Finite Group Databasebeta

← #11882276

Subgroups — #11882276

Order 1152.

832 conjugacy classes of subgroups.

The subgroup lattice has 589 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5578C211yesmaximal, characteristic, complemented
2#10593897C211yesmaximal, characteristic
3#10592719C211yesmaximal, characteristic, complemented
4C3×#5027C211yesmaximal, characteristic, complemented
5#10591634C212yesmaximal, complemented
6#10591564C212yesmaximal, complemented
7#10590501C212yesmaximal, complemented
8#10590465C212yesmaximal, complemented
9#10590364C211yesmaximal, characteristic, complemented
10D3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
11#10590301C211yesmaximal, characteristic, complemented
12#83363—31nomaximal
13#80366—31nomaximal
14C2×#3795—21no—
15C32×C4×Q8C2211yescharacteristic
16#64078C2211yescharacteristic
17C3×#946C2211yescharacteristic
18C3×#944C2211yescharacteristic
19C2×C3×#215C2212yes—
20C3×#897C2211yescharacteristic
21C3×#896—21no—
22C3×#889—21no—
23C3×#888C2211yescharacteristic
24C3×#874C2211yescharacteristic
25C3×#872—21no—
26C3×C42×D3C2211yescharacteristic
27C3×C4×Dic6—21no—
28C3×C4×Dic6C2211yescharacteristic
29#63908—21no—
30#63908C2212yes—
31Dic3×D12—21no—
32Dic3×D12C2212yes—
33#63860—21no—
34C2×#3715C2212yes—
35C2×D3×C3⋊C8C2212yes—
36#63662C2212yes—
37#63635C2212yes—
38C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
39C3×#809C2212yes—
40C3×C4⋊(C3⋊C8)C2211yescharacteristic
41#63573C2212yes—
42Dic3⋊(C3⋊C8)C2212yes—
43#63566C2212yes—
44#63562C2212yes—
45C3×#533—31no—
46#5716—31no—
47#5578D311yescharacteristic, complemented
48#5477—31no—
49C3×#460—31no—
50#5171—32no—
51#5162—32no—
52#5084—32no—
53#5083—32no—
54#5075—31no—
55#5048—32no—
56#5048—32no—
57#5027—31no—
58#5027D311yescharacteristic, complemented
59#5020—31no—
60#5020—31no—
61#5020—31no—
62#5020—61no—
63C2×C4⋊(C3⋊C8)—31no—
64#4851—31no—
65D3×C4⋊C8—31no—
66#4778—32no—
67#4761—32no—
68C2×C32×Q8C2311yescharacteristic
69C2×#634—21no—
70C2×C3×D12—21no—
71C2×C3×D12—21no—
72C2×C3×D12C2312yes—
73C2×C3×C4×D3D411yescharacteristic
74C2×C3×C4×D3D411yescharacteristic
75C2×C3×C4×D3C2311yescharacteristic
76C2×C3×Dic6—21no—
77C2×C3×Dic6C2311yescharacteristic
78C2×#625—22no—
79C2×D3×Dic3—22no—
80#3795—44no—
81C32×C4⋊C4—21no—
82C32×C4⋊C4C2311yescharacteristic
83C32×C42—21no—
84C32×C42C2311yescharacteristic
85C4⋊(C3⋊Dic3)—21no—
86C4⋊(C3⋊Dic3)C2312yes—
87C2×C3⋊(C3⋊C8)C2312yes—
88C3×#215—42no—
89C3×(C2×D3)⋊C4—21no—
90C3×(C2×D3)⋊C4—21no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3C2311yescharacteristic
