Finite Group Databasebeta

← #11920437

Subgroups — #11920437

Order 1152.

529 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 529 conjugacy classes of subgroups — too many to draw. Only its 57 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
1C2×2−1+4⋊C9C211yesmaximal, characteristic
2C2×#63690C211yesmaximal, characteristic, complemented
3#10589526C211yesmaximal, characteristic, complemented
4#10589521C214yesmaximal, complemented
5#84117—31nomaximal
62−1+4⋊C9—22no—
7C2×#41⋊C9C2211yescharacteristic
8C22×Q8⋊C9C2212yes—
9#63690—22no—
10C2×#3688C2212yes—
11#63498—41nomaximal
12#63421C2212yes—
13C2×C3×2−1+4D311yescharacteristic
14#5825—31no—
15C2×#951—31no—
16C22×#216—31no—
17#5239—34no—
18#5234—31no—
19#5233—31no—
20#5228—34no—
21#5225—31no—
22C2×D4×C9—41no—
23C2×Dic18—41no—
24#41⋊C9D412yes—
25C2×Q8⋊C9—22no—
26C2×Q8⋊C9C2311yescharacteristic
27#3688—22no—
28#3676—44no—
29C4×Dic9—41no—
30#3011—91noSylow
31C3×2−1+4—22no—
32C3×2−1+4—62no—
33C2×C3×#41—31no—
34C2×C3×#41—32no—
35C2×C3×#41C2×D311yescharacteristic
36C22×C3×Q8—31no—
37C22×C3×Q8C2×D312yes—
38C22×Dic6—31no—
39#951—62no—
40#951—62no—
41#944—61no—
42C2×#216—34no—
43C2×#216—32no—
44C2×#216—64no—
45#936—61no—
46#935—62no—
47C2×#214—32no—
48#926—31no—
49#924—34no—
50C2×#208—31no—
51C22×C3⋊C8—31no—
52#835—34no—
53#835—32no—
54#832—32no—
55#830—34no—
56C23×C9—42no—
57D4×C9—82no—
58C2×C4×C9—41no—
59C2×Dic9—42no—
60C2×Dic9—42no—
61Dic18—82no—
62Q8⋊C9C2×D411yescharacteristic
63C2×2−1+4D911yescharacteristic
64C2×#137—91no—
65C22×Q16—91no—
66#536—91no—
67#452—94no—
68#451—94no—
69#419—91no—
70#416—91no—
71#408—91no—
72C3×#41—32no—
73C3×#41—62no—
74C3×#41—62no—
75C3×#41—64no—
76C3×#41—64no—
77C3×#41#6712yes—
78C2×C3×Q8—22no—
79C2×C3×Q8—31no—
80C2×C3×Q8—32no—
81C2×C3×Q8—34no—
82C2×C3×Q8—62no—
83C2×C3×Q8—62no—
84C2×C3×Q8C22×D311yescharacteristic
85C2×C3×D4—31no—
86C2×C3×D4—32no—
87C2×C3×D4S411yescharacteristic
88C22×C3×C4—31no—
89C22×C3×C4—32no—
90C22×C3×C4—61no—
91C22×Dic3—61no—
92C2×Dic6—32no—
93C2×Dic6—62no—
94C2×Dic6—62no—
95C2×Dic6—61no—
96#217—61no—
97#217—64no—
98#216—68no—
99#216—62no—
100#216—62no—
101#214—64no—
102C4⋊Dic3—32no—
103Dic3⋊C4—64no—
104C4×Dic3—61no—
105#208—62no—
106C2×C3⋊C8—32no—
107C2×C3⋊C8—32no—
108C2×C3⋊C8—62no—
109C22×C9—41no—
110C22×C9—82no—
111C22×C9—84no—
112C4×C9—42no—
113Dic9—82no—
114Dic9—82no—
1152−1+4—22no—
1162−1+4—62no—
117C2×#41—31no—
118C2×#41—32no—
119C2×#41C2×D911yescharacteristic
120C22×Q8—31no—
121C22×Q8—91no—
122C22×Q8C2×D912yes—
123#137—182no—
124#137—182no—
125C2×Q16—94no—
126C2×Q16—92no—
127C2×Q16—184no—
128C2×SD16—92no—
129C2×M16—91no—
130C22×C8—91no—
131C4⋊Q8—181no—
132#124—181no—
133#123—182no—
134C22⋊Q8—94no—
135#117—91no—
136#103—94no—
