Finite Group Databasebeta

← #11857524

Subgroups — #11857524

Order 1152.

2021 conjugacy classes of subgroups.

The subgroup lattice has 679 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×C3⋊D3C211yesmaximal, characteristic
2#10594969C212yesmaximal, complemented
3C3×#5240C212yesmaximal, complemented
4#10591529C214yesmaximal, complemented
5#10591527C214yesmaximal, complemented
6#10591232C212yesmaximal, complemented
7D3×#410—32nomaximal
8C2×C32×#41C2211yescharacteristic
9#41×C3⋊D3—22no—
10#41×C3⋊D3—22no—
11#41×C3⋊D3—22no—
12#41×C3⋊D3—22no—
13C2×#3832C411yescharacteristic, complemented
14C2×Q8×C3⋊D3C411yescharacteristic, complemented
15C2×#3830C411yescharacteristic, complemented
16C2×#3830C2212yes—
17C2×D4×C3⋊D3C411yescharacteristic, complemented
18C2×D4×C3⋊D3C2212yes—
19C2×#3828C412yescomplemented
20C2×#3828C2211yescharacteristic
21C22×C4×C3⋊D3C412yescomplemented
22C22×C4×C3⋊D3C2211yescharacteristic
23C3×#926C2214yescomplemented
24#63974C2214yes—
25#63957C2214yescomplemented
26#63900—22no—
27C4×#624—22no—
28#63874—22no—
29#63849—22no—
30C3×#834C2218yescomplemented
31#63581C2218yescomplemented
32C2×D3×#41—32no—
33C2×D3×#41—61no—
34D3×#117—34no—
35C3×#410—32no—
36#5240D312yescomplemented
37#5006—34no—
38D3×#99—38no—
39#4740—38no—
40C23×C3⋊D3C2×C412yes—
41C23×C3⋊D3C2311yescharacteristic
42C32×#41—22no—
43C32×#41—22no—
44C2×C32×Q8C2×C411yescharacteristic, complemented
45C2×C32×D4C2×C411yescharacteristic, complemented
46C2×C32×D4C2312yes—
47C22×C32×C4C2×C412yescomplemented
48C22×C32×C4C2311yescharacteristic
49C2×#638C2×C412yes—
50C2×#638C2×C412yescomplemented
51C2×#638C2312yes—
52C22×C3⋊Dic3C2×C412yescomplemented
53C22×C3⋊Dic3C2311yescharacteristic
54#3832—22no—
55#3832—22no—
56Q8×C3⋊D3—22no—
57Q8×C3⋊D3—22no—
58#3830—24no—
59#3830—24no—
60#3830—22no—
61#3830—22no—
62D4×C3⋊D3—24no—
63D4×C3⋊D3—24no—
64D4×C3⋊D3—22no—
65D4×C3⋊D3—22no—
66#3828—22no—
67#3828—22no—
68#3828—24no—
69#3828—24no—
70C2×C4⋊(C3⋊D3)C2×C412yes—
71C2×C4⋊(C3⋊D3)C2×C411yescharacteristic, complemented
72C2×C4×C3⋊D3—22no—
73C2×C4×C3⋊D3—22no—
74C2×C4×C3⋊D3—22no—
75C2×C4×C3⋊D3—22no—
76C2×C4×C3⋊D3C2×C412yes—
77C2×C4×C3⋊D3C2×C411yescharacteristic
78C2×C4×C3⋊D3C2×C411yescharacteristic
79C2×C4×C3⋊D3C2×C411yescharacteristic
80C2×C4×C3⋊D3C2×C411yescharacteristic
81C2×C4×C3⋊D3C2×C412yescomplemented
82C2×C4×C3⋊D3C2×C412yescomplemented
83C2×C4×C3⋊D3D412yes—
84C2×C4×C3⋊D3D412yes—
