Finite Group Databasebeta

← C2×#19143614 #25961098

Subgroups — C2×#19143614 #25961098

Order 11008.

2230 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#10621902C211yesmaximal, characteristic
2#19143614C2116yesmaximal, direct product factor
3C2×Q8×C43⋊C8C211yesmaximal, characteristic, complemented
4C2×#14582978C213yesmaximal, complemented
5C2×#14582976C213yesmaximal, complemented
6C2×#14582955C213yesmaximal, complemented
7C2×C4×#10621872C213yesmaximal, complemented
8C2×C8×Q8×C43C211yesmaximal, characteristic, complemented
9C22×#10621902C411yescharacteristic
10C22×#10621872C2213yes—
11C22×#10621872C2213yes—
12C4×#10621902C418yes—
13C4×#10621902C2218yes—
14C2×Q8×Dic43C411yescharacteristic
15C2×C4×D172C2213yes—
16C2×#13063287C413yes—
17C2×#13063283C413yes—
18C2×C42×D43C2213yes—
19Q8×C43⋊C8C2218yescomplemented
20#14582978C22124yescomplemented
21#14582976C22124yescomplemented
22#14582955C22124yescomplemented
23C2×C4⋊(C43⋊C8)C2213yes—
24C2×(C2×D43)⋊C8C2216yes—
25C4×#10621872C22124yescomplemented
26C2×#13063235C2213yes—
27C2×#13063235C2211yescharacteristic
28C2×C4×C43⋊C8C2213yes—
29C2×C4×Q8×C43C2211yescharacteristic
30C8×Q8×C43C2218yescomplemented
31C2×C4⋊C8×C43C2213yes—
32C2×C4×C8×C43C2213yes—
33C2×#10621902—28no—
34C2×#10621902C2×C418yes—
35C22×D172C2×C413yes—
36C22×C4×D43C2×C413yes—
37C22×C4×D43C2×C413yes—
38C22×C4×D43C2313yes—
39C2×#10621872—212no—
40C2×#10621872—212no—
41C2×#10621872C23112yes—
42C2×#10621872C23112yes—
43C22×C43⋊C8C2313yes—
44C22×C43⋊C8C2311yescharacteristic
45Q8×Dic43C2×C418yes—
46C4×D172C2×C4112yes—
47C4×D172C23112yes—
48#13063287C2×C4124yes—
49#13063283C2×C4124yes—
50C2×C4⋊Dic43C2×C413yes—
51C2×(C2×D43)⋊C4C2×C416yes—
52C2×C4×Dic43C2×C413yes—
53C2×C4×Dic43C2×C413yes—
54C2×C4×Dic43C2311yescharacteristic
55C42×D43C2×C4112yes—
56C42×D43C23112yes—
57C4⋊(C43⋊C8)C23112yes—
58(C2×D43)⋊C8C23124yes—
59#13063235C2314yes—
60#13063235C23112yes—
61C4×C43⋊C8C23112yes—
62C22×Q8×C43C2×C411yescharacteristic
63C22×C8×C43C2313yes—
64C22×C8×C43C2311yescharacteristic
65C4×Q8×C43C2×C414yes—
66C4×Q8×C43C2314yes—
67C2×C4⋊C4×C43C2×C413yes—
68C2×C42×C43C2313yes—
69C4⋊C8×C43C23112yes—
70C4×C8×C43C23112yes—
71C23×D43C22×C413yes—
72C2×Q8×C43M1618yescomplemented
73C2×Q8×C43C22×C414yes—
74C22×C4×C43C22×C413yes—
75C22×C4×C43C22×C413yes—
76C22×C4×C43C2411yescharacteristic
77C22×Dic43C22×C411yescharacteristic
78C22×Dic43C22×C411yescharacteristic
79C22×Dic43C22×C413yes—
80#10621902—232no—
81C2×D172—212no—
82C2×D172C22×C4112yes—
83C2×C4×D43—212no—
84C2×C4×D43—26no—
85C2×C4×D43—26no—
86C2×C4×D43—46no—
87C2×C4×D43C22×C416yes—
88C2×C4×D43C22×C4112yes—
89C2×C4×D43C22×C4112yes—
90C2×C4×D43C2416yes—
91C2×C8×C43—26no—
92C2×C8×C43#4114yescomplemented
93C2×C8×C43C2416yes—
94C2×C8×C43C2412yes—
95C4⋊C4×C43C22×C4112yes—
96C42×C43C22×C416yes—
97C42×C43C2416yes—
98(C2×D43)⋊C4C22×C4124yes—
99C4⋊Dic43C22×C4112yes—
100C4×Dic43C22×C412yes—
101C4×Dic43C22×C4112yes—
102C4×Dic43C22×C4112yes—
103C4×Dic43C2412yes—
104C2×C43⋊C8—26no—
105C2×C43⋊C8#4114yescomplemented
106C2×C43⋊C8C2416yes—
107C2×C43⋊C8C2412yes—
108#10621872—224no—
109#10621872—224no—
110C23×C43C23×C411yescharacteristic
111C22×D43—26no—
112C22×D43—26no—
113C22×D43—26no—
114C22×D43C23×C416yes—
115Q8×C43C2×M16116yescomplemented
116C2×C4×C43—26no—
117C2×C4×C43C2×M16112yes—
118C2×C4×C43C23×C416yes—
119C2×C4×C43C23×C411yescharacteristic
120C2×C4×C43C23×C416yes—
121C2×C4×C43C2×#4112yes—
122C2×C4×C43C2×#4112yes—
123C2×C4×C43C2511yescharacteristic
124C2×Dic43—26no—
125C2×Dic43—22no—
126C2×Dic43—22no—
127C2×Dic43C23×C412yes—
128C2×Dic43C23×C412yes—
129C2×Dic43C23×C416yes—
130D172—224no—
131C4×D43—212no—
132C4×D43—224no—
133C4×D43—26no—
134C4×D43—26no—
135C4×D43—412no—
136C8×C43—26no—
137C8×C43C2×#4114yescomplemented
138C43⋊C8—26no—
139C43⋊C8C2×#4114yescomplemented
140C2×#2971—431nomaximal, Sylow
141C22×C43C4×#4112yes—
142C22×C43C22×M1612yes—
143C22×C43#56812yes—
144C22×C43C24×C411yescharacteristic
145C2×D43—26no—
146C2×D43—26no—
147C2×D43—26no—
