Finite Group Databasebeta

← #34077166

Subgroups — #34077166

Order 19328.

464 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C2×#18012730C211yesmaximal, characteristic, complemented
2C2×#18012725C211yesmaximal, characteristic
3#23752149C211yesmaximal, characteristic, complemented
4#23752148C211yesmaximal, characteristic, complemented
5#23752138C211yesmaximal, characteristic, complemented
6#23752136C212yesmaximal, complemented
7#23752135C212yesmaximal, complemented
8#23752133C212yesmaximal, complemented
9#23752128C212yesmaximal
10#23752076C211yesmaximal, characteristic, complemented
11#397×C151C211yesmaximal, characteristic, complemented
12C22×Dic302C2211yescharacteristic
13C22×C22⋊D151C2211yescharacteristic
14#18012730—24no—
15#18012725—24no—
16C2×C4⋊Dic151C2212yes—
17C2×C4⋊Dic151C2211yescharacteristic
18C2×C4⋊Dic151C2212yes—
19C2×Dic151⋊C4C2212yes—
20C2×Dic151⋊C4C2212yes—
21C2×Dic151⋊C4C2212yes—
22C2×C22⋊Dic151C2211yescharacteristic
23C2×C22⋊Dic151C2212yes—
24C2×(C2×D151)⋊C4C2211yescharacteristic
25C2×(C2×D151)⋊C4C2211yescharacteristic
26C2×(C2×D151)⋊C4C2212yes—
27C2×(C2×D151)⋊C4C2212yes—
28C2×C4×Dic151C2211yescharacteristic
29C151⋊#95C2212yes—
30C151⋊#95C2211yescharacteristic
31C151⋊#95C2212yes—
32C2×C4⋊C4×C151C2211yescharacteristic
33C2×C22⋊C4×C151C2211yescharacteristic
34C2×C22⋊C4×C151C2212yes—
35#95×C151C2211yescharacteristic
36#95×C151C2212yes—
37C23×D151C2311yescharacteristic
38C2×Dic302—22no—
39C2×Dic302—42no—
40C2×C22⋊D151—22no—
41C2×C22⋊D151—42no—
42C22×Dic151C2312yes—
43C22×Dic151C2312yes—
44C22×Dic151C2311yescharacteristic
45C22×Dic151C2311yescharacteristic
46C22×Dic151C2311yescharacteristic
47C4⋊Dic151—24no—
48C4⋊Dic151—22no—
49C4⋊Dic151—42no—
50Dic151⋊C4—24no—
51Dic151⋊C4—42no—
52Dic151⋊C4—42no—
53C22⋊Dic151—22no—
54C22⋊Dic151—42no—
55(C2×D151)⋊C4—22no—
56(C2×D151)⋊C4—22no—
57(C2×D151)⋊C4—42no—
58(C2×D151)⋊C4—42no—
59C4×Dic151D414yes—
60C24×C151C2311yescharacteristic
61C22×C4×C151C2311yescharacteristic
62C22×C4×C151C2312yes—
63C22×C4×C151C2312yes—
64C22×C4×C151C2311yescharacteristic
65C4⋊C4×C151—22no—
66C22⋊C4×C151—22no—
67C22⋊C4×C151—42no—
68C22×D151—21no—
69C22×D151—21no—
70C22×D151—22no—
71C22×D151—22no—
72C22×D151—21no—
73Dic302—44no—
74C22⋊D151—44no—
75C2×Dic151—21no—
76C2×Dic151—22no—
77C2×Dic151—21no—
78C2×Dic151—21no—
79C2×Dic151—22no—
80C2×Dic151—22no—
81C2×Dic151—22no—
82C2×Dic151—22no—
83C2×Dic151—22no—
84C2×Dic151—22no—
85C2×Dic151—22no—
86C2×Dic151C2×D412yes—
87C2×Dic151C2×D412yes—
88C23×C151—21no—
89C23×C151—22no—
90C23×C151—21no—
91C23×C151—22no—
92C23×C151—21no—
93C23×C151C2411yescharacteristic
94C2×C4×C151—22no—
95C2×C4×C151—21no—
96C2×C4×C151—22no—
97C2×C4×C151—22no—
98C2×C4×C151—22no—
99C2×C4×C151—22no—
100C2×C4×C151—22no—
101C2×C4×C151—22no—
102C2×C4×C151—22no—
103C2×C4×C151C2×D412yes—
104C22×C151—41no—
105C22×C151—41no—
106C22×C151—41no—
107C22×C151—42no—
108C22×C151—42no—
109C22×C151C22×D411yescharacteristic
110C22×C151H(5,𝔽2)11yescharacteristic
111C22×C151H(5,𝔽2)12yes—
112C22×C1512−1+412yes—
113C22×C1512−1+411yescharacteristic
114C2×D151—41no—
115C2×D151—41no—
116C2×D151—41no—
117C2×D151—42no—
118C2×D151—42no—
119C4×C151—22no—
120C4×C151—41no—
121C4×C151—42no—
122C4×C151—42no—
123Dic151—22no—
124Dic151—22no—
125Dic151—42no—
126Dic151—41no—
127Dic151—42no—
128C2×C151—81no—
