Finite Group Databasebeta

← C2×#19143313 #25960478

Subgroups — C2×#19143313 #25960478

Order 11008.

2806 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063332C212yesmaximal, complemented
2#19143313C2116yesmaximal, direct product factor
3C2×#14582971C218yesmaximal, complemented
4C2×#14582923C211yesmaximal, characteristic, complemented
5C2×#14582866C212yesmaximal, complemented
6C22×#13063236C211yesmaximal, characteristic, complemented
7C2×C43×#532C211yesmaximal, characteristic
8C2×#13063332—216no—
9C2×#13063332C22116yescomplemented
10C22×#10621877C2214yes—
11C22×#10621877C2212yes—
12C23×C43⋊C8C2211yescharacteristic
13C23×C43⋊C8C2214yes—
14C23×C43⋊C8C2211yescharacteristic
15#14582971C22164yescomplemented
16#14582923C2218yescomplemented
17C2×C4⋊(C43⋊C8)C2214yes—
18#14582866C22116yescomplemented
19C2×C22⋊(C43⋊C8)C2218yes—
20C2×#13063236C2214yes—
21C2×#13063236C2218yescomplemented
22C22×#41×C43C2212yes—
23C43×#532C418yes—
24C43×#532C2218yes—
25C2×C4⋊Q8×C43C411yescharacteristic
26C2×#127×C43C411yescharacteristic
27C2×#124×C43C412yes—
28C2×#121×C43C414yes—
29C2×C4×D4×C43C2214yes—
30C22×C42×C43C2211yescharacteristic
31#13063332—264no—
32C2×#10621877—28no—
33C2×#10621877—216no—
34C2×#10621877C2318yes—
35C2×#10621877C23116yes—
36C22×C43⋊C8—24no—
37C22×C43⋊C8—216no—
38C22×C43⋊C8D418yescomplemented
39C22×C43⋊C8C2312yes—
40C22×C43⋊C8C2314yes—
41C22×C43⋊C8C2314yes—
42C22×C43⋊C8C23116yes—
43C22×C43⋊C8C2312yes—
44C22×C43⋊C8C2314yes—
45C4⋊(C43⋊C8)C23116yes—
46C22⋊(C43⋊C8)C23132yes—
47#13063236C23116yes—
48C2×#41×C43—28no—
49C2×#41×C43—28no—
50C2×#41×C43C2×C418yes—
51C2×#41×C43C2318yes—
52C22×Q8×C43C2×C412yes—
53C22×D4×C43C2×C414yes—
54C22×D4×C43C2×C412yes—
55C22×D4×C43C2×C414yes—
56C23×C4×C43C2×C412yes—
57C23×C4×C43C2314yes—
58C23×C4×C43C2311yescharacteristic
59C4⋊Q8×C43C2×C418yes—
60#127×C43C2×C418yes—
61#124×C43C2×C4116yes—
62#121×C43C2×C4132yes—
63C4×D4×C43C2×C4116yes—
64C4×D4×C43C23116yes—
65C2×C4⋊C4×C43C2×C414yes—
66C2×C22⋊C4×C43C2×C418yes—
67C2×C42×C43C2×C411yescharacteristic
68C2×C42×C43C2×C411yescharacteristic
69C2×C42×C43C2×C414yes—
70C2×C42×C43C2312yes—
71C2×C42×C43C2314yes—
72C24×C43C22×C414yes—
73C24×C43C22×C411yescharacteristic
74#41×C43—232no—
75#41×C43—216no—
76#41×C43—216no—
77C2×Q8×C43—28no—
78C2×Q8×C43C22×C418yes—
79C2×D4×C43—28no—
80C2×D4×C43—216no—
81C2×D4×C43—48no—
82C2×D4×C43C22×C4116yes—
83C2×D4×C43C22×C418yes—
84C2×D4×C43C22×C4116yes—
85C22×C4×C43—28no—
86C22×C4×C43—28no—
87C22×C4×C43—44no—
88C22×C4×C43C22×C412yes—
89C22×C4×C43C22×C412yes—
90C22×C4×C43C22×C414yes—
91C22×C4×C43C22×C418yes—
92C22×C4×C43C22×C418yes—
93C22×C4×C43C22×C411yescharacteristic
94C22×C4×C43C22×C412yes—
95C22×C4×C43C2×D414yes—
96C22×C4×C43#4114yes—
97C22×C4×C43C2418yes—
98C22×C4×C43C2412yes—
99C22×C4×C43C2411yescharacteristic
100C4⋊C4×C43C22×C4116yes—
101C22⋊C4×C43C22×C4132yes—
102C42×C43C22×C414yes—
103C42×C43C22×C414yes—
104C42×C43C22×C414yes—
105C42×C43C2414yes—
106#10621877—216no—
107#10621877—232no—
