Finite Group Databasebeta

← #11870525

Subgroups — #11870525

Order 1152.

950 conjugacy classes of subgroups.

The subgroup lattice has 629 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5728C211yesmaximal, characteristic, complemented
2C4×D3×D12C211yesmaximal, characteristic
3#10592783C211yesmaximal, characteristic, complemented
4C3×#5084C211yesmaximal, characteristic, complemented
5#10590596C212yesmaximal
6#10590458C212yesmaximal, complemented
7#10590453C212yesmaximal, complemented
8#10590439C212yesmaximal, complemented
9#10590379C211yesmaximal, characteristic, complemented
10#10590363C211yesmaximal, characteristic, complemented
11#10590248C211yesmaximal, characteristic, complemented
12#83351—31nomaximal
13#81044—31nomaximal
14C2×D3×D12C2211yescharacteristic
15C2×C4×D32—21no—
16C32×C4⋊Q8C2211yescharacteristic, complemented
17C4×C4⋊(C3⋊D3)C2211yescharacteristic
18C3×#946—21no—
19C3×Q8×Dic3—21no—
20C3×#897C2212yes—
21C3×#892—21no—
22C3×#890—21no—
23C3×#887C2212yescomplemented
24C3×C4×D12C2211yescharacteristic
25C3×C42×D3C2211yescharacteristic
26C3×#869C2211yescharacteristic, complemented
27D3×(C2×D3)⋊C4—21no—
28C4×#626—21no—
29#63894C2211yescharacteristic
30Dic3×D12C2211yescharacteristic
31D3×C4⋊Dic3C2211yescharacteristic
32#63880—21no—
33C2×#3717C2212yes—
34C2×#3715C2212yes—
35#63636C2212yes—
36#63635C2212yescomplemented
37C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
38C3×#809C2212yes—
39C3×#808C2212yescomplemented
40C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
41#63566C2212yescomplemented
42#63565C2212yescomplemented
43(C2×D3)⋊(C3⋊C8)C2212yes—
44Dic3×C3⋊C8C2212yescomplemented
45C3×#533—31no—
46#5728D311yescharacteristic, complemented
47C4×D3×D4—31no—
48C2×C4×D12—31no—
49C3×#476—31no—
50#5084—31no—
51#5084—31no—
52#5084—61no—
53#5084D311yescharacteristic, complemented
54#5083—31no—
55#5083—31no—
56#5046—32no—
57#5043—32no—
58C4×#215—32no—
59C4×#215—32no—
60#5019—31no—
61#4925—31no—
62#4862—32no—
63#4852—32no—
64#4841—31no—
65#4833—31no—
66#4776—32no—
67#4758—32no—
68C22×D32—21no—
69C2×C32×Q8—21no—
70C2×C4⋊(C3⋊D3)C2311yescharacteristic
71C2×C4×C3⋊D3—21no—
72C2×C3×D12C2311yescharacteristic
73C2×C3×C4×D3—21no—
74C2×C3×C4×D3D411yescharacteristic
75C2×C3×C4×D3D411yescharacteristic
76C2×C3×C4×D3C2311yescharacteristic
77C2×C3×Dic6C2312yes—
78C2×#626—21no—
79C2×#624—21no—
80C2×D3×Dic3—21no—
81C2×D3×Dic3—21no—
82D3×D12—22no—
83D3×D12—22no—
84C4×D32—44no—
85C32×C4⋊C4—21no—
86C32×C4⋊C4C2312yes—
87C32×C42C2311yescharacteristic
88#3752—21no—
89C4⋊(C3⋊Dic3)C2311yescharacteristic
90C2×C3⋊(C3⋊C8)C2312yes—
91C3×(C2×D3)⋊C4—22no—
92C3×(C2×D3)⋊C4—21no—
93C3×C4⋊Dic3—21no—
94C3×C4⋊Dic3—21no—
95C3×C4⋊Dic3—22no—
96C3×C4⋊Dic3C2311yescharacteristic
97C3×Dic3⋊C4—22no—
98C3×C4×Dic3—22no—
99C3×C4×Dic3D411yescharacteristic
