Finite Group Databasebeta

← #11858169

Subgroups — #11858169

Order 1152.

1366 conjugacy classes of subgroups.

The subgroup lattice has 729 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64306C211yesmaximal, characteristic
2C2×#64286C211yesmaximal, characteristic, complemented
3C2×#63818C211yesmaximal, characteristic, complemented
4#10593325C214yesmaximal, complemented
5#10593324C214yesmaximal, complemented
6#10593323C214yesmaximal, complemented
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×C3×#235—21no—
9C2×#3811—21no—
10C2×#3805C412yescomplemented
11#64306—21no—
12#64306—21no—
13#64306—21no—
14#64306—21no—
15#64306C412yescomplemented
16#64306C412yescomplemented
17#64306C2212yes—
18#64306C2212yes—
19C2×#3802C411yescharacteristic, complemented
20C2×C4×D32—21no—
21C2×#3798C2212yes—
22C2×#3797C411yescharacteristic, complemented
23C2×#3796—21no—
24C2×C22⋊#157—21no—
25#64286—21no—
26#64286—21no—
27#64286C2212yescomplemented
28#64286C2212yescomplemented
29C2×C4⋊#157—21no—
30C2×C4×#157C2212yescomplemented
31C2×C3×#208—21no—
32C2×#3712C2212yescomplemented
33#63818—21no—
34#63818—21no—
35#63818C2212yescomplemented
36#63818C2212yescomplemented
37C2×#3710—21no—
38#63731C22116yescomplemented
39C2×D3×#41—61no—
40C2×D3×M16—61no—
41C23×C3⋊D3D411yescharacteristic
42C22×D32—21no—
43C22×#157—22no—
44C22×C32×C4D411yescharacteristic
45C22×C3⋊Dic3C2×C411yescharacteristic
46C2×C4×C3⋊D3C2×C411yescharacteristic
47C2×C4×C3⋊D3C2×C411yescharacteristic
48C2×C4×C3⋊D3C2×C411yescharacteristic
49C2×C4×C3⋊D3D411yescharacteristic
50C2×C4×C3⋊D3D411yescharacteristic
51C2×C4×C3⋊D3D411yescharacteristic
52C2×C4×C3⋊D3D411yescharacteristic
53C2×C4×C3⋊D3D411yescharacteristic
54C2×C4×C3⋊D3D411yescharacteristic
55C2×C4×C3⋊D3C2311yescharacteristic
56C2×C4×C3⋊D3C2311yescharacteristic
57C2×C4×C3⋊D3C2311yescharacteristic
58C2×C3×#67—22no—
59C3×#235—22no—
60C3×#235—22no—
61C3×#235—22no—
62C3×#235—22no—
63C2×C3×D12—21no—
64C2×C3×C4×D3—22no—
65C2×C3×Dic6—21no—
66#3811—22no—
67#3811—22no—
68#3811—22no—
69#3811—22no—
70C2×#627C2×C412yescomplemented
71C2×#626—22no—
72C2×#625C2×C412yescomplemented
73C2×#624—21no—
74#3805—22no—
75#3805—22no—
76#3805C2×C414yes—
77#3805C2×C414yescomplemented
78C2×D3×Dic3—22no—
79#3802—21no—
80#3802—21no—
81#3802C2×C412yes—
82#3802C2×C412yescomplemented
83C4×D32—22no—
84C4×D32—22no—
85C4×D32—22no—
86C4×D32—22no—
87#3798—22no—
88#3798—22no—
89#3798C2×C414yescomplemented
90#3798C2314yes—
91#3797—21no—
92#3797—21no—
93#3797C2×C412yes—
