Finite Group Databasebeta

← #11857953

Subgroups — #11857953

Order 1152.

1662 conjugacy classes of subgroups.

The subgroup lattice has 697 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×C3⋊D3C211yesmaximal, characteristic
2C2×#64286C211yesmaximal, characteristic, complemented
3C2×#64283C211yesmaximal, characteristic, complemented
4#10593841C214yesmaximal, complemented
5#10593840C214yesmaximal, complemented
6#10593829C212yesmaximal, complemented
7#10593814C212yesmaximal, complemented
8C2×C32×#41C411yescharacteristic, complemented
9#41×C3⋊D3—21no—
10#41×C3⋊D3—21no—
11#41×C3⋊D3—21no—
12#41×C3⋊D3—21no—
13#41×C3⋊D3C412yescomplemented
14#41×C3⋊D3C412yescomplemented
15#41×C3⋊D3C2212yes—
16#41×C3⋊D3C2212yes—
17C2×#3832C411yescharacteristic, complemented
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×#3830—21no—
20C2×#3830C411yescharacteristic, complemented
21C2×D4×C3⋊D3—21no—
22C2×D4×C3⋊D3C2211yescharacteristic
23C2×#3828—21no—
24C2×#3828C411yescharacteristic, complemented
25C22×C4×C3⋊D3—21no—
26C22×C4×C3⋊D3C2211yescharacteristic
27C2×C22⋊#157—21no—
28C2×#3792—21no—
29#64286—21no—
30#64286—21no—
31#64286C2212yes—
32#64286C2212yescomplemented
33C2×C4⋊#157C2212yescomplemented
34C2×C4×#157—21no—
35#64283—21no—
36#64283—21no—
37#64283C2212yes—
38#64283C2212yescomplemented
39C2×#3788—21no—
40C2×#3787C2212yescomplemented
41#63784C2218yescomplemented
42#63782C2218yescomplemented
43C2×D3×#41—62no—
44C23×C3⋊D3—21no—
45C23×C3⋊D3D411yescharacteristic
46C22×#157—22no—
47C32×#41—21no—
48C32×#41—21no—
49C32×#41C2×C412yes—
50C32×#41C2×C412yescomplemented
51C2×C32×Q8C2×C411yescharacteristic, complemented
52C2×C32×D4—21no—
53C2×C32×D4C2×C411yescharacteristic, complemented
54C22×C32×C4—21no—
55C22×C32×C4C2×C411yescharacteristic
56C2×#638—21no—
57C2×#638—21no—
58C2×#638—21no—
59C22×C3⋊Dic3—21no—
60C22×C3⋊Dic3D411yescharacteristic
61#3832—21no—
62#3832—21no—
63#3832C2×C412yes—
64#3832C2×C412yescomplemented
65Q8×C3⋊D3—21no—
66Q8×C3⋊D3—21no—
67Q8×C3⋊D3C2×C412yescomplemented
68Q8×C3⋊D3C2312yes—
69#3830—22no—
70#3830—22no—
71#3830—22no—
72#3830—22no—
73#3830—21no—
74#3830—21no—
75#3830C2×C412yes—
76#3830C2×C412yescomplemented
77D4×C3⋊D3—22no—
78D4×C3⋊D3—22no—
79D4×C3⋊D3—22no—
80D4×C3⋊D3—22no—
81D4×C3⋊D3—21no—
82D4×C3⋊D3—21no—
83D4×C3⋊D3C2×C412yescomplemented
84D4×C3⋊D3C2312yes—
85#3828—21no—
86#3828—21no—
87#3828—22no—
88#3828—22no—
89#3828—22no—
90#3828—22no—
91#3828C2×C412yes—
92#3828C2×C412yescomplemented
93C2×C4⋊(C3⋊D3)—21no—
94C2×C4⋊(C3⋊D3)C2×C411yescharacteristic, complemented
