Finite Group Databasebeta

← #2759×C151 #34066091

Subgroups — #2759×C151 #34066091

Order 19328.

394 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#401×C151C211yesmaximal, characteristic, complemented
2#397×C151C211yesmaximal, characteristic
3#397×C151C211yesmaximal, characteristic
4#395×C151C211yesmaximal, characteristic, complemented
5#393×C151C211yesmaximal, characteristic
6#393×C151C211yesmaximal, characteristic
7#391×C151C211yesmaximal, characteristic, complemented
8#391×C151C211yesmaximal, characteristic, complemented
9#391×C151C211yesmaximal, characteristic, complemented
10#388×C151C211yesmaximal, characteristic
11#388×C151C211yesmaximal, characteristic
12#388×C151C211yesmaximal, characteristic
13#387×C151C211yesmaximal, characteristic, complemented
14#387×C151C211yesmaximal, characteristic, complemented
15#383×C151C211yesmaximal, characteristic, complemented
16C22×Q8×C151C2211yescharacteristic
17C22×Q8×C151C2211yescharacteristic
18C2×C4⋊C4×C151C2211yescharacteristic
19C2×C4⋊C4×C151C2211yescharacteristic
20C2×C4⋊C4×C151C2211yescharacteristic
21C2×C4⋊C4×C151C2211yescharacteristic
22C2×C4⋊C4×C151C2211yescharacteristic
23C2×C22⋊C4×C151C2211yescharacteristic
24C2×C22⋊C4×C151C2211yescharacteristic
25C2×C22⋊C4×C151C2211yescharacteristic
26C2×C22⋊C4×C151C2211yescharacteristic
27C2×C22⋊C4×C151C2211yescharacteristic
28C2×C22⋊C4×C151C2211yescharacteristic
29C2×C22⋊C4×C151C2211yescharacteristic
30C2×C42×C151C2211yescharacteristic
31C2×C42×C151C2211yescharacteristic
32C2×C42×C151C2211yescharacteristic
33#95×C151C2211yescharacteristic
34#95×C151C2211yescharacteristic
35#95×C151C2211yescharacteristic
36#95×C151C2211yescharacteristic
37#95×C151C2211yescharacteristic
38#95×C151C2211yescharacteristic
39#95×C151C2211yescharacteristic
40#95×C151C2211yescharacteristic
41#95×C151C2211yescharacteristic
42#95×C151C2211yescharacteristic
43#95×C151C2211yescharacteristic
44#95×C151C2211yescharacteristic
45#95×C151C2211yescharacteristic
46#95×C151C2211yescharacteristic
47#95×C151C2211yescharacteristic
48#95×C151C2211yescharacteristic
49#95×C151C2211yescharacteristic
50#95×C151C2211yescharacteristic
51C24×C151C2311yescharacteristic
52C2×Q8×C151—22no—
53C2×Q8×C151—22no—
54C2×Q8×C151—22no—
55C2×Q8×C151—41no—
56C2×Q8×C151—41no—
57C2×Q8×C151—41no—
58C22×C4×C151C2311yescharacteristic
59C22×C4×C151C2311yescharacteristic
60C22×C4×C151C2311yescharacteristic
61C22×C4×C151C2311yescharacteristic
62C22×C4×C151C2311yescharacteristic
63C22×C4×C151C2311yescharacteristic
64C22×C4×C151C2311yescharacteristic
65C22×C4×C151C2311yescharacteristic
66C22×C4×C151C2311yescharacteristic
67C22×C4×C151C2311yescharacteristic
68C22×C4×C151C2311yescharacteristic
69C22×C4×C151C2311yescharacteristic
70C22×C4×C151C2311yescharacteristic
71C22×C4×C151C2311yescharacteristic
72C4⋊C4×C151—22no—
73C4⋊C4×C151—22no—
74C4⋊C4×C151—41no—
75C4⋊C4×C151—41no—
76C4⋊C4×C151—41no—
77C22⋊C4×C151—22no—
78C22⋊C4×C151—22no—
79C22⋊C4×C151—22no—
80C22⋊C4×C151—41no—
81C22⋊C4×C151—41no—
82C22⋊C4×C151—41no—
83C22⋊C4×C151—41no—
84C42×C151—22no—
85C42×C151—41no—
86C42×C151—41no—
87C23×C151—21no—
88C23×C151—21no—
89C23×C151—21no—
90C23×C151—21no—
