Finite Group Databasebeta

← #11781402

Subgroups — #11781402

Order 1152.

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

normal subgroups only

This group has 327 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
1C3×#4851C211yesmaximal, characteristic
2#10590384C211yesmaximal, characteristic
3#10590290C211yesmaximal, characteristic
4#10590250C211yesmaximal, characteristic
5#10589346C211yesmaximal, characteristic
6C3×#4482C211yesmaximal, characteristic
7#10589093C211yesmaximal, characteristic
8#71118—31nomaximal
9#68469—31nomaximal
10C3×#869C2211yescharacteristic
11C3×#869C2211yescharacteristic
12C3×C4×Dic6C2211yescharacteristic
13C2×#3718—21no—
14C32×C4⋊C8C2211yescharacteristic
15C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
16C4×C3⋊(C3⋊C8)C2211yescharacteristic
17C3×#817—21no—
18C3×#816—21no—
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20Dic3⋊(C3⋊C8)—21no—
21#63565—21no—
22#63565—21no—
23#63565—21no—
24Dic3×C3⋊C8—21no—
25C3×#475—31no—
26#5093—31no—
27#5090—31no—
28#5079—31no—
29#5031—31no—
30Q8×C3⋊C8—31no—
31#4851D311yescharacteristic
32#4830—31no—
33C3×#332—31no—
34#4547—31no—
35#4482—31no—
36#4482D311yescharacteristic
37#4480—31no—
38#4480—31no—
39#4480—61no—
40C2×C3×Dic6—21no—
41C2×C3×Dic6—21no—
42C2×C3×Dic6D411yescharacteristic
43C2×C32×C8—21no—
44C32×C42C2311yescharacteristic
45C2×C3⋊(C3⋊C8)—21no—
46C2×C3⋊(C3⋊C8)D411yescharacteristic
47C2×C3⋊(C3⋊C8)D411yescharacteristic
48C3×C4⋊Dic3—21no—
49C3×C4⋊Dic3—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3D411yescharacteristic
53C3×Dic3⋊C4—21no—
54C3×C4×Dic3—21no—
55C2×C3×C3⋊C8—21no—
56#3718—42no—
57#1680—91noSylow
58C3×C4⋊Q8—31no—
59C3×C4⋊Q8—31no—
60C3×C4×Q8—31no—
61C2×#216—61no—
62C2×#216—61no—
63#869C2×D311yescharacteristic
64#869C2×D311yescharacteristic
65C4×Dic6C2×D311yescharacteristic
66C3×#106—61no—
67C3×C4⋊C8—21no—
68C3×C4⋊C8—31no—
69C3×C4⋊C8C2×D311yescharacteristic
70C3×C4⋊C8C2×D311yescharacteristic
71C3×#103—61no—
72#835—61no—
73#835—61no—
74#835—61no—
75#817—21no—
76#816—21no—
77Dic3⋊C8—61no—
78C8×Dic3—61no—
79#810—61no—
80#810—61no—
81#810—61no—
82C4⋊(C3⋊C8)—31no—
83C4⋊(C3⋊C8)—31no—
84C4⋊(C3⋊C8)—61no—
85C4⋊(C3⋊C8)—61no—
86C4⋊(C3⋊C8)C2×D311yescharacteristic
87C4×C3⋊C8—31no—
88C4×C3⋊C8—31no—
89C4×C3⋊C8—61no—
90C4×C3⋊C8—61no—
91C2×C32×C4C2×D411yescharacteristic
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4#4111yescharacteristic
94C2×C3×Dic3—21no—
95C2×C3×Dic3—21no—
96C2×C3×Dic3—41no—
97C2×C3×Dic3—41no—
98C3×Dic6—21no—
99C3×Dic6—41no—
100C3×Dic6—41no—
101C3×Dic6—41no—
102C3×Dic6—41no—
103C3×Dic6SD1612yes—
104C32×C8—41no—
105C3⋊(C3⋊C8)—21no—
106C3⋊(C3⋊C8)—21no—
107C3⋊(C3⋊C8)—41no—
108C3×C3⋊C8—41no—
109#487—91no—
110#475—31no—
111#462—91no—
112C8×Q8—91no—
113#334—91no—
114#332—31no—
115#332—91no—
116C2×C3×Q8—31no—
117C2×C3×Q8—61no—
118C2×C3×Q8—61no—
119C2×Dic6—21no—
120C2×Dic6—21no—
121C2×Dic6#6711yescharacteristic
122C2×C3×C8—21no—
123C2×C3×C8—21no—
124C2×C3×C8—41no—
125C2×C3×C8—61no—
126C3×C4⋊C4—31no—
127C3×C4⋊C4—61no—
128C3×C4⋊C4—61no—
129C3×C4⋊C4—61no—
130C3×C4⋊C4—61no—
131C3×C4⋊C4—61no—
132C3×C42—21no—
133C3×C42—61no—
134C3×C42C22×D311yescharacteristic
135C3×C42C22×D311yescharacteristic
136#216—122no—
137#216—122no—
138C4⋊Dic3—21no—
139C4⋊Dic3—21no—
140C4⋊Dic3—21no—
141C4⋊Dic3—21no—
142C4⋊Dic3#6711yescharacteristic
143Dic3⋊C4—21no—
144C4×Dic3—21no—
145C2×C3⋊C8—21no—
146C2×C3⋊C8—31no—
147C2×C3⋊C8—31no—
148C2×C3⋊C8—31no—
149C2×C3⋊C8—31no—
150C2×C3⋊C8—61no—
151C2×C3⋊C8—61no—
152C2×C3⋊C8—61no—
153C2×C3⋊C8—61no—
154C2×C3⋊C8—121no—
155C22×C32#12111yescharacteristic
156C32×C4—21no—
157C32×C4C2×SD1611yescharacteristic
158C32×C4#13511yescharacteristic