95C2×C4×C3⋊D3—21no—
96C2×C4×C3⋊D3—21no—
97C2×C4×C3⋊D3—21no—
98C2×C4×C3⋊D3—22no—
99C2×C4×C3⋊D3—22no—
100C2×C4×C3⋊D3—22no—
101C2×C4×C3⋊D3—22no—
102C2×C4×C3⋊D3C2×C411yescharacteristic
103C2×C4×C3⋊D3C2×C411yescharacteristic
104C2×C4×C3⋊D3C2×C411yescharacteristic
105C2×C4×C3⋊D3D411yescharacteristic
106C2×C4×C3⋊D3D411yescharacteristic
107C2×C4×C3⋊D3D411yescharacteristic
108C2×C4×C3⋊D3D411yescharacteristic
109C2×C4×C3⋊D3D411yescharacteristic
110C2×C4×C3⋊D3D411yescharacteristic
111C2×C4×C3⋊D3C2311yescharacteristic
112C2×C4×C3⋊D3C2311yescharacteristic
113C2×C4×C3⋊D3C2311yescharacteristic
114C2×#634—21no—
115C2×#634C2×C411yescharacteristic, complemented
116C22⋊#157—22no—
117C22⋊#157—22no—
118#3792—22no—
119#3792—22no—
120C2×#622—22no—
121C4⋊#157—22no—
122C4⋊#157C2314yes—
123C4×#157—22no—
124C4×#157—22no—
125#3788—22no—
126#3788—22no—
127#3787—22no—
128#3787C2314yes—
129#2896—91nomaximal, Sylow
130C2×C3×#41—22no—
131D3×#41—64no—
132D3×#41—64no—
133D3×#41—64no—
134D3×#41—64no—
135D3×#41—64no—
136D3×#41—64no—
137D3×#41—64no—
138D3×#41—64no—
139C2×#239—62no—
140C2×D3×Q8—62no—
141C2×#237—62no—
142C2×#237—64no—
143C2×D3×D4—62no—
144C2×D3×D4—64no—
145C2×#235—62no—
146C2×#235—64no—
147C22×C4×D3—62no—
148C22×C4×D3—64no—
149C23×C32—21no—
150C23×C32C22⋊C411yescharacteristic
151C22×C3⋊D3—21no—
152C22×C3⋊D3—22no—
153C22×C3⋊D3—22no—
154C22×C3⋊D3—42no—
155C22×C3⋊D3—44no—
156C22×C3⋊D3C22⋊C411yescharacteristic
157C22×C3⋊D3C22⋊C411yescharacteristic
158C22×C3⋊D3C22⋊C411yescharacteristic
159C22×C3⋊D3C2×D411yescharacteristic
160C22×C3⋊D3C2×D411yescharacteristic
161C22×C3⋊D3C2×D411yescharacteristic
162C2×#157—24no—
163C2×#157—44no—
164C32×Q8—21no—
165C32×Q8C22×C412yes—
166C32×D4—22no—
167C32×D4—22no—
168C32×D4—21no—
169C32×D4C22×C412yes—
170C2×C32×C4—21no—
171C2×C32×C4—22no—
172C2×C32×C4—22no—
173C2×C32×C4C22⋊C411yescharacteristic
174C2×C32×C4C22⋊C411yescharacteristic
175C2×C32×C4C22⋊C411yescharacteristic
176C2×C32×C4C22×C411yescharacteristic
177C2×C32×C4C22×C411yescharacteristic
178C2×C32×C4C22×C411yescharacteristic
179#638—22no—
180#638—22no—
181#638—22no—
182#638—22no—
183#638—22no—
184#638—22no—
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3—22no—
187C2×C3⋊Dic3—22no—
188C2×C3⋊Dic3C22⋊C411yescharacteristic
189C2×C3⋊Dic3C22⋊C411yescharacteristic
190C2×C3⋊Dic3C22⋊C411yescharacteristic
191C2×C3⋊Dic3C2×D411yescharacteristic
192C2×C3⋊Dic3C2×D411yescharacteristic
193C2×C3⋊Dic3C2×D411yescharacteristic
194C4⋊(C3⋊D3)—22no—
195C4⋊(C3⋊D3)—22no—
