Finite Group Databasebeta

← #11781311

Subgroups — #11781311

Order 1152.

362 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C3×#4830C211yesmaximal, characteristic, complemented
2#10590367C211yesmaximal, characteristic
3#10590310C211yesmaximal, characteristic, complemented
4#10590281C211yesmaximal, characteristic
5#10589351C211yesmaximal, characteristic
6C3×#4481C211yesmaximal, characteristic, complemented
7#10589097C211yesmaximal, characteristic, complemented
8#70940—31nomaximal
9#68510—31nomaximal
10#64083C2211yescharacteristic
11C3×#869C2211yescharacteristic
12C3×C4×Dic6C2211yescharacteristic
13C2×#3717—21no—
14C32×C4⋊C8C2211yescharacteristic
15C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
16C3×Dic3⋊C8—21no—
17C3×C8×Dic3—21no—
18C3×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×C4×C3⋊C8C2211yescharacteristic
20#63576—21no—
21#63565—21no—
22#63564—21no—
23#63564—21no—
24#63564—21no—
25C3×C8×Q8—31no—
26#5091—31no—
27#5088—31no—
28#5027—31no—
29#5021—31no—
30#4848—31no—
31#4830D311yescharacteristic, complemented
32#4694—31no—
33C3×#333—31no—
34#4485—31no—
35#4485—31no—
36#4485—61no—
37#4481D311yescharacteristic, complemented
38#4480—31no—
39#4457—31no—
40C2×C4⋊(C3⋊D3)—21no—
41C2×C4⋊(C3⋊D3)—21no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C3×Dic6—21no—
44C2×C3×Dic6D411yescharacteristic
45C2×C32×C8—21no—
46C32×C42C2311yescharacteristic
47C2×C3⋊(C3⋊C8)—21no—
48C3×C4⋊Dic3—21no—
49C3×C4⋊Dic3—21no—
50C3×C4⋊Dic3D411yescharacteristic
51C3×Dic3⋊C4—21no—
52C3×C4×Dic3—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8D411yescharacteristic
55C2×C3×C3⋊C8D411yescharacteristic
56#3717—42no—
57#1678—91noSylow
58C3×C4⋊Q8—31no—
59C3×C4×Q8—31no—
60C2×#215—61no—
61C2×#204—61no—
62#874—31no—
63#874—31no—
64#874—61no—
65#869C2×D311yescharacteristic
66C4×Dic6C2×D311yescharacteristic
67C3×C4⋊C8—21no—
68C3×C4⋊C8—31no—
69C3×C4⋊C8—61no—
70C3×C4⋊C8C2×D311yescharacteristic
71C3×C4⋊C8C2×D311yescharacteristic
72C3×C4×C8—31no—
73C3×C4×C8—61no—
74#835—61no—
75#821—61no—
76#821—61no—
77#821—61no—
78Dic3⋊C8—21no—
79C8×Dic3—21no—
80#810—61no—
81#809—61no—
82#809—61no—
83#809—61no—
84#807—61no—
85#807—61no—
86C4⋊(C3⋊C8)—31no—
87C4⋊(C3⋊C8)—31no—
88C4⋊(C3⋊C8)—61no—
89C4⋊(C3⋊C8)C2×D311yescharacteristic
90C4×C3⋊C8C2×D311yescharacteristic
91C22×C3⋊D3—41no—
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4#4111yescharacteristic
95C4⋊(C3⋊D3)—41no—
96C4⋊(C3⋊D3)—41no—
97C4⋊(C3⋊D3)—41no—
98C4⋊(C3⋊D3)—41no—
99C4⋊(C3⋊D3)—81no—
100C2×C3×Dic3—21no—
101C2×C3×Dic3—21no—
102C2×C3×Dic3—41no—
103C3×Dic6—21no—
104C3×Dic6—81no—
105C3×Dic6SD1612yes—
106C32×C8—41no—
