Finite Group Databasebeta

← #11882264

Subgroups — #11882264

Order 1152.

838 conjugacy classes of subgroups.

The subgroup lattice has 613 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5728C211yesmaximal, characteristic, complemented
2#10593968C211yesmaximal, characteristic
3#10592783C211yesmaximal, characteristic, complemented
4C3×#5084C211yesmaximal, characteristic, complemented
5#10590577C212yesmaximal, complemented
6#10590556C212yesmaximal, complemented
7#10590549C212yesmaximal, complemented
8#10590501C212yesmaximal, complemented
9#10590379C211yesmaximal, characteristic, complemented
10#10590363C211yesmaximal, characteristic, complemented
11D3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
12#83363—31nomaximal
13#81070—31nomaximal
14C2×#3798—21no—
15C32×C4⋊Q8C2211yescharacteristic
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17C3×#946—21no—
18C3×Q8×Dic3—21no—
19C3×#897C2212yes—
20C3×#892—21no—
21C3×#890—21no—
22C3×#887C2212yes—
23C3×C4×D12C2211yescharacteristic
24C3×C42×D3C2211yescharacteristic
25C3×#869C2211yescharacteristic
26#63918C2211yescharacteristic
27#63911C2211yescharacteristic
28#63909C2211yescharacteristic
29#63908C2211yescharacteristic
30#63906—21no—
31C4×#626—21no—
32#63852—21no—
33C2×#3717C2212yes—
34C2×#3715C2212yes—
35C2×D3×C3⋊C8C2212yes—
36#63636C2212yes—
37#63635C2212yes—
38C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
39C3×#809C2212yes—
40C3×#808C2212yes—
41C3×C4⋊(C3⋊C8)C2211yescharacteristic
42Dic3⋊(C3⋊C8)C2212yes—
43#63566C2212yes—
44#63565C2212yes—
45C3×#533—31no—
46#5728D311yescharacteristic, complemented
47#5548—31no—
48#5477—31no—
49C3×#476—31no—
50#5084—31no—
51#5084—31no—
52#5084—61no—
53#5084D311yescharacteristic, complemented
54#5083—31no—
55#5083—31no—
56#5048—32no—
57#5048—32no—
58#5027—32no—
59#5020—32no—
60#5019—31no—
61C2×C4⋊(C3⋊C8)—31no—
62#4864—32no—
63#4854—32no—
64#4841—31no—
65D3×C4⋊C8—31no—
66#4778—32no—
67#4762—32no—
68C2×C32×Q8—21no—
69C2×C4⋊(C3⋊D3)C2311yescharacteristic
70C2×C4×C3⋊D3—21no—
71C2×C3×D12C2311yescharacteristic
72C2×C3×C4×D3—21no—
73C2×C3×C4×D3D411yescharacteristic
74C2×C3×C4×D3D411yescharacteristic
75C2×C3×C4×D3C2311yescharacteristic
76C2×C3×Dic6C2312yes—
77C2×#627—21no—
78C2×#626—21no—
79C2×#626—21no—
80C2×#626—21no—
81C2×#625—21no—
82#3798—44no—
83C32×C4⋊C4—21no—
84C32×C4⋊C4C2312yes—
85C32×C42C2311yescharacteristic
86#3752—21no—
87C4⋊(C3⋊Dic3)C2311yescharacteristic
88C2×C3⋊(C3⋊C8)C2312yes—
89C3×(C2×D3)⋊C4—22no—
90C3×(C2×D3)⋊C4—21no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3—22no—
94C3×C4⋊Dic3C2311yescharacteristic
95C3×Dic3⋊C4—22no—
