Finite Group Databasebeta

← #11781258

Subgroups — #11781258

Order 1152.

411 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 411 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592787C211yesmaximal, characteristic, complemented
2C3×#5084C211yesmaximal, characteristic, complemented
3#10590349C211yesmaximal, characteristic
4#10590329C211yesmaximal, characteristic, complemented
5C3×#4546C211yesmaximal, characteristic, complemented
6#10589098C211yesmaximal, characteristic, complemented
7#10589091C211yesmaximal, characteristic, complemented
8#71134—31nomaximal
9#68498—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11#64083C2211yescharacteristic
12C3×C4×D12C2211yescharacteristic
13C2×#3714—21no—
14C2×D3×C3⋊C8—21no—
15#63636—21no—
16#63636—21no—
17C4×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#809—21no—
19C3×#808—21no—
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23#63564—21no—
24(C2×D3)⋊(C3⋊C8)—21no—
25C3×#476—31no—
26#5088—31no—
27#5088—31no—
28#5088—61no—
29#5084D311yescharacteristic, complemented
30#5015—31no—
31D4×C3⋊C8—31no—
32#4843—31no—
33#4834—31no—
34C3×#333—31no—
35#4546D311yescharacteristic, complemented
36#4485—31no—
37#4485—31no—
38#4480—31no—
39#4480—31no—
40C2×C32×Q8—21no—
41C2×C4⋊(C3⋊D3)—21no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C3×D12D411yescharacteristic
45C2×C3×C4×D3—21no—
46C32×C4⋊C4—21no—
47C32×C4⋊C4—21no—
48C32×C42C2311yescharacteristic
49C2×C3⋊(C3⋊C8)D411yescharacteristic
50C2×C3⋊(C3⋊C8)D411yescharacteristic
51C3×(C2×D3)⋊C4—21no—
52C3×C4⋊Dic3D411yescharacteristic
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—21no—
56#3714—42no—
57D3×C3⋊C8—42no—
58#1677—91noSylow
59C3×C4⋊Q8—21no—
60C3×C4⋊Q8C2×D311yescharacteristic
61C3×C4⋊Q8C2×D311yescharacteristic
62C3×C4×D4—31no—
63C2×#213—61no—
64C22×C3⋊C8—61no—
65C2×D24—61no—
66C2×D3×C8—61no—
67#874—31no—
68#874—31no—
69#874—61no—
70C4×D12C2×D311yescharacteristic
71C3×#106—61no—
72C3×C4⋊C8—31no—
73C3×C4⋊C8—31no—
74C3×C4⋊C8—31no—
75C3×#102—61no—
76#830—61no—
77#821—61no—
78(C2×D3)⋊C8—61no—
79#809—21no—
80#809—61no—
81#809—61no—
82#809—61no—
83#809—61no—
84#809—61no—
85#809—62no—
86#809—62no—
87#808—21no—
88C4⋊(C3⋊C8)C2×D311yescharacteristic
89C4⋊(C3⋊C8)C2×D311yescharacteristic
90C4⋊(C3⋊C8)C2×D311yescharacteristic
91C4×C3⋊C8—31no—
92C4×C3⋊C8—31no—
93C4×C3⋊C8—61no—
94C22×C3⋊D3—41no—
95C22×C3×D3—21no—
96C32×Q8—81no—
97C2×C32×C4—41no—
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4#4111yescharacteristic
101C4⋊(C3⋊D3)—41no—
102C4⋊(C3⋊D3)—41no—
103C4⋊(C3⋊D3)—41no—
104C4⋊(C3⋊D3)—41no—
105C4⋊(C3⋊D3)—81no—
106C2×C3×Dic3—21no—
107C3×D12—21no—
108C3×D12SD1612yes—
109C3×C4×D3—41no—
110C3×C4×D3—41no—
111C3⋊(C3⋊C8)—21no—
112C3⋊(C3⋊C8)—21no—
113C3×C3⋊C8—41no—
114C3×C3⋊C8—41no—
115C3×C3⋊C8—41no—
116#486—91no—
117#476—31no—
118#459—91no—
