Finite Group Databasebeta

← C151×#11804 #50316729

Subgroups — C151×#11804 #50316729

Order 38656.

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

normal subgroups only

This group has 472 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#2392×C151C211yesmaximal, characteristic
2#1822×C151C211yesmaximal, characteristic, complemented
3#1464×C151C211yesmaximal, characteristic, complemented
4#1346×C151C212yesmaximal, complemented
5#1345×C151C212yesmaximal, complemented
6C2×C4×D4×C151—21no—
7C2×C4×D4×C151C411yescharacteristic
8C2×#117×C151C2211yescharacteristic
9#432×C151—21no—
10#407×C151—21no—
11#398×C151C2211yescharacteristic
12#397×C151C411yescharacteristic
13#396×C151—21no—
14#394×C151—21no—
15#394×C151C2211yescharacteristic
16#392×C151C411yescharacteristic
17C4×C4⋊C4×C151C411yescharacteristic
18C4×C22⋊C4×C151—21no—
19#343×C151—21no—
20#343×C151C2212yes—
21#324×C151C2212yes—
22#323×C151—21no—
23C22×D4×C151—21no—
24C22×D4×C151C2×C411yescharacteristic
25C23×C4×C151—21no—
26C23×C4×C151D411yescharacteristic
27C2×M16×C151—22no—
28C4×D4×C151—41no—
29C4×D4×C151—41no—
30C4×D4×C151—44no—
31#117×C151—41no—
32#117×C151—41no—
33C2×C4⋊C4×C151—21no—
34C2×C4⋊C4×C151—21no—
35C2×C4⋊C4×C151C2×C411yescharacteristic
36C2×C4⋊C4×C151D411yescharacteristic
37C2×C4⋊C4×C151C2311yescharacteristic
38C2×C22⋊C4×C151—21no—
39C2×C22⋊C4×C151—21no—
40C2×C22⋊C4×C151—21no—
41C2×C22⋊C4×C151—21no—
42C2×C22⋊C4×C151—21no—
43C2×C22⋊C4×C151C2×C411yescharacteristic
44C2×C22⋊C4×C151D411yescharacteristic
45C2×C42×C151—21no—
46C2×C42×C151C2×C411yescharacteristic
47C2×C42×C151D411yescharacteristic
48C4⋊C8×C151—41no—
49C22⋊C8×C151—22no—
50C22⋊C8×C151—41no—
51C22⋊C8×C151—41no—
52#97×C151—41no—
53#95×C151—21no—
54#95×C151—21no—
55#95×C151C2×C411yescharacteristic
56#95×C151C2×C411yescharacteristic
57C24×C151—21no—
58C24×C151C22⋊C411yescharacteristic
59C2×D4×C151—41no—
60C2×D4×C151—42no—
61C2×D4×C151—42no—
62C2×D4×C151—42no—
63C2×D4×C151—42no—
64C22×C4×C151—21no—
65C22×C4×C151—21no—
66C22×C4×C151—21no—
67C22×C4×C151—22no—
68C22×C4×C151—21no—
69C22×C4×C151—21no—
70C22×C4×C151—41no—
71C22×C4×C151—42no—
72C22×C4×C151—42no—
73C22×C4×C151—41no—
74C22×C4×C151—41no—
75C22×C4×C151C22⋊C411yescharacteristic
76C22×C4×C151C22⋊C411yescharacteristic
77C22×C4×C151C22⋊C411yescharacteristic
78C22×C4×C151C22×C411yescharacteristic
79C22×C4×C151C2×D411yescharacteristic
80C22×C4×C151C2×D411yescharacteristic
81M16×C151—42no—
82M16×C151—42no—
83C2×C8×C151—42no—
84C2×C8×C151—42no—
85C4⋊C4×C151—41no—
86C4⋊C4×C151—41no—
87C4⋊C4×C151—41no—
88C4⋊C4×C151—42no—
89C4⋊C4×C151—42no—
90C22⋊C4×C151—41no—
91C22⋊C4×C151—41no—
92C22⋊C4×C151—42no—
93C22⋊C4×C151—42no—
94C22⋊C4×C151—42no—
95C22⋊C4×C151—42no—
96C22⋊C4×C151—42no—
97C42×C151—21no—
98C42×C151—21no—
99C42×C151—21no—
100C42×C151—21no—
101C42×C151—42no—
102C23×C151—22no—
