Finite Group Databasebeta

← #34056152

Subgroups — #34056152

Order 19072.

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

normal subgroups only

This group has 346 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#23750246C212yesmaximal, complemented
2#23749921C212yesmaximal, complemented
3#23749906C212yesmaximal, complemented
4#23749871C212yesmaximal, complemented
5#23749866C211yesmaximal, characteristic, complemented
6#23749861C211yesmaximal, characteristic
7#23749848C212yesmaximal, complemented
8#23749841C212yesmaximal, complemented
9#424×C149C211yesmaximal, characteristic, complemented
10C2×Dic596C2211yescharacteristic
11C2×#14558725C2212yes—
12C2×D1192C2211yescharacteristic
13#18011911C2212yes—
14#18011906—22no—
15#18011899C2212yes—
16#18011897—22no—
17#18011893—22no—
18#18011890C2212yes—
19#18011889—22no—
20#18011885C2212yes—
21C4×Dic298C2212yes—
22C4×D596C2212yes—
23#18011845C2211yescharacteristic
24#18011845C2212yes—
25#18011845C2211yescharacteristic
26#18011836C2212yes—
27#18011836C2212yes—
28#18011833C2212yes—
29#18011833C2212yes—
30C2×M16×C149C2211yescharacteristic
31C22×C8×C149C2211yescharacteristic
32#117×C149C2211yescharacteristic
33C4⋊C8×C149C2212yes—
34C4⋊C8×C149C2212yes—
35C2×Dic298—22no—
36C2×Dic298C2312yes—
37C2×D596C2312yes—
38C2×C22⋊D149—22no—
39C2×C4×D149—22no—
40Dic596—41no—
41#14558725—42no—
42D1192—41no—
43C4⋊Dic149—22no—
44C4⋊Dic149C2312yes—
45C4⋊Dic149C2312yes—
46#14558715—22no—
47#14558715—22no—
48C22⋊Dic149—22no—
49#14558713—22no—
50#14558713—22no—
51#14558713—22no—
52#14558713—22no—
53C4×Dic149—22no—
54C22×C4×C149C2311yescharacteristic
55M16×C149—41no—
56C2×C8×C149—41no—
57C2×C8×C149C2311yescharacteristic
58C2×C8×C149C2312yes—
59C2×C8×C149C2311yescharacteristic
60C4⋊C4×C149D411yescharacteristic
61C4⋊C4×C149D411yescharacteristic
62C22⋊C4×C149D412yes—
63C42×C149C2312yes—
64C22×D149—22no—
65Dic298—22no—
66Dic298—22no—
67Dic298—82no—
68D596—22no—
69D596—22no—
70C22⋊D149—82no—
71C2×Dic149—22no—
72C2×Dic149—22no—
73C2×Dic149—22no—
74C4×D149—82no—
75C23×C149C2×D411yescharacteristic
76C2×C4×C149—21no—
77C2×C4×C149—21no—
78C2×C4×C149C2×D412yes—
79C2×C4×C149C2×D412yes—
80C2×C4×C149C2×D411yescharacteristic
81C2×C4×C149C2411yescharacteristic
82C8×C149—21no—
83C8×C149—22no—
84C8×C149—21no—
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—22no—
94C4×C149—22no—
95C4×C149H(5,𝔽2)11yescharacteristic
96C4×C1492−1+411yescharacteristic
97Dic149—42no—
98Dic149—42no—
99Dic149—42no—
100C2×C149—41no—
101C2×C149#53711yescharacteristic
102C2×C149#57611yescharacteristic
103C2×C149#57811yescharacteristic
104D149—82no—
105C149#326211yescharacteristic, complemented, Sylow
106#3262—1491nomaximal, Sylow
107#542—1492no—
108#477—1492no—
109#474—1492no—
110#468—1492no—
111#467—1491no—
112#466—1491no—
113#464—1492no—
114#463—1492no—
115#424D14911yescharacteristic, complemented
116C2×Q16—1491no—
117C2×SD16—1492no—
118C2×D8—1491no—
119C2×M16C2×D14911yescharacteristic
120C22×C8C2×D14911yescharacteristic
121C4⋊Q8—1492no—
122#126—2982no—
123#124—2982no—
124#124—1492no—
125#123—2982no—
126C22⋊Q8—2982no—
127C22⋊Q8—1492no—
128#121—1492no—
129C4×Q8—1492no—
130C4×D4—1492no—
131#117C2×D14911yescharacteristic
132#107—1491no—
133#107—1491no—
134#107—1492no—
135C4⋊C8C2×D14912yes—
136C4⋊C8C2×D14912yes—
137#103—1492no—
138#103—1492no—
139#102—1492no—
140#102—1492no—
141C2×Q8—2982no—
142C2×Q8—1492no—
143C2×D4—2982no—
144C2×D4—1492no—
145C22×C4—2982no—
146C22×C4C22×D14911yescharacteristic
147Q16—5961no—
148SD16—5962no—
149D8—5961no—
150M16—41no—
151C2×C8—41no—
152C2×C8C22×D14911yescharacteristic
153C2×C8C22×D14912yes—
154C2×C8C22×D14911yescharacteristic
155C4⋊C4—2982no—
156C4⋊C4—2982no—
157C4⋊C4—2982no—
158C4⋊C4—1492no—
159C4⋊C4—1492no—
160C4⋊C4D59611yescharacteristic
161C4⋊C4D59611yescharacteristic
162C22⋊C4—2982no—
163C22⋊C4—2982no—
164C22⋊C4—2982no—
165C22⋊C4—2982no—
166C22⋊C4—2982no—
167C22⋊C4D59612yes—
168C42—2982no—
169C42C22×D14912yes—
170C23—2982no—
171C23C2×D59611yescharacteristic
172Q8—2982no—
173Q8—2982no—
174Q8—11922no—
175D4—2982no—
176D4—2982no—
177D4—11922no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—2982no—
181C2×C4—2982no—
182C2×C4—2982no—
183C2×C4—11922no—
184C2×C4C2×D59612yes—
185C2×C4C2×D59612yes—
186C2×C4C2×D59611yescharacteristic
187C2×C4C23×D14911yescharacteristic
188C8—21no—
189C8—21no—
190C8—22no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—5962no—
195C22—5962no—
196C22—5962no—
197C22C22×D59611yescharacteristic
198C4—22no—
199C4—22no—
200C4—21no—
201C4—5962no—
202C4—5962no—
203C4—5962no—
204C4#1801195611yescharacteristic
205C4#1801195911yescharacteristic
206C2—41no—
207C2—11922no—
208C2#2375020611yescharacteristic
209C2#2375043011yescharacteristic
210C2#2375044211yescharacteristic
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#424×C149C2
socleC22×C149C22×D4
prime radical#23749861C2
hypercenter#424D149
hypocenterC149#3262
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
1. #23750246C2semidirect
2. #23749921C2semidirect
3. #23749906C2semidirect
4. #23749871C2semidirect
5. #23749866C2semidirect
7. #23749848C2semidirect
8. #23749841C2semidirect
9. #424×C149C2semidirect
105. C149#3262semidirect
115. #424D149semidirect

Maximal subgroups

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

subgroupindex
#237502462
#237499212
#237499062
#237498712
#237498662
#237498612
#237498482
#237498412
#424×C1492
#3262149