Finite Group Databasebeta

← #11887569

Subgroups — #11887569

Order 1152.

901 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593904C211yesmaximal, characteristic, complemented
2#10593896C211yesmaximal, characteristic
3C4×#3744C211yesmaximal, characteristic, complemented
4C3×C8×D12C211yesmaximal, characteristic, complemented
5C3×#4681C211yesmaximal, characteristic, complemented
6#10590951C212yesmaximal, complemented
7#10590847C212yesmaximal, complemented
8#10590675C212yesmaximal, complemented
9D3×#816C212yesmaximal, complemented
10#10590379C211yesmaximal, characteristic, complemented
11#10590307C211yesmaximal, characteristic, complemented
12#81612—31nomaximal
13#79447—31nomaximal
14C2×#3796—21no—
15C2×D3×Dic6C2212yes—
16C2×#3744C2211yescharacteristic
17C4×C4⋊(C3⋊D3)C2211yescharacteristic
18C4×#634C2211yescharacteristic
19C2×C3×D3×C8C2212yes—
20C3×C4×D12C2211yescharacteristic
21C3×#869C2211yescharacteristic
22C3×#869C2211yescharacteristic
23#63919—21no—
24#63909C2212yes—
25#63899—22no—
26#63898—21no—
27#63890—22no—
28D3×C4⋊Dic3C2212yes—
29#63871—21no—
30#63856C2212yes—
31C2×#3717C2212yes—
32C32×C4×C8C2211yescharacteristic
33#63648C2211yescharacteristic
34#63644C2211yescharacteristic
35#63643C2211yescharacteristic
36C3×(C2×D3)⋊C8C2212yes—
37C3×#816C2212yes—
38C3×#816C2212yes—
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40#63573C2212yes—
41#63567C2212yes—
42#63566C2212yes—
43#5727—31no—
44#5726—31no—
45#5555—31no—
46D4×Dic6—31no—
47C3×#487—31no—
48C3×C8×D4—31no—
49#5114—32no—
50C2×#816—32no—
51#5094—31no—
52#5083—31no—
53#4851—31no—
54#4841—31no—
55#4807—32no—
56#4806—32no—
57#4805—32no—
58D3×#103—32no—
59#4738—32no—
60#4721—32no—
61C4×#204—31no—
62C4×#204—31no—
63C4×#204—61no—
64C8×D12D311yescharacteristic, complemented
65#4681D311yescharacteristic, complemented
66C2×C4⋊(C3⋊D3)C2311yescharacteristic
67C2×C4×C3⋊D3—21no—
68C2×#634C2311yescharacteristic
69C2×C3×D12D411yescharacteristic
70C2×C3×C4×D3C2312yes—
71C2×C3×Dic6—21no—
72C2×C3×Dic6C2312yes—
73C2×#627—22no—
74C2×#626—22no—
75C2×D3×Dic3—22no—
76C2×D3×Dic3—22no—
77#3796—44no—
78D3×Dic6—24no—
79D3×Dic6—42no—
80C2×C32×C8C2311yescharacteristic
81C2×C32×C8C2311yescharacteristic
82C32×C42C2311yescharacteristic
83#3752—21no—
84C4⋊(C3⋊Dic3)C2311yescharacteristic
85C4⋊(C3⋊Dic3)C2311yescharacteristic
86#3750—21no—
87C4×C3⋊Dic3—21no—
88#3744—22no—
89C3×(C2×D3)⋊C4D412yes—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3D411yescharacteristic
94C3×C4⋊Dic3C2312yes—
95C2×C3×C3⋊C8C2312yes—
96C3×D3×C8—42no—
97#3724—22no—
98Dic3⋊Dic3—22no—
99#3722—22no—
100(C2×D3)⋊Dic3—22no—
101#3717—42no—
102#3298—91noSylow
103C2×#239—61no—
104C2×D3×Q8—32no—
105C2×#237—61no—
106C22×Dic6—32no—
107C22×C3×C8—32no—
108C3×C4⋊Q8—31no—
109C3×C4⋊Q8—31no—
110C3×C4×D4—31no—
111#946—32no—
112#946—61no—
113C2×#215—32no—
114D4×Dic3—61no—
115#930—32no—
116C2×C4⋊Dic3—32no—
117#924—32no—
118C2×#204—31no—
119C2×#204—31no—
120C2×#204—32no—
121C2×#204—61no—
122C2×D3×C8C2×D312yes—
123#897—61no—
124#896—62no—
