Finite Group Databasebeta

← #34052815

Subgroups — #34052815

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#23749554C212yesmaximal, complemented
2#23749543C212yesmaximal, complemented
3#23749542C211yesmaximal, characteristic, complemented
4#23749542C212yesmaximal, complemented
5#23749535C212yesmaximal, complemented
6#23749535C212yesmaximal, complemented
7#23749526C211yesmaximal, characteristic, complemented
8#23749514C212yesmaximal, complemented
9#400×C149C211yesmaximal, characteristic, complemented
10C22×D596C2211yescharacteristic
11C22×D596C2212yes—
12C22×D596C2211yescharacteristic
13C22×D596C2212yes—
14C2×#14558715C2212yes—
15C2×#14558713C2212yes—
16C2×#14558713C2212yes—
17C2×#14558713C2212yes—
18C2×#14558713C2212yes—
19C2×#14558713C2212yes—
20C2×#14558713C2212yes—
21C2×#14558713C2212yes—
22C2×#14558713C2212yes—
23C2×C4×Dic149C2211yescharacteristic
24#18011818C2212yes—
25#18011818C2211yescharacteristic
26C2×C4⋊C4×C149C2211yescharacteristic
27C2×C4⋊C4×C149C2211yescharacteristic
28#95×C149C2212yes—
29#95×C149C2212yes—
30#95×C149C2211yescharacteristic
31C23×D149C2312yes—
32C23×D149C2312yes—
33C2×D596—22no—
34C2×D596—41no—
35C2×D596—41no—
36C2×D596—41no—
37C2×D596—42no—
38C2×D596—42no—
39C2×D596—42no—
40C2×D596—42no—
41C2×D596—42no—
42C2×D596—42no—
43C2×D596—42no—
44C22×Dic149C2312yes—
45C22×Dic149C2312yes—
46#14558715—42no—
47#14558713—24no—
48#14558713—42no—
49#14558713—42no—
50#14558713—42no—
51#14558713—42no—
52#14558713—42no—
53#14558713—42no—
54#14558713—42no—
55C4×Dic149—41no—
56C22×C4×C149C2312yes—
57C22×C4×C149C2312yes—
58C22×C4×C149C2311yescharacteristic
59C22×C4×C149C2311yescharacteristic
60C22×C4×C149C2311yescharacteristic
61C4⋊C4×C149—41no—
62C4⋊C4×C149—41no—
63C22×D149—22no—
64C22×D149—22no—
65C22×D149—22no—
66C22×D149—22no—
67C22×D149—22no—
68C22×D149—22no—
69C22×D149—22no—
70C22×D149—22no—
71C22×D149—22no—
72C22×D149—22no—
73C22×D149—22no—
74C22×D149—22no—
75C22×D149—22no—
76C22×D149—22no—
77D596—44no—
78D596—44no—
79D596—48no—
80D596—48no—
81C2×Dic149—22no—
82C2×Dic149—22no—
83C2×Dic149—22no—
84C2×Dic149—22no—
85C2×Dic149—22no—
86C2×Dic149—22no—
87C23×C149C2411yescharacteristic
88C2×C4×C149—21no—
89C2×C4×C149—21no—
90C2×C4×C149—21no—
91C2×C4×C149—22no—
92C2×C4×C149—22no—
93C2×C4×C149—22no—
94C2×C4×C149—22no—
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×C149C2×#4111yescharacteristic
102C22×C149H(5,𝔽2)11yescharacteristic
103C22×C149H(5,𝔽2)11yescharacteristic
104C22×C149H(5,𝔽2)12yes—
105C22×C149H(5,𝔽2)12yes—
106C2×D149—42no—
107C2×D149—42no—
108C2×D149—42no—
109C2×D149—42no—
110C2×D149—42no—
111C2×D149—42no—
112C2×D149—42no—
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—41no—
123C4×C149—42no—
124C4×C149—42no—
125Dic149—42no—
126Dic149—42no—
127C2×C149#53811yescharacteristic
128C2×C149#54012yes—
129C2×C149#56011yescharacteristic
130C2×C149#56012yes—
131C2×C149H(3,𝔽4)11yescharacteristic
132D149—82no—
