Finite Group Databasebeta

← #11781392

Subgroups — #11781392

Order 1152.

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

normal subgroups only

This group has 332 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×#5094C211yesmaximal, characteristic
2C3×#5079C211yesmaximal, characteristic
3#10590384C211yesmaximal, characteristic
4C3⋊C8×Dic6C211yesmaximal, characteristic
5#10589413C211yesmaximal, characteristic
6#10589097C211yesmaximal, characteristic
7#10589093C211yesmaximal, characteristic
8#71240—31nomaximal
9#71118—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11C3×#869C2211yescharacteristic
12C3×C4×Dic6C2211yescharacteristic
13C2×#3718—21no—
14C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
15C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
16C3×#835—21no—
17C3×#835—21no—
18C3×#810—21no—
19C3×#808—21no—
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4×C3⋊C8C2211yescharacteristic
22Dic3⋊(C3⋊C8)—21no—
23#63565—21no—
24Dic3×C3⋊C8—21no—
25C3×#487—31no—
26C3×#475—31no—
27#5094D311yescharacteristic
28#5090—31no—
29#5079D311yescharacteristic
30#5031—31no—
31Q8×C3⋊C8—31no—
32C8×Dic6—31no—
33#4547—31no—
34#4547—31no—
35#4547—31no—
36#4547—61no—
37#4482—31no—
38#4480—31no—
39#4457—31no—
40C2×C32×Q8—21no—
41C2×C3×Dic6—21no—
42C2×C3×Dic6D411yescharacteristic
43C32×C4⋊C4—21no—
44C32×C4⋊C4—21no—
45C32×C42C2311yescharacteristic
46C2×C3⋊(C3⋊C8)—21no—
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#3718—42no—
57#1680—91noSylow
58C3×C4⋊Q8—21no—
59C3×C4⋊Q8—31no—
60C3×C4⋊Q8C2×D311yescharacteristic
61C3×C4⋊Q8C2×D311yescharacteristic
62C3×C4×Q8—31no—
63C2×#216—61no—
64C2×#216—61no—
65#869C2×D311yescharacteristic
66C4×Dic6C2×D311yescharacteristic
67C3×#106—61no—
68C3×C4⋊C8—31no—
69C3×#103—61no—
70C3×#103—61no—
71C3×#103—61no—
72C3×C4×C8—31no—
73#835—21no—
74#835—21no—
75#835—61no—
76Dic3⋊C8—61no—
77C8×Dic3—61no—
78#810—21no—
79#810—61no—
80#808—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
91C32×Q8—41no—
92C32×Q8—41no—
93C2×C32×C4—41no—
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4#4111yescharacteristic
97C2×C3×Dic3—21no—
98C2×C3×Dic3—21no—
99C2×C3×Dic3—41no—
100C3×Dic6—21no—
101C3×Dic6—41no—
102C3×Dic6—41no—
103C3×Dic6SD1612yes—
104C3⋊(C3⋊C8)—41no—
105C3⋊(C3⋊C8)—41no—
106C3×C3⋊C8—21no—
107C3×C3⋊C8—21no—
108C3×C3⋊C8—41no—
109#487—31no—
110#475—31no—
111#462—91no—
112C8×Q8—91no—
113#334—91no—
114#332—91no—
115#332—91no—
116C2×C3×Q8—21no—
117C2×C3×Q8—21no—
118C2×C3×Q8—31no—
119C2×C3×Q8—41no—
120C2×C3×Q8—61no—
121C2×Dic6—21no—
122C2×Dic6#6711yescharacteristic
123C2×C3×C8—31no—
124C2×C3×C8—31no—
125C2×C3×C8—61no—
126C3×C4⋊C4—22no—
127C3×C4⋊C4—21no—
128C3×C4⋊C4—21no—
129C3×C4⋊C4—21no—
130C3×C4⋊C4—21no—
131C3×C4⋊C4—31no—
132C3×C4⋊C4—41no—
133C3×C4⋊C4—61no—
134C3×C4⋊C4—61no—
135C3×C4⋊C4—61no—
136C3×C42—21no—
137C3×C42—61no—
138C3×C42C22×D311yescharacteristic
139C3×C42C22×D311yescharacteristic
140#216—122no—
141#216—122no—
142C4⋊Dic3—21no—
143C4⋊Dic3—21no—
144C4⋊Dic3#6711yescharacteristic
145Dic3⋊C4—21no—
146C4×Dic3—21no—
147C2×C3⋊C8—21no—
148C2×C3⋊C8—61no—
149C2×C3⋊C8—61no—
150C2×C3⋊C8—61no—
151C2×C3⋊C8—61no—
152C2×C3⋊C8—121no—
153C2×C3⋊C8—121no—
154C2×C3⋊C8#6711yescharacteristic
155C2×C3⋊C8#6711yescharacteristic
156C22×C32#12111yescharacteristic
157C32×C4—21no—
158C32×C4—81no—
159C32×C4C2×SD1611yescharacteristic
160C32×C4#13511yescharacteristic
161C32×C4#13511yescharacteristic
162C32×C4#13711yescharacteristic
163C3×Dic3—22no—
164C3×Dic3—41no—
165C3×Dic3—81no—
166C2×Q16—181no—
