Finite Group Databasebeta

← #34077109

Subgroups — #34077109

Order 19328.

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

normal subgroups only

This group has 578 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×#18012721C211yesmaximal, characteristic, complemented
2C2×#18012710C211yesmaximal, characteristic, complemented
3#23752152C211yesmaximal, characteristic, complemented
4#23752148C211yesmaximal, characteristic, complemented
5#23752135C212yesmaximal, complemented
6#23752127C212yesmaximal, complemented
7#23752126C212yesmaximal, complemented
8#23752126C211yesmaximal, characteristic, complemented
9#23752120C212yesmaximal, complemented
10#23752071C211yesmaximal, characteristic, complemented
11#392×C151C211yesmaximal, characteristic, complemented
12C22×C22⋊D151C2211yescharacteristic
13C22×C22⋊D151C2212yes—
14C22×C4×D151C2211yescharacteristic
15#18012721—24no—
16#18012710—24no—
17C2×C4⋊Dic151C2211yescharacteristic
18C2×C4⋊Dic151C2211yescharacteristic
19C2×Dic151⋊C4C2211yescharacteristic
20C2×Dic151⋊C4C2212yes—
21C2×Dic151⋊C4C2212yes—
22C2×C22⋊Dic151C2211yescharacteristic
23C2×C22⋊Dic151C2212yes—
24C2×C22⋊Dic151C2212yes—
25C2×C22⋊Dic151C2212yes—
26C2×C22⋊Dic151C2212yes—
27C2×(C2×D151)⋊C4C2211yescharacteristic
28C2×(C2×D151)⋊C4C2212yes—
29C151⋊#95C2211yescharacteristic
30C151⋊#95C2212yes—
31C151⋊#95C2212yes—
32C22×D4×C151C2211yescharacteristic
33C22×D4×C151C2212yes—
34C2×C22⋊C4×C151C2211yescharacteristic
35C2×C22⋊C4×C151C2212yes—
36#95×C151C2211yescharacteristic
37C23×D151C2311yescharacteristic
38C2×C22⋊D151—24no—
39C2×C22⋊D151—22no—
40C2×C22⋊D151—42no—
41C2×C22⋊D151—42no—
42C2×C22⋊D151—42no—
43C22×Dic151C2312yes—
44C22×Dic151C2311yescharacteristic
45C22×Dic151C2312yes—
46C22×Dic151C2311yescharacteristic
47C22×Dic151C2311yescharacteristic
48C2×C4×D151—42no—
49C2×C4×D151D414yescomplemented
50C4⋊Dic151—22no—
51C4⋊Dic151—22no—
52Dic151⋊C4—22no—
53Dic151⋊C4—42no—
54Dic151⋊C4—42no—
55C22⋊Dic151—24no—
56C22⋊Dic151—22no—
57C22⋊Dic151—42no—
58C22⋊Dic151—42no—
59C22⋊Dic151—42no—
60(C2×D151)⋊C4—22no—
61(C2×D151)⋊C4—42no—
62C24×C151C2311yescharacteristic
63C24×C151C2312yes—
64C2×D4×C151—22no—
65C2×D4×C151—42no—
66C2×D4×C151—42no—
67C2×D4×C151—42no—
68C2×D4×C151—42no—
69C22×C4×C151C2311yescharacteristic
70C22×C4×C151C2312yes—
71C22×C4×C151C2311yescharacteristic
72C22⋊C4×C151—22no—
73C22⋊C4×C151—42no—
74C22×D151—21no—
75C22×D151—22no—
76C22×D151—22no—
77C22×D151—21no—
78C22×D151C2×D412yes—
79C22⋊D151—44no—
80C22⋊D151—48no—
81C2×Dic151—22no—
82C2×Dic151—21no—
83C2×Dic151—22no—
84C2×Dic151—21no—
85C2×Dic151—22no—
86C2×Dic151—21no—
87C2×Dic151—22no—
88C2×Dic151—22no—
89C2×Dic151—22no—
90C2×Dic151—22no—
91C2×Dic151—22no—
92C2×Dic151—21no—
93C2×Dic151C2×D412yes—
94C4×D151—44no—
95C23×C151—21no—
96C23×C151—22no—
97C23×C151—22no—
98C23×C151—22no—
99C23×C151—22no—
100C23×C151—22no—
101C23×C151—22no—
102C23×C151—22no—
103C23×C151—22no—
104C23×C151—21no—
105C23×C151—21no—
106C23×C151—22no—
107C23×C151C2411yescharacteristic
108D4×C151—44no—
109D4×C151—48no—
110C2×C4×C151—22no—
111C2×C4×C151—21no—
112C2×C4×C151—22no—
113C2×C4×C151—22no—
114C2×C4×C151—22no—
115C2×C4×C151—22no—
116C2×C4×C151C2×D412yes—
117C22×C151—42no—
118C22×C151—41no—
119C22×C151—41no—
120C22×C151—42no—
121C22×C151—41no—
122C22×C151—42no—
123C22×C151—42no—
124C22×C151—42no—
125C22×C151—42no—
126C22×C151—42no—
127C22×C151—42no—
128C22×C151—42no—
129C22×C151C22×D411yescharacteristic
130C22×C151H(5,𝔽2)12yes—
131C22×C151H(5,𝔽2)12yes—
132C22×C151H(5,𝔽2)11yescharacteristic
133C22×C1512−1+411yescharacteristic
134C2×D151—22no—
135C2×D151—22no—
136C2×D151—22no—
137C2×D151—42no—
138C2×D151—42no—
139C4×C151—22no—
140C4×C151—41no—
141C4×C151—42no—
142Dic151—22no—
143Dic151—41no—
144Dic151—42no—
