Finite Group Databasebeta

← #34077152

Subgroups — #34077152

Order 19328.

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

normal subgroups only

This group has 630 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×#18012735C211yesmaximal, characteristic, complemented
2C2×#18012734C211yesmaximal, characteristic, complemented
3#23752129C211yesmaximal, characteristic, complemented
4#23752128C212yesmaximal, complemented
5#23752127C212yesmaximal, complemented
6#23752122C211yesmaximal, characteristic, complemented
7#23752121C212yesmaximal, complemented
8#23752121C212yesmaximal, complemented
9#23752120C211yesmaximal, characteristic, complemented
10#23752079C211yesmaximal, characteristic, complemented
11#394×C151C211yesmaximal, characteristic, complemented
12C22×D604C2211yescharacteristic
13C22×D604C2212yes—
14C22×C22⋊D151C2212yes—
15C22×C22⋊D151C2212yes—
16C22×C22⋊D151C2212yes—
17#18012735—24no—
18#18012734—24no—
19C2×C4⋊Dic151C2211yescharacteristic
20C2×Dic151⋊C4C2211yescharacteristic
21C2×C22⋊Dic151C2212yes—
22C2×(C2×D151)⋊C4C2211yescharacteristic
23C2×(C2×D151)⋊C4C2211yescharacteristic
24C2×(C2×D151)⋊C4C2211yescharacteristic
25C2×(C2×D151)⋊C4C2212yes—
26C2×(C2×D151)⋊C4C2212yes—
27C2×(C2×D151)⋊C4C2212yes—
28C2×C4×Dic151C2211yescharacteristic
29C151⋊#95C2211yescharacteristic
30C151⋊#95C2212yes—
31C151⋊#95C2212yes—
32C22×D4×C151C2211yescharacteristic
33C2×C4⋊C4×C151C2211yescharacteristic
34C2×C22⋊C4×C151C2212yes—
35C2×C22⋊C4×C151C2212yes—
36#95×C151C2211yescharacteristic
37C23×D151C2311yescharacteristic
38C23×D151C2312yes—
39C2×D604—22no—
40C2×D604—42no—
41C2×D604—42no—
42C2×D604—42no—
43C2×D604—42no—
44C2×C22⋊D151—24no—
45C2×C22⋊D151—24no—
46C2×C22⋊D151—42no—
47C2×C22⋊D151—42no—
48C2×C22⋊D151—42no—
49C2×C22⋊D151—42no—
50C2×C22⋊D151—42no—
51C2×C22⋊D151—42no—
52C2×C22⋊D151—42no—
53C22×Dic151C2311yescharacteristic
54C22×Dic151C2312yes—
55C22×Dic151C2311yescharacteristic
56C22×Dic151C2311yescharacteristic
57C4⋊Dic151—22no—
58Dic151⋊C4—22no—
59C22⋊Dic151—42no—
60(C2×D151)⋊C4—22no—
61(C2×D151)⋊C4—22no—
62(C2×D151)⋊C4—22no—
63(C2×D151)⋊C4—42no—
64(C2×D151)⋊C4—42no—
65(C2×D151)⋊C4—42no—
66C4×Dic151D414yescomplemented
67C24×C151C2312yes—
68C2×D4×C151—22no—
69C2×D4×C151—42no—
70C22×C4×C151C2311yescharacteristic
71C22×C4×C151C2311yescharacteristic
72C22×C4×C151C2312yes—
73C22×C4×C151C2311yescharacteristic
74C4⋊C4×C151—22no—
75C22⋊C4×C151—42no—
76C22⋊C4×C151—42no—
77C22×D151—21no—
78C22×D151—22no—
79C22×D151—22no—
80C22×D151—22no—
81C22×D151—22no—
82C22×D151—21no—
83C22×D151—22no—
84C22×D151—22no—
85C22×D151—22no—