103C23×C151—21no—
104C23×C151—21no—
105C23×C151—21no—
106C23×C151—41no—
107C23×C151—41no—
108C23×C151—41no—
109C23×C151—41no—
110C23×C151—41no—
111C23×C151—41no—
112C23×C151—41no—
113C23×C151—41no—
114C23×C151C2×C22⋊C411yescharacteristic
115D4×C151—42no—
116D4×C151—48no—
117D4×C151—42no—
118C2×C4×C151—21no—
119C2×C4×C151—21no—
120C2×C4×C151—21no—
121C2×C4×C151—21no—
122C2×C4×C151—22no—
123C2×C4×C151—21no—
124C2×C4×C151—21no—
125C2×C4×C151—21no—
126C2×C4×C151—21no—
127C2×C4×C151—42no—
128C2×C4×C151—42no—
129C2×C4×C151—41no—
130C2×C4×C151—41no—
131C2×C4×C151—41no—
132C2×C4×C151—41no—
133C2×C4×C151—41no—
134C2×C4×C151—41no—
135C2×C4×C151—41no—
136C2×C4×C151—41no—
137C2×C4×C151—41no—
138C2×C4×C151—41no—
139C2×C4×C151—41no—
140C2×C4×C151—41no—
141C2×C4×C151—82no—
142C2×C4×C151—82no—
143C2×C4×C151#9911yescharacteristic
144C2×C4×C151#9911yescharacteristic
145C2×C4×C151AGL(1,ℤ/8)12yes—
146C8×C151—82no—
147C8×C151—82no—
148C22×C151—21no—
149C22×C151—21no—
150C22×C151—42no—
151C22×C151—42no—
152C22×C151—42no—
153C22×C151—42no—
154C22×C151—41no—
155C22×C151—41no—
156C22×C151—41no—
157C22×C151—81no—
158C22×C151—81no—
159C22×C151—81no—
160C22×C151—81no—
161C22×C151—81no—
162C22×C151C2×#9911yescharacteristic
163C22×C151#41811yescharacteristic
164C22×C151#42111yescharacteristic
165C4×C151—22no—
166C4×C151—21no—
167C4×C151—21no—
168C4×C151—42no—
169C4×C151—41no—
170C4×C151—41no—
171C4×C151—41no—
172C4×C151—41no—
173C4×C151—81no—
174C4×C151—81no—
175C2×C151—21no—
176C2×C151—21no—
177C2×C151—81no—
178C2×C151—82no—
179C2×C151#151011yescharacteristic
180C2×C151#212011yescharacteristic
181C2×C151#213211yescharacteristic
182#11804C15111yesmaximal, characteristic, direct product factor, Sylow
183C151#1180411yescharacteristic, direct product factor, Sylow
184#2392C2×C15111yescharacteristic
185#1822C2×C15111yescharacteristic, complemented
186#1464C2×C15111yescharacteristic, complemented
187#1346C2×C15112yescomplemented
188#1345C2×C15112yescomplemented
189C2×C4×D4—21no—
190C2×C4×D4C4×C15111yescharacteristic
191C2×#117C22×C15111yescharacteristic
192#432—21no—
193#407—21no—
194#398C22×C15111yescharacteristic
195#397C4×C15111yescharacteristic
196#396—21no—
197#394—21no—
198#394C22×C15111yescharacteristic
199#392C4×C15111yescharacteristic
200C4×C4⋊C4C4×C15111yescharacteristic
201C4×C22⋊C4—21no—
202#343—21no—
203#343C22×C15112yes—
204#324C22×C15112yes—
205#323—21no—
206C22×D4—21no—
207C22×D4C2×C4×C15111yescharacteristic
208C23×C4—21no—
209C23×C4D4×C15111yescharacteristic
210C2×M16—22no—
211C4×D4—41no—
212C4×D4—41no—
213C4×D4—44no—
214#117—41no—
215#117—41no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4C2×C4×C15111yescharacteristic
219C2×C4⋊C4D4×C15111yescharacteristic
220C2×C4⋊C4C23×C15111yescharacteristic
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4C2×C4×C15111yescharacteristic
