Finite Group Databasebeta

← C151×#9024 #50313949

Subgroups — C151×#9024 #50313949

Order 38656.

740 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 740 conjugacy classes of subgroups — too many to draw. Only its 150 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
1C2×#399×C151C211yesmaximal, characteristic
2#2312×C151C211yesmaximal, characteristic
3#1824×C151C212yesmaximal, complemented
4C2×#323×C151C211yesmaximal, characteristic
5#1294×C151C212yesmaximal, complemented
6C22×C4⋊C4×C151—21no—
7C22×C4⋊C4×C151C2211yescharacteristic
8C22×C22⋊C4×C151—21no—
9C22×C22⋊C4×C151C2211yescharacteristic
10C2×C22⋊C8×C151C2212yes—
11#399×C151—22no—
12#399×C151C414yescomplemented
13#388×C151—24no—
14#380×C151C2212yes—
15#379×C151—21no—
16C4×C22⋊C4×C151—21no—
17C2×#95×C151C2211yescharacteristic
18#340×C151—24no—
19#323×C151—22no—
20C25×C151D411yescharacteristic
21C23×C4×C151—21no—
22C23×C4×C151—21no—
23C23×C4×C151D411yescharacteristic
24C23×C4×C151C2311yescharacteristic
25C22×C8×C151—22no—
26C2×C4⋊C4×C151—22no—
27C2×C4⋊C4×C151—22no—
28C2×C4⋊C4×C151—24no—
29C2×C4⋊C4×C151—21no—
30C2×C4⋊C4×C151—44no—
31C2×C4⋊C4×C151C2×C412yes—
32C2×C4⋊C4×C151D414yes—
33C2×C22⋊C4×C151—22no—
34C2×C22⋊C4×C151—22no—
35C2×C22⋊C4×C151—22no—
36C2×C22⋊C4×C151—22no—
37C2×C22⋊C4×C151—24no—
38C2×C22⋊C4×C151—22no—
39C2×C22⋊C4×C151—44no—
40C2×C22⋊C4×C151C2×C412yes—
41C2×C22⋊C4×C151D412yes—
42C2×C42×C151—22no—
43C22⋊C8×C151—22no—
44C22⋊C8×C151—22no—
45#95×C151—22no—
46#95×C151—21no—
47#95×C151—22no—
48#95×C151C2×C412yes—
49C24×C151—21no—
50C24×C151—22no—
51C24×C151—21no—
52C24×C151—22no—
53C24×C151—42no—
54C24×C151—42no—
55C24×C151C22⋊C412yes—
56C24×C151C2×D411yescharacteristic
57C22×C4×C151—24no—
58C22×C4×C151—22no—
59C22×C4×C151—21no—
60C22×C4×C151—21no—
61C22×C4×C151—22no—
62C22×C4×C151—24no—
63C22×C4×C151—42no—
64C22×C4×C151—42no—
65C22×C4×C151—42no—
66C22×C4×C151—42no—
67C22×C4×C151—42no—
68C22×C4×C151—42no—
69C22×C4×C151—41no—
70C22×C4×C151—41no—
71C22×C4×C151C22⋊C412yes—
72C22×C4×C151C22×C411yescharacteristic
73C22×C4×C151C2×D412yes—
74C22×C4×C151C2×D411yescharacteristic
75C22×C4×C151#4112yes—
76C2×C8×C151—44no—
77C2×C8×C151—42no—
78C4⋊C4×C151—24no—
79C4⋊C4×C151—44no—
80C4⋊C4×C151—48no—
81C4⋊C4×C151—42no—
82C22⋊C4×C151—24no—
83C22⋊C4×C151—24no—
84C22⋊C4×C151—48no—
85C22⋊C4×C151—42no—
86C22⋊C4×C151—42no—
87C22⋊C4×C151—82no—
88C22⋊C4×C151—82no—
89C42×C151—82no—
90C23×C151—22no—
91C23×C151—22no—
92C23×C151—22no—
93C23×C151—22no—
94C23×C151—22no—
95C23×C151—42no—
96C23×C151—42no—
97C23×C151—48no—
98C23×C151—42no—
99C23×C151—42no—
100C23×C151—42no—
101C23×C151—42no—
102C23×C151—81no—
103C23×C151—81no—
104C23×C151—84no—
105C23×C151C2×C22⋊C411yescharacteristic
106C23×C151#12011yescharacteristic
107C23×C151#12311yescharacteristic
108C23×C151#13512yes—
109C23×C151#13712yes—
110C2×C4×C151—24no—
111C2×C4×C151—24no—
112C2×C4×C151—22no—
113C2×C4×C151—41no—
114C2×C4×C151—41no—
115C2×C4×C151—42no—
116C2×C4×C151—48no—
117C2×C4×C151—42no—
118C2×C4×C151—42no—
119C2×C4×C151—42no—
120C2×C4×C151—42no—
121C2×C4×C151—42no—
122C2×C4×C151—42no—
123C2×C4×C151—42no—
124C2×C4×C151—44no—
125C2×C4×C151—44no—
126C2×C4×C151—44no—
127C2×C4×C151—81no—
128C2×C4×C151—82no—
129C2×C4×C151—82no—
130C2×C4×C151C4×D412yes—
131C2×C4×C151#12112yes—
132C8×C151—82no—
133C22×C151—24no—
134C22×C151—24no—
135C22×C151—21no—
136C22×C151—21no—
137C22×C151—21no—
138C22×C151—21no—
139C22×C151—44no—
140C22×C151—42no—
141C22×C151—42no—
142C22×C151—42no—
143C22×C151—82no—
144C22×C151—84no—
145C22×C151—84no—
146C22×C151#38611yescharacteristic
147C22×C151#41611yescharacteristic
148C22×C151#41911yescharacteristic
149C22×C151#45212yes—
150C22×C151#45312yes—
151C22×C151#45812yes—
152C22×C151#48512yes—
153C4×C151—22no—
154C4×C151—22no—
155C4×C151—44no—
156C4×C151—42no—
157C4×C151—84no—
158C4×C151—82no—
159C2×C151—21no—
160C2×C151—21no—
161C2×C151—22no—
162C2×C151—82no—
