Finite Group Databasebeta

← #34077139

Subgroups — #34077139

Order 19328.

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

normal subgroups only

This group has 528 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×#18012719C211yesmaximal, characteristic, complemented
2C2×#18012712C211yesmaximal, characteristic
3#23752147C211yesmaximal, characteristic, complemented
4#23752145C212yesmaximal, complemented
5#23752129C212yesmaximal, complemented
6#23752128C212yesmaximal, complemented
7#23752127C212yesmaximal, complemented
8#23752125C211yesmaximal, characteristic, complemented
9#23752124C211yesmaximal, characteristic, complemented
10#23752074C211yesmaximal, characteristic, complemented
11#399×C151C211yesmaximal, characteristic, complemented
12C22×Dic302C2211yescharacteristic
13C22×D604C2211yescharacteristic
14C22×C22⋊D151C2211yescharacteristic
15C22×C22⋊D151C2211yescharacteristic
16C22×C4×D151C2211yescharacteristic
17#18012719—24no—
18#18012712—24no—
19C2×C4⋊Dic151C2212yes—
20C2×Dic151⋊C4C2211yescharacteristic
21C2×Dic151⋊C4C2212yes—
22C2×C22⋊Dic151C2212yes—
23C2×(C2×D151)⋊C4C2212yes—
24C2×(C2×D151)⋊C4C2211yescharacteristic
25C2×(C2×D151)⋊C4C2212yes—
26C2×(C2×D151)⋊C4C2212yes—
27C2×(C2×D151)⋊C4C2212yes—
28C151⋊#95C2211yescharacteristic
29C151⋊#95C2212yes—
30C151⋊#95C2212yes—
31C151⋊#95C2212yes—
32C2×C4⋊C4×C151C2211yescharacteristic
33C2×C4⋊C4×C151C2212yes—
34C2×C22⋊C4×C151C2211yescharacteristic
35C2×C22⋊C4×C151C2212yes—
36#95×C151C2211yescharacteristic
37C23×D151C2311yescharacteristic
38C23×D151C2311yescharacteristic
39C2×Dic302—22no—
40C2×Dic302—42no—
41C2×D604—22no—
42C2×D604—42no—
43C2×C22⋊D151—22no—
44C2×C22⋊D151—22no—
45C2×C22⋊D151—42no—
46C2×C22⋊D151—42no—
47C22×Dic151C2312yes—
48C22×Dic151C2312yes—
49C22×Dic151C2311yescharacteristic
50C22×Dic151C2311yescharacteristic
51C2×C4×D151—42no—
52C2×C4×D151D414yes—
53C4⋊Dic151—24no—
54Dic151⋊C4—22no—
55Dic151⋊C4—42no—
56C22⋊Dic151—42no—
57(C2×D151)⋊C4—24no—
58(C2×D151)⋊C4—22no—
59(C2×D151)⋊C4—42no—
60(C2×D151)⋊C4—42no—
61(C2×D151)⋊C4—42no—
62C24×C151C2311yescharacteristic
63C22×C4×C151C2312yes—
64C22×C4×C151C2312yes—
65C22×C4×C151C2311yescharacteristic
66C22×C4×C151C2311yescharacteristic
67C4⋊C4×C151—22no—
68C4⋊C4×C151—42no—
69C22⋊C4×C151—22no—
70C22⋊C4×C151—42no—
71C22×D151—22no—
72C22×D151—22no—
73C22×D151—21no—
74C22×D151—21no—
75C22×D151—21no—
76C22×D151—22no—
77C22×D151—22no—
78C22×D151—21no—
79C22×D151—21no—
80C22×D151C2×D412yes—
81Dic302—44no—
82D604—44no—
83C22⋊D151—44no—
84C22⋊D151—44no—
85C2×Dic151—22no—
86C2×Dic151—21no—
87C2×Dic151—22no—
88C2×Dic151—22no—
89C2×Dic151—22no—
90C2×Dic151—22no—
91C2×Dic151—22no—
92C2×Dic151—22no—
93C2×Dic151—22no—
94C2×Dic151C2×D412yes—
95C4×D151—44no—
96C23×C151—21no—
97C23×C151—22no—
98C23×C151—22no—
99C23×C151—21no—
100C23×C151—21no—
101C23×C151C2411yescharacteristic
102C2×C4×C151—22no—
103C2×C4×C151—22no—
104C2×C4×C151—21no—
105C2×C4×C151—22no—
106C2×C4×C151—22no—
107C2×C4×C151—22no—
108C2×C4×C151—22no—
109C2×C4×C151—22no—
110C2×C4×C151—22no—
111C2×C4×C151C2×D412yes—
112C22×C151—41no—
113C22×C151—41no—
114C22×C151—41no—
115C22×C151—42no—
116C22×C151—42no—
117C22×C151C22×D411yescharacteristic
118C22×C151H(5,𝔽2)12yes—
119C22×C151H(5,𝔽2)12yes—
120C22×C1512−1+411yescharacteristic
121C22×C1512−1+411yescharacteristic
122C2×D151—22no—
123C2×D151—22no—
124C2×D151—22no—
125C2×D151—42no—
126C2×D151—42no—
127C2×D151—41no—
128C2×D151—41no—
129C2×D151—41no—
130C2×D151—42no—
131C2×D151—42no—
132C4×C151—22no—
133C4×C151—42no—
134C4×C151—41no—
135C4×C151—42no—
136Dic151—22no—
137Dic151—42no—
138Dic151—41no—
