Finite Group Databasebeta

← #11781307

Subgroups — #11781307

Order 1152.

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

normal subgroups only

This group has 352 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×#5091C211yesmaximal, characteristic, complemented
2C3×#5088C211yesmaximal, characteristic
3#10590364C211yesmaximal, characteristic
4C3⋊C8×Dic6C211yesmaximal, characteristic, complemented
5#10589412C211yesmaximal, characteristic, complemented
6#10589097C211yesmaximal, characteristic, complemented
7#10589090C211yesmaximal, characteristic
8#71208—31nomaximal
9#71150—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11C3×#874C2211yescharacteristic
12C3×C4×Dic6C2211yescharacteristic
13C2×#3715—21no—
14C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
15C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
16C3×#810—21no—
17C3×#809—21no—
18C3×#809—21no—
19C3×#807—21no—
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4×C3⋊C8C2211yescharacteristic
22Dic3⋊(C3⋊C8)—21no—
23#63562—21no—
24Dic3×C3⋊C8—21no—
25C3×#486—31no—
26C3×#477—31no—
27#5091D311yescharacteristic, complemented
28#5088D311yescharacteristic
29#5075—31no—
30#5027—31no—
31Q8×C3⋊C8—31no—
32C8×Dic6—31no—
33#4546—31no—
34#4546—31no—
35#4546—61no—
36#4544—31no—
37#4485—31no—
38#4480—31no—
39#4457—31no—
40C2×C32×Q8—21no—
41C2×C3×D12—21no—
42C2×C3×D12—21no—
43C2×C3×D12—21no—
44C2×C3×Dic6D411yescharacteristic
45C32×C4⋊C4—21no—
46C32×C4⋊C4—21no—
47C32×C42C2311yescharacteristic
48C2×C3⋊(C3⋊C8)—21no—
49C2×C3⋊(C3⋊C8)—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#3715—42no—
57#1678—91noSylow
58C3×C4⋊Q8—21no—
59C3×C4⋊Q8C2×D311yescharacteristic
60C3×C4⋊Q8C2×D311yescharacteristic
61C3×#127—31no—
62C3×C4×Q8—31no—
63C2×#215—61no—
64C2×#214—61no—
65#874C2×D311yescharacteristic
66C4×Dic6C2×D311yescharacteristic
67C3×#107—61no—
68C3×C4⋊C8—31no—
69C3×#103—61no—
70C3×#102—61no—
71C3×#102—61no—
72C3×C4×C8—31no—
73#832—61no—
74Dic3⋊C8—61no—
75C8×Dic3—61no—
76#810—21no—
77#809—21no—
78#809—21no—
79#809—61no—
80#807—21no—
81C4⋊(C3⋊C8)—31no—
82C4⋊(C3⋊C8)—31no—
83C4⋊(C3⋊C8)—31no—
84C4⋊(C3⋊C8)—31no—
85C4⋊(C3⋊C8)—61no—
86C4⋊(C3⋊C8)—61no—
87C4⋊(C3⋊C8)—61no—
88C4⋊(C3⋊C8)C2×D311yescharacteristic
89C4×C3⋊C8—61no—
90C4×C3⋊C8C2×D311yescharacteristic
91C22×C3×D3—41no—
92C32×Q8—81no—
93C2×C32×C4—41no—
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4#4111yescharacteristic
97C2×C3×Dic3—21no—
98C2×C3×Dic3—21no—
99C3×D12—41no—
100C3×D12—41no—
101C3×D12—41no—
102C3×D12—41no—
103C3×D12—81no—
104C3×Dic6—21no—
105C3×Dic6SD1612yes—
106C3⋊(C3⋊C8)—41no—
107C3⋊(C3⋊C8)—41no—
108C3×C3⋊C8—21no—
109C3×C3⋊C8—21no—
110C3×C3⋊C8—41no—
111#486—31no—
112#477—31no—
113#460—91no—
114C8×Q8—91no—
115#334—91no—
116#333—91no—
117#331—91no—
118C2×C3×Q8—22no—
119C2×C3×Q8—21no—
120C2×C3×Q8—21no—
121C2×C3×Q8—31no—
122C2×C3×D4—61no—
123C2×C3×D4—61no—
124C2×C3×D4—61no—
125C2×D12—21no—
126C2×D12—21no—
127C2×D12—21no—
128C2×Dic6#6711yescharacteristic
129C2×C3×C8—31no—
130C2×C3×C8—31no—
131C2×C3×C8—61no—
132C3×C4⋊C4—21no—
133C3×C4⋊C4—21no—
134C3×C4⋊C4—21no—
135C3×C4⋊C4—21no—
136C3×C4⋊C4—31no—
137C3×C4⋊C4—41no—
138C3×C4⋊C4—41no—
139C3×C4⋊C4—61no—
140C3×C42—21no—
141C3×C42—61no—
142C3×C42C22×D311yescharacteristic
143C3×C42C22×D311yescharacteristic
144#215—122no—
145#214—122no—
146C4⋊Dic3#6711yescharacteristic
147Dic3⋊C4—21no—
148C4×Dic3—21no—
149C2×C3⋊C8—21no—
150C2×C3⋊C8—61no—
151C2×C3⋊C8—61no—
152C2×C3⋊C8—61no—
153C2×C3⋊C8—61no—
154C2×C3⋊C8—121no—
155C2×C3⋊C8—121no—
156C2×C3⋊C8#6711yescharacteristic
157C2×C3⋊C8#6711yescharacteristic
158C22×C32#12111yescharacteristic
159C2×C3×D3—81no—
160C2×C3×D3—81no—
161C2×C3×D3—81no—
162C32×C4—21no—
163C32×C4—81no—
164C32×C4C2×SD1611yescharacteristic
165C32×C4#13511yescharacteristic
166C32×C4#13511yescharacteristic
167C32×C4#13711yescharacteristic
168C3×Dic3—22no—
169C3×Dic3—41no—