159C32×C4#13511yescharacteristic
160C32×C4#13711yescharacteristic
161C3×Dic3—22no—
162C3×Dic3—41no—
163C3×Dic3—81no—
164C3×Dic3—81no—
165C2×Q16—181no—
166C4⋊Q8—31no—
167C4⋊Q8—31no—
168C4×Q8—31no—
169#106—61no—
170C4⋊C8—31no—
171C4⋊C8—91no—
172C4⋊C8—181no—
173C4⋊C8D3211yescharacteristic
174#103—61no—
175#103—181no—
176#103—181no—
177#103—181no—
178C4×C8—91no—
179C4×C8—181no—
180C3×Q8—32no—
181C3×Q8—61no—
182C3×Q8—121no—
183C3×Q8—121no—
184C3×Q8—121no—
185C3×Q8—121no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—61no—
190C2×C3×C4—61no—
191C2×C3×C4—121no—
192C2×C3×C4—121no—
193C2×C3×C4#23511yescharacteristic
194C2×C3×C4D3×D411yescharacteristic
195C2×C3×C4D3×D411yescharacteristic
196C2×C3×C4D3×D411yescharacteristic
197C2×C3×C4#23711yescharacteristic
198C2×C3×C4C2×#6711yescharacteristic
199C2×Dic3—21no—
200C2×Dic3—21no—
201C2×Dic3—41no—
202C2×Dic3—41no—
203Dic6—21no—
204Dic6—41no—
205Dic6—41no—
206Dic6—41no—
207Dic6—41no—
208Dic6#21512yes—
209C3×C8—41no—
210C3×C8—41no—
211C3×C8—81no—
212C3×C8—121no—
213C3⋊C8—41no—
214C3⋊C8—62no—
215C3⋊C8—61no—
216C3⋊C8—61no—
217C3⋊C8—61no—
218C3⋊C8—61no—
219C3⋊C8—121no—
220C3⋊C8—121no—
221C3⋊C8—121no—
222C3⋊C8—241no—
223C2×C32#46411yescharacteristic
224C2×C32#46511yescharacteristic
225C2×C32#47311yescharacteristic
226C2×Q8—31no—
227C2×Q8—61no—
228C2×Q8—61no—
229Q16—362no—
230C2×C8—21no—
231C2×C8—61no—
232C2×C8—91no—
233C2×C8—91no—
234C2×C8—181no—
235C4⋊C4—31no—
236C4⋊C4—61no—
237C4⋊C4—61no—
238C4⋊C4—61no—
239C4⋊C4—61no—
240C4⋊C4—61no—
241C42—61no—
242C42C2×D3211yescharacteristic
243C22×C3—21no—
244C22×C3#88411yescharacteristic
245C22×C3#93911yescharacteristic
246C3×C4—21no—
247C3×C4—21no—
248C3×C4—21no—
249C3×C4—21no—
250C3×C4—21no—
251C3×C4—21no—
252C3×C4—41no—
253C3×C4—62no—
254C3×C4—121no—
255C3×C4—241no—
256C3×C4—241no—
257C3×C4#91211yescharacteristic
258C3×C4D3×SD1611yescharacteristic
259C3×C4#91511yescharacteristic
260C3×C4#91611yescharacteristic
261C3×C4#91611yescharacteristic
262C3×C4#91811yescharacteristic
263C3×C4C2×#21511yescharacteristic
264C3×C4#95011yescharacteristic
265Dic3—22no—
266Dic3—41no—
267Dic3—81no—
268Dic3—81no—
269C32#168011yescharacteristic, complemented, Sylow
270Q8—32no—
271Q8—61no—
272Q8—121no—
273Q8—121no—
274Q8—121no—
275Q8—121no—
276C2×C4—61no—
277C2×C4—61no—
278C2×C4—121no—
279C2×C4—121no—
280C2×C4#379511yescharacteristic
281C2×C4#380211yescharacteristic
282C2×C4D3×#6711yescharacteristic
283C8—41no—
284C8—121no—
285C8—181no—
286C8—181no—
287C8—361no—
288C2×C3—21no—
289C2×C3—21no—
290C2×C3—21no—
291C2×C3#475511yescharacteristic
292C2×C3#477811yescharacteristic
293C2×C3#479811yescharacteristic
294C2×C3#504811yescharacteristic
295C2×C3#516611yescharacteristic
296C2×C3#520411yescharacteristic
297C22#6388511yescharacteristic
298C4—21no—
299C4—62no—
300C4—121no—
301C4—241no—
302C4—241no—
303C4#6380911yescharacteristic
304C4#6381111yescharacteristic
305C4#6393311yescharacteristic
306C4D3×#21511yescharacteristic
307C3—21no—
308C3#6846911yescharacteristic, complemented
309C3#7111811yescharacteristic, complemented
310C2#1059050111yescharacteristic
311C2#1059079611yescharacteristic
312C2#1059098111yescharacteristic
subgroupG/H
centerC22#63885
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socle, prime radicalC22×C32#121
hypercenterC4⋊C8D32
hypocenterC32#1680
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
269. C32#1680semidirect
308. C3#68469semidirect
309. C3#71118semidirect

Maximal subgroups

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

subgroupindex
C3×#48512
#105903842
#105902902
#105902502
#105893462
C3×#44822
#105890932
#711183
#684693