Finite Group Databasebeta

← #34057581

Subgroups — #34057581

Order 19072.

324 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 125 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#23750354C211yesmaximal, characteristic
2#23750350C211yesmaximal, characteristic
3#23750028C211yesmaximal, characteristic
4#23750025C212yesmaximal
5#23749935C212yesmaximal
6#23749930C212yesmaximal
7#23749911C211yesmaximal, characteristic
8#23749749C211yesmaximal, characteristic
9C4×#14558726C211yesmaximal, characteristic
10#23749717C212yesmaximal
11#475×C149C211yesmaximal, characteristic
12C2×#14558726C2211yescharacteristic
13#18011911—21no—
14#18011911C2211yescharacteristic
15#18011909—21no—
16#18011902—22no—
17#18011902C2212yes—
18#18011902C2212yes—
19#18011901—22no—
20Q8×Dic149—21no—
21Q8×Dic149C2212yes—
22C4×Dic298—21no—
23C4×Dic298C2211yescharacteristic
24C4×Dic298C2211yescharacteristic
25#18011876C2212yes—
26#18011844C2212yes—
27#18011844C2212yes—
28#18011844C2211yescharacteristic
29#18011843C2212yes—
30#18011840C2212yes—
31#18011836C2212yes—
32#18011835C2211yescharacteristic
33#18011834C2211yescharacteristic
34C4×#11924746C2211yescharacteristic
35C8×Dic149C2212yes—
36C4⋊Q8×C149C2211yescharacteristic
37C4×Q8×C149C2211yescharacteristic
38#106×C149C2212yes—
39C4⋊C8×C149C2211yescharacteristic
40#103×C149C2212yes—
41C2×Dic298—21no—
42C2×Dic298D411yescharacteristic
43C2×Dic298C2311yescharacteristic
44#14558726Q814yescomplemented
45C2×#11924746C2311yescharacteristic
46C2×#11924746C2311yescharacteristic
47C4⋊Dic149—22no—
48C4⋊Dic149—22no—
49C4⋊Dic149—22no—
50C4⋊Dic149—21no—
51C4⋊Dic149D411yescharacteristic
52C4⋊Dic149C2312yes—
53C4⋊Dic149C2311yescharacteristic
54#14558715—22no—
55#14558715—22no—
56#14558715—22no—
57#14558715—21no—
58#14558715D412yes—
59C4×Dic149—22no—
60C4×Dic149—22no—
61C4×Dic149—21no—
62C4×Dic149C2312yes—
63C2×Q8×C149—21no—
64C2×Q8×C149C2311yescharacteristic
65C2×C8×C149C2312yes—
66C4⋊C4×C149—21no—
67C4⋊C4×C149—21no—
68C4⋊C4×C149C2312yes—
69C4⋊C4×C149C2311yescharacteristic
70C42×C149—21no—
71C42×C149C2311yescharacteristic
72Dic298—22no—
73Dic298—21no—
74Dic298—42no—
75Dic298C2×Q812yes—
76C2×Dic149—21no—
77C2×Dic149—22no—
78C2×Dic149—21no—
79C2×Dic149C2×D412yes—
80C2×Dic149C2×D412yes—
81#11924746—21no—
82#11924746C2×Q812yes—
83Q8×C149—21no—
84Q8×C149—42no—
85Q8×C149C2×Q812yes—
86C2×C4×C149—21no—
87C2×C4×C149—21no—
88C2×C4×C149—22no—
89C2×C4×C149C2×D411yescharacteristic
90C2×C4×C149C2×D411yescharacteristic
91C2×C4×C149C2411yescharacteristic
92C8×C149—22no—
93C22×C149C22×D411yescharacteristic
94C4×C149—22no—
95C4×C149—21no—
96C4×C149—42no—
97C4×C149—41no—
98C4×C149#13512yes—
99C4×C149C22×Q811yescharacteristic
100C4×C1492−1+411yescharacteristic
101Dic149—22no—
102Dic149—22no—
