Finite Group Databasebeta

← #34054787

Subgroups — #34054787

Order 19072.

444 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 119 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
1#23750177C211yesmaximal, characteristic, complemented
2C2×#18011873C211yesmaximal, characteristic
3#23749960C211yesmaximal, characteristic, complemented
4#23749904C212yesmaximal, complemented
5#23749829C212yesmaximal, complemented
6#23749778C211yesmaximal, characteristic
7#23749775C211yesmaximal, characteristic
8#23749728C212yesmaximal, complemented
9#23749724C212yesmaximal, complemented
10#23749679C211yesmaximal, characteristic, complemented
11#484×C149C211yesmaximal, characteristic, complemented
12C22×D596C2211yescharacteristic
13C22×C4×D149—21no—
14C2×#14558725C2212yes—
15C2×#14558723C2212yes—
16#18011910C2211yescharacteristic, complemented
17#18011909C2211yescharacteristic, complemented
18#18011901—21no—
19#18011890C2211yescharacteristic
20#18011888—21no—
21Q8×Dic149C2211yescharacteristic, complemented
22#18011876—21no—
23#18011876C2211yescharacteristic, complemented
24#18011873—21no—
25#18011873—21no—
26#18011873C2212yes—
27#18011873C2212yes—
28#18011867—21no—
29C2×#14558713—21no—
30C2×C4×Dic149C2211yescharacteristic
31#18011844C2212yescomplemented
32#18011840C2212yescomplemented
33#18011834C2212yescomplemented
34#18011833C2212yes—
35#18011831C2212yes—
36C22⋊#11924746C2211yescharacteristic
37#18011821C2212yescomplemented
38C22⋊Q8×C149C2211yescharacteristic
39C2×C4⋊C4×C149C2211yescharacteristic
40#107×C149C2212yescomplemented
41#103×C149C2212yescomplemented
42C22⋊C8×C149C2211yescharacteristic
43C23×D149—21no—
44C2×Dic298—21no—
45C2×Dic298C2311yescharacteristic
46C2×D596—24no—
47C2×D596—21no—
48C2×D596C2312yes—
49C22×Dic149D411yescharacteristic
50C22×Dic149D411yescharacteristic
51C2×C4×D149—22no—
52C2×C4×D149—22no—
53C2×C4×D149—44no—
54#14558725—24no—
55#14558723—24no—
56C2×#11924746C2312yes—
57C4⋊Dic149—21no—
58C4⋊Dic149C2311yescharacteristic
59#14558715—21no—
60#14558715—21no—
61#14558715—21no—
62#14558715—21no—
63#14558715—21no—
64C22⋊Dic149—21no—
65#14558713—22no—
66#14558713—22no—
67C4×Dic149—21no—
68C4×Dic149—21no—
69C4×Dic149D411yescharacteristic
70C4×Dic149D411yescharacteristic
71C4×Dic149C2311yescharacteristic
72C4×Dic149C2311yescharacteristic
73C2×Q8×C149C2311yescharacteristic
74C22×C4×C149—21no—
75C22×C4×C149C2311yescharacteristic
76C2×C8×C149C2312yes—
77C4⋊C4×C149—21no—
78C4⋊C4×C149—21no—
79C4⋊C4×C149C2311yescharacteristic
80C4⋊C4×C149C2312yes—
81C22⋊C4×C149—21no—
82C22×D149—24no—
83C22×D149—22no—
84C22×D149—42no—
85C22×D149—42no—
86Dic298—22no—
87Dic298—42no—
88D596—24no—
89D596—22no—
90D596#4114yes—
91C2×Dic149—22no—
92C2×Dic149—22no—
93C2×Dic149—21no—
94C2×Dic149—21no—
95C2×Dic149C2×D411yescharacteristic
96C2×Dic149C2×D411yescharacteristic
97C2×Dic149C2×D411yescharacteristic
98C2×Dic149C2×D411yescharacteristic
99C4×D149—44no—
100C4×D149—44no—
101#11924746—22no—
102C23×C149C2×D411yescharacteristic
103Q8×C149—22no—
104C2×C4×C149—22no—
105C2×C4×C149—22no—
106C2×C4×C149—21no—
107C2×C4×C149—21no—
108C2×C4×C149—42no—
109C2×C4×C149C2×D411yescharacteristic
110C2×C4×C149C2411yescharacteristic
111C8×C149—22no—
112C22×C149—21no—
113C22×C149—21no—
114C22×C149#13712yes—
115C22×C149C22×D411yescharacteristic
116C2×D149—24no—
117C2×D149—48no—
118C2×D149—42no—
119C2×D149—42no—
120C4×C149—21no—
121C4×C149—41no—
122C4×C149—42no—
123C4×C149—41no—
124C4×C149C2×#4112yes—
125Dic149—21no—
126Dic149—21no—
127Dic149—21no—
128Dic149—41no—
129Dic149—41no—
130Dic149AGL(1,ℤ/8)12yes—
131C2×C149—22no—
132C2×C149#52511yescharacteristic
