Finite Group Databasebeta

← C2×#10590856 #11867027

Subgroups — C2×#10590856 #11867027

Order 1152.

1133 conjugacy classes of subgroups; only the 220 normal subgroups are shown.

normal subgroups only

This group has 1133 conjugacy classes of subgroups — too many to draw. Only its 220 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×#3743C211yesmaximal, characteristic
2C2×#63871C212yesmaximal
3C22×#3718C211yesmaximal, characteristic, complemented
4C2×C3×#816C212yesmaximal, complemented
5C2×#63574C211yesmaximal, characteristic, complemented
6#10590856C218yesmaximal, direct product factor
7C2×#4816—32nomaximal
8C22×C4×C3⋊D3C2211yescharacteristic
9C22×C3×Dic6C2212yes—
10C22×C32×C8C2211yescharacteristic
11C22×C3⋊(C3⋊C8)C2211yescharacteristic
12C2×#3743—24no—
13C2×#3743C2214yes—
14C2×C3×C4⋊Dic3C2212yes—
15C2×Dic3⋊Dic3—22no—
16C2×#3722—22no—
17#63871—24no—
18#63871C2218yes—
19C2×#3718—24no—
20C2×#3718C2214yescomplemented
21C3×#816C2218yescomplemented
22#63574C2214yescomplemented
23C2×#946—32no—
24C22×#216—32no—
25C22×ΓL(1,𝔽25)—32no—
26C22×ΓL(1,𝔽25)—61no—
27C2×#897—32no—
28C2×C3×#103—32no—
29C2×#816D312yescomplemented
30C2×#808—32no—
31#4816—316no—
32C23×C3⋊D3D411yescharacteristic
33C22×C32×C4C2311yescharacteristic
34C22×C3⋊Dic3D411yescharacteristic
35C2×C4×C3⋊D3—22no—
36C2×C4×C3⋊D3—22no—
37C2×C4×C3⋊D3D412yes—
38C2×C4×C3⋊D3C2312yes—
39C22×C3×Dic3—22no—
40C22×C3×Dic3—22no—
41C2×C3×Dic6—24no—
42C2×C3×Dic6—24no—
43C2×C3×Dic6—22no—
44C2×C3×Dic6C2314yes—
45C2×C32×C8—22no—
46C2×C32×C8C2312yes—
47C2×C3⋊(C3⋊C8)D414yes—
48C2×C3⋊(C3⋊C8)C2312yes—
49#3743—28no—
50C3×C4⋊Dic3—22no—
51C3×C4⋊Dic3C2314yes—
52Dic3⋊Dic3—28no—
53#3722—28no—
54#3718—28no—
55C2×#470—91noSylow
56C22×C3×Q8—32no—
57C22×C4×D3—32no—
58C22×C4×D3—61no—
59C22×Dic6C2×D312yes—
60C22×C3×C8—21no—
61C22×C3×C8C2×D312yes—
62C2×C3×C4⋊C4—32no—
63#946—38no—
64#946—64no—
65C2×#216—38no—
66C2×#216—68no—
67C2×(C2×D3)⋊C4—62no—
68C2×(C2×D3)⋊C4—62no—
69C2×C4⋊Dic3—62no—
70C2×C4⋊Dic3C2×D312yes—
71C2×Dic3⋊C4—62no—
72C22×C3⋊C8—32no—
73C22×C3⋊C8—61no—
74C2×ΓL(1,𝔽25)—38no—
75C2×ΓL(1,𝔽25)—64no—
76C2×ΓL(1,𝔽25)—68no—
77C2×ΓL(1,𝔽25)—68no—
78#897—38no—
79#897—64no—
80C3×#103—38no—
81#816C2×D318yescomplemented
82#808—38no—
83C23×C32C2×D411yescharacteristic
84C22×C3⋊D3—22no—
85C22×C3⋊D3—24no—
86C22×C3⋊D3C2×D412yes—
87C2×C32×C4C2×D411yescharacteristic
88C2×C32×C4C2×D412yes—
89C2×C32×C4#4112yes—
90C2×C32×C4C2411yescharacteristic
91C2×C3⋊Dic3—22no—
92C2×C3⋊Dic3C2×D412yes—
93C4×C3⋊D3—24no—