93C3×Dic3⋊C4—21no—
94C3×Dic3⋊C4—21no—
95C3×Dic3⋊C4—21no—
96C3×Dic3⋊C4—21no—
97C3×Dic3⋊C4—21no—
98C3×C4×Dic3—21no—
99C3×C4×Dic3D411yescharacteristic
100C3×C4×Dic3D411yescharacteristic
101C3×C4×Dic3C2311yescharacteristic
102C2×C3×C3⋊C8C2312yes—
103(C2×D3)⋊Dic3—22no—
104(C2×D3)⋊Dic3—22no—
105#3715—42no—
106D3×C3⋊C8—42no—
107#3246—91noSylow
108C2×#237—61no—
109C2×#235—61no—
110C2×C3×SD16—32no—
111C3×C4⋊Q8—31no—
112C3×C4⋊Q8—31no—
113C3×#127—31no—
114C3×#125—61no—
115C3×C22⋊Q8—31no—
116C3×C22⋊Q8—31no—
117C3×C22⋊Q8—61no—
118C3×C4×Q8—21no—
119C3×C4×Q8—31no—
120C3×C4×Q8—61no—
121C3×C4×Q8C2×D311yescharacteristic
122C3×C4×Q8C2×D311yescharacteristic
123C3×#117—61no—
124C2×C3×C42—31no—
125#946C2×D311yescharacteristic
126#944C2×D311yescharacteristic
127C2×#215—32no—
128C2×#215C2×D312yes—
129#938—32no—
130#938—61no—
131#936—61no—
132D4×Dic3—32no—
133D4×Dic3—61no—
134C2×#214—32no—
135#930—32no—
136#930—61no—
137C22×C3⋊C8—32no—
138C2×D3×C8—32no—
139#897C2×D311yescharacteristic
140#896—21no—
141#889—21no—
142#888C2×D311yescharacteristic
143#875—61no—
144#874C2×D311yescharacteristic
145C4×D12—32no—
146C4×D12—61no—
147#872—21no—
148C42×D3C2×D311yescharacteristic
149#869—31no—
150#869—31no—
151#869—61no—
152C4×Dic6—21no—
153C4×Dic6C2×D311yescharacteristic
154C3×C4⋊C8—31no—
155C3×#102—32no—
156#835—32no—
157#835—32no—
158#835—32no—
159#835—62no—
160#832—32no—
161#817—32no—
162#816—32no—
163Dic3⋊C8—32no—
164#809—32no—
165#809C2×D312yes—
166#808—32no—
167#808—32no—
168#808—32no—
169#808—62no—
170C4⋊(C3⋊C8)—31no—
171C4⋊(C3⋊C8)—31no—
172C4⋊(C3⋊C8)—32no—
173C4⋊(C3⋊C8)—61no—
174C4⋊(C3⋊C8)C2×D311yescharacteristic
175C22×C3×D3—22no—
176C22×C3×D3C2×D411yescharacteristic
177C32×Q8—21no—
178C32×Q8—21no—
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2411yescharacteristic
184C2×C3⋊Dic3—22no—
185#634—42no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3C2×D411yescharacteristic
189C2×C3×Dic3C2×D411yescharacteristic
190C2×C3×Dic3C2×D411yescharacteristic
191C3×D12—22no—
192C3×D12—22no—
193C3×D12—42no—
194C3×D12—42no—
195C3×C4×D3—21no—
196C3×C4×D3—21no—
197C3×C4×D3—41no—
198C3×C4×D3SD1614yescomplemented
199C3×Dic6—21no—
200C3×Dic6—21no—
201C3×Dic6—42no—
202#625—44no—
203D3×Dic3—44no—
204C3⋊(C3⋊C8)—22no—
205C3×C3⋊C8—22no—
206#533—31no—
207#532—91no—
208#476—92no—
209#475—91no—
210#475—91no—
211#465—92no—
212#465—92no—
213#461—92no—
214#460—31no—
215#460—91no—
216C2×C4⋊C8—91no—
217C2×C3×Q8—21no—
218C2×C3×Q8—31no—
219C2×C3×Q8—61no—
220C2×C3×Q8C22×D311yescharacteristic
221C2×C3×Q8C22×D311yescharacteristic
