Finite Group Databasebeta

← #34055891

Subgroups — #34055891

Order 19072.

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

normal subgroups only

This group has 366 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#23750034C212yesmaximal, complemented
4#23749990C212yesmaximal, complemented
5#23749950C214yesmaximal, complemented
6#23749916C212yesmaximal, complemented
7#23749906C212yesmaximal, complemented
8#432×C149C211yesmaximal, characteristic, complemented
9C2×#14558736—21no—
10#18011911C2211yescharacteristic
11#18011911C2211yescharacteristic
12#18011911C2211yescharacteristic
13#18011908C2211yescharacteristic
14#18011903C2212yes—
15#18011899—21no—
16#18011890—21no—
17#18011890—21no—
18#18011885—21no—
19#18011885C2212yes—
20C4×Dic298—21no—
21C4×Dic298—21no—
22C4×D596—21no—
23C4×D596C2212yes—
24#18011870C2212yes—
25#18011845C2214yes—
26#18011843C2214yes—
27#18011833C2214yes—
28#18011833C2214yes—
29C2×C42×C149C2211yescharacteristic
30C4⋊C8×C149C2212yes—
31C22⋊C8×C149C2212yes—
32#97×C149C2212yes—
33#14558736—44no—
34C2×Dic298—21no—
35C2×Dic298—21no—
36C2×Dic298—21no—
37C2×D596—21no—
38C2×D596—21no—
39C2×D596C2312yes—
40C2×C22⋊D149—22no—
41C2×C4×D149—22no—
42C4⋊Dic149—21no—
43C4⋊Dic149—21no—
44C4⋊Dic149—21no—
45C4⋊Dic149C2312yes—
46C4⋊Dic149C2312yes—
47C4⋊Dic149C2312yes—
48#14558715—22no—
49#14558715—22no—
50C22⋊Dic149—22no—
51#14558713—22no—
52#14558713—22no—
53C4×Dic149—22no—
54C22×C4×C149D411yescharacteristic
55C22×C4×C149D411yescharacteristic
56C22×C4×C149C2311yescharacteristic
57C2×C8×C149C2314yes—
58C42×C149D411yescharacteristic
59C42×C149D411yescharacteristic
60C42×C149C2311yescharacteristic
61C42×C149C2311yescharacteristic
62C22×D149—22no—
63Dic298—42no—
64Dic298—42no—
65Dic298—42no—
66D596—24no—
67D596—42no—
68D596—42no—
69C22⋊D149—44no—
70C2×Dic149—22no—
71C2×Dic149—22no—
72C2×Dic149—22no—
73C4×D149—44no—
74C23×C149C2×D411yescharacteristic
75C2×C4×C149—22no—
76C2×C4×C149—22no—
77C2×C4×C149—41no—
78C2×C4×C149C2×D411yescharacteristic
79C2×C4×C149C2×D411yescharacteristic
80C2×C4×C149C2×D411yescharacteristic
81C2×C4×C149C2×D411yescharacteristic
82C2×C4×C149C2×D411yescharacteristic
83C2×C4×C149C2411yescharacteristic
84C8×C149—24no—
85C22×C149—21no—
86C22×C149—21no—
87C22×C149—21no—
88C22×C149C22×D411yescharacteristic
89C2×D149—42no—
90C2×D149—42no—
91C2×D149—42no—
92C4×C149—21no—
93C4×C149—21no—
94C4×C149—21no—
95C4×C149—21no—
96C4×C149AGL(1,ℤ/8)12yes—
97C4×C1492−1+412yes—
98Dic149—42no—
99Dic149—42no—
100Dic149—42no—
101C2×C149—41no—
102C2×C149#53611yescharacteristic
103C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
104C2×C149#57511yescharacteristic
105D149—82no—
106C149#323511yescharacteristic, complemented, Sylow
107#3235—1491nomaximal, Sylow
108#533—1491no—
109#532—1491no—
110#501—1492no—
111#490—1492no—
112#482—1494no—
113#476—1492no—
114#474—1492no—
115#432D14911yescharacteristic, complemented
116C2×#41—2981no—
117C4⋊Q8—1491no—
118C4⋊Q8—1491no—
119C4⋊Q8—1491no—
120#127—1491no—
121#125—1492no—
122#124—2981no—
123C22⋊Q8—2981no—
124C22⋊Q8—2981no—
125#121—2981no—
126#121—1492no—
127C4×Q8—2981no—
128C4×Q8—2981no—
129C4×D4—2981no—
130C4×D4—1492no—
131#117—1492no—
132C2×C42C2×D14911yescharacteristic
133#107—1494no—
134#106—1494no—
135C4⋊C8C2×D14912yes—
136#102—1494no—
137#102—1494no—
138C22⋊C8C2×D14912yes—
139#97C2×D14912yes—
140#41—5964no—
141C2×Q8—2981no—
142C2×Q8—2981no—
143C2×Q8—2981no—
144C2×D4—2982no—
145C2×D4—2981no—
146C2×D4—2981no—
147C2×D4—1492no—
148C22×C4—2982no—
149C22×C4D59611yescharacteristic
150C22×C4D59611yescharacteristic
151C22×C4C22×D14911yescharacteristic
152C2×C8C22×D14914yes—
153C4⋊C4—2981no—
154C4⋊C4—2982no—
155C4⋊C4—2982no—
156C4⋊C4—2981no—
157C4⋊C4—2981no—
158C4⋊C4—1492no—
159C4⋊C4—1492no—
160C4⋊C4—1492no—
161C22⋊C4—2982no—
162C22⋊C4—2982no—
163C22⋊C4—2982no—
164C42—2982no—
165C42D59611yescharacteristic
166C42D59611yescharacteristic
167C42C22×D14911yescharacteristic
168C42C22×D14911yescharacteristic
169C23—2982no—
170C23C2×D59611yescharacteristic
171Q8—5962no—
172Q8—5962no—
173Q8—5962no—
174D4—2984no—
175D4—5962no—
176D4—5962no—
177D4—5964no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—41no—
181C2×C4—2982no—
182C2×C4—2982no—
183C2×C4—2982no—
184C2×C4—5964no—
185C2×C4C2×D59611yescharacteristic
186C2×C4C2×D59611yescharacteristic
187C2×C4C2×D59611yescharacteristic
188C2×C4C2×D59611yescharacteristic
189C2×C4C2×D59611yescharacteristic
190C2×C4C23×D14911yescharacteristic
191C8—24no—
192C22—21no—
193C22—21no—
194C22—21no—
195C22—5962no—
196C22—5962no—
197C22—5962no—
198C22C22×D59611yescharacteristic
199C4—21no—
200C4—21no—
201C4—21no—
202C4—21no—
203C4—5962no—
204C4—5962no—
205C4—5962no—
206C4#1801193912yes—
207C4#1801195812yes—
208C2—41no—
209C2—11922no—
210C2#2375020111yescharacteristic
211C2C2×#1801193911yescharacteristic
212C2#2375042511yescharacteristic
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#432×C149C2
socleC22×C149C22×D4
prime radical#23750175C2
hypercenter#432D149
hypocenterC149#3235
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. #23750034C2semidirect
4. #23749990C2semidirect
5. #23749950C2semidirect
6. #23749916C2semidirect
7. #23749906C2semidirect
8. #432×C149C2semidirect
106. C149#3235semidirect
115. #432D149semidirect

Maximal subgroups

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

subgroupindex
#237501822
#237501752
#237500342
#237499902
#237499502
#237499162
#237499062
#432×C1492
#3235149