119C8×D4—91no—
120#334—91no—
121#333—31no—
122#331—91no—
123C2×C3×Q8—21no—
124C2×C3×Q8—21no—
125C2×C3×Q8—41no—
126C2×C3×D4—31no—
127C22×C3×C4—61no—
128C2×D12—62no—
129C2×D12—61no—
130C2×D12—61no—
131C2×D12—61no—
132C2×D12—61no—
133C2×D12—61no—
134C2×D12—61no—
135C2×D12—121no—
136C2×D12—121no—
137C2×D12#6711yescharacteristic
138C2×C4×D3—21no—
139C2×C3×C8—61no—
140C2×C3×C8—61no—
141C2×C3×C8—61no—
142C3×C4⋊C4—22no—
143C3×C4⋊C4—21no—
144C3×C4⋊C4—21no—
145C3×C4⋊C4—21no—
146C3×C4⋊C4—21no—
147C3×C4⋊C4—31no—
148C3×C4⋊C4—41no—
149C3×C22⋊C4—61no—
150C3×C42—21no—
151C3×C42C22×D311yescharacteristic
152C3×C42C22×D311yescharacteristic
153#213—122no—
154(C2×D3)⋊C4—21no—
155C4⋊Dic3#6711yescharacteristic
156C2×C3⋊C8—21no—
157C2×C3⋊C8—21no—
158C2×C3⋊C8—21no—
159C2×C3⋊C8—31no—
160C2×C3⋊C8—31no—
161C2×C3⋊C8—31no—
162C2×C3⋊C8—31no—
163C2×C3⋊C8—61no—
164C2×C3⋊C8—61no—
165C2×C3⋊C8—122no—
166D24—122no—
167D3×C8—122no—
168C22×C32#12111yescharacteristic
169C2×C3⋊D3—81no—
170C2×C3⋊D3—81no—
171C2×C3⋊D3—81no—
172C2×C3×D3—22no—
173C2×C3×D3—41no—
174C2×C3×D3—41no—
175C32×C4—21no—
176C32×C4—81no—
177C32×C4C2×SD1611yescharacteristic
178C32×C4#13511yescharacteristic
179C32×C4#13511yescharacteristic
180C32×C4AGL(1,ℤ/8)11yescharacteristic
181C3×Dic3—41no—
182C2×D8—181no—
183C22×C8—181no—
184C4⋊Q8D3211yescharacteristic
185#127—91no—
186C4×D4—31no—
187#106—61no—
188C4⋊C8—31no—
189C4⋊C8—31no—
190C4⋊C8—31no—
191#102—61no—
192#102—181no—
193#102—181no—
194#102—181no—
195C22⋊C8—181no—
196C4×C8—91no—
197C23×C3—61no—
198C22×D3—21no—
199C22×D3—122no—
200C22×D3—121no—
201C22×D3—121no—
202C3×Q8—81no—
203C3×Q8—81no—
204C3×Q8—82no—
205C3×D4—32no—
206C3×D4—61no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—42no—
211C2×C3×C4—41no—
212C2×C3×C4—41no—
213C2×C3×C4—61no—
214C2×C3×C4—121no—
215C2×C3×C4—121no—
216C2×C3×C4#23511yescharacteristic
217C2×C3×C4D3×D411yescharacteristic
218C2×C3×C4D3×D411yescharacteristic
219C2×C3×C4D3×D411yescharacteristic
220C2×C3×C4#23711yescharacteristic
221C2×C3×C4C2×#6711yescharacteristic
222C2×Dic3—21no—
223D12—21no—
224D12—122no—
225D12—122no—
226D12—121no—
227D12—121no—
228D12—121no—
229D12—121no—
230D12—121no—
231D12—121no—
232D12—121no—
233D12—121no—
234D12—241no—
235D12—241no—
236D12—241no—
237D12—241no—
238D12—242no—
239D12#21512yes—
240C4×D3—41no—
241C4×D3—41no—
242C3×C8—121no—
243C3×C8—121no—
244C3×C8—121no—
245C3⋊C8—41no—
246C3⋊C8—41no—
247C3⋊C8—41no—
248C3⋊C8—61no—
249C3⋊C8—61no—
250C3⋊C8—61no—
251C3⋊C8—61no—
252C3⋊C8—121no—
253C3⋊C8—121no—
254C2×C32#46311yescharacteristic
255C2×C32#46511yescharacteristic
256C2×C32#47211yescharacteristic
257C3⋊D3—161no—
258C3×D3—42no—
259C2×Q8—21no—
260C2×D4—31no—
261C2×D4—181no—
262C2×D4—181no—
263C2×D4—181no—
264C22×C4—61no—
265D8—362no—
266C2×C8—61no—
267C2×C8—61no—
268C2×C8—61no—
269C2×C8—91no—
270C2×C8—91no—
