Finite Group Databasebeta

← #34060672

Subgroups — #34060672

Order 19072.

376 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C22×#14558746C211yesmaximal, characteristic, complemented
2C2×#18011976C212yesmaximal, complemented
3C4×C22⋊#10597010C211yesmaximal, characteristic, complemented
4#23750495C212yesmaximal, complemented
5#23750138C211yesmaximal, characteristic
6C2×#14558746—24no—
7C2×#14558746—21no—
8C2×#14558746C2212yes—
9C22×#11924753—21no—
10C2×C22⋊#10597010—21no—
11C2×C4×#10597010C2212yes—
12#18011976—24no—
13(C2×#10597010)⋊C4—21no—
14C2×#14558737C2211yescharacteristic
15C22×C4×D149C2211yescharacteristic
16#18011896—21no—
17#18011887C411yescharacteristic, complemented
18#18011886C411yescharacteristic, complemented
19#18011885C411yescharacteristic, complemented
20#18011881—21no—
21#18011873—21no—
22#18011871—21no—
23#18011869C2211yescharacteristic
24C22⋊Q8×C149C411yescharacteristic, complemented
25C22×#10597010—22no—
26#14558746—24no—
27#14558746—22no—
28#14558746D414yescomplemented
29C2×#11924753—24no—
30C2×#11924753—22no—
31C22⋊#10597010—24no—
32C4×#10597010—22no—
33C4×#10597010—22no—
34C23×D149D411yescharacteristic
35#14558737—22no—
36#14558737—22no—
37C2×D596—21no—
38C2×D596—21no—
39C2×D596C2×C411yescharacteristic
40C2×C22⋊D149—21no—
41C22×Dic149D411yescharacteristic
42C2×C4×D149—22no—
43C2×C4×D149—22no—
44C2×C4×D149—21no—
45C2×C4×D149C2×C411yescharacteristic
46C2×C4×D149D411yescharacteristic
47C2×C4×D149D411yescharacteristic
48C2×C4×D149C2311yescharacteristic
49C4⋊Dic149C2×C411yescharacteristic
50#14558715—21no—
51#14558713—21no—
52#14558713—21no—
53#14558713—21no—
54#14558713—21no—
55C4×Dic149—21no—
56C2×Q8×C149C2×C411yescharacteristic
57C22×C4×C149C2×C411yescharacteristic
58C4⋊C4×C149—21no—
59C4⋊C4×C149C2×C411yescharacteristic
60C22⋊C4×C149—21no—
61C2×#10597010—24no—
62C2×#10597010—42no—
63C2×#10597010—42no—
64#11924753—24no—
65C22×D149—22no—
66C22×D149—22no—
67C22×D149—21no—
68C22×D149—41no—
69C22×D149C22⋊C411yescharacteristic
70C22×D149C2×D411yescharacteristic
71D596—22no—
72D596—42no—
73D596—42no—
74C22⋊D149—42no—
75C2×Dic149—21no—
76C2×Dic149—21no—
77C2×Dic149—21no—
78C2×Dic149C22⋊C411yescharacteristic
79C2×Dic149C2×D411yescharacteristic
80C4×D149—22no—
81C4×D149—22no—
82C4×D149—21no—
83C4×D149—21no—
84C4×D149—41no—
85C4×D149—41no—
86C4×D149C2×D412yes—
87C4×D149#4112yes—
88C23×C149C22⋊C411yescharacteristic
89Q8×C149—22no—
90C2×C4×C149—22no—
91C2×C4×C149—21no—
92C2×C4×C149—21no—
93C2×C4×C149C22⋊C411yescharacteristic
94C2×C4×C149C22×C411yescharacteristic
95C22×C149—21no—
96C22×C149—21no—
97C22×C149#10412yescomplemented
98C22×C149C2×C22⋊C411yescharacteristic
99C2×D149—21no—
100C2×D149—21no—
101C2×D149—21no—
102C2×D149—21no—
103C2×D149—21no—
104C2×D149—44no—
105C2×D149—41no—
106C2×D149—41no—
107C2×D149—41no—
108C2×D149#12112yes—
109#10597010—44no—
110C4×C149—21no—
111C4×C149—41no—
112C4×C149—41no—
113C4×C149C4×D412yes—
114Dic149—21no—
115Dic149—41no—
116Dic149#12011yescharacteristic
117Dic149#12311yescharacteristic
118C2×C149—22no—
119C2×C149#38611yescharacteristic
120C2×C149C2×#10411yescharacteristic
121C2×C149#42111yescharacteristic
122D149—22no—
