Finite Group Databasebeta

← C2×#10590430 #11868262

Subgroups — C2×#10590430 #11868262

Order 1152.

1173 conjugacy classes of subgroups; only the 228 normal subgroups are shown.

normal subgroups only

This group has 1173 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×#64102C211yesmaximal, characteristic
2C2×#63919C211yesmaximal, characteristic, complemented
3C2×C3×#807C212yesmaximal, complemented
4C2×#63572C211yesmaximal, characteristic, complemented
5C2×#63564C212yesmaximal
6#10590430C218yesmaximal, direct product factor
7C2×#4890—32nomaximal
8C22×C4⋊(C3⋊D3)C2211yescharacteristic
9C22×C4×C3⋊D3—21no—
10C22×#627—21no—
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×#3752—21no—
13C2×C4×C3⋊Dic3C2211yescharacteristic
14#64102—22no—
15#64102C2214yes—
16C2×C3×C4⋊Dic3C2212yes—
17C22×C3×C3⋊C8C2212yes—
18C2×#3724—21no—
19#63919—22no—
20#63919C2214yescomplemented
21C3×#807C2218yescomplemented
22#63572C2214yescomplemented
23#63564C2218yes—
24C2×#893—32no—
25C2×#893—61no—
26C2×#888—32no—
27C2×C3×#107—32no—
28C2×#821—32no—
29C2×Dic3⋊C8—32no—
30C2×#809—32no—
31C2×#807D312yescomplemented
32#4890—316no—
33C23×C3⋊D3—21no—
34C22×C32×C4—21no—
35C22×C32×C4C2311yescharacteristic
36C22×C3⋊Dic3D411yescharacteristic
37C22×C3⋊Dic3D411yescharacteristic
38C2×C4⋊(C3⋊D3)—21no—
39C2×C4⋊(C3⋊D3)—22no—
40C2×C4⋊(C3⋊D3)Q814yescomplemented
41C2×C4⋊(C3⋊D3)C2312yes—
42C2×C4×C3⋊D3—24no—
43C2×C4×C3⋊D3—44no—
44C22×C3×Dic3—22no—
45C2×#627—24no—
46C2×#627—44no—
47C32×C4⋊C4—21no—
48C32×C4⋊C4C2312yes—
49#3752—24no—
50C4×C3⋊Dic3D412yes—
51C4×C3⋊Dic3C2312yes—
52C3×C4⋊Dic3—22no—
53C3×C4⋊Dic3C2314yes—
54C2×C3×C3⋊C8—24no—
55C2×C3×C3⋊C8C2314yes—
56#3724—24no—
57C2×#474—91noSylow
58C22×D12—32no—
59C22×D12—61no—
60C22×C4×D3—62no—
61C22×C4×D3—62no—
62C22×Dic6—62no—
63C22×C3×C8—32no—
64C2×C3×C4⋊C4—21no—
65C2×C3×C4⋊C4—32no—
66C2×C3×C4⋊C4C2×D312yes—
67C2×(C2×D3)⋊C4—62no—
68C2×(C2×D3)⋊C4—62no—
69C2×C4⋊Dic3C2×D312yes—
70C2×Dic3⋊C4—62no—
71C2×C4×Dic3—32no—
72C2×C4×Dic3—61no—
73C22×C3⋊C8C2×D312yes—
74#893—38no—
75#893—64no—
76#893—64no—
77#893—64no—
78#888—38no—
79#888—64no—
80C3×#107—38no—
81#821—38no—
82Dic3⋊C8—38no—
83#809—38no—
84#807C2×D318yescomplemented
85C23×C32C2×D411yescharacteristic
86C22×C3⋊D3—24no—
87C22×C3⋊D3—22no—
88C22×C3⋊D3—42no—
89C22×C3⋊D3—42no—
90C2×C32×C4—22no—
91C2×C32×C4—42no—
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4C2×Q812yes—
94C2×C32×C4#4112yes—
95C2×C32×C4C2411yescharacteristic
96C2×C3⋊Dic3—22no—
97C2×C3⋊Dic3D814yes—
98C2×C3⋊Dic3C2×D412yes—
99C2×C3⋊Dic3C2×D412yes—
100C4⋊(C3⋊D3)—24no—
101C4⋊(C3⋊D3)—22no—
102C4⋊(C3⋊D3)C2×Q814yescomplemented
103C4×C3⋊D3—48no—
