Finite Group Databasebeta

← C2×#23752870 #34082575

Subgroups — C2×#23752870 #34082575

Order 19328.

1620 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×#14559003C211yesmaximal, characteristic, complemented
2C22×Q8×D151C211yesmaximal, characteristic, complemented
3#23752870C2116yesmaximal, direct product factor
4C2×#18012725C212yesmaximal, complemented
5C2×#18012716C212yesmaximal, complemented
6C2×#18012715C211yesmaximal, characteristic, complemented
7C2×#18012712C212yesmaximal, complemented
8C2×#18012710C211yesmaximal, characteristic, complemented
9C2×C4×Dic302C211yesmaximal, characteristic, complemented
10C2×C4×D604C211yesmaximal, characteristic, complemented
11C2×(C22⋊D151)⋊C4C212yesmaximal, complemented
12C2×#124×C151C211yesmaximal, characteristic, complemented
13C2×#14559003—28no—
14C2×#14559003C2218yescomplemented
15C22×Dic302C2212yes—
16C22×Dic302C2211yescharacteristic
17C2×Q8×D151—28no—
18C2×Q8×D151C2218yescomplemented
19C22×D604C2211yescharacteristic
20C22×C22⋊D151C2212yes—
21C22×C22⋊D151C2212yes—
22C23×Dic151C2212yes—
23C22×C4×D151C2211yescharacteristic
24C22×C4×D151C2212yes—
25C22×C4×D151C2211yescharacteristic
26#18012725C22116yescomplemented
27#18012716C22116yescomplemented
28#18012715C2218yescomplemented
29#18012712C22116yescomplemented
30#18012710C2218yescomplemented
31C4×Dic302C2218yescomplemented
32C4×D604C2218yescomplemented
33(C22⋊D151)⋊C4C22116yescomplemented
34C2×C4⋊Dic151C2211yescharacteristic
35C2×C4⋊Dic151C2211yescharacteristic
36C2×Dic151⋊C4C2212yes—
37C2×Dic151⋊C4C2212yes—
38C2×C22⋊Dic151C2212yes—
39C2×(C2×D151)⋊C4C2212yes—
40C2×(C2×D151)⋊C4C2211yescharacteristic
41C2×(C2×D151)⋊C4C2211yescharacteristic
42C2×C4×Dic151C2212yes—
43C22×Q8×C151C2211yescharacteristic
44C22×D4×C151C2211yescharacteristic
45#124×C151C2218yescomplemented
46C2×C22⋊C4×C151C2212yes—
47C2×C22⋊C4×C151C2212yes—
48C2×C42×C151C2211yescharacteristic
49C23×D151C2311yescharacteristic
50C23×D151C2311yescharacteristic
51#14559003—232no—
52C2×Dic302—28no—
53C2×Dic302D418yescomplemented
54C2×Dic302C2318yes—
55C2×Dic302C2314yes—
56Q8×D151—232no—
57C2×D604—24no—
58C2×D604C2314yes—
59C2×C22⋊D151—28no—
60C2×C22⋊D151—28no—
61C2×C22⋊D151C2318yes—
62C2×C22⋊D151C2318yes—
63C22×Dic151—28no—
64C22×Dic151C2312yes—
65C22×Dic151C2311yescharacteristic
66C22×Dic151C2311yescharacteristic
67C22×Dic151C2318yes—
68C22×Dic151C2312yes—
69C2×C4×D151—28no—
70C2×C4×D151—24no—
71C2×C4×D151—24no—
72C2×C4×D151C2318yes—
73C2×C4×D151C2314yes—
74C2×C4×D151C2314yes—
75C4⋊Dic151C2314yes—
76C4⋊Dic151C2314yes—
77Dic151⋊C4C2318yes—
78Dic151⋊C4C2318yes—
79C22⋊Dic151C2318yes—
80(C2×D151)⋊C4C2314yes—
81(C2×D151)⋊C4C2314yes—
82(C2×D151)⋊C4C2318yes—
83C4×Dic151C2318yes—
84C24×C151C2312yes—
85C2×Q8×C151—24no—
86C2×Q8×C151C2314yes—
87C2×D4×C151—24no—
88C2×D4×C151C2314yes—
89C22×C4×C151C2311yescharacteristic
90C22×C4×C151C2312yes—
91C22×C4×C151C2311yescharacteristic
92C22×C4×C151C2311yescharacteristic
93C22⋊C4×C151C2318yes—
94C22⋊C4×C151C2318yes—
95C42×C151C2314yes—
96C22×D151—22no—
97C22×D151—22no—
98C22×D151—22no—