196C4⋊(C3⋊D3)—21no—
197C4⋊(C3⋊D3)C22×C412yes—
198C4×C3⋊D3—22no—
199C4×C3⋊D3—22no—
200C4×C3⋊D3—22no—
201C4×C3⋊D3—22no—
202C4×C3⋊D3—22no—
203C4×C3⋊D3—22no—
204C4×C3⋊D3C22⋊C411yescharacteristic
205C4×C3⋊D3C22⋊C411yescharacteristic
206C4×C3⋊D3C22⋊C411yescharacteristic
207C4×C3⋊D3C22⋊C411yescharacteristic
208C4×C3⋊D3C22⋊C411yescharacteristic
209C4×C3⋊D3C22⋊C411yescharacteristic
210C4×C3⋊D3C22×C411yescharacteristic
211C4×C3⋊D3C22×C411yescharacteristic
212C4×C3⋊D3C22×C411yescharacteristic
213C4×C3⋊D3C2×D411yescharacteristic
214C4×C3⋊D3C2×D411yescharacteristic
215C4×C3⋊D3C2×D411yescharacteristic
216C4×C3⋊D3C2×D411yescharacteristic
217C4×C3⋊D3C2×D411yescharacteristic
218C4×C3⋊D3C2×D411yescharacteristic
219C4×C3⋊D3C2411yescharacteristic
220#634—21no—
221#634—22no—
222#634—22no—
223#634C22×C412yes—
224#622—24no—
225C22×#41—91no—
226C22×M16—91no—
227C2×#117—91no—
228#419—92no—
229#418—92no—
230#417—94no—
231#416—94no—
232C23×D3—62no—
233C23×D3—64no—
234C3×#41—24no—
235C3×#41—24no—
236C3×#41—24no—
237C3×#41—24no—
238C2×C3×Q8—22no—
239C2×C3×D4—24no—
240C2×C3×D4—22no—
241C22×C3×C4—24no—
242C22×C3×C4—22no—
243C2×#67—64no—
244C2×#67—64no—
245C2×#67—64no—
246C22×Dic3—62no—
247C22×Dic3—64no—
248#239—64no—
249#239—64no—
250#239—64no—
251#239—64no—
252D3×Q8—64no—
253D3×Q8—64no—
254D3×Q8—64no—
255D3×Q8—64no—
256#237—64no—
257#237—64no—
258#237—64no—
259#237—64no—
260#237—68no—
261#237—68no—
262#237—68no—
263#237—68no—
264D3×D4—64no—
265D3×D4—64no—
266D3×D4—64no—
267D3×D4—64no—
268D3×D4—68no—
269D3×D4—68no—
270D3×D4—68no—
271D3×D4—68no—
272#235—64no—
273#235—64no—
274#235—68no—
275#235—68no—
276#235—68no—
277#235—68no—
278#235—64no—
279#235—64no—
280C2×D12—62no—
281C2×D12—64no—
282C2×C4×D3—62no—
283C2×C4×D3—62no—
284C2×C4×D3—62no—
285C2×C4×D3—62no—
286C2×C4×D3—62no—
287C2×C4×D3—62no—
288C2×C4×D3—62no—
289C2×C4×D3—62no—
290C2×C4×D3—62no—
291C2×C4×D3—62no—
292C2×C4×D3—62no—
293C2×C4×D3—62no—
294C2×C4×D3—64no—
295C2×C4×D3—64no—
296C2×C4×D3—64no—
297C2×C4×D3—68no—
298C2×C4×D3—68no—
299C2×C4×D3—68no—
300C2×C4×D3—68no—
301C2×Dic6—62no—
302C2×Dic6—64no—
303C22×C32—22no—
304C22×C32—41no—
305C22×C32—42no—
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—22no—
313C2×C3⋊D3—41no—
314C2×C3⋊D3—41no—
315C2×C3⋊D3—41no—
316C2×C3⋊D3—44no—
317C2×C3⋊D3—42no—
318C2×C3⋊D3—44no—
319C2×C3⋊D3C2×C22⋊C411yescharacteristic
320C2×C3⋊D3C2×C22⋊C411yescharacteristic
321C2×C3⋊D3C2×C22⋊C411yescharacteristic
322C2×C3⋊D3C22×D411yescharacteristic
323#157—44no—
324C32×C4—22no—
325C32×C4C2×C22⋊C411yescharacteristic