125#895—32no—
126#894—62no—
127#893—61no—
128D3×C4⋊C4—32no—
129#888—61no—
130#888—61no—
131#886—62no—
132#878—62no—
133C4×D12—31no—
134C4×D12—31no—
135C4×D12—61no—
136C4×D12C2×D311yescharacteristic
137#869C2×D311yescharacteristic
138#869C2×D311yescharacteristic
139C4×Dic6—31no—
140C4×Dic6—31no—
141C4×Dic6—61no—
142C3×C4⋊C8—31no—
143C3×#103—32no—
144C3×#103—32no—
145C3×C22⋊C8—32no—
146C3×C4×C8—21no—
147C3×C4×C8C2×D311yescharacteristic
148C3×C4×C8C2×D311yescharacteristic
149#835—32no—
150#821—31no—
151#821—31no—
152#821—61no—
153(C2×D3)⋊C8C2×D312yes—
154#817—31no—
155#817—31no—
156#817—32no—
157#817—61no—
158#816—32no—
159#816—31no—
160#816—31no—
161#816—32no—
162#816—61no—
163#816C2×D312yes—
164#816C2×D312yes—
165#810—32no—
166#808—32no—
167C4⋊(C3⋊C8)C2×D311yescharacteristic
168C22×C3⋊D3—21no—
169C22×C3×D3C2×D412yes—
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2411yescharacteristic
173C2×C3⋊Dic3—21no—
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3—21no—
176C4⋊(C3⋊D3)—21no—
177C4⋊(C3⋊D3)—21no—
178C4×C3⋊D3—42no—
179#634—21no—
180#634#4112yescomplemented
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3C2×D412yes—
184C3×D12SD1614yescomplemented
185C3×C4×D3—22no—
186C3×C4×D3—22no—
187C3×Dic6—22no—
188C3×Dic6—22no—
189C3×Dic6—42no—
190#627—44no—
191#626—44no—
192D3×Dic3—44no—
193D3×Dic3—44no—
194C32×C8—21no—
195C32×C8—21no—
196C3×C3⋊C8—22no—
197D4×Q8—91no—
198#547—91no—
199#487—31no—
200#483—92no—
201#475—91no—
202#465—92no—
203#461—91no—
204#448—92no—
205C4×SD16—91no—
206C8×D4—31no—
207C2×#103—92no—
208C2×C3×Q8—32no—
209C2×C3×Q8—61no—
210C2×C3×D4—31no—
211C22×C3×C4—32no—
212C2×#67—62no—
213C22×Dic3—62no—
214C22×Dic3—62no—
215#239—124no—
216D3×Q8—64no—
217D3×Q8—122no—
218#237—124no—
219C2×D12—31no—
220C2×D12—31no—
221C2×D12—61no—
222C2×D12—62no—
223C2×D12D1211yescharacteristic
224C2×C4×D3—62no—
225C2×C4×D3—62no—
226C2×C4×D3—61no—
227C2×C4×D3—61no—
228C2×C4×D3—121no—
229C2×C4×D3C22×D312yes—
230C2×Dic6—21no—
231C2×Dic6—31no—
232C2×Dic6—31no—
233C2×Dic6—61no—
234C2×Dic6—64no—
235C2×Dic6—62no—
236C2×Dic6—62no—
237C2×Dic6—122no—
238C2×Dic6C22×D312yes—
239C2×C3×C8—21no—
240C2×C3×C8—21no—
241C2×C3×C8—32no—
242C2×C3×C8—122no—
243C2×C3×C8C22×D311yescharacteristic
244C2×C3×C8C22×D311yescharacteristic
245C2×C3×C8C22×D311yescharacteristic
246C2×C3×C8C22×D311yescharacteristic
247C3×C4⋊C4—31no—
248C3×C4⋊C4—32no—
249C3×C4⋊C4—61no—
250C3×C4⋊C4—61no—
251C3×C4⋊C4—61no—
252C3×C22⋊C4—32no—
253C3×C42—21no—
254C3×C42C22×D311yescharacteristic
255C3×C42C22×D311yescharacteristic
256#217—62no—
257#215—122no—
258(C2×D3)⋊C4—62no—
259(C2×D3)⋊C4—62no—
260(C2×D3)⋊C4—61no—
261(C2×D3)⋊C4—61no—
262(C2×D3)⋊C4—62no—
263(C2×D3)⋊C4—121no—
264(C2×D3)⋊C4D1212yes—
265C4⋊Dic3—21no—
266C4⋊Dic3—21no—
267C4⋊Dic3—21no—
268C4⋊Dic3—31no—
269C4⋊Dic3—31no—
270C4⋊Dic3—31no—
271C4⋊Dic3—31no—
272C4⋊Dic3—61no—
273C4⋊Dic3—61no—
274C4⋊Dic3—62no—
275C4⋊Dic3D1211yescharacteristic
276C4⋊Dic3C22×D312yes—
277Dic3⋊C4—62no—
278Dic3⋊C4—61no—
279Dic3⋊C4—61no—
280Dic3⋊C4—62no—
281Dic3⋊C4—62no—
