Finite Group Databasebeta

← #11781911

Subgroups — #11781911

Order 1152.

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

normal subgroups only

This group has 324 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×#4850C211yesmaximal, characteristic
2#10590385C211yesmaximal, characteristic
3#10590303C211yesmaximal, characteristic
4#10590258C211yesmaximal, characteristic
5#10589348C211yesmaximal, characteristic
6C3×#4479C211yesmaximal, characteristic
7#10589095C211yesmaximal, characteristic
8#71152—31nomaximal
9#68593—31nomaximal
10#64078C2211yescharacteristic
11C3×#869C2211yescharacteristic
12C3×C4×Dic6C2211yescharacteristic
13C2×#3719—21no—
14C32×C4⋊C8C2211yescharacteristic
15C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
16C3×#818—21no—
17C3×#816—21no—
18C3×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×C4×C3⋊C8C2211yescharacteristic
20#63573—21no—
21#63573—21no—
22Dic3⋊(C3⋊C8)—21no—
23#63567—21no—
24#63554—21no—
25C3×#477—31no—
26#5080—31no—
27#5031—31no—
28#5024—31no—
29#4850D311yescharacteristic
30#4849—31no—
31#4680—31no—
32#4679—31no—
33C3×#335—31no—
34#4546—31no—
35#4482—31no—
36#4482—31no—
37#4482—61no—
38#4481—31no—
39#4479D311yescharacteristic
40C2×#634—21no—
41C2×C3×Dic6—21no—
42C2×C3×Dic6D411yescharacteristic
43C2×C32×C8—21no—
44C32×C42C2311yescharacteristic
45C4⋊(C3⋊Dic3)—21no—
46C4⋊(C3⋊Dic3)—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#3719—42no—
57#1692—91noSylow
58C3×C4⋊Q8—31no—
59C3×C4×Q8—31no—
60C2×#216—61no—
61C2×Dic12—61no—
62#869—31no—
63#869—31no—
64#869—61no—
65#869C2×D311yescharacteristic
66C4×Dic6C2×D311yescharacteristic
67C3×#107—61no—
68C3×C4⋊C8—21no—
69C3×C4⋊C8—31no—
70C3×C4⋊C8C2×D311yescharacteristic
71C3×C4⋊C8C2×D311yescharacteristic
72C3×#103—61no—
73C3×C4×C8—31no—
74#818—21no—
75#817—61no—
76#817—61no—
77#816—21no—
78#816—61no—
79#815—61no—
80Dic3⋊C8—61no—
81#810—61no—
82#808—61no—
83#808—61no—
84C4⋊(C3⋊C8)—31no—
85C4⋊(C3⋊C8)—31no—
86C4⋊(C3⋊C8)—61no—
87C4⋊(C3⋊C8)—61no—
88C4⋊(C3⋊C8)C2×D311yescharacteristic
89#803—61no—
90C4×C3⋊C8C2×D311yescharacteristic
91C2×C32×C4C2×D411yescharacteristic
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4#4111yescharacteristic
94C2×C3⋊Dic3—41no—
95#634—41no—
96#634—41no—
97C2×C3×Dic3—21no—
98C2×C3×Dic3—21no—
99C2×C3×Dic3—41no—
100C3×Dic6—21no—
101C3×Dic6—21no—
102C3×Dic6—81no—
103C32×C8—41no—
104C3⋊(C3⋊C8)—41no—
105C3×C3⋊C8—21no—
106C3×C3⋊C8—41no—
107C3×C3⋊C8Q1612yescomplemented
108#498—91no—
109#477—31no—
110#462—91no—
111#446—91no—
112#335—31no—
113#333—91no—
114#332—91no—
115C2×C3×Q8—31no—
116C2×C3×Q8—61no—
117C2×Dic6—21no—
118C2×Dic6—61no—
119C2×Dic6—61no—
120C2×Dic6—121no—
121C2×Dic6#6711yescharacteristic
122C2×C3×C8—21no—
123C2×C3×C8—21no—
124C2×C3×C8—31no—
125C2×C3×C8—31no—
126C2×C3×C8—41no—
127C2×C3×C8—61no—
128C3×C4⋊C4—31no—
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—
137C4⋊Dic3—21no—
138C4⋊Dic3—21no—
139C4⋊Dic3—62no—
140C4⋊Dic3—61no—
141C4⋊Dic3—61no—
142C4⋊Dic3—61no—
143C4⋊Dic3—61no—
144C4⋊Dic3—121no—
145C4⋊Dic3#6711yescharacteristic
146Dic3⋊C4—21no—
147C4×Dic3—21no—
148C2×C3⋊C8—21no—
149C2×C3⋊C8—61no—
150C2×C3⋊C8—61no—
151C2×C3⋊C8—121no—
152C2×C3⋊C8D1211yescharacteristic
153C2×C3⋊C8D1211yescharacteristic
154Dic12—122no—
155C22×C32#12111yescharacteristic
156C32×C4—21no—
157C32×C4C2×Q1611yescharacteristic
158C32×C4AGL(1,ℤ/8)11yescharacteristic
159C32×C4#13711yescharacteristic
160C32×C4#13711yescharacteristic
161C3⋊Dic3—81no—
162C3×Dic3—41no—
163C3×Dic3—41no—
164C3×Dic3—81no—
165C2×Q16—181no—