107C3⋊(C3⋊C8)—41no—
108C3×C3⋊C8—21no—
109C3×C3⋊C8—21no—
110C3×C3⋊C8—41no—
111#486—91no—
112#477—91no—
113#460—91no—
114C8×Q8—31no—
115#334—91no—
116#333—31no—
117#331—91no—
118C2×C3×Q8—31no—
119C2×C3×Q8—61no—
120C2×D12—61no—
121C2×D12—61no—
122C2×D12—61no—
123C2×D12—61no—
124C2×D12—62no—
125C2×D12—61no—
126C2×D12—61no—
127C2×D12—121no—
128C2×D12—121no—
129C2×Dic6—21no—
130C2×Dic6D1211yescharacteristic
131C2×C3×C8—21no—
132C2×C3×C8—21no—
133C2×C3×C8—31no—
134C2×C3×C8—31no—
135C2×C3×C8—41no—
136C2×C3×C8—61no—
137C3×C4⋊C4—31no—
138C3×C4⋊C4—61no—
139C3×C4⋊C4—61no—
140C3×C4⋊C4—61no—
141C3×C42—21no—
142C3×C42—61no—
143C3×C42C22×D311yescharacteristic
144C3×C42C22×D311yescharacteristic
145#215—122no—
146C4⋊Dic3—21no—
147C4⋊Dic3—21no—
148C4⋊Dic3D1211yescharacteristic
149Dic3⋊C4—21no—
150C4×Dic3—21no—
151C2×C3⋊C8—21no—
152C2×C3⋊C8—61no—
153C2×C3⋊C8—61no—
154C2×C3⋊C8—121no—
155C2×C3⋊C8#6711yescharacteristic
156C2×C3⋊C8#6711yescharacteristic
157#204—122no—
158C22×C32#12111yescharacteristic
159C2×C3⋊D3—81no—
160C2×C3⋊D3—81no—
161C2×C3⋊D3—81no—
162C32×C4—21no—
163C32×C4C2×SD1611yescharacteristic
164C32×C4#13511yescharacteristic
165C32×C4#13511yescharacteristic
166C32×C4#13711yescharacteristic
167C3×Dic3—22no—
168C3×Dic3—41no—
169C3×Dic3—81no—
170C2×SD16—181no—
171C4⋊Q8—31no—
172#127—91no—
173C4×Q8—31no—
174#107—181no—
175C4⋊C8—31no—
176C4⋊C8—61no—
177C4⋊C8—91no—
178C4⋊C8D3211yescharacteristic
179#103—181no—
180#102—181no—
181#102—181no—
182#102—181no—
183C4×C8—31no—
184C4×C8—61no—
185C22×D3—122no—
186C22×D3—121no—
187C22×D3—121no—
188C3×Q8—32no—
189C3×Q8—61no—
190C3×Q8—241no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4—61no—
195C2×C3×C4—61no—
196C2×C3×C4—121no—
197C2×C3×C4C2×D1211yescharacteristic
198C2×C3×C4#23511yescharacteristic
199C2×C3×C4#23511yescharacteristic
200C2×C3×C4D3×D411yescharacteristic
201C2×C3×C4D3×D411yescharacteristic
202C2×C3×C4C2×#6711yescharacteristic
203C2×Dic3—21no—
204C2×Dic3—21no—
205C2×Dic3—41no—
206D12—121no—
207D12—121no—
208D12—121no—
209D12—121no—
210D12—121no—
211D12—121no—
212D12—121no—
213D12—121no—
214D12—241no—
215D12—241no—
216D12—241no—
217D12—241no—
218D12—241no—
219D12—241no—
220D12—242no—
221Dic6—21no—
222Dic6—81no—
223Dic6#20412yes—
224C3×C8—41no—
225C3×C8—41no—
226C3×C8—61no—
227C3×C8—61no—
228C3×C8—81no—
229C3×C8—121no—
230C3⋊C8—21no—
231C3⋊C8—21no—
232C3⋊C8—41no—
233C3⋊C8—121no—
234C3⋊C8—121no—
235C3⋊C8—241no—
236C2×C32#46411yescharacteristic
237C2×C32#46511yescharacteristic
238C2×C32#47211yescharacteristic
239C3⋊D3—161no—
240C2×Q8—31no—
241C2×Q8—61no—
242C2×D4—181no—
243C2×D4—181no—
244C2×D4—181no—
245SD16—362no—