145Dic151—41no—
146Dic151—42no—
147C2×C151—82no—
148C2×C151—81no—
149C2×C151#53411yescharacteristic
150C2×C151#53511yescharacteristic
151C2×C151#53711yescharacteristic
152C2×C151#56012yes—
153C2×C151#56212yes—
154D151—42no—
155C151#281311yescharacteristic, complemented, Sylow
156#2813—1511nomaximal, Sylow
157C2×#123—1511no—
158C2×#121—1511no—
159#400—1511no—
160#399—1511no—
161#396—1512no—
162#394—1511no—
163#394—1512no—
164#394—1512no—
165#392—1512no—
166#392D15111yescharacteristic, complemented
167#380—1511no—
168C22×D4—1512no—
169C22×D4—1511no—
170C22×D4C2×D15111yescharacteristic
171C22×D4C2×D15112yes—
172C23×C4—1511no—
173#123—3024no—
174#121—3024no—
175C2×C4⋊C4—1511no—
176C2×C4⋊C4—1511no—
177C2×C4⋊C4—1511no—
178C2×C4⋊C4—1512no—
179C2×C4⋊C4—1512no—
180C2×C22⋊C4—1512no—
181C2×C22⋊C4—1511no—
182C2×C22⋊C4—1511no—
183C2×C22⋊C4—1512no—
184C2×C22⋊C4—1512no—
185C2×C22⋊C4—1512no—
186C2×C22⋊C4—1512no—
187C2×C22⋊C4C2×D15111yescharacteristic
188C2×C22⋊C4C2×D15112yes—
189#95—1511no—
190#95—1512no—
191#95—1512no—
192#95C2×D15111yescharacteristic
193C24—1511no—
194C24C22×D15111yescharacteristic
195C24C22×D15112yes—
196C2×D4—22no—
197C2×D4—42no—
198C2×D4—42no—
199C2×D4—42no—
200C2×D4—42no—
201C2×D4—3024no—
202C2×D4—3022no—
203C2×D4—6042no—
204C2×D4—6042no—
205C2×D4—6042no—
206C22×C4—6042no—
207C22×C4—1511no—
208C22×C4—1512no—
209C22×C4—1511no—
210C22×C4—1512no—
211C22×C4—1511no—
212C22×C4—1514no—
213C22×C4C22×D15112yes—
214C22×C4C22×D15111yescharacteristic
215C22×C4C22×D15111yescharacteristic
216C4⋊C4—3022no—
217C4⋊C4—3022no—
218C4⋊C4—3022no—
219C4⋊C4—6042no—
220C4⋊C4—6042no—
221C22⋊C4—22no—
222C22⋊C4—42no—
223C22⋊C4—3022no—
224C22⋊C4—3024no—
225C22⋊C4—3022no—
226C22⋊C4—6042no—
227C22⋊C4—6042no—
228C22⋊C4—6042no—
229C22⋊C4—6042no—
230C23—21no—
231C23—22no—
232C23—22no—
233C23—22no—
234C23—22no—
235C23—22no—
236C23—22no—
237C23—21no—
238C23—22no—
239C23—22no—
240C23—21no—
241C23—22no—
242C23—3021no—
243C23—3022no—
244C23—3022no—
245C23—3021no—
246C23—1512no—
247C23C23×D15111yescharacteristic
248D4—44no—
249D4—48no—
250D4—6044no—
251D4—6048no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—3022no—
259C2×C4—3021no—
260C2×C4—3022no—
261C2×C4—3021no—
262C2×C4—3021no—
263C2×C4—3022no—
264C2×C4—3022no—
265C2×C4—3022no—
266C2×C4—3022no—
267C2×C4—3022no—
268C2×C4—3022no—
269C2×C4—3021no—
270C2×C4—6044no—
271C2×C4—1512no—
272C2×C4D4×D15112yes—
273C22—42no—
274C22—41no—
275C22—42no—
276C22—41no—
277C22—41no—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—42no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—3022no—
286C22—3022no—
287C22—3022no—
288C22—6042no—
289C22—6042no—
290C22C2×D4×D15111yescharacteristic
291C22#1801278412yes—
292C22#1801278412yes—
293C22#1801278411yescharacteristic
294C22#1801278611yescharacteristic
295C4—22no—
296C4—41no—
297C4—42no—
298C4—3022no—
299C4—6041no—
300C4—6042no—
301C4—6041no—
302C4—6042no—
303C2—82no—
304C2—81no—
305C2—6042no—
306C2#2375277211yescharacteristic
307C2#2375277511yescharacteristic
308C2#2375279111yescharacteristic
309C2#2375295112yes—
310C2#2375295712yes—
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting#392×C151C2
hypercenter#392D151
hypocenterC151#2813
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#18012721C2semidirect
2. C2×#18012710C2semidirect
3. #23752152C2semidirect
4. #23752148C2semidirect
5. #23752135C2semidirect
6. #23752127C2semidirect
7. #23752126C2semidirect
8. #23752126C2semidirect
9. #23752120C2semidirect
10. #23752071C2semidirect
11. #392×C151C2semidirect
49. C2×C4×D151D4semidirect
155. C151#2813semidirect
166. #392D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127212
C2×#180127102
#237521522
#237521482
#237521352
#237521272
#237521262
#237521202
#237520712
#392×C1512
#2813151