Finite Group Databasebeta

← C2×#10593340 #11808365

Subgroups — C2×#10593340 #11808365

Order 1152.

1110 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 1110 conjugacy classes of subgroups — too many to draw. Only its 183 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
1C22×C4⋊#157C211yesmaximal, characteristic
2C22×#3773C211yesmaximal, characteristic
3C2×#63883C212yesmaximal
4C2×#63737C212yesmaximal
5C2×#63737C211yesmaximal, characteristic
6#10593340C218yesmaximal, direct product factor
7C23×#157C2211yescharacteristic
8C23×#157C2211yescharacteristic
9C22×C4×C3⋊D3C2211yescharacteristic
10C22×#624C2212yes—
11C22×#624C2212yes—
12C2×C4⋊#157—24no—
13C2×C4⋊#157C2214yes—
14C2×#3773—24no—
15C2×#3773C2214yes—
16C2×C3×Dic3⋊C4—22no—
17C2×Dic3⋊Dic3—22no—
18#63883—24no—
19#63883C2218yes—
20#63737C2218yes—
21#63737C2214yes—
22C2×D3×C4⋊C4—62no—
23C23×C3⋊D3C2311yescharacteristic
24C22×#157—24no—
25C22×#157—22no—
26C22×#157—24no—
27C22×#157D414yes—
28C22×#157C2312yes—
29C22×#157C2312yes—
30C22×C32×C4D411yescharacteristic
31C22×C3⋊Dic3D411yescharacteristic
32C2×C4×C3⋊D3—22no—
33C2×C4×C3⋊D3—22no—
34C2×C4×C3⋊D3D412yes—
35C2×C4×C3⋊D3C2312yes—
36C22×C3×Dic3—22no—
37C22×C3×Dic3—22no—
38C2×#624—22no—
39C2×#624—24no—
40C2×#624—24no—
41C2×#624—24no—
42C2×#624—22no—
43C2×#624Q818yes—
44C2×#624C2314yes—
45C2×#624C2314yes—
46C4⋊#157—28no—
47#3773—28no—
48C3×Dic3⋊C4—28no—
49Dic3⋊Dic3—28no—
50C2×#398—91nomaximal, Sylow
51C22×C4×D3—62no—
52C22×C4×D3—62no—
53C22×C4×D3—62no—
54C2×C3×C4⋊C4—62no—
55C2×C4⋊Dic3—62no—
56C2×Dic3⋊C4—22no—
57C2×Dic3⋊C4—62no—
58D3×C4⋊C4—68no—
59D3×C4⋊C4—68no—
60C23×C32C2×D411yescharacteristic
61C22×C3⋊D3C2×D411yescharacteristic
62C22×C3⋊D3C2×D412yes—
63C22×C3⋊D3C2×Q814yes—
64C22×C3⋊D3#4112yes—
65C22×C3⋊D3#4114yes—
66C22×C3⋊D3C2411yescharacteristic
67C2×#157—28no—
68C2×#157—24no—
69C2×#157—22no—
70C2×#157—24no—
71C2×#157—44no—
72C2×#157C2×D414yes—
73C2×C32×C4—22no—
74C2×C32×C4C2×D412yes—
75C2×C3⋊Dic3—22no—
76C2×C3⋊Dic3C2×D412yes—
77C4×C3⋊D3—24no—
78C4×C3⋊D3—22no—
79C4×C3⋊D3—22no—
80C2×C3×Dic3—28no—
81C2×C3×Dic3—24no—
82C2×C3×Dic3—24no—
83C2×C3×Dic3—44no—
84#624—28no—
85#624—24no—
86#624—24no—
87#624—24no—
88#624—44no—
89#624C2×Q818yes—
90C22×C4⋊C4—92no—
91C22×C4⋊C4—91no—
92C22×C4⋊C4—91no—
93#398—98no—
94C2×#95—91no—
95C2×#95—92no—
96C23×D3—62no—
97C22×C3×C4—22no—
98C22×C3×C4—62no—
99C22×C3×C4—62no—
100C22×Dic3—22no—
101C22×Dic3—22no—
102C22×Dic3—62no—
103C2×C4×D3—64no—
104C2×C4×D3—68no—
105C2×C4×D3—64no—
106C2×C4×D3—64no—
107C2×C4×D3—64no—
108C2×C4×D3—64no—
109C2×C4×D3—68no—
110C2×C4×D3—64no—
111C2×C4×D3—124no—
112C2×C4×D3—124no—
113C2×C4×D3—124no—
114C2×C4×D3—124no—
115C3×C4⋊C4—68no—
116C4⋊Dic3—68no—
117Dic3⋊C4—28no—
118Dic3⋊C4—68no—
119C22×C32#12112yes—
120C22×C32C22⋊Q814yes—
121C22×C32C22×D411yescharacteristic
122C2×C3⋊D3#12112yes—
123C2×C3⋊D3C22⋊Q814yes—
124C2×C3⋊D3#12314yes—
125C2×C3⋊D3#12518yes—
126C2×C3⋊D3C4⋊Q814yes—
127C2×C3⋊D3C22×D411yescharacteristic
128C2×C3⋊D3C22×Q812yes—
129C2×C3⋊D3C2×#4112yes—
130C2×C3⋊D3C2×#4111yescharacteristic
131#157—24no—
132#157—42no—
133C32×C4—22no—
134C3⋊Dic3—22no—
135C3×Dic3—28no—
136C3×Dic3—44no—
137C23×C4—92no—
138C23×C4—92no—
139C23×C4—91no—
140C23×C4—91no—
141C23×C4—91no—
142C2×C4⋊C4—62no—
143C2×C4⋊C4—98no—
144C2×C4⋊C4—94no—