94#3797C2×C412yescomplemented
95#3796—22no—
96#3796—22no—
97#3796—22no—
98#3796—22no—
99C22⋊#157—22no—
100C22⋊#157—22no—
101C4⋊#157—22no—
102C4⋊#157—22no—
103C4×#157—22no—
104C4×#157C2314yescomplemented
105C3×#208—22no—
106C3×#208—22no—
107C2×C3×C3⋊C8—22no—
108#3712—22no—
109#3712C2314yescomplemented
110#3710—22no—
111#3710—22no—
112C2×#421—91nomaximal, Sylow
113C2×C3×#41—61no—
114D3×#41—62no—
115D3×#41—62no—
116D3×#41—62no—
117D3×#41—62no—
118D3×#41—62no—
119D3×#41—62no—
120D3×#41—62no—
121D3×#41—62no—
122C2×#239—61no—
123C2×D3×Q8—61no—
124C2×#237—62no—
125C2×#237—61no—
126C2×D3×D4—61no—
127C2×D3×D4—62no—
128C2×#235—21no—
129C2×#235—62no—
130C22×C4×D3—61no—
131C22×C4×D3—61no—
132C22×C4×D3—62no—
133C2×C3×M16—61no—
134C2×#208—21no—
135D3×M16—62no—
136D3×M16—62no—
137D3×M16—62no—
138D3×M16—62no—
139C2×ΓL(1,𝔽25)—62no—
140C2×D3×C8—62no—
141C23×C32C22⋊C411yescharacteristic
142C22×C3⋊D3—42no—
143C22×C3⋊D3C22⋊C411yescharacteristic
144C22×C3⋊D3C22⋊C411yescharacteristic
145C22×C3⋊D3C22⋊C411yescharacteristic
146C22×C3⋊D3C2×D411yescharacteristic
147C22×C3⋊D3C2×D411yescharacteristic
148C22×C3⋊D3C2×D411yescharacteristic
149C22×C3×D3—22no—
150C2×D32—22no—
151C2×D32—22no—
152C2×D32—44no—
153C2×#157—24no—
154C2×#157—44no—
155C2×C32×C4C22⋊C411yescharacteristic
156C2×C32×C4C22⋊C411yescharacteristic
157C2×C32×C4C22⋊C411yescharacteristic
158C2×C32×C4C2×D411yescharacteristic
159C2×C32×C4C2×D411yescharacteristic
160C2×C32×C4C2×D411yescharacteristic
161C2×C3⋊Dic3C22⋊C411yescharacteristic
162C2×C3⋊Dic3C22⋊C411yescharacteristic
163C2×C3⋊Dic3C22⋊C411yescharacteristic
164C2×C3⋊Dic3C22×C411yescharacteristic
165C2×C3⋊Dic3C22×C411yescharacteristic
166C2×C3⋊Dic3C22×C411yescharacteristic
167C4×C3⋊D3C22⋊C411yescharacteristic
168C4×C3⋊D3C22⋊C411yescharacteristic
169C4×C3⋊D3C22⋊C411yescharacteristic
170C4×C3⋊D3C22⋊C411yescharacteristic
171C4×C3⋊D3C22⋊C411yescharacteristic
172C4×C3⋊D3C22⋊C411yescharacteristic
173C4×C3⋊D3C22×C411yescharacteristic
174C4×C3⋊D3C22×C411yescharacteristic
175C4×C3⋊D3C22×C411yescharacteristic
176C4×C3⋊D3C2×D411yescharacteristic
177C4×C3⋊D3C2×D411yescharacteristic
178C4×C3⋊D3C2×D411yescharacteristic
179C4×C3⋊D3C2×D411yescharacteristic
180C4×C3⋊D3C2×D411yescharacteristic
181C4×C3⋊D3C2×D411yescharacteristic
182C4×C3⋊D3C2411yescharacteristic
183C3×#67—24no—
184C3×#67—24no—
185C2×C3×Dic3—22no—
186C3×D12—22no—
187C3×D12—22no—
188C3×C4×D3—24no—
189C3×C4×D3—24no—
190C3×Dic6—22no—
191C3×Dic6—22no—
192#627—22no—
193#627C22×C414yes—
194#626—24no—
