Finite Group Databasebeta

← #11857533

Subgroups — #11857533

Order 1152.

1398 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64306C211yesmaximal, characteristic
2C2×#64286C211yesmaximal, characteristic, complemented
3#10594969C211yesmaximal, characteristic, complemented
4#10593490C214yesmaximal, complemented
5#10593346C214yesmaximal, complemented
6#10593345C214yesmaximal, complemented
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×C3×#235—21no—
9C2×#3811C2212yes—
10C2×#3805—21no—
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×D32C412yescomplemented
21C2×#3798—21no—
22C2×#3797C411yescharacteristic, complemented
23C2×#3796—21no—
24C2×C22⋊#157C2212yes—
25#64286—21no—
26#64286—21no—
27#64286C2212yescomplemented
28#64286C2212yescomplemented
29C2×C4⋊#157—21no—
30C2×C4×#157—21no—
31C3×#926—21no—
32#63974C2212yes—
33#63957—21no—
34#63900—21no—
35C4×#624—21no—
36#63874C2212yescomplemented
37#63849C2212yescomplemented
38#63738C22116yescomplemented
39C2×D3×#41—61no—
40D3×#117—61no—
41C23×C3⋊D3C2311yescharacteristic
42C22×D32C2×C412yes—
43C22×#157—22no—
44C22×C32×C4D411yescharacteristic
45C22×C3⋊Dic3D411yescharacteristic
46C2×C4×C3⋊D3C2×C411yescharacteristic
47C2×C4×C3⋊D3C2×C411yescharacteristic
48C2×C4×C3⋊D3C2×C411yescharacteristic
49C2×C4×C3⋊D3C2×C411yescharacteristic
50C2×C4×C3⋊D3D411yescharacteristic
51C2×C4×C3⋊D3D411yescharacteristic
52C2×C4×C3⋊D3D411yescharacteristic
53C2×C4×C3⋊D3D411yescharacteristic
54C2×C4×C3⋊D3D411yescharacteristic
55C2×C4×C3⋊D3D411yescharacteristic
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#3811C2×C414yes—
69#3811C2314yes—
70C2×#627—21no—
71C2×#626—22no—
72C2×#625—21no—
73C2×#624—22no—
74C2×#624C2×C412yes—
75#3805—22no—
76#3805—22no—
77#3805—22no—
78#3805—22no—
79C2×D3×Dic3—22no—
80#3802—21no—
81#3802—21no—
82#3802C2×C412yescomplemented
83#3802C2×C412yescomplemented
84C4×D32—22no—
85C4×D32—22no—
86C4×D32C2×C414yescomplemented
87C4×D32C2×C414yescomplemented
88#3798—22no—
89#3798—22no—
90#3798—22no—
91#3798—22no—
92#3797—21no—
93#3797—21no—
94#3797C2×C412yescomplemented
95#3797C2×C412yescomplemented
96#3796—22no—
97#3796—22no—
98#3796—22no—
99#3796—22no—
100C22⋊#157—22no—
101C22⋊#157C2314yes—
102C4⋊#157—22no—
103C4⋊#157—22no—
104C4×#157—22no—
105C4×#157—22no—
106C3×#217—22no—
107C3×C4⋊Dic3—22no—
108C3×C4×Dic3—22no—
109#3724—22no—
110#3722C2314yes—
111Dic32—22no—
112C2×#410—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—61no—
125C2×#237—62no—
126C2×D3×D4—61no—
127C2×D3×D4—62no—
128C2×#235—21no—
129C2×#235—62no—
130C22×C4×D3—62no—
131C22×C4×D3—61no—
132C22×C4×D3—61no—
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⋊D3C2×D411yescharacteristic
146C22×C3⋊D3C2×D411yescharacteristic
147C22×C3⋊D3C2×D411yescharacteristic
148C22×C3⋊D3C2411yescharacteristic
149C22×C3×D3—22no—
150C2×D32—22no—
151C2×D32—44no—
152C2×D32C22×C414yes—
153C2×#157—24no—
154C2×#157—44no—
155C2×C32×C4C22⋊C411yescharacteristic
156C2×C32×C4C22⋊C411yescharacteristic
157C2×C32×C4C22⋊C411yescharacteristic
158C2×C32×C4C22⋊C411yescharacteristic
