Finite Group Databasebeta

← #25960049

Subgroups — #25960049

Order 11008.

5134 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583666C212yesmaximal, complemented
2#19143044C2116yesmaximal, complemented
3#19143040C216yesmaximal, complemented
4C2×#14582863C216yesmaximal, complemented
5C23×#41×C43C211yesmaximal, characteristic
6#14583666—216no—
7C2×#13063332C22116yescomplemented
8C22×#10621877C22112yescomplemented
9#14582866C22148yescomplemented
10#14582863C2214yes—
11#14582863C22124yescomplemented
12#14582863C22112yescomplemented
13C2×C22⋊(C43⋊C8)C22124yescomplemented
14C22×#41×C43—216no—
15C22×#41×C43C418yes—
16C22×#41×C43C411yescharacteristic
17C22×#41×C43C413yes—
18C22×#41×C43C2213yes—
19C22×#41×C43C2218yes—
20C22×#41×C43C2211yescharacteristic
21C23×Q8×C43C411yescharacteristic
22C23×D4×C43C413yes—
23C24×C4×C43C2213yes—
24#13063332—264no—
25C2×#10621877—248no—
26C2×#10621877C2318yes—
27C2×#10621877C23124yescomplemented
28C22×C43⋊C8C23124yescomplemented
29C22⋊(C43⋊C8)C23116yes—
30C22⋊(C43⋊C8)C23148yescomplemented
31C25×C43C2×C413yes—
32C2×#41×C43—264no—
33C2×#41×C43—264no—
34C2×#41×C43—28no—
35C2×#41×C43—224no—
36C2×#41×C43—224no—
37C2×#41×C43C2×C418yes—
38C2×#41×C43C2×C4124yes—
39C2×#41×C43C2×C4112yes—
40C2×#41×C43C2×C414yes—
41C2×#41×C43D4116yes—
42C2×#41×C43C23112yes—
43C2×#41×C43C2314yes—
44C22×Q8×C43—28no—
45C22×Q8×C43C2×C418yes—
46C22×Q8×C43C2×C413yes—
47C22×Q8×C43C2×C411yescharacteristic
48C22×D4×C43—224no—
49C22×D4×C43C2×C4124yes—
50C22×D4×C43C2×C416yes—
51C22×D4×C43C2×C413yes—
52C22×D4×C43C2×C413yes—
53C23×C4×C43—224no—
54C23×C4×C43C2×C413yes—
55C23×C4×C43C2×C4112yes—
56C23×C4×C43C2×C413yes—
57C23×C4×C43C2×C413yes—
58C23×C4×C43C23112yes—
59C23×C4×C43C2311yescharacteristic
60C23×C4×C43C2313yes—
61C23×C4×C43C2313yes—
62C24×C43—212no—
63C24×C43—412no—
64C24×C43C22×C411yescharacteristic
65C24×C43C22×C4112yes—
66C24×C43C22×C413yes—
67C24×C43C22×C413yes—
68#41×C43—232no—
69#41×C43—296no—
70#41×C43—248no—
71#41×C43—248no—
72#41×C43C22⋊C4132yes—
73#41×C43C2×D4132yes—
74C2×Q8×C43—232no—
75C2×Q8×C43—212no—
76C2×Q8×C43C22⋊C418yes—
77C2×Q8×C43C22×C4112yes—
78C2×Q8×C43C22×C414yes—
79C2×D4×C43—296no—
80C2×D4×C43—212no—
81C2×D4×C43—224no—
82C2×D4×C43C22⋊C4124yes—
83C2×D4×C43C22×C4112yes—
84C2×D4×C43C22×C4124yes—
85C2×D4×C43C22×C4112yes—
86C22×C4×C43—212no—
87C22×C4×C43—212no—
88C22×C4×C43—248no—
89C22×C4×C43—24no—
90C22×C4×C43—212no—
91C22×C4×C43—248no—
92C22×C4×C43—212no—
93C22×C4×C43C22×C411yescharacteristic
94C22×C4×C43C22×C412yes—
95C22×C4×C43C22×C413yes—
96C22×C4×C43C22×C4112yes—
97C22×C4×C43C22×C4112yes—
98C22×C4×C43C22×C416yes—
99C22×C4×C43C22×C4112yes—
100C22×C4×C43C22×C413yes—
101C22×C4×C43C22×C416yes—
102C22×C4×C43C2×D4124yes—
103C22×C4×C43C2412yes—
104C22×C4×C43C2416yes—
105C22×C4×C43C2411yescharacteristic
106C22×C4×C43C2416yes—
107#10621877—216no—
108#10621877—248no—
109C2×C43⋊C8—248no—
110C2×C43⋊C8C24116yes—
111C23×C43—22no—
112C23×C43—24no—
113C23×C43—224no—
114C23×C43—26no—
