Finite Group Databasebeta

← C22×#63730 #11857764

Subgroups — C22×#63730 #11857764

Order 1152.

1410 conjugacy classes of subgroups; only the 247 normal subgroups are shown.

normal subgroups only

This group has 1410 conjugacy classes of subgroups — too many to draw. Only its 247 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×#3797C211yesmaximal, characteristic
2C22×C4⋊#157C211yesmaximal, characteristic
3C22×#3710C211yesmaximal, characteristic
4C2×#63730C2112yesmaximal, direct product factor
5C23×#157—21no—
6C22×C4×C3⋊D3C2211yescharacteristic
7C22×C3×Dic6—21no—
8C22×#627C412yescomplemented
9C22×#624—21no—
10C2×#3797—23no—
11C2×#3797—23no—
12C2×#3797C416yescomplemented
13C2×#3797C2216yes—
14C2×C4⋊#157—23no—
15C2×C4⋊#157C2216yes—
16C22×C3×C3⋊C8—21no—
17C2×#3710—23no—
18C2×#3710C2216yes—
19#63730C22116yesdirect product factor
20C22×D3×Q8—61no—
21C22×D3×C8—61no—
22C23×C3⋊D3D411yescharacteristic
23C22×#157—26no—
24C22×#157—44no—
25C22×C32×C4D411yescharacteristic
26C22×C3⋊Dic3C2×C411yescharacteristic
27C2×C4×C3⋊D3C2×C413yes—
28C2×C4×C3⋊D3D413yes—
29C2×C4×C3⋊D3D413yes—
30C2×C4×C3⋊D3C2313yes—
31C22×C3×Dic3—22no—
32C2×C3×Dic6—26no—
33C2×C3×Dic6—26no—
34C2×#627—26no—
35C2×#627C2×C4112yescomplemented
36C2×#624—26no—
37C2×#624—26no—
38#3797—212no—
39#3797—26no—
40#3797—26no—
41#3797C2×C4112yescomplemented
42#3797C2314yes—
43C4⋊#157—26no—
44C4⋊#157C2314yes—
45C2×C3×C3⋊C8—26no—
46#3710—26no—
47#3710C2314yes—
48C22×#103—91nomaximal, Sylow
49C22×C3×Q8—61no—
50C2×D3×Q8—66no—
51C2×D3×Q8—66no—
52C2×D3×Q8—66no—
53C2×D3×Q8—66no—
54C22×C4×D3—61no—
55C22×C4×D3—61no—
56C22×C4×D3—62no—
57C22×Dic6—21no—
58C22×Dic6—62no—
59C22×C3×C8—61no—
60C22×C3⋊C8—21no—
61C2×D3×C8—66no—
62C2×D3×C8—66no—
63C23×C32C22⋊C411yescharacteristic
64C22×C3⋊D3C22⋊C413yes—
65C22×C3⋊D3SD1614yes—
66C22×C3⋊D3Q1614yes—
67C22×C3⋊D3C2×D413yes—
68C2×#157—24no—
69C2×#157—412no—
70C2×C32×C4C22⋊C413yes—
71C2×C32×C4C2×D413yes—
72C2×C3⋊Dic3C22⋊C413yes—
73C2×C3⋊Dic3C22×C413yes—
74C4×C3⋊D3C22⋊C416yes—
75C4×C3⋊D3C22×C413yes—
76C4×C3⋊D3C2×D413yes—
77C4×C3⋊D3C2×D413yes—
78C4×C3⋊D3C2411yescharacteristic
79C2×C3×Dic3—212no—
80C3×Dic6—212no—
81C3×Dic6—24no—
82#627—212no—
83#627C22×C418yescomplemented
84#624—212no—
85#624—24no—
86C3×C3⋊C8—24no—
87C23×Q8—91no—
88C23×C8—91no—
89C22×C4⋊C4—91no—
90C2×#103—912no—
91C23×D3—61no—
92C23×D3—61no—
93C2×C3×Q8—66no—
94C2×C3×Q8—66no—
95C22×C3×C4—21no—
96C22×C3×C4—21no—
97C22×C3×C4—62no—
98C22×Dic3—22no—
99C22×Dic3—61no—
100C22×Dic3—61no—
101D3×Q8—612no—
102D3×Q8—64no—
103D3×Q8—624no—
104D3×Q8—612no—
105D3×Q8—612no—
106C2×C4×D3—63no—
107C2×C4×D3—63no—
108C2×C4×D3—63no—
109C2×C4×D3—63no—
110C2×C4×D3—63no—
111C2×C4×D3—63no—
112C2×C4×D3—63no—
113C2×C4×D3—63no—
114C2×C4×D3—612no—
115C2×C4×D3—612no—
116C2×Dic6—26no—
117C2×Dic6—26no—
118C2×Dic6—612no—
119C2×Dic6—612no—
120C2×C3×C8—66no—
121C2×C3⋊C8—26no—
122D3×C8—64no—
123D3×C8—612no—
124C22×C32#10314yescomplemented
125C22×C32C2×C22⋊C413yes—
126C2×C3⋊D3#103112yescomplemented
127C2×C3⋊D3C2×C22⋊C413yes—
128C2×C3⋊D3C2×SD1616yes—
129C2×C3⋊D3C2×Q1616yes—
130C2×C3⋊D3C22×D411yescharacteristic
131#157—44no—
132C32×C4C2×C22⋊C413yes—
133C32×C4C22×D411yescharacteristic
134C3⋊Dic3C2×C22⋊C413yes—
135C3⋊Dic3C23×C411yescharacteristic
136C3×Dic3—28no—
137C22×Q8—61no—
138C22×Q8—92no—
139C22×Q8—96no—
140C22×Q8—96no—
141C22×Q8—183no—
142C22×Q8—183no—
143C23×C4—91no—
144C23×C4—181no—
145C23×C4—181no—
146C22×C8—61no—
147C22×C8—96no—
