Finite Group Databasebeta

← C2×#19137079 #25254980

Subgroups — C2×#19137079 #25254980

Order 11008.

3854 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
1C22×#13063284C211yesmaximal, characteristic
2C23×C4×Dic43C211yesmaximal, characteristic
3#19137079C2116yesmaximal, direct product factor
4C2×#14582798C214yesmaximal, complemented
5C2×#14582774C214yesmaximal
6C2×C4×C4⋊Dic43C214yesmaximal, complemented
7C22×#117×C43C211yesmaximal, characteristic
8C24×Dic43C2212yes—
9C2×#13063284—28no—
10C2×#13063284C2218yes—
11C22×C4⋊Dic43C2212yes—
12C22×C4⋊Dic43C2218yes—
13C22×C22⋊Dic43C2212yes—
14C22×C4×Dic43—28no—
15C22×C4×Dic43C2212yes—
16C22×C4×Dic43C2218yes—
17C22×C4×Dic43C2212yes—
18C22×C4×Dic43C2212yes—
19#14582798C22132yescomplemented
20#14582774C22132yes—
21C4×C4⋊Dic43C22132yescomplemented
22C2×C43⋊#95C2218yes—
23C24×C4×C43C2211yescharacteristic
24C2×#117×C43C4116yescomplemented
25C2×#117×C43C2218yes—
26C22×C4⋊C4×C43C2212yes—
27C22×C22⋊C4×C43C2212yes—
28C22×C42×C43C2212yes—
29C23×Dic43—28no—
30C23×Dic43—216no—
31C23×Dic43C2318yes—
32C23×Dic43C2314yes—
33C23×Dic43C2314yes—
34#13063284—232no—
35C2×C4⋊Dic43—28no—
36C2×C4⋊Dic43—232no—
37C2×C4⋊Dic43C2318yes—
38C2×C4⋊Dic43C23132yes—
39C2×C22⋊Dic43—28no—
40C2×C22⋊Dic43C2318yes—
41C2×C4×Dic43—28no—
42C2×C4×Dic43—28no—
43C2×C4×Dic43—232no—
44C2×C4×Dic43—28no—
45C2×C4×Dic43C2318yes—
46C2×C4×Dic43C2318yes—
47C2×C4×Dic43C2318yes—
48C43⋊#95C23132yes—
49C25×C43C2311yescharacteristic
50C23×C4×C43C2×C418yes—
51C23×C4×C43D418yes—
52C23×C4×C43Q818yes—
53C23×C4×C43C2314yes—
54C23×C4×C43C2311yescharacteristic
55C23×C4×C43C2314yes—
56C23×C4×C43C2311yescharacteristic
57#117×C43C2×C4164yescomplemented
58C2×C4⋊C4×C43C2×C4116yescomplemented
59C2×C4⋊C4×C43C2318yes—
60C2×C22⋊C4×C43C2×C4116yes—
61C2×C22⋊C4×C43C2318yes—
62C2×C42×C43C2×C4116yescomplemented
63C2×C42×C43C2318yes—
64C24×C43—28no—
65C24×C43C22×C414yes—
66C24×C43C2×D414yes—
67C24×C43C2×Q814yes—
68C24×C43C2412yes—
69C24×C43C2411yescharacteristic
70C22×C4×C43—216no—
71C22×C4×C43C4⋊C4164yescomplemented
72C22×C4×C43C22×C4116yes—
73C22×C4×C43C22×C414yes—
74C22×C4×C43C22×C414yes—
75C22×C4×C43C22×C4116yes—
76C22×C4×C43C2×D414yes—
77C22×C4×C43C2×D414yes—
78C22×C4×C43C2×D4116yes—
79C22×C4×C43C2×Q814yes—
80C22×C4×C43C2×Q814yes—
81C22×C4×C43C2×Q8116yes—
82C22×C4×C43C2418yes—
83C22×C4×C43C2412yes—
84C22×C4×C43C2412yes—
85C22×Dic43—264no—
86C22×Dic43—232no—
87C22×Dic43—216no—
88C22×Dic43—28no—
89C22×Dic43—28no—
90C22×Dic43—28no—
91C22×Dic43—216no—
92C22×Dic43#41116yes—
93C22×Dic43C2418yes—
94C22×Dic43C2418yes—
95C4⋊C4×C43C22×C4132yescomplemented
96C22⋊C4×C43C22×C4132yes—
97C42×C43C22×C4132yescomplemented
98C22⋊Dic43—216no—
99C4⋊Dic43—216no—
100C4⋊Dic43—264no—
101C4×Dic43—216no—
102C4×Dic43—216no—
103C4×Dic43—216no—
104C23×C43—216no—
105C23×C43—216no—
106C23×C43—216no—
107C23×C43—28no—
108C23×C43C2×C4⋊C4116yes—
109C23×C43C23×C414yes—
110C23×C43C23×C412yes—
111C23×C43C22×D414yes—