94C4×C3⋊D3—22no—
95C4×C3⋊D3—22no—
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—
103C32×C8—22no—
104C3⋊(C3⋊C8)C2×D414yes—
105C22×Q16—91no—
106C22×M16—91no—
107C2×C22⋊Q8—92no—
108#470—98no—
109C2×#106—91no—
110C2×#103—32no—
111C23×D3—32no—
112C23×D3—61no—
113C2×C3×Q8—34no—
114C2×C3×Q8—62no—
115C2×C3×Q8—64no—
116C2×C3×Q8—64no—
117C22×C3×C4—21no—
118C22×C3×C4—62no—
119C22×C3×C4—62no—
120C22×C3×C4C22×D312yes—
121C22×Dic3—22no—
122C22×Dic3—22no—
123C22×Dic3—32no—
124C22×Dic3—61no—
125C2×C4×D3—34no—
126C2×C4×D3—34no—
127C2×C4×D3—62no—
128C2×C4×D3—62no—
129C2×C4×D3—64no—
130C2×C4×D3—64no—
131C2×C4×D3—64no—
132C2×C4×D3—64no—
133C2×Dic6—24no—
134C2×Dic6—24no—
135C2×Dic6—22no—
136C2×Dic6C22×D314yes—
137C2×C3×C8—24no—
138C2×C3×C8—24no—
139C2×C3×C8—22no—
140C2×C3×C8C22×D314yes—
141C3×C4⋊C4—34no—
142C3×C4⋊C4—62no—
143#216—616no—
144(C2×D3)⋊C4—68no—
145(C2×D3)⋊C4—68no—
146C4⋊Dic3—22no—
147C4⋊Dic3—68no—
148C4⋊Dic3C22×D314yes—
149Dic3⋊C4—68no—
150C2×C3⋊C8—38no—
151C2×C3⋊C8—34no—
152C2×C3⋊C8—64no—
153C2×C3⋊C8—62no—
154ΓL(1,𝔽25)—616no—
155ΓL(1,𝔽25)—616no—
156C22×C32#12112yes—
157C22×C32#13714yes—
158C22×C32C22×D411yescharacteristic
159C2×C3⋊D3—22no—
160C2×C3⋊D3—24no—
161C2×C3⋊D3—44no—
162C32×C4#12112yes—
163C32×C4C22×D411yescharacteristic
164C32×C4C2×#4111yescharacteristic
165C3⋊Dic3—22no—
166C3×Dic3—44no—
167C3×Dic3—44no—
168C22×Q8—32no—
169C23×C4—91no—
170C2×Q16—94no—
171C2×Q16—184no—
172C2×M16—94no—
173C2×M16—184no—
174C22×C8—91no—
175C22×C8D3211yescharacteristic
176C22⋊Q8—98no—
177C22⋊Q8—184no—
178C2×C4⋊C4—32no—
179C2×C4⋊C4—182no—
180C2×C22⋊C4—182no—
181#106—94no—
182#103—38no—
183C23×C3—21no—
184C23×C3D3×D412yes—
185C22×D3—34no—
186C22×D3—62no—
187C22×D3—64no—
188C22×D3—64no—
189C22×D3—64no—
190C22×D3—64no—
191C22×D3—124no—
192C3×Q8—64no—
193C3×Q8—64no—
194C3×Q8—124no—
195C2×C3×C4—21no—
196C2×C3×C4—22no—
197C2×C3×C4—21no—
198C2×C3×C4—22no—
199C2×C3×C4—64no—
200C2×C3×C4—64no—
201C2×C3×C4—124no—
202C2×C3×C4—124no—
203C2×C3×C4#23514yes—
204C2×C3×C4D3×D412yes—
205C2×C3×C4D3×D414yes—
206C2×C3×C4C23×D312yes—
207C2×Dic3—24no—
208C2×Dic3—24no—
209C2×Dic3—34no—
210C2×Dic3—44no—
211C2×Dic3—44no—
212C2×Dic3—62no—
213C2×Dic3—64no—
214C2×Dic3—64no—
215C4×D3—64no—
216C4×D3—64no—
217C4×D3—68no—
218C4×D3—68no—
219C4×D3—64no—
220C4×D3—64no—
221Dic6—24no—
222Dic6—24no—
223Dic6—44no—
224C3×C8—24no—
225C3×C8—24no—
226C3⋊C8—38no—
227C3⋊C8—64no—
228C2×C32#47014yescomplemented
229C2×C32C2×#12111yescharacteristic
230C2×C32C2×#13712yes—
231C3⋊D3—42no—