145C2×C4⋊C4—94no—
146C2×C4⋊C4—184no—
147C2×C4⋊C4—182no—
148C2×C4⋊C4—184no—
149C2×C4⋊C4—184no—
150#95—94no—
151#95—98no—
152C23×C3—22no—
153C22×D3—62no—
154C22×D3—64no—
155C22×D3—64no—
156C22×D3—64no—
157C22×D3—64no—
158C22×D3—64no—
159C22×D3—64no—
160C22×D3—62no—
161C2×C3×C4—24no—
162C2×C3×C4—44no—
163C2×C3×C4—64no—
164C2×C3×C4—68no—
165C2×C3×C4—64no—
166C2×C3×C4—124no—
167C2×Dic3—24no—
168C2×Dic3—28no—
169C2×Dic3—24no—
170C2×Dic3—44no—
171C2×Dic3—64no—
172C2×Dic3—124no—
173C4×D3—68no—
174C4×D3—616no—
175C4×D3—68no—
176C4×D3—124no—
177C4×D3—124no—
178C4×D3—124no—
179C4×D3—128no—
180C4×D3—124no—
181C4×D3—128no—
182C2×C32#39814yescomplemented
183C2×C32C2×#12111yescharacteristic
184C2×C32C2×C22⋊Q812yes—
185C3⋊D3#39814yescomplemented
186C3⋊D3C2×#12311yescharacteristic
187C3⋊D3C2×#12512yes—
188C3⋊D3C2×C4⋊Q811yescharacteristic
189C24—91no—
190C22×C4—62no—
191C22×C4—62no—
192C22×C4—94no—
193C22×C4—98no—
194C22×C4—94no—
195C22×C4—94no—
196C22×C4—92no—
197C22×C4—91no—
198C22×C4—92no—
199C22×C4—92no—
200C22×C4—92no—
201C22×C4—182no—
202C22×C4—182no—
203C22×C4—182no—
204C22×C4—184no—
205C22×C4—182no—
206C22×C4—184no—
207C22×C4—184no—
208C22×C4—184no—
209C22×C4—182no—
210C22×C4—184no—
211C22×C4GO+(4,𝔽2)11yescharacteristic
212C4⋊C4—68no—
213C4⋊C4—188no—
214C4⋊C4—188no—
215C4⋊C4—188no—
216C22×C3—22no—
217C22×C3—24no—
218C22×C3—24no—
219C22×C3—24no—
220C2×D3—64no—
221C2×D3—62no—
222C2×D3—62no—
223C2×D3—64no—
224C2×D3—62no—
225C2×D3—62no—
226C2×D3—64no—
227C2×D3—68no—
228C2×D3—68no—
229C2×D3—68no—
230C2×D3—68no—
231C2×D3—62no—
232C2×D3—62no—
233C3×C4—44no—
234C3×C4—68no—
235C3×C4—124no—
236Dic3—28no—
237Dic3—44no—
238Dic3—124no—
239C32C2×#39811yescharacteristic, complemented, Sylow
240C23—91no—
241C23—91no—
242C23—94no—
243C23—94no—
244C23—92no—
245C23—92no—
246C23C2×GO+(4,𝔽2)11yescharacteristic
247C2×C4—22no—
248C2×C4—64no—
249C2×C4—68no—
250C2×C4—64no—
251C2×C4—98no—
252C2×C4—94no—
253C2×C4—92no—
254C2×C4—124no—
255C2×C4—182no—
256C2×C4—182no—
257C2×C4—184no—
258C2×C4—184no—
259C2×C4—188no—
260C2×C4—184no—
261C2×C4—184no—
262C2×C4—188no—
263C2×C4—184no—
264C2×C4—182no—
265C2×C4—182no—
266C2×C4—184no—
267C2×C4—364no—
268C2×C4—364no—
269C2×C4C2×GO+(4,𝔽2)12yes—
270C2×C3—28no—
271C2×C3—22no—
272C2×C3—22no—
273C2×C3—22no—
274D3—62no—
275D3—62no—
276D3—62no—
277D3—62no—
278D3—68no—
279C22—94no—
280C22—94no—
281C22—98no—
282C22—92no—
283C22—92no—
284C22—94no—
285C22—91no—
286C22—91no—
287C22—92no—
288C22D32⋊Q814yes—
289C22#6424212yes—
290C22C22×GO+(4,𝔽2)11yescharacteristic
291C4—22no—
292C4—68no—
293C4—124no—
294C4—184no—
295C4—182no—
296C4—362no—
297C3—22no—
298C2—91no—
299C2—94no—
300C2—91no—
301C2—92no—
302C2#1059334014yesdirect product factor
303C2C2×D32⋊Q812yes—
304C2C2×#6424211yescharacteristic
subgroupG/H
centerC23C2×GO+(4,𝔽2)
commutator, cosocleC22×C3⋊D3C24
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC23×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#398
LCSG ▷ C22×C3⋊D3 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
6. #10593340C2direct (N × H)
182. C2×C32#398semidirect
185. C3⋊D3#398semidirect
239. C32C2×#398semidirect
302. C2#10593340direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4⋊#1572
C22×#37732
C2×#638832
C2×#637372
#105933402
C2×#3989