Finite Group Databasebeta

← #11782561

Subgroups — #11782561

Order 1152.

385 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 385 conjugacy classes of subgroups — too many to draw. Only its 108 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#10592380C211yesmaximal, characteristic
2C3×#4681C211yesmaximal, characteristic
3#10590311C211yesmaximal, characteristic
4#10590311C211yesmaximal, characteristic
5#10590288C211yesmaximal, characteristic
6#10590287C211yesmaximal, characteristic
7C3×C8×C3⋊C8C211yesmaximal, characteristic
8#71214—31nomaximal
9#68064—31nomaximal
10#64078C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C32×C4×C8C2211yescharacteristic
15#63643—22no—
16C3×#816—22no—
17C3×C4×C3⋊C8C2211yescharacteristic
18C3×C4×C3⋊C8C2211yescharacteristic
19#63575—22no—
20#63575—22no—
21#63567—22no—
22#63566—22no—
23C3×#487—31no—
24#5093—31no—
25#5079—31no—
26#5078—31no—
27#5078—31no—
28#4682—31no—
29#4682—31no—
30#4681—31no—
31#4681—31no—
32#4681—31no—
33#4681—31no—
34#4681—61no—
35#4681D311yescharacteristic
36C3×C82—31no—
37C8×C3⋊C8D311yescharacteristic
38C2×#634—21no—
39C2×#634—21no—
40C2×C3×Dic6—21no—
41C2×C3×Dic6—21no—
42C2×C32×C8D412yes—
43C32×C42C2311yescharacteristic
44C4⋊(C3⋊Dic3)—21no—
45C4⋊(C3⋊Dic3)—21no—
46C4⋊(C3⋊Dic3)—21no—
47C4⋊(C3⋊Dic3)—21no—
48C3×C4⋊Dic3—21no—
49C3×C4⋊Dic3—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C2×C3×C3⋊C8D412yes—
53C2×C3×C3⋊C8D412yes—
54#1710—91noSylow
55C3×C4⋊Q8—31no—
56C3×C4⋊Q8—31no—
57#869—31no—
58#869—31no—
59#869—31no—
60#869—31no—
61#869—61no—
62#869—61no—
63#869C2×D311yescharacteristic
64#869C2×D311yescharacteristic
65C3×#103—62no—
66C3×C4×C8—21no—
67C3×C4×C8—31no—
68C3×C4×C8—31no—
69C3×C4×C8C2×D311yescharacteristic
70C3×C4×C8C2×D311yescharacteristic
71#835—62no—
72#818—62no—
73#818—62no—
74#816—22no—
75#816—62no—
76#816—64no—
77#816—62no—
78#816—62no—
79#816—62no—
80#810—62no—
81#807—62no—
82#807—62no—
83C4×C3⋊C8C2×D311yescharacteristic
84C4×C3⋊C8C2×D311yescharacteristic
85C2×C32×C4C2×D411yescharacteristic
86C2×C32×C4C2×D411yescharacteristic
87C2×C32×C4C2×D411yescharacteristic
88C2×C3⋊Dic3—41no—
89C2×C3⋊Dic3—41no—
90#634—42no—
91#634—42no—
92C2×C3×Dic3—41no—
93C2×C3×Dic3—41no—
94C3×Dic6—42no—
95C3×Dic6—42no—
96C32×C8—22no—
97C3×C3⋊C8—22no—
98C3×C3⋊C8Q1614yes—
99#500—91no—
100#500—91no—
101#487—31no—
102#487—91no—
103#487—91no—
104#487—91no—
105C82—31no—
106C2×C3×Q8—61no—
107C2×C3×Q8—61no—
108C2×Dic6—21no—
109C2×Dic6—21no—
110C2×Dic6—62no—
111C2×Dic6—61no—
112C2×Dic6—61no—
113C2×Dic6—61no—
114C2×Dic6—61no—
115C2×Dic6—121no—
116C2×C3×C8—22no—
117C2×C3×C8—32no—
118C2×C3×C8—32no—
119C2×C3×C8D1212yes—
120C2×C3×C8#6712yes—
121C3×C4⋊C4—61no—
122C3×C4⋊C4—61no—
123C3×C4⋊C4—61no—
124C3×C4⋊C4—61no—
125C3×C42—21no—
126C3×C42C22×D311yescharacteristic
127C3×C42C22×D311yescharacteristic
128C4⋊Dic3—21no—
129C4⋊Dic3—21no—
130C4⋊Dic3—21no—
131C4⋊Dic3—21no—
132C4⋊Dic3—62no—
133C4⋊Dic3—61no—
134C4⋊Dic3—61no—
135C4⋊Dic3—61no—
136C4⋊Dic3—61no—
137C4⋊Dic3—61no—
138C4⋊Dic3—61no—
139C4⋊Dic3—61no—
140C4⋊Dic3—61no—
141C4⋊Dic3—121no—
142C4⋊Dic3—121no—
143C4⋊Dic3—121no—
144C2×C3⋊C8D1212yes—
145C2×C3⋊C8D1212yes—
146C22×C32#12711yescharacteristic
