Finite Group Databasebeta

← C2×#10591189 #11867022

Subgroups — C2×#10591189 #11867022

Order 1152.

1133 conjugacy classes of subgroups; only the 244 normal subgroups are shown.

normal subgroups only

This group has 1133 conjugacy classes of subgroups — too many to draw. Only its 244 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
1C22×#3748C211yesmaximal, characteristic
2C2×C3×#924C212yesmaximal
3C22×#3718C211yesmaximal, characteristic, complemented
4#10591189C218yesmaximal, direct product factor
5C2×#63574C211yesmaximal, characteristic, complemented
6C2×#63565C212yesmaximal, complemented
7C2×#5052—32nomaximal
8C23×C32×C4C2211yescharacteristic
9C22×C3×Dic6C2212yes—
10C2×#3748—24no—
11C2×#3748C2214yes—
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×#217—22no—
15C2×C3×C4⋊Dic3C2212yes—
16C3×#924—24no—
17C3×#924C2218yes—
18C2×C3×Dic3⋊C4—22no—
19C2×#3718—24no—
20C2×#3718C2214yescomplemented
21#63574C2214yescomplemented
22#63565C2218yescomplemented
23C2×C3×C22⋊Q8—32no—
24C22×#216—32no—
25C2×#924D312yes—
26C22×#208—32no—
27C22×#208—61no—
28C2×#835—32no—
29#5052—316no—
30C2×#810—32no—
31C2×#808—32no—
32C24×C32D411yescharacteristic
33C22×C32×C4—22no—
34C22×C32×C4—22no—
35C22×C32×C4D411yescharacteristic
36C22×C32×C4D412yes—
37C22×C32×C4C2312yes—
38C22×C32×C4C2311yescharacteristic
39C22×C3×Dic3—22no—
40C22×C3×Dic3—22no—
41C2×C3×Dic6—24no—
42C2×C3×Dic6—24no—
43C2×C3×Dic6—22no—
44C2×C3×Dic6C2314yes—
45#3748—28no—
46C2×C3⋊(C3⋊C8)—22no—
47C2×C3⋊(C3⋊C8)D414yes—
48C2×C3⋊(C3⋊C8)C2312yes—
49C2×C3⋊(C3⋊C8)C2312yes—
50C3×#217—28no—
51C3×C4⋊Dic3—22no—
52C3×C4⋊Dic3C2314yes—
53C3×Dic3⋊C4—28no—
54#3718—28no—
55C2×#470—91noSylow
56C22×C3×Q8—32no—
57C23×C3×C4—21no—
58C23×C3×C4C2×D312yes—
59C22×Dic6C2×D312yes—
60C3×C22⋊Q8—38no—
61C3×C22⋊Q8—64no—
62C2×C3×C4⋊C4—32no—
63C2×C3×C4⋊C4—62no—
64C2×C3×C22⋊C4—62no—
65C2×#217—22no—
66C2×#216—38no—
67C2×#216—68no—
68C2×C4⋊Dic3C2×D312yes—
69#924—24no—
70#924C2×D318yes—
71C2×Dic3⋊C4—22no—
72C2×#208—38no—
73C2×#208—64no—
74C2×#208—68no—
75C2×#208—68no—
76C22×C3⋊C8—32no—
77C22×C3⋊C8—32no—
78C22×C3⋊C8—61no—
79C22×C3⋊C8—61no—
80#835—38no—
81#810—38no—
82#808—38no—
83C23×C32—22no—
84C23×C32—24no—
85C23×C32C2×D412yes—
86C23×C32C2×D411yescharacteristic
87C2×C32×C4—22no—
88C2×C32×C4—24no—
89C2×C32×C4—22no—
90C2×C32×C4—22no—
91C2×C32×C4C2×D412yes—
92C2×C32×C4C2×D412yes—
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4#4112yes—
95C2×C32×C4C2411yescharacteristic
96C2×C3×Dic3—24no—
97C2×C3×Dic3—24no—
98C2×C3×Dic3—44no—