167C4⋊Q8—31no—
168C4⋊Q8D3211yescharacteristic
169C4×Q8—31no—
170#106—61no—
171C4⋊C8—31no—
172C4⋊C8—91no—
173C4⋊C8—91no—
174C4⋊C8—181no—
175#103—61no—
176#103—61no—
177#103—61no—
178#103—181no—
179C4×C8—31no—
180C4×C8—181no—
181C3×Q8—32no—
182C3×Q8—41no—
183C3×Q8—41no—
184C3×Q8—41no—
185C3×Q8—41no—
186C3×Q8—61no—
187C3×Q8—81no—
188C3×Q8—81no—
189C3×Q8—121no—
190C3×Q8—121no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4—42no—
195C2×C3×C4—41no—
196C2×C3×C4—41no—
197C2×C3×C4—61no—
198C2×C3×C4—61no—
199C2×C3×C4—121no—
200C2×C3×C4D3×D411yescharacteristic
201C2×C3×C4D3×D411yescharacteristic
202C2×C3×C4#23711yescharacteristic
203C2×C3×C4#23711yescharacteristic
204C2×C3×C4C2×#6711yescharacteristic
205C2×C3×C4C2×#6711yescharacteristic
206C2×Dic3—21no—
207C2×Dic3—21no—
208C2×Dic3—41no—
209Dic6—21no—
210Dic6—41no—
211Dic6—41no—
212Dic6#21512yes—
213C3×C8—61no—
214C3×C8—61no—
215C3×C8—121no—
216C3⋊C8—21no—
217C3⋊C8—21no—
218C3⋊C8—41no—
219C3⋊C8—121no—
220C3⋊C8—121no—
221C3⋊C8—121no—
222C3⋊C8—121no—
223C3⋊C8—241no—
224C3⋊C8—241no—
225C2×C32#46411yescharacteristic
226C2×C32#46511yescharacteristic
227C2×C32#47311yescharacteristic
228C2×Q8—21no—
229C2×Q8—31no—
230C2×Q8—61no—
231Q16—362no—
232C2×C8—31no—
233C2×C8—31no—
234C2×C8—61no—
235C2×C8—181no—
236C2×C8—181no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—31no—
240C4⋊C4—61no—
241C4⋊C4—61no—
242C4⋊C4—61no—
243C42—61no—
244C42C2×D3211yescharacteristic
245C22×C3—21no—
246C22×C3#93811yescharacteristic
247C22×C3#93911yescharacteristic
248C3×C4—21no—
249C3×C4—21no—
250C3×C4—21no—
251C3×C4—21no—
252C3×C4—21no—
253C3×C4—21no—
254C3×C4—41no—
255C3×C4—62no—
256C3×C4—82no—
257C3×C4—81no—
258C3×C4—81no—
259C3×C4—121no—
260C3×C4—241no—
261C3×C4D3×SD1611yescharacteristic
262C3×C4#91511yescharacteristic
263C3×C4#91611yescharacteristic
264C3×C4#91611yescharacteristic
265C3×C4C2×#21511yescharacteristic
266C3×C4#95011yescharacteristic
267C3×C4#95011yescharacteristic
268C3×C4#95111yescharacteristic
269Dic3—22no—
270Dic3—41no—
271Dic3—81no—
272C32#168011yescharacteristic, complemented, Sylow
273Q8—32no—
274Q8—41no—
275Q8—41no—
276Q8—61no—
277Q8—121no—
278Q8—121no—
279C2×C4—41no—
280C2×C4—61no—
281C2×C4—61no—
282C2×C4—121no—
283C2×C4#380511yescharacteristic
284C2×C4D3×#6711yescharacteristic
285C2×C4D3×#6711yescharacteristic
286C8—61no—
287C8—61no—
288C8—121no—
289C8—361no—
290C8—361no—
291C2×C3—21no—
292C2×C3—21no—
293C2×C3—21no—
294C2×C3#504811yescharacteristic
295C2×C3#505411yescharacteristic
296C2×C3#516611yescharacteristic
297C2×C3#517111yescharacteristic
298C2×C3#519211yescharacteristic
299C2×C3#520411yescharacteristic
300C22#6397011yescharacteristic
301C4—21no—
302C4—62no—
303C4—81no—
304C4—121no—
305C4—241no—
306C4#6392911yescharacteristic
307C4#6393511yescharacteristic
308C4D3×#21511yescharacteristic
309C4#6394711yescharacteristic
310C3—21no—
311C3#7111811yescharacteristic, complemented
312C3#7124011yescharacteristic, complemented
313C2#1059144211yescharacteristic
314C2#1059163411yescharacteristic
315C2#1059164111yescharacteristic
subgroupG/H
centerC22#63970
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socle, prime radicalC22×C32#121
hypercenterC4⋊Q8D32
hypocenterC32#1680
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
272. C32#1680semidirect
311. C3#71118semidirect
312. C3#71240semidirect

Maximal subgroups

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

subgroupindex
C3×#50942
C3×#50792
#105903842
C3⋊C8×Dic62
#105894132
#105890972
#105890932
#712403
#711183