86C22×D151—22no—
87C22×D151—22no—
88C22×D151—21no—
89D604—44no—
90D604—48no—
91C22⋊D151—48no—
92C22⋊D151—48no—
93C22⋊D151—48no—
94C2×Dic151—21no—
95C2×Dic151—21no—
96C2×Dic151—22no—
97C2×Dic151—21no—
98C2×Dic151—22no—
99C2×Dic151—22no—
100C2×Dic151—22no—
101C2×Dic151—22no—
102C2×Dic151C2×D412yes—
103C2×Dic151C2×D412yes—
104C23×C151—22no—
105C23×C151—22no—
106C23×C151—22no—
107C23×C151—22no—
108C23×C151—22no—
109C23×C151—22no—
110C23×C151—22no—
111C23×C151C2411yescharacteristic
112D4×C151—44no—
113C2×C4×C151—22no—
114C2×C4×C151—21no—
115C2×C4×C151—21no—
116C2×C4×C151—21no—
117C2×C4×C151—22no—
118C2×C4×C151—22no—
119C2×C4×C151—22no—
120C2×C4×C151—22no—
121C2×C4×C151—21no—
122C2×C4×C151C2×D412yes—
123C22×C151—42no—
124C22×C151—42no—
125C22×C151—42no—
126C22×C151—42no—
127C22×C151—42no—
128C22×C151—42no—
129C22×C151—42no—
130C22×C151C22×D411yescharacteristic
131C22×C151H(5,𝔽2)12yes—
132C22×C151H(5,𝔽2)11yescharacteristic
133C22×C151H(5,𝔽2)11yescharacteristic
134C22×C151H(5,𝔽2)12yes—
135C2×D151—42no—
136C2×D151—42no—
137C2×D151—42no—
138C2×D151—41no—
139C2×D151—41no—
140C2×D151—41no—
141C2×D151—42no—
142C2×D151—42no—
143C2×D151—42no—
144C2×D151—42no—
145C2×D151—42no—
146C2×D151—42no—
147C4×C151—22no—
148C4×C151—41no—
149C4×C151—41no—
150C4×C151—42no—
151Dic151—22no—
152Dic151—22no—
153Dic151—41no—
154Dic151—42no—
155C2×C151—82no—
156C2×C151#53511yescharacteristic
157C2×C151#53511yescharacteristic
158C2×C151#53511yescharacteristic
159C2×C151#56012yes—
160C2×C151#56012yes—
161D151—82no—
162D151—81no—
163C151#281811yescharacteristic, complemented, Sylow
164#2818—1511nomaximal, Sylow
165C2×#127—1511no—
166C2×#126—1511no—
167#394—1511no—
168#394—1512no—
169#394—1512no—
170#394D15111yescharacteristic, complemented
171#392—1511no—
172#392—1512no—
173#392—1512no—
174#392—1511no—
175#383—1511no—
176C22×D4—1512no—
177C22×D4—1512no—
178C22×D4—1512no—
179C22×D4—1511no—
180C22×D4—1512no—
181C22×D4C2×D15111yescharacteristic
182#127—3024no—
183#126—3024no—
184C2×C4⋊C4—1511no—
185C2×C4⋊C4—1511no—
186C2×C4⋊C4C2×D15111yescharacteristic
187C2×C22⋊C4—1511no—
188C2×C22⋊C4—1511no—
189C2×C22⋊C4—1511no—
190C2×C22⋊C4—1512no—
191C2×C22⋊C4—1512no—
192C2×C22⋊C4—1512no—
193C2×C22⋊C4—1512no—
194C2×C22⋊C4C2×D15112yes—
195C2×C22⋊C4C2×D15112yes—
196C2×C42—1511no—
197#95—1511no—
198#95—1512no—
199#95—1512no—
200#95C2×D15111yescharacteristic
201C24—1511no—
202C24—1512no—
203C24C22×D15112yes—
204C2×D4—22no—
205C2×D4—42no—
206C2×D4—3024no—
207C2×D4—3024no—
208C2×D4—3022no—
209C2×D4—6042no—
210C2×D4—6042no—
211C2×D4—6042no—
212C2×D4—6042no—
213C2×D4—6042no—
