Finite Group Databasebeta

← #34045840

Subgroups — #34045840

Order 19072.

258 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 85 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×#18011902C211yesmaximal, characteristic
2C2×#18011835C211yesmaximal, characteristic
3#23749532C211yesmaximal, characteristic
4#23749388C211yesmaximal, characteristic
5#23749387C211yesmaximal, characteristic
6#23749379C211yesmaximal, characteristic
7C2×#103×C149C211yesmaximal, characteristic
8C22×#11924746C2211yescharacteristic
9#18011902—22no—
10#18011902—22no—
11C2×C4⋊Dic149—21no—
12C2×C4⋊Dic149C2211yescharacteristic
13C2×C4⋊Dic149C2211yescharacteristic
14C2×#14558715—21no—
15C2×C4×Dic149C2211yescharacteristic
16#18011835—22no—
17#18011818—21no—
18#18011818—21no—
19C22×Q8×C149C2211yescharacteristic
20C22×C8×C149C2211yescharacteristic
21C2×C4⋊C4×C149C2211yescharacteristic
22#103×C149—22no—
23C22×Dic149—21no—
24C22×Dic149—21no—
25C22×Dic149D411yescharacteristic
26C22×Dic149D411yescharacteristic
27C2×#11924746—21no—
28C2×#11924746—21no—
29C2×#11924746—21no—
30C4⋊Dic149—24no—
31C4⋊Dic149—21no—
32C4⋊Dic149—21no—
33C4⋊Dic149—21no—
34C4⋊Dic149D412yes—
35#14558715—24no—
36C4×Dic149—21no—
37C4×Dic149—21no—
38C2×Q8×C149—21no—
39C2×Q8×C149—21no—
40C2×Q8×C149—21no—
41C2×Q8×C149—21no—
42C2×Q8×C149—21no—
43C2×Q8×C149Q812yes—
44C22×C4×C149—21no—
45C22×C4×C149—21no—
46C22×C4×C149C2311yescharacteristic
47C2×C8×C149—21no—
48C2×C8×C149—21no—
49C2×C8×C149—21no—
50C4⋊C4×C149—21no—
51C4⋊C4×C149D412yes—
52C2×Dic149—22no—
53C2×Dic149—21no—
54C2×Dic149—21no—
55C2×Dic149—21no—
56C2×Dic149—21no—
57C2×Dic149—21no—
58C2×Dic149—21no—
59C2×Dic149—41no—
60C2×Dic149—41no—
61C2×Dic149—41no—
62C2×Dic149—41no—
63C2×Dic149—41no—
64#11924746—41no—
65C23×C149C2×D411yescharacteristic
66Q8×C149—22no—
67Q8×C149—22no—
68Q8×C149—41no—
69Q8×C149—41no—
70C2×C4×C149—22no—
71C2×C4×C149—22no—
72C2×C4×C149—41no—
73C2×C4×C149—41no—
74C2×C4×C149—41no—
75C2×C4×C149—41no—
76C2×C4×C149C2×D411yescharacteristic
77C2×C4×C149C2×D411yescharacteristic
78C2×C4×C149C2×Q811yescharacteristic
79C2×C4×C149#4111yescharacteristic
80C2×C4×C149#4111yescharacteristic
81C2×C4×C149#4111yescharacteristic
82C8×C149—41no—
83C22×C149#12011yescharacteristic
84C22×C149C22⋊Q811yescharacteristic
85C22×C149#12411yescharacteristic
86C22×C149#13511yescharacteristic
87C22×C149#13511yescharacteristic
88C22×C149#13711yescharacteristic
89C22×C149#13711yescharacteristic
90C4×C149—42no—
91C4×C149—42no—
92C4×C149C22⋊Q811yescharacteristic
93C4×C149C22⋊Q811yescharacteristic
94C4×C149#12411yescharacteristic
95C4×C149#12411yescharacteristic
96Dic149—41no—
97Dic149—41no—
98Dic149—42no—
99Dic149—81no—
100C2×C149#39311yescharacteristic
101C2×C149#45211yescharacteristic
102C2×C149#45211yescharacteristic
103C2×C149#47911yescharacteristic
104C2×C149#47911yescharacteristic
