Finite Group Databasebeta

← #34055640

Subgroups — #34055640

Order 19072.

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

normal subgroups only

This group has 384 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#23750180C211yesmaximal, characteristic
2C4⋊Q8×D149C211yesmaximal, characteristic
3#23750005C211yesmaximal, characteristic, complemented
4#23750004C211yesmaximal, characteristic, complemented
5#23749977C211yesmaximal, characteristic, complemented
6#23749834C214yesmaximal, complemented
7#23749782C214yesmaximal
8#23749676C211yesmaximal, characteristic
9#487×C149C211yesmaximal, characteristic, complemented
10C2×Q8×D149C2212yes—
11C2×Dic596C2214yes—
12C2×#14558726C2214yes—
13#18011911C2211yescharacteristic
14#18011911C2211yescharacteristic
15#18011910—21no—
16#18011910—21no—
17#18011909C2212yes—
18#18011902—21no—
19#18011891C2212yes—
20#18011887—21no—
21Q8×Dic149—21no—
22#18011876C2212yes—
23#18011869—21no—
24C4⋊C4×D149—21no—
25C4⋊C4×D149—21no—
26C42×D149C2211yescharacteristic
27#18011840C2212yes—
28#18011834C2214yes—
29#18011823C2212yes—
30C4×#11924746C2211yescharacteristic
31C4⋊Q8×C149C2211yescharacteristic
32C4⋊Q8×C149C2211yescharacteristic
33#103×C149C2214yes—
34C4×C8×C149C2211yescharacteristic
35C2×Dic298—22no—
36C2×Dic298C2312yes—
37C2×Dic298C2312yes—
38Q8×D149—44no—
39C2×C4×D149—22no—
40C2×C4×D149D411yescharacteristic
41C2×C4×D149D411yescharacteristic
42C2×C4×D149C2311yescharacteristic
43Dic596—44no—
44#14558726—44no—
45C2×#11924746C2312yes—
46C4⋊Dic149—22no—
47C4⋊Dic149—21no—
48C4⋊Dic149—21no—
49C4⋊Dic149—21no—
50C4⋊Dic149—21no—
51#14558715—22no—
52#14558715—22no—
53#14558715—22no—
54#14558713—22no—
55C4×Dic149—22no—
56C4×Dic149D411yescharacteristic
57C4×Dic149D411yescharacteristic
58C4×Dic149C2311yescharacteristic
59C2×Q8×C149—21no—
60C2×Q8×C149C2312yes—
61C2×C8×C149C2312yes—
62C4⋊C4×C149—21no—
63C4⋊C4×C149—21no—
64C4⋊C4×C149—21no—
65C4⋊C4×C149C2312yes—
66C42×C149C2311yescharacteristic
67C22×D149C2×D411yescharacteristic
68Dic298—24no—
69Dic298—24no—
70Dic298—44no—
71C2×Dic149—22no—
72C2×Dic149—22no—
73C2×Dic149C2×D411yescharacteristic
74C2×Dic149C2×D411yescharacteristic
75C2×Dic149C2×D411yescharacteristic
76C4×D149—22no—
77C4×D149—22no—
78C4×D149—44no—
79C4×D149Q1614yescomplemented
80#11924746—22no—
81Q8×C149—24no—
82Q8×C149—42no—
83C2×C4×C149—22no—
84C2×C4×C149—22no—
85C2×C4×C149C2×D411yescharacteristic
86C2×C4×C149C2×D411yescharacteristic
87C2×C4×C149C2411yescharacteristic
88C8×C149—22no—
89C22×C149C22×D411yescharacteristic
90C2×D149—21no—
91C2×D149—21no—
92C2×D149C2×Q1612yes—
93C4×C149—42no—
94C4×C149—42no—
95C4×C149C2×Q1612yes—
96C4×C149#13712yes—
97C4×C149H(5,𝔽2)12yes—
98Dic149—21no—
99Dic149—21no—
100Dic149—42no—
101Dic149—42no—
102Dic149C2×Q1612yes—
103C2×C149#53511yescharacteristic
