Finite Group Databasebeta

← #34072235

Subgroups — #34072235

Order 19328.

496 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012734C211yesmaximal, characteristic
2#23752107C211yesmaximal, characteristic, complemented
3#23752103C211yesmaximal, characteristic
4#23752103C211yesmaximal, characteristic
5#23752102C211yesmaximal, characteristic
6#23752098C211yesmaximal, characteristic, complemented
7#23752096C211yesmaximal, characteristic, complemented
8#23752095C211yesmaximal, characteristic, complemented
9#23752086C211yesmaximal, characteristic
10C4×C4⋊Dic151C211yesmaximal, characteristic, complemented
11#23752063C211yesmaximal, characteristic, complemented
12C4×(C2×D151)⋊C4C211yesmaximal, characteristic
13#23752059C211yesmaximal, characteristic
14#23752058C211yesmaximal, characteristic, complemented
15C4×C4⋊C4×C151C211yesmaximal, characteristic, complemented
16C22×C4×D151C2211yescharacteristic
17#18012734C418yescomplemented
18C2×C4⋊Dic151C2211yescharacteristic
19C2×C4⋊Dic151C2211yescharacteristic
20C2×Dic151⋊C4C2211yescharacteristic
21C2×Dic151⋊C4C2211yescharacteristic
22C2×Dic151⋊C4C2211yescharacteristic
23C2×Dic151⋊C4C2211yescharacteristic
24C2×(C2×D151)⋊C4C2211yescharacteristic
25C2×(C2×D151)⋊C4C2211yescharacteristic
26C2×(C2×D151)⋊C4C2211yescharacteristic
27C2×(C2×D151)⋊C4C2211yescharacteristic
28C2×(C2×D151)⋊C4C2211yescharacteristic
29C2×(C2×D151)⋊C4C2211yescharacteristic
30C2×C4×Dic151C2211yescharacteristic
31C2×C4×Dic151C2211yescharacteristic
32C2×C4×Dic151C2211yescharacteristic
33C2×C4×Dic151C2211yescharacteristic
34C2×C4×Dic151C2211yescharacteristic
35C151⋊#95C2211yescharacteristic
36C151⋊#95C2211yescharacteristic
37C151⋊#95C2211yescharacteristic
38C151⋊#95C2211yescharacteristic
39C151⋊#95C2211yescharacteristic
40C151⋊#95C2211yescharacteristic
41C151⋊#95C2211yescharacteristic
42C151⋊#95C2211yescharacteristic
43C151⋊#95C2211yescharacteristic
44C151⋊#95C2211yescharacteristic
45C2×C4⋊C4×C151C2211yescharacteristic
46C2×C4⋊C4×C151C2211yescharacteristic
47C2×C42×C151C2211yescharacteristic
48C2×C42×C151C2211yescharacteristic
49C2×C42×C151C2211yescharacteristic
50#95×C151C2211yescharacteristic
51#95×C151C2211yescharacteristic
52C23×D151C2311yescharacteristic
53C22×Dic151C2311yescharacteristic
54C22×Dic151C2311yescharacteristic
55C22×Dic151C2311yescharacteristic
56C22×Dic151C2311yescharacteristic
57C22×Dic151C2311yescharacteristic
58C22×Dic151C2311yescharacteristic
59C22×Dic151C2311yescharacteristic
60C2×C4×D151—22no—
61C2×C4×D151—22no—
62C2×C4×D151—41no—
63C4⋊Dic151—22no—
64C4⋊Dic151C2×C414yescomplemented
65Dic151⋊C4—22no—
66Dic151⋊C4—22no—
67Dic151⋊C4—41no—
68Dic151⋊C4C2×C414yescomplemented
69(C2×D151)⋊C4—22no—
70(C2×D151)⋊C4—22no—
71(C2×D151)⋊C4—41no—
72(C2×D151)⋊C4C2×C414yes—
73(C2×D151)⋊C4C2×C414yes—
74(C2×D151)⋊C4C2×C414yes—
75C4×Dic151—22no—
76C4×Dic151—41no—
77C4×Dic151—41no—
78C4×Dic151—41no—
79C4×Dic151C2×C414yescomplemented
80C22×C4×C151C2311yescharacteristic
81C22×C4×C151C2311yescharacteristic
