Finite Group Databasebeta

← #34055934

Subgroups — #34055934

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#23750160C211yesmaximal, characteristic
3#23750035C211yesmaximal, characteristic, complemented
4#23749987C211yesmaximal, characteristic, complemented
5#23749985C211yesmaximal, characteristic, complemented
6#23749969C212yesmaximal, complemented
7#23749952C212yesmaximal
8#23749931C212yesmaximal, complemented
9#23749924C212yesmaximal, complemented
10#23749680C211yesmaximal, characteristic, complemented
11#501×C149C211yesmaximal, characteristic, complemented
12#18011911C2211yescharacteristic
13#18011906—21no—
14#18011902C2212yes—
15#18011899C2211yescharacteristic
16#18011896—21no—
17#18011891—21no—
18#18011891C2211yescharacteristic
19#18011887—21no—
20#18011886C2211yescharacteristic
21Q8×Dic149—21no—
22#18011876—21no—
23#18011876C2211yescharacteristic
24#18011873—21no—
25#18011873C2211yescharacteristic
26#18011869—21no—
27#18011869C2212yes—
28C42×D149C2211yescharacteristic
29#18011844C2212yes—
30#18011842C2212yes—
31#18011840C2212yes—
32#18011836C2212yes—
33#18011834C2212yes—
34#18011833C2212yes—
35#18011831C2212yes—
36#18011823C2212yes—
37#18011822C2211yescharacteristic
38C4⋊Q8×C149C2211yescharacteristic
39#125×C149C2211yescharacteristic
40#107×C149C2212yes—
41#106×C149C2212yes—
42#97×C149C2211yescharacteristic
43C2×Dic298—21no—
44C2×Dic298C2311yescharacteristic
45C2×D596—21no—
46C2×D596C2311yescharacteristic
47C2×C4×D149—21no—
48C2×C4×D149D411yescharacteristic
49C2×C4×D149D411yescharacteristic
50C2×C4×D149C2311yescharacteristic
51C2×#11924746C2312yes—
52C4⋊Dic149—21no—
53C4⋊Dic149—22no—
54C4⋊Dic149—21no—
55C4⋊Dic149C2312yes—
56#14558715—21no—
57#14558715—22no—
58#14558713—22no—
59#14558713—21no—
60#14558713—21no—
61#14558713—21no—
62#14558713—21no—
63#14558713—21no—
64C4×Dic149—21no—
65C4×Dic149—22no—
66C4×Dic149D411yescharacteristic
67C4×Dic149D411yescharacteristic
68C4×Dic149C2311yescharacteristic
69C2×Q8×C149—21no—
70C2×C8×C149C2312yes—
71C4⋊C4×C149—21no—
72C4⋊C4×C149—21no—
73C4⋊C4×C149—21no—
74C4⋊C4×C149C2311yescharacteristic
75C4⋊C4×C149C2312yes—
76C4⋊C4×C149C2311yescharacteristic
77C42×C149C2311yescharacteristic
78C22×D149—21no—
79C22×D149C2×D411yescharacteristic
80Dic298—22no—
81Dic298—42no—
82D596—22no—
83D596—42no—
84C2×Dic149—22no—
85C2×Dic149—21no—
86C2×Dic149C2×D411yescharacteristic
87C2×Dic149C2×D411yescharacteristic
88C2×Dic149C2×D411yescharacteristic
89C4×D149—22no—
90C4×D149—41no—
91C4×D149—41no—
92C4×D149—42no—
93#11924746—22no—
94Q8×C149—42no—
95C2×C4×C149—21no—
96C2×C4×C149—21no—
97C2×C4×C149—22no—
98C2×C4×C149C2×D411yescharacteristic
99C2×C4×C149C2×D411yescharacteristic
100C2×C4×C149C2411yescharacteristic
101C8×C149—22no—
102C22×C149C22×D411yescharacteristic
103C2×D149—21no—
104C2×D149—21no—
105C2×D149—21no—
106C2×D149—41no—
107C2×D149—41no—
108C2×D149—41no—
109C4×C149—21no—
