Finite Group Databasebeta

← #11858172

Subgroups — #11858172

Order 1152.

1382 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64306C211yesmaximal, characteristic
2C2×#64283C211yesmaximal, characteristic, complemented
3#10594969C211yesmaximal, characteristic, complemented
4#10593506C214yesmaximal, complemented
5#10593381C214yesmaximal, complemented
6#10593380C214yesmaximal, complemented
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×C3×#235—21no—
9C2×#3811—21no—
10C2×#3805C2212yes—
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×#3798C412yescomplemented
22C2×#3797C411yescharacteristic, complemented
23C2×#3796—21no—
24C2×#3792C2212yescomplemented
25#64283—21no—
26#64283—21no—
27#64283C2212yescomplemented
28#64283C2212yescomplemented
29C2×#3788—21no—
30C2×#3787—21no—
31C3×#926—21no—
32#63974—21no—
33#63957C2212yescomplemented
34#63900—21no—
35C4×#624C2212yescomplemented
36#63874—21no—
37#63849C2212yescomplemented
38#63741C22116yescomplemented
39C2×D3×#41—61no—
40D3×#117—61no—
41C23×C3⋊D3D411yescharacteristic
42C22×D32—21no—
43C22×C32×C4D411yescharacteristic
44C22×C3⋊Dic3C2311yescharacteristic
45C2×C4×C3⋊D3C2×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×C3×#67—22no—
58C3×#235—22no—
59C3×#235—22no—
60C3×#235—22no—
61C3×#235—22no—
62C2×C3×D12—21no—
63C2×C3×C4×D3—22no—
64C2×C3×Dic6—21no—
65#3811—22no—
66#3811—22no—
67#3811—22no—
68#3811—22no—
69C2×#627C2×C412yescomplemented
70C2×#626—22no—
71C2×#625C2×C412yescomplemented
72C2×#624—21no—
73C2×#624—22no—
74#3805—22no—
75#3805—22no—
76#3805C2×C414yescomplemented
77#3805C2314yes—
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×C414yes—
90#3798C2×C414yescomplemented
91#3797—21no—
92#3797—21no—
93#3797C2×C412yes—
94#3797C2×C412yescomplemented
95#3796—22no—
96#3796—22no—
97#3796—22no—
98#3796—22no—
99#3792—22no—
100#3792C2314yescomplemented
101C2×#622—22no—
102#3788—22no—
103#3788—22no—
104#3787—22no—
105#3787—22no—
106C3×#217—22no—
107C3×C4⋊Dic3—22no—
108C3×C4×Dic3—22no—
109#3724—22no—
110#3722—22no—
111Dic32C2314yescomplemented
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—
133C3×#117—61no—
134#926—21no—
135#892—62no—
136D3×C4⋊C4—62no—
137D3×C22⋊C4—62no—
138#877—62no—
139#872—62no—
140C42×D3—62no—
141C23×C32C2×D411yescharacteristic
142C22×C3⋊D3—42no—
143C22×C3⋊D3C22⋊C411yescharacteristic
144C22×C3⋊D3C22⋊C411yescharacteristic
145C22×C3⋊D3C22⋊C411yescharacteristic
146C22×C3⋊D3C22⋊C411yescharacteristic
147C22×C3⋊D3C2×D411yescharacteristic
148C22×C3⋊D3C2×D411yescharacteristic
149C22×C3×D3—22no—
150C2×D32—22no—
151C2×D32—22no—
152C2×D32—44no—
153C2×C32×C4C22⋊C411yescharacteristic
154C2×C32×C4C22⋊C411yescharacteristic
155C2×C32×C4C22⋊C411yescharacteristic
156C2×C32×C4C22⋊C411yescharacteristic
157C2×C32×C4C2×D411yescharacteristic
158C2×C32×C4C2×D411yescharacteristic
159C2×C3⋊Dic3C22×C411yescharacteristic
160C2×C3⋊Dic3C22×C411yescharacteristic
161C2×C3⋊Dic3C2×D411yescharacteristic
162C2×C3⋊Dic3C2×D411yescharacteristic
163C2×C3⋊Dic3C2×D411yescharacteristic
164C2×C3⋊Dic3C2411yescharacteristic
165C4×C3⋊D3C22⋊C411yescharacteristic
166C4×C3⋊D3C22⋊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⋊D3C22×C411yescharacteristic
177C4×C3⋊D3C2×D411yescharacteristic
178C4×C3⋊D3C2×D411yescharacteristic
179C4×C3⋊D3C2×D411yescharacteristic
180C4×C3⋊D3C2×D411yescharacteristic
181C3×#67—24no—