222C2×C3×D4—32no—
223C2×C3×D4—61no—
224C2×C3×D4—61no—
225C22×C3×C4—31no—
226C22×C3×C4—31no—
227C22×C3×C4—31no—
228C2×#67—62no—
229C2×#67—62no—
230C22×Dic3—62no—
231#237—124no—
232#235—124no—
233C2×D12—21no—
234C2×D12—21no—
235C2×D12C22×D312yes—
236C2×C4×D3—62no—
237C2×C4×D3#6711yescharacteristic
238C2×C4×D3#6711yescharacteristic
239C2×C4×D3C22×D311yescharacteristic
240C2×Dic6—21no—
241C2×Dic6—61no—
242C2×Dic6—61no—
243C2×Dic6—121no—
244C2×Dic6C22×D311yescharacteristic
245C3×SD16—122no—
246C2×C3×C8—32no—
247C3×C4⋊C4—21no—
248C3×C4⋊C4—21no—
249C3×C4⋊C4—21no—
250C3×C4⋊C4—31no—
251C3×C4⋊C4—41no—
252C3×C4⋊C4—61no—
253C3×C4⋊C4—61no—
254C3×C4⋊C4—61no—
255C3×C4⋊C4—61no—
256C3×C4⋊C4—61no—
257C3×C4⋊C4—61no—
258C3×C4⋊C4C22×D311yescharacteristic
259C3×C4⋊C4C22×D311yescharacteristic
260C3×C22⋊C4—61no—
261C3×C22⋊C4—61no—
262C3×C42—21no—
263C3×C42—21no—
264C3×C42—21no—
265C3×C42—31no—
266C3×C42—31no—
267C3×C42—31no—
268C3×C42—41no—
269C3×C42—61no—
270C3×C42C22×D311yescharacteristic
271C3×C42C22×D311yescharacteristic
272#217—62no—
273#217—62no—
274#215—42no—
275#215—122no—
276#214—122no—
277(C2×D3)⋊C4—21no—
278(C2×D3)⋊C4—21no—
279(C2×D3)⋊C4—62no—
280(C2×D3)⋊C4—62no—
281C4⋊Dic3—21no—
282C4⋊Dic3—32no—
283C4⋊Dic3—32no—
284C4⋊Dic3—62no—
285C4⋊Dic3—61no—
286C4⋊Dic3—61no—
287C4⋊Dic3—121no—
288C4⋊Dic3C22×D311yescharacteristic
289Dic3⋊C4—21no—
290Dic3⋊C4—21no—
291Dic3⋊C4—21no—
292Dic3⋊C4—21no—
293Dic3⋊C4—21no—
294C4×Dic3—21no—
295C4×Dic3#6711yescharacteristic
296C4×Dic3#6711yescharacteristic
297C4×Dic3C22×D311yescharacteristic
298C2×C3⋊C8—32no—
299C2×C3⋊C8—32no—
300C2×C3⋊C8—62no—
301C2×C3⋊C8—122no—
302C2×C3⋊C8C22×D312yes—
303D3×C8—122no—
304C22×C32C22×D411yescharacteristic
305C2×C3×D3—21no—
306C2×C3×D3—21no—
307C2×C3×D3—42no—
308C2×C3×D3—42no—
309C2×C3×D3—42no—
310C2×C3×D3C2×SD1612yes—
311C32×C4—21no—
312C32×C4—41no—
313C32×C4—41no—
314C32×C4C2×SD1612yes—
315C32×C4H(5,𝔽2)11yescharacteristic
316C32×C42−1+411yescharacteristic
317C3⋊Dic3—42no—
318C3×Dic3—21no—
319C3×Dic3—21no—
320C3×Dic3—41no—
321C3×Dic3—41no—
322C3×Dic3C2×SD1612yes—
323C2×#41—181no—
324C2×SD16—32no—
325C2×SD16—92no—
326C22×C8—92no—
327C4⋊Q8—31no—
328C4⋊Q8—31no—
329C4⋊Q8—91no—
330#127—31no—
331#125—61no—
332#124—181no—
333C22⋊Q8—31no—
334C22⋊Q8—31no—
335C22⋊Q8—61no—
336#121—92no—
337#121—181no—
338C4×Q8—31no—
339C4×Q8—61no—
340C4×Q8D3211yescharacteristic
341C4×D4—92no—
342C4×D4—181no—
343#117—61no—
344C2×C42—31no—
345#106—92no—
346#106—92no—
347C4⋊C8—31no—
348C4⋊C8—92no—
349C4⋊C8—91no—
350#103—92no—
351#103—92no—
352#102—32no—
353#102—92no—
