Finite Group Databasebeta

← #34055933

Subgroups — #34055933

Order 19072.

328 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 117 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#23750182C211yesmaximal, characteristic, complemented
2#23750159C211yesmaximal, characteristic
3#23750034C211yesmaximal, characteristic, complemented
4#23750034C211yesmaximal, characteristic, complemented
5#23749985C211yesmaximal, characteristic, complemented
6#23749985C211yesmaximal, characteristic, complemented
7#23749967C212yesmaximal, complemented
8#23749950C212yesmaximal
9#23749933C212yesmaximal, complemented
10#23749926C212yesmaximal, complemented
11#432×C149C211yesmaximal, characteristic, complemented
12#18011911C2211yescharacteristic
13#18011911C2211yescharacteristic
14#18011905—21no—
15#18011903C2211yescharacteristic
16#18011903C2212yes—
17#18011899C2211yescharacteristic
18#18011894—21no—
19#18011890—21no—
20#18011890—21no—
21#18011890C2211yescharacteristic
22#18011885C2211yescharacteristic
23C4×Dic298—21no—
24C4×Dic298—21no—
25C4×Dic298C2211yescharacteristic
26C4×D596C2211yescharacteristic
27C4×C22⋊D149—21no—
28#18011870C2212yes—
29#18011868—21no—
30#18011845C2212yes—
31#18011845C2212yes—
32#18011843C2212yes—
33#18011843C2212yes—
34#18011836C2212yes—
35#18011836C2212yes—
36#18011833C2212yes—
37#18011833C2212yes—
38C2×C42×C149C2211yescharacteristic
39C4⋊C8×C149C2212yes—
40C22⋊C8×C149C2212yes—
41#97×C149C2211yescharacteristic
42#97×C149C2211yescharacteristic
43C2×Dic298—21no—
44C2×Dic298—21no—
45C2×Dic298C2311yescharacteristic
46C2×D596C2311yescharacteristic
47C2×C22⋊D149—21no—
48C2×C4×D149—21no—
49C4⋊Dic149—21no—
50C4⋊Dic149—21no—
51C4⋊Dic149C2312yes—
52C4⋊Dic149C2312yes—
53C4⋊Dic149C2311yescharacteristic
54C4⋊Dic149C2311yescharacteristic
55#14558715—21no—
56#14558715—21no—
57#14558715—21no—
58#14558715—21no—
59#14558715—22no—
60#14558715—22no—
61C22⋊Dic149—22no—
62C22⋊Dic149—21no—
63#14558713—21no—
64#14558713—21no—
65#14558713—21no—
66#14558713—21no—
67C4×Dic149—21no—
68C4×Dic149—22no—
69C22×C4×C149D411yescharacteristic
70C22×C4×C149D411yescharacteristic
71C22×C4×C149C2311yescharacteristic
72C2×C8×C149C2312yes—
73C2×C8×C149C2312yes—
74C42×C149D411yescharacteristic
75C42×C149D411yescharacteristic
76C42×C149C2311yescharacteristic
77C42×C149C2311yescharacteristic
78C22×D149—21no—
79Dic298—22no—
80Dic298—42no—
81Dic298—42no—
82D596—22no—
83C22⋊D149—42no—
84C2×Dic149—21no—
85C2×Dic149—21no—
86C2×Dic149—22no—
87C2×Dic149—22no—
88C2×Dic149—21no—
89C4×D149—42no—
90C23×C149C2×D411yescharacteristic
91C2×C4×C149—22no—
92C2×C4×C149—41no—
93C2×C4×C149—41no—
94C2×C4×C149C2×D411yescharacteristic
95C2×C4×C149C2×D411yescharacteristic
96C2×C4×C149C2×D411yescharacteristic
97C2×C4×C149C2×D411yescharacteristic
98C2×C4×C149C2×D411yescharacteristic
99C2×C4×C149C2411yescharacteristic
100C8×C149—22no—
101C8×C149—22no—
102C22×C149—21no—
103C22×C149—21no—
104C22×C149—21no—
105C22×C149C22×D411yescharacteristic
106C2×D149—41no—
107C2×D149—41no—
108C2×D149—41no—
109C4×C149—21no—
110C4×C149—21no—
111C4×C149—21no—
112C4×C149—21no—
113C4×C149—21no—
114C4×C1492−1+412yes—
115Dic149—41no—
116Dic149—41no—
117Dic149—41no—
118Dic149—42no—