148C2×D43—412no—
149C4×C43—26no—
150C4×C43C4×#4112yes—
151C4×C43C22×M16112yes—
152C4×C43C22×#4111yescharacteristic
153C4×C43C22×#4111yescharacteristic
154Dic43—26no—
155Dic43—22no—
156Dic43—22no—
157C2×C4×#41—431no—
158#2971—4316no—
159C2×C8×Q8—431no—
160C2×C8×Q8D4311yescharacteristic, complemented
161C2×#436—433no—
162C2×#436—433no—
163C2×#432—433no—
164C2×C4×M16—433no—
165C2×C43#297114yescomplemented
166C2×C43C2×C4×#4111yescharacteristic
167C2×C43C23×M1611yescharacteristic
168C2×C43C2×#56811yescharacteristic
169D43—46no—
170C22×#41—431no—
171C22×M16—433no—
172C22×M16—433no—
173C4×#41—438no—
174C4×#41—438no—
175C2×C4×Q8—431no—
176C2×C4×Q8C2×D4311yescharacteristic
177C2×C4×D4—433no—
178C2×C4×D4—433no—
179C2×#117—433no—
180C22×C42—433no—
181C8×Q8—438no—
182C8×Q8C2×D4318yescomplemented
183#436—4324no—
184#436—4324no—
185#432—4324no—
186C2×C4⋊C8—433no—
187C2×C4⋊C8C2×D4313yes—
188C2×C22⋊C8—436no—
189C4×M16—4324no—
190C2×#97—431no—
191C2×#97—433no—
192C2×C4×C8—433no—
193C2×C4×C8C2×D4313yes—
194C43C2×#297111yescharacteristic, complemented, Sylow
195C2×#41—438no—
196C2×#41—868no—
197C22×Q8C4×D4311yescharacteristic
198C22×D4—433no—
199C23×C4—433no—
200C23×C4—433no—
201C23×C4—433no—
202C2×M16—4312no—
203C2×M16—4312no—
204C2×M16—8612no—
205C2×M16—8612no—
206C22×C8—431no—
207C22×C8—433no—
208C22×C8C22×D4313yes—
209C22×C8C22×D4311yescharacteristic
210C4×Q8—438no—
211C4×Q8C4×D4314yes—
212C4×Q8C22×D4314yes—
213C4×D4—4324no—
214C4×D4—4312no—
215C4×D4—4312no—
216#117—4324no—
217C2×C4⋊C4—433no—
218C2×C4⋊C4C4×D4313yes—
219C2×C22⋊C4—436no—
220C2×C42—433no—
221C2×C42—433no—
222C2×C42—431no—
223C2×C42—4312no—
224C2×C42—4312no—
225C2×C42C22×D4313yes—
226C4⋊C8—4312no—
227C4⋊C8C22×D43112yes—
228C22⋊C8—4324no—
229#97—434no—
230#97—4312no—
231C4×C8—4312no—
232C4×C8C22×D43112yes—
233C24—433no—
234#41—8632no—
235C2×Q8#1062187218yescomplemented
236C2×Q8C2×C4×D4314yes—
237C2×D4—4312no—
238C2×D4—8612no—
239C22×C4—431no—
240C22×C4—431no—
241C22×C4—433no—
242C22×C4—4312no—
243C22×C4—436no—
244C22×C4—436no—
245C22×C4—4312no—
246C22×C4—8612no—
247C22×C4—866no—
248C22×C4—866no—
249C22×C4—1726no—
250C22×C4C2×C4×D4313yes—
251C22×C4C2×C4×D4313yes—
252C22×C4C23×D4311yescharacteristic
253M16—8624no—
254M16—8624no—
255C2×C8—26no—
256C2×C8—434no—
257C2×C8—432no—
258C2×C8—436no—
259C2×C8—866no—
260C2×C8#1062190214yescomplemented
261C2×C8C23×D4316yes—
262C2×C8C23×D4312yes—
263C4⋊C4—4312no—
264C4⋊C4C2×C4×D43112yes—
265C22⋊C4—4324no—
266C42—432no—
267C42—4312no—
268C42—4312no—
269C42—432no—
270C42C2×C4×D4316yes—
271C42C23×D4316yes—
272C23—436no—
273C23—866no—
274C23—866no—
275C23—866no—
276C23C22×C4×D4311yescharacteristic
277Q8C2×#10621872116yescomplemented
278D4—8624no—
279C2×C4—26no—
280C2×C4—432no—
281C2×C4—432no—
282C2×C4—436no—
283C2×C4—866no—
284C2×C4—862no—
285C2×C4—862no—
286C2×C4—8612no—
287C2×C4—8624no—
288C2×C4—866no—
289C2×C4—866no—
290C2×C4—17212no—
291C2×C4C2×#10621872112yes—
292C2×C4C22×C4×D4316yes—
293C2×C4C22×C4×D4311yescharacteristic
294C2×C4C22×C4×D4316yes—
295C2×C4#41×D4312yes—
296C2×C4C2×#1062190212yes—
297C2×C4C24×D4311yescharacteristic
298C8—26no—
299C8—434no—
300C8—866no—
301C8C2×#1062190214yescomplemented
302C22—866no—
303C22—866no—
304C22—866no—
305C22—17212no—
306C22C4×#1062190212yes—
307C22C22×#1062187212yes—
308C22#1458366412yes—
309C22C23×C4×D4311yescharacteristic
310C4—26no—
311C4—866no—
312C4—862no—
313C4—862no—
314C4C4×#1062190212yes—
315C4C22×#10621872112yes—
316C4C2×#41×D4311yescharacteristic
317C4C22×#1062190211yescharacteristic
318C2—1726no—
319C2#1914361414yesdirect product factor
320C2C2×C4×#1062190211yescharacteristic
321C2C23×#1062187211yescharacteristic
322C2C2×#1458366411yescharacteristic
subgroupG/H
centerC22×C4C23×D43
commutatorC22×C43C24×C4
FrattiniC2×C4C24×D43
FittingC2×C8×Q8×C43C2
socleC23×C43C23×C4
prime radicalC22×#10621902C4
cosocleC2×C4×C43C25
hypercenterC2×C8×Q8D43
hypocenterC43C2×#2971
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C8×Q8

