Finite Group Databasebeta

← C2×#10595421 #11903730

Subgroups — C2×#10595421 #11903730

Order 1152.

2369 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64153C211yesmaximal, characteristic
2C2×C3×#944C212yesmaximal
3#10595421C2116yesmaximal, direct product factor
4C2×#63840C212yesmaximal
5C2×#63839C214yesmaximal
6C2×#63838C212yesmaximal
7C2×#63837C214yesmaximal
8C2×#5722—32nomaximal
9C22×C32×Q8C2211yescharacteristic
10C22×#634C2211yescharacteristic
11C22×C3×Dic6C2212yes—
12C22×#627C2212yes—
13C22×#627C2212yes—
14#64153C2218yes—
15C2×#3750C2214yes—
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C3×#944C22116yes—
18C2×C3×Dic3⋊C4C2214yes—
19C2×C3×Dic3⋊C4C2214yes—
20C2×C3×C4×Dic3C2212yes—
21C2×#3724C2212yes—
22C2×Dic3⋊Dic3C2214yes—
23C2×Dic32C2212yes—
24C2×Dic32C2214yes—
25#63840C22116yes—
26#63839C22132yes—
27#63838C22116yes—
28#63837C22132yes—
29C2×C3×C4⋊Q8—32no—
30C2×#944—32no—
31C2×#944—34no—
32C2×#944—61no—
33C2×#944D312yes—
34#5722—332no—
35C2×#888—34no—
36C2×#888—34no—
37C2×#887—34no—
38C2×#887—34no—
39C2×C4×Dic6—34no—
40C2×C32×Q8—42no—
41C2×C32×Q8C2314yes—
42C22×C32×C4C2312yes—
43C22×C32×C4C2311yescharacteristic
44C22×C3⋊Dic3C2312yes—
45C22×C3⋊Dic3C2312yes—
46C2×#634—42no—
47C2×#634C2314yes—
48C22×C3×Dic3C2314yes—
49C22×C3×Dic3C2314yes—
50C2×C3×Dic6—44no—
51C2×C3×Dic6C2318yes—
52C2×#627—44no—
53C2×#627Q8116yescomplemented
54C2×#627C2318yes—
55C2×#627C2318yes—
56#3750C23116yes—
57C4×C3⋊Dic3C2314yes—
58C3×Dic3⋊C4C23116yes—
59C3×Dic3⋊C4C23116yes—
60C3×C4×Dic3C2318yes—
61#3724C2318yes—
62Dic3⋊Dic3C23116yes—
63Dic32C2318yes—
64Dic32C23116yes—
65C2×Q82—91noSylow
66C22×C3×Q8—21no—
67C22×C3×Q8—32no—
68C22×C3×Q8C2×D312yes—
69C22×Dic6—34no—
70C22×Dic6—32no—
71C22×Dic6—34no—
72C22×Dic6—61no—
73C22×Dic6C2×D312yes—
74C3×C4⋊Q8—316no—
75C2×C3×C4⋊C4—34no—
76C2×C3×C4⋊C4—34no—
77C2×C3×C42—32no—
78#944—316no—
79#944—332no—
80#944—68no—
81#944C2×D3116yes—
82C2×C4⋊Dic3—34no—
83C2×Dic3⋊C4—34no—
84C2×Dic3⋊C4—34no—
85C2×Dic3⋊C4—34no—
86C2×Dic3⋊C4—34no—
87C2×Dic3⋊C4—64no—
88C2×Dic3⋊C4C2×D314yes—
89C2×Dic3⋊C4C2×D314yes—
90C2×C4×Dic3—32no—
91C2×C4×Dic3—34no—
92C2×C4×Dic3—34no—
93C2×C4×Dic3—34no—
94C2×C4×Dic3—61no—
95C2×C4×Dic3C2×D312yes—
96#888—332no—
97#888—332no—
98#887—332no—
99#887—332no—
100C4×Dic6—332no—
101C23×C32C2411yescharacteristic
102C32×Q8—44no—
103C2×C32×C4—22no—
