Finite Group Databasebeta

← #34071095

Subgroups — #34071095

Order 19328.

354 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 41 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#23752844C211yesmaximal, characteristic, complemented
2#23752400C211yesmaximal, characteristic, complemented
3#23752398C211yesmaximal, characteristic, complemented
4#23752382C211yesmaximal, characteristic, complemented
5#23752004C211yesmaximal, characteristic, complemented
6#23752000C211yesmaximal, characteristic, complemented
7AΣL(1,𝔽16)×C151C211yesmaximal, characteristic, complemented
8#18012784C2211yescharacteristic, complemented
9C22×C22⋊D151—21no—
10C2×D4×D151—21no—
11#18012767—21no—
12#18012735C2211yescharacteristic
13#18012712—21no—
14#18012711—21no—
15#18012709—21no—
16#18012709—21no—
17#18012708—21no—
18#18012707C2211yescharacteristic
19(C22⋊D151)⋊C4—21no—
20#18012665—21no—
21#18012654C2211yescharacteristic, complemented
22#18012653—21no—
23#18012653—21no—
24#120×C151C2211yescharacteristic
25#100×C151C2211yescharacteristic, complemented
26#99×C151C2211yescharacteristic, complemented
27C23×D151—21no—
28C23×D151D411yescharacteristic, complemented
29#14559004—21no—
30#14559003—41no—
31C2×D604—21no—
32C2×D604—41no—
33C2×D604D411yescharacteristic, complemented
34C2×C22⋊D151—21no—
35C2×C22⋊D151—21no—
36C2×C22⋊D151—21no—
37C2×C22⋊D151—21no—
38C2×C22⋊D151—21no—
39C2×C22⋊D151—21no—
40C2×C22⋊D151—21no—
41C2×C22⋊D151—44no—
42C2×C22⋊D151—41no—
43D4×D151—44no—
44D4×D151—41no—
45C22×Dic151—21no—
46C2×C4×D151—21no—
47#14558993—41no—
48D1208—41no—
49Dic151⋊C4—21no—
50C22⋊Dic151—21no—
51C22⋊Dic151—41no—
52C22⋊Dic151D411yescharacteristic, complemented
53(C2×D151)⋊C4—21no—
54(C2×D151)⋊C4—21no—
55(C2×D151)⋊C4—41no—
56C4×Dic151D411yescharacteristic, complemented
57C24×C151D411yescharacteristic, complemented
58C2×D4×C151—21no—
59C2×D4×C151C2311yescharacteristic
60M16×C151—21no—
61C22⋊C4×C151—21no—
62C22⋊C4×C151—21no—
63C22⋊C4×C151D411yescharacteristic, complemented
64C22×D151—21no—
65C22×D151—21no—
66C22×D151—21no—
67C22×D151—21no—
68C22×D151—42no—
69C22×D151—42no—
70C22×D151—41no—
71C22×D151—42no—
72C22×D151—81no—
73Dic302—21no—
74D604—21no—
75D604—41no—
76D604—42no—
77D604—82no—
78C22⋊D151—24no—
79C22⋊D151—42no—
80C22⋊D151—42no—
81C22⋊D151—42no—
82C22⋊D151—41no—
83C22⋊D151—41no—
84C22⋊D151—42no—
85C22⋊D151—41no—
86C22⋊D151—82no—
87C2×Dic151—21no—
88C2×Dic151—21no—
89C2×Dic151—21no—
90C2×Dic151—21no—
91C2×Dic151—42no—
92C2×Dic151—41no—
93C4×D151—42no—
94C4×D151—41no—
95C23×C151—21no—
96C23×C151—41no—
97C23×C151—42no—
98C23×C151C2×D411yescharacteristic
99C23×C151C2×D411yescharacteristic
100D4×C151—41no—
101D4×C151—42no—
102C2×C4×C151—21no—
103C2×C4×C151—41no—
104C2×C4×C151C2×D411yescharacteristic
105C8×C151—41no—
106C22×C151—22no—
107C22×C151—21no—
108C22×C151—21no—
109C22×C151—41no—
110C22×C151—41no—
111C22×C151—41no—
112C22×C151—42no—
113C22×C151—41no—
114C22×C151—81no—
115C22×C151#12011yescharacteristic
116C2×D151—22no—
117C2×D151—41no—
118C2×D151—41no—
119C2×D151—42no—
120C2×D151—41no—
121C2×D151—41no—
122C2×D151—41no—
123C2×D151—41no—
124C2×D151—81no—
125C2×D151—84no—
126C2×D151—81no—
127C2×D151—81no—
128C4×C151—21no—
129C4×C151—41no—
130C4×C151—81no—
131Dic151—22no—
132Dic151—41no—
133Dic151—41no—
134Dic151—81no—
135C2×C151—21no—
136C2×C151—41no—
137C2×C151—41no—
138C2×C151—42no—
139C2×C151B(4,𝔽2)11yescharacteristic
140D151—42no—
141D151—81no—
142D151—81no—
143C151#219611yescharacteristic, complemented, Sylow
144#2196—1511nomaximal, Sylow
145D42—1511no—
146B(4,𝔽2)—1511no—
147B(4,𝔽2)—1511no—