147C32×C4C2×Q1612yes—
148C32×C4#13512yes—
149C32×C4#13512yes—
150C3⋊Dic3—81no—
151C3⋊Dic3—81no—
152C3×Dic3—81no—
153C3×Dic3—81no—
154C4⋊Q8—31no—
155C4⋊Q8—31no—
156C4⋊Q8—91no—
157C4⋊Q8—91no—
158#107—182no—
159#107—182no—
160#103—62no—
161#103—182no—
162#103—182no—
163#103—182no—
164C4×C8—31no—
165C4×C8—31no—
166C4×C8D3211yescharacteristic
167C3×Q8—122no—
168C3×Q8—122no—
169C2×C3×C4—21no—
170C2×C3×C4—21no—
171C2×C3×C4—21no—
172C2×C3×C4—121no—
173C2×C3×C4—121no—
174C2×C3×C4C2×D1211yescharacteristic
175C2×C3×C4C2×D1211yescharacteristic
176C2×C3×C4C2×D1211yescharacteristic
177C2×C3×C4D3×D411yescharacteristic
178C2×C3×C4D3×D411yescharacteristic
179C2×C3×C4C2×#6711yescharacteristic
180C2×Dic3—41no—
181C2×Dic3—41no—
182C2×Dic3—122no—
183C2×Dic3—122no—
184C2×Dic3—121no—
185C2×Dic3—121no—
186C2×Dic3—121no—
187C2×Dic3—121no—
188Dic6—42no—
189Dic6—42no—
190Dic6—124no—
191Dic6—122no—
192Dic6—122no—
193Dic6—122no—
194Dic6—122no—
195Dic6—242no—
196C3×C8—22no—
197C3×C8—22no—
198C3×C8—34no—
199C3×C8—42no—
200C3×C8—62no—
201C3⋊C8—22no—
202C3⋊C8Dic1214yes—
203C2×C32#49411yescharacteristic
204C2×C32#49511yescharacteristic
205C2×C32#49511yescharacteristic
206C2×Q8—61no—
207C2×Q8—61no—
208C2×Q8—181no—
209C2×Q8—181no—
210C2×C8—32no—
211C2×C8—32no—
212C2×C8#62612yes—
213C4⋊C4—61no—
214C4⋊C4—61no—
215C4⋊C4—61no—
216C4⋊C4—61no—
217C4⋊C4—181no—
218C4⋊C4—181no—
219C4⋊C4—181no—
220C4⋊C4—181no—
221C42C2×D3211yescharacteristic
222C22×C3—21no—
223C22×C3#87411yescharacteristic
224C22×C3#94011yescharacteristic
225C3×C4—22no—
226C3×C4—22no—
227C3×C4—22no—
228C3×C4—241no—
229C3×C4—241no—
230C3×C4#90412yes—
231C3×C4#90412yes—
232C3×C4C2×Dic1212yes—
233C3×C4#91612yes—
234C3×C4D3×Q1612yes—
235C3×C4#95012yes—
236Dic3—81no—
237Dic3—81no—
238Dic3—242no—
239Dic3—242no—
240Dic3—241no—
241Dic3—241no—
242Dic3—241no—
243Dic3—241no—
244C32#171011yescharacteristic, complemented, Sylow
245Q8—122no—
246Q8—122no—
247Q8—362no—
248Q8—362no—
249C2×C4—121no—
250C2×C4—121no—
251C2×C4—361no—
252C2×C4—361no—
253C2×C4D3×D1211yescharacteristic
254C2×C4D3×D1211yescharacteristic
255C2×C4C2×#62611yescharacteristic
256C8—22no—
257C8—34no—
258C8—62no—
259C2×C3—21no—
260C2×C3—21no—
261C2×C3—21no—
262C2×C3#469611yescharacteristic
263C2×C3#469611yescharacteristic
264C2×C3#469911yescharacteristic
265C2×C3#505911yescharacteristic
266C2×C3#516811yescharacteristic
267C2×C3#518311yescharacteristic
268C22#6391111yescharacteristic
269C4—241no—
270C4—241no—
271C4—721no—
272C4—721no—
273C4D3×Dic1212yes—
274C4#6380612yes—
275C4#6382912yes—
276C3—21no—
277C3#6806411yescharacteristic, complemented
278C3#7121411yescharacteristic, complemented
279C2#1059037011yescharacteristic
280C2#1059086211yescharacteristic
281C2#1059089611yescharacteristic
subgroupG/H
centerC22#63911
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socle, prime radicalC22×C32#127
hypercenterC4×C8D32
hypocenterC32#1710
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
244. C32#1710semidirect
277. C3#68064semidirect
278. C3#71214semidirect

Maximal subgroups

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

subgroupindex
#105923802
C3×#46812
#105903112
#105902882
#105902872
C3×C8×C3⋊C82
#712143
#680643