Finite Group Databasebeta

← C2×#382×D43 #25254869

Subgroups — C2×#382×D43 #25254869

Order 11008.

4286 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D43C212yesmaximal
2C22×C42×D43C211yesmaximal, characteristic
3C2×#14582765C211yesmaximal, characteristic, complemented
4C2×#14582764C212yesmaximal, complemented
5C2×#14582763C214yesmaximal, complemented
6#382×D43C2116yesmaximal, direct product factor
7C2×#95×D43C214yesmaximal
8C2×C43×#382C211yesmaximal, characteristic, complemented
9C23×C4×D43C2214yes—
10C23×C4×D43C2212yes—
11C23×C4×D43C2211yescharacteristic
12C22×C4⋊Dic43C2212yes—
13C22×Dic43⋊C4C2214yes—
14C2×C4⋊C4×D43—216no—
15C2×C4⋊C4×D43C22116yes—
16C22×C4×Dic43C2212yes—
17C22×C4×Dic43C2211yescharacteristic
18C2×C42×D43C4116yescomplemented
19C2×C42×D43C2218yes—
20#14582765C2218yescomplemented
21#14582764C22116yescomplemented
22#14582763C22132yescomplemented
23C2×C43⋊#95C2218yes—
24C2×C43⋊#95C2214yes—
25#95×D43C22132yes—
26C22×C4⋊C4×C43C2212yes—
27C22×C42×C43C2211yescharacteristic
28C43×#382C2218yescomplemented
29C2×#95×C43C2214yes—
30C24×D43C2311yescharacteristic
31C23×Dic43C2314yes—
32C23×Dic43C2312yes—
33C23×Dic43C2311yescharacteristic
34C22×C4×D43—216no—
35C22×C4×D43—216no—
36C22×C4×D43—232no—
37C22×C4×D43C2×C4116yes—
38C22×C4×D43C2×C418yes—
39C22×C4×D43D418yes—
40C22×C4×D43Q818yes—
41C22×C4×D43C23116yes—
42C22×C4×D43C2318yes—
43C22×C4×D43C2314yes—
44C2×C4⋊Dic43—28no—
45C2×C4⋊Dic43C2318yes—
46C2×Dic43⋊C4—216no—
47C2×Dic43⋊C4C23116yes—
48C4⋊C4×D43—264no—
49C2×C4×Dic43C2×C418yescomplemented
50C2×C4×Dic43C2×C4116yescomplemented
51C2×C4×Dic43C2318yes—
52C2×C4×Dic43C2314yes—
53C42×D43C2×C4164yescomplemented
54C43⋊#95C23132yes—
55C43⋊#95C23116yes—
56C23×C4×C43C2314yes—
57C23×C4×C43C2312yes—
58C23×C4×C43C2311yescharacteristic
59C2×C4⋊C4×C43—28no—
60C2×C4⋊C4×C43C2318yes—
61C2×C42×C43C2×C418yescomplemented
62C2×C42×C43C2314yes—
63#95×C43C23116yes—
64C24×C43C2411yescharacteristic
65C23×D43C22×C414yes—
66C23×D43C2×D414yes—
67C23×D43C2×Q814yes—
68C23×D43#41116yes—
69C23×D43C2412yes—
70C22×C4×C43—28no—
71C22×C4×C43—28no—
72C22×C4×C43—216no—
73C22×C4×C43C22×C418yes—
74C22×C4×C43C22×C414yes—
75C22×C4×C43C2×D414yes—
76C22×C4×C43C2×Q814yes—
77C22×C4×C43C2418yes—
78C22×C4×C43C2414yes—
79C22×C4×C43C2412yes—
80C22×Dic43—28no—
81C22×Dic43—28no—
82C22×Dic43—216no—
83C22×Dic43C22×C418yes—
84C22×Dic43C22×C414yes—
85C22×Dic43C2×D414yes—
86C22×Dic43C2×Q814yes—
87C22×Dic43C2418yes—
88C22×Dic43C2414yes—
89C22×Dic43C2412yes—
90C2×C4×D43—264no—
91C2×C4×D43—232no—
92C2×C4×D43—232no—
93C2×C4×D43—264no—
94C2×C4×D43—464no—
95C2×C4×D43C4⋊C4164yes—
96C2×C4×D43C22×C4132yes—
97C2×C4×D43C22×C4116yes—
98C2×C4×D43C2×D4116yes—
99C2×C4×D43C2×Q8116yes—
100C4⋊C4×C43—216no—
101C42×C43C22×C4116yescomplemented
102C4⋊Dic43—216no—
103Dic43⋊C4—232no—
104C4×Dic43C22×C4116yescomplemented
105C4×Dic43C22×C4132yescomplemented
106C23×C43C23×C412yes—
107C23×C43C22×D412yes—
108C23×C43C22×Q812yes—
109C23×C43C2×#4118yes—