115C23×C43—224no—
116C23×C43—46no—
117C23×C43—412no—
118C23×C43—46no—
119C23×C43—448no—
120C23×C43C2×C22⋊C4112yes—
121C23×C43C23×C416yes—
122C23×C43C23×C411yescharacteristic
123C23×C43C23×C416yes—
124C23×C43C23×C412yes—
125Q8×C43—224no—
126Q8×C43C2×C22⋊C4116yes—
127D4×C43—248no—
128D4×C43—224no—
129D4×C43C2×C22⋊C4148yes—
130C2×C4×C43—22no—
131C2×C4×C43—26no—
132C2×C4×C43—224no—
133C2×C4×C43—24no—
134C2×C4×C43—224no—
135C2×C4×C43—224no—
136C2×C4×C43—212no—
137C2×C4×C43—24no—
138C2×C4×C43—212no—
139C2×C4×C43C2×C22⋊C4112yes—
140C2×C4×C43C2×C22⋊C4124yes—
141C2×C4×C43C23×C412yes—
142C2×C4×C43C23×C416yes—
143C2×C4×C43C23×C411yescharacteristic
144C2×C4×C43C23×C416yes—
145C2×C4×C43C22×D4124yes—
146C2×C4×C43C22×D414yes—
147C2×C4×C43C2511yescharacteristic
148C43⋊C8—216no—
149#60064—431nomaximal, Sylow
150C22×C43—28no—
151C22×C43—22no—
152C22×C43—22no—
153C22×C43—22no—
154C22×C43—212no—
155C22×C43—26no—
156C22×C43—212no—
157C22×C43—412no—
158C22×C43—448no—
159C22×C43—412no—
160C22×C43C22×C22⋊C412yes—
161C22×C43C22×C22⋊C4112yes—
162C22×C43#56814yescomplemented
163C22×C43C24×C411yescharacteristic
164C4×C43—22no—
165C4×C43—26no—
166C4×C43C22×C22⋊C412yes—
167C4×C43C22×C22⋊C4112yes—
168C4×C43C23×D412yes—
169C23×#41D4311yescharacteristic
170C2×#568—432no—
171#2880—4316no—
172#2879—436no—
173C2×#407—436no—
174C2×C43—22no—
175C2×C43—24no—
176C2×C43—212no—
177C2×C43—46no—
178C2×C43C23×C22⋊C411yescharacteristic
179C2×C43C2×#56812yes—
180C22×#41—216no—
181C22×#41Dic4318yes—
182C22×#41Dic4311yescharacteristic
183C22×#41Dic4313yes—
184C22×#41C2×D4313yes—
185C22×#41C2×D4318yes—
186C22×#41C2×D4311yescharacteristic
187C23×Q8Dic4311yescharacteristic
188C23×D4Dic4313yes—
189C24×C4C2×D4313yes—
190#568—8616no—
191C2×#131—4316no—
192C22×M16—4312no—
193#408—4348no—
194#407—434no—
195#407—4312no—
196#407—4324no—
197C2×C22⋊C8—4324no—
198C43#6006411yescharacteristic, complemented, Sylow
199C25C2×Dic4313yes—
200C2×#41—264no—
201C2×#41—264no—
202C2×#41—28no—
203C2×#41—224no—
204C2×#41—224no—
205C2×#41C2×Dic4318yes—
206C2×#41C2×Dic43124yes—
207C2×#41C2×Dic43112yes—
208C2×#41C2×Dic4314yes—
209C2×#41C22⋊D43116yes—
210C2×#41C22×D43112yes—
211C2×#41C22×D4314yes—
212C22×Q8—28no—
213C22×Q8C2×Dic4318yes—
214C22×Q8C2×Dic4313yes—
215C22×Q8C2×Dic4311yescharacteristic
216C22×D4—224no—
217C22×D4C2×Dic4316yes—
218C22×D4C2×Dic43124yes—
219C22×D4C2×Dic4313yes—
220C22×D4C2×Dic4313yes—
221C23×C4—224no—
222C23×C4C2×Dic4313yes—
223C23×C4C2×Dic4313yes—
224C23×C4C2×Dic43112yes—
225C23×C4C2×Dic4313yes—
226C23×C4C22×D4311yescharacteristic
227C23×C4C22×D43112yes—
228C23×C4C22×D4313yes—
229C23×C4C22×D4313yes—
230#131—8664no—
231C2×M16—438no—
232C2×M16—4324no—
233C2×M16—8648no—
234C22×C8—4324no—
235C22⋊C8—4316no—
236C22⋊C8—4348no—
237C24—212no—
238C24—412no—
239C24C22×Dic4311yescharacteristic
240C24C22×Dic43112yes—
241C24C22×Dic4313yes—
242C24C22×Dic4313yes—
243#41—232no—
244#41—296no—
245#41—248no—
246#41—248no—
247#41C22⋊Dic43132yes—
248#41C2×C22⋊D43132yes—