Complements

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

NH ≅ G/Ntype
2. #19143614C2direct (N × H)
3. C2×Q8×C43⋊C8C2semidirect
4. C2×#14582978C2semidirect
5. C2×#14582976C2semidirect
6. C2×#14582955C2semidirect
7. C2×C4×#10621872C2semidirect
8. C2×C8×Q8×C43C2semidirect
19. Q8×C43⋊C8C22semidirect
20. #14582978C22semidirect
21. #14582976C22semidirect
22. #14582955C22semidirect
25. C4×#10621872C22semidirect
30. C8×Q8×C43C22semidirect
72. C2×Q8×C43M16semidirect
92. C2×C8×C43#41semidirect
105. C2×C43⋊C8#41semidirect
115. Q8×C43C2×M16semidirect
137. C8×C43C2×#41semidirect
139. C43⋊C8C2×#41semidirect
160. C2×C8×Q8D43semidirect
165. C2×C43#2971semidirect
182. C8×Q8C2×D43semidirect
194. C43C2×#2971semidirect
235. C2×Q8#10621872semidirect
260. C2×C8#10621902semidirect
277. Q8C2×#10621872semidirect
301. C8C2×#10621902semidirect
319. C2#19143614direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#106219022
#191436142
C2×Q8×C43⋊C82
C2×#145829782
C2×#145829762
C2×#145829552
C2×C4×#106218722
C2×C8×Q8×C432
C2×#297143