85C2×C4×C3⋊D3D412yes—
86C2×C4×C3⋊D3D412yes—
87C2×#634C2×C412yescomplemented
88C2×#634C2×C411yescharacteristic, complemented
89C2×#624—24no—
90C3×#217C2318yes—
91C3×C4⋊Dic3—24no—
92C3×C4×Dic3—24no—
93#3724—24no—
94#3722—24no—
95Dic32—24no—
96C2×#410—91noSylow
97C2×C3×#41—21no—
98C2×C3×#41C2×D312yes—
99D3×#41—64no—
100D3×#41—64no—
101D3×#41—64no—
102D3×#41—64no—
103D3×#41—64no—
104D3×#41—64no—
105D3×#41—64no—
106D3×#41—64no—
107C2×#239—32no—
108C2×#239—61no—
109C2×D3×Q8—32no—
110C2×D3×Q8—61no—
111C2×#237—32no—
112C2×#237—34no—
113C2×#237—61no—
114C2×#237—62no—
115C2×D3×D4—32no—
116C2×D3×D4—34no—
117C2×D3×D4—61no—
118C2×D3×D4—62no—
119C2×#235—34no—
120C2×#235—32no—
121C2×#235—62no—
122C2×#235—61no—
123C22×C4×D3—32no—
124C22×C4×D3—34no—
125C22×C4×D3—62no—
126C22×C4×D3—61no—
127C3×#117—34no—
128#926C2×D314yescomplemented
129#892—64no—
130D3×C4⋊C4—64no—
131D3×C22⋊C4—38no—
132#877—38no—
133#872—64no—
134C42×D3—64no—
135C3×#99—38no—
136#834C2×D318yescomplemented
137#806—316no—
138C23×C32C22×C412yes—
139C23×C32C2411yescharacteristic
140C22×C3⋊D3—22no—
141C22×C3⋊D3—22no—
142C22×C3⋊D3—42no—
143C22×C3⋊D3—44no—
144C22×C3⋊D3C22×C411yescharacteristic
145C22×C3⋊D3C22×C412yes—
146C22×C3⋊D3C22×C411yescharacteristic
147C22×C3⋊D3C2×D412yes—
148C22×C3⋊D3C2×D412yes—
149C32×Q8—22no—
150C32×D4—24no—
151C32×D4—22no—
152C2×C32×C4—22no—
153C2×C32×C4—22no—
154C2×C32×C4C22×C412yes—
155C2×C32×C4C22×C411yescharacteristic
156C2×C32×C4C22×C411yescharacteristic
157C2×C32×C4C2×D412yes—
158C2×C32×C4C2×D412yes—
159#638—24no—
160#638—24no—
161#638—24no—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3C22×C412yes—
165C2×C3⋊Dic3C22×C411yescharacteristic
166C2×C3⋊Dic3C22×C411yescharacteristic
167C2×C3⋊Dic3C2×D412yes—
168C2×C3⋊Dic3C2×D412yes—
169C4⋊(C3⋊D3)—24no—
170C4⋊(C3⋊D3)—22no—
171C4×C3⋊D3—22no—
172C4×C3⋊D3—22no—
173C4×C3⋊D3—22no—
174C4×C3⋊D3—22no—
175C4×C3⋊D3—22no—
176C4×C3⋊D3—22no—
177C4×C3⋊D3C22⋊C411yescharacteristic
178C4×C3⋊D3C22⋊C411yescharacteristic
179C4×C3⋊D3C22⋊C411yescharacteristic
180C4×C3⋊D3C22⋊C411yescharacteristic
181C4×C3⋊D3C22⋊C412yes—
182C4×C3⋊D3C22⋊C412yes—
183C4×C3⋊D3C22⋊C412yes—
184C4×C3⋊D3C22⋊C412yes—
185C4×C3⋊D3C22⋊C412yes—
186C4×C3⋊D3C22⋊C412yes—
187#634—22no—
188#634—24no—
189C2×C3×Dic3—28no—
190#624—48no—
191C22×#41—91no—
192C2×#117—92no—
193#410—32no—
194#410—94no—
195#410—92no—
196C2×#99—94no—
197C23×D3—32no—
198C23×D3—34no—
199C23×D3—62no—