119Dic149—42no—
120C2×C149—41no—
121C2×C149#53611yescharacteristic
122C2×C149#57511yescharacteristic
123C2×C149#57511yescharacteristic
124D149—81no—
125C149#324011yescharacteristic, complemented, Sylow
126#3240—1491nomaximal, Sylow
127#533—1491no—
128#529—1491no—
129#501—1491no—
130#501—1491no—
131#489—1491no—
132#489—1491no—
133#485—1492no—
134#482—1492no—
135#479—1492no—
136#478—1492no—
137#432D14911yescharacteristic, complemented
138C4⋊Q8—1491no—
139C4⋊Q8—1491no—
140#126—2981no—
141#125—1491no—
142#125—1492no—
143#124—1491no—
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×C42C2×D14911yescharacteristic
157#107—1492no—
158#107—1492no—
159#106—1492no—
160#106—1492no—
161C4⋊C8C2×D14912yes—
162#103—1492no—
163#103—1492no—
164#102—1492no—
165#102—1492no—
166C22⋊C8C2×D14912yes—
167#97C2×D14911yescharacteristic
168#97C2×D14911yescharacteristic
169C2×Q8—2981no—
170C2×Q8—2981no—
171C2×Q8—1491no—
172C2×D4—2981no—
173C2×D4—1491no—
174C22×C4—2981no—
175C22×C4D59611yescharacteristic
176C22×C4D59611yescharacteristic
177C22×C4C22×D14911yescharacteristic
178C2×C8C22×D14912yes—
179C2×C8C22×D14912yes—
180C4⋊C4—2981no—
181C4⋊C4—2981no—
182C4⋊C4—2981no—
183C4⋊C4—2982no—
184C4⋊C4—2982no—
185C4⋊C4—2981no—
186C4⋊C4—2981no—
187C4⋊C4—2981no—
188C4⋊C4—1492no—
189C4⋊C4—1492no—
190C4⋊C4—1491no—
191C4⋊C4—1491no—
192C22⋊C4—2982no—
193C22⋊C4—2981no—
194C22⋊C4—2981no—
195C22⋊C4—2981no—
196C22⋊C4—2981no—
197C22⋊C4—2981no—
198C42—2981no—
199C42—2982no—
200C42D59611yescharacteristic
201C42D59611yescharacteristic
202C42C22×D14911yescharacteristic
203C42C22×D14911yescharacteristic
204C23—2981no—
205C23C2×D59611yescharacteristic
206Q8—2982no—
207Q8—5962no—
208Q8—5962no—
209D4—2982no—
210D4—5962no—
211C2×C4—22no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—2981no—
215C2×C4—2981no—
216C2×C4—2982no—
217C2×C4—2982no—
218C2×C4—2981no—
219C2×C4—5962no—
220C2×C4C2×D59611yescharacteristic
221C2×C4C2×D59611yescharacteristic
222C2×C4C2×D59611yescharacteristic
223C2×C4C2×D59611yescharacteristic
224C2×C4C2×D59611yescharacteristic
225C2×C4C23×D14911yescharacteristic
226C8—22no—
227C8—22no—
228C22—21no—
229C22—21no—
230C22—21no—
231C22—5961no—
232C22—5961no—
233C22—5961no—
234C22C22×D59611yescharacteristic
235C4—21no—
236C4—21no—
237C4—21no—
238C4—21no—
239C4—21no—
240C4—5961no—
241C4—5961no—
242C4—5962no—
243C4—5962no—
244C4—5961no—
245C4#1801195812yes—
246C2—41no—
247C2—11921no—
248C2#2375020111yescharacteristic
249C2#2375042511yescharacteristic
250C2#2375042511yescharacteristic
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#432×C149C2
socleC22×C149C22×D4
prime radical#18011885C22
hypercenter#432D149
hypocenterC149#3240
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #23750182C2semidirect
3. #23750034C2semidirect
4. #23750034C2semidirect
5. #23749985C2semidirect
6. #23749985C2semidirect
7. #23749967C2semidirect
9. #23749933C2semidirect
10. #23749926C2semidirect
11. #432×C149C2semidirect
125. C149#3240semidirect
137. #432D149semidirect

Maximal subgroups

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

subgroupindex
#237501822
#237501592
#237500342
#237499852
#237499672
#237499502
#237499332
#237499262
#432×C1492
#3240149