Finite Group Databasebeta

← #34055928

Subgroups — #34055928

Order 19072.

328 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 109 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#23750180C211yesmaximal, characteristic, complemented
2#23750154C211yesmaximal, characteristic
3#23750034C211yesmaximal, characteristic, complemented
4#23750031C211yesmaximal, characteristic, complemented
5#23749984C211yesmaximal, characteristic, complemented
6#23749965C212yesmaximal, complemented
7#23749948C212yesmaximal
8#23749930C212yesmaximal, complemented
9#23749923C212yesmaximal, complemented
10#23749680C211yesmaximal, characteristic, complemented
11#489×C149C211yesmaximal, characteristic, complemented
12#18011911C2211yescharacteristic
13#18011904—21no—
14#18011903C2211yescharacteristic
15#18011902C2212yes—
16#18011893—21no—
17#18011891—21no—
18#18011887—21no—
19#18011887C2211yescharacteristic
20#18011882C2211yescharacteristic
21Q8×Dic149—21no—
22Q8×Dic149C2211yescharacteristic
23#18011876—21no—
24D4×Dic149C2211yescharacteristic
25#18011871—21no—
26#18011869C2212yes—
27#18011867—21no—
28C42×D149C2211yescharacteristic
29#18011845C2212yes—
30#18011844C2212yes—
31#18011843C2212yes—
32#18011842C2212yes—
33#18011840C2212yes—
34#18011835C2212yes—
35#18011832C2212yes—
36#18011823C2212yes—
37#18011822C2211yescharacteristic
38C4⋊Q8×C149C2211yescharacteristic
39#124×C149C2211yescharacteristic
40#103×C149C2212yes—
41#102×C149C2212yes—
42#97×C149C2211yescharacteristic
43C2×Dic298—21no—
44C2×C22⋊D149—21no—
45C22×Dic149—21no—
46C2×C4×D149D411yescharacteristic
47C2×C4×D149D411yescharacteristic
48C2×C4×D149C2311yescharacteristic
49C2×#11924746C2312yes—
50C4⋊Dic149—21no—
51C4⋊Dic149—22no—
52C4⋊Dic149—21no—
53C4⋊Dic149C2312yes—
54C4⋊Dic149C2311yescharacteristic
55C4⋊Dic149C2311yescharacteristic
56#14558715—21no—
57#14558715—22no—
58#14558715—21no—
59#14558715—21no—
60C22⋊Dic149—21no—
61C22⋊Dic149—21no—
62#14558713—22no—
63#14558713—21no—
64C4×Dic149—21no—
65C4×Dic149—22no—
66C4×Dic149D411yescharacteristic
67C4×Dic149D411yescharacteristic
68C4×Dic149C2311yescharacteristic
69C2×Q8×C149—21no—
70C2×Q8×C149C2311yescharacteristic
71C2×D4×C149C2311yescharacteristic
72C2×C8×C149C2312yes—
73C4⋊C4×C149—21no—
74C4⋊C4×C149C2312yes—
75C22⋊C4×C149—21no—
76C22⋊C4×C149—21no—
77C42×C149C2311yescharacteristic
78C22×D149C2×D411yescharacteristic
79Dic298—42no—
80C22⋊D149—42no—
81C2×Dic149—21no—
82C2×Dic149—21no—
83C2×Dic149—22no—
84C2×Dic149—42no—
85C2×Dic149C2×D411yescharacteristic
86C2×Dic149C2×D411yescharacteristic
87C2×Dic149C2×D411yescharacteristic
88C4×D149—22no—
89C4×D149—41no—
90C4×D149—41no—
91#11924746—22no—
92C23×C149—21no—
93Q8×C149—22no—
94Q8×C149—42no—
95D4×C149—22no—
96C2×C4×C149—21no—
97C2×C4×C149—22no—
98C2×C4×C149C2×D411yescharacteristic
99C2×C4×C149C2×D411yescharacteristic
100C2×C4×C149C2411yescharacteristic
101C8×C149—22no—
102C22×C149—41no—
103C22×C149—41no—
104C22×C149—41no—
105C22×C149C22×D411yescharacteristic
106C2×D149—21no—
107C2×D149—21no—
108C2×D149—21no—
109C4×C149—21no—
110C4×C149—21no—
111C4×C149—41no—
112C4×C149—42no—
113C4×C1492−1+412yes—
114Dic149—21no—
115Dic149—21no—
116Dic149—21no—
117Dic149—41no—
118Dic149—41no—
119Dic149—42no—
