Finite Group Databasebeta

← C151×#12921 #50317846

Subgroups — C151×#12921 #50317846

Order 38656.

442 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#427×C151C211yesmaximal, characteristic
2C2×#367×C151C211yesmaximal, characteristic, complemented
3C2×#366×C151C211yesmaximal, characteristic, complemented
4C2×C22⋊C16×C151C211yesmaximal, characteristic
5#1808×C151C211yesmaximal, characteristic
6#1380×C151C211yesmaximal, characteristic, complemented
7#1380×C151C211yesmaximal, characteristic, complemented
8C23×C8×C151C2211yescharacteristic
9C2×#117×C151—21no—
10C22×C16×C151C2211yescharacteristic
11C22×C16×C151C2211yescharacteristic
12#427×C151—22no—
13#427×C151—22no—
14C2×#107×C151C2211yescharacteristic
15C2×#107×C151C2211yescharacteristic
16C2×#107×C151C2211yescharacteristic
17C2×#107×C151C2211yescharacteristic
18C2×#106×C151—21no—
19#380×C151—21no—
20#367×C151—22no—
21#366×C151—22no—
22C22⋊C16×C151C414yescomplemented
23#340×C151—21no—
24C23×C4×C151D411yescharacteristic
25C22×C8×C151—21no—
26C22×C8×C151—21no—
27C22×C8×C151—21no—
28C22×C8×C151—21no—
29C22×C8×C151C2×C412yes—
30C22×C8×C151D411yescharacteristic
31C22×C8×C151Q812yes—
32C22×C8×C151C2311yescharacteristic
33#117×C151—24no—
34#117×C151—42no—
35C2×C4⋊C4×C151—21no—
36C2×C4⋊C4×C151—21no—
37C2×C4⋊C4×C151—21no—
38C2×C4⋊C4×C151—21no—
39C2×C22⋊C4×C151—41no—
40C2×C22⋊C4×C151—41no—
41C2×C42×C151—41no—
42C2×C16×C151—21no—
43C2×C16×C151—21no—
44C2×C16×C151—21no—
45C2×C16×C151—21no—
46C2×C16×C151C2×C412yes—
47C2×C16×C151C2×C412yes—
48#107×C151—21no—
49#107×C151—21no—
50#107×C151—21no—
51#107×C151—21no—
52#107×C151—21no—
53#107×C151—21no—
54#107×C151D412yes—
55#107×C151D412yes—
56#106×C151—24no—
57#95×C151—41no—
58C24×C151D811yescharacteristic
59C22×C4×C151—21no—
60C22×C4×C151—21no—
61C22×C4×C151—21no—
62C22×C4×C151—21no—
63C22×C4×C151—41no—
64C22×C4×C151—41no—
65C22×C4×C151—41no—
66C22×C4×C151—41no—
67C22×C4×C151C4⋊C412yes—
68C22×C4×C151D811yescharacteristic
69C22×C4×C151Q1612yes—
70C22×C4×C151C2×D411yescharacteristic
71C2×C8×C151—21no—
72C2×C8×C151—21no—
73C2×C8×C151—22no—
74C2×C8×C151—22no—
75C2×C8×C151—22no—
76C2×C8×C151—22no—
77C2×C8×C151C4⋊C412yes—
78C2×C8×C151C22×C411yescharacteristic
79C2×C8×C151C2×D411yescharacteristic
80C2×C8×C151C2×D411yescharacteristic
81C2×C8×C151C2×Q811yescharacteristic
82C2×C8×C151#4111yescharacteristic
83C2×C8×C151#4111yescharacteristic
84C4⋊C4×C151—22no—
85C4⋊C4×C151—22no—
86C4⋊C4×C151—41no—
87C4⋊C4×C151—41no—
88C4⋊C4×C151—41no—
89C4⋊C4×C151—41no—
90C4⋊C4×C151—41no—
91C4⋊C4×C151—41no—
92C22⋊C4×C151—44no—
93C22⋊C4×C151—82no—
94C42×C151—44no—
95C16×C151—22no—
96C16×C151—22no—
97C23×C151—21no—
98C23×C151—21no—
99C23×C151—21no—
100C23×C151—21no—
101C23×C151—21no—
102C23×C151—21no—
103C23×C151#10712yes—
104C23×C151C2×D811yescharacteristic
105C2×C4×C151—21no—
106C2×C4×C151—21no—
107C2×C4×C151—22no—
108C2×C4×C151—22no—
109C2×C4×C151—22no—
110C2×C4×C151—22no—
111C2×C4×C151—42no—
