Finite Group Databasebeta

← #34053172

Subgroups — #34053172

Order 19072.

704 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 704 conjugacy classes of subgroups — too many to draw. Only its 209 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
1C2×#18011958C211yesmaximal, characteristic
2#23750391C212yesmaximal, complemented
3#23749609C211yesmaximal, characteristic, complemented
4#23749606C214yesmaximal, complemented
5C2×#18011829C212yesmaximal, complemented
6#101×D149C214yesmaximal, complemented
7#413×C149C211yesmaximal, characteristic, complemented
8#18011958—24no—
9#18011958—24no—
10C2×#14558736C412yes—
11C2×#14558736C2211yescharacteristic
12C2×#14558735C414yes—
13C2×#14558735C2212yes—
14C22×Dic298C412yes—
15C22×Dic298C2211yescharacteristic
16C2×Q8×D149C2212yes—
17#18011919—24no—
18#18011917—24no—
19C2×#14558720C2212yes—
20M16×D149C2218yes—
21#18011830C2212yes—
22#18011829C2218yes—
23#18011828C2212yes—
24C2×#41×C149C2211yescharacteristic
25C2×M16×C149C2212yes—
26#101×C149C2212yes—
27#100×C149C2212yes—
28#14558736—24no—
29#14558736—24no—
30#14558736D414yes—
31#14558736D414yes—
32#14558735—216no—
33#14558735—28no—
34C2×Dic298—24no—
35C2×Dic298—24no—
36C2×Dic298—22no—
37C2×Dic298—22no—
38C2×Dic298C2×C414yes—
39C2×Dic298C2×C412yes—
40C2×Dic298C2×C411yescharacteristic
41C2×Dic298C2312yes—
42Q8×D149—28no—
43C2×D596C2×C411yescharacteristic
44C2×C22⋊D149C2×C414yes—
45C2×C22⋊D149C2×C412yes—
46C22×Dic149C2×C414yes—
47C22×Dic149C2×C412yes—
48C2×C4×D149C2×C414yes—
49C2×C4×D149C2312yes—
50#14558720—22no—
51#14558720C2314yes—
52#14558719—28no—
53C2×#11924746—22no—
54C8×D149—28no—
55#41×C149—22no—
56#41×C149—22no—
57C2×Q8×C149C2311yescharacteristic
58C2×D4×C149C2×C412yes—
59C2×D4×C149C2311yescharacteristic
60C22×C4×C149C2×C412yes—
61C22×C4×C149C2311yescharacteristic
62M16×C149—22no—
63M16×C149C2314yes—
64C2×C8×C149—22no—
65C22×D149C22×C412yes—
66Dic298—22no—
67Dic298—22no—
68Dic298—24no—
69Dic298—28no—
70Dic298C22⋊C412yes—
71Dic298C22⋊C412yes—
72D596C22⋊C412yes—
73D596C22⋊C412yes—
74C22⋊D149—28no—
75C22⋊D149C22⋊C418yes—
76C2×Dic149—24no—
77C2×Dic149—28no—
78C2×Dic149C22×C414yes—
79C2×Dic149C22×C412yes—
80C4×D149—28no—
81C4×D149C2×D418yes—
82#11924746—24no—
83C23×C149C22×C412yes—
84C23×C149C22×C411yescharacteristic
85Q8×C149—22no—
86D4×C149—24no—
87D4×C149—22no—
88C2×C4×C149—22no—
89C2×C4×C149—22no—
90C2×C4×C149C22×C412yes—
91C2×C4×C149C22×C411yescharacteristic
92C2×C4×C149C2×D412yes—
93C2×C4×C149C2×D412yes—
94C2×C4×C149C2411yescharacteristic
95C8×C149—24no—
96C22×C149—22no—
97C22×C149—41no—
98C22×C149—42no—
99C22×C149C2×C22⋊C412yes—
100C22×C149C23×C411yescharacteristic
101C2×D149—42no—
102C2×D149C2×C22⋊C414yes—
103C4×C149—22no—
104C4×C149C2×C22⋊C411yescharacteristic
105C4×C149C2×C22⋊C411yescharacteristic
106C4×C149C22×D412yes—
107Dic149—24no—
108Dic149C2×C22⋊C414yes—
109C2×C149—21no—
110C2×C149—22no—