200C23×D3—61no—
201C3×#41—24no—
202C3×#41—24no—
203C3×#41—24no—
204C3×#41—24no—
205C2×C3×Q8—21no—
206C2×C3×Q8C4×D312yescomplemented
207C2×C3×D4—21no—
208C2×C3×D4—22no—
209C2×C3×D4C4×D312yescomplemented
210C2×C3×D4C22×D314yes—
211C22×C3×C4—22no—
212C22×C3×C4—21no—
213C22×C3×C4C4×D314yescomplemented
214C22×C3×C4C22×D312yes—
215C2×#67—34no—
216C2×#67—34no—
217C2×#67—34no—
218C2×#67—62no—
219C2×#67—62no—
220C2×#67—62no—
221C22×Dic3—32no—
222C22×Dic3—34no—
223C22×Dic3—62no—
224C22×Dic3—61no—
225#239—64no—
226#239—64no—
227#239—64no—
228#239—64no—
229D3×Q8—64no—
230D3×Q8—64no—
231D3×Q8—64no—
232D3×Q8—64no—
233#237—64no—
234#237—64no—
235#237—68no—
236#237—68no—
237#237—64no—
238#237—64no—
239#237—68no—
240#237—68no—
241D3×D4—64no—
242D3×D4—64no—
243D3×D4—68no—
244D3×D4—68no—
245D3×D4—64no—
246D3×D4—64no—
247D3×D4—68no—
248D3×D4—68no—
249#235—68no—
250#235—68no—
251#235—68no—
252#235—68no—
253#235—64no—
254#235—64no—
255#235—64no—
256#235—64no—
257C2×D12—34no—
258C2×D12—32no—
259C2×D12—62no—
260C2×D12—61no—
261C2×C4×D3—32no—
262C2×C4×D3—32no—
263C2×C4×D3—32no—
264C2×C4×D3—32no—
265C2×C4×D3—34no—
266C2×C4×D3—34no—
267C2×C4×D3—34no—
268C2×C4×D3—34no—
269C2×C4×D3—34no—
270C2×C4×D3—34no—
271C2×C4×D3—34no—
272C2×C4×D3—61no—
273C2×C4×D3—61no—
274C2×C4×D3—62no—
275C2×C4×D3—61no—
276C2×C4×D3—62no—
277C2×C4×D3—61no—
278C2×C4×D3—62no—
279C2×C4×D3—62no—
280C2×C4×D3—62no—
281C2×C4×D3—62no—
282C2×C4×D3—62no—
283C2×C4×D3—64no—
284C2×C4×D3—64no—
285C2×C4×D3—64no—
286C2×C4×D3—64no—
287C2×C4×D3—64no—
288C2×C4×D3—64no—
289C2×C4×D3—64no—
290C2×C4×D3—64no—
291C2×C4×D3—68no—
292C2×Dic6—34no—
293C2×Dic6—32no—
294C2×Dic6—62no—
295C2×Dic6—61no—
296C3×C4⋊C4—64no—
297C3×C22⋊C4—38no—
298C3×C42—64no—
299#217C22×D318yes—
300(C2×D3)⋊C4—68no—
301C4⋊Dic3—24no—
302Dic3⋊C4—68no—
303C4×Dic3—24no—
304C4×Dic3—68no—
305C22×C32—22no—
306C22×C32—41no—
307C22×C32—42no—
308C22×C32C23×C411yescharacteristic
309C22×C32C22×D412yes—
310C2×C3⋊D3—22no—
311C2×C3⋊D3—22no—
312C2×C3⋊D3—24no—
313C2×C3⋊D3—41no—
314C2×C3⋊D3—42no—
315C2×C3⋊D3—44no—
316C2×C3⋊D3—44no—
317C2×C3⋊D3—42no—
318C2×C3⋊D3C2×C22⋊C411yescharacteristic
319C2×C3⋊D3C2×C22⋊C412yes—
320C2×C3⋊D3C2×C22⋊C411yescharacteristic
321C32×C4—22no—
322C32×C4C2×C22⋊C412yes—
323C32×C4C2×C22⋊C411yescharacteristic
324C32×C4C2×C22⋊C411yescharacteristic
325C3⋊Dic3—22no—
326C3⋊Dic3C2×C22⋊C412yes—
327C3⋊Dic3C2×C22⋊C411yescharacteristic
328C3⋊Dic3C2×C22⋊C411yescharacteristic