249C2×Q8—232no—
250C2×Q8—212no—
251C2×Q8C22⋊Dic4318yes—
252C2×Q8C22×Dic43112yes—
253C2×Q8C22×Dic4314yes—
254C2×D4—224no—
255C2×D4—296no—
256C2×D4—212no—
257C2×D4C22⋊Dic43124yes—
258C2×D4C22×Dic43124yes—
259C2×D4C22×Dic43112yes—
260C2×D4C22×Dic43112yes—
261C22×C4—212no—
262C22×C4—212no—
263C22×C4—212no—
264C22×C4—248no—
265C22×C4—24no—
266C22×C4—212no—
267C22×C4—248no—
268C22×C4C22×Dic4311yescharacteristic
269C22×C4C22×Dic4312yes—
270C22×C4C22×Dic4313yes—
271C22×C4C22×Dic43112yes—
272C22×C4C22×Dic43112yes—
273C22×C4C22×Dic43112yes—
274C22×C4C22×Dic4316yes—
275C22×C4C22×Dic4313yes—
276C22×C4C22×Dic4316yes—
277C22×C4C2×C22⋊D43124yes—
278C22×C4C23×D4312yes—
279C22×C4C23×D4316yes—
280C22×C4C23×D4316yes—
281C22×C4C23×D4311yescharacteristic
282M16—8616no—
283M16—8648no—
284C2×C8—4316no—
285C2×C8—8648no—
286C23—22no—
287C23—24no—
288C23—224no—
289C23—26no—
290C23—224no—
291C23—46no—
292C23—412no—
293C23—46no—
294C23—448no—
295C23C2×C22⋊Dic43112yes—
296C23C23×Dic4316yes—
297C23C23×Dic4311yescharacteristic
298C23C23×Dic4316yes—
299C23C23×Dic4312yes—
300Q8—224no—
301Q8C2×C22⋊Dic43116yes—
302D4—248no—
303D4—224no—
304D4C2×C22⋊Dic43148yes—
305C2×C4—22no—
306C2×C4—26no—
307C2×C4—224no—
308C2×C4—24no—
309C2×C4—224no—
310C2×C4—224no—
311C2×C4—212no—
312C2×C4—24no—
313C2×C4—212no—
314C2×C4C2×C22⋊Dic43112yes—
315C2×C4C2×C22⋊Dic43124yes—
316C2×C4C23×Dic4312yes—
317C2×C4C23×Dic4316yes—
318C2×C4C23×Dic4311yescharacteristic
319C2×C4C23×Dic4316yes—
320C2×C4C22×C22⋊D43124yes—
321C2×C4C22×C22⋊D4314yes—
322C2×C4C24×D4311yescharacteristic
323C8—8616no—
324C22—28no—
325C22—22no—
326C22—22no—
327C22—22no—
328C22—212no—
329C22—26no—
330C22—212no—
331C22—412no—
332C22—448no—
333C22—412no—
334C22C22×C22⋊Dic4312yes—
335C22C22×C22⋊Dic43112yes—
336C22#1458366614yescomplemented
337C22C24×Dic4311yescharacteristic
338C4—22no—
339C4—26no—
340C4C22×C22⋊Dic4312yes—
341C4C22×C22⋊Dic43112yes—
342C4C23×C22⋊D4312yes—
343C2—22no—
344C2—24no—
345C2—212no—
346C2—46no—
347C2C23×C22⋊Dic4311yescharacteristic
348C2C2×#1458366612yes—
subgroupG/H
center, FrattiniC2×C4C24×D43
commutator, socleC22×C43C24×C4
Fitting, prime radicalC23×#41×C43C2
cosocleC2×C4×C43C25
hypercenterC23×#41D43
hypocenterC43#60064
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×#41

Complements

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

NH ≅ G/Ntype
1. C2×#14583666C2semidirect
2. #19143044C2semidirect
3. #19143040C2semidirect
4. C2×#14582863C2semidirect
7. C2×#13063332C22semidirect
8. C22×#10621877C22semidirect
9. #14582866C22semidirect
11. #14582863C22semidirect
12. #14582863C22semidirect
13. C2×C22⋊(C43⋊C8)C22semidirect
27. C2×#10621877C23semidirect
28. C22×C43⋊C8C23semidirect
30. C22⋊(C43⋊C8)C23semidirect
162. C22×C43#568semidirect
198. C43#60064semidirect
336. C22#14583666semidirect

Maximal subgroups

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

subgroupindex
C2×#145836662
#191430442
#191430402
C2×#145828632
C23×#41×C432
#6006443