Finite Group Databasebeta

← C151×#12340 #50317265

Subgroups — C151×#12340 #50317265

Order 38656.

346 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3334×C151C211yesmaximal, characteristic, complemented
2#2240×C151C211yesmaximal, characteristic, complemented
3#2206×C151C211yesmaximal, characteristic, complemented
4#1667×C151C211yesmaximal, characteristic, complemented
5#1364×C151C211yesmaximal, characteristic, complemented
6#1331×C151C211yesmaximal, characteristic, complemented
7D4⋊C16×C151C211yesmaximal, characteristic, complemented
8#547×C151—21no—
9C2×D16×C151—21no—
10#500×C151C2211yescharacteristic
11#493×C151C2211yescharacteristic
12#480×C151—22no—
13#474×C151—21no—
14#466×C151—21no—
15#459×C151—21no—
16C4×D8×C151C2211yescharacteristic
17C8×D4×C151C2211yescharacteristic
18C2×#107×C151—21no—
19C4⋊C16×C151C2211yescharacteristic
20#357×C151—21no—
21#357×C151—22no—
22C4×C16×C151C2211yescharacteristic
23#335×C151C2211yescharacteristic
24#331×C151—21no—
25C2×#41×C151—41no—
26C2×D8×C151—21no—
27C2×D8×C151—21no—
28C2×D8×C151—41no—
29C2×D8×C151D411yescharacteristic
30C22×C8×C151—21no—
31C4⋊Q8×C151—21no—
32#127×C151—21no—
33#123×C151—42no—
34C22⋊Q8×C151—41no—
35#121×C151—22no—
36C4×D4×C151—21no—
37C4×D4×C151D411yescharacteristic
38C2×C4⋊C4×C151—22no—
39D16×C151—42no—
40C2×C16×C151—21no—
41C2×C16×C151—21no—
42#107×C151—22no—
43#107×C151—21no—
44#107×C151D411yescharacteristic
45#107×C151D412yes—
46C4⋊C8×C151—21no—
47C4⋊C8×C151D411yescharacteristic
48#102×C151—22no—
49#102×C151—21no—
50#102×C151—41no—
51C22⋊C8×C151—21no—
52C4×C8×C151C2311yescharacteristic
53#41×C151—82no—
54#41×C151—82no—
55C2×Q8×C151—41no—
56C2×D4×C151—21no—
57C2×D4×C151—42no—
58C2×D4×C151—41no—
59C2×D4×C151—41no—
60C2×D4×C151—41no—
61C2×D4×C151D811yescharacteristic
62C22×C4×C151—21no—
63C22×C4×C151—42no—
64C22×C4×C151—41no—
65D8×C151—21no—
66D8×C151—21no—
67D8×C151—42no—
68D8×C151—41no—
69D8×C151—41no—
70D8×C151—82no—
71C2×C8×C151—21no—
72C2×C8×C151—41no—
73C2×C8×C151—41no—
74C2×C8×C151—41no—
75C2×C8×C151C2×D411yescharacteristic
76C2×C8×C151C2×D411yescharacteristic
77C4⋊C4×C151—21no—
78C4⋊C4×C151—22no—
79C4⋊C4×C151—42no—
80C4⋊C4×C151—41no—
81C4⋊C4×C151D811yescharacteristic
82C22⋊C4×C151—21no—
83C22⋊C4×C151—42no—
84C22⋊C4×C151—41no—
85C42×C151C2×D411yescharacteristic
86C16×C151—41no—
87C16×C151—41no—
88C23×C151—21no—
89C23×C151—41no—
90C23×C151—81no—
91Q8×C151—81no—
92Q8×C151—81no—
93D4×C151—21no—
94D4×C151—41no—
95D4×C151—41no—
96D4×C151—84no—
97D4×C151—81no—
98D4×C151—81no—
99D4×C151—81no—
100D4×C151—81no—
101D4×C151—161no—
102D4×C151D1612yescomplemented
103C2×C4×C151—21no—
104C2×C4×C151—41no—
105C2×C4×C151—41no—
106C2×C4×C151—42no—
107C2×C4×C151—41no—
108C2×C4×C151—84no—
109C2×C4×C151—81no—
110C2×C4×C151—81no—
111C2×C4×C151#12011yescharacteristic
112C2×C4×C151C2×D811yescharacteristic
113C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
114C8×C151—21no—
115C8×C151—41no—
116C8×C151—81no—
117C8×C151#13511yescharacteristic
118C8×C151AGL(1,ℤ/8)11yescharacteristic
119C22×C151—22no—
120C22×C151—41no—
121C22×C151—41no—
122C22×C151—81no—
123C22×C151—81no—
124C22×C151—81no—
125C22×C151—161no—
126C22×C151—161no—
127C22×C151—161no—
128C22×C151#44711yescharacteristic
129C4×C151—21no—
130C4×C151—41no—
131C4×C151—81no—
132C4×C151—82no—
133C4×C151#44911yescharacteristic
134C4×C151#45411yescharacteristic
135C4×C151C2×D1611yescharacteristic
136C4×C151#50911yescharacteristic
137C2×C151—42no—
138C2×C151—161no—
139C2×C151—321no—
140C2×C151#162511yescharacteristic
141C2×C151#218411yescharacteristic
142C2×C151#219311yescharacteristic
143#12340C15111yesmaximal, characteristic, direct product factor, Sylow
144C151#1234011yescharacteristic, direct product factor, Sylow
145#3334C2×C15111yescharacteristic, complemented
