Finite Group Databasebeta

← C151×#7814 #50312739

Subgroups — C151×#7814 #50312739

Order 38656.

378 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 102 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#2806×C151C211yesmaximal, characteristic
2#2096×C151C211yesmaximal, characteristic
3#2084×C151C211yesmaximal, characteristic
4#2072×C151C211yesmaximal, characteristic
5#1272×C151C211yesmaximal, characteristic
6#1272×C151C211yesmaximal, characteristic
7#1271×C151C211yesmaximal, characteristic
8C2×#106×C151—21no—
9C2×#106×C151—21no—
10C2×#103×C151—21no—
11C2×#103×C151—21no—
12#398×C151—21no—
13#398×C151—21no—
14#395×C151—21no—
15#391×C151—21no—
16#391×C151C2211yescharacteristic
17#391×C151C2211yescharacteristic
18#389×C151—21no—
19#389×C151C2211yescharacteristic
20#387×C151—21no—
21#384×C151C2211yescharacteristic
22#340×C151—21no—
23#340×C151—21no—
24#336×C151C2211yescharacteristic
25#336×C151C2211yescharacteristic
26#336×C151C2211yescharacteristic
27C22×Q8×C151D411yescharacteristic
28C22×Q8×C151D411yescharacteristic
29C22×C8×C151—21no—
30C22×C8×C151—21no—
31C22×C8×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×C151—21no—
39C2×C4⋊C4×C151—21no—
40C2×C4⋊C4×C151D411yescharacteristic
41C2×C4⋊C4×C151D411yescharacteristic
42C2×C4⋊C4×C151D411yescharacteristic
43C2×C4⋊C4×C151D411yescharacteristic
44C2×C42×C151—21no—
45C2×C42×C151C2311yescharacteristic
46#106×C151—42no—
47#106×C151—42no—
48#103×C151—42no—
49#103×C151—42no—
50#95×C151—21no—
51#95×C151—21no—
52#95×C151—21no—
53#95×C151—21no—
54#95×C151—21no—
55#95×C151—21no—
56#95×C151—21no—
57#95×C151—21no—
58C2×Q8×C151—21no—
59C2×Q8×C151—21no—
60C2×Q8×C151—21no—
61C2×Q8×C151—41no—
62C2×Q8×C151—41no—
63C2×Q8×C151—41no—
64C2×Q8×C151—41no—
65C2×Q8×C151SD1612yes—
66C22×C4×C151—21no—
67C22×C4×C151—21no—
68C22×C4×C151—21no—
69C22×C4×C151—21no—
70C22×C4×C151—21no—
71C22×C4×C151—21no—
72C22×C4×C151—41no—
73C22×C4×C151C2×D411yescharacteristic
74C22×C4×C151C2×D411yescharacteristic
75C22×C4×C151C2×D411yescharacteristic
76C2×C8×C151—22no—
77C2×C8×C151—22no—
78C2×C8×C151—41no—
79C2×C8×C151—41no—
80C2×C8×C151—41no—
81C2×C8×C151—41no—
82C2×C8×C151—41no—
83C2×C8×C151—41no—
84C2×C8×C151—41no—
85C4⋊C4×C151—21no—
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—41no—
95C4⋊C4×C151—41no—
96C4⋊C4×C151—41no—
97C4⋊C4×C151—81no—
98C4⋊C4×C151—81no—
99C4⋊C4×C151—81no—
100C4⋊C4×C151—81no—
101C4⋊C4×C151SD1612yes—
102C42×C151—41no—
103C42×C151—81no—
104C23×C151#12011yescharacteristic
105Q8×C151—42no—
106Q8×C151—42no—
107Q8×C151—81no—
108Q8×C151—81no—
109C2×C4×C151—21no—
110C2×C4×C151—21no—
111C2×C4×C151—21no—
112C2×C4×C151—21no—
113C2×C4×C151—21no—
114C2×C4×C151—21no—
115C2×C4×C151—22no—
116C2×C4×C151—22no—
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—41no—
127C2×C4×C151—41no—
128C2×C4×C151—41no—
129C2×C4×C151—41no—
130C2×C4×C151—41no—
131C2×C4×C151—41no—
132C2×C4×C151—41no—
133C2×C4×C151—81no—
134C2×C4×C151—81no—
135C2×C4×C151—81no—
136C2×C4×C151C2×SD1611yescharacteristic
137C2×C4×C151C2×SD1611yescharacteristic
138C2×C4×C151#13511yescharacteristic
139C2×C4×C151#13711yescharacteristic
140C2×C4×C151#13711yescharacteristic
141C2×C4×C151#13711yescharacteristic
142C8×C151—42no—
143C8×C151—42no—
144C8×C151—81no—
145C22×C151#44811yescharacteristic
146C22×C151#44811yescharacteristic
147C22×C151#45211yescharacteristic
148C22×C151#45311yescharacteristic
149C22×C151#45511yescharacteristic
150C22×C151#45611yescharacteristic
151C22×C151#45811yescharacteristic
152C4×C151—21no—
153C4×C151—21no—
154C4×C151—21no—
155C4×C151—21no—
156C4×C151—21no—