110C23×C43C2511yescharacteristic
111C22×D43C2×C4⋊C4116yes—
112C22×D43#117132yes—
113C22×D43#124132yes—
114C22×D43#125132yes—
115C22×D43C23×C414yes—
116C22×D43C22×D414yes—
117C22×D43C22×Q814yes—
118C22×D43C2×#41116yes—
119C2×C4×C43—216no—
120C2×C4×C43—28no—
121C2×C4×C43—28no—
122C2×C4×C43—216no—
123C2×C4×C43—416no—
124C2×C4×C43C2×C4⋊C4116yes—
125C2×C4×C43C23×C418yes—
126C2×C4×C43C23×C414yes—
127C2×C4×C43C22×D414yes—
128C2×C4×C43C22×Q814yes—
129C2×Dic43—216no—
130C2×Dic43—28no—
131C2×Dic43—28no—
132C2×Dic43—216no—
133C2×Dic43—416no—
134C2×Dic43C2×C4⋊C4116yes—
135C2×Dic43C23×C418yes—
136C2×Dic43C23×C414yes—
137C2×Dic43C22×D414yes—
138C2×Dic43C22×Q814yes—
139C4×D43—264no—
140C4×D43—464no—
141C4×D43C2×C4⋊C4164yes—
142C22×#382—431nomaximal, Sylow
143C22×C43C22×C4⋊C414yes—
144C22×C43C2×#11718yes—
145C22×C43C2×#12418yes—
146C22×C43C2×#12518yes—
147C22×C43C24×C411yescharacteristic
148C22×C43C23×D411yescharacteristic
149C22×C43C23×Q811yescharacteristic
150C22×C43C22×#4114yes—
151C2×D43#382164yesdirect product factor
152C2×D43C22×C4⋊C418yes—
153C2×D43C2×#117116yes—
154C2×D43C2×#124116yes—
155C2×D43C2×#125116yes—
156C4×C43—28no—
157C4×C43—48no—
158C4×C43C22×C4⋊C418yes—
159Dic43—28no—
160Dic43—48no—
161Dic43C22×C4⋊C418yes—
162C23×C4⋊C4—432no—
163C23×C42—431no—
164C2×#382—431no—
165C2×#382—4316no—
166C2×#382—434no—
167C2×#382—432no—
168C2×#382D4311yescharacteristic, direct product factor
169C22×#95—434no—
170C2×C43C2×#38218yescomplemented
171C2×C43C23×C4⋊C411yescharacteristic
172C2×C43C22×#11712yes—
173C2×C43C22×#12412yes—
174C2×C43C22×#12512yes—
175D43C2×#382116yesdirect product factor
176C24×C4—431no—
177C24×C4—432no—
178C24×C4—434no—
179C22×C4⋊C4—434no—
180C22×C4⋊C4—432no—
181C22×C4⋊C4—4316no—
182C22×C4⋊C4—8616no—
183C22×C4⋊C4C2×D4312yes—
184C22×C42—432no—
185C22×C42—431no—
186C22×C42—438no—
187C22×C42—4316no—
188C22×C42C2×D4311yescharacteristic
189#382—4316no—
190#382—438no—
191#382—4332no—
192#382C2×D4318yesdirect product factor
193C2×#95—438no—
194C2×#95—434no—
195C2×#95—4332no—
196C2×#95C2×D4314yes—
197C43C22×#38211yescharacteristic, complemented, Sylow
198C25—431no—
199C23×C4—431no—
200C23×C4—438no—
201C23×C4—438no—
202C23×C4—438no—
203C23×C4—434no—
204C23×C4—432no—
205C23×C4—4316no—
206C23×C4—438no—
207C23×C4—434no—
208C23×C4—4316no—
209C23×C4—8616no—
210C23×C4—8616no—
211C23×C4—8632no—
212C23×C4C22×D4314yes—
213C23×C4C22×D4312yes—
214C23×C4C22×D4311yescharacteristic
215C2×C4⋊C4—28no—
216C2×C4⋊C4—4316no—
217C2×C4⋊C4—438no—
218C2×C4⋊C4—8664no—
219C2×C4⋊C4—8616no—
220C2×C4⋊C4—868no—
221C2×C4⋊C4C22×D4318yes—
222C2×C42—4316no—
223C2×C42—438no—
224C2×C42—438no—
225C2×C42—434no—
226C2×C42—4364no—
227C2×C42C4×D4318yescomplemented
228C2×C42C22×D4314yes—
229#95—4332no—
230#95—4316no—
231#95C22×D43116yes—
232C24—434no—
233C24—434no—
234C24—434no—
235C24—4316no—
236C24—432no—
237C24C23×D4311yescharacteristic
238C22×C4—28no—
239C22×C4—28no—
240C22×C4—216no—
241C22×C4—434no—