214C2×D4—6042no—
215C2×D4—6042no—
216C2×D4—6042no—
217C2×D4—6042no—
218C2×D4—6042no—
219C2×D4—6042no—
220C22×C4—1512no—
221C22×C4—1511no—
222C22×C4—1511no—
223C22×C4—1511no—
224C22×C4C22×D15112yes—
225C22×C4C22×D15111yescharacteristic
226C22×C4C22×D15111yescharacteristic
227C22×C4C22×D15111yescharacteristic
228C4⋊C4—22no—
229C4⋊C4—3022no—
230C4⋊C4—3022no—
231C22⋊C4—42no—
232C22⋊C4—42no—
233C22⋊C4—3022no—
234C22⋊C4—3022no—
235C22⋊C4—3022no—
236C22⋊C4—6042no—
237C22⋊C4—6042no—
238C22⋊C4—6042no—
239C22⋊C4—6042no—
240C42—1514no—
241C23—22no—
242C23—22no—
243C23—22no—
244C23—22no—
245C23—22no—
246C23—22no—
247C23—22no—
248C23—3021no—
249C23—3022no—
250C23—3022no—
251C23—3022no—
252C23—3022no—
253C23—3022no—
254C23—3021no—
255C23—3022no—
256C23—3022no—
257C23—3021no—
258C23—3022no—
259C23—3022no—
260C23C23×D15111yescharacteristic
261D4—44no—
262D4—6044no—
263D4—6048no—
264D4—6048no—
265D4—6048no—
266D4—6048no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—21no—
275C2×C4—22no—
276C2×C4—3021no—
277C2×C4—3021no—
278C2×C4—3022no—
279C2×C4—3021no—
280C2×C4—3022no—
281C2×C4—3022no—
282C2×C4—3022no—
283C2×C4—3022no—
284C2×C4—1512no—
285C2×C4—1512no—
286C2×C4D4×D15112yes—
287C22—42no—
288C22—42no—
289C22—42no—
290C22—42no—
291C22—42no—
292C22—42no—
293C22—42no—
294C22—6042no—
295C22—6041no—
296C22—6042no—
297C22—6041no—
298C22—6042no—
299C22—6041no—
300C22—6042no—
301C22—6042no—
302C22—6042no—
303C22—6042no—
304C22—6042no—
305C22—6042no—
306C22C2×D4×D15111yescharacteristic
307C22#1801278412yes—
308C22#1801278411yescharacteristic
309C22#1801278511yescharacteristic
310C22#1801278512yes—
311C4—22no—
312C4—41no—
313C4—41no—
314C4—42no—
315C4—3022no—
316C4—3022no—
317C4—6041no—
318C4—6042no—
319C2—82no—
320C2—12082no—
321C2—12081no—
322C2#2375277711yescharacteristic
323C2#2375277811yescharacteristic
324C2#2375278011yescharacteristic
325C2#2375295012yes—
326C2#2375295212yes—
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting#394×C151C2
hypercenter#394D151
hypocenterC151#2818
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#18012735C2semidirect
2. C2×#18012734C2semidirect
3. #23752129C2semidirect
4. #23752128C2semidirect
5. #23752127C2semidirect
6. #23752122C2semidirect
7. #23752121C2semidirect
8. #23752121C2semidirect
9. #23752120C2semidirect
10. #23752079C2semidirect
11. #394×C151C2semidirect
66. C4×Dic151D4semidirect
163. C151#2818semidirect
170. #394D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127352
C2×#180127342
#237521292
#237521282
#237521272
#237521222
#237521212
#237521202
#237520792
#394×C1512
#2818151