166C4⋊Q8—31no—
167C4⋊Q8—91no—
168C4×Q8—31no—
169#107—61no—
170#106—181no—
171#106—181no—
172C4⋊C8—31no—
173C4⋊C8—91no—
174C4⋊C8—181no—
175C4⋊C8D3211yescharacteristic
176#103—61no—
177#103—181no—
178#97—181no—
179C4×C8—31no—
180C3×Q8—61no—
181C3×Q8—61no—
182C3×Q8—241no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—61no—
187C2×C3×C4—61no—
188C2×C3×C4—121no—
189C2×C3×C4C2×D1211yescharacteristic
190C2×C3×C4D3×D411yescharacteristic
191C2×C3×C4D3×D411yescharacteristic
192C2×C3×C4#23711yescharacteristic
193C2×C3×C4#23911yescharacteristic
194C2×C3×C4C2×#6711yescharacteristic
195C2×Dic3—21no—
196C2×Dic3—21no—
197C2×Dic3—41no—
198C2×Dic3—122no—
199C2×Dic3—121no—
200C2×Dic3—121no—
201Dic6—21no—
202Dic6—21no—
203Dic6—81no—
204Dic6—121no—
205Dic6—121no—
206Dic6—121no—
207Dic6—121no—
208Dic6—241no—
209Dic6—241no—
210C3×C8—32no—
211C3×C8—41no—
212C3×C8—41no—
213C3×C8—61no—
214C3×C8—81no—
215C3×C8—121no—
216C3⋊C8—21no—
217C3⋊C8—41no—
218C3⋊C8—121no—
219C3⋊C8—121no—
220C3⋊C8—241no—
221C3⋊C8Dic1212yescomplemented
222C2×C32#46211yescharacteristic
223C2×C32#46811yescharacteristic
224C2×C32#47111yescharacteristic
225C2×Q8—31no—
226C2×Q8—61no—
227C2×Q8—181no—
228Q16—362no—
229C2×C8—21no—
230C2×C8—31no—
231C2×C8—31no—
232C2×C8—61no—
233C2×C8—181no—
234C4⋊C4—31no—
235C4⋊C4—61no—
236C4⋊C4—61no—
237C4⋊C4—61no—
238C4⋊C4—181no—
239C4⋊C4—181no—
240C42—61no—
241C42C2×D3211yescharacteristic
242C22×C3—21no—
243C22×C3#89511yescharacteristic
244C22×C3#93911yescharacteristic
245C3×C4—21no—
246C3×C4—21no—
247C3×C4—21no—
248C3×C4—21no—
249C3×C4—21no—
250C3×C4—21no—
251C3×C4—41no—
252C3×C4—121no—
253C3×C4—121no—
254C3×C4—241no—
255C3×C4C2×Dic1211yescharacteristic
256C3×C4#90911yescharacteristic
257C3×C4#91111yescharacteristic
258C3×C4D3×Q1611yescharacteristic
259C3×C4#91811yescharacteristic
260C3×C4#91811yescharacteristic
261C3×C4#94211yescharacteristic
262C3×C4#94911yescharacteristic
263Dic3—41no—
264Dic3—41no—
265Dic3—81no—
266Dic3—242no—
267Dic3—241no—
268Dic3—241no—
269C32#169211yescharacteristic, complemented, Sylow
270Q8—61no—
271Q8—61no—
272Q8—241no—
273Q8—361no—
274Q8—361no—
275C2×C4—61no—
276C2×C4—61no—
277C2×C4—121no—
278C2×C4—361no—
279C2×C4#379611yescharacteristic
280C2×C4D3×D1211yescharacteristic
281C2×C4D3×#6711yescharacteristic
282C8—32no—
283C8—41no—
284C8—61no—
285C8—121no—
286C8—361no—
287C2×C3—21no—
288C2×C3—21no—
289C2×C3—21no—
290C2×C3#484911yescharacteristic
291C2×C3#488611yescharacteristic
292C2×C3#489811yescharacteristic
293C2×C3#504911yescharacteristic
294C2×C3#518211yescharacteristic
295C2×C3#520011yescharacteristic
296C22#6388611yescharacteristic
297C4—21no—
298C4—121no—
299C4—121no—
300C4—241no—
301C4—721no—
302C4D3×Dic1211yescharacteristic
303C4#6380111yescharacteristic
304C4#6392511yescharacteristic
305C4#6394811yescharacteristic
306C3—21no—
307C3#6859311yescharacteristic, complemented
308C3#7115211yescharacteristic, complemented
309C2#1059058511yescharacteristic
310C2#1059080011yescharacteristic
311C2#1059098611yescharacteristic
subgroupG/H
centerC22#63886
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socle, prime radicalC22×C32#121
hypercenterC4⋊C8D32
hypocenterC32#1692
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
107. C3×C3⋊C8Q16semidirect
221. C3⋊C8Dic12semidirect
269. C32#1692semidirect
307. C3#68593semidirect
308. C3#71152semidirect

Maximal subgroups

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

subgroupindex
C3×#48502
#105903852
#105903032
#105902582
#105893482
C3×#44792
#105890952
#711523
#685933