Finite Group Databasebeta

← C2×#19137707 #25256276

Subgroups — C2×#19137707 #25256276

Order 11008.

3158 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
1#19137707C2116yesmaximal, direct product factor
2C2×#14582806C212yesmaximal, complemented
3C2×#14582792C214yesmaximal, complemented
4C2×#14582779C212yesmaximal
5C2×C22⋊C4×Dic43C214yesmaximal, complemented
6C2×#14582745C212yesmaximal, complemented
7C22×#124×C43C211yesmaximal, characteristic
8C24×Dic43C2212yes—
9C22×C4⋊Dic43C2212yes—
10C22×C22⋊Dic43C2214yes—
11C22×C22⋊Dic43C2212yes—
12C22×C4×Dic43C2214yes—
13C22×C4×Dic43C2212yes—
14#14582806C22116yescomplemented
15#14582792C22132yescomplemented
16#14582779C22116yes—
17C22⋊C4×Dic43C22132yescomplemented
18#14582745C22116yescomplemented
19C2×C43⋊#95C2212yes—
20C2×C43⋊#95C2214yes—
21C2×C43⋊#95C2214yes—
22C2×C43⋊#95C2212yes—
23C23×Q8×C43C2211yescharacteristic
24C23×D4×C43C2211yescharacteristic
25C2×#124×C43C4116yescomplemented
26C2×#124×C43C2218yes—
27C22×C22⋊C4×C43C2214yes—
28C22×C42×C43C2211yescharacteristic
29C23×Dic43—216no—
30C23×Dic43—44no—
31C23×Dic43C2314yes—
32C23×Dic43C2318yes—
33C23×Dic43C2314yes—
34C2×C4⋊Dic43—44no—
35C2×C4⋊Dic43C2318yes—
36C2×C22⋊Dic43—216no—
37C2×C22⋊Dic43—44no—
38C2×C22⋊Dic43C23116yes—
39C2×C22⋊Dic43C2318yes—
40C2×C4×Dic43—216no—
41C2×C4×Dic43—44no—
42C2×C4×Dic43C23116yes—
43C2×C4×Dic43C2318yes—
44C43⋊#95C2318yes—
45C43⋊#95C23116yes—
46C43⋊#95C23116yes—
47C43⋊#95C2318yes—
48C25×C43C2312yes—
49C22×Q8×C43—42no—
50C22×Q8×C43—42no—
51C22×Q8×C43C2×C418yescomplemented
52C22×Q8×C43C2314yes—
53C22×D4×C43—42no—
54C22×D4×C43—42no—
55C22×D4×C43C2×C418yes—
56C22×D4×C43C2314yes—
57C23×C4×C43C2312yes—
58C23×C4×C43C2311yescharacteristic
59C23×C4×C43C2312yes—
60#124×C43C2×C4164yescomplemented
61C2×C22⋊C4×C43C2×C4132yescomplemented
62C2×C22⋊C4×C43C23116yes—
63C2×C42×C43C2×C418yescomplemented
64C2×C42×C43C2314yes—
65C24×C43—28no—
66C24×C43—28no—
67C24×C43—24no—
68C24×C43—24no—
69C24×C43C22×C418yes—
70C24×C43C2414yes—
71C24×C43C2411yescharacteristic
72C2×Q8×C43—416no—
73C2×Q8×C43—44no—
74C2×Q8×C43—44no—
75C2×Q8×C43C22×C4116yescomplemented
76C2×D4×C43—416no—
77C2×D4×C43—44no—
78C2×D4×C43—44no—
79C2×D4×C43C22×C4116yes—
80C22×C4×C43—28no—
81C22×C4×C43—22no—
82C22×C4×C43—22no—
83C22×C4×C43—24no—
84C22×C4×C43—24no—
85C22×C4×C43C22×C418yes—
86C22×C4×C43C22×C414yes—
87C22×C4×C43C22×C418yes—
88C22×C4×C43C2414yes—
89C22×C4×C43C2412yes—
90C22×C4×C43C2414yes—
91C22×Dic43—232no—
92C22×Dic43—28no—
93C22×Dic43—28no—
94C22×Dic43—28no—
95C22×Dic43—28no—
96C22×Dic43—28no—
97C22×Dic43—48no—
98C22×Dic43—432no—
99C22×Dic43#41116yes—
100C22×Dic43C2418yes—
101C22×Dic43C2418yes—
102C22⋊C4×C43C22×C4164yescomplemented
103C42×C43C22×C4116yescomplemented
104C22⋊Dic43—232no—
105C22⋊Dic43—48no—
106C4⋊Dic43—48no—
107C4×Dic43—232no—
108C4×Dic43—48no—
109C23×C43—232no—
110C23×C43—216no—
111C23×C43—28no—
112C23×C43—28no—
113C23×C43—24no—
114C23×C43—24no—
115C23×C43—48no—
116C23×C43—48no—
117C23×C43—416no—
118C23×C43C23×C418yes—
119C23×C43C23×C412yes—
120C23×C43C2×#4118yes—
121C23×C43H(5,𝔽2)12yes—
122C23×C43H(5,𝔽2)12yes—
123C23×C43C2511yescharacteristic
124Q8×C43—416no—
125D4×C43—416no—
126C2×C4×C43—216no—
127C2×C4×C43—28no—
128C2×C4×C43—216no—
129C2×C4×C43—28no—
130C2×C4×C43—24no—
131C2×C4×C43—24no—
132C2×C4×C43—22no—
133C2×C4×C43—22no—
134C2×C4×C43C23×C418yes—
135C2×C4×C43C23×C414yes—
136C2×C4×C43C23×C418yes—
137C2×Dic43—232no—
138C2×Dic43—28no—
139C2×Dic43—28no—
140C2×Dic43—28no—
141C2×Dic43—28no—
142C2×Dic43—28no—
143C2×Dic43—432no—
144C2×Dic43—416no—
145C2×Dic43C2×#41116yes—
146C2×#2372—431nomaximal, Sylow
147C22×C43—216no—
148C22×C43—28no—
149C22×C43—432no—
150C22×C43—44no—
151C22×C43—44no—
152C22×C43—48no—
153C22×C43C4×#4118yes—
154C22×C43#51814yes—
155C22×C43#55118yes—
156C22×C43#55518yes—
157C22×C43C24×C411yescharacteristic
158C22×C43C22×#4114yes—
159C22×C43C2×H(5,𝔽2)11yescharacteristic
160C22×C43C2×H(5,𝔽2)11yescharacteristic
161C4×C43—28no—