105C2×C149#48811yescharacteristic
106C2×C149#49111yescharacteristic
107C149#202611yescharacteristic, complemented, Sylow
108#2026—1491nomaximal, Sylow
109C2×#125—1491no—
110C2×#103—1491no—
111C2×#103D14911yescharacteristic
112#391—1491no—
113#340—1491no—
114#340—1491no—
115#336—1491no—
116C22×Q8C2×D14911yescharacteristic
117C22×C8—1491no—
118C22×C8C2×D14911yescharacteristic
119#125—2982no—
120#125—2982no—
121C2×C4⋊C4—2981no—
122C2×C4⋊C4—2981no—
123C2×C4⋊C4—1491no—
124C2×C4⋊C4—1491no—
125C2×C4⋊C4C2×D14911yescharacteristic
126C2×C42—1491no—
127#103—22no—
128#103—2982no—
129#95—2981no—
130#95—2981no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8Dic29812yes—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—2981no—
140C22×C4—2981no—
141C22×C4—1491no—
142C22×C4—1491no—
143C22×C4C22×D14911yescharacteristic
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—21no—
147C2×C8—2981no—
148C2×C8—2981no—
149C2×C8—2981no—
150C4⋊C4—21no—
151C4⋊C4—2984no—
152C4⋊C4—2984no—
153C4⋊C4—2981no—
154C4⋊C4—2981no—
155C4⋊C4—2981no—
156C4⋊C4—1492no—
157C4⋊C4C22⋊D14912yes—
158C42—2981no—
159C42—2981no—
160C23D4×D14911yescharacteristic
161Q8—22no—
162Q8—22no—
163Q8—41no—
164Q8—41no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—2981no—
172C2×C4—2981no—
173C2×C4—2981no—
174C2×C4—2981no—
175C2×C4—2981no—
176C2×C4—2981no—
177C2×C4—2982no—
178C2×C4—5961no—
179C2×C4—5961no—
180C2×C4—5961no—
181C2×C4—5961no—
182C2×C4—5961no—
183C2×C4D4×D14911yescharacteristic
184C2×C4C2×C22⋊D14911yescharacteristic
185C2×C4C2×Dic29811yescharacteristic
186C2×C4#1455873511yescharacteristic
187C2×C4#1455873511yescharacteristic
188C2×C4#1455873611yescharacteristic
189C8—41no—
190C8—5961no—
191C22#1801187911yescharacteristic
192C22#1801188811yescharacteristic
193C22#1801189711yescharacteristic
194C22#1801193211yescharacteristic
195C22#1801193411yescharacteristic
196C22#1801194011yescharacteristic
197C22#1801194311yescharacteristic
198C4—42no—
199C4—42no—
200C4—5961no—
201C4—5961no—
202C4—5962no—
203C4—11921no—
204C4#1801188811yescharacteristic
205C4#1801189011yescharacteristic
206C4#1801189711yescharacteristic
207C4#1801189811yescharacteristic
208C2#2374953711yescharacteristic
209C2#2374978411yescharacteristic
210C2#2374978611yescharacteristic
211C2#2374993011yescharacteristic
212C2#2374993411yescharacteristic
213C2#2374998111yescharacteristic
214C2#2374999211yescharacteristic
subgroupG/H
centerC23D4×D149
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
FittingC2×#103×C149C2
socle, prime radicalC23×C149C2×D4
hypercenterC2×#103D149
hypocenterC149#2026
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
107. C149#2026semidirect

Maximal subgroups

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

subgroupindex
C2×#180119022
C2×#180118352
#237495322
#237493882
#237493872
#237493792
C2×#103×C1492
#2026149