Finite Group Databasebeta

← C2×#10593123 #11919895

Subgroups — C2×#10593123 #11919895

Order 1152.

2269 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 2269 conjugacy classes of subgroups — too many to draw. Only its 87 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
1#10593123C212yesmaximal, direct product factor
2C2×C22⋊(Q8⋊C9)C211yesmaximal, characteristic, complemented
3C23×C3×#41C311yesmaximal, characteristic
4C22⋊(Q8⋊C9)C2211yescharacteristic, complemented
5C2×#41⋊C9—44nomaximal
6C2×C4×C22⋊C9—41nomaximal
7C22×C3×#41—38no—
8C22×C3×#41—34no—
9C22×C3×#41—34no—
10C22×C3×#41—32no—
11C22×C3×#41C2×C312yes—
12C23×C3×Q8C2×C311yescharacteristic
13C23×C3×D4—31no—
14C24×C3×C4—31no—
15C22×C22⋊C9—41no—
16#41⋊C9—48no—
17C2×Q8⋊C9—44no—
18C4×C22⋊C9—42no—
19C23×#41C911yescharacteristic, complemented, Sylow
20C25×C3—31no—
21C2×C3×#41—38no—
22C2×C3×#41—312no—
23C2×C3×#41—324no—
24C2×C3×#41—324no—
25C2×C3×#41—324no—
26C2×C3×#41—324no—
27C2×C3×#41—38no—
28C2×C3×#41—34no—
29C2×C3×#41—38no—
30C2×C3×#41—38no—
31C2×C3×#41—34no—
32C2×C3×#41A414yes—
33C22×C3×Q8—34no—
34C22×C3×Q8—34no—
35C22×C3×Q8—31no—
36C22×C3×Q8C22×C311yescharacteristic
37C22×C3×D4—32no—
38C22×C3×D4—312no—
39C22×C3×D4—312no—
40C22×C3×D4—32no—
41C23×C3×C4—312no—
42C23×C3×C4—36no—
43C23×C3×C4—36no—
44C23×C3×C4—31no—
45C23×C3×C4—32no—
46C23×C3×C4—32no—
47C23×C3×C4A411yescharacteristic
48C2×C22⋊C9—42no—
49C2×C22⋊C9—41no—
50C2×C4×C9—161no—
51Q8⋊C9—44no—
52C22×#41—38no—
53C22×#41—34no—
54C22×#41—34no—
55C22×#41—32no—
56C22×#41C2×C912yescomplemented
57C23×Q8C2×C911yescharacteristic
58C23×D4—31no—
59C24×C4—31no—
60C24×C3—36no—
61C24×C3—36no—
62C24×C3—32no—
63C24×C3—66no—
64C24×C3—62no—
65C24×C3C2×A411yescharacteristic
66C3×#41—324no—
67C3×#41—324no—
68C3×#41—324no—
69C3×#41—348no—
70C3×#41—324no—
71C3×#41—38no—
72C3×#41—38no—
73C3×#41—38no—
74C3×#41C2×A418yes—
75C2×C3×Q8—312no—
76C2×C3×Q8—312no—
77C2×C3×Q8—34no—
78C2×C3×Q8—34no—
79C2×C3×Q8—34no—
80C2×C3×Q8C2×A414yes—
81C2×C3×D4—34no—
82C2×C3×D4—324no—
83C2×C3×D4—324no—
84C2×C3×D4—324no—
85C2×C3×D4—324no—
86C2×C3×D4—312no—
87C22×C3×C4—36no—
88C22×C3×C4—36no—
89C22×C3×C4—324no—
90C22×C3×C4—312no—
91C22×C3×C4—312no—
92C22×C3×C4—324no—
93C22×C3×C4—312no—
94C22×C3×C4—312no—
95C22×C3×C4—312no—
96C22×C3×C4—31no—
97C22×C3×C4—31no—
98C22×C3×C4—31no—
99C22×C3×C4—34no—
100C22×C3×C4—31no—
101C22×C3×C4—32no—
102C22×C3×C4C2×A412yes—
103C22×C9—161no—
104C22⋊C9—41no—
105C4×C9—162no—
106C25—31no—
107C2×#41—38no—
108C2×#41—312no—
109C2×#41—324no—
110C2×#41—324no—
111C2×#41—324no—
112C2×#41—324no—
113C2×#41—38no—
114C2×#41—34no—
115C2×#41—38no—
116C2×#41—38no—
117C2×#41—34no—
118C2×#41C22⋊C914yescomplemented
119C22×Q8—34no—
120C22×Q8—34no—
121C22×Q8—31no—
122C22×Q8C22×C911yescharacteristic
123C22×D4—32no—
124C22×D4—312no—
125C22×D4—312no—
126C22×D4—32no—
127C23×C4—312no—
128C23×C4—36no—
129C23×C4—36no—
130C23×C4—31no—
131C23×C4—32no—
132C23×C4—32no—
133C23×C4C22⋊C911yescharacteristic
134C23×C3—31no—
135C23×C3—32no—
136C23×C3—31no—
137C23×C3—312no—
138C23×C3—312no—
139C23×C3—34no—
140C23×C3—612no—
141C23×C3—66no—
142C23×C3—612no—
143C23×C3—612no—
144C23×C3—612no—
145C23×C3—62no—
146C23×C3#41⋊C312yes—
147C23×C3C22×A411yescharacteristic
148C3×Q8—34no—
149C3×Q8—312no—
150C3×Q8—34no—
151C3×Q8C22×A414yes—
152C3×D4—38no—
153C3×D4—38no—
154C3×D4—324no—
