Finite Group Databasebeta

← C2×#10593820 #11859212

Subgroups — C2×#10593820 #11859212

Order 1152.

990 conjugacy classes of subgroups; only the 194 normal subgroups are shown.

normal subgroups only

This group has 990 conjugacy classes of subgroups — too many to draw. Only its 194 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×#3792C211yesmaximal, characteristic, complemented
2C23×#622C211yesmaximal, characteristic, complemented
3C2×D4×C3⋊Dic3C211yesmaximal, characteristic
4C2×C22⋊#622C211yesmaximal, characteristic, complemented
5C2×C22⋊#622C211yesmaximal, characteristic, complemented
6#10593820C218yesmaximal, direct product factor
7C2×#63779C211yesmaximal, characteristic, complemented
8C2×#63777C211yesmaximal, characteristic, complemented
9C22×C32×D4C411yescharacteristic
10C23×C3⋊Dic3C2211yescharacteristic
11C23×C3⋊Dic3C2211yescharacteristic
12C2×#3792—24no—
13C2×#3792C2214yescomplemented
14C22×#622—24no—
15C22×#622C2211yescharacteristic
16C22×#622C2211yescharacteristic
17C22×#622C2211yescharacteristic
18C22×#622C2211yescharacteristic
19C22×#622C2214yescomplemented
20C2×#3757C411yescharacteristic
21C2×#3757C411yescharacteristic
22D4×C3⋊Dic3C414yes—
23D4×C3⋊Dic3C2214yes—
24C2×C4⋊(C3⋊Dic3)C411yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic
26C22⋊#622C2214yescomplemented
27C22⋊#622C2214yescomplemented
28#63779C2214yescomplemented
29#63777C2214yescomplemented
30C2×D4×Dic3—62no—
31C24×C32C2×C411yescharacteristic
32C24×C32C2×C411yescharacteristic
33C2×C32×D4—24no—
34C2×C32×D4C2×C414yes—
35C22×C32×C4C2×C411yescharacteristic
36C22×C3⋊Dic3—22no—
37C22×C3⋊Dic3—22no—
38C22×C3⋊Dic3—22no—
39C22×C3⋊Dic3—22no—
40C22×C3⋊Dic3C2×C411yescharacteristic
41C22×C3⋊Dic3C2×C411yescharacteristic
42C22×C3⋊Dic3C2×C412yes—
43C22×C3⋊Dic3C2×C412yes—
44C22×C3⋊Dic3C2×C411yescharacteristic
45C22×C3⋊Dic3C2312yes—
46C22×C3⋊Dic3C2312yes—
47C22×C3⋊Dic3C2311yescharacteristic
48#3792—28no—
49C2×#622—22no—
50C2×#622—22no—
51C2×#622—22no—
52C2×#622—28no—
53C2×#622D414yescomplemented
54C2×#622C2312yes—
55C2×#622C2312yes—
56C2×#622C2312yes—
57C2×#622C2312yes—
58#3757C2×C414yes—
59#3757C2×C414yes—
60C4⋊(C3⋊Dic3)C2×C414yes—
61C4×C3⋊Dic3C2×C412yes—
62C4×C3⋊Dic3C2312yes—
63C2×#435—91nomaximal, Sylow
64C22×C3×D4—22no—
65C23×Dic3—62no—
66C23×Dic3—62no—
67C2×#217—62no—
68C2×#217—62no—
69D4×Dic3—68no—
70D4×Dic3—68no—
71C2×C4⋊Dic3—62no—
72C2×C4×Dic3—62no—
73C23×C32—22no—
74C23×C32—22no—
75C23×C32—22no—
76C23×C32—22no—
77C23×C32—22no—
78C23×C32M1614yescomplemented
79C23×C32C22×C412yes—
80C23×C32C22×C412yes—
81C23×C32C22×C411yescharacteristic
82C32×D4—28no—
83C2×C32×C4—22no—
84C2×C32×C4C22×C412yes—
85C2×C3⋊Dic3—22no—
86C2×C3⋊Dic3—22no—
