Finite Group Databasebeta

← #11781584

Subgroups — #11781584

Order 1152.

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

normal subgroups only

This group has 337 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#10592792C211yesmaximal, characteristic
2C3×#5091C211yesmaximal, characteristic
3#10590301C211yesmaximal, characteristic
4#10590250C211yesmaximal, characteristic
5C3×#4546C211yesmaximal, characteristic
6#10589100C211yesmaximal, characteristic
7#10589094C211yesmaximal, characteristic
8#71151—31nomaximal
9#68511—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×C4×Dic6C2211yescharacteristic
13#63637—21no—
14#63637—21no—
15C4×C3⋊(C3⋊C8)C2211yescharacteristic
16C3×#810—21no—
17C3×#807—21no—
18C3×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21#63573—21no—
22Dic3⋊(C3⋊C8)—21no—
23#63566—21no—
24Dic3×C3⋊C8—21no—
25C3×#477—31no—
26#5093—31no—
27#5093—31no—
28#5093—61no—
29#5091D311yescharacteristic
30Q8×C3⋊C8—31no—
31#5020—31no—
32#4851—31no—
33#4830—31no—
34C3×#333—31no—
35#4546D311yescharacteristic
36#4486—31no—
37#4482—31no—
38#4479—31no—
39#4479—31no—
40C2×C32×Q8—21no—
41C2×#634—21no—
42C2×C3×Dic6D411yescharacteristic
43C32×C4⋊C4—21no—
44C32×C4⋊C4—21no—
45C32×C42C2311yescharacteristic
46C4⋊(C3⋊Dic3)—21no—
47C4⋊(C3⋊Dic3)—21no—
48C2×C3⋊(C3⋊C8)D411yescharacteristic
49C2×C3⋊(C3⋊C8)D411yescharacteristic
50C3×C4⋊Dic3D411yescharacteristic
51C3×Dic3⋊C4—21no—
52C3×C4×Dic3—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—21no—
56#1684—91noSylow
57C3×C4⋊Q8—21no—
58C3×C4⋊Q8C2×D311yescharacteristic
59C3×C4⋊Q8C2×D311yescharacteristic
60C3×C4×Q8—31no—
61#869—31no—
62#869—31no—
63#869—61no—
64C4×Dic6C2×D311yescharacteristic
65C3×#107—61no—
66C3×C4⋊C8—31no—
67C3×C4⋊C8—31no—
68C3×C4⋊C8—31no—
69C3×#103—61no—
70#835—61no—
71#817—61no—
72#816—61no—
73Dic3⋊C8—61no—
74C8×Dic3—61no—
75#810—21no—
76#810—61no—
77#810—61no—
78#810—61no—
79#810—61no—
80#810—62no—
81#810—62no—
82#808—61no—
83#807—21no—
84C4⋊(C3⋊C8)—61no—
85C4⋊(C3⋊C8)C2×D311yescharacteristic
86C4⋊(C3⋊C8)C2×D311yescharacteristic
87C4⋊(C3⋊C8)C2×D311yescharacteristic
88C4×C3⋊C8—31no—
89C4×C3⋊C8—31no—
90C4×C3⋊C8—61no—
91C4×C3⋊C8—61no—
92C32×Q8—81no—
93C2×C32×C4—41no—
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4#4111yescharacteristic
97C2×C3⋊Dic3—41no—
98#634—41no—
99#634—41no—
100C2×C3×Dic3—21no—
101C2×C3×Dic3—21no—
102C3×Dic6—21no—
103C3×Dic6Q1612yes—
104C3⋊(C3⋊C8)—21no—
105C3⋊(C3⋊C8)—21no—
106C3×C3⋊C8—41no—
107C3×C3⋊C8—41no—
108C3×C3⋊C8—41no—
109#487—91no—
110#477—31no—
111#475—91no—
112C8×Q8—91no—
113#335—91no—
114#333—31no—
115#332—91no—
116C2×C3×Q8—21no—
117C2×C3×Q8—21no—
118C2×C3×Q8—31no—
119C2×C3×Q8—41no—
120C2×Dic6—62no—
121C2×Dic6—61no—
122C2×Dic6—61no—
123C2×Dic6#6711yescharacteristic
124C2×C3×C8—61no—
125C2×C3×C8—61no—
126C2×C3×C8—61no—
127C3×C4⋊C4—22no—
128C3×C4⋊C4—21no—
129C3×C4⋊C4—21no—
130C3×C4⋊C4—21no—
131C3×C4⋊C4—21no—
132C3×C4⋊C4—31no—
133C3×C4⋊C4—41no—
134C3×C4⋊C4—61no—
135C3×C42—21no—
136C3×C42—61no—
137C3×C42C22×D311yescharacteristic
138C3×C42C22×D311yescharacteristic
139C4⋊Dic3—61no—
140C4⋊Dic3—61no—
141C4⋊Dic3—61no—
142C4⋊Dic3—61no—
143C4⋊Dic3—121no—
144C4⋊Dic3—121no—
145C4⋊Dic3#6711yescharacteristic
146Dic3⋊C4—21no—
147C4×Dic3—21no—
148C2×C3⋊C8—21no—
149C2×C3⋊C8—21no—
150C2×C3⋊C8—21no—
151C2×C3⋊C8—31no—
152C2×C3⋊C8—31no—
153C2×C3⋊C8—31no—
154C2×C3⋊C8—31no—
155C2×C3⋊C8—61no—
156C2×C3⋊C8—61no—
157C22×C32#12111yescharacteristic
158C32×C4—21no—
159C32×C4—81no—
160C32×C4C2×Q1611yescharacteristic
161C32×C4#13511yescharacteristic
162C32×C4#13511yescharacteristic
163C32×C4#13711yescharacteristic