282Dic3⋊C4—121no—
283C4×Dic3—61no—
284C4×Dic3—61no—
285C4×Dic3—121no—
286C2×C3⋊C8C22×D312yes—
287#204—62no—
288#204—62no—
289#204—64no—
290#204—122no—
291D3×C8—42no—
292C22×C32C22×D411yescharacteristic
293C2×C3⋊D3—41no—
294C2×C3⋊D3—41no—
295C2×C3⋊D3—41no—
296C2×C3×D3—22no—
297C2×C3×D3—22no—
298C2×C3×D3C2×SD1614yes—
299C32×C4—21no—
300C32×C4C2×SD1612yes—
301C32×C4C2×#4111yescharacteristic
302C32×C4H(5,𝔽2)11yescharacteristic
303C3⋊Dic3—22no—
304C3⋊Dic3—41no—
305C3⋊Dic3—41no—
306C3×Dic3—22no—
307C3×Dic3—42no—
308C3×Dic3—42no—
309C2×#41—181no—
310C22×Q8—92no—
311C2×SD16—92no—
312C2×SD16—91no—
313C22×C8—32no—
314C4⋊Q8—31no—
315C4⋊Q8—31no—
316C4⋊Q8—181no—
317#123—182no—
318C22⋊Q8—92no—
319C22⋊Q8—182no—
320C22⋊Q8—181no—
321#121—92no—
322C4×Q8—91no—
323C4×D4—31no—
324C4×D4—91no—
325C4×D4—181no—
326C2×C4⋊C4—92no—
327#106—92no—
328#106—91no—
329C4⋊C8—31no—
330#103—32no—
331#103—32no—
332#103—92no—
333#103—92no—
334#103—91no—
335#102—91no—
336C22⋊C8—32no—
337C4×C8D3211yescharacteristic
338C23×C3—32no—
339C22×D3—61no—
340C22×D3—61no—
341C22×D3—121no—
342C22×D3C2×D1212yes—
343C3×Q8—62no—
344C3×Q8—62no—
345C3×Q8—122no—
346C3×D4—34no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—32no—
351C2×C3×C4—62no—
352C2×C3×C4—62no—
353C2×C3×C4—62no—
354C2×C3×C4—62no—
355C2×C3×C4C2×D1211yescharacteristic
356C2×C3×C4C2×D1211yescharacteristic
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4C23×D311yescharacteristic
360C2×C3×C4C23×D311yescharacteristic
361#67—124no—
362C2×Dic3—22no—
363C2×Dic3—22no—
364C2×Dic3—61no—
365C2×Dic3—61no—
366C2×Dic3—61no—
367C2×Dic3—61no—
368C2×Dic3—61no—
369C2×Dic3—61no—
370C2×Dic3—121no—
371C2×Dic3—121no—
372C2×Dic3—121no—
373C2×Dic3—124no—
374C2×Dic3—124no—
375C2×Dic3C2×D1212yes—
376D12—62no—
377D12—61no—
378D12—61no—
379D12—61no—
380D12—61no—
381D12—121no—
382D12—124no—
383D12#20414yescomplemented
384C4×D3—22no—
385C4×D3—22no—
386C4×D3—124no—
387C4×D3—124no—
388C4×D3—122no—
389C4×D3—122no—
390C4×D3—242no—
391Dic6—22no—
392Dic6—22no—
393Dic6—32no—
394Dic6—32no—
395Dic6—42no—
396Dic6—62no—
397Dic6—61no—
398Dic6—61no—
399Dic6—121no—
400Dic6—124no—
401Dic6—124no—
402C3×C8—22no—
403C3×C8—21no—
404C3×C8—21no—
405C3×C8—21no—
406C3×C8—21no—
407C3×C8—41no—
408C3×C8—62no—
409C3⋊C8—22no—
410C2×C32#54611yescharacteristic
411C2×C32C22×SD1611yescharacteristic
412C2×C32#57811yescharacteristic
413C3⋊D3—81no—
414C3×D3—24no—
415#41—364no—
416C2×Q8—32no—
417C2×Q8—61no—
418C2×Q8—91no—
419C2×Q8—182no—
420C2×Q8—184no—
421C2×Q8—362no—
422C2×D4—31no—
423C2×D4—91no—
424C2×D4—182no—
425C22×C4—32no—
426C22×C4—182no—
427C22×C4—182no—
428C22×C4—181no—
429SD16—182no—
430SD16—362no—
431C2×C8—32no—
432C2×C8—122no—
433C2×C8C2×D3211yescharacteristic
434C2×C8C2×D3211yescharacteristic
435C4⋊C4—31no—
436C4⋊C4—32no—
437C4⋊C4—61no—
438C4⋊C4—61no—
439C4⋊C4—61no—
440C4⋊C4—91no—
441C4⋊C4—91no—
442C4⋊C4—182no—
443C4⋊C4—182no—
444C4⋊C4—181no—
445C22⋊C4—32no—
446C22⋊C4—182no—
447C22⋊C4—182no—
448C22⋊C4—181no—
449C42—181no—
450C42C2×D3211yescharacteristic