82C22×C4×C151C2311yescharacteristic
83C22×C4×C151C2311yescharacteristic
84C22×C4×C151C2311yescharacteristic
85C22×C4×C151C2311yescharacteristic
86C22×C4×C151C2311yescharacteristic
87C4⋊C4×C151—22no—
88C4⋊C4×C151C2×C414yescomplemented
89C42×C151—22no—
90C42×C151—22no—
91C42×C151—22no—
92C22×D151—21no—
93C22×D151—21no—
94C22×D151—21no—
95C22×D151—21no—
96C22×D151—21no—
97C22×D151—21no—
98C22×D151C22×C412yes—
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—21no—
112C2×Dic151—21no—
113C2×Dic151—21no—
114C2×Dic151—21no—
115C2×Dic151—21no—
116C2×Dic151C22×C412yes—
117C2×Dic151C22×C412yes—
118C2×Dic151C22×C412yes—
119C2×Dic151#4112yes—
120C4×D151—44no—
121C23×C151C2411yescharacteristic
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×C151C22×C412yes—
138C2×C4×C151C22×C412yes—
139C2×C4×C151C22×C412yes—
140C2×C4×C151#4112yes—
141C2×C4×C151#4112yes—
142C2×C4×C151#4112yes—
143C22×C151C23×C411yescharacteristic
144C22×C151C2×#4111yescharacteristic
145C22×C151C2×#4111yescharacteristic
146C22×C151C2×#4111yescharacteristic
147C22×C151C2×#4111yescharacteristic
148C22×C151H(5,𝔽2)11yescharacteristic
149C22×C1512−1+411yescharacteristic
150C2×D151—22no—
151C2×D151—22no—
152C2×D151—22no—
153C2×D151—41no—
154C2×D151—41no—
155C2×D151—41no—
156C2×D151—41no—
157C4×C151—22no—
158C4×C151—22no—
159C4×C151—22no—
160C4×C151—22no—
161C4×C151—22no—
162C4×C151—22no—
163C4×C151—41no—
164Dic151—22no—
165Dic151—22no—
166Dic151—22no—
167Dic151—22no—
168Dic151—41no—
169Dic151—41no—
170Dic151—41no—
171C2×C151C4×#4111yescharacteristic
172C2×C151C4×#4111yescharacteristic
173C2×C151#52011yescharacteristic
174C2×C151#55111yescharacteristic
175C2×C151#55211yescharacteristic
176C2×C151#55311yescharacteristic
177C2×C151#55611yescharacteristic
178D151—42no—
179C151#237311yescharacteristic, complemented, Sylow
180#2373—1511nomaximal, Sylow
181C2×#126—1511no—
182#389—1511no—
183#388—1511no—
184#388—1511no—
185#388—1511no—
186#387—1511no—
187#387—1511no—
188#387—1511no—
189#385—1511no—
190C4×C4⋊C4—1511no—
191C4×C4⋊C4—1511no—
192C4×C4⋊C4D15111yescharacteristic, complemented
193C4×C22⋊C4—1511no—
194C4×C22⋊C4—1511no—
195#376—1511no—
196C23×C4—1511no—
197#126—1518no—
198C2×C4⋊C4—1511no—
199C2×C4⋊C4—1511no—
200C2×C4⋊C4—1511no—
201C2×C4⋊C4—1511no—
202C2×C4⋊C4—1511no—
203C2×C4⋊C4—1511no—
204C2×C4⋊C4C2×D15111yescharacteristic
205C2×C4⋊C4C2×D15111yescharacteristic
206C2×C22⋊C4—1511no—
207C2×C22⋊C4—1511no—
208C2×C22⋊C4—1511no—
209C2×C22⋊C4—1511no—
210C2×C22⋊C4—1511no—
211C2×C22⋊C4—1511no—
212C2×C42—1511no—
213C2×C42—1511no—
214C2×C42—1511no—
215C2×C42—1511no—
216C2×C42—1511no—
217C2×C42C2×D15111yescharacteristic
218C2×C42C2×D15111yescharacteristic
219C2×C42C2×D15111yescharacteristic
220#95—1511no—
221#95—1511no—
222#95—1511no—
223#95—1511no—
224#95—1511no—
225#95—1511no—
226#95—1511no—
227#95—1511no—
228#95—1511no—
229#95—1511no—
230#95C2×D15111yescharacteristic
231#95C2×D15111yescharacteristic
232C24—1511no—
233C22×C4—3022no—
234C22×C4—3022no—