195#626—24no—
196#625—22no—
197#625C22×C414yes—
198#624—22no—
199#624—22no—
200D3×Dic3—24no—
201D3×Dic3—24no—
202C3×C3⋊C8—24no—
203C22×#41—91no—
204C22×M16—91no—
205C2×#117—91no—
206#421—94no—
207#421—94no—
208C2×#104—94no—
209C23×D3—61no—
210C23×D3—61no—
211C23×D3—62no—
212C3×#41—62no—
213C3×#41—62no—
214C3×#41—62no—
215C3×#41—62no—
216C2×C3×Q8—61no—
217C2×C3×D4—61no—
218C2×C3×D4—62no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—62no—
222C2×#67—22no—
223C2×#67—62no—
224C2×#67—62no—
225C22×Dic3—61no—
226C22×Dic3—61no—
227C22×Dic3—62no—
228#239—62no—
229#239—62no—
230#239—62no—
231#239—62no—
232D3×Q8—62no—
233D3×Q8—62no—
234D3×Q8—62no—
235D3×Q8—62no—
236#237—64no—
237#237—64no—
238#237—62no—
239#237—62no—
240#237—62no—
241#237—62no—
242#237—64no—
243#237—64no—
244D3×D4—62no—
245D3×D4—62no—
246D3×D4—62no—
247D3×D4—62no—
248D3×D4—64no—
249D3×D4—64no—
250D3×D4—64no—
251D3×D4—64no—
252#235—22no—
253#235—22no—
254#235—22no—
255#235—22no—
256#235—64no—
257#235—64no—
258#235—64no—
259#235—64no—
260C2×D12—21no—
261C2×D12—62no—
262C2×C4×D3—22no—
263C2×C4×D3—61no—
264C2×C4×D3—61no—
265C2×C4×D3—61no—
266C2×C4×D3—61no—
267C2×C4×D3—61no—
268C2×C4×D3—61no—
269C2×C4×D3—61no—
270C2×C4×D3—61no—
271C2×C4×D3—61no—
272C2×C4×D3—61no—
273C2×C4×D3—61no—
274C2×C4×D3—61no—
275C2×C4×D3—61no—
276C2×C4×D3—61no—
277C2×C4×D3—61no—
278C2×C4×D3—61no—
279C2×C4×D3—61no—
280C2×C4×D3—61no—
281C2×C4×D3—61no—
282C2×C4×D3—61no—
283C2×C4×D3—61no—
284C2×C4×D3—61no—
285C2×C4×D3—61no—
286C2×C4×D3—61no—
287C2×C4×D3—64no—
288C2×C4×D3—64no—
289C2×C4×D3—64no—
290C2×C4×D3—64no—
291C2×C4×D3—62no—
292C2×C4×D3—62no—
293C2×Dic6—21no—
294C2×Dic6—62no—
295C3×M16—62no—
296C3×M16—62no—
297C2×C3×C8—62no—
298#208—22no—
299#208—22no—
300C2×C3⋊C8—22no—
301ΓL(1,𝔽25)—64no—
302ΓL(1,𝔽25)—64no—
303D3×C8—64no—
304D3×C8—64no—
305C22×C32—41no—
306C22×C32C2×C22⋊C411yescharacteristic
307C22×C32C2×C22⋊C411yescharacteristic
308C22×C32C2×C22⋊C411yescharacteristic
309C2×C3⋊D3—22no—
310C2×C3⋊D3—22no—
311C2×C3⋊D3—22no—
312C2×C3⋊D3—41no—
313C2×C3⋊D3—41no—
314C2×C3⋊D3—41no—
315C2×C3⋊D3C2×C22⋊C411yescharacteristic
316C2×C3⋊D3C2×C22⋊C411yescharacteristic
317C2×C3⋊D3C2×C22⋊C411yescharacteristic
318C2×C3⋊D3C22×D411yescharacteristic
319C2×C3×D3—24no—
320C2×C3×D3—44no—
321D32—44no—
322D32—44no—
323#157—44no—
324C32×C4C2×C22⋊C411yescharacteristic
325C32×C4C2×C22⋊C411yescharacteristic
326C32×C4C2×C22⋊C411yescharacteristic
327C32×C4C22×D411yescharacteristic
328C3⋊Dic3C2×C22⋊C411yescharacteristic