162C4×C43—24no—
163C4×C43—28no—
164Dic43—216no—
165Dic43—48no—
166C22×#124D4311yescharacteristic
167#2372—4316no—
168C2×#391—432no—
169C2×#388—434no—
170C2×#386—432no—
171C2×C4×C22⋊C4—434no—
172C2×#376—432no—
173C2×C43—48no—
174C2×C43#237218yescomplemented
175C2×C43C2×C4×#4112yes—
176C2×C43C2×#51811yescharacteristic
177C2×C43C2×#55112yes—
178C2×C43C2×#55512yes—
179C23×Q8C2×D4311yescharacteristic
180C23×D4C2×D4311yescharacteristic
181C24×C4—432no—
182C2×#124Dic43116yescomplemented
183C2×#124C2×D4318yes—
184C22×C4⋊C4—432no—
185C22×C22⋊C4—434no—
186C22×C22⋊C4—432no—
187C22×C22⋊C4C2×D4314yes—
188C22×C42—434no—
189C22×C42—432no—
190C22×C42C2×D4311yescharacteristic
191#391—4316no—
192#388—4332no—
193#386—4316no—
194C4×C22⋊C4—4332no—
195#376—4316no—
196C2×#95—432no—
197C2×#95—434no—
198C2×#95—432no—
199C2×#95—434no—
200C43C2×#237211yescharacteristic, complemented, Sylow
201C25C22×D4312yes—
202C22×Q8—42no—
203C22×Q8—42no—
204C22×Q8C2×Dic4318yescomplemented
205C22×Q8C22×D4314yes—
206C22×D4—42no—
207C22×D4—42no—
208C22×D4C2×Dic4318yes—
209C22×D4C22×D4314yes—
210C23×C4—434no—
211C23×C4—434no—
212C23×C4—438no—
213C23×C4—8616no—
214C23×C4—1724no—
215C23×C4C22×D4312yes—
216C23×C4C22×D4312yes—
217C23×C4C22×D4311yescharacteristic
218#124C2×Dic43164yescomplemented
219C2×C4⋊C4—438no—
220C2×C4⋊C4—1724no—
221C2×C22⋊C4—4316no—
222C2×C22⋊C4—438no—
223C2×C22⋊C4—8616no—
224C2×C22⋊C4—1724no—
225C2×C22⋊C4C2×Dic43132yescomplemented
226C2×C22⋊C4C22×D43116yes—
227C2×C42—4316no—
228C2×C42—438no—
229C2×C42—8616no—
230C2×C42—1724no—
231C2×C42C2×Dic4318yescomplemented
232C2×C42C22×D4314yes—
233#95—438no—
234#95—4316no—
235#95—438no—
236#95—4316no—
237C24—28no—
238C24—28no—
239C24—24no—
240C24—24no—
241C24C22×Dic4318yes—
242C24C23×D4314yes—
243C24C23×D4311yescharacteristic
244C2×Q8—44no—
245C2×Q8—44no—
246C2×Q8—416no—
247C2×Q8C22×Dic43116yescomplemented
248C2×D4—44no—
249C2×D4—44no—
250C2×D4—416no—
251C2×D4C22×Dic43116yes—
252C22×C4—28no—
253C22×C4—24no—
254C22×C4—24no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—4316no—
258C22×C4—438no—
259C22×C4—438no—
260C22×C4—8632no—
261C22×C4—868no—
262C22×C4—868no—
263C22×C4—868no—
264C22×C4—868no—
265C22×C4—868no—
266C22×C4—1728no—
267C22×C4—17232no—
268C22×C4C22×Dic4318yes—
269C22×C4C22×Dic4314yes—
270C22×C4C22×Dic4318yes—
271C22×C4C23×D4312yes—
272C22×C4C23×D4314yes—
273C22×C4C23×D4314yes—
274C4⋊C4—1728no—
275C22⋊C4—8632no—
276C22⋊C4—1728no—
277C22⋊C4C22×Dic43164yescomplemented
278C42—8632no—
279C42—1728no—
280C42C22×Dic43116yescomplemented
281C23—232no—
282C23—216no—
283C23—28no—
284C23—28no—
285C23—24no—
286C23—24no—
287C23—48no—
288C23—48no—
289C23—416no—
290C23C23×Dic4318yes—
291C23C23×Dic4312yes—
292C23#41×D4318yes—
293C23#1306337012yes—
294C23#1306337012yes—
295C23C24×D4311yescharacteristic
296Q8—416no—
297D4—416no—
298C2×C4—216no—
299C2×C4—28no—
300C2×C4—216no—
301C2×C4—28no—
302C2×C4—24no—
303C2×C4—24no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—4316no—
307C2×C4—8632no—
308C2×C4—868no—
309C2×C4—868no—
310C2×C4—868no—
311C2×C4—868no—
312C2×C4—868no—
313C2×C4—17232no—
314C2×C4—17216no—
315C2×C4C23×Dic4318yes—
316C2×C4C23×Dic4314yes—
317C2×C4C23×Dic4318yes—
318C22—216no—
319C22—28no—
320C22—44no—
321C22—44no—
322C22—48no—
323C22—432no—
324C22#41×Dic4318yes—
325C22#1458337414yes—
326C22#1458357918yes—
327C22#1458361118yes—
328C22C24×Dic4311yescharacteristic
329C22C2×#41×D4314yes—
330C22C2×#1306337011yescharacteristic
331C22C2×#1306337011yescharacteristic
332C4—28no—
333C4—24no—
334C4—28no—
335C4—8616no—
336C4—1728no—
337C2—48no—
338C2#1913770718yesdirect product factor
339C2C2×#41×Dic4312yes—
340C2C2×#1458337411yescharacteristic
341C2C2×#1458357912yes—
342C2C2×#1458361112yes—
subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC22×#124×C43C2
socleC24×C43C24
prime radicalC23×D4×C43C22
cosocleC23×C43C25
hypercenterC22×#124D43
hypocenterC43C2×#2372
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×#124