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⋊Dic3C2×D411yescharacteristic
166C2×C3⋊Dic3C2×D411yescharacteristic
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⋊D3C22×C411yescharacteristic
178C4×C3⋊D3C22×C411yescharacteristic
179C4×C3⋊D3C2×D411yescharacteristic
180C4×C3⋊D3C2×D411yescharacteristic
181C4×C3⋊D3C2×D411yescharacteristic
182C4×C3⋊D3C2×D411yescharacteristic
183C3×#67—24no—
184C3×#67—24no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—24no—
187C3×D12—22no—
188C3×D12—22no—
189C3×C4×D3—24no—
190C3×C4×D3—24no—
191C3×Dic6—22no—
192C3×Dic6—22no—
193#627—22no—
194#627—22no—
195#626—24no—
196#626—24no—
197#625—22no—
198#625—22no—
199#624—22no—
200#624—44no—
201#624C22×C414yes—
202D3×Dic3—24no—
203D3×Dic3—24no—
204C22×#41—91no—
205C2×#117—91no—
206C2×#117—91no—
207#410—94no—
208#410—94no—
209C2×#99—94no—
210C23×D3—62no—
211C23×D3—61no—
212C23×D3—61no—
213C3×#41—62no—
214C3×#41—62no—
215C3×#41—62no—
216C3×#41—62no—
217C2×C3×Q8—61no—
218C2×C3×D4—61no—
219C2×C3×D4—62no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—62no—
223C2×#67—22no—
224C2×#67—62no—
225C2×#67—62no—
226C22×Dic3—61no—
227C22×Dic3—61no—
228C22×Dic3—62no—
229#239—62no—
230#239—62no—
231#239—62no—
232#239—62no—
233D3×Q8—62no—
234D3×Q8—62no—
235D3×Q8—62no—
236D3×Q8—62no—
237#237—62no—
238#237—62no—
239#237—62no—
240#237—62no—
241#237—64no—
242#237—64no—
243#237—64no—
244#237—64no—
245D3×D4—62no—
246D3×D4—62no—
247D3×D4—64no—
248D3×D4—64no—
249D3×D4—62no—
250D3×D4—62no—
251D3×D4—64no—
252D3×D4—64no—
253#235—22no—
254#235—22no—
255#235—22no—
256#235—22no—
257#235—64no—
258#235—64no—
259#235—64no—
260#235—64no—
261C2×D12—21no—
262C2×D12—62no—
263C2×C4×D3—22no—
264C2×C4×D3—64no—
265C2×C4×D3—64no—
266C2×C4×D3—62no—
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—61no—
288C2×C4×D3—61no—
289C2×C4×D3—61no—
290C2×C4×D3—61no—
291C2×C4×D3—64no—
292C2×C4×D3—64no—
293C2×C4×D3—62no—
294C2×C4×D3—64no—
295C2×Dic6—21no—
296C2×Dic6—62no—
297C3×C4⋊C4—62no—
298C3×C22⋊C4—62no—
299C3×C42—62no—
300#217—22no—
301(C2×D3)⋊C4—64no—
302C4⋊Dic3—22no—
303Dic3⋊C4—64no—
304C4×Dic3—22no—
305C4×Dic3—64no—
306C22×C32—41no—
307C22×C32C2×C22⋊C411yescharacteristic
308C22×C32C2×C22⋊C411yescharacteristic
309C22×C32C22×D411yescharacteristic
310C2×C3⋊D3—22no—
311C2×C3⋊D3—22no—
312C2×C3⋊D3—22no—
313C2×C3⋊D3—41no—
314C2×C3⋊D3—41no—
315C2×C3⋊D3—41no—
316C2×C3⋊D3C2×C22⋊C411yescharacteristic
317C2×C3⋊D3C2×C22⋊C411yescharacteristic
318C2×C3⋊D3C23×C411yescharacteristic
319C2×C3⋊D3C22×D411yescharacteristic
320C2×C3×D3—24no—
321C2×C3×D3—44no—
322D32—44no—
323D32—44no—
324#157—44no—
325C32×C4C2×C22⋊C411yescharacteristic
326C32×C4C2×C22⋊C411yescharacteristic
327C32×C4C2×C22⋊C411yescharacteristic
328C32×C4C2×C22⋊C411yescharacteristic
329C3⋊Dic3C2×C22⋊C411yescharacteristic
330C3⋊Dic3C2×C22⋊C411yescharacteristic
331C3⋊Dic3C2×C22⋊C411yescharacteristic
332C3⋊Dic3C2×C22⋊C411yescharacteristic
333C3×Dic3—24no—
334C3×Dic3—44no—
335C2×#41—61no—
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—
345C2×#41—181no—
346C2×#41—181no—
347C22×Q8—91no—
348C22×D4—92no—
349C22×D4—91no—
350C23×C4—92no—