104C2×C3×Dic3—24no—
105C2×C3×Dic3—44no—
106#627—48no—
107C3×C3⋊C8—24no—
108C2×C4⋊Q8—91no—
109C2×C4×D4—91no—
110#474—98no—
111C2×#107—32no—
112C2×C4⋊C8—91no—
113C2×#102—92no—
114C23×D3—62no—
115C23×D3—62no—
116C22×C3×C4—22no—
117C22×C3×C4—22no—
118C22×C3×C4—21no—
119C22×C3×C4—62no—
120C22×C3×C4C22×D312yes—
121C22×Dic3—22no—
122C22×Dic3—32no—
123C22×Dic3—32no—
124C22×Dic3—61no—
125C22×Dic3—61no—
126C2×D12—38no—
127C2×D12—34no—
128C2×D12—62no—
129C2×D12—64no—
130C2×D12—62no—
131C2×D12—64no—
132C2×D12—64no—
133C2×D12—62no—
134C2×C4×D3—68no—
135C2×C4×D3—68no—
136C2×C4×D3—128no—
137C2×C4×D3—128no—
138C2×Dic6—68no—
139C2×Dic6—128no—
140C2×C3×C8—34no—
141C2×C3×C8—64no—
142C3×C4⋊C4—22no—
143C3×C4⋊C4—22no—
144C3×C4⋊C4—22no—
145C3×C4⋊C4—34no—
146C3×C4⋊C4—62no—
147C3×C4⋊C4C22×D314yes—
148(C2×D3)⋊C4—68no—
149(C2×D3)⋊C4—68no—
150C4⋊Dic3—22no—
151C4⋊Dic3C22×D314yes—
152Dic3⋊C4—68no—
153C4×Dic3—34no—
154C4×Dic3—34no—
155C4×Dic3—62no—
156C4×Dic3—62no—
157C2×C3⋊C8—24no—
158C2×C3⋊C8C22×D314yes—
159C22×C32C22⋊Q812yes—
160C22×C32C2×D812yes—
161C22×C32#13712yes—
162C22×C32C22×D411yescharacteristic
163C2×C3⋊D3—24no—
164C2×C3⋊D3—42no—
165C2×C3⋊D3—42no—
166C2×C3⋊D3—48no—
167C32×C4—42no—
168C32×C4C22⋊Q812yes—
169C32×C4C22×Q811yescharacteristic
170C32×C4C2×#4111yescharacteristic
171C3⋊Dic3—22no—
172C3⋊Dic3C2×D814yes—
173C3×Dic3—44no—
174C22×Q8—181no—
175C22×D4—91no—
176C23×C4—181no—
177C22×C8—32no—
178C4⋊Q8—94no—
179C4⋊Q8—182no—
180C4×D4—94no—
181C4×D4—182no—
182C2×C4⋊C4—32no—
183C2×C4⋊C4—181no—
184C2×C4⋊C4D3211yescharacteristic
185C2×C22⋊C4—181no—
186C2×C42—91no—
187#107—38no—
188C4⋊C8—94no—
189#102—98no—
190C23×C3—21no—
191C23×C3D3×D412yes—
192C22×D3—64no—
193C22×D3—68no—
194C22×D3—68no—
195C22×D3—64no—
196C22×D3—124no—
197C22×D3—124no—
198C22×D3—124no—
199C22×D3—124no—
200C2×C3×C4—24no—
201C2×C3×C4—24no—
202C2×C3×C4—21no—
203C2×C3×C4—22no—
204C2×C3×C4—22no—
205C2×C3×C4—21no—
206C2×C3×C4—44no—
207C2×C3×C4—44no—
208C2×C3×C4—64no—
209C2×C3×C4—124no—
210C2×C3×C4#23514yes—
211C2×C3×C4D3×D412yes—
212C2×C3×C4D3×Q814yes—
213C2×C3×C4C23×D312yes—
214C2×Dic3—24no—
215C2×Dic3—38no—
216C2×Dic3—34no—
217C2×Dic3—34no—
218C2×Dic3—44no—
219C2×Dic3—64no—
220C2×Dic3—62no—
221C2×Dic3—62no—
222C2×Dic3—64no—
223C2×Dic3—122no—
224D12—38no—
225D12—64no—
226D12—64no—
227D12—68no—
228D12—68no—
229D12—64no—
230C4×D3—1216no—
231C4×D3—1216no—
232Dic6—1216no—
233C3×C8—64no—
234C3⋊C8—24no—
235C2×C32#47414yescomplemented
236C2×C32C2×C22⋊Q811yescharacteristic
237C2×C32C22×D811yescharacteristic
238C2×C32C2×#13711yescharacteristic
239C3⋊D3—44no—
240C24—181no—
241C2×Q8—184no—
242C2×Q8—364no—
243C2×D4—92no—