108C2×C43⋊C8—28no—
109C2×C43⋊C8—24no—
110C2×C43⋊C8—28no—
111C2×C43⋊C8—232no—
112C2×C43⋊C8C2×D418yes—
113C2×C43⋊C8C2×D4116yescomplemented
114C2×C43⋊C8C2414yes—
115C2×C43⋊C8C2418yes—
116C2×C43⋊C8C2414yes—
117C23×C43—24no—
118C23×C43—28no—
119C23×C43—216no—
120C23×C43C4×D414yes—
121C23×C43C23×C418yes—
122C23×C43C23×C412yes—
123C23×C43C23×C411yescharacteristic
124Q8×C43—216no—
125D4×C43—232no—
126D4×C43—216no—
127D4×C43—416no—
128C2×C4×C43—28no—
129C2×C4×C43—24no—
130C2×C4×C43—24no—
131C2×C4×C43—216no—
132C2×C4×C43—28no—
133C2×C4×C43—28no—
134C2×C4×C43—48no—
135C2×C4×C43C4×D414yes—
136C2×C4×C43C4×D418yes—
137C2×C4×C43C23×C414yes—
138C2×C4×C43C23×C414yes—
139C2×C4×C43C23×C418yes—
140C2×C4×C43C23×C411yescharacteristic
141C2×C4×C43C23×C412yes—
142C2×C4×C43C22×D412yes—
143C2×C4×C43C22×D414yes—
144C2×C4×C43C2×#4112yes—
145C2×C4×C43C2×#4114yes—
146C2×C4×C43C2511yescharacteristic
147C43⋊C8—28no—
148C43⋊C8—24no—
149C43⋊C8C22×D418yes—
150C2×#2932—431nomaximal, Sylow
151C22×C43—28no—
152C22×C43—24no—
153C22×C43—28no—
154C22×C43—216no—
155C22×C43—416no—
156C22×C43C2×C4×D414yes—
157C22×C43C2×C4×D412yes—
158C22×C43#56814yes—
159C22×C43C24×C411yescharacteristic
160C4×C43—28no—
161C4×C43—24no—
162C4×C43—24no—
163C4×C43C2×C4×D412yes—
164C4×C43C2×C4×D414yes—
165C4×C43C23×D411yescharacteristic
166C4×C43C22×#4111yescharacteristic
167C22×#131—432no—
168C2×#532D4311yescharacteristic
169#2932—4316no—
170C2×#435—438no—
171C2×#423—431no—
172C2×#408—432no—
173C22×#97—431no—
174C2×C43—24no—
175C2×C43—48no—
176C2×C43#293214yescomplemented
177C2×C43C22×C4×D411yescharacteristic
178C2×C43C2×#56812yes—
179C22×#41C2×D4312yes—
180C2×#131—4316no—
181C2×#131—8616no—
182C22×M16—432no—
183C22×M16—434no—
184C23×C8—431no—
185C23×C8—431no—
186C23×C8—434no—
187#532Dic4318yes—
188#532C2×D4318yes—
189C2×C4⋊Q8Dic4311yescharacteristic
190C2×#127Dic4311yescharacteristic
191C2×#124Dic4312yes—
192C2×#121Dic4314yes—
193C2×C4×D4C2×D4314yes—
194C22×C42C2×D4311yescharacteristic
195#435—4364no—
196#423—438no—
197C2×C4⋊C8—434no—
198#408—4316no—
199C2×C22⋊C8—438no—
200C2×#97—434no—
201C2×#97—438no—
202C43C2×#293211yescharacteristic, complemented, Sylow
203C2×#41—28no—
204C2×#41—28no—
205C2×#41C2×Dic4318yes—
206C2×#41C22×D4318yes—
207C22×Q8C2×Dic4312yes—
208C22×D4C2×Dic4314yes—
209C22×D4C2×Dic4312yes—
210C22×D4C2×Dic4314yes—
211C23×C4C2×Dic4312yes—
212C23×C4C22×D4314yes—
213C23×C4C22×D4311yescharacteristic
214#131—8664no—
215C2×M16—438no—
216C2×M16—4316no—
217C2×M16—8616no—
218C2×M16—868no—
219C22×C8—438no—
220C22×C8—434no—
221C22×C8—432no—
222C22×C8—4316no—
223C22×C8—434no—
224C22×C8—434no—
225C22×C8—432no—
226C22×C8—8616no—
227C22×C8—864no—
228C4⋊Q8C2×Dic4318yes—
229#127C2×Dic4318yes—
230#124C2×Dic43116yes—
231#121C2×Dic43132yes—
232C4×D4C2×Dic43116yes—
233C4×D4C22×D43116yes—
234C2×C4⋊C4C2×Dic4314yes—
235C2×C22⋊C4C2×Dic4318yes—
236C2×C42C2×Dic4311yescharacteristic
237C2×C42C2×Dic4311yescharacteristic
238C2×C42C2×Dic4314yes—
239C2×C42C22×D4314yes—