329C3⋊Dic3C2×C22⋊C411yescharacteristic
330C3⋊Dic3C2×C22⋊C411yescharacteristic
331C3⋊Dic3C23×C411yescharacteristic
332C3×Dic3—24no—
333C2×#41—61no—
334C2×#41—92no—
335C2×#41—92no—
336C2×#41—92no—
337C2×#41—92no—
338C2×#41—92no—
339C2×#41—92no—
340C2×#41—181no—
341C2×#41—181no—
342C2×#41—181no—
343C2×#41—181no—
344C2×#41—181no—
345C22×Q8—91no—
346C22×D4—91no—
347C22×D4—181no—
348C23×C4—91no—
349C23×C4—181no—
350C2×M16—61no—
351C2×M16—92no—
352C2×M16—92no—
353C2×M16—92no—
354C2×M16—181no—
355C2×M16—181no—
356C22×C8—181no—
357#117—92no—
358#117—92no—
359#117—181no—
360#117—181no—
361C2×C4⋊C4—181no—
362C2×C22⋊C4—181no—
363C2×C42—92no—
364#104—916no—
365C23×C3—21no—
366C23×C3—21no—
367C23×C3—62no—
368C22×D3—22no—
369C22×D3—61no—
370C22×D3—61no—
371C22×D3—61no—
372C22×D3—61no—
373C22×D3—61no—
374C22×D3—61no—
375C22×D3—61no—
376C22×D3—61no—
377C22×D3—61no—
378C22×D3—61no—
379C22×D3—61no—
380C22×D3—61no—
381C22×D3—64no—
382C22×D3—64no—
383C22×D3—128no—
384C22×D3—124no—
385C22×D3—124no—
386C3×Q8—62no—
387C3×Q8—62no—
388C3×D4—62no—
389C3×D4—62no—
390C3×D4—64no—
391C3×D4—64no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—64no—
405C2×C3×C4—64no—
406C2×C3×C4—62no—
407#67—24no—
408#67—24no—
409#67—64no—
410#67—64no—
411#67—64no—
412#67—64no—
413C2×Dic3—22no—
414C2×Dic3—61no—
415C2×Dic3—61no—
416C2×Dic3—61no—
417C2×Dic3—61no—
418C2×Dic3—61no—
419C2×Dic3—61no—
420C2×Dic3—61no—
421C2×Dic3—61no—
422C2×Dic3—61no—
423C2×Dic3—61no—
424C2×Dic3—61no—
425C2×Dic3—61no—
426C2×Dic3—64no—
427C2×Dic3—64no—
428D12—22no—
429D12—22no—
430D12—64no—
431D12—64no—
432C4×D3—24no—
433C4×D3—24no—
434C4×D3—61no—
435C4×D3—61no—
436C4×D3—61no—
437C4×D3—61no—
438C4×D3—61no—
439C4×D3—61no—
440C4×D3—61no—
441C4×D3—61no—
442C4×D3—61no—
443C4×D3—61no—
444C4×D3—61no—
445C4×D3—61no—
446C4×D3—61no—
447C4×D3—61no—
448C4×D3—61no—
449C4×D3—61no—
450C4×D3—61no—
451C4×D3—61no—
452C4×D3—61no—
453C4×D3—61no—
454C4×D3—61no—
455C4×D3—61no—
456C4×D3—61no—
457C4×D3—61no—
458C4×D3—61no—
459C4×D3—61no—
460C4×D3—61no—
461C4×D3—61no—
462C4×D3—61no—
463C4×D3—61no—
464C4×D3—61no—
465C4×D3—61no—
466C4×D3—64no—
467C4×D3—64no—
468C4×D3—64no—
469C4×D3—64no—
470Dic6—22no—
471Dic6—22no—
472Dic6—64no—
473Dic6—64no—
474C3×C8—64no—
475C3⋊C8—24no—
476C2×C32—21no—
477C2×C32—21no—
478C2×C32—21no—
479C2×C32C22×C22⋊C411yescharacteristic
480C3⋊D3—21no—
481C3⋊D3—21no—
482C3⋊D3—21no—
483C3⋊D3#42112yescomplemented
484C3×D3—44no—
485C24—91no—
486C24—181no—
487#41—62no—
488#41—62no—
489#41—62no—
490#41—62no—