120C2×C149—81no—
121C2×C149#53611yescharacteristic
122C2×C149#57511yescharacteristic
123C2×C149#57511yescharacteristic
124D149—41no—
125C149#324011yescharacteristic, complemented, Sylow
126#3240—1491nomaximal, Sylow
127#533—1491no—
128#529—1491no—
129#501—1491no—
130#501—1491no—
131#489—1491no—
132#489D14911yescharacteristic, complemented
133#485—1492no—
134#482—1492no—
135#479—1492no—
136#478—1492no—
137#432—1491no—
138C4⋊Q8—1491no—
139C4⋊Q8C2×D14911yescharacteristic
140#126—2981no—
141#125—1492no—
142#125—1491no—
143#124C2×D14911yescharacteristic
144#123—2981no—
145C22⋊Q8—2981no—
146C22⋊Q8—2981no—
147C22⋊Q8—1491no—
148#121—1491no—
149C4×Q8—2981no—
150C4×Q8—2981no—
151C4×Q8—1491no—
152C4×D4—2981no—
153C4×D4—1491no—
154#117—2981no—
155#117—1492no—
156C2×C42—1491no—
157#107—1492no—
158#107—1492no—
159#106—1492no—
160#106—1492no—
161C4⋊C8—1492no—
162#103—1492no—
163#103C2×D14912yes—
164#102—1492no—
165#102C2×D14912yes—
166C22⋊C8—1492no—
167#97—1491no—
168#97C2×D14911yescharacteristic
169C2×Q8—21no—
170C2×Q8—2981no—
171C2×Q8C22×D14911yescharacteristic
172C2×D4—2981no—
173C2×D4C22×D14911yescharacteristic
174C22×C4—2981no—
175C22×C4—1491no—
176C22×C4—1491no—
177C22×C4—1491no—
178C2×C8—1492no—
179C2×C8C22×D14912yes—
180C4⋊C4—21no—
181C4⋊C4—2981no—
182C4⋊C4—2982no—
183C4⋊C4—2982no—
184C4⋊C4—2981no—
185C4⋊C4—2981no—
186C4⋊C4—2981no—
187C4⋊C4—2981no—
188C4⋊C4—1492no—
189C4⋊C4—1491no—
190C4⋊C4—1491no—
191C4⋊C4C22×D14912yes—
192C22⋊C4—21no—
193C22⋊C4—21no—
194C22⋊C4—2982no—
195C22⋊C4—2981no—
196C22⋊C4—2981no—
197C22⋊C4—2981no—
198C42—2981no—
199C42—2982no—
200C42—1491no—
201C42—1491no—
202C42—1491no—
203C42C22×D14911yescharacteristic
204C23—21no—
205C23—1491no—
206Q8—22no—
207Q8—42no—
208Q8—5962no—
209D4—22no—
210D4—5962no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—2982no—
214C2×C4—2981no—
215C2×C4—2982no—
216C2×C4—2981no—
217C2×C4—5961no—
218C2×C4—5961no—
219C2×C4—5962no—
220C2×C4—1491no—
221C2×C4—1491no—
222C2×C4—1491no—
223C2×C4D4×D14911yescharacteristic
224C2×C4D4×D14911yescharacteristic
225C2×C4C23×D14911yescharacteristic
226C8—22no—
227C8—2982no—
228C22—41no—
229C22—41no—
230C22—41no—
231C22—2981no—
232C22—2981no—
233C22—2981no—
234C22C2×D4×D14911yescharacteristic
235C4—21no—
236C4—21no—
237C4—42no—
238C4—41no—
239C4—2981no—
240C4—2981no—
241C4—2981no—
242C4—5961no—
243C4—5961no—
244C4—5962no—
245C4#1801195812yes—
246C2—81no—
247C2—5961no—
248C2#2375019511yescharacteristic
249C2#2375042111yescharacteristic
250C2#2375042411yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#489×C149C2
socleC22×C149C22×D4
prime radical#18011882C22
hypercenter#489D149
hypocenterC149#3240
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #23750180C2semidirect
3. #23750034C2semidirect
4. #23750031C2semidirect
5. #23749984C2semidirect
6. #23749965C2semidirect
8. #23749930C2semidirect
9. #23749923C2semidirect
10. #23749680C2semidirect
11. #489×C149C2semidirect
125. C149#3240semidirect
132. #489D149semidirect

Maximal subgroups

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

subgroupindex
#237501802
#237501542
#237500342
#237500312
#237499842
#237499652
#237499482
#237499302
#237499232
#237496802
#489×C1492
#3240149