96C3×C4×Dic3—22no—
97C3×C4×Dic3D411yescharacteristic
98C3×C4×Dic3D411yescharacteristic
99C3×C4×Dic3C2311yescharacteristic
100C2×C3×C3⋊C8C2312yes—
101Dic3⋊Dic3—21no—
102#3722—21no—
103(C2×D3)⋊Dic3—21no—
104#3717—42no—
105#3715—42no—
106D3×C3⋊C8—42no—
107#3246—91noSylow
108C2×#235—61no—
109C2×#235—61no—
110C3×C4⋊Q8—21no—
111C3×C4⋊Q8—31no—
112C3×C4⋊Q8C2×D311yescharacteristic
113C3×C4⋊Q8C2×D311yescharacteristic
114C3×#125—61no—
115C3×C22⋊Q8—32no—
116C3×C22⋊Q8—61no—
117C3×C4×Q8—32no—
118C3×C4×Q8—61no—
119C3×C4×D4—31no—
120C3×#117—61no—
121C2×C3×C42—31no—
122#946—21no—
123Q8×Dic3—21no—
124C2×#215—32no—
125C2×#215—32no—
126#940—31no—
127#938—31no—
128C2×#214—32no—
129#930—31no—
130#930—31no—
131#930—61no—
132C4×#67—61no—
133C22×C3⋊C8—32no—
134C2×#204—32no—
135C2×D3×C8—32no—
136#897C2×D312yes—
137#895—31no—
138#892—21no—
139#890—21no—
140#888—31no—
141#887C2×D312yes—
142#885—61no—
143#884—61no—
144#875—61no—
145#874—31no—
146C4×D12—31no—
147C4×D12—31no—
148C4×D12—61no—
149C4×D12—61no—
150C4×D12C2×D311yescharacteristic
151C42×D3C2×D311yescharacteristic
152#869—31no—
153#869C2×D311yescharacteristic
154C3×#106—32no—
155C3×C4⋊C8—31no—
156C3×#102—32no—
157#835—32no—
158#835—32no—
159#816—32no—
160Dic3⋊C8—32no—
161#810—32no—
162#809—32no—
163#809—32no—
164#809—62no—
165#809C2×D312yes—
166#808—32no—
167#808—32no—
168#808—62no—
169#808C2×D312yes—
170C4⋊(C3⋊C8)—31no—
171C4⋊(C3⋊C8)—31no—
172C4⋊(C3⋊C8)—32no—
173C4⋊(C3⋊C8)—61no—
174C4⋊(C3⋊C8)C2×D311yescharacteristic
175C22×C3⋊D3—21no—
176C22×C3×D3—21no—
177C22×C3×D3C2×D411yescharacteristic
178C32×Q8—42no—
179C2×C32×C4—22no—
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2411yescharacteristic
183C2×C3⋊Dic3—21no—
184C4⋊(C3⋊D3)—21no—
185C4⋊(C3⋊D3)—21no—
186C4×C3⋊D3—42no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3C2×D411yescharacteristic
190C2×C3×Dic3C2×D411yescharacteristic
191C2×C3×Dic3C2×D411yescharacteristic
192C3×D12—21no—
193C3×D12—21no—
194C3×C4×D3—21no—
195C3×C4×D3—21no—
196C3×C4×D3—41no—
197C3×C4×D3—42no—
198C3×C4×D3SD1614yescomplemented
199C3×Dic6—22no—
200C3×Dic6—22no—
201#627—42no—
202#626—42no—
203#626—42no—
204#626—42no—
205#625—42no—
206C3⋊(C3⋊C8)—22no—
207C3×C3⋊C8—22no—
208#533—31no—
209#532—91no—
210#476—31no—
211#476—91no—
212#475—92no—
213#465—92no—
214#465—92no—
215#461—91no—
216#461—91no—
217#460—92no—
218C2×C4⋊C8—91no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—32no—
222C2×C3×Q8—41no—
223C2×C3×D4—31no—
224C22×C3×C4—31no—
225C22×C3×C4—31no—
226C22×C3×C4—31no—
227C22×C3×C4—61no—
228C2×#67—61no—
229C2×#67—61no—
230C2×#67—61no—
231C2×#67—61no—
232C2×#67—61no—