104C2×C149C22×Q1611yescharacteristic
105C2×C149C2×#13711yescharacteristic
106D149—22no—
107C149#320911yescharacteristic, complemented, Sylow
108#3209—1491nomaximal, Sylow
109#533—1491no—
110C2×C4⋊Q8—1491no—
111#494—1491no—
112#494—1491no—
113#487—1491no—
114#487D14911yescharacteristic, complemented
115#462—1494no—
116#451—1494no—
117#431—1491no—
118C22×Q8—1492no—
119C2×Q16—1494no—
120C2×Q16—1494no—
121C4⋊Q8—2981no—
122C4⋊Q8—2981no—
123C4⋊Q8—1492no—
124C4⋊Q8—1491no—
125C4⋊Q8—1491no—
126C4⋊Q8C2×D14911yescharacteristic
127C4⋊Q8C2×D14911yescharacteristic
128#125—2981no—
129C22⋊Q8—2981no—
130C22⋊Q8—1492no—
131C4×Q8—2981no—
132C4×Q8—1492no—
133#117—2981no—
134C2×C4⋊C4—2981no—
135C2×C4⋊C4—2981no—
136C2×C42—1491no—
137C4⋊C8—1492no—
138#103—1494no—
139#103C2×D14914yes—
140C22⋊C8—1492no—
141C4×C8—1491no—
142C4×C8C2×D14911yescharacteristic
143C2×Q8—21no—
144C2×Q8—2982no—
145C2×Q8—5964no—
146C2×Q8—1492no—
147C2×Q8—1492no—
148C2×Q8C22×D14912yes—
149C22×C4—2982no—
150C22×C4—1491no—
151C22×C4—1491no—
152C22×C4—1491no—
153Q16—5964no—
154Q16—5964no—
155C2×C8—1492no—
156C2×C8C22×D14912yes—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—2982no—
161C4⋊C4—2982no—
162C4⋊C4—2982no—
163C4⋊C4—2982no—
164C4⋊C4—2981no—
165C4⋊C4—2981no—
166C4⋊C4—2981no—
167C4⋊C4—2981no—
168C4⋊C4C22×D14912yes—
169C22⋊C4—2982no—
170C42—2982no—
171C42—1491no—
172C42—1491no—
173C42—1491no—
174C42C22×D14911yescharacteristic
175C23—1491no—
176Q8—24no—
177Q8—42no—
178Q8—2984no—
179Q8—2984no—
180Q8—5964no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—2982no—
184C2×C4—2982no—
185C2×C4—2982no—
186C2×C4—2982no—
187C2×C4—5964no—
188C2×C4—1491no—
189C2×C4—1491no—
190C2×C4—1491no—
191C2×C4—1494no—
192C2×C4D4×D14911yescharacteristic
193C2×C4D4×D14911yescharacteristic
194C2×C4C23×D14911yescharacteristic
195C8—22no—
196C8—2982no—
197C22—2981no—
198C22—2981no—
199C22—1492no—
200C22C2×D4×D14911yescharacteristic
201C4—42no—
202C4—42no—
203C4—2981no—
204C4—2981no—
205C4—5962no—
206C4—5962no—
207C4—1492no—
208C4Q16×D14912yes—
209C4#1801194012yes—
210C4#1801195712yes—
211C2—2982no—
212C2#2375019311yescharacteristic
213C2C2×Q16×D14911yescharacteristic
214C2C2×#1801194011yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#487×C149C2
socleC22×C149C22×D4
prime radicalC22×D149C2×D4
hypercenter#487D149
hypocenterC149#3209
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. #23750005C2semidirect
4. #23750004C2semidirect
5. #23749977C2semidirect
6. #23749834C2semidirect
9. #487×C149C2semidirect
79. C4×D149Q16semidirect
107. C149#3209semidirect
114. #487D149semidirect

Maximal subgroups

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

subgroupindex
#237501802
C4⋊Q8×D1492
#237500052
#237500042
#237499772
#237498342
#237497822
#237496762
#487×C1492
#3209149