Finite Group Databasebeta

← C2×#19135394 #25100182

Subgroups — C2×#19135394 #25100182

Order 11008.

2094 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×C4⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
2C22×C22⋊(C43⋊C8)C214yesmaximal, complemented
3C22×#13063236C211yesmaximal, characteristic, complemented
4#19135394C218yesmaximal, direct product factor
5C22×C4×D4×C43C211yesmaximal, characteristic
6C23×C43⋊C8C2212yes—
7C23×C43⋊C8C2212yes—
8C2×C4⋊(C43⋊C8)—24no—
9C2×C4⋊(C43⋊C8)C2214yescomplemented
10C2×C22⋊(C43⋊C8)—216no—
11C2×C22⋊(C43⋊C8)C22116yescomplemented
12C2×#13063236—24no—
13C2×#13063236C2214yescomplemented
14C23×D4×C43C411yescharacteristic
15C24×C4×C43C2212yes—
16C2×C4×D4×C43—24no—
17C2×C4×D4×C43—24no—
18C2×C4×D4×C43C414yes—
19C2×C4×D4×C43C2214yes—
20C22×C4⋊C4×C43C411yescharacteristic
21C22×C22⋊C4×C43C412yes—
22C22×C42×C43C2211yescharacteristic
23C22×C43⋊C8—24no—
24C22×C43⋊C8—24no—
25C22×C43⋊C8—28no—
26C22×C43⋊C8—24no—
27C22×C43⋊C8D418yescomplemented
28C22×C43⋊C8C2314yes—
29C22×C43⋊C8C2314yes—
30C4⋊(C43⋊C8)—28no—
31C22⋊(C43⋊C8)—232no—
32#13063236—28no—
33C25×C43C2×C412yes—
34C22×D4×C43—28no—
35C22×D4×C43—24no—
36C22×D4×C43C2×C414yes—
37C23×C4×C43—24no—
38C23×C4×C43—24no—
39C23×C4×C43—28no—
40C23×C4×C43—28no—
41C23×C4×C43C2×C412yes—
42C23×C4×C43C2×C414yes—
43C23×C4×C43C2×C411yescharacteristic
44C23×C4×C43C2×C411yescharacteristic
45C23×C4×C43C2314yes—
46C23×C4×C43C2311yescharacteristic
47C4×D4×C43—216no—
48C4×D4×C43—28no—
49C4×D4×C43—28no—
50C2×C4⋊C4×C43—24no—
51C2×C4⋊C4×C43C2×C414yes—
52C2×C22⋊C4×C43—28no—
53C2×C22⋊C4×C43C2×C418yes—
54C2×C42×C43C2×C412yes—
55C2×C42×C43D414yes—
56C2×C42×C43D414yes—
57C2×C42×C43C2312yes—
58C24×C43—24no—
59C24×C43—28no—
60C24×C43—24no—
61C24×C43—28no—
62C24×C43M1618yes—
63C24×C43C22×C414yes—
64C24×C43C22×C411yescharacteristic
65C2×D4×C43—232no—
66C2×D4×C43—28no—
67C2×D4×C43—216no—
68C22×C4×C43—28no—
69C22×C4×C43—216no—
70C22×C4×C43—24no—
71C22×C4×C43—24no—
72C22×C4×C43—28no—
73C22×C4×C43—28no—
74C22×C4×C43—24no—
75C22×C4×C43—28no—
76C22×C4×C43—24no—
77C22×C4×C43—24no—
78C22×C4×C43—416no—
79C22×C4×C43—48no—
80C22×C4×C43—48no—
81C22×C4×C43C22⋊C414yes—
82C22×C4×C43C22⋊C414yes—
83C22×C4×C43C22×C414yes—
84C22×C4×C43C22×C412yes—
85C22×C4×C43C22×C412yes—
86C22×C4×C43C22×C411yescharacteristic
87C22×C4×C43C2×D412yes—
88C22×C4×C43C2×D412yes—
89C22×C4×C43C2×D414yes—
90C22×C4×C43#4114yes—
91C22×C4×C43C2411yescharacteristic
92C4⋊C4×C43—28no—
93C22⋊C4×C43—216no—
94C42×C43C22⋊C418yes—
95C42×C43C2×D414yes—
96C42×C43C2×D414yes—
97C2×C43⋊C8—216no—
98C2×C43⋊C8—24no—
99C2×C43⋊C8—24no—
100C2×C43⋊C8—28no—
101C2×C43⋊C8—24no—
102C2×C43⋊C8—48no—
103C2×C43⋊C8C2×D418yescomplemented
104C23×C43—24no—
105C23×C43—28no—
106C23×C43—24no—
107C23×C43—28no—
108C23×C43—216no—
109C23×C43—232no—
110C23×C43—48no—
111C23×C43—48no—
112C23×C43—416no—
113C23×C43C2×C22⋊C412yes—
