Finite Group Databasebeta

← #34060717

Subgroups — #34060717

Order 19072.

390 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 72 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×D149⋊M16C211yesmaximal, characteristic, complemented
2C2×#18011971C212yesmaximal, complemented
3#23750597C211yesmaximal, characteristic, complemented
4#23750505C212yesmaximal, complemented
5C2×#18011884C211yesmaximal, characteristic
6C2×#14558746—21no—
7D149⋊M16—24no—
8C2×#14558745C2212yes—
9C2×#14558745C2212yes—
10C2×D149⋊C8—21no—
11#18011971—24no—
12#18011968—21no—
13#18011968—21no—
14C22×D596C411yescharacteristic
15C22×C22⋊D149C411yescharacteristic
16C22×C22⋊D149C2211yescharacteristic
17C22×C4×D149C2211yescharacteristic
18#18011884—21no—
19#18011884—21no—
20#18011884—21no—
21#18011884—21no—
22C2×#14558715C2211yescharacteristic
23C2×#14558713C411yescharacteristic
24C2×C22⋊C4×C149C411yescharacteristic
25#14558746—24no—
26#14558745—22no—
27#14558745—22no—
28#14558745—22no—
29#14558745D414yescomplemented
30D149⋊C8—24no—
31C2×#11924753—22no—
32C2×#11924753—22no—
33C23×D149C2×C411yescharacteristic
34C23×D149C2×C411yescharacteristic
35C2×D596—21no—
36C2×D596—21no—
37C2×D596—42no—
38C2×C22⋊D149—21no—
39C2×C22⋊D149—21no—
40C2×C22⋊D149—22no—
41C2×C22⋊D149—21no—
42C2×C22⋊D149—21no—
43C2×C22⋊D149—22no—
44C2×C22⋊D149—42no—
45C22×Dic149C2×C411yescharacteristic
46C22×Dic149C2311yescharacteristic
47C2×C4×D149—22no—
48C2×C4×D149—22no—
49C2×C4×D149D411yescharacteristic
50C2×C4×D149D411yescharacteristic
51C2×C4×D149D411yescharacteristic
52C2×C4×D149D411yescharacteristic
53#14558715—21no—
54#14558715—21no—
55#14558713—21no—
56#14558713—21no—
57C24×C149C2×C411yescharacteristic
58C22×C4×C149C2×C411yescharacteristic
59C22×C4×C149C2×C411yescharacteristic
60C22⋊C4×C149—21no—
61C22⋊C4×C149—21no—
62#11924753—24no—
63#11924753—42no—
64C22×D149—22no—
65C22×D149—22no—
66C22×D149—21no—
67C22×D149—22no—
68C22×D149—41no—
69C22×D149—41no—
70C22×D149—41no—
71C22×D149C22⋊C411yescharacteristic
72C22×D149C22⋊C411yescharacteristic
73D596—42no—
74D596—42no—
75C22⋊D149—42no—
76C22⋊D149—42no—
77C22⋊D149—41no—
78C22⋊D149—42no—
79C22⋊D149—41no—
80C2×Dic149—21no—
81C2×Dic149—41no—
82C2×Dic149C2×D412yes—
83C2×Dic149C2×D411yescharacteristic
84C2×Dic149C2×D411yescharacteristic
85C2×Dic149#4112yes—
86C4×D149—21no—
87C4×D149—21no—
88C4×D149—22no—
89C4×D149—22no—
90C4×D149—21no—
91C4×D149—21no—
92C23×C149—21no—
93C23×C149—22no—
94C23×C149—41no—
95C23×C149—41no—
96C23×C149C22×C411yescharacteristic
97C2×C4×C149—22no—
98C2×C4×C149—21no—
99C2×C4×C149—41no—
100C2×C4×C149C22⋊C411yescharacteristic
101C2×C4×C149C22⋊C411yescharacteristic
102C22×C149—21no—
103C22×C149—21no—
104C22×C149—41no—
105C22×C149—41no—
106C22×C149—41no—
107C22×C149—82no—
108C22×C149C2×C22⋊C411yescharacteristic
109C22×C149C4×D412yes—
110C2×D149—21no—
111C2×D149—21no—
112C2×D149—21no—
113C2×D149—21no—
114C2×D149—21no—
115C2×D149—44no—
116C2×D149—41no—
117C2×D149—41no—
118C2×D149—41no—
119C2×D149—82no—
120C2×D149#10012yescomplemented
121C4×C149—21no—
122C4×C149—21no—
123C4×C149—41no—
124Dic149—41no—
125Dic149#12011yescharacteristic
126Dic149#12112yes—
127Dic149#12311yescharacteristic
128C2×C149—22no—
129C2×C149—81no—
130C2×C149#38611yescharacteristic