112C2×C4×C151—42no—
113C2×C4×C151—81no—
114C2×C4×C151—81no—
115C2×C4×C151—81no—
116C2×C4×C151—81no—
117C2×C4×C151—81no—
118C2×C4×C151—81no—
119C2×C4×C151—81no—
120C2×C4×C151—81no—
121C2×C4×C151—81no—
122C2×C4×C151—81no—
123C2×C4×C151#10712yes—
124C2×C4×C151C2×C4⋊C411yescharacteristic
125C2×C4×C151#12011yescharacteristic
126C2×C4×C151#12311yescharacteristic
127C2×C4×C151C2×Q1611yescharacteristic
128C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C151#13711yescharacteristic
130C8×C151—22no—
131C8×C151C4×D411yescharacteristic
132C8×C151C4×D411yescharacteristic
133C8×C151C22⋊Q811yescharacteristic
134C8×C151C22⋊Q811yescharacteristic
135C22×C151—22no—
136C22×C151—22no—
137C22×C151—22no—
138C22×C151—41no—
139C22×C151—41no—
140C22×C151—41no—
141C22×C151—41no—
142C22×C151C2×#10711yescharacteristic
143C22×C151#44711yescharacteristic
144C22×C151#48011yescharacteristic
145C22×C151#50811yescharacteristic
146C22×C151#50811yescharacteristic
147C22×C151#50911yescharacteristic
148C22×C151#51011yescharacteristic
149C4×C151—22no—
150C4×C151—82no—
151C4×C151—82no—
152C4×C151—161no—
153C4×C151—161no—
154C4×C151#38511yescharacteristic
155C4×C151#42811yescharacteristic
156C4×C151#45111yescharacteristic
157C4×C151#48411yescharacteristic
158C2×C151—42no—
159C2×C151#185211yescharacteristic
160C2×C151#215811yescharacteristic
161C2×C151#215911yescharacteristic
162C2×C151#218611yescharacteristic
163C2×C151#218911yescharacteristic
164C2×C151#223411yescharacteristic
165C2×C151#223711yescharacteristic
166#12921C15111yesmaximal, characteristic, direct product factor, Sylow
167C151#1292111yescharacteristic, direct product factor, Sylow
168C2×#427C2×C15111yescharacteristic
169C2×#367C2×C15111yescharacteristic, complemented
170C2×#366C2×C15111yescharacteristic, complemented
171C2×C22⋊C16C2×C15111yescharacteristic
172#1808C2×C15111yescharacteristic
173#1380C2×C15111yescharacteristic, complemented
174#1380C2×C15111yescharacteristic, complemented
175C23×C8C22×C15111yescharacteristic
176C2×#117—21no—
177C22×C16C22×C15111yescharacteristic
178C22×C16C22×C15111yescharacteristic
179#427—22no—
180#427—22no—
181C2×#107C22×C15111yescharacteristic
182C2×#107C22×C15111yescharacteristic
183C2×#107C22×C15111yescharacteristic
184C2×#107C22×C15111yescharacteristic
185C2×#106—21no—
186#380—21no—
187#367—22no—
188#366—22no—
189C22⋊C16C4×C15114yescomplemented
190#340—21no—
191C23×C4D4×C15111yescharacteristic
192C22×C8—21no—
193C22×C8—21no—
194C22×C8—21no—
195C22×C8—21no—
196C22×C8C2×C4×C15112yes—
197C22×C8D4×C15111yescharacteristic
198C22×C8Q8×C15112yes—
199C22×C8C23×C15111yescharacteristic
200#117—24no—
201#117—42no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C22⋊C4—41no—
207C2×C22⋊C4—41no—
208C2×C42—41no—
209C2×C16—21no—
210C2×C16—21no—
211C2×C16—21no—
212C2×C16—21no—
213C2×C16C2×C4×C15112yes—
214C2×C16C2×C4×C15112yes—
215#107—21no—
216#107—21no—
217#107—21no—
218#107—21no—
219#107—21no—
220#107—21no—
