Finite Group Databasebeta

← C151×#13230 #50318155

Subgroups — C151×#13230 #50318155

Order 38656.

436 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3059×C151C211yesmaximal, characteristic
2#2129×C151C212yesmaximal
3#2123×C151C212yesmaximal
4#1812×C151C211yesmaximal, characteristic
5#1757×C151C211yesmaximal, characteristic
6C22×Q16×C151C411yescharacteristic, complemented
7C2×#131×C151C2211yescharacteristic
8#536×C151C2212yes—
9#470×C151—21no—
10#470×C151—21no—
11#467×C151—21no—
12#467×C151—21no—
13#427×C151—21no—
14#427×C151C411yescharacteristic, complemented
15#419×C151C412yescomplemented
16#413×C151C2211yescharacteristic
17#410×C151C2212yes—
18#410×C151C2211yescharacteristic
19#405×C151—21no—
20#354×C151—24no—
21#352×C151—24no—
22#344×C151—21no—
23H(3,ℤ/4)×C151—21no—
24C2×#41×C151C2311yescharacteristic
25C22×Q8×C151C2×C412yes—
26C2×Q16×C151—21no—
27C2×Q16×C151—21no—
28C2×Q16×C151—41no—
29C2×Q16×C151—41no—
30#131×C151—41no—
31#131×C151—41no—
32C2×M16×C151—21no—
33C2×M16×C151C2×C411yescharacteristic
34C2×M16×C151D411yescharacteristic
35C2×M16×C151D411yescharacteristic
36C22×C8×C151C2×C411yescharacteristic
37C22×C8×C151D411yescharacteristic
38C22×C8×C151D411yescharacteristic
39C4⋊Q8×C151—22no—
40#124×C151—22no—
41#123×C151—22no—
42#123×C151—22no—
43C22⋊Q8×C151—22no—
44C22⋊Q8×C151—22no—
45#117×C151—21no—
46#117×C151—22no—
47#117×C151C2×C412yes—
48#107×C151—21no—
49#107×C151—41no—
50#106×C151—21no—
51#106×C151—41no—
52#103×C151—22no—
53#103×C151—22no—
54#101×C151—21no—
55#100×C151D412yes—
56#99×C151—21no—
57#99×C151—22no—
58#99×C151—22no—
59#99×C151D412yes—
60#97×C151—41no—
61C4×C8×C151—41no—
62#41×C151—41no—
63#41×C151—41no—
64C2×Q8×C151—22no—
65C2×Q8×C151—22no—
66C2×Q8×C151—42no—
67C2×Q8×C151—42no—
68C2×Q8×C151#4111yescharacteristic
69C2×D4×C151C2×D411yescharacteristic
70C2×D4×C151C2×D411yescharacteristic
71C2×D4×C151#4111yescharacteristic
72C22×C4×C151—22no—
73C22×C4×C151C22×C411yescharacteristic
74C22×C4×C151C2×D411yescharacteristic
75C22×C4×C151C2×D411yescharacteristic
76Q16×C151—42no—
77Q16×C151—41no—
78Q16×C151—41no—
79M16×C151—22no—
80M16×C151—41no—
81M16×C151—41no—
82M16×C151—41no—
83M16×C151—41no—
84C2×C8×C151—21no—
85C2×C8×C151—21no—
86C2×C8×C151—21no—
87C2×C8×C151—21no—
88C2×C8×C151—21no—
89C2×C8×C151—21no—
90C2×C8×C151—41no—
91C2×C8×C151C22⋊C411yescharacteristic
92C2×C8×C151C22⋊C411yescharacteristic
93C2×C8×C151C22⋊C411yescharacteristic
94C2×C8×C151C22⋊C411yescharacteristic
95C4⋊C4×C151—22no—
96C4⋊C4×C151—41no—
97C4⋊C4×C151—42no—
98C4⋊C4×C151—42no—
99C4⋊C4×C151—42no—
100C22⋊C4×C151—22no—
101C22⋊C4×C151—22no—
102C22⋊C4×C151—42no—
