Finite Group Databasebeta

← #34077131

Subgroups — #34077131

Order 19328.

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

normal subgroups only

This group has 644 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×#18012712C211yesmaximal, characteristic, complemented
2C2×#18012710C211yesmaximal, characteristic, complemented
3#23752140C212yesmaximal, complemented
4#23752139C211yesmaximal, characteristic, complemented
5#23752137C211yesmaximal, characteristic, complemented
6#23752121C212yesmaximal, complemented
7#23752120C211yesmaximal, characteristic, complemented
8#23752120C212yesmaximal, complemented
9#23752120C212yesmaximal, complemented
10#23752074C211yesmaximal, characteristic, complemented
11#392×C151C211yesmaximal, characteristic, complemented
12C22×D604C2211yescharacteristic
13C22×C22⋊D151C2211yescharacteristic
14C22×C22⋊D151C2211yescharacteristic
15C22×C22⋊D151C2212yes—
16C22×C22⋊D151C2212yes—
17C22×C4×D151C2211yescharacteristic
18#18012712—24no—
19#18012710—24no—
20C2×C4⋊Dic151C2211yescharacteristic
21C2×Dic151⋊C4C2211yescharacteristic
22C2×C22⋊Dic151C2212yes—
23C2×C22⋊Dic151C2212yes—
24C2×C22⋊Dic151C2212yes—
25C2×(C2×D151)⋊C4C2211yescharacteristic
26C2×(C2×D151)⋊C4C2212yes—
27C2×(C2×D151)⋊C4C2212yes—
28C151⋊#95C2211yescharacteristic
29C151⋊#95C2212yes—
30C151⋊#95C2212yes—
31C151⋊#95C2212yes—
32C22×D4×C151C2211yescharacteristic
33C22×D4×C151C2212yes—
34C2×C22⋊C4×C151C2211yescharacteristic
35C2×C22⋊C4×C151C2212yes—
36#95×C151C2211yescharacteristic
37C23×D151C2311yescharacteristic
38C23×D151C2311yescharacteristic
39C2×D604—22no—
40C2×D604—42no—
41C2×C22⋊D151—24no—
42C2×C22⋊D151—22no—
43C2×C22⋊D151—22no—
44C2×C22⋊D151—42no—
45C2×C22⋊D151—42no—
46C2×C22⋊D151—42no—
47C2×C22⋊D151—42no—
48C2×C22⋊D151—42no—
49C2×C22⋊D151—42no—
50C2×C22⋊D151—42no—
51C22×Dic151C2311yescharacteristic
52C22×Dic151C2312yes—
53C22×Dic151C2312yes—
54C22×Dic151C2311yescharacteristic
55C2×C4×D151—42no—
56C2×C4×D151D414yescomplemented
57C4⋊Dic151—22no—
58Dic151⋊C4—22no—
59C22⋊Dic151—24no—
60C22⋊Dic151—42no—
61C22⋊Dic151—42no—
62(C2×D151)⋊C4—22no—
63(C2×D151)⋊C4—42no—
64(C2×D151)⋊C4—42no—
65C24×C151C2312yes—
66C24×C151C2311yescharacteristic
67C2×D4×C151—22no—
68C2×D4×C151—42no—
69C2×D4×C151—42no—
70C2×D4×C151—42no—
71C2×D4×C151—42no—
72C22×C4×C151C2312yes—
73C22×C4×C151C2311yescharacteristic
74C22×C4×C151C2311yescharacteristic
75C22⋊C4×C151—22no—
76C22⋊C4×C151—42no—
77C22×D151—22no—
78C22×D151—21no—
79C22×D151—21no—
80C22×D151—22no—
81C22×D151—21no—
82C22×D151—21no—
83C22×D151—22no—
84C22×D151—21no—
85C22×D151—22no—
86C22×D151C2×D412yes—
87D604—44no—
88C22⋊D151—44no—
