Finite Group Databasebeta

← C2×#10590568 #11873618

Subgroups — C2×#10590568 #11873618

Order 1152.

881 conjugacy classes of subgroups; only the 212 normal subgroups are shown.

normal subgroups only

This group has 881 conjugacy classes of subgroups — too many to draw. Only its 212 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×#64099C211yesmaximal, characteristic
2C2×#63873C211yesmaximal, characteristic
3C2×C3×#810C212yesmaximal
4C2×#63566C212yesmaximal
5C2×#63555C211yesmaximal, characteristic
6#10590568C218yesmaximal, direct product factor
7C2×#4797—32nomaximal
8C22×C3×Dic6C2212yes—
9C2×C32×C4⋊C4C2211yescharacteristic
10C2×C4⋊(C3⋊Dic3)—21no—
11C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
12C2×#3750—21no—
13C2×C4×C3⋊Dic3C2211yescharacteristic
14#64099—22no—
15#64099C2214yes—
16C22×C3×C3⋊C8C2212yes—
17C2×#3724—21no—
18C2×#3724—21no—
19#63873—22no—
20#63873C2214yes—
21C3×#810C2218yes—
22#63566C2218yes—
23#63555C2214yes—
24C2×#944—32no—
25C2×#890—32no—
26C2×#890—61no—
27C2×C3×#103—32no—
28C2×#835—32no—
29C2×#816—32no—
30C2×#815—32no—
31C2×#810D312yes—
32#4797—316no—
33C22×C32×C4—21no—
34C22×C32×C4C2311yescharacteristic
35C22×C3⋊Dic3—21no—
36C22×C3⋊Dic3D411yescharacteristic
37C22×C3⋊Dic3D411yescharacteristic
38C22×C3×Dic3—22no—
39C2×C3×Dic6—24no—
40C2×C3×Dic6—24no—
41C2×C3×Dic6—22no—
42C2×C3×Dic6C2314yes—
43C32×C4⋊C4—21no—
44C32×C4⋊C4C2312yes—
45C4⋊(C3⋊Dic3)—21no—
46C4⋊(C3⋊Dic3)—24no—
47C4⋊(C3⋊Dic3)C2312yes—
48#3750—24no—
49C4×C3⋊Dic3D412yes—
50C4×C3⋊Dic3C2312yes—
51C2×C3×C3⋊C8—24no—
52C2×C3×C3⋊C8C2314yes—
53#3724—24no—
54#3724—24no—
55C2×#491—91noSylow
56C22×C3×Q8—32no—
57C22×Dic6C2×D312yes—
58C22×C3×C8—32no—
59C2×C3×C4⋊C4—21no—
60C2×C3×C4⋊C4C2×D312yes—
61#944—38no—
62#944—64no—
63C2×C4⋊Dic3—32no—
64C2×C4⋊Dic3—61no—
65C2×C4⋊Dic3—62no—
66C2×C4⋊Dic3—62no—
67C2×Dic3⋊C4—62no—
68C2×Dic3⋊C4—62no—
69C2×Dic3⋊C4—62no—
70C2×Dic3⋊C4—62no—
71C2×C4×Dic3—32no—
72C2×C4×Dic3—61no—
73C22×C3⋊C8C2×D312yes—
74#890—38no—
75#890—64no—
76#890—64no—
77#890—64no—
78C3×#103—38no—
79#835—38no—
80#816—38no—
81#815—38no—
82#810C2×D318yes—
83C23×C32C2×D411yescharacteristic
84C2×C32×C4—22no—
85C2×C32×C4—42no—
86C2×C32×C4C2×D411yescharacteristic
87C2×C32×C4#4114yes—
88C2×C32×C4C2411yescharacteristic
89C2×C3⋊Dic3—22no—
90C2×C3⋊Dic3—22no—
91C2×C3⋊Dic3—22no—
92C2×C3⋊Dic3—42no—
93C2×C3⋊Dic3C2×D412yes—
94C2×C3⋊Dic3C2×D412yes—
95C2×C3×Dic3—24no—
96C2×C3×Dic3—44no—
97C3×Dic6—24no—
98C3×Dic6—24no—
99C3×Dic6—44no—
100C3×C3⋊C8—24no—
101C2×C4⋊Q8—91no—
102C2×#125—91no—
103#491—98no—
104C2×#103—32no—
105C2×#103—92no—
106C2×#97—91no—
107C2×C3×Q8—34no—
108C2×C3×Q8—62no—
109C2×C3×Q8—64no—
110C2×C3×Q8—64no—
111C22×C3×C4—22no—
112C22×C3×C4—22no—
113C22×C3×C4—21no—
114C22×C3×C4—62no—
115C22×C3×C4C22×D312yes—
116C22×Dic3—22no—
117C22×Dic3—32no—
118C22×Dic3—32no—
119C22×Dic3—61no—
120C22×Dic3—61no—
121C22×Dic3—62no—
122C22×Dic3—62no—
123C2×Dic6—24no—
124C2×Dic6—24no—
125C2×Dic6—22no—
126C2×Dic6C22×D314yes—
127C2×C3×C8—34no—
128C2×C3×C8—64no—
129C3×C4⋊C4—22no—
130C3×C4⋊C4—22no—
131C3×C4⋊C4—22no—
132C3×C4⋊C4C22×D314yes—
133C4⋊Dic3—34no—
134C4⋊Dic3—62no—
135C4⋊Dic3—68no—
136C4⋊Dic3—68no—
137C4⋊Dic3—62no—
138C4⋊Dic3—62no—
139Dic3⋊C4—68no—
140Dic3⋊C4—68no—
141Dic3⋊C4—68no—
142Dic3⋊C4—68no—
143C4×Dic3—34no—
144C4×Dic3—34no—
145C4×Dic3—62no—
146C4×Dic3—62no—
147C2×C3⋊C8—24no—
148C2×C3⋊C8C22×D314yes—
149C22×C32#12412yes—
150C22×C32#13712yes—
