Finite Group Databasebeta

← #34052810

Subgroups — #34052810

Order 19072.

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

normal subgroups only

This group has 508 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#23749564C211yesmaximal, characteristic, complemented
2#23749553C212yesmaximal, complemented
3#23749542C211yesmaximal, characteristic, complemented
4#23749541C212yesmaximal, complemented
5#23749540C212yesmaximal, complemented
6#23749534C212yesmaximal, complemented
7#23749533C212yesmaximal, complemented
8#23749516C212yesmaximal, complemented
9#390×C149C211yesmaximal, characteristic, complemented
10C22×D596C2211yescharacteristic
11C22×C22⋊D149C2212yes—
12C22×C22⋊D149C2212yes—
13C2×C4⋊Dic149C2211yescharacteristic
14C2×#14558715C2212yes—
15C2×C22⋊Dic149C2212yes—
16C2×C22⋊Dic149C2212yes—
17C2×#14558713C2212yes—
18C2×#14558713C2212yes—
19C2×#14558713C2212yes—
20C2×#14558713C2212yes—
21#18011818C2212yes—
22#18011818C2212yes—
23#18011818C2212yes—
24#18011818C2211yescharacteristic
25#18011818C2211yescharacteristic
26C22×D4×C149C2211yescharacteristic
27C2×C4⋊C4×C149C2211yescharacteristic
28C2×C22⋊C4×C149C2212yes—
29C2×C22⋊C4×C149C2212yes—
30C2×C42×C149C2211yescharacteristic
31C23×D149C2312yes—
32C2×D596—42no—
33C2×D596—41no—
34C2×C22⋊D149—42no—
35C2×C22⋊D149—42no—
36C2×C22⋊D149—42no—
37C2×C22⋊D149—42no—
38C2×C22⋊D149—42no—
39C2×C22⋊D149—42no—
40C22×Dic149C2312yes—
41C22×Dic149C2312yes—
42C22×Dic149C2312yes—
43C4⋊Dic149—41no—
44#14558715—42no—
45C22⋊Dic149—42no—
46C22⋊Dic149—42no—
47#14558713—24no—
48#14558713—42no—
49#14558713—42no—
50#14558713—42no—
51C24×C149C2312yes—
52C2×D4×C149—22no—
53C2×D4×C149—41no—
54C2×D4×C149—41no—
55C22×C4×C149C2311yescharacteristic
56C22×C4×C149C2312yes—
57C22×C4×C149C2311yescharacteristic
58C22×C4×C149C2311yescharacteristic
59C4⋊C4×C149—41no—
60C22⋊C4×C149—42no—
61C22⋊C4×C149—42no—
62C42×C149—41no—
63C22×D149—22no—
64C22×D149—22no—
65C22×D149—22no—
66C22×D149—22no—
67C22×D149—22no—
68C22×D149—22no—
69C22×D149—22no—
70D596—44no—
71C22⋊D149—48no—
72C22⋊D149—48no—
73C2×Dic149—22no—
74C2×Dic149—22no—
75C2×Dic149—22no—
76C2×Dic149—22no—
77C2×Dic149—22no—
78C2×Dic149—22no—
79C2×Dic149—22no—
80C2×Dic149—22no—
81C2×Dic149—22no—
82C23×C149—22no—
83C23×C149—22no—
84C23×C149—22no—
85C23×C149—22no—
86C23×C149—22no—
87C23×C149—22no—
88C23×C149—22no—
89C23×C149C2411yescharacteristic
90D4×C149—44no—
91C2×C4×C149—21no—
92C2×C4×C149—21no—
93C2×C4×C149—22no—
94C2×C4×C149—21no—
95C2×C4×C149—22no—
96C2×C4×C149—22no—
97C2×C4×C149—22no—
98C2×C4×C149—21no—
99C2×C4×C149—22no—
100C2×C4×C149#4112yes—
101C22×C149—42no—
102C22×C149—42no—
103C22×C149—42no—
104C22×C149—42no—
105C22×C149—42no—
106C22×C149—42no—
107C22×C149—42no—
108C22×C149C2×#4111yescharacteristic
109C22×C149H(5,𝔽2)11yescharacteristic
110C22×C149H(5,𝔽2)11yescharacteristic
111C22×C149H(5,𝔽2)12yes—
112C22×C149H(5,𝔽2)12yes—
113C2×D149—42no—
114C2×D149—42no—
115C2×D149—42no—
116C2×D149—42no—
117C2×D149—42no—
118C2×D149—42no—
119C2×D149—42no—
120C4×C149—22no—
121C4×C149—41no—
122C4×C149—42no—
123C4×C149—41no—
124Dic149—42no—
125Dic149—42no—
126Dic149—42no—
127C2×C149—82no—
128C2×C149#53811yescharacteristic
129C2×C149#54012yes—
130C2×C149#56011yescharacteristic