170C2×SD16—181no—
171C4⋊Q8D3211yescharacteristic
172#127—31no—
173C4×Q8—31no—
174#107—61no—
175C4⋊C8—31no—
176C4⋊C8—91no—
177C4⋊C8—91no—
178C4⋊C8—181no—
179#103—61no—
180#102—61no—
181#102—61no—
182#102—181no—
183C4×C8—31no—
184C4×C8—181no—
185C23×C3—121no—
186C22×D3—41no—
187C3×Q8—32no—
188C3×Q8—61no—
189C3×Q8—81no—
190C3×Q8—81no—
191C3×Q8—82no—
192C3×D4—121no—
193C3×D4—121no—
194C3×D4—121no—
195C3×D4—121no—
196C3×D4—241no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—42no—
201C2×C3×C4—41no—
202C2×C3×C4—41no—
203C2×C3×C4—61no—
204C2×C3×C4—61no—
205C2×C3×C4D3×D411yescharacteristic
206C2×C3×C4D3×D411yescharacteristic
207C2×C3×C4#23711yescharacteristic
208C2×C3×C4#23711yescharacteristic
209C2×C3×C4C2×#6711yescharacteristic
210C2×C3×C4C2×#6711yescharacteristic
211C2×Dic3—21no—
212C2×Dic3—21no—
213D12—41no—
214D12—41no—
215D12—41no—
216D12—41no—
217D12—81no—
218Dic6—21no—
219Dic6#21512yes—
220C3×C8—61no—
221C3×C8—61no—
222C3×C8—121no—
223C3⋊C8—21no—
224C3⋊C8—21no—
225C3⋊C8—41no—
226C3⋊C8—121no—
227C3⋊C8—121no—
228C3⋊C8—121no—
229C3⋊C8—121no—
230C3⋊C8—241no—
231C3⋊C8—241no—
232C2×C32#46411yescharacteristic
233C2×C32#46511yescharacteristic
234C2×C32#47211yescharacteristic
235C3×D3—161no—
236C2×Q8—21no—
237C2×Q8—31no—
238C2×D4—61no—
239C2×D4—61no—
240C2×D4—61no—
241SD16—362no—
242C2×C8—31no—
243C2×C8—31no—
244C2×C8—61no—
245C2×C8—181no—
246C2×C8—181no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—31no—
250C4⋊C4—61no—
251C42—61no—
252C42C2×D3211yescharacteristic
253C22×C3—21no—
254C22×C3—241no—
255C22×C3—241no—
256C22×C3—241no—
257C22×C3#93811yescharacteristic
258C22×C3#93911yescharacteristic
259C2×D3—81no—
260C2×D3—81no—
261C2×D3—81no—
262C3×C4—21no—
263C3×C4—21no—
264C3×C4—21no—
265C3×C4—21no—
266C3×C4—21no—
267C3×C4—21no—
268C3×C4—41no—
269C3×C4—62no—
270C3×C4—82no—
271C3×C4—81no—
272C3×C4—81no—
273C3×C4—121no—
274C3×C4D3×SD1611yescharacteristic
275C3×C4#91611yescharacteristic
276C3×C4#91811yescharacteristic
277C3×C4#91911yescharacteristic
278C3×C4C2×#21511yescharacteristic
279C3×C4#95011yescharacteristic
280C3×C4#95011yescharacteristic
281C3×C4#95111yescharacteristic
282Dic3—22no—
283Dic3—41no—
284C32#167811yescharacteristic, complemented, Sylow
285C23—121no—
286Q8—32no—
287Q8—61no—
288Q8—81no—
289D4—121no—
290D4—121no—
291D4—121no—
292D4—121no—
293D4—241no—
294C2×C4—41no—
295C2×C4—61no—
296C2×C4—61no—
297C2×C4#380511yescharacteristic
298C2×C4D3×#6711yescharacteristic
299C2×C4D3×#6711yescharacteristic
300C8—61no—
301C8—61no—
302C8—121no—
303C8—361no—
304C8—361no—
305C2×C3—21no—
306C2×C3—21no—
307C2×C3—21no—
308C2×C3—481no—
309C2×C3#504811yescharacteristic
310C2×C3#505411yescharacteristic
311C2×C3#516011yescharacteristic
312C2×C3#517111yescharacteristic
313C2×C3#518511yescharacteristic
314C2×C3#519911yescharacteristic
315D3—161no—
316C22—241no—
317C22—241no—
318C22—241no—
319C22#6397011yescharacteristic
320C4—21no—
321C4—62no—
322C4—81no—
323C4—121no—
324C4D3×#21511yescharacteristic
325C4#6394311yescharacteristic
326C4#6394711yescharacteristic
327C4#6394911yescharacteristic
328C3—21no—
329C3#7115011yescharacteristic, complemented
330C3#7120811yescharacteristic, complemented
331C2—481no—
332C2#1059150511yescharacteristic
333C2#1059157811yescharacteristic
334C2#1059163411yescharacteristic
subgroupG/H
centerC22#63970
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#121
prime radicalC3×#874C22
hypercenterC4⋊Q8D32
hypocenterC32#1678
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. C3×#5091C2semidirect
4. C3⋊C8×Dic6C2semidirect
5. #10589412C2semidirect
6. #10589097C2semidirect
27. #5091D3semidirect
284. C32#1678semidirect
329. C3#71150semidirect
330. C3#71208semidirect

Maximal subgroups

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

subgroupindex
C3×#50912
C3×#50882
#105903642
C3⋊C8×Dic62
#105894122
#105890972
#105890902
#712083
#711503