Finite Group Databasebeta

← #11773194

Subgroups — #11773194

Order 1152.

898 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 898 conjugacy classes of subgroups — too many to draw. Only its 151 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
2C2×#63737C212yesmaximal
3C2×#63737C212yesmaximal
4#10591370C212yesmaximal
5C23×#157C2211yescharacteristic
6C23×#157C2211yescharacteristic
7C22×C4×C3⋊D3C2211yescharacteristic
8C22×#624C2214yes—
9C2×C4×#157—24no—
10C2×C4×#157C414yescomplemented
11#63737—24no—
12#63737C418yescomplemented
13C3×C3⋊#95—22no—
14#63579—22no—
15D3×#95—62no—
16C23×C3⋊D3C2311yescharacteristic
17C22×#157—22no—
18C22×#157—22no—
19C22×#157—22no—
20C22×#157—22no—
21C22×#157C2×C412yes—
22C22×#157C2×C414yes—
23C22×#157C2×C412yes—
24C22×#157D414yes—
25C22×C32×C4D411yescharacteristic
26C22×C3⋊Dic3D411yescharacteristic
27C2×C4×C3⋊D3—22no—
28C2×C4×C3⋊D3—22no—
29C2×C4×C3⋊D3C2×C412yes—
30C2×C4×C3⋊D3Q812yes—
31C22×C3×Dic3—24no—
32C2×#624—24no—
33C2×#624—24no—
34C2×#624—24no—
35C2×#624—24no—
36C2×#624—24no—
37C2×#624C2×C418yes—
38C4×#157—28no—
39#1434—91nomaximal, Sylow
40C22×C4×D3—64no—
41C22×C4×D3—62no—
42C3×#95—62no—
43C3⋊#95—22no—
44C3⋊#95—64no—
45C23×C32C2×D411yescharacteristic
46C22×C3⋊D3C22×C411yescharacteristic
47C22×C3⋊D3C22×C412yes—
48C22×C3⋊D3C2×D412yes—
49C22×C3⋊D3C2×Q811yescharacteristic
50C22×C3⋊D3#4112yes—
51C22×C3⋊D3#4112yes—
52C22×C3⋊D3#4112yes—
53C22×C3⋊D3#4112yes—
54C2×#157—22no—
55C2×#157—22no—
56C2×#157—22no—
57C2×#157—22no—
58C2×#157—28no—
59C2×#157—28no—
60C2×#157C4214yes—
61C2×#157C22⋊C414yes—
62C2×C32×C4—22no—
63C2×C32×C4C4⋊C412yes—
64C2×C3⋊Dic3—22no—
65C2×C3⋊Dic3C4⋊C412yes—
66C4×C3⋊D3—22no—
67C4×C3⋊D3—22no—
68C4×C3⋊D3—24no—
69C2×C3×Dic3—28no—
70C2×C3×Dic3—44no—
71C2×C3×Dic3—44no—
72#624—28no—
73#624—28no—
74#624—44no—
75#624—44no—
76C22×C42—91no—
77C2×#95—92no—
78C2×#95—92no—
79C2×#95—92no—
80C23×D3—62no—
81C22×C3×C4—22no—
82C22×C3×C4—64no—
83C22×Dic3—24no—
84C22×Dic3—62no—
85C2×C4×D3—68no—
86C2×C4×D3—64no—
87C2×C4×D3—64no—
88C2×C4×D3—68no—
89C2×C4×D3—124no—
90C2×C4×D3—124no—
91C2×C4×D3—124no—
92C2×C4×D3—124no—
93C2×C4×D3—124no—
94C2×C4×D3—124no—
95C22×C32C2×C4⋊C411yescharacteristic
96C22×C32C4×D412yes—
97C22×C32#12112yes—
98C22×C32#12412yes—
99C2×C3⋊D3C2×C4211yescharacteristic
100C2×C3⋊D3C2×C22⋊C411yescharacteristic
101C2×C3⋊D3#11711yescharacteristic
102C2×C3⋊D3#11711yescharacteristic
103C2×C3⋊D3#11714yes—
104C2×C3⋊D3#11711yescharacteristic
105C2×C3⋊D3#11711yescharacteristic
106C2×C3⋊D3C4×D414yes—
107C2×C3⋊D3C4×Q812yes—
108C2×C3⋊D3C22⋊Q812yes—
109C2×C3⋊D3#12314yes—
110C2×C3⋊D3#12512yes—
111C2×C3⋊D3#12614yes—
112#157—24no—
113#157—24no—
114C32×C4—22no—
115C3⋊Dic3—22no—
116C3×Dic3—48no—
117C23×C4—94no—
118C23×C4—91no—
119C23×C4—91no—
120C23×C4—91no—
121C2×C42—94no—
122C2×C42—184no—
123#95—62no—
124#95—98no—
125#95—182no—
126#95—184no—
127C23×C3—22no—
128C22×D3—64no—
129C22×D3—62no—
130C22×D3—64no—
131C22×D3—62no—
132C22×D3—64no—
133C22×D3—62no—
134C22×D3—62no—
135C22×D3—64no—
136C22×D3—62no—
137C22×D3—62no—
138C2×C3×C4—24no—