351C23×C4—91no—
352#117—61no—
353#117—92no—
354#117—92no—
355#117—92no—
356#117—92no—
357#117—181no—
358#117—181no—
359#117—181no—
360C2×C4⋊C4—181no—
361C2×C4⋊C4—181no—
362C2×C22⋊C4—92no—
363C2×C22⋊C4—92no—
364C2×C42—181no—
365C2×C42—181no—
366#99—916no—
367C23×C3—21no—
368C23×C3—21no—
369C23×C3—62no—
370C22×D3—22no—
371C22×D3—64no—
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—61no—
382C22×D3—61no—
383C22×D3—61no—
384C22×D3—64no—
385C22×D3—128no—
386C22×D3—124no—
387C22×D3—124no—
388C3×Q8—62no—
389C3×Q8—62no—
390C3×D4—62no—
391C3×D4—62no—
392C3×D4—64no—
393C3×D4—64no—
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—21no—
405C2×C3×C4—21no—
406C2×C3×C4—64no—
407C2×C3×C4—64no—
408C2×C3×C4—62no—
409C2×C3×C4—64no—
410#67—24no—
411#67—24no—
412#67—64no—
413#67—64no—
414#67—64no—
415#67—64no—
416C2×Dic3—22no—
417C2×Dic3—24no—
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—61no—
429C2×Dic3—61no—
430C2×Dic3—64no—
431C2×Dic3—64no—
432D12—22no—
433D12—22no—
434D12—64no—
435D12—64no—
436C4×D3—24no—
437C4×D3—24no—
438C4×D3—64no—
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—61no—
469C4×D3—61no—
470C4×D3—61no—
471C4×D3—64no—
472C4×D3—64no—
473C4×D3—64no—
474C4×D3—128no—
475Dic6—22no—
476Dic6—22no—
477Dic6—64no—
478Dic6—64no—
479C2×C32—21no—
480C2×C32—21no—
481C2×C32—21no—
482C2×C32C22×C22⋊C411yescharacteristic
483C3⋊D3—21no—
484C3⋊D3—21no—
485C3⋊D3—21no—
486C3⋊D3#41012yescomplemented
487C3×D3—44no—
488C24—92no—
489C24—91no—
490#41—62no—
491#41—62no—
492#41—62no—
493#41—62no—
494#41—182no—
495#41—182no—
496#41—182no—
497#41—182no—
498#41—182no—
499#41—182no—
500#41—182no—
501#41—182no—
502#41—182no—
503#41—182no—
504#41—182no—
505#41—182no—
506C2×Q8—61no—
507C2×Q8—92no—
508C2×Q8—92no—
509C2×Q8—181no—
510C2×Q8—181no—
511C2×Q8—181no—
512C2×D4—62no—
513C2×D4—61no—
514C2×D4—94no—
515C2×D4—94no—
516C2×D4—92no—
517C2×D4—92no—
518C2×D4—182no—
519C2×D4—181no—
520C2×D4—181no—
521C2×D4—181no—
522C2×D4—182no—
523C2×D4—182no—
524C22×C4—62no—
525C22×C4—92no—
526C22×C4—94no—
527C22×C4—94no—
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—91no—
537C22×C4—91no—
538C22×C4—91no—
539C22×C4—91no—
540C22×C4—91no—
541C22×C4—182no—
542C22×C4—182no—
543C22×C4—182no—
544C22×C4—182no—
545C22×C4—182no—
546C22×C4GO+(4,𝔽2)11yescharacteristic
547C4⋊C4—62no—
548C4⋊C4—182no—
549C4⋊C4—182no—
550C4⋊C4—182no—
551C22⋊C4—62no—
552C22⋊C4—94no—
553C22⋊C4—94no—
554C22⋊C4—182no—
555C42—62no—
556C42—182no—
557C42—182no—
558C42—182no—
559C22×C3—21no—
560C22×C3—21no—
561C22×C3—21no—
562C22×C3—21no—
563C22×C3—21no—
564C22×C3—21no—
565C22×C3—42no—
566C22×C3—42no—
567C22×C3—64no—
568C22×C3—124no—
569C2×D3—24no—
570C2×D3—44no—
571C2×D3—61no—
572C2×D3—61no—
573C2×D3—61no—
574C2×D3—61no—
575C2×D3—61no—
576C2×D3—61no—
577C2×D3—61no—
578C2×D3—61no—
579C2×D3—64no—
580C2×D3—64no—
581C2×D3—122no—
582C2×D3—122no—
583C2×D3—122no—
584C2×D3—122no—
585C2×D3—128no—
586C2×D3—128no—
587C2×D3—122no—
588C2×D3—122no—
589C2×D3—122no—
590C2×D3—122no—
591C2×D3—122no—
592C2×D3—122no—
593C3×C4—21no—
594C3×C4—21no—
595C3×C4—21no—
596C3×C4—21no—
