Finite Group Databasebeta

← #34077342

Subgroups — #34077342

Order 19328.

366 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C151⋊#401C211yesmaximal, characteristic, complemented
2#23752153C211yesmaximal, characteristic, complemented
3#23752152C211yesmaximal, characteristic, complemented
4#23752148C211yesmaximal, characteristic
5#23752145C211yesmaximal, characteristic, complemented
6#23752140C211yesmaximal, characteristic
7#23752137C211yesmaximal, characteristic
8#23752135C211yesmaximal, characteristic
9#23752133C211yesmaximal, characteristic, complemented
10#23752132C211yesmaximal, characteristic, complemented
11#23752124C211yesmaximal, characteristic
12#23752109C211yesmaximal, characteristic, complemented
13#23752100C211yesmaximal, characteristic
14#23752099C211yesmaximal, characteristic, complemented
15#397×C151C211yesmaximal, characteristic
16C22×Dic302C2211yescharacteristic
17C2×C4⋊Dic151C2211yescharacteristic
18C2×C4⋊Dic151C2211yescharacteristic
19C2×C4⋊Dic151C2211yescharacteristic
20C2×Dic151⋊C4C2211yescharacteristic
21C2×Dic151⋊C4C2211yescharacteristic
22C2×Dic151⋊C4C2211yescharacteristic
23C2×Dic151⋊C4C2211yescharacteristic
24C2×Dic151⋊C4C2211yescharacteristic
25C2×Dic151⋊C4C2211yescharacteristic
26C2×C22⋊Dic151C2211yescharacteristic
27C2×C22⋊Dic151C2211yescharacteristic
28C2×C22⋊Dic151C2211yescharacteristic
29C2×C22⋊Dic151C2211yescharacteristic
30C2×C4×Dic151C2211yescharacteristic
31C151⋊#95C2211yescharacteristic
32C151⋊#95C2211yescharacteristic
33C151⋊#95C2211yescharacteristic
34C151⋊#95C2211yescharacteristic
35C151⋊#95C2211yescharacteristic
36C151⋊#95C2211yescharacteristic
37C151⋊#95C2211yescharacteristic
38C151⋊#95C2211yescharacteristic
39C151⋊#95C2211yescharacteristic
40C151⋊#95C2211yescharacteristic
41C151⋊#95C2211yescharacteristic
42C151⋊#95C2211yescharacteristic
43C151⋊#95C2211yescharacteristic
44C2×C4⋊C4×C151C2211yescharacteristic
45C2×C22⋊C4×C151C2211yescharacteristic
46C2×C22⋊C4×C151C2211yescharacteristic
47C2×C22⋊C4×C151C2211yescharacteristic
48#95×C151C2211yescharacteristic
49#95×C151C2211yescharacteristic
50#95×C151C2211yescharacteristic
51C2×Dic302—41no—
52C2×Dic302—41no—
53C2×Dic302—41no—
54C22×Dic151C2311yescharacteristic
55C22×Dic151C2311yescharacteristic
56C22×Dic151C2311yescharacteristic
57C22×Dic151C2311yescharacteristic
58C22×Dic151C2311yescharacteristic
59C22×Dic151C2311yescharacteristic
60C22×Dic151C2311yescharacteristic
61C22×Dic151C2311yescharacteristic
62C4⋊Dic151—41no—
63C4⋊Dic151—41no—
64C4⋊Dic151—41no—
65Dic151⋊C4—22no—
66Dic151⋊C4—22no—
67Dic151⋊C4—41no—
68Dic151⋊C4—41no—
69Dic151⋊C4—41no—
70Dic151⋊C4—41no—
71C22⋊Dic151—22no—
72C22⋊Dic151—41no—
73C22⋊Dic151—41no—
74C22⋊Dic151—41no—
75C4×Dic151—41no—
76C24×C151C2311yescharacteristic
77C22×C4×C151C2311yescharacteristic
78C22×C4×C151C2311yescharacteristic