112C23×C43C22×D412yes—
113C23×C43C22×Q814yes—
114C23×C43C22×Q812yes—
115C23×C43C2×#4118yes—
116C23×C43C2511yescharacteristic
117C2×C4×C43—232no—
118C2×C4×C43—216no—
119C2×C4×C43C2×C4⋊C4116yes—
120C2×C4×C43C2×C4⋊C4116yes—
121C2×C4×C43C2×C4⋊C4164yescomplemented
122C2×C4×C43C23×C4116yes—
123C2×C4×C43C23×C414yes—
124C2×C4×C43C23×C414yes—
125C2×C4×C43C22×D414yes—
126C2×C4×C43C22×D414yes—
127C2×C4×C43C22×Q814yes—
128C2×C4×C43C22×Q814yes—
129C2×Dic43—264no—
130C2×Dic43—232no—
131C2×Dic43—28no—
132C2×Dic43—28no—
133C2×Dic43—28no—
134C2×Dic43—216no—
135C2×Dic43—416no—
136C2×Dic43C2×#41116yes—
137C2×#2296—431nomaximal, Sylow
138C22×C43—28no—
139C22×C43—28no—
140C22×C43—28no—
141C22×C43—232no—
142C22×C43C22×C4⋊C418yes—
143C22×C43C22×C4⋊C414yes—
144C22×C43C4×#4118yes—
145C22×C43#52518yes—
146C22×C43#53318yes—
147C22×C43C24×C411yescharacteristic
148C22×C43C23×D411yescharacteristic
149C22×C43C23×Q811yescharacteristic
150C22×C43C22×#4114yes—
151C4×C43—216no—
152C4×C43C22×C4⋊C418yes—
153C4×C43C22×C4⋊C418yes—
154Dic43—216no—
155Dic43—48no—
156C22×#117—431no—
157C22×#117D4311yescharacteristic
158C23×C42—431no—
159#2296—4316no—
160C2×#389—434no—
161C2×#385—434no—
162C2×C4×C4⋊C4—434no—
163C2×C43—28no—
164C2×C43#229618yescomplemented
165C2×C43C23×C4⋊C411yescharacteristic
166C2×C43C2×C4×#4112yes—
167C2×C43C2×#52512yes—
168C2×C43C2×#53312yes—
169C24×C4—432no—
170C24×C4C2×D4311yescharacteristic
171C2×#117—438no—
172C2×#117—868no—
173C2×#117Dic43116yescomplemented
174C2×#117C2×D4318yes—
175C22×C4⋊C4—432no—
176C22×C4⋊C4—438no—
177C22×C4⋊C4C2×D4312yes—
178C22×C22⋊C4—432no—
179C22×C22⋊C4C2×D4312yes—
180C22×C42—432no—
181C22×C42—438no—
182C22×C42—432no—
183C22×C42—432no—
184C22×C42—868no—
185C22×C42C2×D4312yes—
186#389—4332no—
187#385—4332no—
188C4×C4⋊C4—4332no—
189C2×#95—438no—
190C43C2×#229611yescharacteristic, complemented, Sylow
191C25C22×D4311yescharacteristic
192C23×C4—434no—
193C23×C4—434no—
194C23×C4—438no—
195C23×C4—8616no—
196C23×C4—868no—
197C23×C4Dic8618yes—
198C23×C4D17218yes—
199C23×C4C2×Dic4318yes—
200C23×C4C22×D4314yes—
201C23×C4C22×D4311yescharacteristic
202C23×C4C22×D4314yes—
203C23×C4C22×D4311yescharacteristic
204#117—8632no—
205#117C2×Dic43164yescomplemented
206C2×C4⋊C4—438no—
207C2×C4⋊C4—4332no—
208C2×C4⋊C4—8632no—
209C2×C4⋊C4—868no—
210C2×C4⋊C4C2×Dic43116yescomplemented
211C2×C4⋊C4C22×D4318yes—
212C2×C22⋊C4—438no—
213C2×C22⋊C4—868no—
214C2×C22⋊C4C2×Dic43116yes—
215C2×C22⋊C4C22×D4318yes—
216C2×C42—438no—
217C2×C42—438no—
218C2×C42—438no—
219C2×C42—868no—
220C2×C42—868no—
221C2×C42—868no—
222C2×C42—8632no—
223C2×C42C2×Dic43116yescomplemented
224C2×C42C22×D4318yes—
225#95—4332no—
226C24—28no—
227C24C2×Dic8614yes—
228C24C2×D17214yes—
229C24C22×Dic4314yes—
230C24C23×D4312yes—
231C24C23×D4311yescharacteristic
232C22×C4—216no—
233C22×C4—4316no—
234C22×C4—438no—
235C22×C4—438no—
236C22×C4—8632no—
237C22×C4—8664no—
238C22×C4—8616no—
239C22×C4—868no—
240C22×C4—868no—
241C22×C4—868no—