100C3×C4×Dic3D411yescharacteristic
101C3×C4×Dic3C2311yescharacteristic
102C2×C3×C3⋊C8C2312yes—
103Dic3⋊Dic3—21no—
104#3722—21no—
105(C2×D3)⋊Dic3—21no—
106#3717—24no—
107#3715—24no—
108#3101—91noSylow
109C2×D3×D4—31no—
110C22×D12—31no—
111C22×C4×D3—61no—
112C22×C4×D3—61no—
113C3×C4⋊Q8—21no—
114C3×C4⋊Q8—31no—
115C3×C4⋊Q8C2×D311yescharacteristic, complemented
116C3×C4⋊Q8C2×D311yescharacteristic, complemented
117C3×#125—61no—
118C3×C22⋊Q8—32no—
119C3×C22⋊Q8—61no—
120C3×C4×Q8—32no—
121C3×C4×Q8—61no—
122C3×C4×D4—31no—
123C3×#117—61no—
124C2×C3×C42—31no—
125#946—21no—
126Q8×Dic3—21no—
127C2×#215—32no—
128C2×#215—32no—
129D4×Dic3—31no—
130C2×#214—32no—
131C4×#67—61no—
132C2×(C2×D3)⋊C4—61no—
133C2×C4⋊Dic3—31no—
134C2×#204—32no—
135#897C2×D312yes—
136#893—31no—
137#892—21no—
138D3×C4⋊C4—31no—
139#890—21no—
140#887C2×D312yescomplemented
141#67⋊C4—61no—
142D3×C22⋊C4—61no—
143C4×D12—31no—
144C4×D12—31no—
145C4×D12—31no—
146C4×D12—31no—
147C4×D12—61no—
148C4×D12—61no—
149C4×D12—61no—
150C4×D12C2×D311yescharacteristic
151C42×D3C2×D311yescharacteristic
152#869C2×D311yescharacteristic, complemented
153C3×#106—32no—
154C3×C4⋊C8—31no—
155C3×#102—32no—
156#835—32no—
157#835—32no—
158#830—32no—
159(C2×D3)⋊C8—32no—
160#816—32no—
161C8×Dic3—32no—
162#810—32no—
163#809—32no—
164#809—32no—
165#809—62no—
166#809C2×D312yes—
167#808—32no—
168#808—32no—
169#808—62no—
170#808C2×D312yescomplemented
171C4⋊(C3⋊C8)—31no—
172C4⋊(C3⋊C8)—31no—
173C4⋊(C3⋊C8)—61no—
174C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
175C4×C3⋊C8—32no—
176C22×C3⋊D3—21no—
177C22×C3×D3—21no—
178C22×C3×D3C2×D411yescharacteristic
179C2×D32—24no—
180C2×D32—42no—
181C2×D32—42no—
182C32×Q8—42no—
183C2×C32×C4—22no—
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4C2411yescharacteristic
187C2×C3⋊Dic3—21no—
188C4⋊(C3⋊D3)—21no—
189C4⋊(C3⋊D3)#4112yes—
190C4×C3⋊D3—42no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3C2×D411yescharacteristic
194C2×C3×Dic3C2×D411yescharacteristic
195C2×C3×Dic3C2×D411yescharacteristic
196C3×D12—21no—
197C3×D12#4112yes—
198C3×C4×D3—21no—
199C3×C4×D3—21no—
200C3×C4×D3—41no—
201C3×C4×D3—42no—
202C3×C4×D3SD1614yescomplemented
203C3×Dic6—22no—
204C3×Dic6—22no—
205#626—24no—
206#624—42no—
207D3×Dic3—42no—
208D3×Dic3—42no—
209C3⋊(C3⋊C8)—22no—
210C3×C3⋊C8—22no—
211#533—31no—
212C2×C4×D4—91no—
213#483—92no—
214#476—31no—
215#476—91no—
216#461—91no—
217#461—91no—
218#450—92no—
219C4×SD16—92no—
220C4×SD16—92no—
221#431—91no—
222C23×D3—61no—
223C23×D3—61no—
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8—32no—
227C2×C3×Q8—41no—
228C2×C3×D4—31no—
229C22×C3×C4—31no—
230C22×C3×C4—31no—
231C22×C3×C4—31no—
232C22×C3×C4—61no—
233C2×#67—61no—
234C22×Dic3—61no—
235C22×Dic3—61no—
236D3×D4—62no—
237D3×D4—62no—
238C2×D12—31no—
239C2×D12—31no—
240C2×D12—61no—
241C2×D12—62no—
