Finite Group Databasebeta

← C151×#10495 #50315420

Subgroups — C151×#10495 #50315420

Order 38656.

344 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 98 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#3230×C151C211yesmaximal, characteristic
2#1997×C151C211yesmaximal, characteristic
3#1574×C151C211yesmaximal, characteristic
4#1561×C151C211yesmaximal, characteristic
5#1546×C151C211yesmaximal, characteristic
6#1485×C151C211yesmaximal, characteristic
7#1299×C151C211yesmaximal, characteristic
8#533×C151C2211yescharacteristic
9C2×C4⋊Q8×C151C2211yescharacteristic
10#500×C151—21no—
11#487×C151—21no—
12#484×C151—22no—
13#477×C151—21no—
14#477×C151—21no—
15#431×C151C2211yescharacteristic
16#431×C151C2211yescharacteristic
17#423×C151C2211yescharacteristic
18#423×C151C2211yescharacteristic
19C4×M16×C151C2211yescharacteristic
20#343×C151—22no—
21#335×C151—21no—
22#334×C151—21no—
23#332×C151—21no—
24#332×C151—21no—
25#332×C151—22no—
26Q8⋊C8×C151—22no—
27C22×Q8×C151—21no—
28C2×M16×C151—21no—
29C2×M16×C151—21no—
30C2×M16×C151—21no—
31C4⋊Q8×C151—21no—
32C4⋊Q8×C151—21no—
33C4⋊Q8×C151—21no—
34C4⋊Q8×C151—21no—
35C4⋊Q8×C151D411yescharacteristic
36C4⋊Q8×C151D411yescharacteristic
37#125×C151—21no—
38C22⋊Q8×C151—21no—
39C22⋊Q8×C151—21no—
40C4×Q8×C151—21no—
41C4×Q8×C151—21no—
42#117×C151—21no—
43C2×C4⋊C4×C151—21no—
44C2×C4⋊C4×C151D412yes—
45C2×C42×C151C2311yescharacteristic
46#107×C151—22no—
47#107×C151—22no—
48C4⋊C8×C151—21no—
49C4⋊C8×C151—21no—
50C4⋊C8×C151—21no—
51C4⋊C8×C151—21no—
52C4⋊C8×C151D411yescharacteristic
53C4⋊C8×C151D411yescharacteristic
54C4⋊C8×C151D412yes—
55#103×C151—22no—
56#103×C151—22no—
57C22⋊C8×C151—21no—
58C22⋊C8×C151—21no—
59#97×C151—21no—
60C4×C8×C151—21no—
61C4×C8×C151—21no—
62C4×C8×C151—21no—
63C2×Q8×C151—21no—
64C2×Q8×C151—21no—
65C2×Q8×C151—41no—
66C2×Q8×C151—41no—
67C2×Q8×C151—81no—
68C2×Q8×C151—81no—
69C22×C4×C151—22no—
70C22×C4×C151C2×D411yescharacteristic
71C22×C4×C151#4111yescharacteristic
72C22×C4×C151#4111yescharacteristic
73M16×C151—22no—
74M16×C151—41no—
75M16×C151—42no—
76M16×C151—81no—
77C2×C8×C151—21no—
78C2×C8×C151—21no—
79C2×C8×C151—22no—
80C2×C8×C151—41no—
81C2×C8×C151—41no—
82C2×C8×C151—41no—
83C4⋊C4×C151—22no—
84C4⋊C4×C151—21no—
85C4⋊C4×C151—22no—
86C4⋊C4×C151—21no—
87C4⋊C4×C151—21no—
88C4⋊C4×C151—21no—
89C4⋊C4×C151—41no—
90C4⋊C4×C151—41no—
91C4⋊C4×C151—41no—
92C4⋊C4×C151—41no—
93C22⋊C4×C151—41no—
94C42×C151—41no—
95C42×C151C2×D411yescharacteristic
96C42×C151C2×D411yescharacteristic
97C42×C151C2×D411yescharacteristic
98C42×C151#4111yescharacteristic
99C23×C151#12311yescharacteristic
100Q8×C151—41no—
101Q8×C151—41no—
102Q8×C151—41no—
103Q8×C151—41no—
104Q8×C151—82no—
105Q8×C151—81no—
106Q8×C151—81no—
107C2×C4×C151—21no—
108C2×C4×C151—21no—
109C2×C4×C151—21no—
110C2×C4×C151—21no—
111C2×C4×C151—22no—
112C2×C4×C151—41no—
113C2×C4×C151—41no—
114C2×C4×C151—42no—
115C2×C4×C151—82no—
116C2×C4×C151#12011yescharacteristic
117C2×C4×C151#12111yescharacteristic
118C2×C4×C151#12111yescharacteristic
119C2×C4×C151#12111yescharacteristic
120C2×C4×C151#12311yescharacteristic
121C2×C4×C151#12411yescharacteristic
122C8×C151—42no—
123C8×C151—41no—
124C8×C151—41no—
125C8×C151—42no—
126C8×C151—81no—
127C8×C151—81no—
128C22×C151—21no—
129C22×C151—21no—
130C22×C151—21no—
131C22×C151#39411yescharacteristic
132C4×C151—21no—
133C4×C151—21no—
134C4×C151—21no—
135C4×C151—82no—
136C4×C151—81no—
137C4×C151—81no—
138C4×C151#45411yescharacteristic
139C4×C151#45611yescharacteristic
140C4×C151#47111yescharacteristic
141C4×C151#47211yescharacteristic
142C4×C151#47312yes—
