Finite Group Databasebeta

← C2×#10590415 #11874954

Subgroups — C2×#10590415 #11874954

Order 1152.

993 conjugacy classes of subgroups; only the 260 normal subgroups are shown.

normal subgroups only

This group has 993 conjugacy classes of subgroups — too many to draw. Only its 260 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×#64097C211yesmaximal, characteristic
2C2×#63919C211yesmaximal, characteristic
3C2×C3×#807C212yesmaximal
4C2×#63575C212yesmaximal
5C2×#63553C211yesmaximal, characteristic
6#10590415C218yesmaximal, direct product factor
7C2×#4874—32nomaximal
8C22×#634—21no—
9C22×#627—21no—
10C2×C32×C4⋊C4C2211yescharacteristic
11C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
12C2×#3750—21no—
13C2×C4×C3⋊Dic3C2211yescharacteristic
14#64097—22no—
15#64097C2214yes—
16C2×C3×C4⋊Dic3C2212yes—
17C22×C3×C3⋊C8C2212yes—
18C2×#3724—21no—
19#63919—22no—
20#63919C2214yes—
21C3×#807C2218yes—
22#63575C2218yes—
23#63553C2214yes—
24C2×#888—32no—
25C2×#888—32no—
26C2×#888—61no—
27C2×C3×#107—32no—
28C2×#818—32no—
29C2×C8×Dic3—32no—
30C2×#807—32no—
31C2×#807D312yes—
32#4874—316no—
33C22×C32×C4—21no—
34C22×C32×C4C2311yescharacteristic
35C22×C3⋊Dic3—21no—
36C22×C3⋊Dic3D411yescharacteristic
37C22×C3⋊Dic3D411yescharacteristic
38C2×#634—24no—
39C2×#634—44no—
40C22×C3×Dic3—22no—
41C2×#627—24no—
42C2×#627—44no—
43C32×C4⋊C4—21no—
44C32×C4⋊C4C2312yes—
45C4⋊(C3⋊Dic3)—21no—
46C4⋊(C3⋊Dic3)C2312yes—
47#3750—24no—
48C4×C3⋊Dic3D412yes—
49C4×C3⋊Dic3C2312yes—
50C3×C4⋊Dic3—22no—
51C3×C4⋊Dic3C2314yes—
52C2×C3×C3⋊C8Q818yescomplemented
53C2×C3×C3⋊C8C2314yes—
54#3724—24no—
55C2×#500—91noSylow
56C22×Dic6—62no—
57C22×Dic6—62no—
58C22×Dic6—62no—
59C22×C3×C8—32no—
60C2×C3×C4⋊C4—21no—
61C2×C3×C4⋊C4—32no—
62C2×C3×C4⋊C4C2×D312yes—
63C2×C4⋊Dic3—32no—
64C2×C4⋊Dic3—61no—
65C2×C4⋊Dic3C2×D312yes—
66C2×Dic3⋊C4—62no—
67C2×Dic3⋊C4—62no—
68C2×Dic3⋊C4—62no—
69C2×C4×Dic3—32no—
70C2×C4×Dic3—61no—
71C22×C3⋊C8C2×D312yes—
72#888—38no—
73#888—38no—
74#888—64no—
75#888—64no—
76#888—64no—
77#888—64no—
78C3×#107—38no—
79#818—38no—
80C8×Dic3—38no—
81#807—38no—
82#807C2×D318yes—
83C23×C32C2×D411yescharacteristic
84C2×C32×C4—22no—
85C2×C32×C4—42no—
86C2×C32×C4C2×D411yescharacteristic
87C2×C32×C4C2×Q814yes—
88C2×C32×C4C2411yescharacteristic
89C2×C3⋊Dic3—22no—
90C2×C3⋊Dic3—42no—
91C2×C3⋊Dic3D814yes—
