Finite Group Databasebeta

← C151×#8772 #50313697

Subgroups — C151×#8772 #50313697

Order 38656.

446 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 114 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#2353×C151C211yesmaximal, characteristic
2C4×#100×C151C211yesmaximal, characteristic
3#1466×C151C211yesmaximal, characteristic
4#1300×C151C212yesmaximal, complemented
5#1288×C151C212yesmaximal, complemented
6C2×C4×D4×C151C2211yescharacteristic
7#432×C151C2212yes—
8C2×#100×C151—21no—
9C4×M16×C151C2212yes—
10#388×C151—21no—
11#387×C151—21no—
12#386×C151—21no—
13#383×C151C2211yescharacteristic
14#381×C151C411yescharacteristic
15#380×C151C411yescharacteristic
16C4×C22⋊C4×C151—21no—
17C4×C22⋊C4×C151C411yescharacteristic
18#376×C151C2211yescharacteristic
19C2×#95×C151C411yescharacteristic
20#343×C151—21no—
21#323×C151—21no—
22#323×C151—21no—
23C22×D4×C151D411yescharacteristic
24C23×C4×C151—21no—
25C23×C4×C151C2×C411yescharacteristic
26C23×C4×C151C2×C411yescharacteristic
27C2×M16×C151—22no—
28C4×D4×C151—22no—
29C4×D4×C151—22no—
30C2×C4⋊C4×C151—21no—
31C2×C4⋊C4×C151D411yescharacteristic
32C2×C22⋊C4×C151—21no—
33C2×C22⋊C4×C151—21no—
34C2×C22⋊C4×C151—21no—
35C2×C22⋊C4×C151D411yescharacteristic
36C2×C22⋊C4×C151D411yescharacteristic
37C2×C42×C151—21no—
38C2×C42×C151—21no—
39C2×C42×C151C2311yescharacteristic
40C4⋊C8×C151—22no—
41#100×C151—24no—
42C22⋊C8×C151—22no—
43#97×C151—22no—
44#97×C151—22no—
45C4×C8×C151—22no—
46#95×C151—21no—
47#95×C151—21no—
48#95×C151—21no—
49#95×C151—21no—
50#95×C151—21no—
51#95×C151C2×C411yescharacteristic
52#95×C151C2×C411yescharacteristic
53#95×C151C2×C411yescharacteristic
54#95×C151C2×C411yescharacteristic
55C24×C151C22⋊C411yescharacteristic
56C24×C151C22⋊C411yescharacteristic
57C2×D4×C151—22no—
58C2×D4×C151—22no—
59C2×D4×C151—41no—
60C22×C4×C151—21no—
61C22×C4×C151—21no—
62C22×C4×C151—21no—
63C22×C4×C151—21no—
64C22×C4×C151—21no—
65C22×C4×C151—21no—
66C22×C4×C151—21no—
67C22×C4×C151—21no—
68C22×C4×C151—42no—
69C22×C4×C151—42no—
70C22×C4×C151—81no—
71C22×C4×C151—81no—
72C22×C4×C151—81no—
73C22×C4×C151C22⋊C411yescharacteristic
74C22×C4×C151C22⋊C411yescharacteristic
75C22×C4×C151C22×C411yescharacteristic
76C22×C4×C151C2×D411yescharacteristic
77C22×C4×C151C2×D411yescharacteristic
78M16×C151—24no—
79M16×C151—42no—
80C2×C8×C151—42no—
81C2×C8×C151—42no—
82C4⋊C4×C151—22no—
83C4⋊C4×C151—81no—
84C22⋊C4×C151—22no—
85C22⋊C4×C151—22no—
86C22⋊C4×C151—42no—
87C22⋊C4×C151—42no—
88C22⋊C4×C151—81no—
89C42×C151—42no—
90C42×C151—81no—
91C42×C151#4112yes—
92C42×C151#4112yes—
93C23×C151—21no—
94C23×C151—21no—
95C23×C151—21no—
96C23×C151—21no—
97C23×C151—21no—
98C23×C151—41no—
99C23×C151—41no—
100C23×C151—41no—
101C23×C151—41no—
102C23×C151#10412yes—
103C23×C151C2×C22⋊C411yescharacteristic
104D4×C151—44no—
105C2×C4×C151—21no—
106C2×C4×C151—21no—
107C2×C4×C151—22no—
108C2×C4×C151—21no—
109C2×C4×C151—21no—
110C2×C4×C151—41no—
111C2×C4×C151—41no—
112C2×C4×C151—41no—
113C2×C4×C151—41no—
114C2×C4×C151—41no—
115C2×C4×C151—41no—
116C2×C4×C151—41no—
117C2×C4×C151—41no—
118C2×C4×C151—41no—
119C2×C4×C151—41no—
120C2×C4×C151—41no—
121C2×C4×C151—41no—
122C2×C4×C151—41no—
123C2×C4×C151—41no—
124C2×C4×C151—41no—
125C2×C4×C151—81no—
126C2×C4×C151—81no—
127C2×C4×C151—81no—
128C2×C4×C151—81no—
129C2×C4×C151—84no—
130C2×C4×C151#11711yescharacteristic
131C2×C4×C151#11711yescharacteristic
132C2×C4×C151#12312yes—
133C2×C4×C151#12312yes—
134C8×C151—44no—
135C8×C151—82no—
136C22×C151—21no—
137C22×C151—21no—
138C22×C151—22no—
139C22×C151—42no—
140C22×C151—42no—
141C22×C151—41no—
142C22×C151—41no—
143C22×C151—41no—
144C22×C151—41no—
145C22×C151—41no—
146C22×C151—81no—
147C22×C151—81no—
148C22×C151#38111yescharacteristic
149C22×C151C2×#10411yescharacteristic
150C22×C151#42111yescharacteristic
151C4×C151—22no—
152C4×C151—22no—
153C4×C151—21no—
154C4×C151—21no—
