Finite Group Databasebeta

← C151×#7818 #50312743

Subgroups — C151×#7818 #50312743

Order 38656.

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

normal subgroups only

This group has 350 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#2805×C151C211yesmaximal, characteristic
2#2099×C151C211yesmaximal, characteristic
3#2084×C151C211yesmaximal, characteristic
4#2072×C151C211yesmaximal, characteristic
5#1272×C151C211yesmaximal, characteristic
6#1271×C151C211yesmaximal, characteristic
7#1271×C151C211yesmaximal, characteristic
8C2×#106×C151—21no—
9C2×#103×C151—21no—
10#400×C151—21no—
11#400×C151—21no—
12#395×C151—21no—
13#391×C151C2211yescharacteristic
14#389×C151—21no—
15#389×C151C2211yescharacteristic
16#389×C151C2211yescharacteristic
17#387×C151—21no—
18#387×C151—21no—
19#384×C151C2211yescharacteristic
20#340×C151—21no—
21#340×C151—21no—
22#340×C151—21no—
23#340×C151—21no—
24#336×C151C2211yescharacteristic
25#336×C151C2211yescharacteristic
26#336×C151C2211yescharacteristic
27C22×Q8×C151D411yescharacteristic
28C22×C8×C151—21no—
29C22×C8×C151—21no—
30C22×C8×C151—21no—
31C2×C4⋊C4×C151—21no—
32C2×C4⋊C4×C151—21no—
33C2×C4⋊C4×C151—21no—
34C2×C4⋊C4×C151—21no—
35C2×C4⋊C4×C151—21no—
36C2×C4⋊C4×C151—21no—
37C2×C4⋊C4×C151—21no—
38C2×C4⋊C4×C151D411yescharacteristic
39C2×C4⋊C4×C151D411yescharacteristic
40C2×C4⋊C4×C151D411yescharacteristic
41C2×C4⋊C4×C151D411yescharacteristic
42C2×C4⋊C4×C151D411yescharacteristic
43C2×C42×C151—21no—
44C2×C42×C151C2311yescharacteristic
45#106×C151—42no—
46#103×C151—42no—
47#95×C151—21no—
48#95×C151—21no—
49#95×C151—21no—
50#95×C151—21no—
51#95×C151—21no—
52#95×C151—21no—
53#95×C151—21no—
54#95×C151—21no—
55#95×C151—21no—
56C2×Q8×C151—21no—
57C2×Q8×C151—21no—
58C2×Q8×C151—41no—
59C2×Q8×C151—41no—
60C22×C4×C151—21no—
61C22×C4×C151—21no—
62C22×C4×C151—21no—
63C22×C4×C151—21no—
64C22×C4×C151—21no—
65C22×C4×C151—21no—
66C22×C4×C151—41no—
67C22×C4×C151C2×D411yescharacteristic
68C22×C4×C151C2×D411yescharacteristic
69C22×C4×C151C2×D411yescharacteristic
70C2×C8×C151—22no—
71C2×C8×C151—41no—
72C2×C8×C151—41no—
73C2×C8×C151—41no—
74C2×C8×C151—41no—
75C2×C8×C151—41no—
76C2×C8×C151—41no—
77C2×C8×C151—41no—
78C2×C8×C151—41no—
79C4⋊C4×C151—21no—
80C4⋊C4×C151—21no—
81C4⋊C4×C151—21no—
82C4⋊C4×C151—41no—
83C4⋊C4×C151—41no—
84C4⋊C4×C151—41no—
85C4⋊C4×C151—42no—
86C4⋊C4×C151—41no—
87C4⋊C4×C151—41no—
88C4⋊C4×C151—41no—
89C4⋊C4×C151—41no—
90C4⋊C4×C151—41no—
91C4⋊C4×C151—41no—
92C4⋊C4×C151—41no—
93C4⋊C4×C151—41no—
94C4⋊C4×C151—81no—
95C4⋊C4×C151—81no—
96C4⋊C4×C151SD1612yes—
97C42×C151—41no—
98C42×C151—81no—
99C23×C151#12011yescharacteristic
100Q8×C151—42no—
101Q8×C151—81no—
102C2×C4×C151—21no—
103C2×C4×C151—21no—
104C2×C4×C151—21no—
105C2×C4×C151—21no—
106C2×C4×C151—21no—
107C2×C4×C151—21no—
108C2×C4×C151—22no—
109C2×C4×C151—41no—
110C2×C4×C151—41no—
111C2×C4×C151—41no—
112C2×C4×C151—41no—
113C2×C4×C151—41no—
114C2×C4×C151—41no—
115C2×C4×C151—41no—
116C2×C4×C151—41no—
117C2×C4×C151—41no—
118C2×C4×C151—41no—
119C2×C4×C151—41no—
120C2×C4×C151—41no—
121C2×C4×C151—41no—
122C2×C4×C151—41no—
123C2×C4×C151—41no—
124C2×C4×C151—41no—
125C2×C4×C151—41no—
126C2×C4×C151—81no—
127C2×C4×C151—81no—
128C2×C4×C151—81no—
129C2×C4×C151C2×SD1611yescharacteristic
130C2×C4×C151#13511yescharacteristic
131C2×C4×C151#13511yescharacteristic
132C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C151#13711yescharacteristic
134C2×C4×C151#13711yescharacteristic
135C8×C151—42no—
136C8×C151—81no—
137C8×C151—81no—
138C22×C151#44811yescharacteristic
139C22×C151#44911yescharacteristic
140C22×C151#45211yescharacteristic
141C22×C151#45411yescharacteristic
142C22×C151#45511yescharacteristic