233#235—124no—
234#235—124no—
235C2×D12—31no—
236C2×D12—31no—
237C2×D12—61no—
238C2×D12—61no—
239C2×D12—61no—
240C2×D12—61no—
241C2×D12C22×D311yescharacteristic
242C2×C4×D3—21no—
243C2×C4×D3—61no—
244C2×C4×D3—61no—
245C2×C4×D3—121no—
246C2×C4×D3#6711yescharacteristic
247C2×C4×D3#6711yescharacteristic
248C2×C4×D3C22×D311yescharacteristic
249C2×Dic6—61no—
250C2×Dic6—61no—
251C2×Dic6C22×D312yes—
252C2×C3×C8—32no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—21no—
255C3×C4⋊C4—22no—
256C3×C4⋊C4—31no—
257C3×C4⋊C4—41no—
258C3×C4⋊C4—62no—
259C3×C4⋊C4—62no—
260C3×C4⋊C4—61no—
261C3×C4⋊C4—61no—
262C3×C4⋊C4C22×D312yes—
263C3×C4⋊C4C22×D312yes—
264C3×C22⋊C4—62no—
265C3×C22⋊C4—61no—
266C3×C42—21no—
267C3×C42—31no—
268C3×C42—31no—
269C3×C42—31no—
270C3×C42—62no—
271C3×C42C22×D311yescharacteristic
272C3×C42C22×D311yescharacteristic
273#217—61no—
274#215—122no—
275#215—122no—
276#214—122no—
277(C2×D3)⋊C4—22no—
278(C2×D3)⋊C4—21no—
279(C2×D3)⋊C4—61no—
280(C2×D3)⋊C4—61no—
281(C2×D3)⋊C4—61no—
282(C2×D3)⋊C4—61no—
283(C2×D3)⋊C4—61no—
284(C2×D3)⋊C4—121no—
285C4⋊Dic3—21no—
286C4⋊Dic3—21no—
287C4⋊Dic3—22no—
288C4⋊Dic3—31no—
289C4⋊Dic3—31no—
290C4⋊Dic3—61no—
291C4⋊Dic3—61no—
292C4⋊Dic3C22×D311yescharacteristic
293Dic3⋊C4—22no—
294Dic3⋊C4—61no—
295C4×Dic3—22no—
296C4×Dic3#6711yescharacteristic
297C4×Dic3#6711yescharacteristic
298C4×Dic3C22×D311yescharacteristic
299C2×C3⋊C8—32no—
300C2×C3⋊C8—32no—
301C2×C3⋊C8—62no—
302C2×C3⋊C8—122no—
303C2×C3⋊C8C22×D312yes—
304#204—122no—
305D3×C8—122no—
306C22×C32C22×D411yescharacteristic
307C2×C3⋊D3—41no—
308C2×C3⋊D3—41no—
309C2×C3⋊D3—41no—
310C2×C3×D3—21no—
311C2×C3×D3—21no—
312C2×C3×D3—41no—
313C2×C3×D3—41no—
314C2×C3×D3—41no—
315C2×C3×D3C2×SD1612yes—
316C32×C4—21no—
317C32×C4—42no—
318C32×C4C2×SD1612yes—
319C32×C4H(5,𝔽2)11yescharacteristic
320C32×C42−1+411yescharacteristic
321C3⋊Dic3—41no—
322C3×Dic3—21no—
323C3×Dic3—21no—
324C3×Dic3—42no—
325C3×Dic3—41no—
326C3×Dic3C2×SD1612yes—
327C2×#41—181no—
328C2×SD16—92no—
329C2×SD16—92no—
330C22×C8—92no—
331C4⋊Q8—31no—
332C4⋊Q8—91no—
333C4⋊Q8D3211yescharacteristic
334#127—91no—
335#125—61no—
336#124—181no—
337C22⋊Q8—32no—
338C22⋊Q8—61no—
339#121—91no—
340#121—91no—
341#121—181no—
342C4×Q8—32no—
343C4×Q8—61no—
344C4×D4—31no—
345C4×D4—91no—
346C4×D4—181no—
347#117—61no—
348C2×C42—31no—
349#106—32no—
350#106—92no—
351C4⋊C8—31no—
352C4⋊C8—92no—
353C4⋊C8—91no—
354#103—92no—
355#103—92no—
356#102—32no—
357#102—92no—
358C23×C3—31no—
359C23×C3—61no—
360C22×D3—21no—
361C22×D3—61no—
362C22×D3—61no—
363C22×D3—121no—
364C22×D3C2×#6711yescharacteristic
365C3×Q8—42no—
366C3×Q8—42no—