597C3×C4—21no—
598C3×C4—21no—
599C3×C4—21no—
600C3×C4—21no—
601C3×C4—64no—
602C3×C4—124no—
603Dic3—24no—
604Dic3—44no—
605Dic3—61no—
606Dic3—61no—
607Dic3—61no—
608Dic3—61no—
609Dic3—61no—
610Dic3—61no—
611Dic3—61no—
612Dic3—61no—
613C32C2×#41011yescharacteristic, complemented, Sylow
614C23—62no—
615C23—94no—
616C23—91no—
617C23—91no—
618C23—91no—
619C23—91no—
620C23—91no—
621C23—91no—
622C23—182no—
623C23—362no—
624C23—364no—
625C23C2×GO+(4,𝔽2)11yescharacteristic
626Q8—62no—
627Q8—62no—
628Q8—182no—
629Q8—182no—
630D4—64no—
631D4—64no—
632D4—62no—
633D4—62no—
634D4—184no—
635D4—184no—
636D4—182no—
637D4—182no—
638C2×C4—62no—
639C2×C4—64no—
640C2×C4—64no—
641C2×C4—64no—
642C2×C4—94no—
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—91no—
663C2×C4—91no—
664C2×C4—91no—
665C2×C4—182no—
666C2×C4—184no—
667C2×C4—184no—
668C2×C4—184no—
669C2×C4—364no—
670C2×C4—364no—
671C2×C4D32⋊C411yescharacteristic
672C2×C4D32⋊C411yescharacteristic
673C2×C4D32⋊C411yescharacteristic
674C2×C4D32⋊C411yescharacteristic
675C2×C4C2×GO+(4,𝔽2)11yescharacteristic
676C2×C4C2×GO+(4,𝔽2)11yescharacteristic
677C2×C3—22no—
678C2×C3—22no—
679C2×C3—21no—
680C2×C3—21no—
681C2×C3—41no—
682C2×C3—41no—
683C2×C3—41no—
684C2×C3—41no—
685C2×C3—124no—
686D3—44no—
687D3—62no—
688D3—62no—
689D3—62no—
690D3—62no—
691D3—121no—
692D3—121no—
693D3—121no—
694D3—121no—
695C22—41no—
696C22—64no—
697C22—91no—
698C22—91no—
699C22—91no—
700C22—91no—
701C22—124no—
702C22—182no—
703C22—182no—
704C22—182no—
705C22—361no—
706C22—361no—
707C22—361no—
708C22—364no—
709C22—364no—
710C22C2×D32⋊C411yescharacteristic
711C22C2×D32⋊C411yescharacteristic
712C22C22×GO+(4,𝔽2)11yescharacteristic
713C4—64no—
714C4—91no—
715C4—91no—
716C4—91no—
717C4—91no—
718C4—124no—
719C4—364no—
720C4C2×D32⋊C411yescharacteristic
721C4C2×D32⋊C411yescharacteristic
722C4C2×D32⋊C411yescharacteristic
723C4C2×D32⋊C411yescharacteristic
724C3—21no—
725C3—21no—
726C2—21no—
727C2—21no—
728C2—21no—
729C2—92no—
730C2—124no—
731C2—181no—
732C2—181no—
733C2—181no—
734C2C22×D32⋊C411yescharacteristic
subgroupG/H
centerC4C2×D32⋊C4
commutatorC2×C3⋊D3C23×C4
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC2×C32C22×C22⋊C4
prime radicalC2×#64306C2
cosocleC22×C3⋊D3C24
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#410
LCSG ▷ C2×C3⋊D3 ▷ 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. #10594969C2semidirect
4. #10593490C2semidirect
5. #10593346C2semidirect
6. #10593345C2semidirect
15. #64306C4semidirect
16. #64306C4semidirect
19. C2×#3802C4semidirect
20. C2×C4×D32C4semidirect
22. C2×#3797C4semidirect
27. #64286C22semidirect
28. #64286C22semidirect
36. #63874C22semidirect
37. #63849C22semidirect
38. #63738C22semidirect
82. #3802C2×C4semidirect
83. #3802C2×C4semidirect
86. C4×D32C2×C4semidirect
87. C4×D32C2×C4semidirect
94. #3797C2×C4semidirect
95. #3797C2×C4semidirect
486. C3⋊D3#410semidirect
613. C32C2×#410semidirect

Maximal subgroups

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

subgroupindex
C2×#643062
C2×#642862
#105949692
#105934902
#105933462
#105933452
C2×#4109