99C2×C3×Dic3—44no—
100C3×Dic6—24no—
101C3×Dic6—24no—
102C3×Dic6—44no—
103C3⋊(C3⋊C8)—22no—
104C3⋊(C3⋊C8)C2×D414yes—
105C22×Q16—91no—
106C22×M16—91no—
107C2×C22⋊Q8—32no—
108#470—98no—
109C2×#106—91no—
110C2×#103—92no—
111C24×C3—21no—
112C24×C3#6712yes—
113C2×C3×Q8—34no—
114C2×C3×Q8—62no—
115C2×C3×Q8—64no—
116C2×C3×Q8—64no—
117C22×C3×C4—24no—
118C22×C3×C4—24no—
119C22×C3×C4—24no—
120C22×C3×C4—24no—
121C22×C3×C4—22no—
122C22×C3×C4—21no—
123C22×C3×C4—21no—
124C22×C3×C4—22no—
125C22×C3×C4—62no—
126C22×C3×C4—62no—
127C22×C3×C4#6712yes—
128C22×C3×C4#6714yes—
129C22×C3×C4C22×D314yes—
130C22×C3×C4C22×D312yes—
131C22×Dic3—22no—
132C22×Dic3—22no—
133C2×Dic6—24no—
134C2×Dic6—24no—
135C2×Dic6—22no—
136C2×Dic6C22×D314yes—
137C3×C4⋊C4—34no—
138C3×C4⋊C4—68no—
139C3×C4⋊C4—62no—
140C3×C22⋊C4—68no—
141#217—28no—
142#216—616no—
143C4⋊Dic3—22no—
144C4⋊Dic3C22×D314yes—
145Dic3⋊C4—28no—
146#208—616no—
147#208—616no—
148C2×C3⋊C8—38no—
149C2×C3⋊C8—34no—
150C2×C3⋊C8—34no—
151C2×C3⋊C8—64no—
152C2×C3⋊C8—62no—
153C2×C3⋊C8—62no—
154C2×C3⋊C8—64no—
155C2×C3⋊C8—64no—
156C22×C32—22no—
157C22×C32—24no—
158C22×C32—44no—
159C22×C32#12112yes—
160C22×C32#13714yes—
161C22×C32C22×D411yescharacteristic
162C32×C4—22no—
163C32×C4#12112yes—
164C32×C4C22×D411yescharacteristic
165C32×C4C2×#4111yescharacteristic
166C3×Dic3—44no—
167C3×Dic3—44no—
168C22×Q8—32no—
169C23×C4D3211yescharacteristic
170C2×Q16—94no—
171C2×Q16—184no—
172C2×M16—94no—
173C2×M16—184no—
174C22×C8—91no—
175C22×C8—91no—
176C22⋊Q8—38no—
177C22⋊Q8—64no—
178C2×C4⋊C4—32no—
179C2×C4⋊C4—62no—
180C2×C22⋊C4—62no—
181#106—94no—
182#103—98no—
183C23×C3—24no—
184C23×C3—24no—
185C23×C3—24no—
186C23×C3—24no—
187C23×C3—22no—
188C23×C3—21no—
189C23×C3—44no—
190C23×C3C2×#6714yes—
191C23×C3C2×#6712yes—
192C3×Q8—64no—
193C3×Q8—64no—
194C3×Q8—124no—
195C2×C3×C4—24no—
196C2×C3×C4—24no—
197C2×C3×C4—24no—
198C2×C3×C4—28no—
199C2×C3×C4—24no—
200C2×C3×C4—28no—
201C2×C3×C4—24no—
202C2×C3×C4—24no—
203C2×C3×C4—21no—
204C2×C3×C4—22no—
205C2×C3×C4—22no—
206C2×C3×C4—21no—
207C2×C3×C4—22no—
208C2×C3×C4—64no—
209C2×C3×C4—64no—
210C2×C3×C4—124no—
211C2×C3×C4—124no—
212C2×C3×C4D3×D414yes—
213C2×C3×C4#23714yes—
214C2×C3×C4C2×#6714yes—
215C2×C3×C4C2×#6712yes—
216C2×C3×C4C23×D312yes—
217C2×Dic3—24no—
218C2×Dic3—24no—
219C2×Dic3—44no—
220C2×Dic3—44no—
221Dic6—24no—
222Dic6—24no—
223Dic6—44no—
224C3⋊C8—38no—
225C3⋊C8—64no—
226C3⋊C8—64no—
227C3⋊C8—64no—
228C2×C32—42no—
229C2×C32#47014yescomplemented
230C2×C32C2×#12111yescharacteristic
231C2×C32C2×#13712yes—