491#41—94no—
492#41—94no—
493#41—94no—
494#41—94no—
495#41—182no—
496#41—182no—
497#41—182no—
498#41—182no—
499#41—182no—
500#41—182no—
501#41—182no—
502#41—182no—
503C2×Q8—61no—
504C2×Q8—92no—
505C2×Q8—92no—
506C2×Q8—92no—
507C2×Q8—181no—
508C2×Q8—181no—
509C2×D4—62no—
510C2×D4—61no—
511C2×D4—92no—
512C2×D4—92no—
513C2×D4—92no—
514C2×D4—182no—
515C2×D4—181no—
516C2×D4—181no—
517C2×D4—182no—
518C2×D4—182no—
519C2×D4—182no—
520C2×D4—182no—
521C22×C4—62no—
522C22×C4—91no—
523C22×C4—91no—
524C22×C4—91no—
525C22×C4—91no—
526C22×C4—91no—
527C22×C4—91no—
528C22×C4—91no—
529C22×C4—91no—
530C22×C4—91no—
531C22×C4—91no—
532C22×C4—91no—
533C22×C4—91no—
534C22×C4—91no—
535C22×C4—182no—
536C22×C4—182no—
537C22×C4—182no—
538C22×C4—182no—
539C22×C4—181no—
540C22×C4—182no—
541C22×C4—182no—
542C22×C4GO+(4,𝔽2)11yescharacteristic
543M16—62no—
544M16—62no—
545M16—94no—
546M16—182no—
547C2×C8—62no—
548C2×C8—182no—
549C2×C8—182no—
550C4⋊C4—182no—
551C4⋊C4—182no—
552C22⋊C4—182no—
553C22⋊C4—182no—
554C42—94no—
555C42—182no—
556C22×C3—21no—
557C22×C3—21no—
558C22×C3—21no—
559C22×C3—21no—
560C22×C3—21no—
561C22×C3—21no—
562C22×C3—42no—
563C22×C3—42no—
564C22×C3—64no—
565C22×C3—124no—
566C2×D3—24no—
567C2×D3—44no—
568C2×D3—61no—
569C2×D3—61no—
570C2×D3—61no—
571C2×D3—61no—
572C2×D3—61no—
573C2×D3—61no—
574C2×D3—61no—
575C2×D3—61no—
576C2×D3—64no—
577C2×D3—64no—
578C2×D3—122no—
579C2×D3—122no—
580C2×D3—122no—
581C2×D3—122no—
582C2×D3—128no—
583C2×D3—128no—
584C2×D3—122no—
585C2×D3—122no—
586C2×D3—122no—
587C2×D3—122no—
588C2×D3—122no—
589C2×D3—122no—
590C3×C4—21no—
591C3×C4—21no—
592C3×C4—21no—
593C3×C4—21no—
594C3×C4—21no—
595C3×C4—21no—
596C3×C4—21no—
597C3×C4—21no—
598C3×C4—64no—
599Dic3—24no—
600Dic3—61no—
601Dic3—61no—
602Dic3—61no—
603Dic3—61no—
604Dic3—61no—
605Dic3—61no—
606Dic3—61no—
607Dic3—61no—
608C32C2×#42111yescharacteristic, complemented, Sylow
609C23—62no—
610C23—91no—
611C23—91no—
612C23—91no—
613C23—91no—
614C23—91no—
615C23—91no—
616C23—182no—
617C23—182no—
618C23—362no—
619C23—364no—
620C23D32⋊C411yescharacteristic
621Q8—62no—
622Q8—62no—
623Q8—94no—
624Q8—182no—
625D4—64no—
626D4—64no—
627D4—62no—
628D4—62no—
629D4—94no—
630D4—184no—
631D4—184no—
632D4—182no—
633C2×C4—62no—
634C2×C4—64no—
635C2×C4—64no—
636C2×C4—91no—
637C2×C4—91no—
638C2×C4—91no—
639C2×C4—91no—
640C2×C4—91no—
641C2×C4—91no—
642C2×C4—91no—
643C2×C4—91no—
644C2×C4—91no—
645C2×C4—91no—
646C2×C4—91no—
647C2×C4—91no—
648C2×C4—91no—
649C2×C4—91no—
650C2×C4—91no—
651C2×C4—91no—