99C22×D151—22no—
100C22×D151—22no—
101C22×D151#4114yescomplemented
102C22×D151C2412yes—
103C22×D151C2412yes—
104Dic302—216no—
105Dic302C2×D4116yescomplemented
106D604—28no—
107C22⋊D151—216no—
108C22⋊D151—216no—
109C2×Dic151—22no—
110C2×Dic151—22no—
111C2×Dic151—24no—
112C2×Dic151—216no—
113C2×Dic151C2×D418yes—
114C2×Dic151C2414yes—
115C2×Dic151C2412yes—
116C2×Dic151C2412yes—
117C2×Dic151C2414yes—
118C4×D151—28no—
119C4×D151—28no—
120C4×D151—216no—
121C23×C151—24no—
122C23×C151—24no—
123C23×C151—24no—
124C23×C151C2414yes—
125C23×C151C2411yescharacteristic
126Q8×C151—28no—
127D4×C151—28no—
128C2×C4×C151—24no—
129C2×C4×C151—22no—
130C2×C4×C151—22no—
131C2×C4×C151C2×D414yes—
132C2×C4×C151C2414yes—
133C2×C4×C151C2412yes—
134C2×C4×C151C2412yes—
135C2×C4×C151C2412yes—
136C22×C151—24no—
137C22×C151—24no—
138C22×C151—24no—
139C22×C151—48no—
140C22×C151C22×D412yes—
141C22×C151C2×#4112yes—
142C22×C1512−1+412yes—
143C22×C151C2511yescharacteristic
144C2×D151—28no—
145C2×D151—22no—
146C2×D151—22no—
147C2×D151—22no—
148C2×D151—22no—
149C2×D151—22no—
150C2×D151—44no—
151C2×D151C2×#4114yescomplemented
152C4×C151—24no—
153C4×C151—22no—
154C4×C151—22no—
155C4×C151C22×D414yes—
156Dic151—22no—
157Dic151—22no—
158Dic151—24no—
159Dic151C22×D418yes—
160C2×C151—44no—
161C2×C151#54814yescomplemented
162C2×C151C23×D411yescharacteristic
163C2×C151C22×#4111yescharacteristic
164C2×C151C2×2−1+411yescharacteristic
165D151—24no—
166D151—42no—
167C151C2×#54811yescharacteristic, complemented, Sylow
168C2×#548—1511nomaximal, Sylow
169C22×#41—1511no—
170C23×Q8—1511no—
171#548—15116no—
172C2×#124—1512no—
173C2×#124D15111yescharacteristic, complemented
174C2×C22⋊Q8—1511no—
175C2×C22⋊Q8—1512no—
176C2×#121—1511no—
177C2×#121—1512no—
178C2×C4×Q8—1511no—
179C2×C4×D4—1512no—
180C2×C4×D4—1511no—
181C2×#41—3028no—
182C2×#41—1518no—
183C22×Q8—3028no—
184C22×Q8—1518no—
185C22×Q8—1512no—
186C22×Q8—1511no—
187C22×Q8C2×D15111yescharacteristic
188C22×D4—1512no—
189C22×D4—1512no—
190C22×D4—1511no—
191C22×D4C2×D15111yescharacteristic
192C23×C4—1512no—
193C23×C4—1512no—
194C23×C4—1511no—
195C23×C4—1511no—
196#124—15116no—
197#124C2×D15118yescomplemented
198C22⋊Q8—1518no—
199C22⋊Q8—15116no—
200#121—1518no—
201#121—15116no—
202C4×Q8—1518no—
203C4×D4—15116no—
204C4×D4—1518no—
205C2×C4⋊C4—1512no—
206C2×C4⋊C4—1511no—
207C2×C4⋊C4—1512no—
208C2×C4⋊C4—1511no—
209C2×C22⋊C4—1512no—
210C2×C22⋊C4—1511no—
211C2×C22⋊C4—1511no—
212C2×C22⋊C4—1512no—
213C2×C22⋊C4C2×D15112yes—
214C2×C22⋊C4C2×D15112yes—
215C2×C42—1512no—
216C2×C42C2×D15111yescharacteristic
217C24—1511no—
218C24—1511no—
219C24C22×D15112yes—
220#41—30232no—
221C2×Q8—24no—
222C2×Q8—3028no—
223C2×Q8—30232no—
224C2×Q8—1518no—
225C2×Q8—1518no—
226C2×Q8—1514no—
227C2×Q8C22×D15114yes—
228C2×D4—24no—
229C2×D4—3024no—
230C2×D4—3028no—
231C2×D4—3028no—
232C2×D4—1518no—
233C2×D4—1518no—
234C2×D4—1514no—
235C2×D4C22×D15114yes—
236C22×C4—3028no—
237C22×C4—3028no—
238C22×C4—3024no—
239C22×C4—3024no—
240C22×C4—1518no—
241C22×C4—1512no—
242C22×C4—1511no—
243C22×C4—1511no—
244C22×C4—1518no—
