Finite Group Databasebeta

← #11866811

Subgroups — #11866811

Order 1152.

834 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 834 conjugacy classes of subgroups — too many to draw. Only its 129 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×#3787C211yesmaximal, characteristic
2C2×#64228C211yesmaximal, characteristic, complemented
3#10594925C212yesmaximal
4#10593527C214yesmaximal, complemented
5#10593446C214yesmaximal, complemented
6#10593396C211yesmaximal, characteristic, complemented
7#10593375C212yesmaximal, complemented
8C22×C4×C3⋊D3C2211yescharacteristic
9C2×#3797C2212yes—
10C22×#622C2212yes—
11C2×#3787—24no—
12C2×#3787C2211yescharacteristic
13C2×#3787C2212yes—
14C2×#3787C2211yescharacteristic
15C2×#3776C2214yescomplemented
16#64228—24no—
17C3×#924—22no—
18#63982C2214yes—
19#63974—22no—
20#63900C2212yes—
21#63883—22no—
22#63871—22no—
23#63865C2214yes—
24#63743C2214yescomplemented
25#63740C2218yescomplemented
26D3×C22⋊Q8—62no—
27C23×C3⋊D3D411yescharacteristic
28C22×C32×C4D411yescharacteristic
29C22×C3⋊Dic3C2311yescharacteristic
30C2×C4×C3⋊D3—22no—
31C2×C4×C3⋊D3—22no—
32C2×C4×C3⋊D3D411yescharacteristic
33C2×C4×C3⋊D3D411yescharacteristic
34C2×C4×C3⋊D3C2311yescharacteristic
35C2×C4×C3⋊D3C2311yescharacteristic
36C2×C3×Dic6—22no—
37C2×#627C2314yes—
38C2×#624—22no—
39C2×#624—22no—
40#3797—24no—
41#3797—24no—
42C2×#622—24no—
43C2×#622C2312yes—
44C2×#622C2312yes—
45#3787—22no—
46#3787—24no—
47#3787D414yes—
48#3776—28no—
49C3×#217—24no—
50C3×C4⋊Dic3—22no—
51C3×Dic3⋊C4—24no—
52#3724C2314yes—
53Dic3⋊Dic3—24no—
54#3722—24no—
55C2×#467—91nomaximal, Sylow
56C2×D3×Q8—62no—
57C22×C4×D3—62no—
58C3×C22⋊Q8—62no—
59#946—62no—
60#924—22no—
61#897—62no—
62#896—64no—
63D3×C4⋊C4—62no—
64D3×C4⋊C4—64no—
65D3×C22⋊C4—64no—
66#878—64no—
67C23×C32C2×D411yescharacteristic
68C22×C3⋊D3—22no—
69C22×C3⋊D3—22no—
70C22×C3⋊D3Q1614yescomplemented
71C22×C3⋊D3C2×D411yescharacteristic
72C22×C3⋊D3C2×D411yescharacteristic
73C2×C32×C4—22no—
74C2×C32×C4C2×D411yescharacteristic
75C2×C32×C4C2×D411yescharacteristic
76C2×C3⋊Dic3—21no—
77C2×C3⋊Dic3—21no—
78C2×C3⋊Dic3C2×D411yescharacteristic
79C2×C3⋊Dic3C2411yescharacteristic
80C4×C3⋊D3—22no—
81C4×C3⋊D3—22no—
82C4×C3⋊D3—21no—
83C4×C3⋊D3—21no—
84C4×C3⋊D3C2×D412yes—
85C4×C3⋊D3#4112yes—
86C2×C3×Dic3—24no—
87C2×C3×Dic3—24no—
88C3×Dic6—44no—
89#627—24no—
90#627—24no—
91#624—44no—
92#624—44no—
93#622—22no—
94#622C2×D414yes—
95C22×Q16—91no—
96C23×C8—91no—
97C2×C22⋊Q8—92no—
98#467—94no—
99#467—94no—
100C2×#107—91no—
101C2×#103—92no—
102C23×D3—62no—
103C2×C3×Q8—62no—
104C22×C3×C4—22no—
105C22×Dic3—62no—
106D3×Q8—124no—
107D3×Q8—124no—
108C2×C4×D3—62no—
109C2×C4×D3—62no—
110C2×C4×D3—62no—
111C2×C4×D3—62no—
112C2×C4×D3—64no—
113C2×C4×D3—64no—
114C2×C4×D3—124no—
115C2×C4×D3—124no—
116C2×Dic6—22no—
117C2×Dic6—64no—
118C3×C4⋊C4—64no—
119C3×C4⋊C4—62no—
120C3×C22⋊C4—64no—
121#217—24no—
122(C2×D3)⋊C4—64no—
123(C2×D3)⋊C4—64no—
124C4⋊Dic3—22no—
125C4⋊Dic3—64no—
126Dic3⋊C4—24no—
127Dic3⋊C4—64no—
128Dic3⋊C4—64no—
129C22×C32—21no—
130C22×C32—21no—
131C22×C32C2×Q1612yescomplemented
132C22×C32C22×D411yescharacteristic
133C2×C3⋊D3—21no—
134C2×C3⋊D3—21no—
135C2×C3⋊D3—28no—
136C2×C3⋊D3#12112yes—
137C2×C3⋊D3C2×Q1612yes—
138C2×C3⋊D3C2×Q1612yescomplemented
139C2×C3⋊D3#13512yes—
140C32×C4—21no—
141C32×C4#12112yes—
142C3⋊Dic3—21no—
143C3⋊Dic3C22×D411yescharacteristic
144C3⋊Dic3C2×#4111yescharacteristic
145C3×Dic3—44no—
146C3×Dic3—44no—
147C22×Q8—92no—
148C23×C4—91no—
149C2×Q16—94no—
150C2×Q16—184no—