87C2×C3⋊Dic3—22no—
88C2×C3⋊Dic3—24no—
89C2×C3⋊Dic3—24no—
90C2×C3⋊Dic3—22no—
91C2×C3⋊Dic3—22no—
92C2×C3⋊Dic3—22no—
93C2×C3⋊Dic3—22no—
94C2×C3⋊Dic3C22×C412yes—
95C2×C3⋊Dic3C22×C412yes—
96C2×C3⋊Dic3C22×C412yes—
97C2×C3⋊Dic3C22×C411yescharacteristic
98C2×C3⋊Dic3C2×D412yes—
99C2×C3⋊Dic3#4112yes—
100C2×C3⋊Dic3C2411yescharacteristic
101#622—22no—
102#622—22no—
103#622—22no—
104#622C2×D414yescomplemented
105C22×M16—91no—
106C23×C8—91no—
107C2×C4×D4—91no—
108#435—98no—
109C2×C4⋊C8—91no—
110C2×C22⋊C8—91no—
111C2×C22⋊C8—91no—
112C2×#97—91no—
113C24×C3—22no—
114C24×C3—22no—
115C2×C3×D4—216no—
116C2×C3×D4—28no—
117C22×C3×C4—22no—
118C22×Dic3—62no—
119C22×Dic3—62no—
120C22×Dic3—62no—
121C22×Dic3—62no—
122C22×Dic3—64no—
123C22×Dic3—64no—
124C22×Dic3—64no—
125C22×Dic3—64no—
126C22×Dic3—124no—
127C22×Dic3—124no—
128C22×Dic3—124no—
129C22×Dic3—124no—
130#217—68no—
131#217—68no—
132C4⋊Dic3—68no—
133C4×Dic3—64no—
134C4×Dic3—64no—
135C22×C32—22no—
136C22×C32—22no—
137C22×C32—22no—
138C22×C32—28no—
139C22×C32—22no—
140C22×C32—22no—
141C22×C32—44no—
142C22×C32C4×D412yes—
143C22×C32C2×M1612yes—
144C22×C32C2×M1614yescomplemented
145C22×C32#13112yes—
146C22×C32C23×C411yescharacteristic
147C32×C4—22no—
148C3⋊Dic3—22no—
149C3⋊Dic3—22no—
150C3⋊Dic3—22no—
151C3⋊Dic3C4×D412yes—
152C3⋊Dic3C22×D411yescharacteristic
153C3⋊Dic3C2×#4111yescharacteristic
154C22×D4#15711yescharacteristic
155C23×C4—91no—
156C23×C4—91no—
157C2×M16—94no—
158C2×M16—184no—
159C22×C8—91no—
160C22×C8—91no—
161C22×C8—91no—
162C22×C8—91no—
163C22×C8—94no—
164C22×C8—184no—
165C4×D4—94no—
166C4×D4—94no—
167C2×C4⋊C4—91no—
168C2×C22⋊C4—91no—
169C2×C22⋊C4—91no—
170C2×C42—91no—
171C4⋊C8—94no—
172C22⋊C8—94no—
173C22⋊C8—94no—
174#97—94no—
175C23×C3—28no—
176C23×C3—24no—
177C23×C3—24no—
178C23×C3—22no—
179C23×C3—28no—
180C23×C3—44no—
181C23×C3—44no—
182C23×C3—44no—
183C23×C3—44no—
184C3×D4—232no—
185C2×C3×C4—28no—
186C2×C3×C4—24no—
187C2×Dic3—62no—
188C2×Dic3—64no—
189C2×Dic3—64no—
190C2×Dic3—62no—
191C2×Dic3—64no—
192C2×Dic3—64no—
193C2×Dic3—64no—
194C2×Dic3—124no—
195C2×Dic3—124no—
196C2×Dic3—128no—
197C2×Dic3—128no—
198C2×Dic3—124no—
199C2×Dic3—124no—
200C2×Dic3—124no—
201C2×Dic3—124no—
202C2×Dic3—124no—
203C2×C32—24no—
204C2×C32—42no—
205C2×C32#43514yescomplemented
206C2×C32C2×C4×D411yescharacteristic
207C2×C32C22×M1611yescharacteristic
208C2×C32C2×#13111yescharacteristic
209C24C2×#15711yescharacteristic
210C24C2×#15711yescharacteristic
211C2×D4—24no—
212C2×D4C2×#15714yes—
213C22×C4—91no—
214C22×C4—92no—
215C22×C4—92no—
216C22×C4—92no—
217C22×C4—92no—
218C22×C4—91no—
219C22×C4—91no—
220C22×C4—91no—
221C22×C4—182no—
222C22×C4—182no—
223C22×C4—182no—
224C22×C4—182no—