155C4×C151—42no—
156C4×C151—41no—
157C4×C151—41no—
158C4×C151—81no—
159C4×C151—81no—
160C4×C151—81no—
161C2×C151—21no—
162C2×C151—21no—
163C2×C151—42no—
164C2×C151—81no—
165C2×C151#182611yescharacteristic
166C2×C151#182711yescharacteristic
167C2×C151#182911yescharacteristic
168#8772C15111yesmaximal, characteristic, direct product factor, Sylow
169C151#877211yescharacteristic, direct product factor, Sylow
170#2353C2×C15111yescharacteristic
171C4×#100C2×C15111yescharacteristic
172#1466C2×C15111yescharacteristic
173#1300C2×C15112yescomplemented
174#1288C2×C15112yescomplemented
175C2×C4×D4C22×C15111yescharacteristic
176#432C22×C15112yes—
177C2×#100—21no—
178C4×M16C22×C15112yes—
179#388—21no—
180#387—21no—
181#386—21no—
182#383C22×C15111yescharacteristic
183#381C4×C15111yescharacteristic
184#380C4×C15111yescharacteristic
185C4×C22⋊C4—21no—
186C4×C22⋊C4C4×C15111yescharacteristic
187#376C22×C15111yescharacteristic
188C2×#95C4×C15111yescharacteristic
189#343—21no—
190#323—21no—
191#323—21no—
192C22×D4D4×C15111yescharacteristic
193C23×C4—21no—
194C23×C4C2×C4×C15111yescharacteristic
195C23×C4C2×C4×C15111yescharacteristic
196C2×M16—22no—
197C4×D4—22no—
198C4×D4—22no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4D4×C15111yescharacteristic
201C2×C22⋊C4—21no—
202C2×C22⋊C4—21no—
203C2×C22⋊C4—21no—
204C2×C22⋊C4D4×C15111yescharacteristic
205C2×C22⋊C4D4×C15111yescharacteristic
206C2×C42—21no—
207C2×C42—21no—
208C2×C42C23×C15111yescharacteristic
209C4⋊C8—22no—
210#100—24no—
211C22⋊C8—22no—
212#97—22no—
213#97—22no—
214C4×C8—22no—
215#95—21no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95C2×C4×C15111yescharacteristic
221#95C2×C4×C15111yescharacteristic
222#95C2×C4×C15111yescharacteristic
223#95C2×C4×C15111yescharacteristic
224C24C22⋊C4×C15111yescharacteristic
225C24C22⋊C4×C15111yescharacteristic
226C2×D4—22no—
227C2×D4—22no—
228C2×D4—41no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—42no—
238C22×C4—42no—
239C22×C4—81no—
240C22×C4—81no—
241C22×C4—81no—
242C22×C4C22⋊C4×C15111yescharacteristic
243C22×C4C22⋊C4×C15111yescharacteristic
244C22×C4C22×C4×C15111yescharacteristic
245C22×C4C2×D4×C15111yescharacteristic
246C22×C4C2×D4×C15111yescharacteristic
247M16—24no—
248M16—42no—
249C2×C8—42no—
250C2×C8—42no—
251C4⋊C4—22no—
252C4⋊C4—81no—
253C22⋊C4—22no—
254C22⋊C4—22no—
255C22⋊C4—42no—
256C22⋊C4—42no—
257C22⋊C4—81no—
258C42—42no—
259C42—81no—
260C42#41×C15112yes—
261C42#41×C15112yes—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—41no—
268C23—41no—
269C23—41no—
270C23—41no—
271C23#104×C15112yes—
272C23C2×C22⋊C4×C15111yescharacteristic
273D4—44no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—22no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—84no—
299C2×C4#117×C15111yescharacteristic
300C2×C4#117×C15111yescharacteristic
301C2×C4#123×C15112yes—
302C2×C4#123×C15112yes—
303C8—44no—
304C8—82no—
305C22—21no—
306C22—21no—
307C22—22no—
308C22—42no—
309C22—42no—
310C22—41no—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—81no—
316C22—81no—
317C22#381×C15111yescharacteristic
318C22C2×#104×C15111yescharacteristic
319C22#421×C15111yescharacteristic
320C4—22no—
321C4—22no—
322C4—21no—
323C4—21no—
324C4—42no—
325C4—41no—
326C4—41no—
327C4—81no—
328C4—81no—
329C4—81no—
330C2—21no—
331C2—21no—
332C2—42no—
333C2—81no—
334C2#1826×C15111yescharacteristic
335C2#1827×C15111yescharacteristic
336C2#1829×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#381
commutatorC22×C4C22×C4×C151
Frattini, cosocleC2×C42C23×C151
prime radicalC22×D4×C151D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1300×C151C2semidirect
5. #1288×C151C2semidirect
168. #8772C151direct (N × H)
169. C151#8772direct (N × H)
173. #1300C2×C151semidirect
174. #1288C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2353×C1512
C4×#100×C1512
#1466×C1512
#1300×C1512
#1288×C1512
#8772151