Finite Group Databasebeta

← #34055704

Subgroups — #34055704

Order 19072.

390 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 121 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#23750019C212yesmaximal, complemented
4#23749985C212yesmaximal, complemented
5#23749836C212yesmaximal, complemented
6#23749826C212yesmaximal, complemented
7#23749789C214yesmaximal, complemented
8#432×C149C211yesmaximal, characteristic, complemented
9C2×#14558736C2212yes—
10C2×Dic596C2214yes—
11C2×#14558725C2214yes—
12#18011911C2211yescharacteristic
13#18011911C2211yescharacteristic
14#18011911C2211yescharacteristic
15#18011908C2211yescharacteristic
16#18011903—21no—
17#18011899C2212yes—
18#18011890—21no—
19#18011890C2212yes—
20#18011885—21no—
21#18011885—21no—
22C4×Dic298—21no—
23C4×Dic298C2212yes—
24C4×D596—21no—
25C4×D596—21no—
26#18011870—21no—
27#18011836C2214yes—
28#18011833C2214yes—
29C2×C42×C149C2211yescharacteristic
30C4⋊C8×C149C2212yes—
31C22⋊C8×C149C2212yes—
32#97×C149C2212yes—
33#14558736—44no—
34C2×Dic298—21no—
35C2×Dic298C2312yes—
36C2×Dic298C2312yes—
37C2×D596—21no—
38C2×D596—21no—
39C2×D596C2312yes—
40C2×C22⋊D149—22no—
41C2×C4×D149—22no—
42Dic596—44no—
43#14558725—44no—
44C4⋊Dic149—21no—
45C4⋊Dic149—21no—
46C4⋊Dic149—21no—
47C4⋊Dic149—21no—
48C4⋊Dic149—21no—
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×C149C2314yes—
60C42×C149D411yescharacteristic
61C42×C149D411yescharacteristic
62C42×C149C2311yescharacteristic
63C42×C149C2311yescharacteristic
64C22×D149—22no—
65Dic298—22no—
66Dic298—22no—
67Dic298—24no—
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—41no—
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—24no—
88C22×C149—21no—
89C22×C149—21no—
90C22×C149—21no—
91C22×C149C22×D411yescharacteristic
92C2×D149—42no—
93C2×D149—42no—
94C2×D149—42no—
95C4×C149—21no—
96C4×C149—21no—
97C4×C149—21no—
98C4×C149—21no—
99C4×C149#13712yes—
100C4×C149H(5,𝔽2)12yes—
101Dic149—42no—
102Dic149—42no—
103Dic149—42no—
104C2×C149—41no—
105C2×C149#53511yescharacteristic
106C2×C149C2×#13711yescharacteristic
107C2×C149#57511yescharacteristic
108D149—82no—
109C149#321611yescharacteristic, complemented, Sylow
110#3216—1491nomaximal, Sylow
111#533—1491no—
112#532—1491no—
113#497—1492no—
114#489—1492no—
115#462—1492no—
116#460—1492no—
117#452—1494no—
118#432D14911yescharacteristic, complemented
119C2×#41—1492no—
120C2×Q16—1494no—
121C2×SD16—1494no—
122C4⋊Q8—1491no—
123C4⋊Q8—1491no—
124C4⋊Q8—1491no—
125#127—1491no—
126#125—2981no—
127#124—1492no—
128C22⋊Q8—2981no—
129C22⋊Q8—1492no—
130#121—2981no—
131#121—2981no—
132C4×Q8—2981no—
133C4×Q8—1492no—
134C4×D4—2981no—
135C4×D4—2981no—
136#117—2981no—
137C2×C42C2×D14911yescharacteristic
138C4⋊C8C2×D14912yes—
139#103—1494no—
140#102—1494no—
141C22⋊C8C2×D14912yes—
142#97C2×D14912yes—
143#41—5964no—
144C2×Q8—2981no—
145C2×Q8—1492no—
146C2×Q8—1492no—
147C2×D4—2982no—
148C2×D4—2981no—
149C2×D4—2981no—
150C2×D4—1492no—
151C22×C4—2982no—
152C22×C4D59611yescharacteristic
153C22×C4D59611yescharacteristic
154C22×C4C22×D14911yescharacteristic
155Q16—5964no—
156SD16—5964no—
157C2×C8C22×D14914yes—
158C4⋊C4—2981no—
159C4⋊C4—2981no—
160C4⋊C4—2981no—
161C4⋊C4—2981no—
162C4⋊C4—2981no—
163C4⋊C4—2982no—
164C4⋊C4—2982no—
165C4⋊C4—1492no—
166C22⋊C4—2982no—
167C22⋊C4—2982no—
168C22⋊C4—2982no—
169C42—2982no—
170C42D59611yescharacteristic
171C42D59611yescharacteristic
172C42C22×D14911yescharacteristic
173C42C22×D14911yescharacteristic
174C23—2982no—
175C23C2×D59611yescharacteristic
176Q8—2982no—
177Q8—2982no—
178Q8—2984no—
179Q8—5962no—
180D4—2984no—
181D4—5962no—
182D4—5964no—
183D4—5962no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—41no—
187C2×C4—2982no—
188C2×C4—2982no—
189C2×C4—2982no—
190C2×C4—5964no—
191C2×C4C2×D59611yescharacteristic
192C2×C4C2×D59611yescharacteristic
193C2×C4C2×D59611yescharacteristic
194C2×C4C2×D59611yescharacteristic
195C2×C4C2×D59611yescharacteristic
196C2×C4C23×D14911yescharacteristic
197C8—24no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—5962no—
202C22—5962no—
203C22—5962no—
204C22C22×D59611yescharacteristic
205C4—21no—
206C4—21no—
207C4—21no—
208C4—21no—
209C4—5962no—
210C4—5962no—
211C4—5962no—
212C4#1801194412yes—
213C4#1801195712yes—
214C2—41no—
215C2—11922no—
216C2#2375019411yescharacteristic
217C2C2×#1801194411yescharacteristic
218C2#2375042511yescharacteristic
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#432×C149C2
socleC22×C149C22×D4
prime radical#23750175C2
hypercenter#432D149
hypocenterC149#3216
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #23750182C2semidirect
3. #23750019C2semidirect
4. #23749985C2semidirect
5. #23749836C2semidirect
6. #23749826C2semidirect
7. #23749789C2semidirect
8. #432×C149C2semidirect
109. C149#3216semidirect
118. #432D149semidirect

Maximal subgroups

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

subgroupindex
#237501822
#237501752
#237500192
#237499852
#237498362
#237498262
#237497892
#432×C1492
#3216149