Finite Group Databasebeta

← #34055650

Subgroups — #34055650

Order 19072.

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

normal subgroups only

This group has 394 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#23750180C211yesmaximal, characteristic, complemented
2#23750176C211yesmaximal, characteristic
3#23750004C211yesmaximal, characteristic, complemented
4#23749998C211yesmaximal, characteristic, complemented
5#23749973C211yesmaximal, characteristic, complemented
6#23749850C214yesmaximal, complemented
7#23749790C214yesmaximal, complemented
8#23749676C211yesmaximal, characteristic, complemented
9#487×C149C211yesmaximal, characteristic, complemented
10C2×#14558737C2212yes—
11C2×#14558726C2214yes—
12C2×#14558725C2214yes—
13#18011911C2211yescharacteristic
14#18011908C2211yescharacteristic
15#18011902—21no—
16#18011900C2212yes—
17#18011891C2212yes—
18#18011887—21no—
19#18011886—21no—
20#18011886—21no—
21Q8×Dic149—21no—
22#18011876C2212yes—
23#18011873—21no—
24#18011873—21no—
25#18011869—21no—
26C42×D149C2211yescharacteristic
27#18011840C2212yes—
28#18011831C2214yes—
29#18011823C2212yes—
30C4×#11924746C2211yescharacteristic
31C4⋊Q8×C149C2211yescharacteristic
32C4⋊Q8×C149C2211yescharacteristic
33#103×C149C2214yes—
34C4×C8×C149C2211yescharacteristic
35#14558737—44no—
36C2×Dic298C2312yes—
37C2×D596—22no—
38C2×D596—21no—
39C2×D596—21no—
40C2×D596C2312yes—
41C2×C4×D149—22no—
42C2×C4×D149D411yescharacteristic
43C2×C4×D149D411yescharacteristic
44C2×C4×D149C2311yescharacteristic
45#14558726—44no—
46#14558725—44no—
47C2×#11924746C2312yes—
48C4⋊Dic149—22no—
49C4⋊Dic149—21no—
50C4⋊Dic149—21no—
51#14558715—22no—
52#14558713—22no—
53#14558713—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×D149—22no—
68C22×D149C2×D411yescharacteristic
69Dic298—24no—
70D596—24no—
71D596—44no—
72D596—42no—
73D596—42no—
74C2×Dic149—22no—
75C2×Dic149C2×D411yescharacteristic
76C2×Dic149C2×D411yescharacteristic
77C2×Dic149C2×D411yescharacteristic
78C4×D149—22no—
79C4×D149—22no—
80C4×D149—22no—
81C4×D149—44no—
82#11924746—22no—
83Q8×C149—24no—
84Q8×C149—42no—
85C2×C4×C149—22no—
86C2×C4×C149—22no—
87C2×C4×C149C2×D411yescharacteristic
88C2×C4×C149C2×D411yescharacteristic
89C2×C4×C149C2411yescharacteristic
90C8×C149—22no—
91C22×C149C22×D411yescharacteristic
92C2×D149—21no—
93C2×D149—21no—
94C2×D149—21no—
95C2×D149—42no—
96C2×D149—42no—
97C2×D149—42no—
98C4×C149—42no—
99C4×C149—42no—
100C4×C149#13512yes—
101C4×C149#13712yes—
102C4×C149H(5,𝔽2)12yes—
103Dic149—21no—
104Dic149—21no—
105Dic149—21no—
106Dic149—42no—
107C2×C149#53511yescharacteristic
108C2×C149C2×#13511yescharacteristic
109C2×C149C2×#13711yescharacteristic
110D149—41no—
111D149—82no—
112C149#321011yescharacteristic, complemented, Sylow
113#3210—1491nomaximal, Sylow
114#533—1491no—
115#532—1491no—
116#494—1491no—
117#492—1491no—
118#487D14911yescharacteristic, complemented
119#486—1491no—
120#464—1494no—
121#452—1494no—
122#431—1491no—
123C2×#41—1492no—
124C2×Q16—1494no—
125C2×SD16—1494no—
126C4⋊Q8—1491no—
127C4⋊Q8C2×D14911yescharacteristic
128C4⋊Q8C2×D14911yescharacteristic
129#127—1491no—
130#125—2981no—
131#124—1492no—
132C22⋊Q8—2981no—
133C22⋊Q8—1492no—
134#121—2981no—
135#121—2981no—
136C4×Q8—2981no—
137C4×Q8—1492no—
138C4×D4—2981no—
139C4×D4—2981no—
140#117—2981no—
141C2×C42—1491no—
142C4⋊C8—1492no—
143#103C2×D14914yes—
144#102—1494no—
145C22⋊C8—1492no—
146C4×C8—1491no—
147C4×C8C2×D14911yescharacteristic
148#41—5964no—
149C2×Q8—21no—
150C2×Q8—1492no—
151C2×Q8C22×D14912yes—
152C2×D4—2982no—
153C2×D4—2981no—
154C2×D4—2981no—
155C2×D4—1492no—
156C22×C4—2982no—
157C22×C4—1491no—
158C22×C4—1491no—
159C22×C4—1491no—
160Q16—5964no—
161SD16—5964no—
162C2×C8—1492no—
163C2×C8C22×D14912yes—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—2982no—
168C4⋊C4—2982no—
169C4⋊C4—2981no—
170C4⋊C4—2981no—
171C4⋊C4C22×D14912yes—
172C22⋊C4—2982no—
173C22⋊C4—2982no—
174C22⋊C4—2982no—
175C42—2982no—
176C42—1491no—
177C42—1491no—
178C42—1491no—
179C42C22×D14911yescharacteristic
180C23—2982no—
181C23—1491no—
182Q8—24no—
183Q8—42no—
184Q8—2984no—
185D4—2984no—
186D4—5964no—
187D4—5962no—
188D4—5962no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—2982no—
192C2×C4—2982no—
193C2×C4—2982no—
194C2×C4—2982no—
195C2×C4—5964no—
196C2×C4—1491no—
197C2×C4—1491no—
198C2×C4—1491no—
199C2×C4D4×D14911yescharacteristic
200C2×C4D4×D14911yescharacteristic
201C2×C4C23×D14911yescharacteristic
202C8—22no—
203C8—2982no—
204C22—2981no—
205C22—2981no—
206C22—2981no—
207C22—5962no—
208C22—5962no—
209C22—5962no—
210C22C2×D4×D14911yescharacteristic
211C4—42no—
212C4—42no—
213C4—2981no—
214C4—2981no—
215C4—2981no—
216C4—5962no—
217C4#1801193212yes—
218C4#1801194312yes—
219C4#1801195712yes—
220C2—5961no—
221C2—11922no—
222C2#2375019311yescharacteristic
223C2C2×#1801193211yescharacteristic
224C2C2×#1801194311yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#487×C149C2
socleC22×C149C22×D4
prime radical#23750176C2
hypercenter#487D149
hypocenterC149#3210
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
1. #23750180C2semidirect
3. #23750004C2semidirect
4. #23749998C2semidirect
5. #23749973C2semidirect
6. #23749850C2semidirect
7. #23749790C2semidirect
8. #23749676C2semidirect
9. #487×C149C2semidirect
112. C149#3210semidirect
118. #487D149semidirect

Maximal subgroups

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

subgroupindex
#237501802
#237501762
#237500042
#237499982
#237499732
#237498502
#237497902
#237496762
#487×C1492
#3210149