354C23×C3—31no—
355C23×C3—62no—
356C22×D3—22no—
357C22×D3C2×#6711yescharacteristic
358C3×Q8—22no—
359C3×Q8—21no—
360C3×Q8—21no—
361C3×Q8—21no—
362C3×Q8—21no—
363C3×Q8—41no—
364C3×Q8—61no—
365C3×Q8—61no—
366C3×Q8—122no—
367C3×D4—62no—
368C3×D4—62no—
369C3×D4—122no—
370C3×D4—122no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—31no—
379C2×C3×C4—34no—
380C2×C3×C4—31no—
381C2×C3×C4—31no—
382C2×C3×C4—41no—
383C2×C3×C4—41no—
384C2×C3×C4—61no—
385C2×C3×C4—61no—
386C2×C3×C4—61no—
387C2×C3×C4—61no—
388C2×C3×C4—121no—
389C2×C3×C4D3×D411yescharacteristic
390C2×C3×C4D3×D411yescharacteristic
391C2×C3×C4C2×#6711yescharacteristic
392C2×C3×C4C2×#6711yescharacteristic
393C2×C3×C4C23×D311yescharacteristic
394C2×C3×C4C23×D311yescharacteristic
395#67—124no—
396#67—124no—
397C2×Dic3—21no—
398C2×Dic3—21no—
399C2×Dic3—62no—
400C2×Dic3—62no—
401C2×Dic3—122no—
402C2×Dic3—124no—
403C2×Dic3C2×#6711yescharacteristic
404C2×Dic3C2×#6711yescharacteristic
405C2×Dic3C2×#6711yescharacteristic
406D12—22no—
407D12—22no—
408D12—42no—
409D12—42no—
410C4×D3—21no—
411C4×D3—21no—
412C4×D3—41no—
413C4×D3—124no—
414C4×D3#21514yescomplemented
415Dic6—21no—
416Dic6—21no—
417Dic6—42no—
418Dic6—122no—
419Dic6—122no—
420Dic6—242no—
421C3×C8—62no—
422C3⋊C8—22no—
423C3⋊C8—62no—
424C3⋊C8—62no—
425C3⋊C8—122no—
426C2×C32#53711yescharacteristic
427C2×C32C22×SD1611yescharacteristic
428C2×C32#57511yescharacteristic
429C3×D3—22no—
430C3×D3—82no—
431#41—364no—
432C2×Q8—31no—
433C2×Q8—61no—
434C2×Q8—181no—
435C2×Q8C2×D3211yescharacteristic
436C2×D4—32no—
437C2×D4—61no—
438C2×D4—61no—
439C2×D4—182no—
440C22×C4—31no—
441C22×C4—31no—
442C22×C4—31no—
443C22×C4—182no—
444SD16—122no—
445SD16—362no—
446C2×C8—32no—
447C2×C8—92no—
448C2×C8—362no—
449C4⋊C4—21no—
450C4⋊C4—31no—
451C4⋊C4—61no—
452C4⋊C4—61no—
453C4⋊C4—61no—
454C4⋊C4—61no—
455C4⋊C4—61no—
456C4⋊C4—61no—
457C4⋊C4—92no—
458C4⋊C4—181no—
459C4⋊C4C2×D3211yescharacteristic
460C22⋊C4—61no—
461C22⋊C4—61no—
462C22⋊C4—182no—
463C22⋊C4—182no—
464C42—21no—
465C42—31no—
466C42—31no—
467C42—31no—
468C42—61no—
469C42C2×D3211yescharacteristic
470C22×C3—21no—
471C22×C3—32no—
472C22×C3—61no—
473C22×C3—61no—
474C22×C3—122no—
475C22×C3—122no—
476C22×C3—122no—
477C22×C3C2×D3×D411yescharacteristic
478C22×C3C22×#6711yescharacteristic
479C2×D3—21no—
480C2×D3—21no—
481C2×D3—42no—
482C2×D3—42no—
483C2×D3—42no—
484C2×D3C2×#21512yes—
485C3×C4—21no—
486C3×C4—21no—
487C3×C4—21no—
488C3×C4—21no—
489C3×C4—22no—
490C3×C4—32no—
491C3×C4—41no—
492C3×C4—42no—
493C3×C4—41no—
494C3×C4—41no—
495C3×C4—41no—
496C3×C4—41no—