104C2×C32×C4—24no—
105C2×C32×C4C2414yes—
106C2×C32×C4C2412yes—
107C2×C3⋊Dic3—24no—
108C2×C3⋊Dic3C2×Q818yes—
109C2×C3⋊Dic3C2414yes—
110C2×C3⋊Dic3C2414yes—
111#634—44no—
112C2×C3×Dic3—28no—
113C2×C3×Dic3C2×Q8116yes—
114C2×C3×Dic3C2418yes—
115C2×C3×Dic3C2418yes—
116C3×Dic6—48no—
117#627—48no—
118#627C2×Q8132yescomplemented
119Q82—916no—
120C2×C4⋊Q8—32no—
121C2×C4⋊Q8—92no—
122C2×C4⋊Q8—94no—
123C2×C4⋊Q8—91no—
124C2×C4×Q8—94no—
125C2×C4×Q8—92no—
126C2×C3×Q8—24no—
127C2×C3×Q8—38no—
128C2×C3×Q8—44no—
129C2×C3×Q8—44no—
130C2×C3×Q8—124no—
131C2×C3×Q8C22×D318yes—
132C22×C3×C4—21no—
133C22×C3×C4—22no—
134C22×C3×C4—34no—
135C22×C3×C4—34no—
136C22×C3×C4C22×D312yes—
137C22×C3×C4C22×D312yes—
138C22×C3×C4C22×D312yes—
139C22×Dic3—34no—
140C22×Dic3—34no—
141C22×Dic3—62no—
142C22×Dic3—62no—
143C22×Dic3C22×D314yes—
144C22×Dic3C22×D314yes—
145C2×Dic6—332no—
146C2×Dic6—316no—
147C2×Dic6—38no—
148C2×Dic6—316no—
149C2×Dic6—44no—
150C2×Dic6—64no—
151C2×Dic6—128no—
152C2×Dic6—124no—
153C2×Dic6—124no—
154C2×Dic6C22×D318yes—
155C3×C4⋊C4—316no—
156C3×C4⋊C4—316no—
157C3×C42—38no—
158C4⋊Dic3—316no—
159Dic3⋊C4—316no—
160Dic3⋊C4—316no—
161Dic3⋊C4—316no—
162Dic3⋊C4—316no—
163Dic3⋊C4—616no—
164Dic3⋊C4C22×D3116yes—
165Dic3⋊C4C22×D3116yes—
166C4×Dic3—38no—
167C4×Dic3—316no—
168C4×Dic3—316no—
169C4×Dic3—316no—
170C4×Dic3—64no—
171C4×Dic3C22×D318yes—
172C22×C32C22×Q814yes—
173C22×C32H(5,𝔽2)12yes—
174C22×C32C2511yescharacteristic
175C32×C4—22no—
176C32×C4—24no—
177C3⋊Dic3—24no—
178C3⋊Dic3C22×Q818yes—
179C3×Dic3—28no—
180C3×Dic3C22×Q8116yes—
181C22×Q8—32no—
182C22×Q8—92no—
183C22×Q8—92no—
184C22×Q8—91no—
185C22×Q8D3211yescharacteristic
186C4⋊Q8—316no—
187C4⋊Q8—916no—
188C4⋊Q8—932no—
189C4⋊Q8—98no—
190C4×Q8—932no—
191C4×Q8—916no—
192C2×C4⋊C4—34no—
193C2×C4⋊C4—34no—
194C2×C4⋊C4—92no—
195C2×C4⋊C4—94no—
196C2×C4⋊C4—94no—
197C2×C42—32no—
198C2×C42—92no—
199C2×C42—94no—
200C2×C42—91no—
201C23×C3—21no—
202C23×C3C23×D312yes—
203C3×Q8—48no—
204C3×Q8—48no—
205C3×Q8—128no—
206C2×C3×C4—24no—
207C2×C3×C4—24no—
208C2×C3×C4—24no—
209C2×C3×C4—24no—
210C2×C3×C4—22no—
211C2×C3×C4—24no—
212C2×C3×C4—316no—
213C2×C3×C4—38no—
214C2×C3×C4—38no—
215C2×C3×C4—44no—
216C2×C3×C4—68no—
217C2×C3×C4C23×D314yes—
218C2×C3×C4C23×D314yes—
219C2×C3×C4C23×D314yes—
220C2×Dic3—28no—
221C2×Dic3—316no—
222C2×Dic3—38no—
223C2×Dic3—38no—