242C2×D12—61no—
243C2×D12—62no—
244C2×D12C22×D311yescharacteristic
245C2×C4×D3—21no—
246C2×C4×D3—61no—
247C2×C4×D3—61no—
248C2×C4×D3—61no—
249C2×C4×D3—61no—
250C2×C4×D3—61no—
251C2×C4×D3—61no—
252C2×C4×D3—121no—
253C2×C4×D3—124no—
254C2×C4×D3—124no—
255C2×C4×D3#6711yescharacteristic
256C2×C4×D3#6711yescharacteristic
257C2×C4×D3C22×D311yescharacteristic
258C2×Dic6C22×D312yes—
259C2×C3×C8—32no—
260C3×C4⋊C4—21no—
261C3×C4⋊C4—21no—
262C3×C4⋊C4—22no—
263C3×C4⋊C4—31no—
264C3×C4⋊C4—41no—
265C3×C4⋊C4—62no—
266C3×C4⋊C4—62no—
267C3×C4⋊C4—61no—
268C3×C4⋊C4—61no—
269C3×C4⋊C4C22×D312yes—
270C3×C4⋊C4C22×D312yes—
271C3×C22⋊C4—62no—
272C3×C22⋊C4—61no—
273C3×C42—21no—
274C3×C42—31no—
275C3×C42—31no—
276C3×C42—31no—
277C3×C42—62no—
278C3×C42C22×D311yescharacteristic
279C3×C42C22×D311yescharacteristic
280#217—61no—
281#215—64no—
282#215—64no—
283#214—64no—
284(C2×D3)⋊C4—22no—
285(C2×D3)⋊C4—21no—
286(C2×D3)⋊C4—61no—
287(C2×D3)⋊C4—61no—
288(C2×D3)⋊C4—61no—
289(C2×D3)⋊C4—61no—
290(C2×D3)⋊C4—61no—
291(C2×D3)⋊C4—121no—
292C4⋊Dic3—21no—
293C4⋊Dic3—21no—
294C4⋊Dic3—22no—
295C4⋊Dic3—31no—
296C4⋊Dic3—31no—
297C4⋊Dic3—61no—
298C4⋊Dic3—61no—
299C4⋊Dic3C22×D311yescharacteristic
300Dic3⋊C4—22no—
301Dic3⋊C4—61no—
302C4×Dic3—22no—
303C4×Dic3#6711yescharacteristic
304C4×Dic3#6711yescharacteristic
305C4×Dic3C22×D311yescharacteristic
306C2×C3⋊C8—32no—
307C2×C3⋊C8—32no—
308C2×C3⋊C8—62no—
309C2×C3⋊C8C22×D312yes—
310#204—64no—
311C22×C32C22×D411yescharacteristic
312C2×C3⋊D3—22no—
313C2×C3⋊D3—41no—
314C2×C3⋊D3—41no—
315C2×C3×D3—21no—
316C2×C3×D3—21no—
317C2×C3×D3—22no—
318C2×C3×D3—41no—
319C2×C3×D3—41no—
320C2×C3×D3C2×SD1612yes—
321D32—48no—
322C32×C4—21no—
323C32×C4—42no—
324C32×C4C2×SD1612yes—
325C32×C4C2×#4111yescharacteristic
326C32×C4C2×#4111yescharacteristic
327C3⋊Dic3—41no—
328C3×Dic3—21no—
329C3×Dic3—21no—
330C3×Dic3—42no—
331C3×Dic3—41no—
332C3×Dic3C2×SD1612yes—
333C22×D4—91no—
334C23×C4—181no—
335C2×SD16—92no—
336C2×SD16—92no—
337C4⋊Q8—31no—
338C4⋊Q8D3211yescharacteristic, complemented
339#125—61no—
340C22⋊Q8—32no—
341C22⋊Q8—61no—
342C4×Q8—32no—
343C4×Q8—61no—
344C4×D4—31no—
345C4×D4—91no—
346C4×D4—91no—
347C4×D4—91no—
348C4×D4—181no—
349C4×D4—181no—
350#117—61no—
351C2×C4⋊C4—91no—
352C2×C22⋊C4—181no—
353C2×C42—31no—
354#106—32no—
355#106—92no—
356C4⋊C8—31no—
357C4⋊C8—91no—
358#103—92no—
359#103—92no—
360#102—32no—
361#102—92no—
362C22⋊C8—92no—
363C4×C8—92no—
364C23×C3—31no—
365C23×C3—61no—
366C22×D3—21no—
367C22×D3—64no—
368C22×D3—64no—
369C22×D3—61no—
370C22×D3—61no—
371C22×D3—121no—
372C22×D3—122no—
373C22×D3—122no—
374C22×D3—122no—
375C22×D3—122no—
376C22×D3C2×#6711yescharacteristic
377C3×Q8—42no—
378C3×Q8—42no—
379C3×Q8—62no—
380C3×Q8—62no—
381C3×Q8—82no—
382C3×D4—32no—
383C3×D4—61no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—31no—
390C2×C3×C4—34no—