497C3×C4—61no—
498C3×C4—61no—
499C3×C4—81no—
500C3×C4—121no—
501C3×C4—121no—
502C3×C4D3×SD1612yes—
503C3×C4C2×#21512yes—
504C3×C4#100411yescharacteristic
505C3×C4#100911yescharacteristic
506C3×C4#101011yescharacteristic
507C3×C4#101011yescharacteristic
508Dic3—21no—
509Dic3—21no—
510Dic3—41no—
511Dic3—41no—
512Dic3—122no—
513Dic3—122no—
514Dic3—242no—
515Dic3C2×#21512yes—
516C32#324611yescharacteristic, complemented, Sylow
517C23—31no—
518C23—62no—
519Q8—21no—
520Q8—21no—
521Q8—61no—
522Q8—61no—
523Q8—122no—
524Q8—362no—
525D4—62no—
526D4—62no—
527D4—122no—
528D4—122no—
529D4—364no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—31no—
533C2×C4—34no—
534C2×C4—31no—
535C2×C4—31no—
536C2×C4—61no—
537C2×C4—61no—
538C2×C4—61no—
539C2×C4—61no—
540C2×C4—121no—
541C2×C4—182no—
542C2×C4—364no—
543C2×C4D3×#6711yescharacteristic
544C2×C4D3×#6711yescharacteristic
545C2×C4C22×D3211yescharacteristic
546C8—62no—
547C8—182no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—62no—
552C2×C3—242no—
553C2×C3#560811yescharacteristic
554C2×C3C2×D3×SD1611yescharacteristic
555C2×C3#577311yescharacteristic
556C2×C3C22×#21511yescharacteristic
557C2×C3#582211yescharacteristic
558C2×C3#583311yescharacteristic
559D3—22no—
560D3—82no—
561C22—32no—
562C22—61no—
563C22—61no—
564C22—122no—
565C22—122no—
566C22—122no—
567C22C2×D3×#6711yescharacteristic
568C4—21no—
569C4—32no—
570C4—41no—
571C4—41no—
572C4—61no—
573C4—61no—
574C4—121no—
575C4—121no—
576C4—362no—
577C4D3×#21512yes—
578C4#6429811yescharacteristic
579C4#6430711yescharacteristic
580C3—21no—
581C3#8036611yescharacteristic, complemented
582C3#8336311yescharacteristic, complemented
583C2—62no—
584C2—242no—
585C2#1059500411yescharacteristic
586C2C2×D3×#21511yescharacteristic
587C2#1059546911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radical#10593897C2
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×#5578C2semidirect
3. #10592719C2semidirect
4. C3×#5027C2semidirect
5. #10591634C2semidirect
6. #10591564C2semidirect
7. #10590501C2semidirect
8. #10590465C2semidirect
9. #10590364C2semidirect
10. D3×C4⋊(C3⋊C8)C2semidirect
11. #10590301C2semidirect
47. #5578D3semidirect
58. #5027D3semidirect
198. C3×C4×D3SD16semidirect
414. C4×D3#215semidirect
516. C32#3246semidirect
581. C3#80366semidirect
582. C3#83363semidirect

Maximal subgroups

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

subgroupindex
C3×#55782
#105938972
#105927192
C3×#50272
#105916342
#105915642
#105905012
#105904652
#105903642
D3×C4⋊(C3⋊C8)2
#105903012
#833633
#803663