329C3×Dic3—48no—
330C2×#41—91no—
331C2×#41—91no—
332C2×#41—92no—
333C2×#41—92no—
334C2×#41—91no—
335C2×#41—182no—
336C2×#41—182no—
337C2×#41—182no—
338C2×#41—182no—
339C2×#41D3211yescharacteristic
340C22×Q8—91no—
341C22×D4—91no—
342C22×D4—92no—
343C23×C4—91no—
344C23×C4—92no—
345#117—34no—
346#117—94no—
347#117—182no—
348#117—182no—
349C2×C4⋊C4—182no—
350C2×C22⋊C4—94no—
351C2×C42—182no—
352#99—38no—
353#99—98no—
354C23×C3—21no—
355C23×C3—22no—
356C23×C3C2×C4×D314yes—
357C23×C3C23×D312yes—
358C22×D3—32no—
359C22×D3—34no—
360C22×D3—32no—
361C22×D3—34no—
362C22×D3—34no—
363C22×D3—61no—
364C22×D3—61no—
365C22×D3—62no—
366C22×D3—62no—
367C22×D3—62no—
368C22×D3—64no—
369C22×D3—64no—
370C22×D3—64no—
371C22×D3—64no—
372C22×D3—124no—
373C22×D3—124no—
374C22×D3—128no—
375C22×D3—128no—
376C3×Q8—24no—
377C3×Q8—24no—
378C3×D4—28no—
379C3×D4—24no—
380C3×D4—28no—
381C3×D4—24no—
382C2×C3×C4—24no—
383C2×C3×C4—24no—
384C2×C3×C4—24no—
385C2×C3×C4—24no—
386C2×C3×C4—22no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—68no—
392C2×C3×C4C2×C4×D314yes—
393C2×C3×C4C2×C4×D312yes—
394C2×C3×C4C2×C4×D312yes—
395C2×C3×C4D3×D414yes—
396C2×C3×C4D3×D414yes—
397#67—68no—
398#67—68no—
399#67—68no—
400#67—68no—
401#67—68no—
402#67—68no—
403C2×Dic3—28no—
404C2×Dic3—32no—
405C2×Dic3—32no—
406C2×Dic3—34no—
407C2×Dic3—34no—
408C2×Dic3—34no—
409C2×Dic3—61no—
410C2×Dic3—62no—
411C2×Dic3—61no—
412C2×Dic3—62no—
413C2×Dic3—62no—
414C2×Dic3—64no—
415C2×Dic3—64no—
416C2×Dic3—64no—
417C2×Dic3—64no—
418D12—68no—
419D12—68no—
420D12—64no—
421D12—64no—
422C4×D3—32no—
423C4×D3—32no—
424C4×D3—32no—
425C4×D3—32no—
426C4×D3—34no—
427C4×D3—34no—
428C4×D3—34no—
429C4×D3—34no—
430C4×D3—34no—
431C4×D3—34no—
432C4×D3—61no—
433C4×D3—61no—
434C4×D3—61no—
435C4×D3—61no—
436C4×D3—62no—
437C4×D3—62no—
438C4×D3—62no—
439C4×D3—62no—
440C4×D3—62no—
441C4×D3—62no—
442C4×D3—64no—
443C4×D3—64no—
444C4×D3—64no—
445C4×D3—64no—
446C4×D3—64no—
447C4×D3—64no—
448C4×D3—64no—
449C4×D3—64no—
450C4×D3—64no—
451C4×D3—64no—
452C4×D3—64no—
453C4×D3—64no—
454C4×D3—1216no—
455Dic6—68no—
456Dic6—68no—
457Dic6—64no—
458Dic6—64no—
459C2×C32—21no—
460C2×C32—22no—
461C2×C32—42no—
462C2×C32C22×C22⋊C411yescharacteristic
463C3⋊D3—21no—
464C3⋊D3—22no—
465C3⋊D3—42no—
466C3⋊D3#41012yescomplemented
467C24—91no—
468C24—92no—
469#41—22no—
470#41—22no—
471#41—184no—
472#41—184no—
473#41—184no—
474#41—184no—
475#41—182no—
