Finite Group Databasebeta

← #34055340

Subgroups — #34055340

Order 19072.

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

normal subgroups only

This group has 386 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#23750231C211yesmaximal, characteristic, complemented
2#23750229C211yesmaximal, characteristic, complemented
3#23750024C211yesmaximal, characteristic, complemented
4#23750001C211yesmaximal, characteristic, complemented
5#23749990C211yesmaximal, characteristic, complemented
6#23749877C212yesmaximal, complemented
7#23749860C212yesmaximal, complemented
8#23749734C212yesmaximal, complemented
9#23749705C212yesmaximal, complemented
10#23749582C211yesmaximal, characteristic, complemented
11#490×C149C211yesmaximal, characteristic, complemented
12C2×#14558721C2212yes—
13C2×#14558721C2212yes—
14C2×#14558719C2211yescharacteristic
15C2×C8×D149C2211yescharacteristic
16#18011908C2211yescharacteristic
17#18011903C2211yescharacteristic
18#18011896—22no—
19#18011892—22no—
20#18011886—22no—
21#18011886C2212yes—
22#18011883—22no—
23#18011882C2212yes—
24D4×Dic149C2212yes—
25#18011873C2212yes—
26#18011868C2211yescharacteristic
27#18011844C2212yes—
28#18011842C2212yes—
29#18011833C2212yes—
30#18011833C2212yes—
31#18011821C2211yescharacteristic
32C4×#11924746C2211yescharacteristic
33C8×Dic149C2211yescharacteristic
34#127×C149C2211yescharacteristic
35#125×C149C2211yescharacteristic
36#102×C149C2212yes—
37#102×C149C2212yes—
38#97×C149C2211yescharacteristic
39C2×D596—22no—
40C2×D596—22no—
41C2×D596C2312yes—
42C2×C22⋊D149—22no—
43C22×Dic149—22no—
44C2×C4×D149—22no—
45C2×C4×D149C2311yescharacteristic
46#14558721—24no—
47#14558721—24no—
48#14558719—22no—
49C2×#11924746C2311yescharacteristic
50C2×#11924746C2311yescharacteristic
51C8×D149—22no—
52C4⋊Dic149C2312yes—
53#14558715—22no—
54#14558715D412yes—
55C22⋊Dic149—22no—
56C22⋊Dic149—22no—
57#14558713—22no—
58#14558713—22no—
59#14558713D412yes—
60C4×Dic149C2311yescharacteristic
61C2×D4×C149—22no—
62C2×D4×C149C2312yes—
63C2×C8×C149C2311yescharacteristic
64C2×C8×C149C2311yescharacteristic
65C4⋊C4×C149—22no—
66C4⋊C4×C149C2312yes—
67C42×C149C2311yescharacteristic
68C22×D149—22no—
69C22×D149C2×D411yescharacteristic
70D596—22no—
71D596—22no—
72D596—82no—
73D596—82no—
74C22⋊D149—82no—
75C2×Dic149—22no—
76C2×Dic149—82no—
77C2×Dic149C2×D412yes—
78C2×Dic149C2×D411yescharacteristic
79C4×D149—21no—
80C4×D149—21no—
81C4×D149—82no—
82#11924746#4112yes—
83#11924746#4112yes—
84C23×C149—22no—
85D4×C149—22no—
86D4×C149—22no—
87D4×C149—82no—
88C2×C4×C149—22no—
89C2×C4×C149C2×D412yes—
90C2×C4×C149C2411yescharacteristic
91C8×C149—21no—
92C8×C149—21no—
93C22×C149—42no—
94C22×C149—42no—
95C22×C149—42no—
96C22×C149C22×D411yescharacteristic
97C2×D149—21no—
98C2×D149—22no—
99C2×D149—42no—
100C2×D149—42no—
101C2×D149—42no—
102C4×C149—22no—
103C4×C149—42no—
104C4×C149C2×#4111yescharacteristic
105C4×C149C2×#4111yescharacteristic
106Dic149—21no—
107Dic149—22no—
108Dic149—42no—
