Finite Group Databasebeta

← C151×#9188 #50314113

Subgroups — C151×#9188 #50314113

Order 38656.

478 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 122 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#2983×C151C211yesmaximal, characteristic, complemented
2#2632×C151C211yesmaximal, characteristic
3C4×#101×C151C211yesmaximal, characteristic, complemented
4#1527×C151C212yesmaximal
5#1288×C151C212yesmaximal, complemented
6C2×#124×C151C2211yescharacteristic
7C2×C4×Q8×C151C2211yescharacteristic
8#446×C151—24no—
9#432×C151—21no—
10#432×C151C2212yes—
11#431×C151—21no—
12C2×#101×C151—21no—
13C4×M16×C151C2212yes—
14#399×C151—21no—
15#395×C151C411yescharacteristic
16#395×C151C411yescharacteristic
17#394×C151C411yescharacteristic
18#394×C151C411yescharacteristic
19#393×C151—21no—
20#388×C151—21no—
21#388×C151—21no—
22#383×C151C2211yescharacteristic
23#343×C151—21no—
24#329×C151—24no—
25C22×Q8×C151C2×C411yescharacteristic
26C22×Q8×C151D411yescharacteristic
27C22×D4×C151C2×C411yescharacteristic
28C2×M16×C151—22no—
29#124×C151—22no—
30#124×C151—22no—
31C4×Q8×C151—22no—
32C4×Q8×C151—22no—
33C2×C4⋊C4×C151—21no—
34C2×C4⋊C4×C151—21no—
35C2×C4⋊C4×C151C2×C411yescharacteristic
36C2×C4⋊C4×C151C2×C411yescharacteristic
37C2×C4⋊C4×C151D411yescharacteristic
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×C151—21no—
44C2×C42×C151D411yescharacteristic
45C2×C42×C151D411yescharacteristic
46C2×C42×C151C2311yescharacteristic
47C4⋊C8×C151—22no—
48C4⋊C8×C151—22no—
49C4⋊C8×C151—22no—
50#101×C151—24no—
51C22⋊C8×C151—22no—
52#97×C151—22no—
53#97×C151—22no—
54#97×C151D414yes—
55C4×C8×C151—22no—
56C4×C8×C151—22no—
57#95×C151—21no—
58#95×C151—21no—
59#95×C151—21no—
60#95×C151—21no—
61#95×C151C2×C411yescharacteristic
62#95×C151C2×C411yescharacteristic
63C24×C151—21no—
64C2×Q8×C151—22no—
65C2×Q8×C151—22no—
66C2×Q8×C151—22no—
67C2×Q8×C151—41no—
68C2×Q8×C151—81no—
69C2×D4×C151—22no—
70C2×D4×C151—81no—
71C22×C4×C151—21no—
72C22×C4×C151—21no—
73C22×C4×C151—21no—
74C22×C4×C151C22⋊C411yescharacteristic
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—24no—
82M16×C151—42no—
83C2×C8×C151—24no—
84C2×C8×C151—42no—
85C4⋊C4×C151—22no—
86C4⋊C4×C151—22no—
87C4⋊C4×C151—22no—
88C4⋊C4×C151—81no—
89C4⋊C4×C151—81no—
90C22⋊C4×C151—42no—
91C22⋊C4×C151—42no—
92C22⋊C4×C151—41no—
93C22⋊C4×C151—42no—
94C22⋊C4×C151—41no—
95C22⋊C4×C151—81no—
96C22⋊C4×C151—81no—
97C42×C151—21no—
98C42×C151—21no—
99C42×C151—21no—
100C42×C151—21no—
101C42×C151C2×D412yes—
102C42×C151#4112yes—
103C23×C151—41no—
104C23×C151—41no—
105C23×C151—41no—
106C23×C151—41no—
107C23×C151—41no—
108C23×C151—41no—
109C23×C151—41no—
110C23×C151C2×C22⋊C411yescharacteristic
111Q8×C151—44no—
112Q8×C151—82no—
113D4×C151—82no—
114C2×C4×C151—21no—
115C2×C4×C151—21no—
116C2×C4×C151—21no—
117C2×C4×C151—21no—
118C2×C4×C151—21no—
119C2×C4×C151—21no—
120C2×C4×C151—21no—
121C2×C4×C151—21no—
122C2×C4×C151—21no—
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—41no—
134C2×C4×C151—41no—
135C2×C4×C151—41no—
136C2×C4×C151#10412yes—
137C2×C4×C151C4×D412yes—
138C2×C4×C151#12011yescharacteristic
139C2×C4×C151#12112yes—
140C2×C4×C151#12311yescharacteristic
141C8×C151—44no—
142C8×C151—44no—
143C22×C151—21no—
144C22×C151—21no—
145C22×C151—81no—
146C22×C151—81no—
147C22×C151—81no—
148C22×C151—81no—
149C22×C151—81no—
150C22×C151—81no—
151C22×C151—81no—
152C22×C151#38611yescharacteristic
153C22×C151C2×#10411yescharacteristic
154C22×C151#42111yescharacteristic
155C4×C151—22no—
156C4×C151—22no—
157C4×C151—21no—
158C4×C151—21no—
159C4×C151—22no—
160C4×C151—41no—
161C4×C151—41no—
162C4×C151—41no—
163C4×C151—81no—
164C4×C151—81no—
165C4×C151—81no—
166C2×C151—21no—
167C2×C151—21no—
168C2×C151—161no—
169C2×C151#187111yescharacteristic
170C2×C151#191211yescharacteristic
171C2×C151#191411yescharacteristic
