Finite Group Databasebeta

← C151×#10488 #50315413

Subgroups — C151×#10488 #50315413

Order 38656.

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

normal subgroups only

This group has 446 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#3205×C151C211yesmaximal, characteristic
2#1965×C151C211yesmaximal, characteristic, complemented
3#1574×C151C211yesmaximal, characteristic, complemented
4#1560×C151C211yesmaximal, characteristic, complemented
5#1545×C151C211yesmaximal, characteristic, complemented
6#1484×C151C211yesmaximal, characteristic, complemented
7#1299×C151C211yesmaximal, characteristic, complemented
8#532×C151C2211yescharacteristic
9C2×#127×C151C2211yescharacteristic
10#493×C151—21no—
11#486×C151—21no—
12#459×C151—21no—
13#459×C151—21no—
14#447×C151—22no—
15#431×C151C2211yescharacteristic
16#431×C151C2211yescharacteristic
17#423×C151C2211yescharacteristic
18#423×C151C2211yescharacteristic
19C2×#100×C151—22no—
20C4×M16×C151C2211yescharacteristic
21#335×C151—21no—
22#334×C151—21no—
23#333×C151—21no—
24#331×C151—21no—
25#331×C151—22no—
26D4⋊C8×C151—22no—
27C2×#41×C151—21no—
28C22×D4×C151—21no—
29C22×D4×C151—21no—
30C22×D4×C151D412yes—
31C2×D8×C151—22no—
32C2×D8×C151—22no—
33C2×M16×C151—21no—
34C2×M16×C151—21no—
35C2×M16×C151—21no—
36C4⋊Q8×C151D411yescharacteristic
37#127×C151—21no—
38#127×C151—21no—
39#127×C151—21no—
40#127×C151—21no—
41#127×C151D411yescharacteristic
42#124×C151—21no—
43#121×C151—21no—
44#121×C151—21no—
45C4×D4×C151—21no—
46C4×D4×C151—21no—
47C2×C42×C151C2311yescharacteristic
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#102×C151—22no—
56#102×C151—22no—
57#100×C151—44no—
58C22⋊C8×C151—21no—
59C22⋊C8×C151—21no—
60#97×C151—21no—
61C4×C8×C151—21no—
62C4×C8×C151—21no—
63C4×C8×C151—21no—
64C24×C151—22no—
65#41×C151—82no—
66C2×Q8×C151—21no—
67C2×D4×C151—22no—
68C2×D4×C151—21no—
69C2×D4×C151—21no—
70C2×D4×C151—22no—
71C2×D4×C151—21no—
72C2×D4×C151—42no—
73C2×D4×C151—42no—
74C2×D4×C151—41no—
75C2×D4×C151—41no—
76C2×D4×C151—41no—
77C2×D4×C151—41no—
78C2×D4×C151—41no—
79C2×D4×C151—81no—
80C2×D4×C151—82no—
81C2×D4×C151—81no—
82C22×C4×C151—41no—
83C22×C4×C151C2×D411yescharacteristic
84C22×C4×C151#4111yescharacteristic
85C22×C4×C151#4111yescharacteristic
86D8×C151—82no—
87D8×C151—82no—
88M16×C151—22no—
89M16×C151—41no—
90M16×C151—42no—
91M16×C151—81no—
92C2×C8×C151—21no—
93C2×C8×C151—21no—
94C2×C8×C151—22no—
95C2×C8×C151—41no—
96C2×C8×C151—41no—
97C2×C8×C151—41no—
98C4⋊C4×C151—21no—
99C4⋊C4×C151—21no—
100C22⋊C4×C151—41no—
101C22⋊C4×C151—41no—
102C42×C151C2×D411yescharacteristic
103C42×C151C2×D411yescharacteristic
104C42×C151C2×D411yescharacteristic
105C42×C151#4111yescharacteristic
106C23×C151—44no—
107C23×C151—42no—
108C23×C151—41no—
109C23×C151—82no—
110C23×C151—82no—
111C23×C151#12311yescharacteristic
112Q8×C151—81no—
113D4×C151—41no—
114D4×C151—42no—
115D4×C151—41no—
116D4×C151—42no—
117D4×C151—41no—
118D4×C151—41no—
119D4×C151—81no—
120D4×C151—82no—
121D4×C151—82no—
122D4×C151—82no—
123D4×C151—82no—
124D4×C151—81no—
125D4×C151—81no—
126D4×C151—82no—
127C2×C4×C151—21no—
128C2×C4×C151—21no—
129C2×C4×C151—21no—
130C2×C4×C151—22no—
131C2×C4×C151—21no—
132C2×C4×C151—41no—
133C2×C4×C151—82no—
134C2×C4×C151#12011yescharacteristic
135C2×C4×C151#12111yescharacteristic
136C2×C4×C151#12111yescharacteristic
137C2×C4×C151#12111yescharacteristic
138C2×C4×C151#12311yescharacteristic
139C2×C4×C151#12411yescharacteristic
140C8×C151—42no—
141C8×C151—41no—
142C8×C151—41no—
143C8×C151—42no—
144C8×C151—81no—
145C8×C151—81no—
146C22×C151—21no—
147C22×C151—21no—
148C22×C151—21no—
149C22×C151—81no—
150C22×C151—82no—
151C22×C151—82no—
152C22×C151—81no—
153C22×C151—81no—
154C22×C151—82no—
155C22×C151—164no—
156C22×C151#39411yescharacteristic
157C4×C151—21no—
158C4×C151—21no—
159C4×C151—21no—
160C4×C151—81no—
161C4×C151#45311yescharacteristic
162C4×C151#45511yescharacteristic
163C4×C151#47111yescharacteristic
164C4×C151#47211yescharacteristic
165C4×C151#47212yes—
166C2×C151—41no—
167C2×C151—161no—
168C2×C151—162no—
169C2×C151#203711yescharacteristic
170C2×C151#204511yescharacteristic
171C2×C151#205111yescharacteristic