232C24—91no—
233C2×Q8—34no—
234C2×Q8—62no—
235C2×Q8—64no—
236C2×Q8—64no—
237C22×C4—62no—
238C22×C4—62no—
239C22×C4—91no—
240C22×C4—92no—
241C22×C4—92no—
242C22×C4—182no—
243C22×C4—182no—
244C22×C4C2×D3211yescharacteristic
245Q16—188no—
246M16—188no—
247C2×C8—22no—
248C2×C8—92no—
249C2×C8—94no—
250C2×C8C2×D3212yes—
251C4⋊C4—34no—
252C4⋊C4—62no—
253C4⋊C4—188no—
254C22⋊C4—188no—
255C22×C3—21no—
256C22×C3—24no—
257C22×C3—22no—
258C22×C3#88414yes—
259C22×C3#91514yes—
260C22×C3#91814yes—
261C22×C3C2×D3×D412yes—
262C2×D3—64no—
263C2×D3—64no—
264C2×D3—64no—
265C2×D3—64no—
266C2×D3—124no—
267C2×D3—128no—
268C2×D3—128no—
269C3×C4—21no—
270C3×C4—21no—
271C3×C4—22no—
272C3×C4—124no—
273C3×C4—124no—
274C3×C4#88414yes—
275C3×C4C2×#23512yes—
276C3×C4C2×D3×D412yes—
277Dic3—44no—
278Dic3—44no—
279Dic3—64no—
280Dic3—64no—
281C32C2×#47011yescharacteristic, complemented, Sylow
282C23—92no—
283C23—184no—
284C23—182no—
285C23#380211yescharacteristic
286Q8—64no—
287Q8—64no—
288Q8—124no—
289C2×C4—64no—
290C2×C4—64no—
291C2×C4—92no—
292C2×C4—124no—
293C2×C4—124no—
294C2×C4—182no—
295C2×C4—182no—
296C2×C4—182no—
297C2×C4—184no—
298C2×C4#379812yes—
299C2×C4#380211yescharacteristic
300C2×C4#381112yes—
301C2×C4C22×D3211yescharacteristic
302C8—22no—
303C8—94no—
304C2×C3—24no—
305C2×C3—22no—
306C2×C3—21no—
307C2×C3#481618yescomplemented
308C2×C3C2×#88412yes—
309C2×C3C2×#91512yes—
310C2×C3C2×#91812yes—
311D3—124no—
312D3—124no—
313C22—184no—
314C22—182no—
315C22—364no—
316C22#6381114yes—
317C22#6391212yes—
318C22C2×#380211yescharacteristic
319C4—124no—
320C4—124no—
321C4—182no—
322C4#6391212yes—
323C4C2×#379811yescharacteristic
324C4C2×#381111yescharacteristic
325C3—21no—
326C3C2×#481612yescomplemented
327C2—362no—
328C2#1059085614yesdirect product factor
329C2C2×#6381112yes—
330C2C2×#6391211yescharacteristic
subgroupG/H
centerC23#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
hypercenterC22×C8D32
hypocenterC32C2×#470
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
3. C22×#3718C2semidirect
4. C2×C3×#816C2semidirect
5. C2×#63574C2semidirect
6. #10590856C2direct (N × H)
20. C2×#3718C22semidirect
21. C3×#816C22semidirect
22. #63574C22semidirect
29. C2×#816D3semidirect
81. #816C2×D3semidirect
228. C2×C32#470semidirect
281. C32C2×#470semidirect
307. C2×C3#4816semidirect
326. C3C2×#4816semidirect
328. C2#10590856direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37432
C2×#638712
C22×#37182
C2×C3×#8162
C2×#635742
#105908562
C2×#48163