146#2240C2×C15111yescharacteristic, complemented
147#2206C2×C15111yescharacteristic, complemented
148#1667C2×C15111yescharacteristic, complemented
149#1364C2×C15111yescharacteristic, complemented
150#1331C2×C15111yescharacteristic, complemented
151D4⋊C16C2×C15111yescharacteristic, complemented
152#547—21no—
153C2×D16—21no—
154#500C22×C15111yescharacteristic
155#493C22×C15111yescharacteristic
156#480—22no—
157#474—21no—
158#466—21no—
159#459—21no—
160C4×D8C22×C15111yescharacteristic
161C8×D4C22×C15111yescharacteristic
162C2×#107—21no—
163C4⋊C16C22×C15111yescharacteristic
164#357—21no—
165#357—22no—
166C4×C16C22×C15111yescharacteristic
167#335C22×C15111yescharacteristic
168#331—21no—
169C2×#41—41no—
170C2×D8—21no—
171C2×D8—21no—
172C2×D8—41no—
173C2×D8D4×C15111yescharacteristic
174C22×C8—21no—
175C4⋊Q8—21no—
176#127—21no—
177#123—42no—
178C22⋊Q8—41no—
179#121—22no—
180C4×D4—21no—
181C4×D4D4×C15111yescharacteristic
182C2×C4⋊C4—22no—
183D16—42no—
184C2×C16—21no—
185C2×C16—21no—
186#107—22no—
187#107—21no—
188#107D4×C15111yescharacteristic
189#107D4×C15112yes—
190C4⋊C8—21no—
191C4⋊C8D4×C15111yescharacteristic
192#102—22no—
193#102—21no—
194#102—41no—
195C22⋊C8—21no—
196C4×C8C23×C15111yescharacteristic
197#41—82no—
198#41—82no—
199C2×Q8—41no—
200C2×D4—21no—
201C2×D4—42no—
202C2×D4—41no—
203C2×D4—41no—
204C2×D4—41no—
205C2×D4D8×C15111yescharacteristic
206C22×C4—21no—
207C22×C4—42no—
208C22×C4—41no—
209D8—21no—
210D8—21no—
211D8—42no—
212D8—41no—
213D8—41no—
214D8—82no—
215C2×C8—21no—
216C2×C8—41no—
217C2×C8—41no—
218C2×C8—41no—
219C2×C8C2×D4×C15111yescharacteristic
220C2×C8C2×D4×C15111yescharacteristic
221C4⋊C4—21no—
222C4⋊C4—22no—
223C4⋊C4—42no—
224C4⋊C4—41no—
225C4⋊C4D8×C15111yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—42no—
228C22⋊C4—41no—
229C42C2×D4×C15111yescharacteristic
230C16—41no—
231C16—41no—
232C23—21no—
233C23—41no—
234C23—81no—
235Q8—81no—
236Q8—81no—
237D4—21no—
238D4—41no—
239D4—41no—
240D4—84no—
241D4—81no—
242D4—81no—
243D4—81no—
244D4—81no—
245D4—161no—
246D4D16×C15112yescomplemented
247C2×C4—21no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—42no—
252C2×C4—84no—
253C2×C4—81no—
254C2×C4—81no—
255C2×C4#120×C15111yescharacteristic
256C2×C4C2×D8×C15111yescharacteristic
257C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
258C8—21no—
259C8—41no—
260C8—81no—
261C8#135×C15111yescharacteristic
262C8AGL(1,ℤ/8)×C15111yescharacteristic
263C22—22no—
264C22—41no—
265C22—41no—
266C22—81no—
267C22—81no—
268C22—81no—
269C22—161no—
270C22—161no—
271C22—161no—
272C22#447×C15111yescharacteristic
273C4—21no—
274C4—41no—
275C4—81no—
276C4—82no—
277C4#449×C15111yescharacteristic
278C4#454×C15111yescharacteristic
279C4C2×D16×C15111yescharacteristic
280C4#509×C15111yescharacteristic
281C2—42no—
282C2—161no—
283C2—321no—
284C2#1625×C15111yescharacteristic
285C2#2184×C15111yescharacteristic
286C2#2193×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#447
commutator, Frattini, cosocleC4×C8C23×C151
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C42×C151 ◁ C8×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3334×C151C2semidirect
2. #2240×C151C2semidirect
3. #2206×C151C2semidirect
4. #1667×C151C2semidirect
5. #1364×C151C2semidirect
6. #1331×C151C2semidirect
7. D4⋊C16×C151C2semidirect
102. D4×C151D16semidirect
143. #12340C151direct (N × H)
144. C151#12340direct (N × H)
145. #3334C2×C151semidirect
146. #2240C2×C151semidirect
147. #2206C2×C151semidirect
148. #1667C2×C151semidirect
149. #1364C2×C151semidirect
150. #1331C2×C151semidirect
151. D4⋊C16C2×C151semidirect
246. D4D16×C151semidirect

Maximal subgroups

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

subgroupindex
#3334×C1512
#2240×C1512
#2206×C1512
#1667×C1512
#1364×C1512
#1331×C1512
D4⋊C16×C1512
#12340151