109C2×C149—82no—
110C2×C149#53211yescharacteristic
111C2×C149#57612yes—
112D149—41no—
113D149—82no—
114C149#317611yescharacteristic, complemented, Sylow
115#3176—1491nomaximal, Sylow
116#540—1491no—
117#540—1491no—
118#499—1491no—
119#493—1491no—
120#490—1491no—
121#490D14911yescharacteristic, complemented
122#469—1492no—
123#466—1492no—
124#442—1492no—
125C4×D8—1492no—
126#405—1491no—
127C2×D8—1492no—
128C2×D8—1492no—
129C2×M16—1491no—
130C22×C8—1491no—
131#127—1491no—
132#127C2×D14911yescharacteristic
133#125—1491no—
134#125C2×D14911yescharacteristic
135#123—2982no—
136#123—2982no—
137#121—2982no—
138#121—2982no—
139#121—1492no—
140#121—1492no—
141C4×D4—1492no—
142C4×D4—1492no—
143#117—1491no—
144#107—1492no—
145#106—1492no—
146#102—1492no—
147#102—1492no—
148#102C2×D14912yes—
149#102C2×D14912yes—
150#97—1491no—
151#97C2×D14911yescharacteristic
152C4×C8—1491no—
153C4×C8—1491no—
154C2×D4—22no—
155C2×D4—2982no—
156C2×D4—2982no—
157C2×D4—2982no—
158C2×D4—1492no—
159C2×D4C22×D14912yes—
160C22×C4—2982no—
161C22×C4—2982no—
162C22×C4—1491no—
163D8—2984no—
164D8—2984no—
165M16—2982no—
166C2×C8—2982no—
167C2×C8—1491no—
168C2×C8—1491no—
169C2×C8C22×D14911yescharacteristic
170C2×C8C22×D14911yescharacteristic
171C4⋊C4—22no—
172C4⋊C4—2982no—
173C4⋊C4—1492no—
174C4⋊C4—1492no—
175C4⋊C4C22×D14912yes—
176C22⋊C4—2982no—
177C22⋊C4—2982no—
178C22⋊C4—2982no—
179C22⋊C4—2982no—
180C22⋊C4—1492no—
181C42—1491no—
182C42C22×D14911yescharacteristic
183C23—22no—
184C23—2982no—
185C23—1491no—
186D4—22no—
187D4—22no—
188D4—82no—
189D4—2982no—
190D4—2982no—
191D4—11922no—
192D4—11922no—
193D4—11922no—
194C2×C4—22no—
195C2×C4—2981no—
196C2×C4—2981no—
197C2×C4—2982no—
198C2×C4—1492no—
199C2×C4—1491no—
200C2×C4—11922no—
201C2×C4—11922no—
202C2×C4D4×D14912yes—
203C2×C4C23×D14911yescharacteristic
204C8—21no—
205C8—21no—
206C8—1492no—
207C8—1492no—
208C22—42no—
209C22—42no—
210C22—42no—
211C22—2982no—
212C22—2981no—
213C22—5962no—
214C22—5962no—
215C22—5962no—
216C22C2×D4×D14911yescharacteristic
217C4—22no—
218C4—42no—
219C4—2982no—
220C4—2981no—
221C4—5962no—
222C4#41×D14911yescharacteristic
223C4#41×D14911yescharacteristic
224C2—82no—
225C2—5961no—
226C2—11922no—
227C2#2375017411yescharacteristic
228C2#2375042912yes—
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#490×C149C2
socleC22×C149C22×D4
hypercenter#490D149
hypocenterC149#3176
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #23750231C2semidirect
2. #23750229C2semidirect
3. #23750024C2semidirect
4. #23750001C2semidirect
5. #23749990C2semidirect
6. #23749877C2semidirect
7. #23749860C2semidirect
8. #23749734C2semidirect
9. #23749705C2semidirect
10. #23749582C2semidirect
11. #490×C149C2semidirect
114. C149#3176semidirect
121. #490D149semidirect

Maximal subgroups

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

subgroupindex
#237502312
#237502292
#237500242
#237500012
#237499902
#237498772
#237498602
#237497342
#237497052
#237495822
#490×C1492
#3176149