Finite Group Databasebeta

← #34055829

Subgroups — #34055829

Order 19072.

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

normal subgroups only

This group has 370 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#23750182C211yesmaximal, characteristic, complemented
2#23750175C211yesmaximal, characteristic
3#23750030C211yesmaximal, characteristic, complemented
4#23750023C211yesmaximal, characteristic, complemented
5#23749972C211yesmaximal, characteristic, complemented
6#23749972C211yesmaximal, characteristic, complemented
7#23749950C214yesmaximal, complemented
8#23749926C214yesmaximal, complemented
9#431×C149C211yesmaximal, characteristic, complemented
10C2×#14558736—21no—
11#18011911C2211yescharacteristic
12#18011911C2211yescharacteristic
13#18011911C2211yescharacteristic
14#18011908C2211yescharacteristic
15#18011903C2212yes—
16#18011899—21no—
17#18011890—21no—
18#18011890—21no—
19#18011885—21no—
20#18011885C2212yes—
21C4×Dic298—21no—
22C4×Dic298—21no—
23C4×D596—21no—
24C4×D596C2212yes—
25#18011870C2212yes—
26#18011845C2214yes—
27#18011843C2214yes—
28#18011833C2214yes—
29#18011833C2214yes—
30C2×C42×C149C2211yescharacteristic
31C4⋊C8×C149C2212yes—
32C22⋊C8×C149C2212yes—
33C4×C8×C149C2211yescharacteristic
34C4×C8×C149C2211yescharacteristic
35#14558736—44no—
36C2×Dic298—21no—
37C2×Dic298—21no—
38C2×Dic298—21no—
39C2×D596—21no—
40C2×D596—21no—
41C2×D596C2312yes—
42C2×C22⋊D149—22no—
43C2×C4×D149—22no—
44C4⋊Dic149—21no—
45C4⋊Dic149—21no—
46C4⋊Dic149—21no—
47C4⋊Dic149C2312yes—
48C4⋊Dic149C2312yes—
49C4⋊Dic149C2312yes—
50#14558715—22no—
51#14558715—22no—
52C22⋊Dic149—22no—
53#14558713—22no—
54#14558713—22no—
55C4×Dic149—22no—
56C22×C4×C149D411yescharacteristic
57C22×C4×C149D411yescharacteristic
58C22×C4×C149C2311yescharacteristic
59C2×C8×C149C2312yes—
60C2×C8×C149C2312yes—
61C42×C149D411yescharacteristic
62C42×C149D411yescharacteristic
63C42×C149C2311yescharacteristic
64C42×C149C2311yescharacteristic
65C22×D149—22no—
66Dic298—42no—
67Dic298—42no—
68Dic298—42no—
69D596—24no—
70D596—42no—
71D596—42no—
72C22⋊D149—44no—
73C2×Dic149—22no—
74C2×Dic149—22no—
75C2×Dic149—22no—
76C4×D149—44no—
77C23×C149C2×D411yescharacteristic
78C2×C4×C149—22no—
79C2×C4×C149—22no—
80C2×C4×C149—22no—
81C2×C4×C149C2×D411yescharacteristic
82C2×C4×C149C2×D411yescharacteristic
83C2×C4×C149C2×D411yescharacteristic
84C2×C4×C149C2×D411yescharacteristic
85C2×C4×C149C2×D411yescharacteristic
86C2×C4×C149C2411yescharacteristic
87C8×C149—22no—
88C8×C149—22no—
89C22×C149—21no—
90C22×C149—21no—
91C22×C149—21no—
92C22×C149C22×D411yescharacteristic
93C2×D149—42no—
94C2×D149—42no—
95C2×D149—42no—
96C4×C149—21no—
97C4×C149—21no—
98C4×C149—21no—
99C4×C149#13512yes—
100C4×C149AGL(1,ℤ/8)12yes—
101C4×C1492−1+412yes—
102Dic149—42no—
103Dic149—42no—
104Dic149—42no—
105C2×C149—41no—
106C2×C149#53611yescharacteristic
107C2×C149C2×#13511yescharacteristic
108C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