326C32×C4C2×C22⋊C411yescharacteristic
327C32×C4C2×C22⋊C411yescharacteristic
328C32×C4C23×C411yescharacteristic
329C3⋊Dic3—22no—
330C3⋊Dic3C2×C22⋊C411yescharacteristic
331C3⋊Dic3C2×C22⋊C411yescharacteristic
332C3⋊Dic3C2×C22⋊C411yescharacteristic
333C3⋊Dic3C22×D411yescharacteristic
334C2×#41—92no—
335C2×#41—92no—
336C2×#41—92no—
337C2×#41—92no—
338C2×#41—91no—
339C2×#41—91no—
340C2×#41—91no—
341C2×#41—181no—
342C2×#41—181no—
343C2×#41—181no—
344C2×#41—181no—
345C2×#41—181no—
346C2×#41—181no—
347C2×#41#15711yescharacteristic, complemented
348C22×Q8—91no—
349C22×D4—91no—
350C22×D4—181no—
351C23×C4—91no—
352C23×C4—181no—
353C2×M16—92no—
354C2×M16—92no—
355C2×M16—181no—
356C2×M16—181no—
357C2×M16—181no—
358C2×M16—181no—
359C22×C8—92no—
360#117—92no—
361#117—92no—
362#117—181no—
363#117—181no—
364C2×C4⋊C4—92no—
365C2×C22⋊C4—181no—
366C2×C42—181no—
367#103—98no—
368#102—98no—
369C23×C3—24no—
370C23×C3—22no—
371C22×D3—62no—
372C22×D3—62no—
373C22×D3—62no—
374C22×D3—62no—
375C22×D3—62no—
376C22×D3—62no—
377C22×D3—64no—
378C22×D3—68no—
379C22×D3—68no—
380C22×D3—128no—
381C22×D3—1216no—
382C3×Q8—24no—
383C3×Q8—24no—
384C3×D4—28no—
385C3×D4—28no—
386C3×D4—24no—
387C3×D4—24no—
388C2×C3×C4—24no—
389C2×C3×C4—28no—
390C2×C3×C4—28no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397#67—68no—
398#67—68no—
399#67—68no—
400#67—68no—
401#67—68no—
402#67—68no—
403C2×Dic3—62no—
404C2×Dic3—62no—
405C2×Dic3—62no—
406C2×Dic3—62no—
407C2×Dic3—62no—
408C2×Dic3—62no—
409C2×Dic3—64no—
410C2×Dic3—68no—
411C2×Dic3—68no—
412D12—64no—
413D12—68no—
414D12—68no—
415D12—64no—
416C4×D3—62no—
417C4×D3—62no—
418C4×D3—62no—
419C4×D3—62no—
420C4×D3—62no—
421C4×D3—62no—
422C4×D3—62no—
423C4×D3—62no—
424C4×D3—62no—
425C4×D3—62no—
426C4×D3—62no—
427C4×D3—62no—
428C4×D3—62no—
429C4×D3—62no—
430C4×D3—62no—
431C4×D3—62no—
432C4×D3—68no—
433C4×D3—68no—
434C4×D3—68no—
435C4×D3—68no—
436C4×D3—68no—
437C4×D3—68no—
438Dic6—64no—
439Dic6—68no—
440Dic6—68no—
441Dic6—64no—
442C2×C32—21no—
443C2×C32—21no—
444C2×C32—21no—
445C2×C32—42no—
446C2×C32C22×C22⋊C411yescharacteristic
447C3⋊D3—21no—
448C3⋊D3—21no—
449C3⋊D3—21no—
450C3⋊D3—42no—
451C3⋊D3#57512yes—
452C24—91no—
453C24—181no—
454#41—21no—
455#41—21no—
456#41—92no—
457#41—92no—
458#41—92no—
459#41—92no—
460#41—92no—
461#41—92no—
462#41—182no—
463#41—182no—
464#41—182no—
465#41—182no—
466#41—182no—
467#41—182no—
468#41—182no—
469#41—182no—
470#41—181no—
471#41—181no—
472#41—181no—
473#41—181no—
474#41—181no—
475#41—181no—