110C4×C149—21no—
111C4×C149—42no—
112C4×C149—41no—
113C4×C149—41no—
114C4×C1492−1+412yes—
115Dic149—21no—
116Dic149—21no—
117Dic149—21no—
118Dic149—41no—
119Dic149—42no—
120C2×C149#53611yescharacteristic
121C2×C149#57511yescharacteristic
122C2×C149#57511yescharacteristic
123D149—41no—
124D149—81no—
125C149#324011yescharacteristic, complemented, Sylow
126#3240—1491nomaximal, Sylow
127#533—1491no—
128#529—1491no—
129#501—1491no—
130#501D14911yescharacteristic, complemented
131#489—1491no—
132#489—1491no—
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#125C2×D14911yescharacteristic
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×C42—1491no—
157#107—1492no—
158#107C2×D14912yes—
159#106—1492no—
160#106C2×D14912yes—
161C4⋊C8—1492no—
162#103—1492no—
163#103—1492no—
164#102—1492no—
165#102—1492no—
166C22⋊C8—1492no—
167#97—1491no—
168#97C2×D14911yescharacteristic
169C2×Q8—21no—
170C2×Q8—2981no—
171C2×Q8—1491no—
172C2×D4—2981no—
173C2×D4—1491no—
174C22×C4—2981no—
175C22×C4—1491no—
176C22×C4—1491no—
177C22×C4—1491no—
178C2×C8—1492no—
179C2×C8C22×D14912yes—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—2981no—
184C4⋊C4—2982no—
185C4⋊C4—2982no—
186C4⋊C4—2981no—
187C4⋊C4—2981no—
188C4⋊C4—1492no—
189C4⋊C4C22×D14912yes—
190C4⋊C4C22×D14911yescharacteristic
191C4⋊C4C22×D14911yescharacteristic
192C22⋊C4—2982no—
193C22⋊C4—2981no—
194C22⋊C4—2981no—
195C22⋊C4—2981no—
196C22⋊C4—2981no—
197C22⋊C4—2981no—
198C42—2981no—
199C42—2982no—
200C42—1491no—
201C42—1491no—
202C42—1491no—
203C42C22×D14911yescharacteristic
204C23—2981no—
205C23—1491no—
206Q8—42no—
207Q8—2982no—
208Q8—5962no—
209D4—2982no—
210D4—5962no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—21no—
214C2×C4—2982no—
215C2×C4—2981no—
216C2×C4—2982no—
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—2981no—
229C22—2981no—
230C22—2981no—
231C22—5961no—
232C22—5961no—
233C22—5961no—
234C22C2×D4×D14911yescharacteristic
235C4—21no—
236C4—21no—
237C4—41no—
238C4—42no—
239C4—41no—
240C4—2981no—
241C4—2981no—
242C4—2981no—
243C4—5962no—
244C4—5961no—
245C4#1801195912yes—
246C2—5961no—
247C2—11921no—
248C2#2375020011yescharacteristic
249C2#2375042111yescharacteristic
250C2#2375042411yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#501×C149C2
socleC22×C149C22×D4
prime radical#18011886C22
hypercenter#501D149
hypocenterC149#3240
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. #23750180C2semidirect
3. #23750035C2semidirect
4. #23749987C2semidirect
5. #23749985C2semidirect
6. #23749969C2semidirect
8. #23749931C2semidirect
9. #23749924C2semidirect
10. #23749680C2semidirect
11. #501×C149C2semidirect
125. C149#3240semidirect
130. #501D149semidirect

Maximal subgroups

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

subgroupindex
#237501802
#237501602
#237500352
#237499872
#237499852
#237499692
#237499522
#237499312
#237499242
#237496802
#501×C1492
#3240149