391C2×C3×C4—31no—
392C2×C3×C4—31no—
393C2×C3×C4—42no—
394C2×C3×C4—61no—
395C2×C3×C4—61no—
396C2×C3×C4—62no—
397C2×C3×C4—61no—
398C2×C3×C4—121no—
399C2×C3×C4—122no—
400C2×C3×C4D3×D411yescharacteristic
401C2×C3×C4D3×D411yescharacteristic
402C2×C3×C4C2×#6711yescharacteristic
403C2×C3×C4C2×#6711yescharacteristic
404C2×C3×C4C23×D311yescharacteristic
405C2×C3×C4C23×D311yescharacteristic
406#67—64no—
407C2×Dic3—21no—
408C2×Dic3—22no—
409C2×Dic3—61no—
410C2×Dic3—61no—
411C2×Dic3—121no—
412C2×Dic3—122no—
413C2×Dic3—122no—
414C2×Dic3C2×#6711yescharacteristic
415C2×Dic3C2×#6711yescharacteristic
416C2×Dic3C2×#6711yescharacteristic
417D12—21no—
418D12—32no—
419D12—32no—
420D12—62no—
421D12—64no—
422D12—61no—
423D12—61no—
424D12—121no—
425D12#23912yes—
426C4×D3—21no—
427C4×D3—21no—
428C4×D3—41no—
429C4×D3—42no—
430C4×D3—122no—
431C4×D3—122no—
432C4×D3—122no—
433C4×D3—122no—
434C4×D3—122no—
435C4×D3—122no—
436C4×D3—242no—
437C4×D3#21514yescomplemented
438Dic6—22no—
439Dic6—22no—
440C3×C8—62no—
441C3⋊C8—22no—
442C3⋊C8—62no—
443C3⋊C8—62no—
444C3⋊C8—122no—
445C2×C32#52511yescharacteristic
446C2×C32C22×SD1611yescharacteristic
447C2×C32#57511yescharacteristic
448C3⋊D3—42no—
449C3×D3—22no—
450C3×D3—42no—
451C24—181no—
452C2×Q8—21no—
453C2×Q8—32no—
454C2×D4—31no—
455C2×D4—91no—
456C2×D4—181no—
457C2×D4—182no—
458C2×D4—182no—
459C22×C4—31no—
460C22×C4—31no—
461C22×C4—31no—
462C22×C4—61no—
463C22×C4—181no—
464C22×C4—181no—
465C22×C4—181no—
466C22×C4—181no—
467C22×C4—364no—
468SD16—184no—
469SD16—184no—
470C2×C8—32no—
471C2×C8—92no—
472C4⋊C4—21no—
473C4⋊C4—31no—
474C4⋊C4—62no—
475C4⋊C4—62no—
476C4⋊C4—61no—
477C4⋊C4—61no—
478C4⋊C4—91no—
479C4⋊C4—181no—
480C4⋊C4C2×D3212yes—
481C22⋊C4—62no—
482C22⋊C4—61no—
483C22⋊C4—181no—
484C22⋊C4—181no—
485C22⋊C4—181no—
486C42—31no—
487C42—31no—
488C42—31no—
489C42—62no—
490C42C2×D3211yescharacteristic
491C22×C3—21no—
492C22×C3—32no—
493C22×C3—61no—
494C22×C3—61no—
495C22×C3—62no—
496C22×C3—121no—
497C22×C3—121no—
498C22×C3C2×D3×D411yescharacteristic
499C22×C3C22×#6711yescharacteristic
500C2×D3—21no—
501C2×D3—21no—
502C2×D3—22no—
503C2×D3—41no—
504C2×D3—41no—
505C2×D3—62no—
506C2×D3—62no—
507C2×D3—122no—
508C2×D3—128no—
509C2×D3—128no—
510C2×D3—121no—
511C2×D3—121no—
512C2×D3—121no—
513C2×D3—121no—
514C2×D3—241no—
515C2×D3—241no—
516C2×D3C2×#21512yes—
517C3×C4—21no—
518C3×C4—21no—
519C3×C4—21no—
520C3×C4—21no—
521C3×C4—22no—
522C3×C4—32no—
523C3×C4—41no—
524C3×C4—42no—
525C3×C4—42no—
526C3×C4—61no—
527C3×C4—61no—
528C3×C4—82no—
529C3×C4—121no—
530C3×C4—122no—
531C3×C4D3×SD1612yes—
532C3×C4C2×#21512yes—
533C3×C4C2×#23911yescharacteristic
534C3×C4D3×#4111yescharacteristic
535C3×C4D3×#4111yescharacteristic
536C3×C4D3×#4111yescharacteristic
537Dic3—21no—
538Dic3—21no—
539Dic3—41no—
540Dic3—42no—
541Dic3—121no—
542Dic3—121no—