245C22×C4—1514no—
246C22×C4—1514no—
247C22×C4—1512no—
248C22×C4C22×D15111yescharacteristic
249C22×C4C22×D15111yescharacteristic
250C22×C4C22×D15112yes—
251C22×C4C22×D15111yescharacteristic
252C4⋊C4—1518no—
253C4⋊C4—1518no—
254C4⋊C4—1514no—
255C4⋊C4—1514no—
256C22⋊C4—1518no—
257C22⋊C4—1514no—
258C22⋊C4—1514no—
259C22⋊C4—1518no—
260C22⋊C4C22×D15118yes—
261C22⋊C4C22×D15118yes—
262C42—1518no—
263C42C22×D15114yes—
264C23—24no—
265C23—24no—
266C23—24no—
267C23—3022no—
268C23—3022no—
269C23—3022no—
270C23—3022no—
271C23—3022no—
272C23—1512no—
273C23—1514no—
274C23—1512no—
275C23C23×D15114yes—
276C23C23×D15111yescharacteristic
277Q8—28no—
278Q8—30216no—
279Q8—15116no—
280D4—28no—
281D4—3028no—
282D4—30216no—
283D4—30216no—
284C2×C4—24no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—30216no—
288C2×C4—3022no—
289C2×C4—3022no—
290C2×C4—3024no—
291C2×C4—30216no—
292C2×C4—3028no—
293C2×C4—3028no—
294C2×C4—1514no—
295C2×C4—1512no—
296C2×C4—1512no—
297C2×C4—1518no—
298C2×C4—1514no—
299C2×C4D4×D15114yes—
300C2×C4C23×D15112yes—
301C2×C4C23×D15112yes—
302C2×C4C23×D15114yes—
303C2×C4C23×D15112yes—
304C22—24no—
305C22—24no—
306C22—24no—
307C22—48no—
308C22—3022no—
309C22—3022no—
310C22—3028no—
311C22—3022no—
312C22—3022no—
313C22—3022no—
314C22—6044no—
315C22—1514no—
316C22C2×D4×D15112yes—
317C22#41×D15112yes—
318C22#1801278612yes—
319C22C24×D15111yescharacteristic
320C4—24no—
321C4—22no—
322C4—22no—
323C4—3022no—
324C4—3022no—
325C4—3024no—
326C4—1518no—
327C4C2×D4×D15114yes—
328C2—44no—
329C2—3024no—
330C2—6042no—
331C2#2375287014yesdirect product factor
332C2C22×D4×D15111yescharacteristic
333C2C2×#41×D15111yescharacteristic
334C2C2×#1801278611yescharacteristic
subgroupG/H
centerC23C23×D151
commutator, cosocleC22×C151C25
FrattiniC22C24×D151
FittingC2×#124×C151C2
socleC23×C151C24
hypercenterC2×#124D151
hypocenterC151C2×#548
LCSG ▷ C22×C151 ▷ C151
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C22×#14559003C2semidirect
2. C22×Q8×D151C2semidirect
3. #23752870C2direct (N × H)
4. C2×#18012725C2semidirect
5. C2×#18012716C2semidirect
6. C2×#18012715C2semidirect
7. C2×#18012712C2semidirect
8. C2×#18012710C2semidirect
9. C2×C4×Dic302C2semidirect
10. C2×C4×D604C2semidirect
11. C2×(C22⋊D151)⋊C4C2semidirect
12. C2×#124×C151C2semidirect
14. C2×#14559003C22semidirect
18. C2×Q8×D151C22semidirect
26. #18012725C22semidirect
27. #18012716C22semidirect
28. #18012715C22semidirect
29. #18012712C22semidirect
30. #18012710C22semidirect
31. C4×Dic302C22semidirect
32. C4×D604C22semidirect
33. (C22⋊D151)⋊C4C22semidirect
45. #124×C151C22semidirect
53. C2×Dic302D4semidirect
101. C22×D151#41semidirect
105. Dic302C2×D4semidirect
151. C2×D151C2×#41semidirect
161. C2×C151#548semidirect
167. C151C2×#548semidirect
173. C2×#124D151semidirect
197. #124C2×D151semidirect
331. C2#23752870direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145590032
C22×Q8×D1512
#237528702
C2×#180127252
C2×#180127162
C2×#180127152
C2×#180127122
C2×#180127102
C2×C4×Dic3022
C2×C4×D6042
C2×(C22⋊D151)⋊C42
C2×#124×C1512
C2×#548151