131C2×C149C2×#10011yescharacteristic
132C2×C149#41311yescharacteristic
133D149—22no—
134D149—41no—
135D149—81no—
136C149#190011yescharacteristic, complemented, Sylow
137#1900—1491nomaximal, Sylow
138C22×M16—1491no—
139C2×#121—1491no—
140C2×#100—1492no—
141#407—1491no—
142#343—1492no—
143C22×D4—1491no—
144C22×D4—1491no—
145C22×D4—1491no—
146C23×C4—1491no—
147C2×M16—2981no—
148C2×M16—2984no—
149C2×M16—1492no—
150C2×M16—1492no—
151C22×C8—2981no—
152#121—2981no—
153#121—2981no—
154#121—2981no—
155#121—2981no—
156C2×C4⋊C4—1491no—
157C2×C22⋊C4—1491no—
158C2×C22⋊C4#1059701011yescharacteristic
159#100—2984no—
160C22⋊C8—2981no—
161C22⋊C8—2981no—
162C24—1491no—
163C24—1491no—
164C24C2×#1059701011yescharacteristic
165C2×D4—2981no—
166C2×D4—2981no—
167C2×D4—2981no—
168C2×D4—2981no—
169C2×D4—2982no—
170C2×D4—2981no—
171C2×D4—2981no—
172C2×D4—2982no—
173C2×D4—5962no—
174C2×D4—5962no—
175C22×C4—2982no—
176C22×C4—2982no—
177C22×C4—1491no—
178C22×C4—1491no—
179C22×C4—1491no—
180C22×C4—1491no—
181C22×C4—1491no—
182C22×C4—1491no—
183C22×C4C2×#1059701011yescharacteristic
184C22×C4C2×#1059701011yescharacteristic
185M16—2984no—
186M16—2982no—
187M16—2982no—
188M16—2982no—
189M16—1494no—
190C2×C8—2984no—
191C2×C8—2982no—
192C2×C8—2982no—
193C4⋊C4—2981no—
194C4⋊C4—2981no—
195C22⋊C4—21no—
196C22⋊C4—21no—
197C22⋊C4—2981no—
198C22⋊C4—2981no—
199C23—21no—
200C23—22no—
201C23—41no—
202C23—41no—
203C23—2982no—
204C23—2982no—
205C23—2981no—
206C23—2982no—
207C23—5961no—
208C23—5961no—
209C23—5961no—
210C23—1491no—
211C23—1491no—
212C23C22×#1059701011yescharacteristic
213D4—5962no—
214D4—5962no—
215D4—5962no—
216D4—5962no—
217D4—5961no—
218D4—5962no—
219D4—5961no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—41no—
223C2×C4—2981no—
224C2×C4—2981no—
225C2×C4—2982no—
226C2×C4—2982no—
227C2×C4—2981no—
228C2×C4—2981no—
229C2×C4—2981no—
230C2×C4—5961no—
231C2×C4—1491no—
232C2×C4—1491no—
233C2×C4—1492no—
234C2×C4—1492no—
235C2×C4C22⋊#1059701011yescharacteristic
236C2×C4C22⋊#1059701011yescharacteristic
237C8—2984no—
238C8—5962no—
239C22—21no—
240C22—21no—
241C22—41no—
242C22—41no—
243C22—41no—
244C22—82no—
245C22—2981no—
246C22—2981no—
247C22—2981no—
248C22—2981no—
249C22—2981no—
250C22—5964no—
251C22—5961no—
252C22—5961no—
253C22—5961no—
254C22—1492no—
255C22—11922no—
256C22C2×C22⋊#1059701011yescharacteristic
257C22D4×#1059701012yes—
258C4—21no—
259C4—21no—
260C4—41no—
261C4—5961no—
262C4—1491no—
263C4—1492no—
264C4—1491no—
265C2—22no—
266C2—81no—
267C2—2982no—
268C2—5961no—
269C2—11921no—
270C2#2375057311yescharacteristic
271C2D149⋊#10011yescharacteristic
272C2#2375061111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC23×C149C22×C4
FrattiniC23C22×#10597010
FittingC2×C22⋊C4×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC2×#18011884C2
cosocleC22×Dic149C23
hypercenterC2×C22⋊C4#10597010
hypocenterC149#1900
LCSG ▷ C23×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×D149⋊M16C2semidirect
2. C2×#18011971C2semidirect
3. #23750597C2semidirect
4. #23750505C2semidirect
29. #14558745D4semidirect
120. C2×D149#100semidirect
136. C149#1900semidirect

Maximal subgroups

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

subgroupindex
C2×D149⋊M162
C2×#180119712
#237505972
#237505052
C2×#180118842
#1900149