139C2×C3×C4—44no—
140C2×C3×C4—68no—
141C2×C3×C4—124no—
142C2×C3×C4—124no—
143C2×Dic3—28no—
144C2×Dic3—44no—
145C2×Dic3—44no—
146C2×Dic3—64no—
147C2×Dic3—124no—
148C4×D3—128no—
149C4×D3—128no—
150C4×D3—124no—
151C4×D3—124no—
152C4×D3—128no—
153C4×D3—128no—
154C4×D3—128no—
155C2×C32C4×C4⋊C411yescharacteristic
156C2×C32#38011yescharacteristic
157C2×C32#38211yescharacteristic
158C2×C32#38814yes—
159C3⋊D3#37611yescharacteristic
160C3⋊D3C4×C22⋊C411yescharacteristic
161C3⋊D3#38111yescharacteristic
162C3⋊D3#38311yescharacteristic
163C3⋊D3#38714yes—
164C24—91no—
165C22×C4—64no—
166C22×C4—98no—
167C22×C4—94no—
168C22×C4—92no—
169C22×C4—92no—
170C22×C4—94no—
171C22×C4—91no—
172C22×C4—92no—
173C22×C4—92no—
174C22×C4—182no—
175C22×C4—182no—
176C22×C4—184no—
177C22×C4—184no—
178C22×C4—184no—
179C22×C4—184no—
180C22×C4—184no—
181C22×C4—182no—
182C22×C4—182no—
183C22×C4—182no—
184C22×C4—182no—
185C22×C4GO+(4,𝔽2)11yescharacteristic
186C42—188no—
187C22×C3—22no—
188C22×C3—22no—
189C22×C3—24no—
190C22×C3—22no—
191C22×C3—24no—
192C2×D3—62no—
193C2×D3—64no—
194C2×D3—62no—
195C2×D3—64no—
196C2×D3—64no—
197C2×D3—64no—
198C2×D3—64no—
199C2×D3—62no—
200C2×D3—62no—
201C2×D3—62no—
202C2×D3—64no—
203C2×D3—62no—
204C2×D3—64no—
205C2×D3—64no—
206C2×D3—64no—
207C2×D3—62no—
208C2×D3—62no—
209C2×D3—64no—
210C3×C4—44no—
211C3×C4—128no—
212Dic3—48no—
213Dic3—124no—
214C32#143411yescharacteristic, complemented, Sylow
215C23—92no—
216C23—92no—
217C23—92no—
218C23—92no—
219C23—91no—
220C23—91no—
221C23—92no—
222C23—92no—
223C23C2×GO+(4,𝔽2)11yescharacteristic
224C2×C4—22no—
225C2×C4—68no—
226C2×C4—94no—
227C2×C4—94no—
228C2×C4—92no—
229C2×C4—124no—
230C2×C4—124no—
231C2×C4—182no—
232C2×C4—182no—
233C2×C4—184no—
234C2×C4—188no—
235C2×C4—188no—
236C2×C4—182no—
237C2×C4—182no—
238C2×C4—182no—
239C2×C4—188no—
240C2×C4—188no—
241C2×C4—182no—
242C2×C4—182no—
243C2×C4—364no—
244C2×C4—364no—
245C2×C4#377312yes—
246C2×C3—22no—
247C2×C3—24no—
248C2×C3—24no—
249C2×C3—22no—
250C2×C3—22no—
251D3—62no—
252D3—62no—
253D3—62no—
254D3—62no—
255D3—64no—
256D3—64no—
257C22—91no—
258C22—91no—
259C22—92no—
260C22—94no—
261C22—94no—
262C22—94no—
263C22—94no—
264C22—91no—
265C22—91no—
266C22—92no—
267C22—91no—
268C22—91no—
269C22—92no—
270C22#6422112yes—
271C22C4×GO+(4,𝔽2)12yes—
272C22C2×#377311yescharacteristic
273C22#6424212yes—
274C4—22no—
275C4—128no—
276C4—184no—
277C4—184no—
278C4—182no—
279C3—22no—
280C2—91no—
281C2—91no—
282C2—91no—
283C2—91no—
284C2—94no—
285C2#1059334411yescharacteristic
286C2#1059340014yes—
287C2C4×#377311yescharacteristic
288C2#1059351611yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC2×C3⋊D3C2×C42
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radical, cosocleC23×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1434
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
10. C2×C4×#157C4semidirect
12. #63737C4semidirect
214. C32#1434semidirect

Maximal subgroups

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

subgroupindex
C22×C4×#1572
C2×#637372
#105913702
#14349