232C24#62511yescharacteristic
233C2×Q8—34no—
234C2×Q8—62no—
235C2×Q8—64no—
236C2×Q8—64no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—62no—
240C22×C4—62no—
241C22×C4#62512yes—
242C22×C4#62511yescharacteristic
243C22×C4C2×D3212yes—
244C22×C4C2×D3211yescharacteristic
245Q16—188no—
246M16—188no—
247C2×C8—92no—
248C2×C8—94no—
249C2×C8—92no—
250C2×C8—182no—
251C4⋊C4—34no—
252C4⋊C4—62no—
253C4⋊C4—68no—
254C22⋊C4—68no—
255C22×C3—24no—
256C22×C3—24no—
257C22×C3—24no—
258C22×C3—24no—
259C22×C3—21no—
260C22×C3—24no—
261C22×C3—22no—
262C22×C3—44no—
263C22×C3—48no—
264C22×C3—48no—
265C22×C3#93914yes—
266C22×C3#94214yes—
267C22×C3#95114yes—
268C22×C3C22×#6712yes—
269C3×C4—24no—
270C3×C4—24no—
271C3×C4—21no—
272C3×C4—21no—
273C3×C4—22no—
274C3×C4—124no—
275C3×C4—124no—
276C3×C4#93914yes—
277C3×C4C2×D3×D412yes—
278C3×C4C2×#23712yes—
279Dic3—44no—
280Dic3—44no—
281C32C2×#47011yescharacteristic, complemented, Sylow
282C23—24no—
283C23—22no—
284C23C2×#62512yes—
285C23C2×#62511yescharacteristic
286Q8—64no—
287Q8—64no—
288Q8—124no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—24no—
293C2×C4—64no—
294C2×C4—64no—
295C2×C4—124no—
296C2×C4—124no—
297C2×C4#380512yes—
298C2×C4C2×#62512yes—
299C2×C4C2×#62511yescharacteristic
300C2×C4#381112yes—
301C2×C4C22×D3211yescharacteristic
302C8—94no—
303C8—182no—
304C2×C3—21no—
305C2×C3—24no—
306C2×C3—22no—
307C2×C3—44no—
308C2×C3—44no—
309C2×C3#505218yescomplemented
310C2×C3C2×#93912yes—
311C2×C3C2×#94212yes—
312C2×C3C2×#95112yes—
313C22—22no—
314C22—24no—
315C22—44no—
316C22#6382714yes—
317C22#6398012yes—
318C22C22×#62511yescharacteristic
319C4—22no—
320C4—124no—
321C4—124no—
322C4#6398012yes—
323C4C2×#380511yescharacteristic
324C4C2×#381111yescharacteristic
325C3—21no—
326C3C2×#505212yescomplemented
327C2—42no—
328C2#1059118914yesdirect product factor
329C2C2×#6382712yes—
330C2C2×#6398011yescharacteristic
subgroupG/H
centerC23C2×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC23×C32C2×D4
prime radicalC24×C32D4
hypercenterC23×C4D32
hypocenterC32C2×#470
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. C22×#3718C2semidirect
4. #10591189C2direct (N × H)
5. C2×#63574C2semidirect
6. C2×#63565C2semidirect
20. C2×#3718C22semidirect
21. #63574C22semidirect
22. #63565C22semidirect
229. C2×C32#470semidirect
281. C32C2×#470semidirect
309. C2×C3#5052semidirect
326. C3C2×#5052semidirect
328. C2#10591189direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37482
C2×C3×#9242
C22×#37182
#105911892
C2×#635742
C2×#635652
C2×#50523