476#41—182no—
477#41—182no—
478#41—182no—
479#41—182no—
480#41—182no—
481C2×Q8—92no—
482C2×Q8—91no—
483C2×Q8—182no—
484C2×Q8—182no—
485C2×Q8#62411yescharacteristic, complemented
486C2×D4—92no—
487C2×D4—92no—
488C2×D4—92no—
489C2×D4—92no—
490C2×D4—91no—
491C2×D4—182no—
492C2×D4—182no—
493C2×D4—184no—
494C2×D4—184no—
495C2×D4#62411yescharacteristic, complemented
496C2×D4C2×D3212yes—
497C22×C4—91no—
498C22×C4—91no—
499C22×C4—91no—
500C22×C4—91no—
501C22×C4—91no—
502C22×C4—92no—
503C22×C4—92no—
504C22×C4—92no—
505C22×C4—92no—
506C22×C4—92no—
507C22×C4—92no—
508C22×C4—92no—
509C22×C4—92no—
510C22×C4—182no—
511C22×C4—182no—
512C22×C4—182no—
513C22×C4—182no—
514C22×C4—184no—
515C22×C4#62412yescomplemented
516C22×C4C2×D3211yescharacteristic
517C4⋊C4—64no—
518C4⋊C4—184no—
519C22⋊C4—38no—
520C22⋊C4—184no—
521C42—64no—
522C42—184no—
523C22×C3—24no—
524C22×C3—24no—
525C22×C3—21no—
526C22×C3—22no—
527C22×C3—42no—
528C22×C3—44no—
529C22×C3—42no—
530C22×C3—44no—
531C22×C3C22×C4×D312yes—
532C22×C3C2×D3×D414yes—
533C2×D3—32no—
534C2×D3—32no—
535C2×D3—34no—
536C2×D3—61no—
537C2×D3—61no—
538C2×D3—62no—
539C2×D3—68no—
540C2×D3—64no—
541C2×D3—64no—
542C2×D3—64no—
543C2×D3—64no—
544C2×D3—124no—
545C2×D3—128no—
546C2×D3—124no—
547C2×D3—122no—
548C2×D3—124no—
549C2×D3—128no—
550C2×D3—128no—
551C2×D3—128no—
552C2×D3—122no—
553C2×D3—124no—
554C2×D3—124no—
555C3×C4—24no—
556C3×C4—24no—
557C3×C4—22no—
558C3×C4—21no—
559C3×C4—21no—
560C3×C4—128no—
561C3×C4D3×C22⋊C414yes—
562C3×C4D3×C22⋊C412yes—
563C3×C4D3×C22⋊C412yes—
564Dic3—34no—
565Dic3—32no—
566Dic3—32no—
567Dic3—48no—
568Dic3—62no—
569Dic3—61no—
570Dic3—61no—
571Dic3—64no—
572Dic3—64no—
573C32C2×#41011yescharacteristic, complemented, Sylow
574C23—91no—
575C23—92no—
576C23—91no—
577C23—92no—
578C23—92no—
579C23—182no—
580C23—182no—
581C23—362no—
582C23—364no—
583C23C2×#62412yes—
584C23C22×D3211yescharacteristic
585Q8—22no—
586Q8—184no—
587Q8—182no—
588D4—24no—
589D4—22no—
590D4—184no—
591D4—184no—
592D4—184no—
593D4—184no—
594D4—182no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—68no—
598C2×C4—91no—
599C2×C4—91no—
600C2×C4—92no—
601C2×C4—92no—
602C2×C4—91no—
603C2×C4—91no—
604C2×C4—92no—
605C2×C4—92no—
606C2×C4—92no—
607C2×C4—92no—
608C2×C4—92no—
609C2×C4—91no—
610C2×C4—91no—
611C2×C4—92no—
612C2×C4—92no—
613C2×C4—182no—
614C2×C4—182no—
615C2×C4—182no—
616C2×C4—182no—
617C2×C4—182no—
618C2×C4—182no—