240C2×C42C22×D4312yes—
241C4⋊C8—4316no—
242C22⋊C8—4332no—
243#97—4316no—
244C24C22×Dic4314yes—
245C24C22×Dic4311yescharacteristic
246#41—232no—
247#41—216no—
248#41—216no—
249C2×Q8—28no—
250C2×Q8C22×Dic4318yes—
251C2×D4—216no—
252C2×D4—28no—
253C2×D4—48no—
254C2×D4C22×Dic43116yes—
255C2×D4C22×Dic4318yes—
256C2×D4C22×Dic43116yes—
257C22×C4—28no—
258C22×C4—28no—
259C22×C4—44no—
260C22×C4D4×D4314yes—
261C22×C4#1062190014yes—
262C22×C4C22×Dic4312yes—
263C22×C4C22×Dic4312yes—
264C22×C4C22×Dic4314yes—
265C22×C4C22×Dic4318yes—
266C22×C4C22×Dic4318yes—
267C22×C4C22×Dic4311yescharacteristic
268C22×C4C22×Dic4312yes—
269C22×C4C23×D4318yes—
270C22×C4C23×D4312yes—
271C22×C4C23×D4311yescharacteristic
272M16—8632no—
273M16—8616no—
274C2×C8—438no—
275C2×C8—4316no—
276C2×C8—434no—
277C2×C8—434no—
278C2×C8—438no—
279C2×C8—8632no—
280C2×C8—868no—
281C2×C8—864no—
282C2×C8—868no—
283C4⋊C4C22×Dic43116yes—
284C22⋊C4C22×Dic43132yes—
285C42C22×Dic4314yes—
286C42C22×Dic4314yes—
287C42C22×Dic4314yes—
288C42C23×D4314yes—
289C23—24no—
290C23—28no—
291C23—216no—
292C23D4×Dic4314yes—
293C23C23×Dic4318yes—
294C23C23×Dic4312yes—
295C23C23×Dic4311yescharacteristic
296Q8—216no—
297D4—232no—
298D4—216no—
299D4—416no—
300C2×C4—28no—
301C2×C4—24no—
302C2×C4—24no—
303C2×C4—216no—
304C2×C4—28no—
305C2×C4—28no—
306C2×C4—48no—
307C2×C4D4×Dic4314yes—
308C2×C4D4×Dic4318yes—
309C2×C4C23×Dic4314yes—
310C2×C4C23×Dic4314yes—
311C2×C4C23×Dic4318yes—
312C2×C4C23×Dic4311yescharacteristic
313C2×C4C23×Dic4312yes—
314C2×C4C2×D4×D4312yes—
315C2×C4C2×D4×D4314yes—
316C2×C4C2×#1062190012yes—
317C2×C4C2×#1062190014yes—
318C2×C4C24×D4311yescharacteristic
319C8—438no—
320C8—868no—
321C8—864no—
322C22—28no—
323C22—24no—
324C22—28no—
325C22—216no—
326C22—416no—
327C22C2×D4×Dic4314yes—
328C22C2×D4×Dic4312yes—
329C22#1458366614yes—
330C22C24×Dic4311yescharacteristic
331C4—28no—
332C4—24no—
333C4—24no—
334C4C2×D4×Dic4312yes—
335C4C2×D4×Dic4314yes—
336C4C22×D4×D4311yescharacteristic
337C4C22×#1062190011yescharacteristic
338C2—24no—
339C2—48no—
340C2#1914331314yesdirect product factor
341C2C22×D4×Dic4311yescharacteristic
342C2C2×#1458366612yes—
subgroupG/H
centerC22×C4C23×D43
commutatorC22×C43C24×C4
FrattiniC2×C4C24×D43
Fitting, prime radicalC2×C43×#532C2
socleC23×C43C23×C4
cosocleC2×C4×C43C25
hypercenterC2×#532D43
hypocenterC43C2×#2932
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. C22×#13063332C2semidirect
2. #19143313C2direct (N × H)
3. C2×#14582971C2semidirect
4. C2×#14582923C2semidirect
5. C2×#14582866C2semidirect
6. C22×#13063236C2semidirect
9. C2×#13063332C22semidirect
15. #14582971C22semidirect
16. #14582923C22semidirect
18. #14582866C22semidirect
21. C2×#13063236C22semidirect
38. C22×C43⋊C8D4semidirect
113. C2×C43⋊C8C2×D4semidirect
176. C2×C43#2932semidirect
202. C43C2×#2932semidirect
340. C2#19143313direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633322
#191433132
C2×#145829712
C2×#145829232
C2×#145828662
C22×#130632362
C2×C43×#5322
C2×#293243