103C22⋊C4×C151—42no—
104C22⋊C4×C151—42no—
105C42×C151—22no—
106C42×C151—41no—
107C42×C151—42no—
108C23×C151C4×D411yescharacteristic
109C23×C151#12111yescharacteristic
110C23×C151#12711yescharacteristic
111Q8×C151—41no—
112Q8×C151—42no—
113Q8×C151—42no—
114Q8×C151—82no—
115D4×C151—41no—
116D4×C151—41no—
117D4×C151—41no—
118C2×C4×C151—21no—
119C2×C4×C151—21no—
120C2×C4×C151—21no—
121C2×C4×C151—21no—
122C2×C4×C151—21no—
123C2×C4×C151—21no—
124C2×C4×C151—42no—
125C2×C4×C151—42no—
126C2×C4×C151—42no—
127C2×C4×C151—82no—
128C2×C4×C151—82no—
129C2×C4×C151C2×C22⋊C411yescharacteristic
130C2×C4×C151C4×D411yescharacteristic
131C2×C4×C151#12111yescharacteristic
132C2×C4×C151#12411yescharacteristic
133C8×C151—21no—
134C8×C151—21no—
135C8×C151—21no—
136C8×C151—42no—
137C8×C151#9911yescharacteristic
138C8×C151#9911yescharacteristic
139C22×C151—21no—
140C22×C151—21no—
141C22×C151—21no—
142C22×C151—41no—
143C22×C151—41no—
144C22×C151—41no—
145C22×C151#39011yescharacteristic
146C4×C151—21no—
147C4×C151—21no—
148C4×C151—21no—
149C4×C151—82no—
150C4×C151—82no—
151C4×C151—82no—
152C4×C151—162no—
153C4×C151C2×#9911yescharacteristic
154C4×C151#41011yescharacteristic
155C2×C151—21no—
156C2×C151—41no—
157C2×C151—41no—
158C2×C151—41no—
159C2×C151#196411yescharacteristic
160#13230C15111yesmaximal, characteristic, direct product factor, Sylow
161C151#1323011yescharacteristic, direct product factor, Sylow
162#3059C2×C15111yescharacteristic
163#2129C2×C15112yes—
164#2123C2×C15112yes—
165#1812C2×C15111yescharacteristic
166#1757C2×C15111yescharacteristic
167C22×Q16C4×C15111yescharacteristic, complemented
168C2×#131C22×C15111yescharacteristic
169#536C22×C15112yes—
170#470—21no—
171#470—21no—
172#467—21no—
173#467—21no—
174#427—21no—
175#427C4×C15111yescharacteristic, complemented
176#419C4×C15112yescomplemented
177#413C22×C15111yescharacteristic
178#410C22×C15112yes—
179#410C22×C15111yescharacteristic
180#405—21no—
181#354—24no—
182#352—24no—
183#344—21no—
184H(3,ℤ/4)—21no—
185C2×#41C23×C15111yescharacteristic
186C22×Q8C2×C4×C15112yes—
187C2×Q16—21no—
188C2×Q16—21no—
189C2×Q16—41no—
190C2×Q16—41no—
191#131—41no—
192#131—41no—
193C2×M16—21no—
194C2×M16C2×C4×C15111yescharacteristic
195C2×M16D4×C15111yescharacteristic
196C2×M16D4×C15111yescharacteristic
197C22×C8C2×C4×C15111yescharacteristic
198C22×C8D4×C15111yescharacteristic
199C22×C8D4×C15111yescharacteristic
200C4⋊Q8—22no—
201#124—22no—
202#123—22no—
203#123—22no—
204C22⋊Q8—22no—
205C22⋊Q8—22no—
206#117—21no—
207#117—22no—
208#117C2×C4×C15112yes—
209#107—21no—
210#107—41no—
211#106—21no—
212#106—41no—
213#103—22no—
214#103—22no—
215#101—21no—
