Finite Group Databasebeta

← C2×#10590901 #11873405

Subgroups — C2×#10590901 #11873405

Order 1152.

929 conjugacy classes of subgroups; only the 228 normal subgroups are shown.

normal subgroups only

This group has 929 conjugacy classes of subgroups — too many to draw. Only its 228 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
1C2×#63919C211yesmaximal, characteristic
2C2×#63873C211yesmaximal, characteristic
3C2×C8×C3⋊Dic3C211yesmaximal, characteristic
4C2×C3×#816C212yesmaximal
5C2×#63565C212yesmaximal
6#10590901C218yesmaximal, direct product factor
7C2×#4792—32nomaximal
8C22×C3×Dic6C2212yes—
9C22×#627—21no—
10C22×C32×C8C2211yescharacteristic
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C2×C3×C4⋊Dic3C2212yes—
14C2×#3724—21no—
15C2×#3724—21no—
16C2×#3724—21no—
17#63919—22no—
18#63919C2214yes—
19#63873—22no—
20#63873C2214yes—
21C8×C3⋊Dic3C2214yes—
22C3×#816C2218yes—
23#63565C2218yes—
24C2×#944—32no—
25C2×#888—32no—
26C2×C3×#103—32no—
27C2×#835—32no—
28C2×#816D312yes—
29C2×C8×Dic3—32no—
30C2×C8×Dic3—61no—
31C2×#810—32no—
32#4792—316no—
33C22×C32×C4C2311yescharacteristic
34C22×C3⋊Dic3D411yescharacteristic
35C22×C3⋊Dic3D411yescharacteristic
36C22×C3×Dic3—22no—
37C22×C3×Dic3—22no—
38C2×C3×Dic6—24no—
39C2×C3×Dic6—24no—
40C2×C3×Dic6—22no—
41C2×C3×Dic6C2314yes—
42C2×#627—24no—
43C2×#627—44no—
44C2×C32×C8—22no—
45C2×C32×C8C2312yes—
46C4×C3⋊Dic3D412yes—
47C4×C3⋊Dic3C2312yes—
48C2×C3⋊(C3⋊C8)—22no—
49C2×C3⋊(C3⋊C8)C2312yes—
50C3×C4⋊Dic3—22no—
51C3×C4⋊Dic3C2314yes—
52#3724—24no—
53#3724—24no—
54#3724—24no—
55C2×#487—91noSylow
56C22×C3×Q8—32no—
57C22×Dic6—62no—
58C22×Dic6C2×D312yes—
59C22×C3×C8—21no—
60C22×C3×C8C2×D312yes—
61C2×C3×C4⋊C4—32no—
62#944—38no—
63#944—64no—
64C2×C4⋊Dic3C2×D312yes—
65C2×Dic3⋊C4—62no—
66C2×Dic3⋊C4—62no—
67C2×Dic3⋊C4—62no—
68C2×C4×Dic3—32no—
69C2×C4×Dic3—61no—
70C22×C3⋊C8—32no—
71C22×C3⋊C8—61no—
72#888—38no—
73#888—64no—
74C3×#103—38no—
75#835—38no—
76#816C2×D318yes—
77C8×Dic3—38no—
78C8×Dic3—64no—
79#810—38no—
80C23×C32C2×D411yescharacteristic
81C2×C32×C4C2×D411yescharacteristic
82C2×C32×C4#4112yes—
83C2×C32×C4#4112yes—
84C2×C32×C4C2411yescharacteristic
85C2×C3⋊Dic3SD1614yes—
86C2×C3⋊Dic3Q1614yes—
87C2×C3⋊Dic3C2×D412yes—
88C2×C3⋊Dic3C2×D412yes—
89C2×C3×Dic3—24no—
90C2×C3×Dic3—24no—
91C2×C3×Dic3—44no—
92C2×C3×Dic3—44no—
93C3×Dic6—24no—
94C3×Dic6—24no—
95C3×Dic6—44no—
96#627—48no—
97C32×C8—22no—
98C3⋊(C3⋊C8)—22no—
99C2×C4⋊Q8—91no—
100C2×C4⋊Q8—91no—
101#487—98no—
102C2×#103—32no—
103C2×#103—92no—
104C2×C4×C8—91no—
105C2×C3×Q8—34no—
106C2×C3×Q8—62no—
107C2×C3×Q8—64no—
108C2×C3×Q8—64no—
109C22×C3×C4—21no—
110C22×C3×C4—62no—
111C22×C3×C4—62no—
112C22×C3×C4C22×D312yes—
113C22×Dic3—22no—
114C22×Dic3—22no—
115C22×Dic3—32no—
116C22×Dic3—32no—
117C22×Dic3—61no—
118C22×Dic3—61no—
119C2×Dic6—24no—
120C2×Dic6—24no—
121C2×Dic6—22no—
122C2×Dic6—68no—
123C2×Dic6—128no—
124C2×Dic6C22×D314yes—
125C2×C3×C8—24no—
126C2×C3×C8—24no—
127C2×C3×C8—22no—
128C2×C3×C8C22×D314yes—
129C3×C4⋊C4—34no—
130C3×C4⋊C4—62no—
131C4⋊Dic3—22no—
132C4⋊Dic3C22×D314yes—
133Dic3⋊C4—68no—
134Dic3⋊C4—68no—
135Dic3⋊C4—68no—
136C4×Dic3—34no—
137C4×Dic3—34no—
138C4×Dic3—62no—
139C4×Dic3—62no—
140C2×C3⋊C8—34no—
141C2×C3⋊C8—62no—
142C2×C3⋊C8—64no—
143C2×C3⋊C8—64no—
144C22×C32#12412yes—
145C22×C32C2×SD1612yes—
146C22×C32C2×Q1612yes—
147C22×C32C22×D411yescharacteristic
148C32×C4#12412yes—
149C32×C4C2×#4111yescharacteristic