89C22⋊D151—48no—
90C22⋊D151—44no—
91C22⋊D151—48no—
92C2×Dic151—22no—
93C2×Dic151—21no—
94C2×Dic151—22no—
95C2×Dic151—22no—
96C2×Dic151—22no—
97C2×Dic151—22no—
98C2×Dic151—22no—
99C2×Dic151—22no—
100C2×Dic151—22no—
101C2×Dic151C2×D412yes—
102C4×D151—44no—
103C23×C151—22no—
104C23×C151—21no—
105C23×C151—21no—
106C23×C151—22no—
107C23×C151—22no—
108C23×C151—22no—
109C23×C151—22no—
110C23×C151—22no—
111C23×C151—22no—
112C23×C151—22no—
113C23×C151—22no—
114C23×C151—21no—
115C23×C151C2411yescharacteristic
116D4×C151—44no—
117D4×C151—48no—
118C2×C4×C151—22no—
119C2×C4×C151—21no—
120C2×C4×C151—22no—
121C2×C4×C151—22no—
122C2×C4×C151—22no—
123C2×C4×C151—22no—
124C2×C4×C151C2×D412yes—
125C22×C151—42no—
126C22×C151—41no—
127C22×C151—42no—
128C22×C151—41no—
129C22×C151—41no—
130C22×C151—42no—
131C22×C151—42no—
132C22×C151—42no—
133C22×C151—42no—
134C22×C151—42no—
135C22×C151—42no—
136C22×C151—42no—
137C22×C151C22×D411yescharacteristic
138C22×C151H(5,𝔽2)12yes—
139C22×C151H(5,𝔽2)12yes—
140C22×C151H(5,𝔽2)11yescharacteristic
141C22×C151H(5,𝔽2)11yescharacteristic
142C2×D151—22no—
143C2×D151—22no—
144C2×D151—22no—
145C2×D151—42no—
146C2×D151—42no—
147C2×D151—41no—
148C2×D151—41no—
149C2×D151—41no—
150C2×D151—42no—
151C2×D151—42no—
152C4×C151—22no—
153C4×C151—41no—
154C4×C151—42no—
155Dic151—22no—
156Dic151—41no—
157Dic151—42no—
158Dic151—42no—
159C2×C151—82no—
160C2×C151—81no—
161C2×C151#53411yescharacteristic
162C2×C151#53511yescharacteristic
163C2×C151#53511yescharacteristic
164C2×C151#56012yes—
165C2×C151#56012yes—
166D151—42no—
167D151—81no—
168C151#281511yescharacteristic, complemented, Sylow
169#2815—1511nomaximal, Sylow
170C2×#121—1511no—
171C2×#121—1511no—
172#397—1511no—
173#397—1512no—
174#397—1511no—
175#392—1512no—
176#392—1511no—
177#392—1512no—
178#392—1512no—
179#392D15111yescharacteristic, complemented
180#381—1511no—
181C22×D4—1512no—
182C22×D4—1511no—
183C22×D4—1511no—
184C22×D4—1512no—
185C22×D4—1511no—
186C22×D4C2×D15111yescharacteristic
187C22×D4C2×D15112yes—
188C23×C4—1511no—
189#121—3024no—
190#121—3024no—
191C2×C4⋊C4—1511no—
192C2×C4⋊C4—1511no—
193C2×C22⋊C4—1512no—
194C2×C22⋊C4—1511no—
195C2×C22⋊C4—1512no—
196C2×C22⋊C4—1512no—
197C2×C22⋊C4—1512no—
198C2×C22⋊C4—1512no—
199C2×C22⋊C4C2×D15111yescharacteristic
200C2×C22⋊C4C2×D15112yes—
201#95—1511no—
202#95—1512no—
203#95—1512no—
204#95—1512no—
205#95C2×D15111yescharacteristic
206C24—1511no—
207C24—1511no—
208C24C22×D15111yescharacteristic
209C24C22×D15112yes—
210C2×D4—22no—
211C2×D4—42no—
212C2×D4—42no—
213C2×D4—42no—
214C2×D4—42no—
215C2×D4—3022no—
216C2×D4—3022no—
217C2×D4—3024no—
218C2×D4—3022no—
219C2×D4—6042no—
