Finite Group Databasebeta

← C2×#10596192 #11903667

Subgroups — C2×#10596192 #11903667

Order 1152.

3144 conjugacy classes of subgroups.

The subgroup lattice has 294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4⋊Q8C211yesmaximal, characteristic
2C2×Q8×C3⋊Dic3C212yesmaximal
3C2×#64153C212yesmaximal
4#10596192C2116yesmaximal, direct product factor
5C2×#64099C212yesmaximal
6C2×#64098C214yesmaximal
7C2×#64096C212yesmaximal
8C2×C4×#634C211yesmaximal, characteristic
9C2×C4×#634C211yesmaximal, characteristic
10C2×#5721—34nomaximal
11C22×C32×Q8C2212yes—
12C22×#634C2211yescharacteristic
13C22×#634C2211yescharacteristic
14C32×C4⋊Q8C2218yes—
15C2×C32×C4⋊C4C2212yes—
16C2×C32×C4⋊C4C2212yes—
17C2×C32×C42C2211yescharacteristic
18Q8×C3⋊Dic3C22116yes—
19#64153C22116yes—
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2214yes—
23C2×#3750C2212yes—
24C2×#3750C2212yes—
25C2×#3750C2214yes—
26C2×#3750C2214yes—
27C2×C4×C3⋊Dic3C2212yes—
28C2×C4×C3⋊Dic3C2212yes—
29C2×C4×C3⋊Dic3C2214yes—
30#64099C22116yes—
31#64098C22132yes—
32#64096C22116yes—
33C4×#634C2218yes—
34C4×#634C2218yes—
35C2×C3×C4⋊Q8D314yes—
36C2×Q8×Dic3—38no—
37C2×#944—38no—
38#5721—364no—
39C2×#890—38no—
40C2×#889—316no—
41C2×#887—38no—
42C2×C4×Dic6—34no—
43C2×C4×Dic6—34no—
44C2×C32×Q8—28no—
45C2×C32×Q8C2318yes—
46C22×C32×C4C2314yes—
47C22×C32×C4C2311yescharacteristic
48C22×C32×C4C2311yescharacteristic
49C22×C32×C4C2311yescharacteristic
50C22×C3⋊Dic3C2312yes—
51C22×C3⋊Dic3C2312yes—
52C22×C3⋊Dic3C2312yes—
53C22×C3⋊Dic3C2312yes—
54C2×#634—24no—
55C2×#634Q818yescomplemented
56C2×#634C2314yes—
57C2×#634C2314yes—
58C32×C4⋊C4C2318yes—
59C32×C4⋊C4C2318yes—
60C32×C42C2314yes—
61C4⋊(C3⋊Dic3)C2314yes—
62C4⋊(C3⋊Dic3)C2314yes—
63C4⋊(C3⋊Dic3)C23116yes—
64#3750C2318yes—
65#3750C2318yes—
66#3750C23116yes—
67#3750C23116yes—
68C4×C3⋊Dic3C2318yes—
69C4×C3⋊Dic3C2318yes—
70C4×C3⋊Dic3C23116yes—
71C2×#557—91noSylow
72C22×C3×Q8C2×D318yes—
73C22×Dic6—34no—
74C22×Dic6—34no—
75C3×C4⋊Q8C2×D3132yes—
76C2×C3×C4⋊C4C2×D318yes—
77C2×C3×C4⋊C4C2×D318yes—
78C2×C3×C42C2×D314yes—
79Q8×Dic3—364no—
80#944—364no—
81C2×C4⋊Dic3—34no—
82C2×C4⋊Dic3—34no—
83C2×C4⋊Dic3—316no—
84C2×Dic3⋊C4—38no—
85C2×Dic3⋊C4—38no—
86C2×Dic3⋊C4—316no—
87C2×Dic3⋊C4—316no—
88C2×C4×Dic3—38no—
89C2×C4×Dic3—38no—
90C2×C4×Dic3—316no—
91#890—364no—
92#889—3128no—
93#887—364no—
94C4×Dic6—332no—
95C4×Dic6—332no—