103Dic149—22no—
104Dic149—42no—
105Dic149—41no—
106C2×C149D4×Q811yescharacteristic
107C2×C149C2×#13511yescharacteristic
108C2×C149#57811yescharacteristic
109C149#338311yescharacteristic, complemented, Sylow
110#3383—1491nomaximal, Sylow
111#557—1491no—
112#557—1491no—
113#500—1491no—
114#499—1492no—
115#479—1492no—
116#479—1492no—
117#475—1491no—
118#475D14911yescharacteristic
119C8×Q8—1491no—
120C4×Q16—1491no—
121C4×Q16—1492no—
122C2×Q16—1491no—
123C4⋊Q8—2981no—
124C4⋊Q8—2981no—
125C4⋊Q8—1491no—
126C4⋊Q8C2×D14911yescharacteristic
127#125—2982no—
128#125—2982no—
129#125—1492no—
130#125—1492no—
131C4×Q8—2981no—
132C4×Q8—2981no—
133C4×Q8—1492no—
134C4×Q8—1492no—
135C4×Q8—1491no—
136C4×Q8—1491no—
137C4×Q8C2×D14911yescharacteristic
138#107—1491no—
139#107—1492no—
140#107—1492no—
141#106—1492no—
142#106C2×D14912yes—
143C4⋊C8—1492no—
144C4⋊C8C2×D14911yescharacteristic
145#103—1491no—
146#103—1492no—
147#103—1491no—
148#103C2×D14912yes—
149C4×C8—1492no—
150C4×C8—1491no—
151C2×Q8—21no—
152C2×Q8—2981no—
153C2×Q8—1491no—
154C2×Q8—1491no—
155C2×Q8C22×D14911yescharacteristic
156Q16—1494no—
157C2×C8—1491no—
158C2×C8—1491no—
159C2×C8C22×D14912yes—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—2982no—
163C4⋊C4—2982no—
164C4⋊C4—2982no—
165C4⋊C4—2982no—
166C4⋊C4—2982no—
167C4⋊C4—2982no—
168C4⋊C4—2981no—
169C4⋊C4—2981no—
170C4⋊C4—1491no—
171C4⋊C4—1492no—
172C4⋊C4—1491no—
173C4⋊C4—1492no—
174C4⋊C4C22×D14911yescharacteristic
175C4⋊C4C22×D14912yes—
176C42—21no—
177C42—2982no—
178C42—2982no—
179C42—2981no—
180C42—1492no—
181C42C22×D14911yescharacteristic
182Q8—21no—
183Q8—42no—
184Q8—2982no—
185Q8—2981no—
186Q8—5962no—
187Q8—1492no—
188Q8Q8×D14912yes—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—2981no—
193C2×C4—2981no—
194C2×C4—2982no—
195C2×C4—1492no—
196C2×C4—1492no—
197C2×C4D4×D14911yescharacteristic
198C2×C4D4×D14911yescharacteristic
199C2×C4C23×D14911yescharacteristic
200C8—22no—
201C8—2981no—
202C8—1492no—
203C22C2×D4×D14911yescharacteristic
204C4—21no—
205C4—22no—
206C4—42no—
207C4—41no—
208C4—2982no—
209C4—2982no—
210C4—2982no—
211C4—5962no—
212C4—5961no—
213C4#1801193212yes—
214C4C2×Q8×D14911yescharacteristic
215C4#1801195811yescharacteristic
216C2#2375028811yescharacteristic
217C2C2×#1801193211yescharacteristic
218C2#2375044111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#475×C149C2
socle, prime radicalC22×C149C22×D4
hypercenter#475D149
hypocenterC149#3383
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
44. #14558726Q8semidirect
109. C149#3383semidirect

Maximal subgroups

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

subgroupindex
#237503542
#237503502
#237500282
#237500252
#237499352
#237499302
#237499112
#237497492
C4×#145587262
#237497172
#475×C1492
#3383149