Finite Group Databasebeta

← #34056092

Subgroups — #34056092

Order 19072.

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

normal subgroups only

This group has 354 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#23750159C212yesmaximal, complemented
2#23749933C212yesmaximal, complemented
3#23749926C212yesmaximal, complemented
4#23749883C211yesmaximal, characteristic, complemented
5#23749878C211yesmaximal, characteristic
6#23749871C212yesmaximal, complemented
7#23749848C212yesmaximal, complemented
8#23749841C212yesmaximal, complemented
9#423×C149C211yesmaximal, characteristic, complemented
10C2×Dic596C2211yescharacteristic
11C2×#14558725C2212yes—
12C2×D1192C2211yescharacteristic
13#18011905—22no—
14#18011903C2212yes—
15#18011899C2212yes—
16#18011894—22no—
17#18011890C2212yes—
18#18011885C2212yes—
19C4×Dic298C2212yes—
20C4×D596C2212yes—
21C4×C22⋊D149—22no—
22#18011868—22no—
23#18011845C2212yes—
24#18011843C2211yescharacteristic
25#18011843C2211yescharacteristic
26#18011836C2212yes—
27#18011836C2212yes—
28#18011833C2212yes—
29#18011833C2212yes—
30C2×M16×C149C2211yescharacteristic
31C2×M16×C149C2211yescharacteristic
32C2×C42×C149C2211yescharacteristic
33C4⋊C8×C149C2212yes—
34C4⋊C8×C149C2212yes—
35C2×Dic298C2312yes—
36C2×D596C2312yes—
37C2×C22⋊D149—22no—
38C2×C4×D149—22no—
39Dic596—41no—
40#14558725—42no—
41D1192—41no—
42C4⋊Dic149C2312yes—
43C4⋊Dic149C2312yes—
44#14558715—22no—
45#14558715—22no—
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×C149D412yes—
55C22×C4×C149C2311yescharacteristic
56M16×C149—41no—
57M16×C149—41no—
58C2×C8×C149C2311yescharacteristic
59C2×C8×C149C2312yes—
60C2×C8×C149C2311yescharacteristic
61C42×C149D411yescharacteristic
62C42×C149D411yescharacteristic
63C42×C149C2312yes—
64C22×D149—22no—
65Dic298—22no—
66Dic298—22no—
67D596—22no—
68D596—22no—
69C22⋊D149—44no—
70C2×Dic149—22no—
71C2×Dic149—22no—
72C2×Dic149—22no—
73C4×D149—44no—
74C23×C149C2×D411yescharacteristic
75C2×C4×C149—21no—
76C2×C4×C149—21no—
77C2×C4×C149—42no—
78C2×C4×C149C2×D412yes—
79C2×C4×C149C2×D411yescharacteristic
80C2×C4×C149C2×D412yes—
81C2×C4×C149C2411yescharacteristic
82C8×C149—21no—
83C8×C149—22no—
84C8×C149—21no—
85C22×C149—21no—
86C22×C149—22no—
87C22×C149C22×D411yescharacteristic
88C2×D149—42no—
89C2×D149—42no—
90C2×D149—42no—
91C4×C149—21no—
92C4×C149—22no—
93C4×C149—22no—
94C4×C149H(5,𝔽2)11yescharacteristic
95C4×C1492−1+411yescharacteristic
96Dic149—42no—
97Dic149—42no—
98Dic149—42no—
99C2×C149—41no—
100C2×C149#53711yescharacteristic
101C2×C149#57512yes—
102D149—82no—
103C149#325611yescharacteristic, complemented, Sylow
104#3256—1491nomaximal, Sylow
105#529—1492no—
106#479—1492no—
107#478—1492no—
108#470—1491no—
109#469—1491no—
110#468—1492no—
111#464—1492no—
112#463—1492no—
113#423D14911yescharacteristic, complemented
114C2×Q16—1491no—
115C2×SD16—1492no—
116C2×D8—1491no—
117C2×M16C2×D14911yescharacteristic
118C2×M16C2×D14911yescharacteristic
119#126—2982no—
120#125—1492no—
121#124—1492no—
122#123—2982no—
123C22⋊Q8—1492no—
124#121—1492no—
125C4×Q8—1492no—
126C4×D4—2982no—
127C4×D4—1492no—
128#117—2982no—
129C2×C42C2×D14911yescharacteristic
130#107—1492no—
131#106—1491no—
132#106—1491no—
133C4⋊C8C2×D14912yes—
134C4⋊C8C2×D14912yes—
135#103—1492no—
136#103—1492no—
137#102—1492no—
138#102—1492no—
139C2×Q8—1492no—
140C2×D4—2982no—
141C2×D4—1492no—
142C22×C4—2982no—
143C22×C4D59612yes—
144C22×C4C22×D14911yescharacteristic
145Q16—5961no—
146SD16—5962no—
147D8—5961no—
148M16—41no—
149M16—41no—
150C2×C8C22×D14911yescharacteristic
151C2×C8C22×D14912yes—
152C2×C8C22×D14911yescharacteristic
153C4⋊C4—2982no—
154C4⋊C4—2982no—
155C4⋊C4—2982no—
156C4⋊C4—2982no—
157C4⋊C4—1492no—
158C4⋊C4—1492no—
159C22⋊C4—2982no—
160C22⋊C4—2982no—
161C22⋊C4—2982no—
162C22⋊C4—2982no—
163C22⋊C4—2982no—
164C42—2982no—
165C42D59611yescharacteristic
166C42D59611yescharacteristic
167C42C22×D14912yes—
168C23—2982no—
169C23C2×D59611yescharacteristic
170Q8—2982no—
171Q8—2982no—
172D4—2982no—
173D4—2982no—
174D4—5964no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—42no—
178C2×C4—2982no—
179C2×C4—2982no—
180C2×C4—2982no—
181C2×C4—5964no—
182C2×C4C2×D59612yes—
183C2×C4C2×D59611yescharacteristic
184C2×C4C2×D59612yes—
185C2×C4C23×D14911yescharacteristic
186C8—21no—
187C8—22no—
188C8—21no—
189C22—22no—
190C22—21no—
191C22—5962no—
192C22—5962no—
193C22—5962no—
194C22C22×D59611yescharacteristic
195C4—22no—
196C4—22no—
197C4—21no—
198C4—5962no—
199C4—5962no—
200C4—5962no—
201C4#1801195611yescharacteristic
202C4#1801195911yescharacteristic
203C2—41no—
204C2—11922no—
205C2#2375020611yescharacteristic
206C2#2375042512yes—
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#423×C149C2
socleC22×C149C22×D4
prime radical#23749878C2
hypercenter#423D149
hypocenterC149#3256
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
1. #23750159C2semidirect
2. #23749933C2semidirect
3. #23749926C2semidirect
4. #23749883C2semidirect
6. #23749871C2semidirect
7. #23749848C2semidirect
8. #23749841C2semidirect
9. #423×C149C2semidirect
103. C149#3256semidirect
113. #423D149semidirect

Maximal subgroups

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

subgroupindex
#237501592
#237499332
#237499262
#237498832
#237498782
#237498712
#237498482
#237498412
#423×C1492
#3256149