242C22×C4—8616no—
243C22×C4C4⋊Dic43164yescomplemented
244C22×C4C2×Dic8614yes—
245C22×C4C2×Dic8614yes—
246C22×C4C2×Dic86116yes—
247C22×C4C2×D17214yes—
248C22×C4C2×D17214yes—
249C22×C4C2×D172116yes—
250C22×C4C22×Dic43116yes—
251C22×C4C22×Dic4314yes—
252C22×C4C22×Dic4314yes—
253C22×C4C22×Dic43116yes—
254C22×C4C23×D4318yes—
255C22×C4C23×D4312yes—
256C22×C4C23×D4312yes—
257C4⋊C4—8664no—
258C4⋊C4—8616no—
259C4⋊C4C22×Dic43132yescomplemented
260C22⋊C4—8616no—
261C22⋊C4C22×Dic43132yes—
262C42—8616no—
263C42—8616no—
264C42—8616no—
265C42C22×Dic43132yescomplemented
266C23—216no—
267C23—216no—
268C23—216no—
269C23—28no—
270C23C2×C4⋊Dic43116yes—
271C23C23×Dic4314yes—
272C23C23×Dic4312yes—
273C23C22×D17214yes—
274C23C22×D17212yes—
275C23C22×Dic8614yes—
276C23C22×Dic8612yes—
277C23#41×D4318yes—
278C23C24×D4311yescharacteristic
279C2×C4—232no—
280C2×C4—216no—
281C2×C4—4316no—
282C2×C4—8664no—
283C2×C4—8632no—
284C2×C4—868no—
285C2×C4—868no—
286C2×C4—868no—
287C2×C4—8616no—
288C2×C4—17216no—
289C2×C4C2×C4⋊Dic43116yes—
290C2×C4C2×C4⋊Dic43116yes—
291C2×C4C2×C4⋊Dic43164yescomplemented
292C2×C4C23×Dic43116yes—
293C2×C4C23×Dic4314yes—
294C2×C4C23×Dic4314yes—
295C2×C4C22×D17214yes—
296C2×C4C22×D17214yes—
297C2×C4C22×Dic8614yes—
298C2×C4C22×Dic8614yes—
299C22—28no—
300C22—232no—
301C22—28no—
302C22—28no—
303C22C22×C4⋊Dic4318yes—
304C22C22×C4⋊Dic4314yes—
305C22#41×Dic4318yes—
306C22#1458341118yes—
307C22#1458345218yes—
308C22C24×Dic4311yescharacteristic
309C22C23×D17211yescharacteristic
310C22C23×Dic8611yescharacteristic
311C22C2×#41×D4314yes—
312C4—216no—
313C4—8616no—
314C4—1728no—
315C4C22×C4⋊Dic4318yes—
316C4C22×C4⋊Dic4318yes—
317C2—28no—
318C2#1913707918yesdirect product factor
319C2C23×C4⋊Dic4311yescharacteristic
320C2C2×#41×Dic4312yes—
321C2C2×#1458341112yes—
322C2C2×#1458345212yes—
subgroupG/H
centerC23×C4C22×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC22×#117×C43C2
socleC24×C43C24
prime radicalC25×C43C23
cosocleC23×C43C25
hypercenterC22×#117D43
hypocenterC43C2×#2296
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
3. #19137079C2direct (N × H)
4. C2×#14582798C2semidirect
6. C2×C4×C4⋊Dic43C2semidirect
19. #14582798C22semidirect
21. C4×C4⋊Dic43C22semidirect
24. C2×#117×C43C4semidirect
57. #117×C43C2×C4semidirect
58. C2×C4⋊C4×C43C2×C4semidirect
62. C2×C42×C43C2×C4semidirect
71. C22×C4×C43C4⋊C4semidirect
95. C4⋊C4×C43C22×C4semidirect
97. C42×C43C22×C4semidirect
121. C2×C4×C43C2×C4⋊C4semidirect
164. C2×C43#2296semidirect
173. C2×#117Dic43semidirect
190. C43C2×#2296semidirect
205. #117C2×Dic43semidirect
210. C2×C4⋊C4C2×Dic43semidirect
223. C2×C42C2×Dic43semidirect
243. C22×C4C4⋊Dic43semidirect
259. C4⋊C4C22×Dic43semidirect
265. C42C22×Dic43semidirect
291. C2×C4C2×C4⋊Dic43semidirect
318. C2#19137079direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130632842
C23×C4×Dic432
#191370792
C2×#145827982
C2×#145827742
C2×C4×C4⋊Dic432
C22×#117×C432
C2×#229643