79C22×C4×C151C2311yescharacteristic
80C22×C4×C151C2311yescharacteristic
81C22×C4×C151C2311yescharacteristic
82C22×C4×C151C2311yescharacteristic
83C4⋊C4×C151—41no—
84C22⋊C4×C151—41no—
85C22⋊C4×C151—41no—
86C22⋊C4×C151—41no—
87Dic302—44no—
88C2×Dic151—21no—
89C2×Dic151—21no—
90C2×Dic151—21no—
91C2×Dic151—21no—
92C2×Dic151—21no—
93C2×Dic151—21no—
94C2×Dic151—21no—
95C2×Dic151—21no—
96C2×Dic151—21no—
97C2×Dic151—21no—
98C2×Dic151—21no—
99C2×Dic151—21no—
100C2×Dic151—21no—
101C2×Dic151—21no—
102C2×Dic151—21no—
103C2×Dic151—21no—
104C2×Dic151—21no—
105C2×Dic151—21no—
106C2×Dic151—21no—
107C2×Dic151—21no—
108C2×Dic151—21no—
109C2×Dic151—21no—
110C2×Dic151—21no—
111C2×Dic151#4112yes—
112C23×C151—21no—
113C23×C151—21no—
114C23×C151—21no—
115C23×C151—21no—
116C23×C151—21no—
117C23×C151—21no—
118C23×C151—21no—
119C23×C151C2411yescharacteristic
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—21no—
137C2×C4×C151—21no—
138C22×C151—41no—
139C22×C151—41no—
140C22×C151—41no—
141C22×C151—41no—
142C22×C151—41no—
143C22×C151—41no—
144C22×C151—41no—
145C22×C151C2×#4111yescharacteristic
146C22×C151H(5,𝔽2)11yescharacteristic
147C22×C151H(5,𝔽2)11yescharacteristic
148C22×C151H(5,𝔽2)11yescharacteristic
149C22×C1512−1+411yescharacteristic
150C22×C1512−1+411yescharacteristic
151C22×C1512−1+411yescharacteristic
152C4×C151—41no—
153C4×C151—41no—
154C4×C151—41no—
155C4×C151—41no—
156C4×C151—41no—
157C4×C151—41no—
158Dic151—22no—
159Dic151—41no—
160Dic151—41no—
161Dic151—41no—
162Dic151—41no—
163Dic151—41no—
164Dic151—41no—
165Dic151—41no—
166C2×C151—81no—
167C2×C151#53911yescharacteristic
168C2×C151#54211yescharacteristic
169C2×C151#54211yescharacteristic
170C2×C151#56011yescharacteristic
171C2×C151#56311yescharacteristic
172C2×C151#56311yescharacteristic
173C2×C151#56311yescharacteristic
174C151#283811yescharacteristic, complemented, Sylow
175#2838—1511nomaximal, Sylow
176#401—1511no—
177#400—1511no—
178#400—1511no—
179#399—1511no—
180#398—1511no—
181#397—1511no—
182#397—1511no—
183#397D15111yescharacteristic
184#396—1511no—
185#395—1511no—
186#395—1511no—
187#393—1511no—
188#389—1511no—
189#388—1511no—
190#387—1511no—
191C22×Q8—1511no—
192C2×C4⋊C4—1511no—
193C2×C4⋊C4—1511no—
194C2×C4⋊C4—1511no—
195C2×C4⋊C4—1511no—
196C2×C4⋊C4—1511no—
197C2×C4⋊C4—1511no—
198C2×C4⋊C4—1511no—
199C2×C4⋊C4—1511no—
200C2×C4⋊C4—1511no—
201C2×C4⋊C4C2×D15111yescharacteristic
202C2×C22⋊C4—1511no—
203C2×C22⋊C4—1511no—
204C2×C22⋊C4—1511no—
205C2×C22⋊C4—1511no—
206C2×C22⋊C4C2×D15111yescharacteristic
207C2×C22⋊C4C2×D15111yescharacteristic
208C2×C22⋊C4C2×D15111yescharacteristic
209C2×C42—1511no—
210#95—1511no—
211#95—1511no—
212#95—1511no—
213#95—1511no—
214#95—1511no—
215#95—1511no—
216#95—1511no—
217#95—1511no—
218#95—1511no—
219#95—1511no—
220#95—1511no—
221#95—1511no—
222#95—1511no—