131C2×C149#56012yes—
132C2×C149H(3,𝔽4)11yescharacteristic
133D149—82no—
134C149#282811yescharacteristic, complemented, Sylow
135#2828—1491nomaximal, Sylow
136#400—1491no—
137#397—1492no—
138#394—1491no—
139#394—1492no—
140#394—1492no—
141#392—1492no—
142#392—1492no—
143#390D14911yescharacteristic, complemented
144#388—1492no—
145C22×D4—1492no—
146C22×D4—1492no—
147C22×D4—1491no—
148C22×D4C2×D14911yescharacteristic
149C2×C4⋊C4—1492no—
150C2×C4⋊C4—1491no—
151C2×C4⋊C4C2×D14911yescharacteristic
152C2×C22⋊C4—1492no—
153C2×C22⋊C4—1492no—
154C2×C22⋊C4—1492no—
155C2×C22⋊C4—1492no—
156C2×C22⋊C4—1492no—
157C2×C22⋊C4—1492no—
158C2×C22⋊C4C2×D14912yes—
159C2×C22⋊C4C2×D14912yes—
160C2×C42C2×D14911yescharacteristic
161#95—1492no—
162#95—1492no—
163#95—1492no—
164#95—1491no—
165#95—1491no—
166C24—1492no—
167C24C22×D14912yes—
168C2×D4—22no—
169C2×D4—41no—
170C2×D4—41no—
171C2×D4—5962no—
172C2×D4—5961no—
173C2×D4—5962no—
174C2×D4—5962no—
175C2×D4—5962no—
176C2×D4—5962no—
177C2×D4—5962no—
178C2×D4—5962no—
179C22×C4—1492no—
180C22×C4—1492no—
181C22×C4—1492no—
182C22×C4C22×D14911yescharacteristic
183C22×C4C22×D14912yes—
184C22×C4C22×D14911yescharacteristic
185C22×C4C22×D14911yescharacteristic
186C4⋊C4—41no—
187C4⋊C4—5962no—
188C4⋊C4—5961no—
189C22⋊C4—42no—
190C22⋊C4—42no—
191C22⋊C4—2984no—
192C22⋊C4—5962no—
193C22⋊C4—5962no—
194C22⋊C4—5962no—
195C22⋊C4—5962no—
196C22⋊C4—5962no—
197C42—41no—
198C23—22no—
199C23—22no—
200C23—22no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—22no—
205C23—2982no—
206C23—2982no—
207C23—2982no—
208C23—2982no—
209C23—2982no—
210C23—2982no—
211C23—2982no—
212C23C23×D14911yescharacteristic
213D4—44no—
214D4—5964no—
215D4—5968no—
216D4—5968no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—2982no—
227C2×C4—2982no—
228C2×C4—2982no—
229C2×C4—2982no—
230C2×C4—2982no—
231C2×C4—2982no—
232C2×C4—2982no—
233C2×C4—2982no—
234C2×C4—2982no—
235C2×C4#1455873612yes—
236C22—42no—
237C22—42no—
238C22—42no—
239C22—42no—
240C22—42no—
241C22—42no—
242C22—42no—
243C22—5962no—
244C22—5962no—
245C22—5962no—
246C22—5962no—
247C22—5962no—
248C22—5962no—
249C22—5962no—
250C22C2×#1455873611yescharacteristic
251C22#1801195611yescharacteristic
252C22#1801195611yescharacteristic
253C22#1801195612yes—
254C22#1801195712yes—
255C4—22no—
256C4—41no—
257C4—41no—
258C4—42no—
259C4—5962no—
260C4—5962no—
261C4—5962no—
262C2—82no—
263C2—11922no—
264C2#2375021311yescharacteristic
265C2#2375022612yes—
266C2#2375036211yescharacteristic
267C2#2375036312yes—
268C2#2375036711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutator, socle, cosocleC23×C149C24
Fitting#390×C149C2
hypercenter#390D149
hypocenterC149#2828
LCSG ▷ C23×C149 ▷ C149
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #23749564C2semidirect
2. #23749553C2semidirect
3. #23749542C2semidirect
4. #23749541C2semidirect
5. #23749540C2semidirect
6. #23749534C2semidirect
7. #23749533C2semidirect
8. #23749516C2semidirect
9. #390×C149C2semidirect
134. C149#2828semidirect
143. #390D149semidirect

Maximal subgroups

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

subgroupindex
#237495642
#237495532
#237495422
#237495412
#237495402
#237495342
#237495332
#237495162
#390×C1492
#2828149