148#453—1511no—
149#353—1511no—
150AΣL(1,𝔽16)—1511no—
151AΣL(1,𝔽16)D15111yescharacteristic, complemented
152H(5,𝔽2)—1511no—
153C22×D4—3021no—
154C22×D4—3021no—
155AGL(1,ℤ/8)—3021no—
156#127—1511no—
157#121—3021no—
158#121—3021no—
159#120—3021no—
160#120—3021no—
161#120—3021no—
162#120—1511no—
163#120C2×D15111yescharacteristic
164C4×D4—3021no—
165#104—3021no—
166#100C2×D15111yescharacteristic, complemented
167#99—3021no—
168#99—3021no—
169#99—1511no—
170#99C2×D15111yescharacteristic, complemented
171C24—3021no—
172C24—1511no—
173C24D60411yescharacteristic, complemented
174#41—3021no—
175#41—6041no—
176C2×D4—21no—
177C2×D4—3021no—
178C2×D4—3021no—
179C2×D4—3021no—
180C2×D4—3021no—
181C2×D4—3021no—
182C2×D4—3021no—
183C2×D4—3021no—
184C2×D4—3021no—
185C2×D4—6041no—
186C2×D4—6041no—
187C2×D4—6044no—
188C2×D4—6044no—
189C2×D4—6041no—
190C2×D4—1511no—
191C2×D4C22×D15111yescharacteristic
192C22×C4—3021no—
193C22×C4—3021no—
194SD16—6041no—
195D8—6041no—
196M16—21no—
197C4⋊C4—3021no—
198C22⋊C4—21no—
199C22⋊C4—21no—
200C22⋊C4—3021no—
201C22⋊C4—3021no—
202C22⋊C4—3021no—
203C22⋊C4—6041no—
204C22⋊C4—6041no—
205C22⋊C4—1511no—
206C22⋊C4D60411yescharacteristic, complemented
207C42—1511no—
208C23—21no—
209C23—41no—
210C23—42no—
211C23—3021no—
212C23—3021no—
213C23—3021no—
214C23—3021no—
215C23—6041no—
216C23—6042no—
217C23—6042no—
218C23—6042no—
219C23—12081no—
220C23D4×D15111yescharacteristic
221C23C2×D60411yescharacteristic
222Q8—3021no—
223D4—41no—
224D4—42no—
225D4—3021no—
226D4—3024no—
227D4—6041no—
228D4—6042no—
229D4—6042no—
230D4—6042no—
231D4—6042no—
232D4—6041no—
233D4—6041no—
234D4—6042no—
235D4—6041no—
236D4—12082no—
237D4—12082no—
238C2×C4—21no—
239C2×C4—41no—
240C2×C4—3021no—
241C2×C4—3021no—
242C2×C4—3021no—
243C2×C4—3021no—
244C2×C4—6041no—
245C2×C4—6042no—
246C2×C4—6042no—
247C2×C4—6041no—
248C2×C4D4×D15111yescharacteristic
249C8—41no—
250C22—22no—
251C22—21no—
252C22—21no—
253C22—41no—
254C22—41no—
255C22—41no—
256C22—42no—
257C22—41no—
258C22—81no—
259C22—3022no—
260C22—6041no—
261C22—6041no—
262C22—6041no—
263C22—6042no—
264C22—6041no—
265C22—6041no—
266C22—6041no—
267C22—12081no—
268C22—12084no—
269C22—12081no—
270C22—12081no—
271C22#1801270911yescharacteristic
272C4—21no—
273C4—41no—
274C4—81no—
275C4—3022no—
276C4—6041no—
277C4—6041no—
278C4—12081no—
279C2—21no—
280C2—41no—
281C2—41no—
282C2—42no—
283C2—6042no—
284C2—12081no—
285C2—12081no—
286C2#2375240011yescharacteristic
subgroupG/H
centerC2#23752400
commutator, cosocleC2×D4×C151C23
FrattiniC2×D4C22×D151
FittingAΣL(1,𝔽16)×C151C2
socleC2×C151B(4,𝔽2)
hypercenterAΣL(1,𝔽16)D151
hypocenterC151#2196
LCSG ▷ C2×D4×C151 ▷ C22×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ AΣL(1,𝔽16)

Complements

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

NH ≅ G/Ntype
1. #23752844C2semidirect
2. #23752400C2semidirect
3. #23752398C2semidirect
4. #23752382C2semidirect
5. #23752004C2semidirect
6. #23752000C2semidirect
7. AΣL(1,𝔽16)×C151C2semidirect
8. #18012784C22semidirect
21. #18012654C22semidirect
25. #100×C151C22semidirect
26. #99×C151C22semidirect
28. C23×D151D4semidirect
33. C2×D604D4semidirect
52. C22⋊Dic151D4semidirect
56. C4×Dic151D4semidirect
57. C24×C151D4semidirect
63. C22⋊C4×C151D4semidirect
143. C151#2196semidirect
151. AΣL(1,𝔽16)D151semidirect
166. #100C2×D151semidirect
170. #99C2×D151semidirect
173. C24D604semidirect
206. C22⋊C4D604semidirect

Maximal subgroups

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

subgroupindex
#237528442
#237524002
#237523982
#237523822
#237520042
#237520002
AΣL(1,𝔽16)×C1512
#2196151