96C23×C32C2411yescharacteristic
97C32×Q8—216no—
98C2×C32×C4—28no—
99C2×C32×C4—22no—
100C2×C32×C4C2×Q814yes—
101C2×C32×C4#4114yes—
102C2×C32×C4C2418yes—
103C2×C32×C4C2412yes—
104C2×C32×C4C2412yes—
105C2×C32×C4C2412yes—
106C2×C3⋊Dic3—24no—
107C2×C3⋊Dic3—24no—
108C2×C3⋊Dic3—24no—
109C2×C3⋊Dic3C2×Q818yes—
110C2×C3⋊Dic3C2414yes—
111C2×C3⋊Dic3C2414yes—
112C2×C3⋊Dic3C2414yes—
113C2×C3⋊Dic3C2414yes—
114#634—28no—
115#634C2×Q8116yescomplemented
116#557—916no—
117C2×C4⋊Q8—92no—
118C2×C4⋊Q8C3⋊D311yescharacteristic
119C2×#125—94no—
120C2×#125—92no—
121C2×C4×Q8—92no—
122C2×C4×Q8—92no—
123C2×C4×Q8—91no—
124C2×C4×Q8—91no—
125C2×C3×Q8—232no—
126C2×C3×Q8C22×D3132yes—
127C22×C3×C4C22×D3116yes—
128C22×C3×C4C22×D314yes—
129C22×C3×C4C22×D314yes—
130C22×C3×C4C22×D314yes—
131C22×Dic3—38no—
132C22×Dic3—38no—
133C22×Dic3—38no—
134C22×Dic3—38no—
135C2×Dic6—332no—
136C2×Dic6—316no—
137C2×Dic6—316no—
138C2×Dic6—616no—
139C3×C4⋊C4C22×D3132yes—
140C3×C4⋊C4C22×D3132yes—
141C3×C42C22×D3116yes—
142C4⋊Dic3—316no—
143C4⋊Dic3—316no—
144C4⋊Dic3—364no—
145Dic3⋊C4—332no—
146Dic3⋊C4—332no—
147Dic3⋊C4—364no—
148Dic3⋊C4—364no—
149C4×Dic3—332no—
150C4×Dic3—332no—
151C4×Dic3—364no—
152C22×C32C22×Q812yes—
153C22×C32C2×#4112yes—
154C22×C322−1+412yes—
155C22×C32C2511yescharacteristic
156C32×C4—28no—
157C32×C4—22no—
158C32×C4C22×Q814yes—
159C32×C4C2×#4114yes—
160C3⋊Dic3—24no—
161C3⋊Dic3—24no—
162C3⋊Dic3—24no—
163C3⋊Dic3C22×Q818yes—
164C22×Q8—91no—
165C22×Q8—91no—
166C22×Q8C2×C3⋊D312yes—
167C4⋊Q8—916no—
168C4⋊Q8C2×C3⋊D318yes—
169#125—932no—
170#125—916no—
171C4×Q8—916no—
172C4×Q8—916no—
173C4×Q8—98no—
174C4×Q8—98no—
175C2×C4⋊C4—91no—
176C2×C4⋊C4—92no—
177C2×C4⋊C4—92no—
178C2×C4⋊C4—94no—
179C2×C4⋊C4—91no—
180C2×C4⋊C4—94no—
181C2×C4⋊C4—94no—
182C2×C4⋊C4C2×C3⋊D312yes—
183C2×C4⋊C4C2×C3⋊D312yes—
184C2×C42—94no—
185C2×C42—92no—
186C2×C42—92no—
187C2×C42C2×C3⋊D311yescharacteristic
188C23×C3C23×D314yes—
189C3×Q8—264no—
190C2×C3×C4—232no—
191C2×C3×C4—28no—
192C2×C3×C4#237116yes—
193C2×C3×C4D3×Q8116yes—
194C2×C3×C4C23×D3132yes—
195C2×C3×C4C23×D318yes—
196C2×C3×C4C23×D318yes—
197C2×C3×C4C23×D318yes—
198C2×Dic3—332no—
199C2×Dic3—316no—
200C2×Dic3—316no—
201C2×Dic3—316no—
202C2×Dic3—316no—
203C2×Dic3—616no—
204C2×Dic3—616no—
205C2×Dic3—616no—
206Dic6—364no—
207Dic6—632no—
208C2×C32#55714yescomplemented
209C2×C32C23×Q811yescharacteristic