172#10488C15111yesmaximal, characteristic, direct product factor, Sylow
173C151#1048811yescharacteristic, direct product factor, Sylow
174#3205C2×C15111yescharacteristic
175#1965C2×C15111yescharacteristic, complemented
176#1574C2×C15111yescharacteristic, complemented
177#1560C2×C15111yescharacteristic, complemented
178#1545C2×C15111yescharacteristic, complemented
179#1484C2×C15111yescharacteristic, complemented
180#1299C2×C15111yescharacteristic, complemented
181#532C22×C15111yescharacteristic
182C2×#127C22×C15111yescharacteristic
183#493—21no—
184#486—21no—
185#459—21no—
186#459—21no—
187#447—22no—
188#431C22×C15111yescharacteristic
189#431C22×C15111yescharacteristic
190#423C22×C15111yescharacteristic
191#423C22×C15111yescharacteristic
192C2×#100—22no—
193C4×M16C22×C15111yescharacteristic
194#335—21no—
195#334—21no—
196#333—21no—
197#331—21no—
198#331—22no—
199D4⋊C8—22no—
200C2×#41—21no—
201C22×D4—21no—
202C22×D4—21no—
203C22×D4D4×C15112yes—
204C2×D8—22no—
205C2×D8—22no—
206C2×M16—21no—
207C2×M16—21no—
208C2×M16—21no—
209C4⋊Q8D4×C15111yescharacteristic
210#127—21no—
211#127—21no—
212#127—21no—
213#127—21no—
214#127D4×C15111yescharacteristic
215#124—21no—
216#121—21no—
217#121—21no—
218C4×D4—21no—
219C4×D4—21no—
220C2×C42C23×C15111yescharacteristic
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8D4×C15112yes—
226C4⋊C8D4×C15111yescharacteristic
227C4⋊C8D4×C15111yescharacteristic
228#102—22no—
229#102—22no—
230#100—44no—
231C22⋊C8—21no—
232C22⋊C8—21no—
233#97—21no—
234C4×C8—21no—
235C4×C8—21no—
236C4×C8—21no—
237C24—22no—
238#41—82no—
239C2×Q8—21no—
240C2×D4—22no—
241C2×D4—21no—
242C2×D4—21no—
243C2×D4—22no—
244C2×D4—21no—
245C2×D4—42no—
246C2×D4—42no—
247C2×D4—41no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4—41no—
251C2×D4—41no—
252C2×D4—81no—
253C2×D4—81no—
254C2×D4—82no—
255C22×C4—41no—
256C22×C4C2×D4×C15111yescharacteristic
257C22×C4#41×C15111yescharacteristic
258C22×C4#41×C15111yescharacteristic
259D8—82no—
260D8—82no—
261M16—22no—
262M16—41no—
263M16—42no—
264M16—81no—
265C2×C8—21no—
266C2×C8—21no—
267C2×C8—22no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8—41no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C42C2×D4×C15111yescharacteristic
276C42C2×D4×C15111yescharacteristic
277C42C2×D4×C15111yescharacteristic
278C42#41×C15111yescharacteristic
279C23—44no—
280C23—41no—
281C23—42no—
282C23—82no—
283C23—82no—
284C23#123×C15111yescharacteristic
285Q8—81no—
286D4—41no—
287D4—42no—
288D4—41no—
289D4—42no—
290D4—41no—
291D4—41no—
292D4—82no—
293D4—81no—
294D4—82no—
295D4—82no—
296D4—82no—
297D4—81no—
298D4—82no—
299D4—81no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—22no—
305C2×C4—41no—
306C2×C4—82no—
307C2×C4#120×C15111yescharacteristic
308C2×C4#121×C15111yescharacteristic
309C2×C4#121×C15111yescharacteristic
310C2×C4#121×C15111yescharacteristic
311C2×C4#123×C15111yescharacteristic
312C2×C4#124×C15111yescharacteristic
313C8—42no—
314C8—41no—
315C8—41no—
316C8—42no—
317C8—81no—
318C8—81no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—82no—
323C22—81no—
324C22—81no—
325C22—82no—
326C22—81no—
327C22—82no—
328C22—164no—
329C22#394×C15111yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—81no—
334C4#453×C15111yescharacteristic
335C4#455×C15111yescharacteristic
336C4#471×C15111yescharacteristic
337C4#472×C15112yes—
338C4#472×C15111yescharacteristic
339C2—41no—
340C2—162no—
341C2—161no—
342C2#2037×C15111yescharacteristic
343C2#2045×C15111yescharacteristic
344C2#2051×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#394
commutator, Frattini, cosocleC2×C42C23×C151
prime radical#3205×C151C2
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
2. #1965×C151C2semidirect
3. #1574×C151C2semidirect
4. #1560×C151C2semidirect
5. #1545×C151C2semidirect
6. #1484×C151C2semidirect
7. #1299×C151C2semidirect
172. #10488C151direct (N × H)
173. C151#10488direct (N × H)
175. #1965C2×C151semidirect
176. #1574C2×C151semidirect
177. #1560C2×C151semidirect
178. #1545C2×C151semidirect
179. #1484C2×C151semidirect
180. #1299C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3205×C1512
#1965×C1512
#1574×C1512
#1560×C1512
#1545×C1512
#1484×C1512
#1299×C1512
#10488151