109D149—82no—
110C149#322811yescharacteristic, complemented, Sylow
111#3228—1491nomaximal, Sylow
112#533—1491no—
113#532—1491no—
114#500—1491no—
115#498—1491no—
116#486—1491no—
117#486—1491no—
118#482—1494no—
119#478—1494no—
120#431D14911yescharacteristic, complemented
121C2×#41—2981no—
122C4⋊Q8—1491no—
123C4⋊Q8—1491no—
124C4⋊Q8—1491no—
125#127—1491no—
126#125—1492no—
127#124—2981no—
128C22⋊Q8—2981no—
129C22⋊Q8—2981no—
130#121—2981no—
131#121—1492no—
132C4×Q8—2981no—
133C4×Q8—2981no—
134C4×D4—2981no—
135C4×D4—1492no—
136#117—1492no—
137C2×C42C2×D14911yescharacteristic
138#107—1494no—
139#106—1494no—
140C4⋊C8C2×D14912yes—
141#102—1494no—
142#102—1494no—
143C22⋊C8C2×D14912yes—
144C4×C8C2×D14911yescharacteristic
145C4×C8C2×D14911yescharacteristic
146#41—5964no—
147C2×Q8—2981no—
148C2×Q8—2981no—
149C2×Q8—2981no—
150C2×D4—2982no—
151C2×D4—2981no—
152C2×D4—2981no—
153C2×D4—1492no—
154C22×C4—2982no—
155C22×C4D59611yescharacteristic
156C22×C4D59611yescharacteristic
157C22×C4C22×D14911yescharacteristic
158C2×C8C22×D14912yes—
159C2×C8C22×D14912yes—
160C4⋊C4—2981no—
161C4⋊C4—2982no—
162C4⋊C4—2982no—
163C4⋊C4—2981no—
164C4⋊C4—2981no—
165C4⋊C4—1492no—
166C4⋊C4—1492no—
167C4⋊C4—1492no—
168C22⋊C4—2982no—
169C22⋊C4—2982no—
170C22⋊C4—2982no—
171C42—2982no—
172C42D59611yescharacteristic
173C42D59611yescharacteristic
174C42C22×D14911yescharacteristic
175C42C22×D14911yescharacteristic
176C23—2982no—
177C23C2×D59611yescharacteristic
178Q8—5962no—
179Q8—5962no—
180Q8—5962no—
181D4—2984no—
182D4—5964no—
183D4—5962no—
184D4—5962no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—2982no—
189C2×C4—2982no—
190C2×C4—2982no—
191C2×C4—5964no—
192C2×C4C2×D59611yescharacteristic
193C2×C4C2×D59611yescharacteristic
194C2×C4C2×D59611yescharacteristic
195C2×C4C2×D59611yescharacteristic
196C2×C4C2×D59611yescharacteristic
197C2×C4C23×D14911yescharacteristic
198C8—22no—
199C8—22no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—5962no—
204C22—5962no—
205C22—5962no—
206C22C22×D59611yescharacteristic
207C4—21no—
208C4—21no—
209C4—21no—
210C4—5962no—
211C4—5962no—
212C4—5962no—
213C4#1801193312yes—
214C4#1801193912yes—
215C4#1801195812yes—
216C2—41no—
217C2—11922no—
218C2#2375020111yescharacteristic
219C2C2×#1801193311yescharacteristic
220C2C2×#1801193911yescharacteristic
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#431×C149C2
socleC22×C149C22×D4
prime radical#23750175C2
hypercenter#431D149
hypocenterC149#3228
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
1. #23750182C2semidirect
3. #23750030C2semidirect
4. #23750023C2semidirect
5. #23749972C2semidirect
6. #23749972C2semidirect
7. #23749950C2semidirect
8. #23749926C2semidirect
9. #431×C149C2semidirect
110. C149#3228semidirect
120. #431D149semidirect

Maximal subgroups

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

subgroupindex
#237501822
#237501752
#237500302
#237500232
#237499722
#237499502
#237499262
#431×C1492
#3228149