619C2×C4—182no—
620C2×C4—182no—
621C2×C4—368no—
622C2×C4C2×#62412yes—
623C2×C4C2×#62411yescharacteristic
624C2×C4C2×#62411yescharacteristic
625C2×C4#381112yes—
626C2×C4#381112yes—
627C2×C3—22no—
628C2×C3—24no—
629C2×C3—22no—
630C2×C3—21no—
631C2×C3—42no—
632C2×C3—44no—
633C2×C3—44no—
634C2×C3C2×D3×C22⋊C412yes—
635D3—34no—
636D3—62no—
637D3—62no—
638D3—62no—
639D3—64no—
640D3—122no—
641D3—124no—
642D3—124no—
643C22—22no—
644C22—41no—
645C22—42no—
646C22—91no—
647C22—91no—
648C22—92no—
649C22—184no—
650C22—182no—
651C22—182no—
652C22—362no—
653C22—361no—
654C22—362no—
655C22—364no—
656C22—364no—
657C22C22×#62411yescharacteristic
658C22C2×#381112yes—
659C4—22no—
660C4—91no—
661C4—91no—
662C4—92no—
663C4—128no—
664C4—182no—
665C4#6397411yescharacteristic
666C4#6397412yes—
667C4#6397411yescharacteristic
668C3—21no—
669C3D3×#41012yescomplemented
670C2—22no—
671C2—21no—
672C2—42no—
673C2—92no—
674C2—181no—
675C2—182no—
676C2—362no—
677C2C2×#6397411yescharacteristic
subgroupG/H
centerC4#63974
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC2×C32×#41C22
socleC2×C32C22×C22⋊C4
prime radicalC2×#41×C3⋊D3C2
cosocleC23×C32C24
hypercenterC2×#41D32
hypocenterC32C2×#410
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #10594969C2semidirect
3. C3×#5240C2semidirect
4. #10591529C2semidirect
5. #10591527C2semidirect
6. #10591232C2semidirect
13. C2×#3832C4semidirect
14. C2×Q8×C3⋊D3C4semidirect
15. C2×#3830C4semidirect
17. C2×D4×C3⋊D3C4semidirect
19. C2×#3828C4semidirect
21. C22×C4×C3⋊D3C4semidirect
23. C3×#926C22semidirect
25. #63957C22semidirect
30. C3×#834C22semidirect
31. #63581C22semidirect
36. #5240D3semidirect
44. C2×C32×Q8C2×C4semidirect
45. C2×C32×D4C2×C4semidirect
47. C22×C32×C4C2×C4semidirect
50. C2×#638C2×C4semidirect
52. C22×C3⋊Dic3C2×C4semidirect
71. C2×C4⋊(C3⋊D3)C2×C4semidirect
81. C2×C4×C3⋊D3C2×C4semidirect
82. C2×C4×C3⋊D3C2×C4semidirect
87. C2×#634C2×C4semidirect
88. C2×#634C2×C4semidirect
128. #926C2×D3semidirect
136. #834C2×D3semidirect
206. C2×C3×Q8C4×D3semidirect
209. C2×C3×D4C4×D3semidirect
213. C22×C3×C4C4×D3semidirect
466. C3⋊D3#410semidirect
485. C2×Q8#624semidirect
495. C2×D4#624semidirect
515. C22×C4#624semidirect
573. C32C2×#410semidirect
669. C3D3×#410semidirect

Maximal subgroups

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

subgroupindex
C2×#41×C3⋊D32
#105949692
C3×#52402
#105915292
#105915272
#105912322
D3×#4103