216#100D4×C15112yes—
217#99—21no—
218#99—22no—
219#99—22no—
220#99D4×C15112yes—
221#97—41no—
222C4×C8—41no—
223#41—41no—
224#41—41no—
225C2×Q8—22no—
226C2×Q8—22no—
227C2×Q8—42no—
228C2×Q8—42no—
229C2×Q8#41×C15111yescharacteristic
230C2×D4C2×D4×C15111yescharacteristic
231C2×D4C2×D4×C15111yescharacteristic
232C2×D4#41×C15111yescharacteristic
233C22×C4—22no—
234C22×C4C22×C4×C15111yescharacteristic
235C22×C4C2×D4×C15111yescharacteristic
236C22×C4C2×D4×C15111yescharacteristic
237Q16—42no—
238Q16—41no—
239Q16—41no—
240M16—22no—
241M16—41no—
242M16—41no—
243M16—41no—
244M16—41no—
245C2×C8—21no—
246C2×C8—21no—
247C2×C8—21no—
248C2×C8—21no—
249C2×C8—21no—
250C2×C8—21no—
251C2×C8—41no—
252C2×C8C22⋊C4×C15111yescharacteristic
253C2×C8C22⋊C4×C15111yescharacteristic
254C2×C8C22⋊C4×C15111yescharacteristic
255C2×C8C22⋊C4×C15111yescharacteristic
256C4⋊C4—22no—
257C4⋊C4—41no—
258C4⋊C4—42no—
259C4⋊C4—42no—
260C4⋊C4—42no—
261C22⋊C4—22no—
262C22⋊C4—22no—
263C22⋊C4—42no—
264C22⋊C4—42no—
265C22⋊C4—42no—
266C42—22no—
267C42—41no—
268C42—42no—
269C23C4×D4×C15111yescharacteristic
270C23#121×C15111yescharacteristic
271C23#127×C15111yescharacteristic
272Q8—41no—
273Q8—42no—
274Q8—42no—
275Q8—82no—
276D4—41no—
277D4—41no—
278D4—41no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—82no—
289C2×C4—82no—
290C2×C4C2×C22⋊C4×C15111yescharacteristic
291C2×C4C4×D4×C15111yescharacteristic
292C2×C4#121×C15111yescharacteristic
293C2×C4#124×C15111yescharacteristic
294C8—21no—
295C8—21no—
296C8—21no—
297C8—42no—
298C8#99×C15111yescharacteristic
299C8#99×C15111yescharacteristic
300C22—21no—
301C22—21no—
302C22—21no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22#390×C15111yescharacteristic
307C4—21no—
308C4—21no—
309C4—21no—
310C4—82no—
311C4—82no—
312C4—82no—
313C4—162no—
314C4C2×#99×C15111yescharacteristic
315C4#410×C15111yescharacteristic
316C2—21no—
317C2—41no—
318C2—41no—
319C2—41no—
320C2#1964×C15111yescharacteristic
subgroupG/H
center, socleC2×C151#1964
commutatorC22×C4C22×C4×C151
Frattini, cosocleC2×#41C23×C151
prime radicalC2×#41×C151C23
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C151 ◁ C2×C4×C151 ◁ C2×#131×C151 ◁ G

Complements

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

NH ≅ G/Ntype
6. C22×Q16×C151C4semidirect
14. #427×C151C4semidirect
15. #419×C151C4semidirect
160. #13230C151direct (N × H)
161. C151#13230direct (N × H)
167. C22×Q16C4×C151semidirect
175. #427C4×C151semidirect
176. #419C4×C151semidirect

Maximal subgroups

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

subgroupindex
#3059×C1512
#2129×C1512
#2123×C1512
#1812×C1512
#1757×C1512
#13230151