242C22×C4—434no—
243C22×C4—434no—
244C22×C4—432no—
245C22×C4—4364no—
246C22×C4—4316no—
247C22×C4—4316no—
248C22×C4—4316no—
249C22×C4—438no—
250C22×C4—434no—
251C22×C4—4332no—
252C22×C4—438no—
253C22×C4—8664no—
254C22×C4—8632no—
255C22×C4—8632no—
256C22×C4—8664no—
257C22×C4—868no—
258C22×C4—868no—
259C22×C4—8616no—
260C22×C4—17264no—
261C22×C4C2×C4×D4318yes—
262C22×C4C2×C4×D4314yes—
263C22×C4D4×D4314yes—
264C22×C4Q8×D4314yes—
265C22×C4C23×D4318yes—
266C22×C4C23×D4314yes—
267C22×C4C23×D4312yes—
268C4⋊C4—216no—
269C4⋊C4—8632no—
270C4⋊C4—8616no—
271C42—4332no—
272C42—4316no—
273C42C2×C4×D43116yescomplemented
274C23—4316no—
275C23—4332no—
276C23—4332no—
277C23—4332no—
278C23—434no—
279C23—434no—
280C23—434no—
281C23—4316no—
282C23C22×C4×D4312yes—
283C23C2×D4×D4312yes—
284C23C2×Q8×D4312yes—
285C23#41×D4318yes—
286C23C24×D4311yescharacteristic
287C2×C4—216no—
288C2×C4—28no—
289C2×C4—28no—
290C2×C4—216no—
291C2×C4—416no—
292C2×C4—4316no—
293C2×C4—434no—
294C2×C4—434no—
295C2×C4—434no—
296C2×C4—4364no—
297C2×C4—438no—
298C2×C4—8664no—
299C2×C4—8616no—
300C2×C4—868no—
301C2×C4—868no—
302C2×C4—8616no—
303C2×C4—17264no—
304C2×C4—17216no—
305C2×C4C4⋊C4×D43116yes—
306C2×C4C22×C4×D4318yes—
307C2×C4C22×C4×D4314yes—
308C2×C4C2×D4×D4314yes—
309C2×C4C2×Q8×D4314yes—
310C22—4316no—
311C22—4316no—
312C22—4364no—
313C22—438no—
314C22—4316no—
315C22C2×C4⋊C4×D4314yes—
316C22#117×D4318yes—
317C22#124×D4318yes—
318C22#125×D4318yes—
319C22C23×C4×D4311yescharacteristic
320C22C22×D4×D4311yescharacteristic
321C22C22×Q8×D4311yescharacteristic
322C22C2×#41×D4314yes—
323C4—28no—
324C4—48no—
325C4—438no—
326C4—868no—
327C4—1728no—
328C4C2×C4⋊C4×D4318yes—
329C2—4316no—
330C2#382×D4318yesdirect product factor
331C2C22×C4⋊C4×D4311yescharacteristic
332C2C2×#117×D4312yes—
333C2C2×#124×D4312yes—
334C2C2×#125×D4312yes—
subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C43×#382C2
socleC24×C43C24
prime radicalC24×D43C23
cosocleC23×C43C25
hypercenterC2×#382D43
hypocenterC43C22×#382
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
3. C2×#14582765C2semidirect
4. C2×#14582764C2semidirect
5. C2×#14582763C2semidirect
6. #382×D43C2direct (N × H)
8. C2×C43×#382C2semidirect
18. C2×C42×D43C4semidirect
20. #14582765C22semidirect
21. #14582764C22semidirect
22. #14582763C22semidirect
28. C43×#382C22semidirect
49. C2×C4×Dic43C2×C4semidirect
50. C2×C4×Dic43C2×C4semidirect
53. C42×D43C2×C4semidirect
61. C2×C42×C43C2×C4semidirect
101. C42×C43C22×C4semidirect
104. C4×Dic43C22×C4semidirect
105. C4×Dic43C22×C4semidirect
151. C2×D43#382direct (N × H)
168. C2×#382D43direct (N × H)
170. C2×C43C2×#382semidirect
175. D43C2×#382direct (N × H)
192. #382C2×D43direct (N × H)
197. C43C22×#382semidirect
227. C2×C42C4×D43semidirect
273. C42C2×C4×D43semidirect
330. C2#382×D43direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D432
C22×C42×D432
C2×#145827652
C2×#145827642
C2×#145827632
#382×D432
C2×#95×D432
C2×C43×#3822
C22×#38243