129C2×C151#53511yescharacteristic
130C2×C151#53611yescharacteristic
131C2×C151#53711yescharacteristic
132C2×C151#56212yes—
133C2×C151#56312yes—
134D151—81no—
135C151#282011yescharacteristic, complemented, Sylow
136#2820—1511nomaximal, Sylow
137C2×#125—1511no—
138C2×#124—1511no—
139#399—1511no—
140#399—1511no—
141#397—1511no—
142#397D15111yescharacteristic, complemented
143#396—1512no—
144#396—1512no—
145#395—1512no—
146#394—1512no—
147#382—1511no—
148C22×Q8—1511no—
149C22×D4—1511no—
150#125—3024no—
151#124—3024no—
152C2×C4⋊C4—1512no—
153C2×C4⋊C4—1512no—
154C2×C4⋊C4—1511no—
155C2×C4⋊C4—1512no—
156C2×C4⋊C4—1512no—
157C2×C4⋊C4—1512no—
158C2×C4⋊C4C2×D15111yescharacteristic
159C2×C22⋊C4—1511no—
160C2×C22⋊C4—1511no—
161C2×C22⋊C4—1511no—
162C2×C22⋊C4—1512no—
163C2×C22⋊C4—1512no—
164C2×C22⋊C4—1512no—
165C2×C22⋊C4C2×D15111yescharacteristic
166C2×C22⋊C4C2×D15112yes—
167C2×C42—1511no—
168#95—1512no—
169#95—1511no—
170#95—1512no—
171#95C2×D15111yescharacteristic
172#95C2×D15112yes—
173C24—1511no—
174C24C22×D15111yescharacteristic
175C2×Q8—3022no—
176C2×Q8—6042no—
177C2×D4—3022no—
178C2×D4—6042no—
179C22×C4—1512no—
180C22×C4—1511no—
181C22×C4—1512no—
182C22×C4—1511no—
183C22×C4—1511no—
184C22×C4C22×D15112yes—
185C22×C4C22×D15112yes—
186C22×C4C22×D15111yescharacteristic
187C22×C4C22×D15111yescharacteristic
188C4⋊C4—22no—
189C4⋊C4—3024no—
190C4⋊C4—3024no—
191C4⋊C4—3022no—
192C4⋊C4—6042no—
193C4⋊C4—6042no—
194C4⋊C4—6042no—
195C22⋊C4—22no—
196C22⋊C4—42no—
197C22⋊C4—3022no—
198C22⋊C4—3022no—
199C22⋊C4—3022no—
200C22⋊C4—6042no—
201C22⋊C4—6042no—
202C22⋊C4—6042no—
203C42—1514no—
204C23—21no—
205C23—21no—
206C23—22no—
207C23—21no—
208C23—22no—
209C23—3021no—
210C23—3021no—
211C23—3022no—
212C23—3021no—
213C23—3022no—
214C23C23×D15111yescharacteristic
215Q8—6044no—
216D4—6044no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—3021no—
227C2×C4—3022no—
228C2×C4—3021no—
229C2×C4—3021no—
230C2×C4—3022no—
231C2×C4—3022no—
232C2×C4—3022no—
233C2×C4—3022no—
234C2×C4—3022no—
235C2×C4—3022no—
236C2×C4—3022no—
237C2×C4—1512no—
238C2×C4—1512no—
239C2×C4D4×D15112yes—
240C22—42no—
241C22—41no—
242C22—41no—
243C22—41no—
244C22—42no—
245C22—6042no—
246C22—6041no—
247C22—6041no—
248C22—6041no—
249C22—6042no—
250C22C2×D4×D15111yescharacteristic
251C22#1801278411yescharacteristic
252C22#1801278512yes—
253C22#1801278611yescharacteristic
254C22#1801278612yes—
255C4—22no—
256C4—41no—
257C4—42no—
258C4—42no—
259C4—3022no—
260C4—3022no—
261C4—6041no—
262C4—6042no—
263C4—6042no—
264C2—81no—
265C2—12081no—
266C2#2375278011yescharacteristic
267C2#2375278411yescharacteristic
268C2#2375279111yescharacteristic
269C2#2375295912yes—
270C2#2375296412yes—
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting#397×C151C2
prime radicalC22×C22⋊D151C22
hypercenter#397D151
hypocenterC151#2820
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#18012730C2semidirect
3. #23752149C2semidirect
4. #23752148C2semidirect
5. #23752138C2semidirect
6. #23752136C2semidirect
7. #23752135C2semidirect
8. #23752133C2semidirect
10. #23752076C2semidirect
11. #397×C151C2semidirect
135. C151#2820semidirect
142. #397D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127302
C2×#180127252
#237521492
#237521482
#237521382
#237521362
#237521352
#237521332
#237521282
#237520762
#397×C1512
#2820151