133D149—82no—
134C149#282811yescharacteristic, complemented, Sylow
135#2828—1491nomaximal, Sylow
136#400D14911yescharacteristic, complemented
137#397—1492no—
138#394—1492no—
139#394—1491no—
140#394—1492no—
141#392—1492no—
142#392—1492no—
143#390—1491no—
144#388—1492no—
145C22×D4—1491no—
146C22×D4—1492no—
147C22×D4—1491no—
148C22×D4—1492no—
149C2×C4⋊C4—1492no—
150C2×C4⋊C4C2×D14911yescharacteristic
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⋊C4—1492no—
159C2×C22⋊C4—1492no—
160C2×C42—1491no—
161#95—1492no—
162#95—1491no—
163#95C2×D14912yes—
164#95C2×D14912yes—
165#95C2×D14911yescharacteristic
166C24—1492no—
167C24—1492no—
168C2×D4—2982no—
169C2×D4—5961no—
170C2×D4—5961no—
171C2×D4—5961no—
172C2×D4—5962no—
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×C4C22×D14912yes—
182C22×C4C22×D14911yescharacteristic
183C22×C4C22×D14912yes—
184C22×C4C22×D14911yescharacteristic
185C22×C4C22×D14911yescharacteristic
186C4⋊C4—41no—
187C4⋊C4—41no—
188C4⋊C4—5962no—
189C22⋊C4—2984no—
190C22⋊C4—5962no—
191C22⋊C4—5962no—
192C22⋊C4—5962no—
193C22⋊C4—5962no—
194C22⋊C4—5962no—
195C22⋊C4—5962no—
196C22⋊C4—5962no—
197C42—5961no—
198C23—2982no—
199C23—2982no—
200C23—2982no—
201C23—2982no—
202C23—2982no—
203C23—2982no—
204C23—2982no—
205C23—2982no—
206C23—2982no—
207C23—2982no—
208C23—2982no—
209C23—2982no—
210C23—2982no—
211C23—2982no—
212C23C23×D14911yescharacteristic
213D4—5964no—
214D4—5964no—
215D4—5968no—
216D4—5968no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—2982no—
230C2×C4—2982no—
231C2×C4—2982no—
232C2×C4—2982no—
233C2×C4—2982no—
234C2×C4—2982no—
235C2×C4#1455873712yes—
236C22—5962no—
237C22—5962no—
238C22—5962no—
239C22—5962no—
240C22—5962no—
241C22—5962no—
242C22—5962no—
243C22—5962no—
244C22—5962no—
245C22—5962no—
246C22—5962no—
247C22—5962no—
248C22—5962no—
249C22—5962no—
250C22C2×#1455873711yescharacteristic
251C22#1801195611yescharacteristic
252C22#1801195711yescharacteristic
253C22#1801195712yes—
254C22#1801195712yes—
255C4—22no—
256C4—41no—
257C4—41no—
258C4—42no—
259C4—42no—
260C4—5962no—
261C4—5962no—
262C2—11922no—
263C2—11922no—
264C2#2375021511yescharacteristic
265C2#2375023112yes—
266C2#2375036511yescharacteristic
267C2#2375036612yes—
268C2#2375036711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutator, socle, cosocleC23×C149C24
Fitting#400×C149C2
hypercenter#400D149
hypocenterC149#2828
LCSG ▷ C23×C149 ▷ C149
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. #23749554C2semidirect
2. #23749543C2semidirect
3. #23749542C2semidirect
4. #23749542C2semidirect
5. #23749535C2semidirect
6. #23749535C2semidirect
7. #23749526C2semidirect
8. #23749514C2semidirect
9. #400×C149C2semidirect
134. C149#2828semidirect
136. #400D149semidirect

Maximal subgroups

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

subgroupindex
#237495542
#237495432
#237495422
#237495352
#237495262
#237495142
#400×C1492
#2828149