91C23×C151—21no—
92C23×C151—21no—
93C23×C151—21no—
94C23×C151C2411yescharacteristic
95Q8×C151—44no—
96Q8×C151—44no—
97C2×C4×C151—21no—
98C2×C4×C151—21no—
99C2×C4×C151—21no—
100C2×C4×C151—21no—
101C2×C4×C151—21no—
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—21no—
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—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—21no—
124C2×C4×C151—21no—
125C2×C4×C151—21no—
126C2×C4×C151—21no—
127C2×C4×C151—21no—
128C2×C4×C151—21no—
129C2×C4×C151—21no—
130C2×C4×C151—21no—
131C2×C4×C151—21no—
132C2×C4×C151—21no—
133C2×C4×C151—21no—
134C2×C4×C151—21no—
135C2×C4×C151—21no—
136C2×C4×C151#4112yes—
137C2×C4×C151#4112yes—
138C2×C4×C151#4112yes—
139C22×C151—41no—
140C22×C151—41no—
141C22×C151—41no—
142C22×C151—41no—
143C22×C151—41no—
144C22×C151—41no—
145C22×C151—41no—
146C22×C151C2×#4111yescharacteristic
147C22×C151C2×#4111yescharacteristic
148C22×C151C2×#4111yescharacteristic
149C22×C151H(5,𝔽2)11yescharacteristic
150C22×C151H(5,𝔽2)11yescharacteristic
151C22×C1512−1+411yescharacteristic
152C22×C1512−1+411yescharacteristic
153C4×C151—22no—
154C4×C151—22no—
155C4×C151—22no—
156C4×C151—41no—
157C4×C151—41no—
158C4×C151—41no—
159C4×C151—41no—
160C4×C151—41no—
161C4×C151—41no—
162C4×C151—41no—
163C4×C151—41no—
164C4×C151—41no—
165C4×C151—41no—
166C4×C151—41no—
167C2×C151—81no—
168C2×C151#53811yescharacteristic
169C2×C151#54211yescharacteristic
170C2×C151#54211yescharacteristic
171C2×C151#55111yescharacteristic
172C2×C151#55611yescharacteristic
173C2×C151#55611yescharacteristic
174C2×C151#56311yescharacteristic
175C151#275911yescharacteristic, direct product factor, Sylow
176#2759C15111yesmaximal, characteristic, direct product factor, Sylow
177#401C2×C15111yescharacteristic, complemented
178#397C2×C15111yescharacteristic
179#397C2×C15111yescharacteristic
180#395C2×C15111yescharacteristic, complemented
181#393C2×C15111yescharacteristic
182#393C2×C15111yescharacteristic
183#391C2×C15111yescharacteristic, complemented
184#391C2×C15111yescharacteristic, complemented
185#391C2×C15111yescharacteristic, complemented
186#388C2×C15111yescharacteristic
187#388C2×C15111yescharacteristic
188#388C2×C15111yescharacteristic
189#387C2×C15111yescharacteristic, complemented
190#387C2×C15111yescharacteristic, complemented
191#383C2×C15111yescharacteristic, complemented
192C22×Q8C22×C15111yescharacteristic
193C22×Q8C22×C15111yescharacteristic
194C2×C4⋊C4C22×C15111yescharacteristic
195C2×C4⋊C4C22×C15111yescharacteristic
196C2×C4⋊C4C22×C15111yescharacteristic
197C2×C4⋊C4C22×C15111yescharacteristic
198C2×C4⋊C4C22×C15111yescharacteristic
199C2×C22⋊C4C22×C15111yescharacteristic
200C2×C22⋊C4C22×C15111yescharacteristic
201C2×C22⋊C4C22×C15111yescharacteristic
202C2×C22⋊C4C22×C15111yescharacteristic
203C2×C22⋊C4C22×C15111yescharacteristic
204C2×C22⋊C4C22×C15111yescharacteristic
205C2×C22⋊C4C22×C15111yescharacteristic
206C2×C42C22×C15111yescharacteristic
207C2×C42C22×C15111yescharacteristic
208C2×C42C22×C15111yescharacteristic
209#95C22×C15111yescharacteristic
210#95C22×C15111yescharacteristic
211#95C22×C15111yescharacteristic
212#95C22×C15111yescharacteristic