172#9188C15111yesmaximal, characteristic, direct product factor, Sylow
173C151#918811yescharacteristic, direct product factor, Sylow
174#2983C2×C15111yescharacteristic, complemented
175#2632C2×C15111yescharacteristic
176C4×#101C2×C15111yescharacteristic, complemented
177#1527C2×C15112yes—
178#1288C2×C15112yescomplemented
179C2×#124C22×C15111yescharacteristic
180C2×C4×Q8C22×C15111yescharacteristic
181#446—24no—
182#432—21no—
183#432C22×C15112yes—
184#431—21no—
185C2×#101—21no—
186C4×M16C22×C15112yes—
187#399—21no—
188#395C4×C15111yescharacteristic
189#395C4×C15111yescharacteristic
190#394C4×C15111yescharacteristic
191#394C4×C15111yescharacteristic
192#393—21no—
193#388—21no—
194#388—21no—
195#383C22×C15111yescharacteristic
196#343—21no—
197#329—24no—
198C22×Q8C2×C4×C15111yescharacteristic
199C22×Q8D4×C15111yescharacteristic
200C22×D4C2×C4×C15111yescharacteristic
201C2×M16—22no—
202#124—22no—
203#124—22no—
204C4×Q8—22no—
205C4×Q8—22no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4C2×C4×C15111yescharacteristic
209C2×C4⋊C4C2×C4×C15111yescharacteristic
210C2×C4⋊C4D4×C15111yescharacteristic
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C42D4×C15111yescharacteristic
218C2×C42D4×C15111yescharacteristic
219C2×C42C23×C15111yescharacteristic
220C4⋊C8—22no—
221C4⋊C8—22no—
222C4⋊C8—22no—
223#101—24no—
224C22⋊C8—22no—
225#97—22no—
226#97—22no—
227#97D4×C15114yes—
228C4×C8—22no—
229C4×C8—22no—
230#95—21no—
231#95—21no—
232#95—21no—
233#95—21no—
234#95C2×C4×C15111yescharacteristic
235#95C2×C4×C15111yescharacteristic
236C24—21no—
237C2×Q8—22no—
238C2×Q8—22no—
239C2×Q8—22no—
240C2×Q8—41no—
241C2×Q8—81no—
242C2×D4—22no—
243C2×D4—81no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4C22⋊C4×C15111yescharacteristic
248C22×C4C22⋊C4×C15111yescharacteristic
249C22×C4C22⋊C4×C15111yescharacteristic
250C22×C4C22⋊C4×C15111yescharacteristic
251C22×C4C22×C4×C15111yescharacteristic
252C22×C4C2×D4×C15111yescharacteristic
253C22×C4C2×D4×C15111yescharacteristic
254M16—24no—
255M16—42no—
256C2×C8—24no—
257C2×C8—42no—
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4—22no—
261C4⋊C4—81no—
262C4⋊C4—81no—
263C22⋊C4—42no—
264C22⋊C4—42no—
265C22⋊C4—41no—
266C22⋊C4—42no—
267C22⋊C4—41no—
268C22⋊C4—81no—
269C22⋊C4—81no—
270C42—21no—
271C42—21no—
272C42—21no—
273C42—21no—
274C42C2×D4×C15112yes—
275C42#41×C15112yes—
276C23—41no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23C2×C22⋊C4×C15111yescharacteristic
284Q8—44no—
285Q8—82no—
286D4—82no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
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—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4#104×C15112yes—
310C2×C4C4×D4×C15112yes—
311C2×C4#120×C15111yescharacteristic
312C2×C4#121×C15112yes—
313C2×C4#123×C15111yescharacteristic
314C8—44no—
315C8—44no—
316C22—21no—
317C22—21no—
318C22—81no—
319C22—81no—
320C22—81no—
321C22—81no—
322C22—81no—
323C22—81no—
324C22—81no—
325C22#386×C15111yescharacteristic
326C22C2×#104×C15111yescharacteristic
327C22#421×C15111yescharacteristic
328C4—22no—
329C4—22no—
330C4—21no—
331C4—21no—
332C4—22no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—81no—
337C4—81no—
338C4—81no—
339C2—21no—
340C2—21no—
341C2—161no—
342C2#1871×C15111yescharacteristic
343C2#1912×C15111yescharacteristic
344C2#1914×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#386
commutatorC22×C4C22×C4×C151
Frattini, cosocleC2×C42C23×C151
prime radicalC22×D4×C151C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2983×C151C2semidirect
3. C4×#101×C151C2semidirect
5. #1288×C151C2semidirect
172. #9188C151direct (N × H)
173. C151#9188direct (N × H)
174. #2983C2×C151semidirect
176. C4×#101C2×C151semidirect
178. #1288C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2983×C1512
#2632×C1512
C4×#101×C1512
#1527×C1512
#1288×C1512
#9188151