164C3⋊Dic3—81no—
165C3×Dic3—22no—
166C3×Dic3—41no—
167C4⋊Q8—91no—
168C4⋊Q8D3211yescharacteristic
169C4×Q8—31no—
170#107—61no—
171#106—181no—
172C4⋊C8—31no—
173C4⋊C8—31no—
174C4⋊C8—31no—
175C4⋊C8—181no—
176#103—61no—
177#103—181no—
178#103—181no—
179#103—181no—
180C4×C8—91no—
181C4×C8—181no—
182C3×Q8—32no—
183C3×Q8—61no—
184C3×Q8—81no—
185C3×Q8—81no—
186C3×Q8—82no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—42no—
191C2×C3×C4—41no—
192C2×C3×C4—41no—
193C2×C3×C4—61no—
194C2×C3×C4—61no—
195C2×C3×C4#23511yescharacteristic
196C2×C3×C4D3×D411yescharacteristic
197C2×C3×C4D3×D411yescharacteristic
198C2×C3×C4D3×D411yescharacteristic
199C2×C3×C4#23711yescharacteristic
200C2×C3×C4C2×#6711yescharacteristic
201C2×Dic3—21no—
202C2×Dic3—21no—
203C2×Dic3—122no—
204C2×Dic3—121no—
205C2×Dic3—121no—
206Dic6—21no—
207Dic6—122no—
208Dic6—122no—
209Dic6—121no—
210Dic6—121no—
211Dic6—121no—
212Dic6—121no—
213Dic6#21612yes—
214C3×C8—121no—
215C3×C8—121no—
216C3×C8—121no—
217C3⋊C8—41no—
218C3⋊C8—41no—
219C3⋊C8—41no—
220C3⋊C8—61no—
221C3⋊C8—61no—
222C3⋊C8—61no—
223C3⋊C8—61no—
224C3⋊C8—121no—
225C3⋊C8—121no—
226C2×C32#46411yescharacteristic
227C2×C32#46711yescharacteristic
228C2×C32#47111yescharacteristic
229C2×Q8—21no—
230C2×Q8—31no—
231C2×Q8—181no—
232C2×C8—61no—
233C2×C8—61no—
234C2×C8—61no—
235C2×C8—91no—
236C2×C8—91no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—31no—
240C4⋊C4—61no—
241C4⋊C4—181no—
242C4⋊C4—181no—
243C42—61no—
244C42C2×D3211yescharacteristic
245C22×C3—21no—
246C22×C3#88411yescharacteristic
247C22×C3#93911yescharacteristic
248C3×C4—22no—
249C3×C4—21no—
250C3×C4—21no—
251C3×C4—21no—
252C3×C4—21no—
253C3×C4—21no—
254C3×C4—21no—
255C3×C4—62no—
256C3×C4—82no—
257C3×C4—81no—
258C3×C4—81no—
259C3×C4—121no—
260C3×C4#91611yescharacteristic
261C3×C4#91611yescharacteristic
262C3×C4D3×Q1611yescharacteristic
263C3×C4#91811yescharacteristic
264C3×C4#91811yescharacteristic
265C3×C4#91911yescharacteristic
266C3×C4C2×#21611yescharacteristic
267C3×C4#95011yescharacteristic
268Dic3—22no—
269Dic3—41no—
270Dic3—242no—
271Dic3—241no—
272Dic3—241no—
273C32#168411yescharacteristic, complemented, Sylow
274Q8—32no—
275Q8—61no—
276Q8—81no—
277Q8—361no—
278Q8—361no—
279C2×C4—41no—
280C2×C4—61no—
281C2×C4—61no—
282C2×C4—361no—
283C2×C4#380411yescharacteristic
284C2×C4D3×#6711yescharacteristic
285C2×C4#381111yescharacteristic
286C8—121no—
287C8—121no—
288C8—121no—
289C8—181no—
290C8—181no—
291C2×C3—21no—
292C2×C3—21no—
293C2×C3—21no—
294C2×C3#474811yescharacteristic
295C2×C3#479811yescharacteristic
296C2×C3#481311yescharacteristic
297C2×C3#505111yescharacteristic
298C2×C3#518511yescharacteristic
299C2×C3#520011yescharacteristic
300C22#6397111yescharacteristic
301C4—21no—
302C4—62no—
303C4—81no—
304C4—121no—
305C4—721no—
306C4D3×#21611yescharacteristic
307C4#6394511yescharacteristic
308C4#6394711yescharacteristic
309C4#6395011yescharacteristic
310C3—21no—
311C3#6851111yescharacteristic, complemented
312C3#7115111yescharacteristic, complemented
313C2#1059150711yescharacteristic
314C2#1059157911yescharacteristic
315C2#1059159611yescharacteristic
subgroupG/H
centerC22#63971
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socle, prime radicalC22×C32#121
hypercenterC4⋊Q8D32
hypocenterC32#1684
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
273. C32#1684semidirect
311. C3#68511semidirect
312. C3#71151semidirect

Maximal subgroups

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

subgroupindex
#105927922
C3×#50912
#105903012
#105902502
C3×#45462
#105891002
#105890942
#711513
#685113