225C22×C4C2×#15711yescharacteristic
226M16—188no—
227C2×C8—92no—
228C2×C8—94no—
229C2×C8—92no—
230C2×C8—92no—
231C2×C8—92no—
232C2×C8—188no—
233C2×C8—182no—
234C2×C8—182no—
235C2×C8—182no—
236C4⋊C4—94no—
237C22⋊C4—94no—
238C22⋊C4—94no—
239C42—92no—
240C42—92no—
241C22×C3—28no—
242C22×C3—24no—
243C22×C3—24no—
244C22×C3—24no—
245C22×C3—28no—
246C22×C3—22no—
247C22×C3—44no—
248C22×C3—44no—
249C22×C3—416no—
250C22×C3—44no—
251C22×C3—44no—
252C22×C3—416no—
253C3×C4—28no—
254Dic3—64no—
255Dic3—62no—
256Dic3—62no—
257Dic3—124no—
258Dic3—124no—
259Dic3—124no—
260C32C2×#43511yescharacteristic, complemented, Sylow
261C23—22no—
262C23—22no—
263C23—22no—
264C23—22no—
265C23—22no—
266C23#379214yescomplemented
267C23C22×#15712yes—
268C23C22×#15712yes—
269C23C22×#15711yescharacteristic
270D4—28no—
271C2×C4—22no—
272C2×C4—92no—
273C2×C4—92no—
274C2×C4—91no—
275C2×C4—91no—
276C2×C4—92no—
277C2×C4—92no—
278C2×C4—92no—
279C2×C4—182no—
280C2×C4—182no—
281C2×C4—182no—
282C2×C4—182no—
283C2×C4—184no—
284C2×C4—184no—
285C2×C4—182no—
286C2×C4—182no—
287C2×C4—182no—
288C2×C4C22×#15712yes—
289C8—94no—
290C8—182no—
291C8—182no—
292C8—182no—
293C2×C3—28no—
294C2×C3—22no—
295C2×C3—22no—
296C2×C3—22no—
297C2×C3—48no—
298C2×C3—48no—
299C22—28no—
300C22—22no—
301C22—22no—
302C22—22no—
303C22—22no—
304C22—22no—
305C22—44no—
306C22#6428712yes—
307C22D4×#15712yes—
308C22C2×#379212yes—
309C22C2×#379214yescomplemented
310C22C23×#15711yescharacteristic
311C4—22no—
312C4—91no—
313C4—91no—
314C4—92no—
315C4—182no—
316C4—182no—
317C4—182no—
318C3—22no—
319C2—24no—
320C2—42no—
321C2#1059382014yesdirect product factor
322C2C2×#6428711yescharacteristic
323C2C2×D4×#15711yescharacteristic
324C2C22×#379211yescharacteristic
subgroupG/H
centerC23C22×#157
commutatorC22×C32C23×C4
FrattiniC22C23×#157
Fitting, prime radicalC22×C32×D4C4
socleC23×C32C22×C4
cosocleC2×C3⋊Dic3C24
hypercenterC22×D4#157
hypocenterC32C2×#435
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×#3792C2semidirect
2. C23×#622C2semidirect
4. C2×C22⋊#622C2semidirect
5. C2×C22⋊#622C2semidirect
6. #10593820C2direct (N × H)
7. C2×#63779C2semidirect
8. C2×#63777C2semidirect
13. C2×#3792C22semidirect
19. C22×#622C22semidirect
26. C22⋊#622C22semidirect
27. C22⋊#622C22semidirect
28. #63779C22semidirect
29. #63777C22semidirect
53. C2×#622D4semidirect
78. C23×C32M16semidirect
104. #622C2×D4semidirect
144. C22×C32C2×M16semidirect
205. C2×C32#435semidirect
260. C32C2×#435semidirect
266. C23#3792semidirect
309. C22C2×#3792semidirect
321. C2#10593820direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37922
C23×#6222
C2×D4×C3⋊Dic32
C2×C22⋊#6222
#105938202
C2×#637792
C2×#637772
C2×#4359