114C23×C43C4×D414yes—
115C23×C43C2×M1618yes—
116C23×C43C2×M1614yes—
117C23×C43#13114yes—
118C23×C43C23×C411yescharacteristic
119D4×C43—232no—
120C2×C4×C43—24no—
121C2×C4×C43—24no—
122C2×C4×C43—28no—
123C2×C4×C43—28no—
124C2×C4×C43—24no—
125C2×C4×C43—28no—
126C2×C4×C43—48no—
127C2×C4×C43—48no—
128C2×C4×C43—44no—
129C2×C4×C43—44no—
130C2×C4×C43—416no—
131C2×C4×C43C2×C22⋊C414yes—
132C2×C4×C43C2×C22⋊C414yes—
133C2×C4×C43C2×C22⋊C412yes—
134C2×C4×C43C4×D414yes—
135C2×C4×C43#12118yes—
136C2×C4×C43#12414yes—
137C2×C4×C43#12714yes—
138C2×C4×C43C22×D412yes—
139C2×C4×C43C22×D411yescharacteristic
140C2×C4×C43C22×D411yescharacteristic
141C2×C4×C43C2×#4112yes—
142C43⋊C8—28no—
143C43⋊C8—44no—
144C2×#1955—431nomaximal, Sylow
145C22×C43—28no—
146C22×C43—216no—
147C22×C43—44no—
148C22×C43—48no—
149C22×C43—432no—
150C22×C43—44no—
151C22×C43#39014yes—
152C22×C43#40714yes—
153C22×C43#40814yes—
154C22×C43#435116yes—
155C22×C43C22×C22⋊C411yescharacteristic
156C22×C43C2×C4×D412yes—
157C22×C43C22×M1612yes—
158C22×C43C2×#13112yes—
159C4×C43—24no—
160C4×C43—24no—
161C4×C43—44no—
162C4×C43#39014yes—
163C4×C43C2×#12112yes—
164C4×C43C2×#12411yescharacteristic
165C4×C43C2×#12711yescharacteristic
166C22×C4×D4D4311yescharacteristic
167C22×C4⋊C8—431no—
168C22×C22⋊C8—434no—
169C22×#97—431no—
170#1955—438no—
171C2×C43—48no—
172C2×C43#195518yescomplemented
173C2×C43C2×#39011yescharacteristic
174C2×C43C2×#40711yescharacteristic
175C2×C43C2×#40811yescharacteristic
176C2×C43C2×#43514yes—
177C23×D4Dic4311yescharacteristic
178C24×C4C2×D4312yes—
179C23×C8—432no—
180C23×C8—432no—
181C2×C4×D4—24no—
182C2×C4×D4—24no—
183C2×C4×D4Dic4314yes—
184C2×C4×D4C2×D4314yes—
185C22×C4⋊C4Dic4311yescharacteristic
186C22×C22⋊C4Dic4312yes—
187C22×C42C2×D4311yescharacteristic
188C2×C4⋊C8—434no—
189C2×C4⋊C8—864no—
190C2×C22⋊C8—4316no—
191C2×C22⋊C8—8616no—
192C2×#97—434no—
193C2×#97—864no—
194C43C2×#195511yescharacteristic, complemented, Sylow
195C25C2×Dic4312yes—
196C22×D4—28no—
197C22×D4—24no—
198C22×D4C2×Dic4314yes—
199C23×C4—28no—
200C23×C4—28no—
201C23×C4—24no—
202C23×C4—24no—
203C23×C4C2×Dic4312yes—
204C23×C4C2×Dic4314yes—
205C23×C4C2×Dic4311yescharacteristic
206C23×C4C2×Dic4311yescharacteristic
207C23×C4C22×D4314yes—
208C23×C4C22×D4311yescharacteristic
209C22×C8—438no—
210C22×C8—434no—
211C22×C8—434no—
212C22×C8—864no—
213C22×C8—864no—
214C22×C8—868no—
215C22×C8—864no—
216C4×D4—216no—
217C4×D4—28no—
218C4×D4—28no—
219C2×C4⋊C4—24no—
220C2×C4⋊C4C2×Dic4314yes—
221C2×C22⋊C4—28no—
222C2×C22⋊C4C2×Dic4318yes—
223C2×C42C2×Dic4312yes—
224C2×C42C22⋊D4314yes—
225C2×C42C22⋊D4314yes—
226C2×C42C22×D4312yes—
227C4⋊C8—868no—
228C22⋊C8—8632no—
229#97—868no—
230C24—24no—
231C24—28no—
232C24—24no—
233C24—28no—
234C24#1062187718yes—
235C24C22×Dic4314yes—
236C24C22×Dic4311yescharacteristic
237C2×D4—232no—
238C2×D4—216no—
239C2×D4—28no—
240C22×C4—24no—
241C22×C4—24no—