92C2×C3⋊Dic3Q1614yes—
93C2×C3⋊Dic3C2×D412yes—
94C2×C3⋊Dic3C2×D412yes—
95#634—48no—
96C2×C3×Dic3—24no—
97C2×C3×Dic3—44no—
98#627—48no—
99C3×C3⋊C8C2×Q818yescomplemented
100C2×C4⋊Q8—91no—
101C2×C4⋊Q8—91no—
102#500—98no—
103C2×#107—32no—
104C2×#107—92no—
105C2×C4×C8—91no—
106C22×C3×C4—22no—
107C22×C3×C4—22no—
108C22×C3×C4—21no—
109C22×C3×C4—62no—
110C22×C3×C4C22×D312yes—
111C22×Dic3—22no—
112C22×Dic3—32no—
113C22×Dic3—32no—
114C22×Dic3—61no—
115C22×Dic3—61no—
116C22×Dic3—62no—
117C22×Dic3—62no—
118C2×Dic6—68no—
119C2×Dic6—68no—
120C2×Dic6—68no—
121C2×Dic6—128no—
122C2×Dic6—128no—
123C2×Dic6—128no—
124C2×C3×C8—38no—
125C2×C3×C8—34no—
126C3×C4⋊C4—22no—
127C3×C4⋊C4—22no—
128C3×C4⋊C4—22no—
129C3×C4⋊C4—34no—
130C3×C4⋊C4—62no—
131C3×C4⋊C4C22×D314yes—
132C4⋊Dic3—22no—
133C4⋊Dic3—34no—
134C4⋊Dic3—62no—
135C4⋊Dic3—62no—
136C4⋊Dic3—62no—
137C4⋊Dic3C22×D314yes—
138Dic3⋊C4—68no—
139Dic3⋊C4—68no—
140Dic3⋊C4—68no—
141C4×Dic3—34no—
142C4×Dic3—34no—
143C4×Dic3—62no—
144C4×Dic3—62no—
145C2×C3⋊C8Dic618yescomplemented
146C2×C3⋊C8C22×D314yes—
147C22×C32C4⋊Q812yes—
148C22×C32C2×D812yes—
149C22×C32C2×Q1612yes—
150C22×C32C22×D411yescharacteristic
151C32×C4—42no—
152C32×C4C4⋊Q812yes—
153C32×C4C22×Q812yes—
154C3⋊Dic3—42no—
155C3⋊Dic3C2×D814yes—
156C3⋊Dic3C2×Q1614yes—
157C3×Dic3—44no—
158C22×Q8—181no—
159C22×Q8—181no—
160C22×C8—32no—
161C4⋊Q8—94no—
162C4⋊Q8—94no—
163C4⋊Q8—182no—
164C4⋊Q8—182no—
165C2×C4⋊C4—32no—
166C2×C4⋊C4—91no—
167C2×C4⋊C4—181no—
168C2×C4⋊C4—181no—
169C2×C4⋊C4D3211yescharacteristic
170C2×C42—91no—
171#107—38no—
172#107—98no—
173C4×C8—94no—
174C23×C3—21no—
175C23×C3D3×D412yes—
176C2×C3×C4—24no—
177C2×C3×C4—24no—
178C2×C3×C4—21no—
179C2×C3×C4—24no—
180C2×C3×C4—21no—
181C2×C3×C4—44no—
182C2×C3×C4—44no—
183C2×C3×C4—64no—
184C2×C3×C4—124no—
185C2×C3×C4C2×Dic614yes—
186C2×C3×C4D3×D412yes—
187C2×C3×C4D3×Q814yes—
188C2×C3×C4C23×D312yes—
189C2×Dic3—24no—
190C2×Dic3—38no—
191C2×Dic3—38no—
192C2×Dic3—34no—
193C2×Dic3—34no—
194C2×Dic3—44no—
195C2×Dic3—64no—
196C2×Dic3—64no—
197C2×Dic3—62no—
198C2×Dic3—62no—
199C2×Dic3—64no—
200C2×Dic3—64no—
201C2×Dic3—124no—
202C2×Dic3—124no—
203Dic6—1216no—
204Dic6—1216no—
205Dic6—1216no—
206C3×C8—38no—
207C3⋊C8C2×Dic618yescomplemented
208C2×C32#50014yescomplemented
209C2×C32C2×C4⋊Q811yescharacteristic
210C2×C32C22×D811yescharacteristic