139Dic151—42no—
140C2×C151—81no—
141C2×C151#53411yescharacteristic
142C2×C151#53511yescharacteristic
143C2×C151#53611yescharacteristic
144C2×C151#56212yes—
145C2×C151#56212yes—
146D151—42no—
147D151—81no—
148C151#281611yescharacteristic, complemented, Sylow
149#2816—1511nomaximal, Sylow
150C2×C22⋊Q8—1511no—
151C2×#121—1511no—
152#399—1511no—
153#399D15111yescharacteristic, complemented
154#398—1512no—
155#394—1512no—
156#394—1512no—
157#394—1512no—
158#393—1511no—
159#393—1511no—
160#381—1511no—
161C22×Q8—1511no—
162C22×D4—1511no—
163C22×D4—1511no—
164C22×D4—1511no—
165C23×C4—1511no—
166C22⋊Q8—3024no—
167#121—3024no—
168C2×C4⋊C4—1511no—
169C2×C4⋊C4—1512no—
170C2×C4⋊C4—1512no—
171C2×C4⋊C4C2×D15111yescharacteristic
172C2×C4⋊C4C2×D15112yes—
173C2×C22⋊C4—1511no—
174C2×C22⋊C4—1512no—
175C2×C22⋊C4—1512no—
176C2×C22⋊C4—1512no—
177C2×C22⋊C4—1512no—
178C2×C22⋊C4—1512no—
179C2×C22⋊C4C2×D15111yescharacteristic
180C2×C22⋊C4C2×D15112yes—
181#95—1511no—
182#95—1512no—
183#95—1512no—
184#95—1512no—
185#95C2×D15111yescharacteristic
186C24—1511no—
187C24—1511no—
188C24C22×D15111yescharacteristic
189C2×Q8—3022no—
190C2×Q8—6042no—
191C2×D4—3022no—
192C2×D4—3022no—
193C2×D4—3022no—
194C2×D4—6042no—
195C2×D4—6042no—
196C2×D4—6042no—
197C22×C4—6042no—
198C22×C4—1512no—
199C22×C4—1512no—
200C22×C4—1511no—
201C22×C4—1511no—
202C22×C4—1514no—
203C22×C4C22×D15112yes—
204C22×C4C22×D15111yescharacteristic
205C22×C4C22×D15112yes—
206C22×C4C22×D15111yescharacteristic
207C4⋊C4—22no—
208C4⋊C4—42no—
209C4⋊C4—3022no—
210C4⋊C4—3024no—
211C4⋊C4—6042no—
212C22⋊C4—22no—
213C22⋊C4—42no—
214C22⋊C4—3024no—
215C22⋊C4—3022no—
216C22⋊C4—6042no—
217C22⋊C4—6042no—
218C22⋊C4—6042no—
219C22⋊C4—6042no—
220C23—21no—
221C23—22no—
222C23—22no—
223C23—21no—
224C23—21no—
225C23—3022no—
226C23—3022no—
227C23—3021no—
228C23—3021no—
229C23—3021no—
230C23—3022no—
231C23—3022no—
232C23—3021no—
233C23—3021no—
234C23—1512no—
235C23C23×D15111yescharacteristic
236Q8—6044no—
237D4—6044no—
238D4—6044no—
239D4—6044no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—3022no—
250C2×C4—3021no—
251C2×C4—3022no—
252C2×C4—3022no—
253C2×C4—3022no—
254C2×C4—3022no—
255C2×C4—3022no—
256C2×C4—3022no—
257C2×C4—3022no—
258C2×C4—6044no—
259C2×C4—1512no—
260C2×C4D4×D15112yes—
261C22—41no—
262C22—41no—
263C22—41no—
264C22—42no—
265C22—42no—
266C22—3022no—
267C22—3022no—
268C22—3022no—
269C22—6042no—
270C22—6042no—
271C22—6041no—
272C22—6041no—
273C22—6041no—
274C22—6042no—
275C22—6042no—
276C22C2×D4×D15111yescharacteristic
277C22#1801278412yes—
278C22#1801278512yes—
279C22#1801278611yescharacteristic
280C22#1801278711yescharacteristic
281C4—22no—
282C4—41no—
283C4—42no—
284C4—42no—
285C4—3022no—
286C4—6042no—
287C4—6041no—
288C4—6042no—
289C2—81no—
290C2—6042no—
291C2—12081no—
292C2#2375277311yescharacteristic
293C2#2375277511yescharacteristic
294C2#2375278511yescharacteristic
295C2#2375295812yes—
296C2#2375295912yes—
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting#399×C151C2
prime radicalC2×#18012712C2
hypercenter#399D151
hypocenterC151#2816
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#18012719C2semidirect
3. #23752147C2semidirect
4. #23752145C2semidirect
5. #23752129C2semidirect
6. #23752128C2semidirect
7. #23752127C2semidirect
8. #23752125C2semidirect
9. #23752124C2semidirect
10. #23752074C2semidirect
11. #399×C151C2semidirect
148. C151#2816semidirect
153. #399D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127192
C2×#180127122
#237521472
#237521452
#237521292
#237521282
#237521272
#237521252
#237521242
#237520742
#399×C1512
#2816151