224C2×Dic3—68no—
225C2×Dic3—64no—
226C2×Dic3—64no—
227C2×Dic3—68no—
228C2×Dic3—124no—
229C2×Dic3D3×Q8116yes—
230C2×Dic3C23×D318yes—
231C2×Dic3C23×D318yes—
232Dic6—364no—
233Dic6—48no—
234Dic6—1216no—
235Dic6—128no—
236Dic6—128no—
237C2×C32Q8214yescomplemented
238C2×C32C23×Q812yes—
239C2×C32C2×H(5,𝔽2)11yescharacteristic
240C2×Q8—38no—
241C2×Q8—42no—
242C2×Q8—98no—
243C2×Q8—916no—
244C2×Q8—98no—
245C2×Q8—94no—
246C2×Q8—124no—
247C2×Q8—362no—
248C2×Q8—364no—
249C2×Q8C2×D3214yes—
250C22×C4—34no—
251C22×C4—34no—
252C22×C4—92no—
253C22×C4—92no—
254C22×C4C2×D3212yes—
255C22×C4C2×D3211yescharacteristic
256C4⋊C4—316no—
257C4⋊C4—316no—
258C4⋊C4—98no—
259C4⋊C4—916no—
260C4⋊C4—916no—
261C42—38no—
262C42—98no—
263C42—916no—
264C42—94no—
265C22×C3—24no—
266C22×C3—22no—
267C22×C3—21no—
268C22×C3#100414yes—
269C22×C3C2×D3×Q818yes—
270C22×C3C24×D312yes—
271C3×C4—24no—
272C3×C4—24no—
273C3×C4—24no—
274C3×C4—24no—
275C3×C4—316no—
276C3×C4—44no—
277C3×C4—68no—
278Dic3—28no—
279Dic3—316no—
280Dic3—68no—
281Dic3—68no—
282Dic3—124no—
283Dic3C2×D3×Q8116yes—
284C32C2×Q8211yescharacteristic, complemented, Sylow
285C23C22×D3211yescharacteristic
286Q8—44no—
287Q8—932no—
288Q8—128no—
289Q8—364no—
290Q8—368no—
291C2×C4—24no—
292C2×C4—22no—
293C2×C4—316no—
294C2×C4—38no—
295C2×C4—38no—
296C2×C4—68no—
297C2×C4—98no—
298C2×C4—94no—
299C2×C4—94no—
300C2×C4—184no—
301C2×C4C22×D3214yes—
302C2×C4C22×D3212yes—
303C2×C3—22no—
304C2×C3—24no—
305C2×C3—21no—
306C2×C3#572218yescomplemented
307C2×C3C2×#100412yes—
308C2×C3C22×D3×Q814yes—
309C22D32×Q814yes—
310C22#6433012yes—
311C22C23×D3211yescharacteristic
312C4—24no—
313C4—22no—
314C4—316no—
315C4—68no—
316C4—98no—
317C4—184no—
318C3—21no—
319C3C2×#572212yescomplemented
320C2#1059542114yesdirect product factor
321C2C2×D32×Q812yes—
322C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×Q8C22
socle, prime radicalC23×C32C24
hypercenterC22×Q8D32
hypocenterC32C2×Q82
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
3. #10595421C2direct (N × H)
53. C2×#627Q8semidirect
118. #627C2×Q8semidirect
237. C2×C32Q82semidirect
284. C32C2×Q82semidirect
306. C2×C3#5722semidirect
319. C3C2×#5722semidirect
320. C2#10595421direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641532
C2×C3×#9442
#105954212
C2×#638402
C2×#638392
C2×#638382
C2×#638372
C2×#57223