111C2×C149—42no—
112C2×C149C22×C22⋊C411yescharacteristic
113D149—24no—
114C149#288911yescharacteristic, complemented, Sylow
115#2889—1491nomaximal, Sylow
116C2×2−1+4—1491no—
117#568—1492no—
118#413—1491no—
119#413—1494no—
120#413D14911yescharacteristic, complemented
121C2×#101—1492no—
122C2×#101—1494no—
1232−1+4—2984no—
1242−1+4—2984no—
125C2×#41—1494no—
126C2×#41—1492no—
127C2×#41—1492no—
128C2×#41—1491no—
129C2×#41C2×D14911yescharacteristic
130C22×Q8—1492no—
131C22×Q8—1492no—
132C22×Q8—1491no—
133#131—2984no—
134#131—2984no—
135C2×M16—1492no—
136C2×M16—1498no—
137C2×M16C2×D14912yes—
138#101—1492no—
139#101—1498no—
140#101C2×D14912yes—
141#100—1492no—
142#100C2×D14912yes—
143#41—22no—
144#41—22no—
145#41—2984no—
146#41—2984no—
147#41—29816no—
148#41—2988no—
149#41—1494no—
150#41—1494no—
151C2×Q8—2984no—
152C2×Q8—2984no—
153C2×Q8—2988no—
154C2×Q8—2982no—
155C2×Q8—2982no—
156C2×Q8—1492no—
157C2×Q8—1494no—
158C2×Q8—1491no—
159C2×Q8—1492no—
160C2×Q8C22×D14911yescharacteristic
161C2×D4—1494no—
162C2×D4—1492no—
163C2×D4—1491no—
164C2×D4C4×D14912yes—
165C2×D4C22×D14911yescharacteristic
166C22×C4—1492no—
167C22×C4—1494no—
168C22×C4—1494no—
169C22×C4—1492no—
170C22×C4C4×D14912yes—
171C22×C4C22×D14911yescharacteristic
172M16—22no—
173M16—2988no—
174M16—2982no—
175M16—1494no—
176M16C22×D14914yes—
177C2×C8—22no—
178C2×C8—2988no—
179C2×C8—2982no—
180C23—1492no—
181C23C2×C4×D14912yes—
182C23C2×C4×D14911yescharacteristic
183Q8—22no—
184Q8—2988no—
185Q8—2984no—
186Q8—2982no—
187Q8—2982no—
188Q8—1492no—
189Q8—1492no—
190D4—24no—
191D4—22no—
192D4—2988no—
193D4—1498no—
194D4—1492no—
195D4—1492no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—2988no—
199C2×C4—2984no—
200C2×C4—2988no—
201C2×C4—1494no—
202C2×C4—1492no—
203C2×C4—1498no—
204C2×C4C2×C4×D14912yes—
205C2×C4C2×C4×D14911yescharacteristic
206C2×C4D4×D14912yes—
207C2×C4D4×D14912yes—
208C2×C4C23×D14911yescharacteristic
209C8—24no—
210C8—2984no—
211C22—22no—
212C22—41no—
213C22—42no—
214C22—5962no—
215C22—1494no—
216C22C22⋊C4×D14912yes—
217C22C22×C4×D14911yescharacteristic
218C4—22no—
219C4—2984no—
220C4—1494no—
221C4C22⋊C4×D14911yescharacteristic
222C4C22⋊C4×D14911yescharacteristic
223C4C2×D4×D14912yes—
224C2—21no—
225C2—22no—
226C2—42no—
227C2—2984no—
228C2C2×C22⋊C4×D14911yescharacteristic
subgroupG/H
centerC2C2×C22⋊C4×D149
commutatorC22×C149C23×C4
FrattiniC2×C4C23×D149
Fitting#413×C149C2
socleC2×C149C22×C22⋊C4
prime radicalC2×#18011958C2
cosocleC2×C4×C149C24
hypercenter#413D149
hypocenterC149#2889
LCSG ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #23750391C2semidirect
3. #23749609C2semidirect
4. #23749606C2semidirect
5. C2×#18011829C2semidirect
6. #101×D149C2semidirect
7. #413×C149C2semidirect
114. C149#2889semidirect
120. #413D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119582
#237503912
#237496092
#237496062
C2×#180118292
#101×D1492
#413×C1492
#2889149