Finite Group Databasebeta

← #34056068

Subgroups — #34056068

Order 19072.

430 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 113 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#23750170C212yesmaximal, complemented
2#23749914C212yesmaximal, complemented
3#23749913C212yesmaximal, complemented
4#23749878C211yesmaximal, characteristic, complemented
5#23749876C212yesmaximal, complemented
6#23749819C212yesmaximal, complemented
7#23749818C212yesmaximal, complemented
8#23749648C211yesmaximal, characteristic, complemented
9#469×C149C211yesmaximal, characteristic, complemented
10C2×#14558735—22no—
11C2×D1192C2211yescharacteristic
12C2×#14558721C2212yes—
13C2×#14558720C2211yescharacteristic
14#18011910C2212yes—
15#18011907C2212yes—
16#18011897—22no—
17#18011885C2212yes—
18#18011883—22no—
19D4×Dic149C2212yes—
20#18011873C2212yes—
21#18011871—22no—
22C2×C4×Dic149C2211yescharacteristic
23#18011843C2211yescharacteristic
24#18011842C2212yes—
25#18011840C2212yes—
26#18011840C2212yes—
27#18011833C2212yes—
28#18011832C2212yes—
29#18011831C2212yes—
30C2×D8×C149C2211yescharacteristic
31C2×M16×C149C2211yescharacteristic
32#121×C149C2212yes—
33#106×C149C2211yescharacteristic
34#102×C149C2212yes—
35#14558735—48no—
36C2×Dic298—22no—
37C2×D596C2312yes—
38C2×C22⋊D149—22no—
39C2×C22⋊D149—22no—
40C2×C22⋊D149—22no—
41C22×Dic149—22no—
42C22×Dic149D412yes—
43C2×C4×D149—22no—
44D1192—41no—
45#14558721—42no—
46#14558720—41no—
47C2×#11924746C2312yes—
48C4⋊Dic149C2312yes—
49#14558715—22no—
50C22⋊Dic149—22no—
51#14558713—22no—
52#14558713—22no—
53C4×Dic149D411yescharacteristic
54C4×Dic149D411yescharacteristic
55C4×Dic149C2312yes—
56C2×D4×C149—22no—
57C2×D4×C149C2312yes—
58C22×C4×C149C2311yescharacteristic
59D8×C149—41no—
60M16×C149—41no—
61C2×C8×C149C2311yescharacteristic
62C2×C8×C149C2311yescharacteristic
63C4⋊C4×C149C2312yes—
64C22⋊C4×C149—22no—
65C22×D149—22no—
66Dic298—44no—
67D596—22no—
68D596—22no—
69C22⋊D149—44no—
70C22⋊D149—44no—
71C22⋊D149—44no—
72C2×Dic149—24no—
73C2×Dic149—22no—
74C2×Dic149—44no—
75C2×Dic149C2×D412yes—
76C2×Dic149C2×D412yes—
77C4×D149—44no—
78#11924746—22no—
79C23×C149—22no—
80C23×C149C2×D411yescharacteristic
81D4×C149—22no—
82D4×C149—22no—
83D4×C149—44no—
84C2×C4×C149—21no—
85C2×C4×C149—21no—
86C2×C4×C149—22no—
87C2×C4×C149C2×D411yescharacteristic
88C2×C4×C149C2411yescharacteristic
89C8×C149—21no—
90C8×C149—21no—
91C22×C149—21no—
92C22×C149—22no—
93C22×C149—42no—
94C22×C149—42no—
95C22×C149—42no—
96C22×C149C22×D411yescharacteristic
97C2×D149—42no—
98C2×D149—42no—
99C2×D149—42no—
100C4×C149—21no—
101C4×C149—42no—
102C4×C149H(5,𝔽2)11yescharacteristic
103C4×C1492−1+411yescharacteristic
104Dic149—22no—
105Dic149—42no—
106Dic149AGL(1,ℤ/8)14yes—
107C2×C149—41no—
108C2×C149—82no—
109C2×C149#53711yescharacteristic
110C2×C149C2×AGL(1,ℤ/8)12yes—