163C2×C151#161814yes—
164C2×C151#187311yescharacteristic
165C2×C151#188711yescharacteristic
166C2×C151#189011yescharacteristic
167#9024C15111yesmaximal, characteristic, direct product factor, Sylow
168C151#902411yescharacteristic, direct product factor, Sylow
169C2×#399C2×C15111yescharacteristic
170#2312C2×C15111yescharacteristic
171#1824C2×C15112yescomplemented
172C2×#323C2×C15111yescharacteristic
173#1294C2×C15112yescomplemented
174C22×C4⋊C4—21no—
175C22×C4⋊C4C22×C15111yescharacteristic
176C22×C22⋊C4—21no—
177C22×C22⋊C4C22×C15111yescharacteristic
178C2×C22⋊C8C22×C15112yes—
179#399—22no—
180#399C4×C15114yescomplemented
181#388—24no—
182#380C22×C15112yes—
183#379—21no—
184C4×C22⋊C4—21no—
185C2×#95C22×C15111yescharacteristic
186#340—24no—
187#323—22no—
188C25D4×C15111yescharacteristic
189C23×C4—21no—
190C23×C4—21no—
191C23×C4D4×C15111yescharacteristic
192C23×C4C23×C15111yescharacteristic
193C22×C8—22no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—24no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—44no—
199C2×C4⋊C4C2×C4×C15112yes—
200C2×C4⋊C4D4×C15114yes—
201C2×C22⋊C4—22no—
202C2×C22⋊C4—22no—
203C2×C22⋊C4—24no—
204C2×C22⋊C4—22no—
205C2×C22⋊C4—22no—
206C2×C22⋊C4—22no—
207C2×C22⋊C4—44no—
208C2×C22⋊C4C2×C4×C15112yes—
209C2×C22⋊C4D4×C15112yes—
210C2×C42—22no—
211C22⋊C8—22no—
212C22⋊C8—22no—
213#95—22no—
214#95—21no—
215#95—22no—
216#95C2×C4×C15112yes—
217C24—21no—
218C24—22no—
219C24—21no—
220C24—22no—
221C24—42no—
222C24—42no—
223C24C22⋊C4×C15112yes—
224C24C2×D4×C15111yescharacteristic
225C22×C4—24no—
226C22×C4—22no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—22no—
230C22×C4—24no—
231C22×C4—42no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4—41no—
238C22×C4—41no—
239C22×C4C22⋊C4×C15112yes—
240C22×C4C22×C4×C15111yescharacteristic
241C22×C4C2×D4×C15112yes—
242C22×C4C2×D4×C15111yescharacteristic
243C22×C4#41×C15112yes—
244C2×C8—44no—
245C2×C8—42no—
246C4⋊C4—24no—
247C4⋊C4—44no—
248C4⋊C4—48no—
249C4⋊C4—42no—
250C22⋊C4—24no—
251C22⋊C4—24no—
252C22⋊C4—48no—
253C22⋊C4—42no—
254C22⋊C4—42no—
255C22⋊C4—82no—
256C22⋊C4—82no—
257C42—82no—
258C23—22no—
259C23—22no—
260C23—22no—
261C23—22no—
262C23—22no—
263C23—42no—
264C23—42no—
265C23—48no—
266C23—42no—
267C23—42no—
268C23—42no—
269C23—42no—
270C23—81no—
271C23—81no—
272C23—84no—
273C23C2×C22⋊C4×C15111yescharacteristic
274C23#120×C15111yescharacteristic
275C23#123×C15111yescharacteristic
276C23#135×C15112yes—
277C23#137×C15112yes—
278C2×C4—24no—
279C2×C4—24no—
280C2×C4—22no—
281C2×C4—42no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—48no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—44no—
293C2×C4—44no—
294C2×C4—44no—
295C2×C4—81no—
296C2×C4—82no—
297C2×C4—82no—
298C2×C4C4×D4×C15112yes—
299C2×C4#121×C15112yes—
300C8—82no—
301C22—24no—
302C22—24no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—21no—
307C22—44no—
308C22—42no—
309C22—42no—
310C22—42no—
311C22—82no—
312C22—84no—
313C22—84no—
314C22#386×C15111yescharacteristic
315C22#416×C15111yescharacteristic
316C22#419×C15111yescharacteristic
317C22#452×C15112yes—
318C22#453×C15112yes—
319C22#458×C15112yes—
320C22#485×C15112yes—
321C4—22no—
322C4—22no—
323C4—44no—
324C4—42no—
325C4—84no—
326C4—82no—
327C2—21no—
328C2—21no—
329C2—22no—
330C2—82no—
331C2#1618×C15114yes—
332C2#1873×C15111yescharacteristic
333C2#1887×C15111yescharacteristic
334C2#1890×C15111yescharacteristic
subgroupG/H
center, socleC23×C151#120
commutatorC22×C4C22×C4×C151
Frattini, cosocleC23×C4C23×C151
prime radicalC25×C151D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1824×C151C2semidirect
5. #1294×C151C2semidirect
12. #399×C151C4semidirect
167. #9024C151direct (N × H)
168. C151#9024direct (N × H)
171. #1824C2×C151semidirect
173. #1294C2×C151semidirect
180. #399C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#399×C1512
#2312×C1512
#1824×C1512
C2×#323×C1512
#1294×C1512
#9024151