223#95C2×D15111yescharacteristic
224#95C2×D15111yescharacteristic
225#95C2×D15111yescharacteristic
226C24C22×D15111yescharacteristic
227C2×Q8—6041no—
228C2×Q8—6041no—
229C2×Q8—6041no—
230C22×C4—1511no—
231C22×C4—1511no—
232C22×C4—1511no—
233C22×C4—1511no—
234C22×C4—1511no—
235C22×C4—1511no—
236C22×C4—1511no—
237C22×C4—1511no—
238C22×C4C22×D15111yescharacteristic
239C22×C4C22×D15111yescharacteristic
240C22×C4C22×D15111yescharacteristic
241C22×C4C22×D15111yescharacteristic
242C22×C4C22×D15111yescharacteristic
243C22×C4C22×D15111yescharacteristic
244C4⋊C4—41no—
245C4⋊C4—3022no—
246C4⋊C4—3022no—
247C4⋊C4—6041no—
248C4⋊C4—6041no—
249C4⋊C4—6041no—
250C4⋊C4—6041no—
251C4⋊C4—6041no—
252C4⋊C4—6041no—
253C4⋊C4—6041no—
254C22⋊C4—41no—
255C22⋊C4—41no—
256C22⋊C4—41no—
257C22⋊C4—3022no—
258C22⋊C4—6041no—
259C22⋊C4—6041no—
260C22⋊C4—6041no—
261C42—6041no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23—21no—
269C23C23×D15111yescharacteristic
270Q8—6044no—
271C2×C4—21no—
272C2×C4—21no—
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—3021no—
290C2×C4—3021no—
291C2×C4—3021no—
292C2×C4—3021no—
293C2×C4—3021no—
294C2×C4—3021no—
295C2×C4—3021no—
296C2×C4—3021no—
297C2×C4—3021no—
298C2×C4—3021no—
299C2×C4—3021no—
300C2×C4—3021no—
301C2×C4—3021no—
302C2×C4—3021no—
303C2×C4—3021no—
304C2×C4—3021no—
305C2×C4—3021no—
306C2×C4—3021no—
307C2×C4—3021no—
308C2×C4—3021no—
309C2×C4—3021no—
310C2×C4—3021no—
311C2×C4—3021no—
312C2×C4—1512no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22#41×D15111yescharacteristic
321C22#1801278411yescharacteristic
322C22#1801278411yescharacteristic
323C22#1801278511yescharacteristic
324C22#1801278611yescharacteristic
325C22#1801278611yescharacteristic
326C22#1801278611yescharacteristic
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—3022no—
334C4—6041no—
335C4—6041no—
336C4—6041no—
337C4—6041no—
338C4—6041no—
339C4—6041no—
340C4—6041no—
341C2—81no—
342C2#2375280511yescharacteristic
343C2#2375282611yescharacteristic
344C2#2375282811yescharacteristic
345C2#2375295011yescharacteristic
346C2#2375296411yescharacteristic
347C2#2375296511yescharacteristic
348C2#2375296511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting#397×C151C2
prime radicalC24×C151C23
hypercenter#397D151
hypocenterC151#2838
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C151⋊#401C2semidirect
2. #23752153C2semidirect
3. #23752152C2semidirect
5. #23752145C2semidirect
9. #23752133C2semidirect
10. #23752132C2semidirect
12. #23752109C2semidirect
14. #23752099C2semidirect
174. C151#2838semidirect

Maximal subgroups

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

subgroupindex
C151⋊#4012
#237521532
#237521522
#237521482
#237521452
#237521402
#237521372
#237521352
#237521332
#237521322
#237521242
#237521092
#237521002
#237520992
#397×C1512
#2838151