137#103—92no—
138#102—92no—
139C22⋊C8—94no—
140C23×C3—31no—
141C23×C3C2×S412yes—
142C3×Q8—31no—
143C3×Q8—34no—
144C3×Q8—62no—
145C3×Q8—62no—
146C3×Q8C2×#6711yescharacteristic
147C3×D4—22no—
148C3×D4—32no—
149C3×D4—61no—
150C3×D4—64no—
151C2×C3×C4—31no—
152C2×C3×C4—32no—
153C2×C3×C4—32no—
154C2×C3×C4—32no—
155C2×C3×C4—62no—
156C2×C3×C4—62no—
157C2×C3×C4—64no—
158C2×C3×C4C2×S411yescharacteristic
159C2×Dic3—62no—
160C2×Dic3—62no—
161C2×Dic3—122no—
162Dic6—62no—
163Dic6—62no—
164Dic6—122no—
165C3⋊C8—62no—
166C3⋊C8—62no—
167C2×C9—42no—
168C2×C9—41no—
169C2×C9—162no—
170#41—32no—
171#41—62no—
172#41—62no—
173#41—64no—
174#41—64no—
175#41#61112yes—
176C2×Q8—22no—
177C2×Q8—31no—
178C2×Q8—32no—
179C2×Q8—34no—
180C2×Q8—62no—
181C2×Q8—62no—
182C2×Q8—92no—
183C2×Q8—182no—
184C2×Q8—182no—
185C2×Q8—181no—
186C2×Q8C22×D911yescharacteristic
187C2×D4—31no—
188C2×D4—32no—
189C2×D4(C22⋊C9)⋊C211yescharacteristic
190C22×C4—31no—
191C22×C4—32no—
192C22×C4—61no—
193C22×C4—181no—
194Q16—188no—
195Q16—182no—
196Q16—182no—
197SD16—184no—
198M16—182no—
199C2×C8—92no—
200C2×C8—92no—
201C2×C8—182no—
202C4⋊C4—92no—
203C4⋊C4—184no—
204C22⋊C4—181no—
205C22⋊C4—184no—
206C42—181no—
207C22×C3—24no—
208C22×C3—22no—
209C22×C3—32no—
210C22×C3—62no—
211C22×C3C22×S411yescharacteristic
212C3×C4—31no—
213C3×C4—31no—
214C3×C4—62no—
215C3×C4GL(2,ℤ/4)12yes—
216Dic3—122no—
217Dic3—122no—
218C9—41noSylow
219C23—31no—
220C23C2×(C22⋊C9)⋊C212yes—
221Q8—31no—
222Q8—34no—
223Q8—62no—
224Q8—62no—
225Q8—182no—
226Q8—182no—
227Q8—362no—
228Q8C2×#61111yescharacteristic
229D4—22no—
230D4—32no—
231D4—61no—
232D4—64no—
233C2×C4—31no—
234C2×C4—32no—
235C2×C4—32no—
236C2×C4—32no—
237C2×C4—62no—
238C2×C4—62no—
239C2×C4—64no—
240C2×C4—182no—
241C2×C4—182no—
242C2×C4—362no—
243C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
244C8—182no—
245C8—182no—
246C2×C3—42no—
247C2×C3—62no—
248C2×C3#592712yes—
249C2×C3C2×GL(2,ℤ/4)11yescharacteristic
250C22—24no—
251C22—22no—
252C22—32no—
253C22—62no—
254C22C22×(C22⋊C9)⋊C211yescharacteristic
255C4—31no—
256C4—31no—
257C4—62no—
258C4—362no—
259C4—362no—
260C4#6369412yes—
261C3#8553611yescharacteristic
262C2—42no—
263C2—62no—
264C2#1059310212yes—
265C2C2×#6369411yescharacteristic
subgroupG/H
centerC22C22×(C22⋊C9)⋊C2
commutator, cosocleC2×Q8⋊C9C23
Frattini, socleC22×C3C22×S4
Fitting, prime radicalC2×C3×2−1+4D3
hypercenterC2×D4(C22⋊C9)⋊C2
hypocenterQ8⋊C9C2×D4
LCSG ▷ C2×Q8⋊C9 ▷ Q8⋊C9
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. C2×#63690C2semidirect
3. #10589526C2semidirect
4. #10589521C2semidirect

Maximal subgroups

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

subgroupindex
C2×2−1+4⋊C92
C2×#636902
#105895262
#105895212
#841173
#634984