220C2×D4—6042no—
221C2×D4—6042no—
222C2×D4—6042no—
223C2×D4—6042no—
224C2×D4—6042no—
225C2×D4—6042no—
226C2×D4—6042no—
227C22×C4—6042no—
228C22×C4—1512no—
229C22×C4—1511no—
230C22×C4—1512no—
231C22×C4—1511no—
232C22×C4—1514no—
233C22×C4C22×D15112yes—
234C22×C4C22×D15111yescharacteristic
235C22×C4C22×D15111yescharacteristic
236C4⋊C4—3022no—
237C4⋊C4—3022no—
238C22⋊C4—22no—
239C22⋊C4—42no—
240C22⋊C4—3024no—
241C22⋊C4—3022no—
242C22⋊C4—6042no—
243C22⋊C4—6042no—
244C22⋊C4—6042no—
245C22⋊C4—6042no—
246C23—21no—
247C23—22no—
248C23—22no—
249C23—22no—
250C23—21no—
251C23—22no—
252C23—22no—
253C23—22no—
254C23—22no—
255C23—22no—
256C23—21no—
257C23—22no—
258C23—3022no—
259C23—3022no—
260C23—3021no—
261C23—3021no—
262C23—3021no—
263C23—3021no—
264C23—3022no—
265C23—3022no—
266C23—3021no—
267C23—1512no—
268C23C23×D15111yescharacteristic
269D4—44no—
270D4—48no—
271D4—6044no—
272D4—6044no—
273D4—6044no—
274D4—6048no—
275D4—6048no—
276C2×C4—22no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—3022no—
283C2×C4—3021no—
284C2×C4—3022no—
285C2×C4—3022no—
286C2×C4—3022no—
287C2×C4—3022no—
288C2×C4—3022no—
289C2×C4—3022no—
290C2×C4—3022no—
291C2×C4—6044no—
292C2×C4—1512no—
293C2×C4D4×D15112yes—
294C22—42no—
295C22—41no—
296C22—41no—
297C22—42no—
298C22—42no—
299C22—41no—
300C22—42no—
301C22—42no—
302C22—42no—
303C22—42no—
304C22—42no—
305C22—42no—
306C22—3022no—
307C22—3022no—
308C22—3022no—
309C22—6042no—
310C22—6042no—
311C22—6041no—
312C22—6041no—
313C22—6041no—
314C22—6042no—
315C22—6042no—
316C22C2×D4×D15111yescharacteristic
317C22#1801278412yes—
318C22#1801278412yes—
319C22#1801278411yescharacteristic
320C22#1801278511yescharacteristic
321C4—22no—
322C4—41no—
323C4—42no—
324C4—3022no—
325C4—6041no—
326C4—6042no—
327C4—6042no—
328C2—82no—
329C2—81no—
330C2—6042no—
331C2—12081no—
332C2#2375277211yescharacteristic
333C2#2375277511yescharacteristic
334C2#2375277811yescharacteristic
335C2#2375295012yes—
336C2#2375295112yes—
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting#392×C151C2
hypercenter#392D151
hypocenterC151#2815
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#18012712C2semidirect
2. C2×#18012710C2semidirect
3. #23752140C2semidirect
4. #23752139C2semidirect
5. #23752137C2semidirect
6. #23752121C2semidirect
7. #23752120C2semidirect
8. #23752120C2semidirect
9. #23752120C2semidirect
10. #23752074C2semidirect
11. #392×C151C2semidirect
56. C2×C4×D151D4semidirect
168. C151#2815semidirect
179. #392D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127122
C2×#180127102
#237521402
#237521392
#237521372
#237521212
#237521202
#237520742
#392×C1512
#2815151