543Dic3—241no—
544Dic3C2×#21512yes—
545C32#310111yescharacteristic, complemented, Sylow
546C23—31no—
547C23—61no—
548C23—184no—
549C23—181no—
550C23—362no—
551C23—362no—
552Q8—42no—
553Q8—62no—
554Q8—62no—
555D4—32no—
556D4—61no—
557D4—92no—
558D4—184no—
559D4—181no—
560C2×C4—22no—
561C2×C4—31no—
562C2×C4—34no—
563C2×C4—31no—
564C2×C4—31no—
565C2×C4—61no—
566C2×C4—61no—
567C2×C4—62no—
568C2×C4—61no—
569C2×C4—121no—
570C2×C4—122no—
571C2×C4—181no—
572C2×C4—362no—
573C2×C4—362no—
574C2×C4—362no—
575C2×C4—362no—
576C2×C4D3×#6711yescharacteristic
577C2×C4D3×#6711yescharacteristic
578C2×C4C22×D3211yescharacteristic
579C8—62no—
580C8—182no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—62no—
585C2×C3—122no—
586C2×C3#562711yescharacteristic
587C2×C3C2×D3×SD1611yescharacteristic
588C2×C3#577311yescharacteristic
589C2×C3C22×#21511yescharacteristic
590C2×C3#582211yescharacteristic
591C2×C3#582811yescharacteristic
592D3—22no—
593D3—42no—
594D3—122no—
595D3—122no—
596D3—242no—
597C22—32no—
598C22—61no—
599C22—61no—
600C22—62no—
601C22—121no—
602C22—121no—
603C22—182no—
604C22—368no—
605C22—361no—
606C22—361no—
607C22C2×D3×#6711yescharacteristic
608C4—21no—
609C4—32no—
610C4—42no—
611C4—61no—
612C4—61no—
613C4—122no—
614C4—121no—
615C4—361no—
616C4D3×#21512yes—
617C4D3×#23911yescharacteristic
618C4#6431911yescharacteristic
619C3—21no—
620C3#8104411yescharacteristic, complemented
621C3#8335111yescharacteristic, complemented
622C2—62no—
623C2—122no—
624C2—362no—
625C2#1059509511yescharacteristic
626C2C2×D3×#21511yescharacteristic
627C2#1059542411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×D3×D12C22
hypercenterC4⋊Q8D32
hypocenterC32#3101
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5728C2semidirect
3. #10592783C2semidirect
4. C3×#5084C2semidirect
6. #10590458C2semidirect
7. #10590453C2semidirect
8. #10590439C2semidirect
9. #10590379C2semidirect
10. #10590363C2semidirect
11. #10590248C2semidirect
16. C32×C4⋊Q8C22semidirect
23. C3×#887C22semidirect
26. C3×#869C22semidirect
36. #63635C22semidirect
37. C4⋊(C3⋊(C3⋊C8))C22semidirect
39. C3×#808C22semidirect
40. C3×C4⋊(C3⋊C8)C22semidirect
41. #63566C22semidirect
42. #63565C22semidirect
44. Dic3×C3⋊C8C22semidirect
46. #5728D3semidirect
53. #5084D3semidirect
115. C3×C4⋊Q8C2×D3semidirect
116. C3×C4⋊Q8C2×D3semidirect
140. #887C2×D3semidirect
152. #869C2×D3semidirect
170. #808C2×D3semidirect
174. C4⋊(C3⋊C8)C2×D3semidirect
202. C3×C4×D3SD16semidirect
338. C4⋊Q8D32semidirect
437. C4×D3#215semidirect
545. C32#3101semidirect
620. C3#81044semidirect
621. C3#83351semidirect

Maximal subgroups

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

subgroupindex
C3×#57282
C4×D3×D122
#105927832
C3×#50842
#105905962
#105904582
#105904532
#105904392
#105903792
#105903632
#105902482
#833513
#810443