133C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
134C2×C149C2×#13711yescharacteristic
135D149—44no—
136C149#311011yescharacteristic, complemented, Sylow
137#3110—1491nomaximal, Sylow
138#533—1491no—
139C2×C4×D4—1491no—
140#484—1491no—
141#484D14911yescharacteristic, complemented
142#474—1492no—
143#461—1492no—
144#450—1491no—
145#450—1491no—
146#440—1492no—
147#440—1492no—
148#432—1491no—
149C22×D4—1491no—
150C23×C4—2981no—
151C2×SD16—1492no—
152C2×SD16—1492no—
153C4⋊Q8—1491no—
154C4⋊Q8—1491no—
155#125—2981no—
156C22⋊Q8—2981no—
157C22⋊Q8—1491no—
158C22⋊Q8C2×D14911yescharacteristic
159C4×Q8—2981no—
160C4×Q8—1491no—
161C4×Q8—1491no—
162C4×D4—2981no—
163C4×D4—2981no—
164C4×D4—1492no—
165C4×D4—1492no—
166#117—2981no—
167C2×C4⋊C4C2×D14911yescharacteristic
168C2×C22⋊C4—2981no—
169C2×C42—1491no—
170#107—1492no—
171#107C2×D14912yescomplemented
172C4⋊C8—1492no—
173#103—1492no—
174#103C2×D14912yescomplemented
175#102—1492no—
176#102—1492no—
177C22⋊C8—1491no—
178C22⋊C8C2×D14911yescharacteristic
179#97—1492no—
180C24—2981no—
181C2×Q8—2981no—
182C2×Q8—1491no—
183C2×Q8C22×D14911yescharacteristic
184C2×D4—2984no—
185C2×D4—2981no—
186C2×D4—1492no—
187C22×C4—21no—
188C22×C4—2982no—
189C22×C4—2982no—
190C22×C4—5964no—
191C22×C4—1491no—
192C22×C4—1491no—
193C22×C4C22×D14911yescharacteristic
194SD16—2984no—
195SD16—2984no—
196C2×C8—1492no—
197C2×C8C22×D14912yes—
198C4⋊C4—21no—
199C4⋊C4—21no—
200C4⋊C4—2981no—
201C4⋊C4—2981no—
202C4⋊C4—2981no—
203C4⋊C4—2981no—
204C4⋊C4—2981no—
205C4⋊C4—2981no—
206C4⋊C4—1491no—
207C4⋊C4C22×D14911yescharacteristic
208C4⋊C4C22×D14912yes—
209C22⋊C4—21no—
210C22⋊C4—2982no—
211C22⋊C4—2982no—
212C22⋊C4—2981no—
213C42—2981no—
214C42—2981no—
215C42—1491no—
216C42—1491no—
217C42—1491no—
218C42—1491no—
219C23—2984no—
220C23—2982no—
221C23—5962no—
222C23—5962no—
223C23D4×D14911yescharacteristic
224Q8—22no—
225Q8—2982no—
226Q8—5962no—
227D4—2984no—
228D4—2982no—
229D4—1494no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—42no—
235C2×C4—2982no—
236C2×C4—2982no—
237C2×C4—2981no—
238C2×C4—2981no—
239C2×C4—5964no—
240C2×C4—5964no—
241C2×C4—1491no—
242C2×C4—1491no—
243C2×C4—1491no—
244C2×C4—1491no—
245C2×C4D4×D14911yescharacteristic
246C2×C4C23×D14911yescharacteristic
247C8—22no—
248C8—2982no—
249C22—21no—
250C22—21no—
251C22—2984no—
252C22—5968no—
253C22—5962no—
254C22—5962no—
255C22#1801194312yes—
256C22C2×D4×D14911yescharacteristic
257C4—21no—
258C4—42no—
259C4—41no—
260C4—41no—
261C4—2981no—
262C4—2981no—
263C4—2981no—
264C4—5961no—
265C4—5961no—
266C4—1492no—
267C4#41×D14912yes—
268C2—22no—
269C2—5964no—
270C2#2375013311yescharacteristic
271C2AGL(1,ℤ/8)×D14911yescharacteristic
272C2C2×#1801194311yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#484×C149C2
socleC22×C149C22×D4
prime radicalC22×D596C22
hypercenter#484D149
hypocenterC149#3110
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
1. #23750177C2semidirect
3. #23749960C2semidirect
4. #23749904C2semidirect
5. #23749829C2semidirect
8. #23749728C2semidirect
9. #23749724C2semidirect
10. #23749679C2semidirect
11. #484×C149C2semidirect
16. #18011910C22semidirect
17. #18011909C22semidirect
21. Q8×Dic149C22semidirect
23. #18011876C22semidirect
31. #18011844C22semidirect
32. #18011840C22semidirect
33. #18011834C22semidirect
37. #18011821C22semidirect
40. #107×C149C22semidirect
41. #103×C149C22semidirect
136. C149#3110semidirect
141. #484D149semidirect
171. #107C2×D149semidirect
174. #103C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501772
C2×#180118732
#237499602
#237499042
#237498292
#237497782
#237497752
#237497282
#237497242
#237496792
#484×C1492
#3110149