476#41C2×#15712yes—
477#41C2×#15712yescomplemented
478C2×Q8—92no—
479C2×Q8—92no—
480C2×Q8—91no—
481C2×Q8—181no—
482C2×Q8—181no—
483C2×Q8—181no—
484C2×Q8C2×#15711yescharacteristic, complemented
485C2×D4—21no—
486C2×D4—92no—
487C2×D4—92no—
488C2×D4—91no—
489C2×D4—181no—
490C2×D4—181no—
491C2×D4—181no—
492C2×D4—181no—
493C2×D4—182no—
494C2×D4—182no—
495C2×D4—182no—
496C2×D4—182no—
497C2×D4—181no—
498C2×D4—181no—
499C2×D4C2×#15711yescharacteristic, complemented
500C22×C4—21no—
501C22×C4—91no—
502C22×C4—91no—
503C22×C4—91no—
504C22×C4—91no—
505C22×C4—91no—
506C22×C4—91no—
507C22×C4—91no—
508C22×C4—91no—
509C22×C4—91no—
510C22×C4—91no—
511C22×C4—91no—
512C22×C4—91no—
513C22×C4—91no—
514C22×C4—181no—
515C22×C4—182no—
516C22×C4—182no—
517C22×C4—182no—
518C22×C4—182no—
519C22×C4—181no—
520C22×C4—181no—
521C22×C4—181no—
522C22×C4—182no—
523C22×C4C2×#15711yescharacteristic
524M16—182no—
525M16—182no—
526M16—182no—
527M16—182no—
528C2×C8—94no—
529C2×C8—182no—
530C2×C8—182no—
531C4⋊C4—94no—
532C4⋊C4—182no—
533C22⋊C4—182no—
534C22⋊C4—182no—
535C42—182no—
536C42—182no—
537C22×C3—28no—
538C22×C3—22no—
539C22×C3—22no—
540C22×C3—22no—
541C22×C3—44no—
542C22×C3—48no—
543C2×D3—62no—
544C2×D3—62no—
545C2×D3—62no—
546C2×D3—62no—
547C2×D3—68no—
548C2×D3—68no—
549C2×D3—124no—
550C2×D3—124no—
551C2×D3—124no—
552C2×D3—124no—
553C2×D3—1216no—
554C2×D3—1216no—
555C2×D3—124no—
556C2×D3—128no—
557C3×C4—28no—
558C3×C4—22no—
559C3×C4—22no—
560C3×C4—22no—
561C3×C4—22no—
562Dic3—62no—
563Dic3—62no—
564Dic3—62no—
565Dic3—62no—
566Dic3—68no—
567C32#289611yescharacteristic, complemented, Sylow
568C23—21no—
569C23—91no—
570C23—91no—
571C23—91no—
572C23—91no—
573C23—91no—
574C23—91no—
575C23—182no—
576C23—182no—
577C23—181no—
578C23—362no—
579C23—364no—
580C23C22⋊#15711yescharacteristic
581Q8—21no—
582Q8—92no—
583Q8—182no—
584Q8—182no—
585Q8—181no—
586Q8C22×#15712yes—
587D4—22no—
588D4—22no—
589D4—21no—
590D4—92no—
591D4—182no—
592D4—182no—
593D4—182no—
594D4—182no—
595D4—182no—
596D4—182no—
597D4—182no—
598D4—182no—
599D4—181no—
600D4C22×#15712yes—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—91no—
605C2×C4—91no—
606C2×C4—91no—
607C2×C4—91no—
608C2×C4—91no—
609C2×C4—91no—
610C2×C4—91no—
611C2×C4—91no—
612C2×C4—91no—
613C2×C4—91no—
614C2×C4—91no—
615C2×C4—91no—
616C2×C4—91no—
617C2×C4—91no—
618C2×C4—91no—
619C2×C4—91no—
620C2×C4—91no—
621C2×C4—91no—
622C2×C4—91no—
623C2×C4—91no—
624C2×C4—91no—
625C2×C4—91no—
626C2×C4—182no—
627C2×C4—182no—
628C2×C4—182no—
629C2×C4—182no—
630C2×C4—182no—