227C2×C22⋊C4D4×C15111yescharacteristic
228C2×C42—21no—
229C2×C42C2×C4×C15111yescharacteristic
230C2×C42D4×C15111yescharacteristic
231C4⋊C8—41no—
232C22⋊C8—22no—
233C22⋊C8—41no—
234C22⋊C8—41no—
235#97—41no—
236#95—21no—
237#95—21no—
238#95C2×C4×C15111yescharacteristic
239#95C2×C4×C15111yescharacteristic
240C24—21no—
241C24C22⋊C4×C15111yescharacteristic
242C2×D4—41no—
243C2×D4—42no—
244C2×D4—42no—
245C2×D4—42no—
246C2×D4—42no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—22no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—41no—
254C22×C4—42no—
255C22×C4—42no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4C22⋊C4×C15111yescharacteristic
259C22×C4C22⋊C4×C15111yescharacteristic
260C22×C4C22⋊C4×C15111yescharacteristic
261C22×C4C22×C4×C15111yescharacteristic
262C22×C4C2×D4×C15111yescharacteristic
263C22×C4C2×D4×C15111yescharacteristic
264M16—42no—
265M16—42no—
266C2×C8—42no—
267C2×C8—42no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—42no—
272C4⋊C4—42no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—42no—
276C22⋊C4—42no—
277C22⋊C4—42no—
278C22⋊C4—42no—
279C22⋊C4—42no—
280C42—21no—
281C42—21no—
282C42—21no—
283C42—21no—
284C42—42no—
285C23—22no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—41no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23C2×C22⋊C4×C15111yescharacteristic
298D4—42no—
299D4—48no—
300D4—42no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—22no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—82no—
325C2×C4—82no—
326C2×C4#99×C15111yescharacteristic
327C2×C4#99×C15111yescharacteristic
328C2×C4AGL(1,ℤ/8)×C15112yes—
329C8—82no—
330C8—82no—
331C22—21no—
332C22—21no—
333C22—42no—
334C22—42no—
335C22—42no—
336C22—42no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—81no—
341C22—81no—
342C22—81no—
343C22—81no—
344C22—81no—
345C22C2×#99×C15111yescharacteristic
346C22#418×C15111yescharacteristic
347C22#421×C15111yescharacteristic
348C4—22no—
349C4—21no—
350C4—21no—
351C4—42no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—81no—
357C4—81no—
358C2—21no—
359C2—21no—
360C2—81no—
361C2—82no—
362C2#1510×C15111yescharacteristic
363C2#2120×C15111yescharacteristic
364C2#2132×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#99
commutatorC22×C4C22×C4×C151
Frattini, cosocleC2×C4⋊C4C23×C151
prime radical#392×C151C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C22×C4×C151 ◁ C2×#117×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1822×C151C2semidirect
3. #1464×C151C2semidirect
4. #1346×C151C2semidirect
5. #1345×C151C2semidirect
182. #11804C151direct (N × H)
183. C151#11804direct (N × H)
185. #1822C2×C151semidirect
186. #1464C2×C151semidirect
187. #1346C2×C151semidirect
188. #1345C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2392×C1512
#1822×C1512
#1464×C1512
#1346×C1512
#1345×C1512
#11804151