111D149—82no—
112C149#325311yescharacteristic, complemented, Sylow
113#3253—1491nomaximal, Sylow
114#532—1492no—
115#476—1492no—
116#476—1492no—
117#469—1491no—
118#469—1492no—
119#469D14911yescharacteristic, complemented
120#459—1492no—
121#459—1492no—
122#423—1491no—
123C2×#41—2982no—
124C2×D8—1492no—
125C2×D8—1491no—
126C2×D8C2×D14911yescharacteristic
127C2×M16—1491no—
128C2×M16C2×D14911yescharacteristic
129C4⋊Q8—1492no—
130#127—1492no—
131#124—2982no—
132#121—2982no—
133#121—1492no—
134#121C2×D14912yes—
135C4×D4—2982no—
136C4×D4—1492no—
137C4×D4—1492no—
138C2×C42—1491no—
139#106—1491no—
140#106—1492no—
141#106C2×D14911yescharacteristic
142C4⋊C8—1492no—
143C4⋊C8—1492no—
144#102—1492no—
145#102—1492no—
146#102—1492no—
147#102C2×D14912yes—
148#41—5968no—
149C2×Q8—2982no—
150C2×D4—22no—
151C2×D4—2982no—
152C2×D4—2982no—
153C2×D4—2982no—
154C2×D4—1492no—
155C2×D4C22×D14912yes—
156C22×C4—2982no—
157C22×C4—2982no—
158C22×C4—1492no—
159C22×C4C22×D14911yescharacteristic
160D8—41no—
161D8—5961no—
162D8—5962no—
163M16—41no—
164M16—5961no—
165C2×C8—1492no—
166C2×C8C22×D14911yescharacteristic
167C2×C8C22×D14911yescharacteristic
168C4⋊C4—2982no—
169C4⋊C4—1492no—
170C4⋊C4C22×D14912yes—
171C22⋊C4—22no—
172C22⋊C4—2982no—
173C22⋊C4—2982no—
174C22⋊C4—2982no—
175C42—1491no—
176C42—1491no—
177C42—1492no—
178C23—22no—
179C23—2982no—
180C23D4×D14911yescharacteristic
181Q8—5964no—
182D4—22no—
183D4—22no—
184D4—44no—
185D4—2982no—
186D4—2982no—
187D4—5964no—
188D4—5964no—
189D4—5964no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—2984no—
194C2×C4—2982no—
195C2×C4—5964no—
196C2×C4—5964no—
197C2×C4—1492no—
198C2×C4—1492no—
199C2×C4D4×D14911yescharacteristic
200C2×C4C23×D14911yescharacteristic
201C8—21no—
202C8—21no—
203C8—2982no—
204C22—22no—
205C22—21no—
206C22—42no—
207C22—42no—
208C22—42no—
209C22—5962no—
210C22—5962no—
211C22—5962no—
212C22C2×D4×D14911yescharacteristic
213C4—21no—
214C4—42no—
215C4—2982no—
216C4—5962no—
217C4—1494no—
218C4#1801195611yescharacteristic
219C4#1801195811yescharacteristic
220C2—41no—
221C2—82no—
222C2—11922no—
223C2#2375020211yescharacteristic
224C2AGL(1,ℤ/8)×D14912yes—
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#469×C149C2
socleC22×C149C22×D4
hypercenter#469D149
hypocenterC149#3253
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #23750170C2semidirect
2. #23749914C2semidirect
3. #23749913C2semidirect
4. #23749878C2semidirect
5. #23749876C2semidirect
6. #23749819C2semidirect
7. #23749818C2semidirect
8. #23749648C2semidirect
9. #469×C149C2semidirect
112. C149#3253semidirect
119. #469D149semidirect

Maximal subgroups

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

subgroupindex
#237501702
#237499142
#237499132
#237498782
#237498762
#237498192
#237498182
#237496482
#469×C1492
#3253149