148C22×C8—183no—
149C2×C4⋊C4—96no—
150C2×C4⋊C4—183no—
151#103—916no—
152C23×C3—21no—
153C23×C3—21no—
154C22×D3—63no—
155C22×D3—63no—
156C22×D3—64no—
157C22×D3—64no—
158C22×D3—64no—
159C22×D3—64no—
160C22×D3—63no—
161C22×D3—63no—
162C3×Q8—64no—
163C3×Q8—612no—
164C2×C3×C4—23no—
165C2×C3×C4—23no—
166C2×C3×C4—23no—
167C2×C3×C4—23no—
168C2×C3×C4—612no—
169C2×Dic3—212no—
170C2×Dic3—63no—
171C2×Dic3—63no—
172C2×Dic3—63no—
173C2×Dic3—63no—
174C4×D3—66no—
175C4×D3—66no—
176C4×D3—63no—
177C4×D3—63no—
178C4×D3—63no—
179C4×D3—63no—
180C4×D3—63no—
181C4×D3—63no—
182C4×D3—61no—
183C4×D3—61no—
184C4×D3—624no—
185C4×D3—68no—
186Dic6—24no—
187Dic6—212no—
188Dic6—68no—
189Dic6—624no—
190C3×C8—64no—
191C3⋊C8—24no—
192C2×C32C2×#10316yescomplemented
193C2×C32C22×C22⋊C411yescharacteristic
194C3⋊D3C2×#10316yescomplemented
195C3⋊D3C22×SD1611yescharacteristic
196C3⋊D3C22×Q1611yescharacteristic
197C24—91no—
198C2×Q8—66no—
199C2×Q8—66no—
200C2×Q8—912no—
201C2×Q8—94no—
202C2×Q8—912no—
203C2×Q8—186no—
204C2×Q8—186no—
205C2×Q8—186no—
206C2×Q8—1812no—
207C22×C4—62no—
208C22×C4—91no—
209C22×C4—93no—
210C22×C4—93no—
211C22×C4—93no—
212C22×C4—93no—
213C22×C4—186no—
214C22×C4—186no—
215C22×C4—186no—
216C22×C4—364no—
217C22×C4GO+(4,𝔽2)11yescharacteristic
218C2×C8—66no—
219C2×C8—94no—
220C2×C8—186no—
221C4⋊C4—94no—
222C4⋊C4—186no—
223C22×C3—23no—
224C22×C3—23no—
225C22×C3—24no—
226C22×C3—24no—
227C2×D3—63no—
228C2×D3—61no—
229C2×D3—63no—
230C2×D3—61no—
231C2×D3—612no—
232C2×D3—612no—
233C2×D3—66no—
234C2×D3—66no—
235C2×D3—66no—
236C2×D3—66no—
237C3×C4—21no—
238C3×C4—21no—
239C3×C4—23no—
240C3×C4—23no—
241C3×C4—68no—
242Dic3—28no—
243Dic3—63no—
244Dic3—61no—
245Dic3—63no—
246Dic3—61no—
247C32C22×#10311yescharacteristic, complemented, Sylow
248C23—93no—
249C23—93no—
250C23—94no—
251C23—94no—
252C23D32⋊C411yescharacteristic
253Q8—64no—
254Q8—612no—
255Q8—98no—
256Q8—1812no—
257C2×C4—612no—
258C2×C4—93no—
259C2×C4—93no—
260C2×C4—91no—
261C2×C4—93no—
262C2×C4—93no—
263C2×C4—93no—
264C2×C4—96no—
265C2×C4—184no—
266C2×C4—1812no—
267C2×C4—184no—
268C2×C4—3612no—
269C2×C4D32⋊C413yes—
270C2×C4C2×GO+(4,𝔽2)13yes—
271C8—64no—
272C2×C3—26no—
273C2×C3—26no—
274C2×C3—21no—
275C2×C3—21no—
276D3—61no—
277D3—61no—
278D3—61no—
279D3—61no—
280D3—66no—
281D3—66no—
282C22—96no—
283C22—96no—
284C22—912no—
285C22—91no—
286C22—93no—
287C22#6373014yesdirect product factor
288C22C2×D32⋊C413yes—
289C4—68no—
290C4—91no—
291C4—93no—
292C4—364no—
293C4C2×D32⋊C413yes—
294C4C22×GO+(4,𝔽2)11yescharacteristic
295C3—21no—
296C3—21no—
297C2—91no—
298C2—96no—
299C2—91no—
300C2C2×#6373016yesdirect product factor
301C2C22×D32⋊C411yescharacteristic
subgroupG/H
centerC23D32⋊C4
commutatorC3⋊Dic3C23×C4
FrattiniC4C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC23×C32C22⋊C4
prime radicalC23×C3⋊D3D4
cosocleC4×C3⋊D3C24
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C22×#103
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. C2×#63730C2direct (N × H)
8. C22×#627C4semidirect
12. C2×#3797C4semidirect
19. #63730C22direct (N × H)
35. C2×#627C2×C4semidirect
41. #3797C2×C4semidirect
83. #627C22×C4semidirect
124. C22×C32#103semidirect
126. C2×C3⋊D3#103semidirect
192. C2×C32C2×#103semidirect
194. C3⋊D3C2×#103semidirect
247. C32C22×#103semidirect
287. C22#63730direct (N × H)
300. C2C2×#63730direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37972
C22×C4⋊#1572
C22×#37102
C2×#637302
C22×#1039