451C22×C3—21no—
452C22×C3—34no—
453C22×C3—62no—
454C22×C3—62no—
455C22×C3C22×D1211yescharacteristic
456C22×C3C2×D3×D411yescharacteristic
457C2×D3—22no—
458C2×D3—22no—
459C2×D3—122no—
460C2×D3—121no—
461C2×D3—121no—
462C2×D3—121no—
463C2×D3—121no—
464C2×D3—121no—
465C2×D3—121no—
466C2×D3—241no—
467C2×D3—241no—
468C2×D3C2×#20414yes—
469C3×C4—21no—
470C3×C4—21no—
471C3×C4—22no—
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—41no—
475C3×C4—62no—
476C3×C4—122no—
477C3×C4—122no—
478C3×C4C2×#20412yes—
479C3×C4D3×SD1612yes—
480C3×C4#100411yescharacteristic
481C3×C4D3×#4111yescharacteristic
482C3×C4D3×#4111yescharacteristic
483C3×C4#100911yescharacteristic
484Dic3—22no—
485Dic3—42no—
486Dic3—42no—
487Dic3—62no—
488Dic3—62no—
489Dic3—122no—
490Dic3—121no—
491Dic3—121no—
492Dic3—121no—
493Dic3—121no—
494Dic3—241no—
495Dic3—241no—
496C32#329811yescharacteristic, complemented, Sylow
497C23—32no—
498C23—181no—
499Q8—62no—
500Q8—62no—
501Q8—92no—
502Q8—122no—
503Q8—181no—
504Q8—364no—
505D4—34no—
506D4—181no—
507D4—181no—
508D4—364no—
509C2×C4—32no—
510C2×C4—62no—
511C2×C4—62no—
512C2×C4—62no—
513C2×C4—62no—
514C2×C4—181no—
515C2×C4—181no—
516C2×C4—181no—
517C2×C4—364no—
518C2×C4—364no—
519C2×C4—362no—
520C2×C4D3×D1211yescharacteristic
521C2×C4D3×D1211yescharacteristic
522C2×C4C22×D3211yescharacteristic
523C8—21no—
524C8—21no—
525C8—62no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—64no—
530C2×C3#555411yescharacteristic
531C2×C3#567611yescharacteristic
532C2×C3C22×#20411yescharacteristic
533C2×C3#575311yescharacteristic
534C2×C3C2×D3×SD1611yescharacteristic
535C2×C3#576611yescharacteristic
536D3—24no—
537D3—242no—
538D3—241no—
539D3—241no—
540C22—34no—
541C22—62no—
542C22—62no—
543C22—361no—
544C22—361no—
545C22—361no—
546C22C2×D3×D1211yescharacteristic
547C4—21no—
548C4—62no—
549C4—122no—
550C4—122no—
551C4—182no—
552C4—361no—
553C4—361no—
554C4D3×#20412yes—
555C4#6430611yescharacteristic
556C4#6430711yescharacteristic
557C3—21no—
558C3#7944711yescharacteristic, complemented
559C3#8161211yescharacteristic, complemented
560C2—64no—
561C2—721no—
562C2#1059400511yescharacteristic
563C2C2×D3×#20411yescharacteristic
564C2#1059469111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radical#10593896C2
hypercenterC4×C8D32
hypocenterC32#3298
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. #10593904C2semidirect
3. C4×#3744C2semidirect
4. C3×C8×D12C2semidirect
5. C3×#4681C2semidirect
6. #10590951C2semidirect
7. #10590847C2semidirect
8. #10590675C2semidirect
9. D3×#816C2semidirect
10. #10590379C2semidirect
11. #10590307C2semidirect
64. C8×D12D3semidirect
65. #4681D3semidirect
180. #634#41semidirect
184. C3×D12SD16semidirect
383. D12#204semidirect
496. C32#3298semidirect
558. C3#79447semidirect
559. C3#81612semidirect

Maximal subgroups

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

subgroupindex
#105939042
#105938962
C4×#37442
C3×C8×D122
C3×#46812
#105909512
#105908472
#105906752
D3×#8162
#105903792
#105903072
#816123
#794473