Finite Group Databasebeta

← #11779956

Subgroups — #11779956

Order 1152.

312 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 78 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#10589645C211yesmaximal, characteristic
2#10588690C211yesmaximal, characteristic
3#10588513C211yesmaximal, characteristic, complemented
4#10588361C211yesmaximal, characteristic, complemented
5C9×D4⋊C8C211yesmaximal, characteristic
6#10588158C211yesmaximal, characteristic, complemented
7#10588133C211yesmaximal, characteristic, complemented
8#68191—31nomaximal
9C4×D4×C9C2211yescharacteristic
10D4×Dic9—21no—
11C2×C4⋊Dic9—21no—
12#63486—21no—
13C2×Dic36—21no—
14#63452—21no—
15#63440—22no—
16#63431C2211yescharacteristic
17#63431C2211yescharacteristic
18C4×Dic18C2211yescharacteristic
19C9×C4⋊C8C2211yescharacteristic
20C4×C8×C9C2211yescharacteristic
21#63392—21no—
22#63376—22no—
23#63376—21no—
24#63366—21no—
25C4⋊(C9⋊C8)C2211yescharacteristic
26#5543—31no—
27#5007—31no—
28#4849—31no—
29#4681—31no—
30C3×D4⋊C8D311yescharacteristic
31#4481—31no—
32#4456—31no—
33C2×D4×C9D411yescharacteristic
34C22×C4×C9—21no—
35C22×Dic9—22no—
36C2×Dic18—21no—
37C2×Dic18D411yescharacteristic
38C2×Dic18D412yes—
39C2×C8×C9—21no—
40C2×C8×C9—21no—
41C9×C4⋊C4D411yescharacteristic
42C9×C22⋊C4—21no—
43C42×C9C2311yescharacteristic
44#3676—22no—
45C4⋊Dic9—22no—
46C4⋊Dic9—21no—
47C4⋊Dic9—21no—
48C4⋊Dic9—21no—
49C4⋊Dic9—21no—
50C4⋊Dic9D411yescharacteristic
51Dic9⋊C4—22no—
52Dic9⋊C4—21no—
53C4×Dic9—21no—
54C2×C9⋊C8—21no—
55Dic36—42no—
56#1644—91noSylow
57C3×C4×D4C2×D311yescharacteristic
58D4×Dic3—61no—
59C2×C4⋊Dic3—61no—
60#924—61no—
61C2×Dic12—61no—
62#890—61no—
63#878—62no—
64#869—31no—
65#869—31no—
66C4×Dic6—31no—
67C3×C4⋊C8C2×D311yescharacteristic
68C3×C4×C8C2×D311yescharacteristic
69#832—61no—
70#816—61no—
71#816—62no—
72#807—61no—
73C4⋊(C3⋊C8)—31no—
74C23×C9—21no—
75D4×C9—21no—
76D4×C9Q1612yescomplemented
77C2×C4×C9—21no—
78C2×C4×C9—41no—
79C2×C4×C9—41no—
80C2×C4×C9C2×D411yescharacteristic
81C2×C4×C9C2×D411yescharacteristic
82C2×C4×C9C2×D411yescharacteristic
83C2×Dic9—21no—
84C2×Dic9—21no—
85C2×Dic9—22no—
86C2×Dic9—41no—
87C2×Dic9—82no—
88Dic18—21no—
89Dic18—21no—
90Dic18—42no—
91Dic18—41no—
92Dic18—41no—
93C8×C9—41no—
94C8×C9—41no—
95C9⋊C8—41no—
96#554—91no—
97#487—91no—
98#474—91no—
99#462—91no—
100#333—91no—
101Q8⋊C8—91no—
102D4⋊C8D911yescharacteristic
103C2×C3×D4D1211yescharacteristic
104C22×C3×C4—21no—
105C22×Dic3—62no—
106C2×Dic6—31no—
107C2×Dic6—32no—
108C2×Dic6—61no—
109C2×C3×C8—21no—
110C2×C3×C8—21no—
111C3×C4⋊C4D1211yescharacteristic
112C3×C22⋊C4—21no—
113C3×C42C22×D311yescharacteristic
114#217—62no—
115C4⋊Dic3—31no—
116C4⋊Dic3—62no—
117C4⋊Dic3—61no—
118C4⋊Dic3—61no—
119C4⋊Dic3—61no—
120C4⋊Dic3—61no—
121Dic3⋊C4—62no—
122Dic3⋊C4—61no—
123C4×Dic3—61no—
124C2×C3⋊C8—61no—
125Dic12—122no—
126C22×C9—22no—
127C22×C9—41no—
128C22×C9—41no—
129C22×C9#12011yescharacteristic
130C4×C9—21no—
131C4×C9—41no—
132C4×C9C2×Q1611yescharacteristic
133C4×C9#13511yescharacteristic
134C4×C9AGL(1,ℤ/8)11yescharacteristic
135C4×C9#13711yescharacteristic
136Dic9—41no—
137Dic9—42no—
138Dic9—41no—
139Dic9—81no—