155C3×D4—324no—
156C2×C3×C4—32no—
157C2×C3×C4—36no—
158C2×C3×C4—312no—
159C2×C3×C4—36no—
160C2×C3×C4—324no—
161C2×C3×C4—324no—
162C2×C3×C4—31no—
163C2×C3×C4—34no—
164C2×C3×C4—32no—
165C2×C3×C4—32no—
166C2×C3×C4—38no—
167C2×C3×C4—38no—
168C2×C3×C4—32no—
169C2×C3×C4C22⋊A411yescharacteristic
170C2×C9—162no—
171C2×C9—161no—
172C24—36no—
173C24—36no—
174C24—32no—
175C24—66no—
176C24—62no—
177C24C2×C22⋊C911yescharacteristic
178#41—324no—
179#41—324no—
180#41—324no—
181#41—348no—
182#41—38no—
183#41—324no—
184#41—38no—
185#41—38no—
186#41C2×C22⋊C918yescomplemented
187C2×Q8—312no—
188C2×Q8—312no—
189C2×Q8—34no—
190C2×Q8—34no—
191C2×Q8—34no—
192C2×Q8C2×C22⋊C914yes—
193C2×D4—34no—
194C2×D4—324no—
195C2×D4—324no—
196C2×D4—324no—
197C2×D4—324no—
198C2×D4—312no—
199C22×C4—36no—
200C22×C4—36no—
201C22×C4—324no—
202C22×C4—312no—
203C22×C4—312no—
204C22×C4—312no—
205C22×C4—312no—
206C22×C4—324no—
207C22×C4—312no—
208C22×C4—31no—
209C22×C4—31no—
210C22×C4—31no—
211C22×C4—34no—
212C22×C4—31no—
213C22×C4—32no—
214C22×C4C2×C22⋊C912yes—
215C22×C3—32no—
216C22×C3—31no—
217C22×C3—32no—
218C22×C3—32no—
219C22×C3—32no—
220C22×C3—31no—
221C22×C3—31no—
222C22×C3—38no—
223C22×C3—624no—
224C22×C3—612no—
225C22×C3—612no—
226C22×C3—68no—
227C22×C3C2×#41⋊C311yescharacteristic
228C22×C3C2×C22⋊A411yescharacteristic
229C3×C4—32no—
230C3×C4—34no—
231C3×C4—34no—
232C3×C4C2×C22⋊A412yes—
233C9—161noSylow
234C23—31no—
235C23—32no—
236C23—31no—
237C23—312no—
238C23—312no—
239C23—34no—
240C23—612no—
241C23—66no—
242C23—612no—
243C23—612no—
244C23—612no—
245C23—62no—
246C23#41⋊C912yescomplemented
247C23C22×C22⋊C911yescharacteristic
248Q8—34no—
249Q8—34no—
250Q8—312no—
251Q8C22×C22⋊C914yes—
252D4—38no—
253D4—324no—
254D4—38no—
255D4—324no—
256C2×C4—32no—
257C2×C4—36no—
258C2×C4—312no—
259C2×C4—36no—
260C2×C4—324no—
261C2×C4—324no—
262C2×C4—31no—
263C2×C4—34no—
264C2×C4—32no—
265C2×C4—32no—
266C2×C4—38no—
267C2×C4—38no—
268C2×C4—32no—
269C2×C4C22⋊(C22⋊C9)11yescharacteristic
270C2×C3—32no—
271C2×C3—31no—
272C2×C3—31no—
273C2×C3—68no—
274C2×C3#594812yes—
275C2×C3C22×C22⋊A411yescharacteristic
276C22—32no—
277C22—31no—
278C22—32no—
279C22—31no—
280C22—31no—
281C22—32no—
282C22—32no—
283C22—38no—
284C22—612no—
285C22—624no—
286C22—612no—
287C22—68no—
288C22C2×#41⋊C911yescharacteristic, complemented
289C22C2×C22⋊(C22⋊C9)11yescharacteristic
290C4—32no—
291C4—34no—
292C4—34no—
293C4C2×C22⋊(C22⋊C9)12yes—
294C3C2×#594811yescharacteristic
295C2—31no—
296C2—32no—
297C2—31no—
298C2—68no—
299C2#1059312312yesdirect product factor
300C2C22×C22⋊(C22⋊C9)11yescharacteristic
subgroupG/H
center, hypercenterC2×C3×C4C22⋊A4
commutator, hypocenterC22×Q8C22×C9
FrattiniC2×C3C22×C22⋊A4
Fitting, prime radicalC23×C3×#41C3
socleC24×C3C2×A4
cosocleC22×C3×Q8C22×C3
LCSG ▷ C22×Q8
UCSC1 ◁ C2×C3×C4

Complements

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

NH ≅ G/Ntype
1. #10593123C2direct (N × H)
2. C2×C22⋊(Q8⋊C9)C2semidirect
4. C22⋊(Q8⋊C9)C22semidirect
19. C23×#41C9semidirect
56. C22×#41C2×C9semidirect
118. C2×#41C22⋊C9semidirect
186. #41C2×C22⋊C9semidirect
246. C23#41⋊C9semidirect
288. C22C2×#41⋊C9semidirect
299. C2#10593123direct (N × H)

Maximal subgroups

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

subgroupindex
#105931232
C2×C22⋊(Q8⋊C9)2
C23×C3×#413
C2×#41⋊C94
C2×C4×C22⋊C94