581C22×C4—91no—
582C22×C4—91no—
583C22×C4—91no—
584C22×C4—91no—
585C22×C4—184no—
586C22×C4—181no—
587C22×C4—181no—
588C22×C4—182no—
589C22×C4—182no—
590C22×C4—188no—
591C22×C4C2×D3211yescharacteristic
592Q16—64no—
593Q16—184no—
594SD16—64no—
595SD16—184no—
596M16—184no—
597C2×C8—32no—
598C2×C8—32no—
599C4⋊C4—21no—
600C4⋊C4—91no—
601C4⋊C4—181no—
602C4⋊C4—181no—
603C4⋊C4—181no—
604C4⋊C4—181no—
605C4⋊C4C2×D3211yescharacteristic
606C22⋊C4—21no—
607C22⋊C4—181no—
608C22⋊C4—181no—
609C22⋊C4—181no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—22no—
616C22×C3—41no—
617C22×C3—41no—
618C22×C3—64no—
619C22×C3—128no—
620C22×C3—122no—
621C22×C3—122no—
622C22×C3#91512yescomplemented
623C22×C3#91812yescomplemented
624C22×C3C2×D3×D411yescharacteristic
625C22×C3C2×D3×D411yescharacteristic
626C2×D3—24no—
627C2×D3—32no—
628C2×D3—32no—
629C2×D3—48no—
630C2×D3—42no—
631C2×D3—42no—
632C2×D3—62no—
633C2×D3—62no—
634C2×D3—62no—
635C2×D3—61no—
636C2×D3—61no—
637C2×D3—61no—
638C2×D3—61no—
639C2×D3—62no—
640C2×D3—61no—
641C2×D3—61no—
642C2×D3—61no—
643C2×D3—61no—
644C2×D3—61no—
645C2×D3—61no—
646C2×D3—121no—
647C2×D3—121no—
648C2×D3—124no—
649C2×D3—124no—
650C2×D3—128no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—22no—
654C3×C4—41no—
655C3×C4—42no—
656C3×C4—42no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—64no—
662C3×C4C2×D3×D412yes—
663C3×C4C2×D3×D412yes—
664Dic3—24no—
665Dic3—32no—
666Dic3—32no—
667Dic3—62no—
668Dic3—61no—
669Dic3—61no—
670Dic3—121no—
671Dic3—122no—
672Dic3—122no—
673Dic3—121no—
674Dic3—121no—
675Dic3—121no—
676Dic3—121no—
677C32#300711yescharacteristic, complemented, Sylow
678C23—64no—
679C23—62no—
680C23—91no—
681C23—91no—
682C23—122no—
683C23—122no—
684C23—182no—
685C23—182no—
686C23—361no—
687C23#381111yescharacteristic
688Q8—22no—
689Q8—34no—
690Q8—64no—
691Q8—62no—
692Q8—182no—
693Q8—362no—
694D4—34no—
695D4—64no—
696D4—62no—
697D4—188no—
698D4—188no—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—64no—
703C2×C4—62no—
704C2×C4—91no—
705C2×C4—94no—
706C2×C4—91no—
707C2×C4—182no—
708C2×C4—182no—
709C2×C4—188no—
710C2×C4—188no—
711C2×C4—182no—
712C2×C4—182no—
713C2×C4—181no—
714C2×C4—181no—
715C2×C4—362no—
716C2×C4—362no—
717C2×C4#381111yescharacteristic
718C2×C4C22×D3211yescharacteristic
719C8—62no—
720C8—62no—
721C2×C3—22no—
722C2×C3—22no—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—42no—
727C2×C3—124no—
728C2×C3D3×#12011yescharacteristic
729C2×C3D3×#12011yescharacteristic
730C2×C3C2×#91511yescharacteristic
731C2×C3C2×#91811yescharacteristic
732C2×C3#577311yescharacteristic
733C2×C3#577711yescharacteristic
734D3—44no—
735D3—64no—
736D3—62no—
737D3—62no—
738D3—122no—
739D3—121no—
740D3—121no—
741C22—21no—
742C22—21no—
743C22—64no—
744C22—92no—
745C22—128no—
746C22—122no—
747C22—122no—
748C22—181no—
749C22—181no—
750C22—181no—
751C22—181no—
752C22—181no—
753C22—364no—
754C22#6395112yescomplemented
755C22C2×#381111yescharacteristic
756C4—21no—
757C4—41no—
758C4—41no—
759C4—64no—
760C4—92no—
761C4—181no—
762C4—361no—
763C4—361no—
764C4D32×D412yes—
765C3—21no—
766C3#8014711yescharacteristic, complemented
767C3#8018411yescharacteristic, complemented
768C2—22no—
769C2—124no—
770C2—182no—
771C2—361no—
772C2#1059527811yescharacteristic
773C2C2×#6395111yescharacteristic
774C2#1059547111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radicalC22×#3796C2
hypercenterC22⋊Q8D32
hypocenterC32#3007
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C3⋊D3×C22⋊Q8C2semidirect
3. C2×#63951C2semidirect
4. C3×#5050C2semidirect
5. C3×#5046C2semidirect
6. #10591656C2semidirect
7. #10591186C2semidirect
8. #10591172C2semidirect
9. #10591159C2semidirect
10. #10590618C2semidirect
11. #10590612C2semidirect
14. C2×Q8×C3⋊D3C22semidirect
26. #64155C22semidirect
28. #64106C22semidirect
31. C4⋊C4×C3⋊D3C22semidirect
34. C2×C3×#216C22semidirect
35. C2×C3×#215C22semidirect
37. C2×#3719C22semidirect
38. C2×#3716C22semidirect
39. C2×#3712C22semidirect
42. C3×#810C22semidirect
43. C3×#809C22semidirect
44. #63566C22semidirect
45. #63563C22semidirect
46. #63557C22semidirect
60. #5050D3semidirect
61. #5046D3semidirect
156. C2×#216C2×D3semidirect
157. C2×#215C2×D3semidirect
198. #810C2×D3semidirect
199. #809C2×D3semidirect
385. C22×C32#137semidirect
622. C22×C3#915semidirect
623. C22×C3#918semidirect
677. C32#3007semidirect
754. C22#63951semidirect
766. C3#80147semidirect
767. C3#80184semidirect

Maximal subgroups

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

subgroupindex
C22×#37962
C3⋊D3×C22⋊Q82
C2×#639512
C3×#50502
C3×#50462
#105916562
#105911862
#105911722
#105911592
#105906182
#105906122
#801843
#801473