140C2×Q16—181no—
141C4⋊Q8—91no—
142C4⋊Q8—91no—
143#125—181no—
144C22⋊Q8—182no—
145C22⋊Q8—181no—
146C4×Q8—91no—
147C4×D4—181no—
148C4×D4C2×D911yescharacteristic
149C2×C4⋊C4—181no—
150#107—181no—
151C4⋊C8—91no—
152C4⋊C8C2×D911yescharacteristic
153#103—181no—
154#103—182no—
155#102—181no—
156C4×C8C2×D911yescharacteristic
157C23×C3—21no—
158C3×D4—21no—
159C3×D4Dic1212yes—
160C2×C3×C4—21no—
161C2×C3×C4—41no—
162C2×C3×C4—41no—
163C2×C3×C4C2×D1211yescharacteristic
164C2×C3×C4D3×D411yescharacteristic
165C2×C3×C4D3×D411yescharacteristic
166C2×Dic3—61no—
167C2×Dic3—61no—
168C2×Dic3—62no—
169C2×Dic3—121no—
170C2×Dic3—242no—
171Dic6—61no—
172Dic6—61no—
173Dic6—122no—
174Dic6—121no—
175Dic6—121no—
176C3×C8—41no—
177C3×C8—41no—
178C3⋊C8—121no—
179C2×C9—42no—
180C2×C9#44911yescharacteristic
181C2×C9#45111yescharacteristic
182C2×C9#45511yescharacteristic
183C2×Q8—91no—
184C2×Q8—92no—
185C2×Q8—181no—
186C2×D4D3611yescharacteristic
187C22×C4—21no—
188C22×C4—182no—
189Q16—362no—
190C2×C8—21no—
191C2×C8—21no—
192C2×C8—181no—
193C4⋊C4—91no—
194C4⋊C4—182no—
195C4⋊C4—182no—
196C4⋊C4—181no—
197C4⋊C4—181no—
198C4⋊C4—181no—
199C4⋊C4—181no—
200C4⋊C4—181no—
201C4⋊C4D3611yescharacteristic
202C22⋊C4—21no—
203C22⋊C4—182no—
204C42—181no—
205C42C22×D911yescharacteristic
206C22×C3—22no—
207C22×C3—41no—
208C22×C3—41no—
209C22×C3#88211yescharacteristic
210C3×C4—21no—
211C3×C4—41no—
212C3×C4C2×Dic1211yescharacteristic
213C3×C4#90911yescharacteristic
214C3×C4#91111yescharacteristic
215C3×C4#91611yescharacteristic
216Dic3—121no—
217Dic3—122no—
218Dic3—121no—
219Dic3—241no—
220C9#164411yescharacteristic, complemented, Sylow
221C23—21no—
222Q8—181no—
223Q8—181no—
224Q8—362no—
225Q8—361no—
226Q8—361no—
227D4—21no—
228D4Dic3612yescomplemented
229C2×C4—21no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—181no—
233C2×C4—181no—
234C2×C4—182no—
235C2×C4—361no—
236C2×C4—722no—
237C2×C4C2×D3611yescharacteristic
238C2×C4D4×D911yescharacteristic
239C2×C4D4×D911yescharacteristic
240C8—41no—
241C8—41no—
242C8—361no—
243C2×C3—42no—
244C2×C3#473911yescharacteristic
245C2×C3#478111yescharacteristic
246C2×C3#482511yescharacteristic
247C22—22no—
248C22—41no—
249C22—41no—
250C22#6344411yescharacteristic
251C4—21no—
252C4—41no—
253C4—361no—
254C4—361no—
255C4—362no—
256C4—721no—
257C4C2×Dic3611yescharacteristic
258C4#6347111yescharacteristic
259C4#6347311yescharacteristic
260C4#6347811yescharacteristic
261C3#6819111yescharacteristic
262C2—42no—
263C2#1058840511yescharacteristic
264C2#1058846111yescharacteristic
265C2#1058850511yescharacteristic
subgroupG/H
centerC22#63444
commutator, cosocleC42×C9C23
FrattiniC3×C42C22×D3
FittingC9×D4⋊C8C2
socleC22×C3#882
prime radicalC2×C3×D4D12
hypercenterD4⋊C8D9
hypocenterC9#1644
LCSG ▷ C42×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #10588513C2semidirect
4. #10588361C2semidirect
6. #10588158C2semidirect
7. #10588133C2semidirect
76. D4×C9Q16semidirect
220. C9#1644semidirect
228. D4Dic36semidirect

Maximal subgroups

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

subgroupindex
#105896452
#105886902
#105885132
#105883612
C9×D4⋊C82
#105881582
#105881332
#681913