157C4×C151—21no—
158C4×C151—42no—
159C4×C151—42no—
160C4×C151—81no—
161C4×C151—81no—
162C4×C151—81no—
163C4×C151—81no—
164C4×C151—161no—
165C2×C151#160811yescharacteristic
166C2×C151#161111yescharacteristic
167C2×C151#161811yescharacteristic
168C2×C151#162311yescharacteristic
169C2×C151#164311yescharacteristic
170C2×C151#165311yescharacteristic
171C2×C151#166111yescharacteristic
172#7814C15111yesmaximal, characteristic, direct product factor, Sylow
173C151#781411yescharacteristic, direct product factor, Sylow
174#2806C2×C15111yescharacteristic
175#2096C2×C15111yescharacteristic
176#2084C2×C15111yescharacteristic
177#2072C2×C15111yescharacteristic
178#1272C2×C15111yescharacteristic
179#1272C2×C15111yescharacteristic
180#1271C2×C15111yescharacteristic
181C2×#106—21no—
182C2×#106—21no—
183C2×#103—21no—
184C2×#103—21no—
185#398—21no—
186#398—21no—
187#395—21no—
188#391—21no—
189#391C22×C15111yescharacteristic
190#391C22×C15111yescharacteristic
191#389—21no—
192#389C22×C15111yescharacteristic
193#387—21no—
194#384C22×C15111yescharacteristic
195#340—21no—
196#340—21no—
197#336C22×C15111yescharacteristic
198#336C22×C15111yescharacteristic
199#336C22×C15111yescharacteristic
200C22×Q8D4×C15111yescharacteristic
201C22×Q8D4×C15111yescharacteristic
202C22×C8—21no—
203C22×C8—21no—
204C22×C8—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4D4×C15111yescharacteristic
214C2×C4⋊C4D4×C15111yescharacteristic
215C2×C4⋊C4D4×C15111yescharacteristic
216C2×C4⋊C4D4×C15111yescharacteristic
217C2×C42—21no—
218C2×C42C23×C15111yescharacteristic
219#106—42no—
220#106—42no—
221#103—42no—
222#103—42no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231C2×Q8—21no—
232C2×Q8—21no—
233C2×Q8—21no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×Q8—41no—
238C2×Q8SD16×C15112yes—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—41no—
246C22×C4C2×D4×C15111yescharacteristic
247C22×C4C2×D4×C15111yescharacteristic
248C22×C4C2×D4×C15111yescharacteristic
249C2×C8—22no—
250C2×C8—22no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—41no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8—41no—
258C4⋊C4—21no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—81no—
271C4⋊C4—81no—
272C4⋊C4—81no—
273C4⋊C4—81no—
274C4⋊C4SD16×C15112yes—
275C42—41no—
276C42—81no—
277C23#120×C15111yescharacteristic
278Q8—42no—
279Q8—42no—
280Q8—81no—
281Q8—81no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4C2×SD16×C15111yescharacteristic
310C2×C4C2×SD16×C15111yescharacteristic
311C2×C4#135×C15111yescharacteristic
312C2×C4#137×C15111yescharacteristic
313C2×C4#137×C15111yescharacteristic
314C2×C4#137×C15111yescharacteristic
315C8—42no—
316C8—42no—
317C8—81no—
318C22#448×C15111yescharacteristic
319C22#448×C15111yescharacteristic
320C22#452×C15111yescharacteristic
321C22#453×C15111yescharacteristic
322C22#455×C15111yescharacteristic
323C22#456×C15111yescharacteristic
324C22#458×C15111yescharacteristic
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—42no—
332C4—42no—
333C4—81no—
334C4—81no—
335C4—81no—
336C4—81no—
337C4—161no—
338C2#1608×C15111yescharacteristic
339C2#1611×C15111yescharacteristic
340C2#1618×C15111yescharacteristic
341C2#1623×C15111yescharacteristic
342C2#1643×C15111yescharacteristic
343C2#1653×C15111yescharacteristic
344C2#1661×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
172. #7814C151direct (N × H)
173. C151#7814direct (N × H)

Maximal subgroups

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

subgroupindex
#2806×C1512
#2096×C1512
#2084×C1512
#2072×C1512
#1272×C1512
#1271×C1512
#7814151