Complements

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

NH ≅ G/Ntype
1. #19137707C2direct (N × H)
2. C2×#14582806C2semidirect
3. C2×#14582792C2semidirect
5. C2×C22⋊C4×Dic43C2semidirect
6. C2×#14582745C2semidirect
14. #14582806C22semidirect
15. #14582792C22semidirect
17. C22⋊C4×Dic43C22semidirect
18. #14582745C22semidirect
25. C2×#124×C43C4semidirect
51. C22×Q8×C43C2×C4semidirect
60. #124×C43C2×C4semidirect
61. C2×C22⋊C4×C43C2×C4semidirect
63. C2×C42×C43C2×C4semidirect
75. C2×Q8×C43C22×C4semidirect
102. C22⋊C4×C43C22×C4semidirect
103. C42×C43C22×C4semidirect
174. C2×C43#2372semidirect
182. C2×#124Dic43semidirect
200. C43C2×#2372semidirect
204. C22×Q8C2×Dic43semidirect
218. #124C2×Dic43semidirect
225. C2×C22⋊C4C2×Dic43semidirect
231. C2×C42C2×Dic43semidirect
247. C2×Q8C22×Dic43semidirect
277. C22⋊C4C22×Dic43semidirect
280. C42C22×Dic43semidirect
338. C2#19137707direct (N × H)

Maximal subgroups

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

subgroupindex
#191377072
C2×#145828062
C2×#145827922
C2×#145827792
C2×C22⋊C4×Dic432
C2×#145827452
C22×#124×C432
C2×#237243