182C3×#67—24no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—24no—
185C3×D12—22no—
186C3×D12—22no—
187C3×C4×D3—24no—
188C3×C4×D3—24no—
189C3×Dic6—22no—
190C3×Dic6—22no—
191#627—22no—
192#627C22×C414yes—
193#626—24no—
194#626—24no—
195#625—22no—
196#625C22×C414yes—
197#624—22no—
198#624—22no—
199#624—44no—
200D3×Dic3—24no—
201D3×Dic3—24no—
202#622—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×C4×D3—64no—
294C2×Dic6—21no—
295C2×Dic6—62no—
296C3×C4⋊C4—62no—
297C3×C22⋊C4—62no—
298C3×C42—62no—
299#217—22no—
300(C2×D3)⋊C4—64no—
301C4⋊Dic3—22no—
302Dic3⋊C4—64no—
303C4×Dic3—22no—
304C4×Dic3—64no—
305C22×C32—41no—
306C22×C32C2×C22⋊C411yescharacteristic
307C22×C32C2×C22⋊C411yescharacteristic
308C22×C32C22×D411yescharacteristic
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⋊D3C2×C22⋊C411yescharacteristic
319C2×C3×D3—24no—
320C2×C3×D3—44no—
321D32—44no—
322D32—44no—
323C32×C4C2×C22⋊C411yescharacteristic
324C32×C4C2×C22⋊C411yescharacteristic
325C32×C4C2×C22⋊C411yescharacteristic
326C32×C4C2×C22⋊C411yescharacteristic
327C3⋊Dic3C2×C22⋊C411yescharacteristic
328C3⋊Dic3C2×C22⋊C411yescharacteristic
329C3⋊Dic3C23×C411yescharacteristic
330C3⋊Dic3C22×D411yescharacteristic
331C3×Dic3—24no—
332C3×Dic3—44no—
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—92no—
351C2×M16—92no—
352C2×M16—92no—
353C2×M16—181no—
354C2×M16—181no—
355C2×M16—181no—
356C22×C8—181no—
357#117—61no—
358#117—92no—
359#117—92no—
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—
407C2×C3×C4—64no—
408#67—24no—
409#67—24no—
410#67—64no—
411#67—64no—
412#67—64no—
413#67—64no—
414C2×Dic3—22no—
415C2×Dic3—24no—
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—61no—
427C2×Dic3—61no—
428C2×Dic3—64no—
429C2×Dic3—64no—
430D12—22no—
431D12—22no—
432D12—64no—
433D12—64no—
434C4×D3—24no—
435C4×D3—24no—
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—61no—
467C4×D3—61no—
468C4×D3—64no—
469C4×D3—64no—
470C4×D3—64no—
471C4×D3—64no—
472C4×D3—128no—
473Dic6—22no—
474Dic6—22no—
475Dic6—64no—
476Dic6—64no—
477C2×C32—21no—
478C2×C32—21no—
479C2×C32—21no—
480C2×C32C22×C22⋊C411yescharacteristic
481C3⋊D3—21no—
482C3⋊D3—21no—
483C3⋊D3—21no—
484C3⋊D3#42112yescomplemented
485C3×D3—44no—
486C24—91no—
487C24—181no—
488#41—62no—
489#41—62no—
490#41—62no—
491#41—62no—
492#41—94no—
493#41—94no—
494#41—94no—
495#41—94no—
496#41—182no—
497#41—182no—
498#41—182no—
499#41—182no—
500#41—182no—
501#41—182no—
502#41—182no—
503#41—182no—
504C2×Q8—61no—
505C2×Q8—92no—
506C2×Q8—92no—
507C2×Q8—92no—
508C2×Q8—181no—
509C2×Q8—181no—
510C2×D4—62no—
511C2×D4—61no—
512C2×D4—92no—
513C2×D4—92no—
514C2×D4—92no—
515C2×D4—182no—
516C2×D4—181no—
517C2×D4—181no—
518C2×D4—182no—
519C2×D4—182no—
520C2×D4—182no—
521C2×D4—182no—
522C22×C4—62no—
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—91no—
536C22×C4—182no—
537C22×C4—182no—
538C22×C4—182no—
539C22×C4—182no—
540C22×C4—181no—
541C22×C4—182no—
542C22×C4—182no—
543C22×C4GO+(4,𝔽2)11yescharacteristic
544M16—94no—
545M16—182no—
546M16—182no—
547M16—182no—
548C2×C8—182no—
549C2×C8—182no—
550C2×C8—182no—
551C4⋊C4—62no—
552C4⋊C4—182no—
553C22⋊C4—62no—
554C22⋊C4—182no—
555C42—62no—
556C42—94no—
557C22×C3—21no—
558C22×C3—21no—
559C22×C3—21no—
560C22×C3—21no—
561C22×C3—21no—
562C22×C3—21no—
563C22×C3—42no—
564C22×C3—42no—
565C22×C3—64no—
566C22×C3—124no—
567C2×D3—24no—
568C2×D3—44no—
569C2×D3—61no—
570C2×D3—61no—
571C2×D3—61no—
572C2×D3—61no—