271C2×C8—362no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—31no—
275C22⋊C4—61no—
276C42C2×D3211yescharacteristic
277C22×C3—21no—
278C22×C3—62no—
279C22×C3—121no—
280C22×C3—121no—
281C22×C3#88411yescharacteristic
282C22×C3#93911yescharacteristic
283C2×D3—22no—
284C2×D3—41no—
285C2×D3—41no—
286C2×D3—242no—
287C2×D3—242no—
288C2×D3—242no—
289C2×D3—241no—
290C2×D3—241no—
291C2×D3—241no—
292C2×D3—241no—
293C2×D3—241no—
294C2×D3—241no—
295C3×C4—22no—
296C3×C4—21no—
297C3×C4—21no—
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—21no—
301C3×C4—21no—
302C3×C4—82no—
303C3×C4—81no—
304C3×C4—81no—
305C3×C4—121no—
306C3×C4D3×SD1611yescharacteristic
307C3×C4#91411yescharacteristic
308C3×C4#91411yescharacteristic
309C3×C4#91611yescharacteristic
310C3×C4#91911yescharacteristic
311C3×C4#91911yescharacteristic
312C3×C4C2×#21511yescharacteristic
313C3×C4#95011yescharacteristic
314Dic3—41no—
315C32#167711yescharacteristic, complemented, Sylow
316C23—61no—
317C23—361no—
318Q8—81no—
319D4—32no—
320D4—61no—
321D4—361no—
322D4—361no—
323D4—361no—
324D4—361no—
325D4—721no—
326C2×C4—41no—
327C2×C4—61no—
328C2×C4—121no—
329C2×C4—121no—
330C2×C4#380411yescharacteristic
331C2×C4D3×#6711yescharacteristic
332C2×C4#381111yescharacteristic
333C8—121no—
334C8—121no—
335C8—121no—
336C8—181no—
337C8—181no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—21no—
341C2×C3—122no—
342C2×C3#474911yescharacteristic
343C2×C3#480711yescharacteristic
344C2×C3#481911yescharacteristic
345C2×C3#504811yescharacteristic
346C2×C3#516511yescharacteristic
347C2×C3#519911yescharacteristic
348D3—42no—
349D3—482no—
350D3—481no—
351D3—481no—
352C22—62no—
353C22—121no—
354C22—121no—
355C22—721no—
356C22—721no—
357C22—721no—
358C22#6397111yescharacteristic
359C4—21no—
360C4—81no—
361C4—121no—
362C4D3×#21511yescharacteristic
363C4#6394111yescharacteristic
364C4#6394911yescharacteristic
365C4#6395011yescharacteristic
366C3—21no—
367C3#6849811yescharacteristic, complemented
368C3#7113411yescharacteristic, complemented
369C2—122no—
370C2—1441no—
371C2#1059150811yescharacteristic
372C2#1059157011yescharacteristic
373C2#1059158511yescharacteristic
subgroupG/H
centerC22#63971
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#121
prime radical#10590349C2
hypercenterC4⋊Q8D32
hypocenterC32#1677
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10592787C2semidirect
2. C3×#5084C2semidirect
4. #10590329C2semidirect
5. C3×#4546C2semidirect
6. #10589098C2semidirect
7. #10589091C2semidirect
29. #5084D3semidirect
35. #4546D3semidirect
315. C32#1677semidirect
367. C3#68498semidirect
368. C3#71134semidirect

Maximal subgroups

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

subgroupindex
#105927872
C3×#50842
#105903492
#105903292
C3×#45462
#105890982
#105890912
#711343
#684983