143C22×C151#45611yescharacteristic
144C22×C151#45811yescharacteristic
145C4×C151—21no—
146C4×C151—21no—
147C4×C151—21no—
148C4×C151—21no—
149C4×C151—21no—
150C4×C151—21no—
151C4×C151—42no—
152C4×C151—81no—
153C4×C151—81no—
154C4×C151—81no—
155C4×C151—81no—
156C4×C151—81no—
157C4×C151—161no—
158C2×C151#161111yescharacteristic
159C2×C151#161211yescharacteristic
160C2×C151#161511yescharacteristic
161C2×C151#162611yescharacteristic
162C2×C151#164311yescharacteristic
163C2×C151#165211yescharacteristic
164C2×C151#166411yescharacteristic
165#7818C15111yesmaximal, characteristic, direct product factor, Sylow
166C151#781811yescharacteristic, direct product factor, Sylow
167#2805C2×C15111yescharacteristic
168#2099C2×C15111yescharacteristic
169#2084C2×C15111yescharacteristic
170#2072C2×C15111yescharacteristic
171#1272C2×C15111yescharacteristic
172#1271C2×C15111yescharacteristic
173#1271C2×C15111yescharacteristic
174C2×#106—21no—
175C2×#103—21no—
176#400—21no—
177#400—21no—
178#395—21no—
179#391C22×C15111yescharacteristic
180#389—21no—
181#389C22×C15111yescharacteristic
182#389C22×C15111yescharacteristic
183#387—21no—
184#387—21no—
185#384C22×C15111yescharacteristic
186#340—21no—
187#340—21no—
188#340—21no—
189#340—21no—
190#336C22×C15111yescharacteristic
191#336C22×C15111yescharacteristic
192#336C22×C15111yescharacteristic
193C22×Q8D4×C15111yescharacteristic
194C22×C8—21no—
195C22×C8—21no—
196C22×C8—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4D4×C15111yescharacteristic
205C2×C4⋊C4D4×C15111yescharacteristic
206C2×C4⋊C4D4×C15111yescharacteristic
207C2×C4⋊C4D4×C15111yescharacteristic
208C2×C4⋊C4D4×C15111yescharacteristic
209C2×C42—21no—
210C2×C42C23×C15111yescharacteristic
211#106—42no—
212#103—42no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95—21no—
222C2×Q8—21no—
223C2×Q8—21no—
224C2×Q8—41no—
225C2×Q8—41no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—41no—
233C22×C4C2×D4×C15111yescharacteristic
234C22×C4C2×D4×C15111yescharacteristic
235C22×C4C2×D4×C15111yescharacteristic
236C2×C8—22no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—42no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—81no—
261C4⋊C4—81no—
262C4⋊C4SD16×C15112yes—
263C42—41no—
264C42—81no—
265C23#120×C15111yescharacteristic
266Q8—42no—
267Q8—81no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—22no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4C2×SD16×C15111yescharacteristic
296C2×C4#135×C15111yescharacteristic
297C2×C4#135×C15111yescharacteristic
298C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
299C2×C4#137×C15111yescharacteristic
300C2×C4#137×C15111yescharacteristic
301C8—42no—
302C8—81no—
303C8—81no—
304C22#448×C15111yescharacteristic
305C22#449×C15111yescharacteristic
306C22#452×C15111yescharacteristic
307C22#454×C15111yescharacteristic
308C22#455×C15111yescharacteristic
309C22#456×C15111yescharacteristic
310C22#458×C15111yescharacteristic
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—42no—
318C4—81no—
319C4—81no—
320C4—81no—
321C4—81no—
322C4—81no—
323C4—161no—
324C2#1611×C15111yescharacteristic
325C2#1612×C15111yescharacteristic
326C2#1615×C15111yescharacteristic
327C2#1626×C15111yescharacteristic
328C2#1643×C15111yescharacteristic
329C2#1652×C15111yescharacteristic
330C2#1664×C15111yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C151#120
commutator, Frattini, cosocleC2×C42C23×C151
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
165. #7818C151direct (N × H)
166. C151#7818direct (N × H)

Maximal subgroups

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

subgroupindex
#2805×C1512
#2099×C1512
#2084×C1512
#2072×C1512
#1272×C1512
#1271×C1512
#7818151