213#95C22×C15111yescharacteristic
214#95C22×C15111yescharacteristic
215#95C22×C15111yescharacteristic
216#95C22×C15111yescharacteristic
217#95C22×C15111yescharacteristic
218#95C22×C15111yescharacteristic
219#95C22×C15111yescharacteristic
220#95C22×C15111yescharacteristic
221#95C22×C15111yescharacteristic
222#95C22×C15111yescharacteristic
223#95C22×C15111yescharacteristic
224#95C22×C15111yescharacteristic
225#95C22×C15111yescharacteristic
226#95C22×C15111yescharacteristic
227C24C23×C15111yescharacteristic
228C2×Q8—22no—
229C2×Q8—22no—
230C2×Q8—22no—
231C2×Q8—41no—
232C2×Q8—41no—
233C2×Q8—41no—
234C22×C4C23×C15111yescharacteristic
235C22×C4C23×C15111yescharacteristic
236C22×C4C23×C15111yescharacteristic
237C22×C4C23×C15111yescharacteristic
238C22×C4C23×C15111yescharacteristic
239C22×C4C23×C15111yescharacteristic
240C22×C4C23×C15111yescharacteristic
241C22×C4C23×C15111yescharacteristic
242C22×C4C23×C15111yescharacteristic
243C22×C4C23×C15111yescharacteristic
244C22×C4C23×C15111yescharacteristic
245C22×C4C23×C15111yescharacteristic
246C22×C4C23×C15111yescharacteristic
247C22×C4C23×C15111yescharacteristic
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C22⋊C4—22no—
254C22⋊C4—22no—
255C22⋊C4—22no—
256C22⋊C4—41no—
257C22⋊C4—41no—
258C22⋊C4—41no—
259C22⋊C4—41no—
260C42—22no—
261C42—41no—
262C42—41no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23—21no—
269C23—21no—
270C23C24×C15111yescharacteristic
271Q8—44no—
272Q8—44no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
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—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4#41×C15112yes—
313C2×C4#41×C15112yes—
314C2×C4#41×C15112yes—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22C2×#41×C15111yescharacteristic
323C22C2×#41×C15111yescharacteristic
324C22C2×#41×C15111yescharacteristic
325C22H(5,𝔽2)×C15111yescharacteristic
326C22H(5,𝔽2)×C15111yescharacteristic
327C222−1+4×C15111yescharacteristic
328C222−1+4×C15111yescharacteristic
329C4—22no—
330C4—22no—
331C4—22no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C2—81no—
344C2#538×C15111yescharacteristic
345C2#542×C15111yescharacteristic
346C2#542×C15111yescharacteristic
347C2#551×C15111yescharacteristic
348C2#556×C15111yescharacteristic
349C2#556×C15111yescharacteristic
350C2#563×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C24
commutator, Frattini, cosocleC23C24×C151
prime radicalC24×C151C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #401×C151C2semidirect
4. #395×C151C2semidirect
7. #391×C151C2semidirect
8. #391×C151C2semidirect
9. #391×C151C2semidirect
13. #387×C151C2semidirect
14. #387×C151C2semidirect
15. #383×C151C2semidirect
175. C151#2759direct (N × H)
176. #2759C151direct (N × H)
177. #401C2×C151semidirect
180. #395C2×C151semidirect
183. #391C2×C151semidirect
184. #391C2×C151semidirect
185. #391C2×C151semidirect
189. #387C2×C151semidirect
190. #387C2×C151semidirect
191. #383C2×C151semidirect

Maximal subgroups

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

subgroupindex
#401×C1512
#397×C1512
#395×C1512
#393×C1512
#391×C1512
#388×C1512
#387×C1512
#383×C1512
#2759151