210C2×C32C22×#4111yescharacteristic
211C2×C32C2×2−1+411yescharacteristic
212C2×Q8—28no—
213C2×Q8—94no—
214C2×Q8—94no—
215C2×Q8—98no—
216C2×Q8—184no—
217C2×Q8C22×C3⋊D318yes—
218C22×C4—92no—
219C22×C4—92no—
220C22×C4—92no—
221C22×C4—92no—
222C22×C4C22×C3⋊D314yes—
223C22×C4C22×C3⋊D311yescharacteristic
224C22×C4C22×C3⋊D311yescharacteristic
225C22×C4C22×C3⋊D311yescharacteristic
226C4⋊C4—94no—
227C4⋊C4—98no—
228C4⋊C4—98no—
229C4⋊C4—916no—
230C4⋊C4—94no—
231C4⋊C4—916no—
232C4⋊C4—916no—
233C4⋊C4C22×C3⋊D318yes—
234C4⋊C4C22×C3⋊D318yes—
235C42—916no—
236C42—98no—
237C42—98no—
238C42C22×C3⋊D314yes—
239C22×C3C2×#23718yes—
240C22×C3C2×D3×Q818yes—
241C22×C3#100718yes—
242C22×C3C24×D314yes—
243C3×C4—232no—
244C3×C4—28no—
245C3×C4C2×#237116yes—
246C3×C4C2×D3×Q8116yes—
247Dic3—332no—
248Dic3—616no—
249Dic3—616no—
250Dic3—616no—
251C32C2×#55711yescharacteristic, complemented, Sylow
252C23C23×C3⋊D311yescharacteristic
253Q8—216no—
254Q8—916no—
255Q8—188no—
256C2×C4—28no—
257C2×C4—22no—
258C2×C4—98no—
259C2×C4—94no—
260C2×C4—94no—
261C2×C4—94no—
262C2×C4—94no—
263C2×C4—184no—
264C2×C4—184no—
265C2×C4—184no—
266C2×C4#383014yes—
267C2×C4Q8×C3⋊D314yes—
268C2×C4C23×C3⋊D318yes—
269C2×C4C23×C3⋊D312yes—
270C2×C4C23×C3⋊D312yes—
271C2×C4C23×C3⋊D312yes—
272C2×C3#5721116yescomplemented
273C2×C3C22×#23714yes—
274C2×C3C22×D3×Q814yes—
275C2×C3C2×#100714yes—
276C22C2×#383012yes—
277C22C2×Q8×C3⋊D312yes—
278C22#6436412yes—
279C22C24×C3⋊D311yescharacteristic
280C4—28no—
281C4—22no—
282C4—98no—
283C4—184no—
284C4—184no—
285C4—184no—
286C4C2×#383014yes—
287C4C2×Q8×C3⋊D314yes—
288C3C2×#572114yescomplemented
289C2#1059619214yesdirect product factor
290C2C22×#383011yescharacteristic
291C2C22×Q8×C3⋊D311yescharacteristic
292C2C2×#6436411yescharacteristic
subgroupG/H
centerC23C23×C3⋊D3
commutator, cosocleC22×C32C25
FrattiniC22C24×C3⋊D3
FittingC2×C32×C4⋊Q8C2
socle, prime radicalC23×C32C24
hypercenterC2×C4⋊Q8C3⋊D3
hypocenterC32C2×#557
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
4. #10596192C2direct (N × H)
55. C2×#634Q8semidirect
115. #634C2×Q8semidirect
208. C2×C32#557semidirect
251. C32C2×#557semidirect
272. C2×C3#5721semidirect
288. C3C2×#5721semidirect
289. C2#10596192direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C4⋊Q82
C2×Q8×C3⋊Dic32
C2×#641532
#105961922
C2×#640992
C2×#640982
C2×#640962
C2×C4×#6342
C2×#57213