123D149—41no—
124D149—81no—
125C149#187111yescharacteristic, complemented, Sylow
126#1871—1491nomaximal, Sylow
127C22×M16—1491no—
128#525—1491no—
129C2×#104—1492no—
130C4×C22⋊C4—1491no—
131#339—1492no—
132C2×#41—1491no—
133C23×C4—1491no—
134C2×M16—2981no—
135C2×M16—2984no—
136C2×M16—1492no—
137C22×C8—2981no—
138#123—2981no—
139C22⋊Q8—1491no—
140C22⋊Q8#1059701011yescharacteristic, complemented
141#121—1491no—
142#121—1491no—
143#120—2981no—
144C4×D4—2981no—
145C4×D4—2981no—
146#117—1491no—
147C2×C22⋊C4—2981no—
148C2×C42—1492no—
149#104—2984no—
150#95—2981no—
151C24—1491no—
152#41—2982no—
153#41—2982no—
154C2×Q8C2×#1059701011yescharacteristic
155C2×D4—2981no—
156C2×D4—2981no—
157C2×D4—2981no—
158C2×D4—1491no—
159C22×C4—2982no—
160C22×C4—2982no—
161C22×C4—2981no—
162C22×C4—2982no—
163C22×C4—1491no—
164C22×C4—1491no—
165C22×C4—1491no—
166C22×C4—1491no—
167C22×C4—1491no—
168C22×C4C2×#1059701011yescharacteristic
169M16—2984no—
170M16—2982no—
171M16—1494no—
172C2×C8—2984no—
173C2×C8—2982no—
174C4⋊C4—21no—
175C4⋊C4—2981no—
176C4⋊C4—1491no—
177C4⋊C4C2×#1059701011yescharacteristic
178C22⋊C4—21no—
179C22⋊C4—2981no—
180C22⋊C4—2981no—
181C22⋊C4—2981no—
182C22⋊C4—2984no—
183C22⋊C4—2981no—
184C42—2981no—
185C42—2982no—
186C42—2982no—
187C23—2982no—
188C23—2982no—
189C23—2981no—
190C23—5961no—
191C23—1491no—
192C23—1491no—
193C23C22⋊#1059701011yescharacteristic
194Q8—22no—
195D4—2982no—
196D4—5962no—
197D4—5962no—
198D4—5962no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—2982no—
203C2×C4—2981no—
204C2×C4—2981no—
205C2×C4—2981no—
206C2×C4—2981no—
207C2×C4—2982no—
208C2×C4—2984no—
209C2×C4—2981no—
210C2×C4—5961no—
211C2×C4—5961no—
212C2×C4—5962no—
213C2×C4—5962no—
214C2×C4—1491no—
215C2×C4—1491no—
216C2×C4—1492no—
217C2×C4—1492no—
218C2×C4C22⋊#1059701011yescharacteristic
219C2×C4C22×#1059701011yescharacteristic
220C8—2984no—
221C22—21no—
222C22—21no—
223C22—2981no—
224C22—2981no—
225C22—2981no—
226C22—2981no—
227C22—2981no—
228C22—5964no—
229C22—5961no—
230C22—5961no—
231C22—5961no—
232C22—1492no—
233C22#1801197612yescomplemented
234C22C2×C22⋊#1059701011yescharacteristic
235C4—21no—
236C4—41no—
237C4—41no—
238C4—2981no—
239C4—5964no—
240C4—5961no—
241C4—1491no—
242C4—1491no—
243C4D4×#1059701012yes—
244C2—22no—
245C2—2982no—
246C2—5961no—
247C2—11921no—
248C2#2375057311yescharacteristic
249C2C2×#1801197611yescharacteristic
250C2#2375062211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC22⋊Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radical#23750138C2
cosocleC2×C4×D149C23
hypercenterC22⋊Q8#10597010
hypocenterC149#1871
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#14558746C2semidirect
2. C2×#18011976C2semidirect
3. C4×C22⋊#10597010C2semidirect
4. #23750495C2semidirect
17. #18011887C4semidirect
18. #18011886C4semidirect
19. #18011885C4semidirect
24. C22⋊Q8×C149C4semidirect
28. #14558746D4semidirect
97. C22×C149#104semidirect
125. C149#1871semidirect
140. C22⋊Q8#10597010semidirect
233. C22#18011976semidirect

Maximal subgroups

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

subgroupindex
C22×#145587462
C2×#180119762
C4×C22⋊#105970102
#237504952
#237501382
#1871149