652C2×C4—91no—
653C2×C4—91no—
654C2×C4—91no—
655C2×C4—91no—
656C2×C4—91no—
657C2×C4—91no—
658C2×C4—182no—
659C2×C4—182no—
660C2×C4—184no—
661C2×C4—184no—
662C2×C4—184no—
663C2×C4—364no—
664C2×C4D32⋊C411yescharacteristic
665C2×C4D32⋊C411yescharacteristic
666C2×C4D32⋊C411yescharacteristic
667C2×C4C2×GO+(4,𝔽2)11yescharacteristic
668C2×C4C2×GO+(4,𝔽2)11yescharacteristic
669C2×C4C2×GO+(4,𝔽2)11yescharacteristic
670C8—64no—
671C2×C3—22no—
672C2×C3—22no—
673C2×C3—21no—
674C2×C3—21no—
675C2×C3—41no—
676C2×C3—41no—
677C2×C3—41no—
678C2×C3—41no—
679C2×C3—124no—
680D3—44no—
681D3—62no—
682D3—62no—
683D3—62no—
684D3—62no—
685D3—121no—
686D3—121no—
687D3—121no—
688D3—121no—
689C22—41no—
690C22—64no—
691C22—91no—
692C22—91no—
693C22—91no—
694C22—91no—
695C22—124no—
696C22—182no—
697C22—182no—
698C22—182no—
699C22—361no—
700C22—361no—
701C22—361no—
702C22—364no—
703C22—364no—
704C22C2×D32⋊C411yescharacteristic
705C22C2×D32⋊C411yescharacteristic
706C22C2×D32⋊C411yescharacteristic
707C4—64no—
708C4—91no—
709C4—91no—
710C4—91no—
711C4—91no—
712C4—364no—
713C4C2×D32⋊C411yescharacteristic
714C4C2×D32⋊C411yescharacteristic
715C4C2×D32⋊C411yescharacteristic
716C4C22×GO+(4,𝔽2)11yescharacteristic
717C3—21no—
718C3—21no—
719C2—21no—
720C2—21no—
721C2—21no—
722C2—92no—
723C2—124no—
724C2—181no—
725C2—181no—
726C2—181no—
727C2C22×D32⋊C411yescharacteristic
subgroupG/H
center, FrattiniC4C22×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FittingC22×C32×C4D4
socleC2×C32C22×C22⋊C4
prime radicalC2×#64306C2
cosocleC4×C3⋊D3C24
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#421
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×#64286C2semidirect
3. C2×#63818C2semidirect
4. #10593325C2semidirect
5. #10593324C2semidirect
6. #10593323C2semidirect
10. C2×#3805C4semidirect
15. #64306C4semidirect
16. #64306C4semidirect
19. C2×#3802C4semidirect
22. C2×#3797C4semidirect
27. #64286C22semidirect
28. #64286C22semidirect
30. C2×C4×#157C22semidirect
32. C2×#3712C22semidirect
35. #63818C22semidirect
36. #63818C22semidirect
38. #63731C22semidirect
70. C2×#627C2×C4semidirect
72. C2×#625C2×C4semidirect
77. #3805C2×C4semidirect
82. #3802C2×C4semidirect
89. #3798C2×C4semidirect
94. #3797C2×C4semidirect
104. C4×#157C23semidirect
109. #3712C23semidirect
483. C3⋊D3#421semidirect
608. C32C2×#421semidirect

Maximal subgroups

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

subgroupindex
C2×#643062
C2×#642862
C2×#638182
#105933252
#105933242
#105933232
C2×#4219