221#107D4×C15112yes—
222#107D4×C15112yes—
223#106—24no—
224#95—41no—
225C24D8×C15111yescharacteristic
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—41no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4C4⋊C4×C15112yes—
235C22×C4D8×C15111yescharacteristic
236C22×C4Q16×C15112yes—
237C22×C4C2×D4×C15111yescharacteristic
238C2×C8—21no—
239C2×C8—21no—
240C2×C8—22no—
241C2×C8—22no—
242C2×C8—22no—
243C2×C8—22no—
244C2×C8C4⋊C4×C15112yes—
245C2×C8C22×C4×C15111yescharacteristic
246C2×C8C2×D4×C15111yescharacteristic
247C2×C8C2×D4×C15111yescharacteristic
248C2×C8C2×Q8×C15111yescharacteristic
249C2×C8#41×C15111yescharacteristic
250C2×C8#41×C15111yescharacteristic
251C4⋊C4—22no—
252C4⋊C4—22no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C22⋊C4—44no—
260C22⋊C4—82no—
261C42—44no—
262C16—22no—
263C16—22no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23—21no—
269C23—21no—
270C23#107×C15112yes—
271C23C2×D8×C15111yescharacteristic
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4#107×C15112yes—
291C2×C4C2×C4⋊C4×C15111yescharacteristic
292C2×C4#120×C15111yescharacteristic
293C2×C4#123×C15111yescharacteristic
294C2×C4C2×Q16×C15111yescharacteristic
295C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
296C2×C4#137×C15111yescharacteristic
297C8—22no—
298C8C4×D4×C15111yescharacteristic
299C8C4×D4×C15111yescharacteristic
300C8C22⋊Q8×C15111yescharacteristic
301C8C22⋊Q8×C15111yescharacteristic
302C22—22no—
303C22—22no—
304C22—22no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22C2×#107×C15111yescharacteristic
310C22#447×C15111yescharacteristic
311C22#480×C15111yescharacteristic
312C22#508×C15111yescharacteristic
313C22#508×C15111yescharacteristic
314C22#509×C15111yescharacteristic
315C22#510×C15111yescharacteristic
316C4—22no—
317C4—82no—
318C4—82no—
319C4—161no—
320C4—161no—
321C4#385×C15111yescharacteristic
322C4#428×C15111yescharacteristic
323C4#451×C15111yescharacteristic
324C4#484×C15111yescharacteristic
325C2—42no—
326C2#1852×C15111yescharacteristic
327C2#2158×C15111yescharacteristic
328C2#2159×C15111yescharacteristic
329C2#2186×C15111yescharacteristic
330C2#2189×C15111yescharacteristic
331C2#2234×C15111yescharacteristic
332C2#2237×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C2×D8
commutatorC2×C8C22×C4×C151
Frattini, cosocleC22×C8C23×C151
prime radicalC24×C151D8
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C23×C4×C151 ◁ C23×C8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#367×C151C2semidirect
3. C2×#366×C151C2semidirect
6. #1380×C151C2semidirect
7. #1380×C151C2semidirect
22. C22⋊C16×C151C4semidirect
166. #12921C151direct (N × H)
167. C151#12921direct (N × H)
169. C2×#367C2×C151semidirect
170. C2×#366C2×C151semidirect
173. #1380C2×C151semidirect
174. #1380C2×C151semidirect
189. C22⋊C16C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#427×C1512
C2×#367×C1512
C2×#366×C1512
C2×C22⋊C16×C1512
#1808×C1512
#1380×C1512
#12921151