235C22×C4—6041no—
236C22×C4—1511no—
237C22×C4—1511no—
238C22×C4—1511no—
239C22×C4—1511no—
240C22×C4—1511no—
241C22×C4—1511no—
242C22×C4—1511no—
243C22×C4C22×D15111yescharacteristic
244C22×C4C22×D15111yescharacteristic
245C22×C4C22×D15111yescharacteristic
246C22×C4C22×D15111yescharacteristic
247C22×C4C22×D15111yescharacteristic
248C22×C4C22×D15111yescharacteristic
249C22×C4C22×D15111yescharacteristic
250C4⋊C4—22no—
251C4⋊C4—3022no—
252C4⋊C4—3022no—
253C4⋊C4—3022no—
254C4⋊C4—6041no—
255C4⋊C4—1514no—
256C4⋊C4—1514no—
257C4⋊C4C4×D15114yescomplemented
258C22⋊C4—3022no—
259C22⋊C4—3022no—
260C22⋊C4—6041no—
261C22⋊C4—1514no—
262C22⋊C4—1514no—
263C22⋊C4—1514no—
264C42—22no—
265C42—22no—
266C42—22no—
267C42—3022no—
268C42—6041no—
269C42—6041no—
270C42—6041no—
271C42—1514no—
272C23—3021no—
273C23—3021no—
274C23—3021no—
275C23—3021no—
276C23—3021no—
277C23—3021no—
278C23—1512no—
279C23C23×D15111yescharacteristic
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—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—6044no—
313C2×C4—1512no—
314C2×C4—1512no—
315C2×C4—1512no—
316C2×C4—1512no—
317C2×C4C2×C4×D15112yes—
318C2×C4C2×C4×D15112yes—
319C2×C4C2×C4×D15112yes—
320C2×C4#1455900312yes—
321C2×C4#1455900412yes—
322C2×C4#1455900412yes—
323C22—3022no—
324C22—3022no—
325C22—3022no—
326C22—6041no—
327C22—6041no—
328C22—6041no—
329C22—6041no—
330C22C22×C4×D15111yescharacteristic
331C22#41×D15111yescharacteristic
332C22C2×#1455900311yescharacteristic
333C22C2×#1455900411yescharacteristic
334C22C2×#1455900411yescharacteristic
335C22#1801278511yescharacteristic
336C22#1801278711yescharacteristic
337C4—22no—
338C4—22no—
339C4—22no—
340C4—22no—
341C4—22no—
342C4—22no—
343C4—41no—
344C4—3022no—
345C4—3022no—
346C4—3022no—
347C4—3022no—
348C4—6041no—
349C4—6041no—
350C4—6041no—
351C2—6042no—
352C2C4×#1455900311yescharacteristic
353C2C4×#1455900411yescharacteristic
354C2#2375269411yescharacteristic
355C2#2375288611yescharacteristic
356C2#2375289711yescharacteristic
357C2#2375290811yescharacteristic
358C2#2375293411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D151
commutatorC22×C151C23×C4
FittingC4×C4⋊C4×C151C2
socle, cosocleC23×C151C24
prime radicalC23×D151C23
hypercenterC4×C4⋊C4D151
hypocenterC151#2373
LCSG ▷ C22×C151 ▷ C151
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #23752107C2semidirect
6. #23752098C2semidirect
7. #23752096C2semidirect
8. #23752095C2semidirect
10. C4×C4⋊Dic151C2semidirect
11. #23752063C2semidirect
14. #23752058C2semidirect
15. C4×C4⋊C4×C151C2semidirect
17. #18012734C4semidirect
64. C4⋊Dic151C2×C4semidirect
68. Dic151⋊C4C2×C4semidirect
79. C4×Dic151C2×C4semidirect
88. C4⋊C4×C151C2×C4semidirect
179. C151#2373semidirect
192. C4×C4⋊C4D151semidirect
257. C4⋊C4C4×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127342
#237521072
#237521032
#237521022
#237520982
#237520962
#237520952
#237520862
C4×C4⋊Dic1512
#237520632
C4×(C2×D151)⋊C42
#237520592
#237520582
C4×C4⋊C4×C1512
#2373151