244C2×D4—94no—
245C2×D4—182no—
246C2×D4—181no—
247C22×C4—21no—
248C22×C4—62no—
249C22×C4—91no—
250C22×C4—91no—
251C22×C4—184no—
252C22×C4—364no—
253C22×C4C2×D3211yescharacteristic
254C2×C8—34no—
255C2×C8—64no—
256C4⋊C4—21no—
257C4⋊C4—34no—
258C4⋊C4—62no—
259C4⋊C4—184no—
260C4⋊C4C2×D3212yes—
261C22⋊C4—184no—
262C42—92no—
263C42—92no—
264C22×C3—21no—
265C22×C3—22no—
266C22×C3—22no—
267C22×C3—22no—
268C22×C3#89614yes—
269C22×C3D3×D814yes—
270C22×C3#91814yes—
271C22×C3C2×D3×D412yes—
272C2×D3—68no—
273C2×D3—68no—
274C2×D3—124no—
275C2×D3—124no—
276C2×D3—1216no—
277C2×D3—1216no—
278C2×D3—124no—
279C2×D3—124no—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—22no—
283C3×C4—44no—
284C3×C4—44no—
285C3×C4—124no—
286C3×C4#89614yes—
287C3×C4C2×#23512yes—
288C3×C4C2×D3×Q812yes—
289Dic3—38no—
290Dic3—44no—
291Dic3—64no—
292Dic3—64no—
293Dic3—122no—
294C32C2×#47411yescharacteristic, complemented, Sylow
295C23—182no—
296C23—184no—
297C23—362no—
298C23—362no—
299C23#381111yescharacteristic
300Q8—368no—
301D4—94no—
302D4—182no—
303D4—184no—
304C2×C4—22no—
305C2×C4—42no—
306C2×C4—64no—
307C2×C4—92no—
308C2×C4—94no—
309C2×C4—92no—
310C2×C4—124no—
311C2×C4—182no—
312C2×C4—368no—
313C2×C4#379712yes—
314C2×C4#379812yes—
315C2×C4#381111yescharacteristic
316C2×C4C22×D3211yescharacteristic
317C8—64no—
318C2×C3—21no—
319C2×C3—21no—
320C2×C3—21no—
321C2×C3—24no—
322C2×C3#489018yescomplemented
323C2×C3C2×#89612yes—
324C2×C3C2×D3×D812yes—
325C2×C3C2×#91812yes—
326D3—128no—
327D3—128no—
328C22—184no—
329C22—362no—
330C22—362no—
331C22—368no—
332C22#6386512yes—
333C22#6392612yes—
334C22#6394512yes—
335C22C2×#381111yescharacteristic
336C4—42no—
337C4—94no—
338C4—124no—
339C4—182no—
340C4#6386512yes—
341C4C2×#379711yescharacteristic
342C4C2×#379811yescharacteristic
343C3—21no—
344C3C2×#489012yescomplemented
345C2—364no—
346C2#1059043014yesdirect product factor
347C2C2×#6386511yescharacteristic
348C2C2×#6392611yescharacteristic
349C2C2×#6394511yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#474
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
2. C2×#63919C2semidirect
3. C2×C3×#807C2semidirect
4. C2×#63572C2semidirect
6. #10590430C2direct (N × H)
20. #63919C22semidirect
21. C3×#807C22semidirect
22. #63572C22semidirect
31. C2×#807D3semidirect
40. C2×C4⋊(C3⋊D3)Q8semidirect
84. #807C2×D3semidirect
102. C4⋊(C3⋊D3)C2×Q8semidirect
235. C2×C32#474semidirect
294. C32C2×#474semidirect
322. C2×C3#4890semidirect
344. C3C2×#4890semidirect
346. C2#10590430direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641022
C2×#639192
C2×C3×#8072
C2×#635722
C2×#635642
#105904302
C2×#48903