631C2×C4—182no—
632C2×C4—181no—
633C2×C4—182no—
634C2×C4—182no—
635C2×C4—184no—
636C2×C4—364no—
637C2×C4C22⋊#15711yescharacteristic
638C2×C4C22⋊#15711yescharacteristic
639C2×C4C22⋊#15711yescharacteristic
640C2×C4C22×#15711yescharacteristic
641C2×C4C22×#15711yescharacteristic
642C2×C4C22×#15711yescharacteristic
643C8—184no—
644C2×C3—24no—
645C2×C3—22no—
646C2×C3—42no—
647C2×C3—42no—
648C2×C3—48no—
649D3—64no—
650D3—64no—
651D3—122no—
652D3—122no—
653D3—128no—
654C22—22no—
655C22—41no—
656C22—42no—
657C22—91no—
658C22—91no—
659C22—91no—
660C22—91no—
661C22—182no—
662C22—182no—
663C22—182no—
664C22—182no—
665C22—361no—
666C22—361no—
667C22—361no—
668C22—362no—
669C22—364no—
670C22—364no—
671C22C2×C22⋊#15711yescharacteristic
672C22C2×C22⋊#15711yescharacteristic
673C22C2×C22⋊#15711yescharacteristic
674C4—22no—
675C4—91no—
676C4—91no—
677C4—91no—
678C4—91no—
679C4—182no—
680C4—364no—
681C4C2×C22⋊#15711yescharacteristic
682C4C2×C22⋊#15711yescharacteristic
683C4C2×C22⋊#15711yescharacteristic
684C4C23×#15711yescharacteristic
685C3—22no—
686C2—21no—
687C2—21no—
688C2—21no—
689C2—42no—
690C2—92no—
691C2—181no—
692C2—181no—
693C2—181no—
694C2—362no—
695C2C22×C22⋊#15711yescharacteristic
subgroupG/H
centerC4C2×C22⋊#157
commutatorC32×C4C23×C4
FrattiniC4C23×#157
FittingC2×C32×#41C4
socleC2×C32C22×C22⋊C4
prime radicalC2×#41×C3⋊D3C2
cosocleC4×C3⋊D3C24
hypercenterC2×#41#157
hypocenterC32#2896
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×#64286C2semidirect
3. C2×#64283C2semidirect
4. #10593841C2semidirect
5. #10593840C2semidirect
6. #10593829C2semidirect
7. #10593814C2semidirect
8. C2×C32×#41C4semidirect
13. #41×C3⋊D3C4semidirect
14. #41×C3⋊D3C4semidirect
17. C2×#3832C4semidirect
20. C2×#3830C4semidirect
24. C2×#3828C4semidirect
32. #64286C22semidirect
33. C2×C4⋊#157C22semidirect
38. #64283C22semidirect
40. C2×#3787C22semidirect
41. #63784C22semidirect
42. #63782C22semidirect
50. C32×#41C2×C4semidirect
51. C2×C32×Q8C2×C4semidirect
53. C2×C32×D4C2×C4semidirect
64. #3832C2×C4semidirect
67. Q8×C3⋊D3C2×C4semidirect
76. #3830C2×C4semidirect
83. D4×C3⋊D3C2×C4semidirect
92. #3828C2×C4semidirect
94. C2×C4⋊(C3⋊D3)C2×C4semidirect
115. C2×#634C2×C4semidirect
347. C2×#41#157semidirect
477. #41C2×#157semidirect
484. C2×Q8C2×#157semidirect
499. C2×D4C2×#157semidirect
567. C32#2896semidirect

Maximal subgroups

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

subgroupindex
C2×#41×C3⋊D32
C2×#642862
C2×#642832
#105938412
#105938402
#105938292
#105938142
#28969