151C22×C32#13712yes—
152C22×C32C22×D411yescharacteristic
153C32×C4—42no—
154C32×C4#12412yes—
155C32×C4C2×#4112yes—
156C3⋊Dic3—22no—
157C3⋊Dic3—22no—
158C3⋊Dic3—42no—
159C3×Dic3—44no—
160C22×Q8—32no—
161C22×C8—32no—
162C4⋊Q8—94no—
163C4⋊Q8—182no—
164#125—94no—
165#125—182no—
166C2×C4⋊C4—91no—
167C2×C4⋊C4—181no—
168C2×C4⋊C4—181no—
169C2×C4⋊C4—181no—
170C2×C4⋊C4—181no—
171C2×C4⋊C4D3211yescharacteristic
172C2×C42—91no—
173#103—38no—
174#103—98no—
175#97—94no—
176C23×C3—21no—
177C23×C3D3×D412yes—
178C3×Q8—64no—
179C3×Q8—64no—
180C3×Q8—124no—
181C2×C3×C4—24no—
182C2×C3×C4—24no—
183C2×C3×C4—21no—
184C2×C3×C4—24no—
185C2×C3×C4—21no—
186C2×C3×C4—44no—
187C2×C3×C4—44no—
188C2×C3×C4—64no—
189C2×C3×C4—124no—
190C2×C3×C4#23514yes—
191C2×C3×C4D3×D412yes—
192C2×C3×C4#23714yes—
193C2×C3×C4C23×D312yes—
194C2×Dic3—24no—
195C2×Dic3—34no—
196C2×Dic3—34no—
197C2×Dic3—44no—
198C2×Dic3—62no—
199C2×Dic3—62no—
200C2×Dic3—64no—
201C2×Dic3—64no—
202C2×Dic3—64no—
203C2×Dic3—64no—
204C2×Dic3—122no—
205C2×Dic3—122no—
206C2×Dic3—124no—
207C2×Dic3—124no—
208Dic6—24no—
209Dic6—24no—
210Dic6—44no—
211C3×C8—64no—
212C3⋊C8—24no—
213C2×C32#49114yescomplemented
214C2×C32C2×#12411yescharacteristic
215C2×C32C2×#13711yescharacteristic
216C2×C32C2×#13711yescharacteristic
217C2×Q8—34no—
218C2×Q8—62no—
219C2×Q8—64no—
220C2×Q8—64no—
221C22×C4—21no—
222C22×C4—62no—
223C22×C4—91no—
224C22×C4—91no—
225C22×C4—181no—
226C22×C4C2×D3211yescharacteristic
227C2×C8—34no—
228C2×C8—64no—
229C4⋊C4—21no—
230C4⋊C4—92no—
231C4⋊C4—184no—
232C4⋊C4—184no—
233C4⋊C4—184no—
234C4⋊C4—184no—
235C4⋊C4—181no—
236C4⋊C4C2×D3212yes—
237C42—92no—
238C42—92no—
239C22×C3—21no—
240C22×C3—22no—
241C22×C3—22no—
242C22×C3—22no—
243C22×C3#88514yes—
244C22×C3#91514yes—
245C22×C3#91814yes—
246C22×C3C2×D3×D412yes—
247C3×C4—22no—
248C3×C4—22no—
249C3×C4—44no—
250C3×C4—44no—
251C3×C4—124no—
252C3×C4#88514yes—
253C3×C4C2×#23512yes—
254C3×C4C2×#23712yes—
255Dic3—44no—
256Dic3—64no—
257Dic3—64no—
258Dic3—122no—
259Dic3—122no—
260Dic3—124no—
261Dic3—124no—
262C32C2×#49111yescharacteristic, complemented, Sylow
263C23#381111yescharacteristic
264Q8—64no—
265Q8—64no—
266Q8—124no—
267C2×C4—22no—
268C2×C4—42no—
269C2×C4—64no—
270C2×C4—92no—
271C2×C4—92no—
272C2×C4—124no—
273C2×C4—182no—
274C2×C4—182no—
275C2×C4—182no—
276C2×C4—362no—
277C2×C4#379514yes—
278C2×C4#381111yescharacteristic
279C2×C4C22×D3211yescharacteristic
280C8—64no—
281C2×C3—21no—
282C2×C3—21no—
283C2×C3—24no—
284C2×C3—21no—
285C2×C3#479718yescomplemented
286C2×C3C2×#88512yes—
287C2×C3C2×#91512yes—
288C2×C3C2×#91812yes—
289C22#6391312yes—
290C22#6393112yes—
291C22#6394512yes—
292C22C2×#381111yescharacteristic
293C4—42no—
294C4—124no—
295C4—182no—
296C4—182no—
297C4—362no—
298C4#6391312yes—
299C4C2×#379512yes—
300C3—21no—
301C3C2×#479712yescomplemented
302C2#1059056814yesdirect product factor
303C2C2×#6391311yescharacteristic
304C2C2×#6393111yescharacteristic
305C2C2×#6394511yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socle, prime radicalC23×C32C2×D4
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#491
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
6. #10590568C2direct (N × H)
213. C2×C32#491semidirect
262. C32C2×#491semidirect
285. C2×C3#4797semidirect
301. C3C2×#4797semidirect
302. C2#10590568direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640992
C2×#638732
C2×C3×#8102
C2×#635662
C2×#635552
#105905682
C2×#47973