211C2×C32C22×Q1611yescharacteristic
212C2×Q8—184no—
213C2×Q8—184no—
214C2×Q8—364no—
215C2×Q8—364no—
216C22×C4—21no—
217C22×C4—62no—
218C22×C4—91no—
219C22×C4—91no—
220C22×C4—181no—
221C22×C4C2×D3211yescharacteristic
222C2×C8—34no—
223C2×C8—38no—
224C4⋊C4—21no—
225C4⋊C4—34no—
226C4⋊C4—62no—
227C4⋊C4—92no—
228C4⋊C4—184no—
229C4⋊C4—184no—
230C4⋊C4—181no—
231C4⋊C4C2×D3212yes—
232C42—92no—
233C42—92no—
234C22×C3—21no—
235C22×C3—22no—
236C22×C3—22no—
237C22×C3—22no—
238C22×C3#88814yes—
239C22×C3D3×D814yes—
240C22×C3D3×Q1614yes—
241C22×C3C2×D3×D412yes—
242C3×C4—22no—
243C3×C4—22no—
244C3×C4—44no—
245C3×C4—44no—
246C3×C4—124no—
247C3×C4#88814yes—
248C3×C4C22×Dic612yes—
249C3×C4C2×D3×Q812yes—
250Dic3—38no—
251Dic3—38no—
252Dic3—44no—
253Dic3—64no—
254Dic3—64no—
255Dic3—124no—
256Dic3—124no—
257C32C2×#50011yescharacteristic, complemented, Sylow
258C23#381111yescharacteristic
259Q8—368no—
260Q8—368no—
261C2×C4—22no—
262C2×C4—42no—
263C2×C4—64no—
264C2×C4—92no—
265C2×C4—92no—
266C2×C4—94no—
267C2×C4—94no—
268C2×C4—124no—
269C2×C4—182no—
270C2×C4—362no—
271C2×C4D3×Dic614yes—
272C2×C4#381111yescharacteristic
273C2×C4C22×D3211yescharacteristic
274C8—38no—
275C2×C3—21no—
276C2×C3—21no—
277C2×C3—24no—
278C2×C3—21no—
279C2×C3#487418yescomplemented
280C2×C3C2×#88812yes—
281C2×C3C2×D3×D812yes—
282C2×C3C2×D3×Q1612yes—
283C22#6384012yes—
284C22#6392612yes—
285C22#6394412yes—
286C22C2×#381111yescharacteristic
287C4—42no—
288C4—94no—
289C4—94no—
290C4—124no—
291C4—362no—
292C4#6384012yes—
293C4C2×D3×Dic612yes—
294C3—21no—
295C3C2×#487412yescomplemented
296C2#1059041514yesdirect product factor
297C2C2×#6384011yescharacteristic
298C2C2×#6392611yescharacteristic
299C2C2×#6394411yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socle, prime radicalC23×C32C2×D4
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#500
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. #10590415C2direct (N × H)
52. C2×C3×C3⋊C8Q8semidirect
99. C3×C3⋊C8C2×Q8semidirect
145. C2×C3⋊C8Dic6semidirect
207. C3⋊C8C2×Dic6semidirect
208. C2×C32#500semidirect
257. C32C2×#500semidirect
279. C2×C3#4874semidirect
295. C3C2×#4874semidirect
296. C2#10590415direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640972
C2×#639192
C2×C3×#8072
C2×#635752
C2×#635532
#105904152
C2×#48743