151C22×C8—91no—
152C22×C8—91no—
153C22×C8—92no—
154C22×C8—92no—
155C22×C8—184no—
156C22⋊Q8—62no—
157C22⋊Q8—94no—
158C22⋊Q8—94no—
159C22⋊Q8—182no—
160C2×C4⋊C4—92no—
161C2×C4⋊C4—182no—
162C2×C22⋊C4—182no—
163#107—94no—
164#103—98no—
165C23×C3—22no—
166C22×D3—62no—
167C22×D3—68no—
168C22×D3—62no—
169C22×D3—124no—
170C22×D3—124no—
171C3×Q8—124no—
172C2×C3×C4—22no—
173C2×C3×C4—22no—
174C2×C3×C4—44no—
175C2×C3×C4—64no—
176C2×C3×C4—64no—
177C2×Dic3—24no—
178C2×Dic3—24no—
179C2×Dic3—62no—
180C2×Dic3—62no—
181C2×Dic3—122no—
182C2×Dic3—122no—
183C4×D3—64no—
184C4×D3—64no—
185C4×D3—122no—
186C4×D3—122no—
187C4×D3—124no—
188C4×D3—124no—
189C4×D3—128no—
190C4×D3—128no—
191Dic6—44no—
192Dic6—124no—
193Dic6—124no—
194C2×C32—22no—
195C2×C32C2×#12111yescharacteristic
196C2×C32C22×Q1611yescharacteristic
197C2×C32C2×#13511yescharacteristic
198C3⋊D3—22no—
199C3⋊D3#46714yescomplemented
200C24—91no—
201C2×Q8—62no—
202C2×Q8—94no—
203C2×Q8—184no—
204C2×Q8—184no—
205C22×C4—91no—
206C22×C4—91no—
207C22×C4—91no—
208C22×C4—91no—
209C22×C4—91no—
210C22×C4—182no—
211C22×C4—182no—
212C22×C4—182no—
213C22×C4—182no—
214C22×C4GO+(4,𝔽2)11yescharacteristic
215Q16—188no—
216C2×C8—92no—
217C2×C8—94no—
218C2×C8—92no—
219C2×C8—184no—
220C2×C8—184no—
221C2×C8—182no—
222C4⋊C4—62no—
223C4⋊C4—64no—
224C4⋊C4—94no—
225C4⋊C4—184no—
226C22⋊C4—64no—
227C22⋊C4—184no—
228C22×C3—22no—
229C22×C3—24no—
230C22×C3—42no—
231C22×C3—42no—
232C2×D3—64no—
233C2×D3—64no—
234C2×D3—64no—
235C2×D3—64no—
236C2×D3—1216no—
237C2×D3—122no—
238C2×D3—122no—
239C3×C4—24no—
240C3×C4—42no—
241C3×C4—124no—
242C3×C4—124no—
243Dic3—44no—
244Dic3—44no—
245Dic3—62no—
246Dic3—62no—
247Dic3—122no—
248C32C2×#46711yescharacteristic, complemented, Sylow
249C23—91no—
250C23—91no—
251C23—94no—
252C23—182no—
253C23—182no—
254C23C2×GO+(4,𝔽2)11yescharacteristic
255Q8—124no—
256Q8—184no—
257Q8—184no—
258C2×C4—22no—
259C2×C4—64no—
260C2×C4—64no—
261C2×C4—91no—
262C2×C4—92no—
263C2×C4—92no—
264C2×C4—91no—
265C2×C4—181no—
266C2×C4—181no—
267C2×C4—182no—
268C2×C4—181no—
269C2×C4—181no—
270C2×C4—182no—
271C2×C4—364no—
272C2×C4—364no—
273C2×C4C2×GO+(4,𝔽2)11yescharacteristic
274C2×C4C2×GO+(4,𝔽2)11yescharacteristic
275C8—94no—
276C8—182no—
277C2×C3—22no—
278C2×C3—22no—
279C2×C3—22no—
280C2×C3—44no—
281D3—68no—
282D3—124no—
283C22—21no—
284C22—21no—
285C22—92no—
286C22—92no—
287C22—92no—
288C22—92no—
289C22—188no—
290C22—181no—
291C22—181no—
292C22#6422812yescomplemented
293C22C22×GO+(4,𝔽2)11yescharacteristic
294C4—21no—
295C4—91no—
296C4—91no—
297C4—124no—
298C4—124no—
299C4—181no—
300C4#6424212yes—
301C3—22no—
302C2—22no—
303C2—94no—
304C2—182no—
305C2#1059650011yescharacteristic
306C2C2×#6422811yescharacteristic
307C2C2×#6424211yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC22×C32×C4D4
socleC22×C32C22×D4
prime radicalC23×C3⋊D3D4
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#467
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×#64228C2semidirect
4. #10593527C2semidirect
5. #10593446C2semidirect
6. #10593396C2semidirect
7. #10593375C2semidirect
15. C2×#3776C22semidirect
24. #63743C22semidirect
25. #63740C22semidirect
70. C22×C3⋊D3Q16semidirect
131. C22×C32C2×Q16semidirect
138. C2×C3⋊D3C2×Q16semidirect
199. C3⋊D3#467semidirect
248. C32C2×#467semidirect
292. C22#64228semidirect

Maximal subgroups

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

subgroupindex
C22×#37872
C2×#642282
#105949252
#105935272
#105934462
#105933962
#105933752
C2×#4679