242C22×C4—24no—
243C22×C4—28no—
244C22×C4—28no—
245C22×C4—216no—
246C22×C4—28no—
247C22×C4—24no—
248C22×C4—24no—
249C22×C4—28no—
250C22×C4—416no—
251C22×C4—48no—
252C22×C4—48no—
253C22×C4C22⋊Dic4314yes—
254C22×C4C22⋊Dic4314yes—
255C22×C4D4×D4314yes—
256C22×C4#1062190014yes—
257C22×C4C22×Dic4314yes—
258C22×C4C22×Dic4312yes—
259C22×C4C22×Dic4312yes—
260C22×C4C22×Dic4311yescharacteristic
261C22×C4C2×C22⋊D4312yes—
262C22×C4C2×C22⋊D4312yes—
263C22×C4C23×D4311yescharacteristic
264C2×C8—438no—
265C2×C8—8616no—
266C2×C8—864no—
267C2×C8—864no—
268C2×C8—868no—
269C2×C8—864no—
270C2×C8—1728no—
271C4⋊C4—28no—
272C22⋊C4—216no—
273C42C22⋊Dic4318yes—
274C42C2×C22⋊D4314yes—
275C42C2×C22⋊D4314yes—
276C23—24no—
277C23—28no—
278C23—216no—
279C23—24no—
280C23—28no—
281C23—232no—
282C23—48no—
283C23—48no—
284C23—416no—
285C23C2×C22⋊Dic4312yes—
286C23D4×Dic4314yes—
287C23C2×#1062187718yes—
288C23C2×#1062187714yes—
289C23#1306333214yes—
290C23C23×Dic4311yescharacteristic
291D4—232no—
292C2×C4—28no—
293C2×C4—28no—
294C2×C4—24no—
295C2×C4—24no—
296C2×C4—24no—
297C2×C4—28no—
298C2×C4—48no—
299C2×C4—416no—
300C2×C4—48no—
301C2×C4—44no—
302C2×C4—44no—
303C2×C4C2×C22⋊Dic4314yes—
304C2×C4C2×C22⋊Dic4314yes—
305C2×C4C2×C22⋊Dic4312yes—
306C2×C4D4×Dic4314yes—
307C2×C4#1306329618yes—
308C2×C4#1306331214yes—
309C2×C4#1306332114yes—
310C2×C4C2×D4×D4312yes—
311C2×C4C22×C22⋊D4311yescharacteristic
312C2×C4C22×C22⋊D4311yescharacteristic
313C2×C4C2×#1062190012yes—
314C8—868no—
315C8—1724no—
316C22—216no—
317C22—28no—
318C22—44no—
319C22—48no—
320C22—44no—
321C22—432no—
322C22#1458280214yes—
323C22#1458286314yes—
324C22#1458286614yes—
325C22#14582971116yes—
326C22C22×C22⋊Dic4311yescharacteristic
327C22C2×D4×Dic4312yes—
328C22C22×#1062187712yes—
329C22C2×#1306333212yes—
330C4—24no—
331C4—24no—
332C4—44no—
333C4#1458280214yes—
334C4C2×#1306329612yes—
335C4C2×#1306331211yescharacteristic
336C4C2×#1306332111yescharacteristic
337C2—48no—
338C2#1913539418yesdirect product factor
339C2C2×#1458280211yescharacteristic
340C2C2×#1458286311yescharacteristic
341C2C2×#1458286611yescharacteristic
342C2C2×#1458297114yes—
subgroupG/H
centerC23×C4C22×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC22×C4×D4×C43C2
socleC24×C43C22×C4
prime radicalC23×D4×C43C4
cosocleC22×C4×C43C24
hypercenterC22×C4×D4D43
hypocenterC43C2×#1955
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×C4⋊(C43⋊C8)C2semidirect
2. C22×C22⋊(C43⋊C8)C2semidirect
3. C22×#13063236C2semidirect
4. #19135394C2direct (N × H)
9. C2×C4⋊(C43⋊C8)C22semidirect
11. C2×C22⋊(C43⋊C8)C22semidirect
13. C2×#13063236C22semidirect
27. C22×C43⋊C8D4semidirect
103. C2×C43⋊C8C2×D4semidirect
172. C2×C43#1955semidirect
194. C43C2×#1955semidirect
338. C2#19135394direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4⋊(C43⋊C8)2
C22×C22⋊(C43⋊C8)2
C22×#130632362
#191353942
C22×C4×D4×C432
C2×#195543