246C2×C8—21no—
247C2×C8—31no—
248C2×C8—31no—
249C2×C8—61no—
250C2×C8—181no—
251C4⋊C4—31no—
252C4⋊C4—61no—
253C4⋊C4—61no—
254C4⋊C4—61no—
255C42—61no—
256C42C2×D3211yescharacteristic
257C22×C3—21no—
258C22×C3#88411yescharacteristic
259C22×C3#93011yescharacteristic
260C2×D3—242no—
261C2×D3—242no—
262C2×D3—242no—
263C2×D3—241no—
264C2×D3—241no—
265C2×D3—241no—
266C2×D3—241no—
267C2×D3—241no—
268C2×D3—241no—
269C3×C4—21no—
270C3×C4—21no—
271C3×C4—21no—
272C3×C4—21no—
273C3×C4—21no—
274C3×C4—21no—
275C3×C4—41no—
276C3×C4—62no—
277C3×C4—121no—
278C3×C4—241no—
279C3×C4C2×#20411yescharacteristic
280C3×C4#90411yescharacteristic
281C3×C4D3×SD1611yescharacteristic
282C3×C4#91611yescharacteristic
283C3×C4#91811yescharacteristic
284C3×C4#91911yescharacteristic
285C3×C4#94211yescharacteristic
286C3×C4#95011yescharacteristic
287Dic3—22no—
288Dic3—41no—
289Dic3—81no—
290C32#167811yescharacteristic, complemented, Sylow
291C23—361no—
292Q8—32no—
293Q8—61no—
294Q8—241no—
295D4—361no—
296D4—361no—
297D4—361no—
298D4—361no—
299D4—721no—
300C2×C4—61no—
301C2×C4—61no—
302C2×C4—121no—
303C2×C4#379811yescharacteristic
304C2×C4D3×D1211yescharacteristic
305C2×C4D3×#6711yescharacteristic
306C8—41no—
307C8—61no—
308C8—61no—
309C8—121no—
310C8—361no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3—21no—
314C2×C3#474911yescharacteristic
315C2×C3#479811yescharacteristic
316C2×C3#480711yescharacteristic
317C2×C3#502811yescharacteristic
318C2×C3#511411yescharacteristic
319C2×C3#514211yescharacteristic
320D3—482no—
321D3—481no—
322D3—481no—
323C22—721no—
324C22—721no—
325C22—721no—
326C22#6390611yescharacteristic
327C4—21no—
328C4—62no—
329C4—121no—
330C4—241no—
331C4D3×#20411yescharacteristic
332C4#6380811yescharacteristic
333C4#6393511yescharacteristic
334C4#6394811yescharacteristic
335C3—21no—
336C3#6851011yescharacteristic, complemented
337C3#7094011yescharacteristic, complemented
338C2—1441no—
339C2#1059053611yescharacteristic
340C2#1059084711yescharacteristic
341C2#1059099711yescharacteristic
subgroupG/H
centerC22#63906
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#121
prime radical#64083C22
hypercenterC4⋊C8D32
hypocenterC32#1678
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C3×#4830C2semidirect
3. #10590310C2semidirect
6. C3×#4481C2semidirect
7. #10589097C2semidirect
31. #4830D3semidirect
37. #4481D3semidirect
290. C32#1678semidirect
336. C3#68510semidirect
337. C3#70940semidirect

Maximal subgroups

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

subgroupindex
C3×#48302
#105903672
#105903102
#105902812
#105893512
C3×#44812
#105890972
#709403
#685103