573C2×D3—61no—
574C2×D3—61no—
575C2×D3—61no—
576C2×D3—61no—
577C2×D3—64no—
578C2×D3—64no—
579C2×D3—122no—
580C2×D3—122no—
581C2×D3—122no—
582C2×D3—122no—
583C2×D3—128no—
584C2×D3—128no—
585C2×D3—122no—
586C2×D3—122no—
587C2×D3—122no—
588C2×D3—122no—
589C2×D3—122no—
590C2×D3—122no—
591C3×C4—21no—
592C3×C4—21no—
593C3×C4—21no—
594C3×C4—21no—
595C3×C4—21no—
596C3×C4—21no—
597C3×C4—21no—
598C3×C4—21no—
599C3×C4—64no—
600C3×C4—124no—
601Dic3—24no—
602Dic3—44no—
603Dic3—61no—
604Dic3—61no—
605Dic3—61no—
606Dic3—61no—
607Dic3—61no—
608Dic3—61no—
609Dic3—61no—
610Dic3—61no—
611C32C2×#42111yescharacteristic, complemented, Sylow
612C23—62no—
613C23—91no—
614C23—91no—
615C23—91no—
616C23—91no—
617C23—91no—
618C23—91no—
619C23—182no—
620C23—182no—
621C23—362no—
622C23—364no—
623C23C2×GO+(4,𝔽2)11yescharacteristic
624Q8—62no—
625Q8—62no—
626Q8—94no—
627Q8—182no—
628D4—64no—
629D4—64no—
630D4—62no—
631D4—62no—
632D4—94no—
633D4—184no—
634D4—184no—
635D4—182no—
636C2×C4—62no—
637C2×C4—64no—
638C2×C4—64no—
639C2×C4—64no—
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—91no—
659C2×C4—91no—
660C2×C4—91no—
661C2×C4—91no—
662C2×C4—182no—
663C2×C4—182no—
664C2×C4—184no—
665C2×C4—184no—
666C2×C4—364no—
667C2×C4D32⋊C411yescharacteristic
668C2×C4D32⋊C411yescharacteristic
669C2×C4D32⋊C411yescharacteristic
670C2×C4D32⋊C411yescharacteristic
671C2×C4C2×GO+(4,𝔽2)11yescharacteristic
672C2×C4C2×GO+(4,𝔽2)11yescharacteristic
673C8—184no—
674C2×C3—22no—
675C2×C3—22no—
676C2×C3—21no—
677C2×C3—21no—
678C2×C3—41no—
679C2×C3—41no—
680C2×C3—41no—
681C2×C3—41no—
682C2×C3—124no—
683D3—44no—
684D3—62no—
685D3—62no—
686D3—62no—
687D3—62no—
688D3—121no—
689D3—121no—
690D3—121no—
691D3—121no—
692C22—41no—
693C22—64no—
694C22—91no—
695C22—91no—
696C22—91no—
697C22—91no—
698C22—124no—
699C22—182no—
700C22—182no—
701C22—182no—
702C22—361no—
703C22—361no—
704C22—361no—
705C22—364no—
706C22—364no—
707C22C2×D32⋊C411yescharacteristic
708C22C2×D32⋊C411yescharacteristic
709C22C22×GO+(4,𝔽2)11yescharacteristic
710C4—64no—
711C4—91no—
712C4—91no—
713C4—91no—
714C4—91no—
715C4—124no—
716C4C2×D32⋊C411yescharacteristic
717C4C2×D32⋊C411yescharacteristic
718C4C2×D32⋊C411yescharacteristic
719C4C2×D32⋊C411yescharacteristic
720C3—21no—
721C3—21no—
722C2—21no—
723C2—21no—
724C2—21no—
725C2—92no—
726C2—124no—
727C2—181no—
728C2—181no—
729C2—181no—
730C2C22×D32⋊C411yescharacteristic
subgroupG/H
centerC4C2×D32⋊C4
commutatorC3⋊Dic3C23×C4
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC2×C32C22×C22⋊C4
prime radicalC2×#64306C2
cosocleC2×C3⋊Dic3C24
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×#64283C2semidirect
3. #10594969C2semidirect
4. #10593506C2semidirect
5. #10593381C2semidirect
6. #10593380C2semidirect
15. #64306C4semidirect
16. #64306C4semidirect
19. C2×#3802C4semidirect
21. C2×#3798C4semidirect
22. C2×#3797C4semidirect
24. C2×#3792C22semidirect
27. #64283C22semidirect
28. #64283C22semidirect
33. #63957C22semidirect
35. C4×#624C22semidirect
37. #63849C22semidirect
38. #63741C22semidirect
69. C2×#627C2×C4semidirect
71. C2×#625C2×C4semidirect
76. #3805C2×C4semidirect
82. #3802C2×C4semidirect
90. #3798C2×C4semidirect
94. #3797C2×C4semidirect
100. #3792C23semidirect
111. Dic32C23semidirect
484. C3⋊D3#421semidirect
611. 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×#642832
#105949692
#105935062
#105933812
#105933802
C2×#4219