143C2×C151—41no—
144C2×C151#203811yescharacteristic
145C2×C151#204711yescharacteristic
146C2×C151#205111yescharacteristic
147#10495C15111yesmaximal, characteristic, direct product factor, Sylow
148C151#1049511yescharacteristic, direct product factor, Sylow
149#3230C2×C15111yescharacteristic
150#1997C2×C15111yescharacteristic
151#1574C2×C15111yescharacteristic
152#1561C2×C15111yescharacteristic
153#1546C2×C15111yescharacteristic
154#1485C2×C15111yescharacteristic
155#1299C2×C15111yescharacteristic
156#533C22×C15111yescharacteristic
157C2×C4⋊Q8C22×C15111yescharacteristic
158#500—21no—
159#487—21no—
160#484—22no—
161#477—21no—
162#477—21no—
163#431C22×C15111yescharacteristic
164#431C22×C15111yescharacteristic
165#423C22×C15111yescharacteristic
166#423C22×C15111yescharacteristic
167C4×M16C22×C15111yescharacteristic
168#343—22no—
169#335—21no—
170#334—21no—
171#332—21no—
172#332—21no—
173#332—22no—
174Q8⋊C8—22no—
175C22×Q8—21no—
176C2×M16—21no—
177C2×M16—21no—
178C2×M16—21no—
179C4⋊Q8—21no—
180C4⋊Q8—21no—
181C4⋊Q8—21no—
182C4⋊Q8—21no—
183C4⋊Q8D4×C15111yescharacteristic
184C4⋊Q8D4×C15111yescharacteristic
185#125—21no—
186C22⋊Q8—21no—
187C22⋊Q8—21no—
188C4×Q8—21no—
189C4×Q8—21no—
190#117—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4D4×C15112yes—
193C2×C42C23×C15111yescharacteristic
194#107—22no—
195#107—22no—
196C4⋊C8—21no—
197C4⋊C8—21no—
198C4⋊C8—21no—
199C4⋊C8—21no—
200C4⋊C8D4×C15112yes—
201C4⋊C8D4×C15111yescharacteristic
202C4⋊C8D4×C15111yescharacteristic
203#103—22no—
204#103—22no—
205C22⋊C8—21no—
206C22⋊C8—21no—
207#97—21no—
208C4×C8—21no—
209C4×C8—21no—
210C4×C8—21no—
211C2×Q8—21no—
212C2×Q8—21no—
213C2×Q8—41no—
214C2×Q8—41no—
215C2×Q8—81no—
216C2×Q8—81no—
217C22×C4—22no—
218C22×C4C2×D4×C15111yescharacteristic
219C22×C4#41×C15111yescharacteristic
220C22×C4#41×C15111yescharacteristic
221M16—22no—
222M16—41no—
223M16—42no—
224M16—81no—
225C2×C8—21no—
226C2×C8—21no—
227C2×C8—22no—
228C2×C8—41no—
229C2×C8—41no—
230C2×C8—41no—
231C4⋊C4—22no—
232C4⋊C4—21no—
233C4⋊C4—22no—
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C22⋊C4—41no—
242C42—41no—
243C42C2×D4×C15111yescharacteristic
244C42C2×D4×C15111yescharacteristic
245C42C2×D4×C15111yescharacteristic
246C42#41×C15111yescharacteristic
247C23#123×C15111yescharacteristic
248Q8—41no—
249Q8—41no—
250Q8—41no—
251Q8—41no—
252Q8—82no—
253Q8—81no—
254Q8—81no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—42no—
263C2×C4—82no—
264C2×C4#120×C15111yescharacteristic
265C2×C4#121×C15111yescharacteristic
266C2×C4#121×C15111yescharacteristic
267C2×C4#121×C15111yescharacteristic
268C2×C4#123×C15111yescharacteristic
269C2×C4#124×C15111yescharacteristic
270C8—42no—
271C8—41no—
272C8—41no—
273C8—42no—
274C8—81no—
275C8—81no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22#394×C15111yescharacteristic
280C4—21no—
281C4—21no—
282C4—21no—
283C4—81no—
284C4—82no—
285C4—81no—
286C4#454×C15111yescharacteristic
287C4#456×C15111yescharacteristic
288C4#471×C15111yescharacteristic
289C4#472×C15111yescharacteristic
290C4#473×C15112yes—
291C2—41no—
292C2#2038×C15111yescharacteristic
293C2#2047×C15111yescharacteristic
294C2#2051×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#394
commutator, Frattini, cosocleC2×C42C23×C151
prime radicalC23×C151#123
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
147. #10495C151direct (N × H)
148. C151#10495direct (N × H)

Maximal subgroups

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

subgroupindex
#3230×C1512
#1997×C1512
#1574×C1512
#1561×C1512
#1546×C1512
#1485×C1512
#1299×C1512
#10495151