367C3×Q8—62no—
368C3×Q8—62no—
369C3×Q8—82no—
370C3×D4—61no—
371C3×D4—61no—
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—31no—
378C2×C3×C4—34no—
379C2×C3×C4—31no—
380C2×C3×C4—31no—
381C2×C3×C4—42no—
382C2×C3×C4—61no—
383C2×C3×C4—61no—
384C2×C3×C4—62no—
385C2×C3×C4—61no—
386C2×C3×C4—121no—
387C2×C3×C4—122no—
388C2×C3×C4D3×D411yescharacteristic
389C2×C3×C4D3×D411yescharacteristic
390C2×C3×C4C2×#6711yescharacteristic
391C2×C3×C4C2×#6711yescharacteristic
392C2×C3×C4C23×D311yescharacteristic
393C2×C3×C4C23×D311yescharacteristic
394#67—122no—
395#67—122no—
396#67—122no—
397#67—122no—
398#67—122no—
399C2×Dic3—21no—
400C2×Dic3—22no—
401C2×Dic3—61no—
402C2×Dic3—61no—
403C2×Dic3—121no—
404C2×Dic3C2×#6711yescharacteristic
405C2×Dic3C2×#6711yescharacteristic
406C2×Dic3C2×#6711yescharacteristic
407D12—21no—
408D12—21no—
409D12—62no—
410D12—61no—
411D12—61no—
412D12—61no—
413D12—61no—
414D12—121no—
415D12—122no—
416D12—122no—
417D12—122no—
418C4×D3—21no—
419C4×D3—21no—
420C4×D3—41no—
421C4×D3—42no—
422C4×D3—122no—
423C4×D3—122no—
424C4×D3—242no—
425C4×D3#21514yescomplemented
426Dic6—22no—
427Dic6—22no—
428Dic6—122no—
429Dic6—122no—
430C3×C8—62no—
431C3⋊C8—22no—
432C3⋊C8—62no—
433C3⋊C8—62no—
434C3⋊C8—122no—
435C2×C32#53711yescharacteristic
436C2×C32C22×SD1611yescharacteristic
437C2×C32#57511yescharacteristic
438C3⋊D3—81no—
439C3×D3—22no—
440C3×D3—81no—
441#41—364no—
442C2×Q8—21no—
443C2×Q8—32no—
444C2×Q8—181no—
445C2×D4—31no—
446C2×D4—91no—
447C2×D4—181no—
448C2×D4—181no—
449C2×D4—181no—
450C2×D4—181no—
451C22×C4—31no—
452C22×C4—31no—
453C22×C4—31no—
454C22×C4—61no—
455C22×C4—181no—
456SD16—362no—
457SD16—362no—
458C2×C8—32no—
459C2×C8—92no—
460C2×C8—362no—
461C4⋊C4—21no—
462C4⋊C4—31no—
463C4⋊C4—62no—
464C4⋊C4—62no—
465C4⋊C4—61no—
466C4⋊C4—61no—
467C4⋊C4—91no—
468C4⋊C4—181no—
469C4⋊C4C2×D3212yes—
470C22⋊C4—62no—
471C22⋊C4—61no—
472C22⋊C4—181no—
473C22⋊C4—181no—
474C22⋊C4—181no—
475C42—31no—
476C42—31no—
477C42—31no—
478C42—62no—
479C42C2×D3211yescharacteristic
480C22×C3—21no—
481C22×C3—32no—
482C22×C3—61no—
483C22×C3—61no—
484C22×C3—121no—
485C22×C3—121no—
486C22×C3—121no—
487C22×C3C2×D3×D411yescharacteristic
488C22×C3C22×#6711yescharacteristic
489C2×D3—21no—
490C2×D3—21no—
491C2×D3—41no—
492C2×D3—41no—
493C2×D3—41no—
494C2×D3—122no—
495C2×D3—121no—
496C2×D3—121no—
497C2×D3—121no—
498C2×D3—121no—
499C2×D3—121no—
500C2×D3—121no—
501C2×D3—241no—
502C2×D3—241no—
503C2×D3C2×#21512yes—
504C3×C4—21no—
505C3×C4—21no—
506C3×C4—21no—
507C3×C4—21no—
508C3×C4—22no—
509C3×C4—32no—
510C3×C4—41no—
511C3×C4—42no—
512C3×C4—42no—
513C3×C4—61no—