150C32×C4C2×#4111yescharacteristic
151C3⋊Dic3C2×SD1614yes—
152C3⋊Dic3C2×Q1614yes—
153C3×Dic3—44no—
154C3×Dic3—44no—
155C22×Q8—32no—
156C22×Q8—181no—
157C22×C8—91no—
158C22×C8D3211yescharacteristic
159C4⋊Q8—94no—
160C4⋊Q8—94no—
161C4⋊Q8—182no—
162C4⋊Q8—182no—
163C2×C4⋊C4—32no—
164C2×C4⋊C4—181no—
165C2×C4⋊C4—181no—
166C2×C4⋊C4—181no—
167C2×C42—91no—
168#103—38no—
169#103—98no—
170C4×C8—94no—
171C23×C3—21no—
172C23×C3D3×D412yes—
173C3×Q8—64no—
174C3×Q8—64no—
175C3×Q8—124no—
176C2×C3×C4—21no—
177C2×C3×C4—22no—
178C2×C3×C4—21no—
179C2×C3×C4—22no—
180C2×C3×C4—64no—
181C2×C3×C4—64no—
182C2×C3×C4—124no—
183C2×C3×C4—124no—
184C2×C3×C4#23514yes—
185C2×C3×C4D3×D412yes—
186C2×C3×C4#23714yes—
187C2×C3×C4C23×D312yes—
188C2×Dic3—24no—
189C2×Dic3—24no—
190C2×Dic3—38no—
191C2×Dic3—38no—
192C2×Dic3—34no—
193C2×Dic3—34no—
194C2×Dic3—44no—
195C2×Dic3—44no—
196C2×Dic3—64no—
197C2×Dic3—64no—
198C2×Dic3—62no—
199C2×Dic3—62no—
200Dic6—24no—
201Dic6—24no—
202Dic6—44no—
203Dic6—1216no—
204C3×C8—24no—
205C3×C8—24no—
206C3⋊C8—64no—
207C3⋊C8—64no—
208C2×C32#48714yescomplemented
209C2×C32C2×#12411yescharacteristic
210C2×C32C22×SD1611yescharacteristic
211C2×C32C22×Q1611yescharacteristic
212C2×Q8—34no—
213C2×Q8—62no—
214C2×Q8—64no—
215C2×Q8—64no—
216C2×Q8—184no—
217C2×Q8—364no—
218C22×C4—62no—
219C22×C4—62no—
220C22×C4—91no—
221C22×C4—91no—
222C22×C4C2×D3211yescharacteristic
223C2×C8—22no—
224C2×C8—92no—
225C2×C8—182no—
226C2×C8C2×D3212yes—
227C4⋊C4—34no—
228C4⋊C4—62no—
229C4⋊C4—184no—
230C4⋊C4—184no—
231C4⋊C4—184no—
232C42—92no—
233C42—92no—
234C22×C3—21no—
235C22×C3—22no—
236C22×C3—22no—
237C22×C3—22no—
238C22×C3#88514yes—
239C22×C3D3×SD1614yes—
240C22×C3D3×Q1614yes—
241C22×C3C2×D3×D412yes—
242C3×C4—21no—
243C3×C4—21no—
244C3×C4—22no—
245C3×C4—124no—
246C3×C4—124no—
247C3×C4#88514yes—
248C3×C4C2×#23512yes—
249C3×C4C2×#23712yes—
250Dic3—38no—
251Dic3—38no—
252Dic3—44no—
253Dic3—44no—
254Dic3—64no—
255Dic3—64no—
256C32C2×#48711yescharacteristic, complemented, Sylow
257C23#380211yescharacteristic
258Q8—64no—
259Q8—64no—
260Q8—124no—
261Q8—368no—
262C2×C4—64no—
263C2×C4—64no—
264C2×C4—92no—
265C2×C4—92no—
266C2×C4—94no—
267C2×C4—94no—
268C2×C4—124no—
269C2×C4—124no—
270C2×C4#379812yes—
271C2×C4#380211yescharacteristic
272C2×C4#380512yes—
273C2×C4C22×D3211yescharacteristic
274C8—22no—
275C8—182no—
276C2×C3—21no—
277C2×C3—21no—
278C2×C3—24no—
279C2×C3—21no—
280C2×C3#479218yescomplemented
281C2×C3C2×#88512yes—
282C2×C3C2×D3×SD1612yes—
283C2×C3C2×D3×Q1612yes—
284C22#6379612yes—
285C22#6380212yes—
286C22#6391512yes—
287C22C2×#380211yescharacteristic
288C4—94no—
289C4—94no—
290C4—124no—
291C4—124no—
292C4#6391512yes—
293C4C2×#379811yescharacteristic
294C4C2×#380511yescharacteristic
295C3—21no—
296C3C2×#479212yescomplemented
297C2#1059090114yesdirect product factor
298C2C2×#6379611yescharacteristic
299C2C2×#6380211yescharacteristic
300C2C2×#6391511yescharacteristic
subgroupG/H
centerC23#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socle, prime radicalC23×C32C2×D4
hypercenterC22×C8D32
hypocenterC32C2×#487
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
6. #10590901C2direct (N × H)
208. C2×C32#487semidirect
256. C32C2×#487semidirect
280. C2×C3#4792semidirect
296. C3C2×#4792semidirect
297. C2#10590901direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#639192
C2×#638732
C2×C8×C3⋊Dic32
C2×C3×#8162
C2×#635652
#105909012
C2×#47923