514C3×C4—61no—
515C3×C4—82no—
516C3×C4—121no—
517C3×C4—122no—
518C3×C4D3×SD1612yes—
519C3×C4C2×#21512yes—
520C3×C4#100711yescharacteristic
521C3×C4#100911yescharacteristic
522C3×C4#100911yescharacteristic
523C3×C4#101011yescharacteristic
524Dic3—21no—
525Dic3—21no—
526Dic3—41no—
527Dic3—42no—
528Dic3—121no—
529Dic3—121no—
530Dic3—241no—
531Dic3C2×#21512yes—
532C32#324611yescharacteristic, complemented, Sylow
533C23—31no—
534C23—61no—
535C23—181no—
536Q8—42no—
537Q8—62no—
538Q8—62no—
539Q8—362no—
540D4—61no—
541D4—61no—
542D4—181no—
543D4—181no—
544D4—362no—
545D4—362no—
546D4—362no—
547D4—362no—
548C2×C4—22no—
549C2×C4—31no—
550C2×C4—34no—
551C2×C4—31no—
552C2×C4—31no—
553C2×C4—61no—
554C2×C4—61no—
555C2×C4—62no—
556C2×C4—61no—
557C2×C4—121no—
558C2×C4—122no—
559C2×C4—181no—
560C2×C4—362no—
561C2×C4D3×#6711yescharacteristic
562C2×C4D3×#6711yescharacteristic
563C2×C4C22×D3211yescharacteristic
564C8—62no—
565C8—182no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—62no—
570C2×C3—241no—
571C2×C3#562911yescharacteristic
572C2×C3C2×D3×SD1611yescharacteristic
573C2×C3#577311yescharacteristic
574C2×C3C22×#21511yescharacteristic
575C2×C3#582211yescharacteristic
576C2×C3#583311yescharacteristic
577D3—22no—
578D3—81no—
579D3—242no—
580D3—241no—
581D3—241no—
582C22—32no—
583C22—61no—
584C22—61no—
585C22—121no—
586C22—121no—
587C22—121no—
588C22—361no—
589C22—361no—
590C22—361no—
591C22C2×D3×#6711yescharacteristic
592C4—21no—
593C4—32no—
594C4—42no—
595C4—61no—
596C4—61no—
597C4—122no—
598C4—121no—
599C4—361no—
600C4D3×#21512yes—
601C4#6431511yescharacteristic
602C4#6432011yescharacteristic
603C3—21no—
604C3#8107011yescharacteristic, complemented
605C3#8336311yescharacteristic, complemented
606C2—62no—
607C2—241no—
608C2—721no—
609C2#1059509511yescharacteristic
610C2C2×D3×#21511yescharacteristic
611C2#1059539811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radical#10593968C2
hypercenterC4⋊Q8D32
hypocenterC32#3246
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
5. #10590577C2semidirect
6. #10590556C2semidirect
7. #10590549C2semidirect
8. #10590501C2semidirect
9. #10590379C2semidirect
10. #10590363C2semidirect
11. D3×C4⋊(C3⋊C8)C2semidirect
46. #5728D3semidirect
53. #5084D3semidirect
198. C3×C4×D3SD16semidirect
425. C4×D3#215semidirect
532. C32#3246semidirect
604. C3#81070semidirect
605. C3#83363semidirect

Maximal subgroups

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

subgroupindex
C3×#57282
#105939682
#105927832
C3×#50842
#105905772
#105905562
#105905492
#105905012
#105903792
#105903632
D3×C4⋊(C3⋊C8)2
#833633
#810703