Finite Group Databasebeta

← #99×#10597010 #34060439

Subgroups — #99×#10597010 #34060439

Order 19072.

412 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 90 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×D4×#10597010C211yesmaximal, characteristic
2D149⋊#99C211yesmaximal, characteristic
3C22⋊C4×#10597010C212yesmaximal, complemented
4#23750502C212yesmaximal, complemented
5#99×D149C211yesmaximal, characteristic
6C23×#10597010C411yescharacteristic, complemented
7C23×#10597010C2211yescharacteristic
8D4×#10597010—22no—
9D4×#10597010—22no—
10C2×C4⋊#10597010C411yescharacteristic, complemented
11C2×C22⋊#10597010C411yescharacteristic, complemented
12C2×C22⋊#10597010C2211yescharacteristic
13C2×C22⋊#10597010C2212yes—
14C2×C4×#10597010—22no—
15C2×C4×#10597010C411yescharacteristic, complemented
16#18011970C412yescomplemented
17#18011969C412yescomplemented
18(C2×#10597010)⋊C4—22no—
19C2×D4×D149C2211yescharacteristic
20C22⋊C4×D149C2212yes—
21#18011826C411yescharacteristic, complemented
22#18011825C412yescomplemented
23#99×C149C411yescharacteristic, complemented
24C22×#10597010—21no—
25C22×#10597010—21no—
26C22×#10597010—22no—
27C22×#10597010—42no—
28C22×#10597010—42no—
29C22×#10597010C2×C411yescharacteristic
30C22×#10597010C2×C411yescharacteristic
31C22×#10597010C2×C411yescharacteristic
32C22×#10597010C2×C411yescharacteristic
33C22×#10597010D412yes—
34C22×#10597010D412yes—
35C4⋊#10597010—22no—
36C22⋊#10597010—22no—
37C22⋊#10597010—22no—
38C22⋊#10597010—22no—
39C22⋊#10597010C2×C414yescomplemented
40C4×#10597010—21no—
41C4×#10597010—21no—
42C4×#10597010—44no—
43C23×D149C2×C411yescharacteristic
44C23×D149C2311yescharacteristic
45C2×D596C2×C411yescharacteristic
46C2×C22⋊D149C2×C411yescharacteristic
47C2×C22⋊D149C2×C411yescharacteristic
48D4×D149—22no—
49D4×D149—22no—
50C2×C4×D149—22no—
51C2×C4×D149C2×C411yescharacteristic
52C22⋊Dic149C2×C412yescomplemented
53#14558713—22no—
54C2×D4×C149C2×C411yescharacteristic
55C22⋊C4×C149C2×C412yescomplemented
56C2×#10597010—24no—
57C2×#10597010—22no—
58C2×#10597010—21no—
59C2×#10597010—21no—
60C2×#10597010—24no—
61C2×#10597010—41no—
62C2×#10597010—42no—
63C2×#10597010—42no—
64C2×#10597010—42no—
65C2×#10597010—42no—
66C2×#10597010—42no—
67C2×#10597010—41no—
68C2×#10597010—41no—
69C2×#10597010C22⋊C411yescharacteristic
70C2×#10597010C22⋊C412yes—
71C2×#10597010C22⋊C411yescharacteristic
72C22×D149—21no—
73C22×D149—21no—
74C22×D149—41no—
75C22×D149—41no—
76C22×D149—41no—
77C22×D149—41no—
78C22×D149C4211yescharacteristic, complemented
79C22×D149C22×C411yescharacteristic
80C22×D149C22×C411yescharacteristic
81C22×D149C2×D412yes—
82C22×D149#4112yes—
83D596—22no—
84C22⋊D149—22no—
85C22⋊D149—22no—
86C2×Dic149—22no—
87C2×Dic149C4211yescharacteristic, complemented
88C4×D149—21no—
89C4×D149—21no—
90C4×D149—42no—
91C4×D149—42no—
92C23×C149C4211yescharacteristic, complemented
93C23×C149C22×C411yescharacteristic
94D4×C149—22no—
95C2×C4×C149—22no—
96C2×C4×C149C4211yescharacteristic, complemented
97C22×C149—21no—
98C22×C149—41no—
99C22×C149—41no—
100C22×C149C2×C4211yescharacteristic
101C22×C149C4×D412yes—
102C2×D149—22no—
103C2×D149—21no—
104C2×D149—22no—
105C2×D149—21no—
106C2×D149—21no—
107C2×D149—41no—
108C2×D149—42no—
109C2×D149—42no—
110C2×D149—41no—
111C2×D149—41no—
112C2×D149—41no—
113C2×D149C2×C22⋊C411yescharacteristic
114C2×D149#11711yescharacteristic
115C2×D149C4×D412yes—
116#10597010—21no—
117#10597010—22no—
118#10597010—44no—
119#10597010—41no—
120#10597010—41no—
121#10597010#9912yesdirect product factor
122C4×C149—21no—
123C4×C149—42no—
124Dic149—21no—
125Dic149—42no—
126C2×C149—22no—
127C2×C149—21no—
128C2×C149—41no—
129C2×C149C4×C22⋊C411yescharacteristic
130D149—22no—
131D149—21no—
132D149—41no—
133D149C2×#9911yescharacteristic
134D149#41011yescharacteristic
135C149C4×#9911yescharacteristic, complemented, Sylow
136C4×#99—1491nomaximal, Sylow
137C2×C4×D4—1491no—
138C2×#99—1491no—
139C2×#99—1491no—
140C4×C22⋊C4—1492no—
141#342—1492no—
142C22×D4—1491no—
143C23×C4—1491no—
144C23×C4—1491no—
145C4×D4—2982no—
146C4×D4—2982no—
147C2×C4⋊C4—1491no—
148C2×C22⋊C4—1491no—
149C2×C22⋊C4—1491no—
150C2×C22⋊C4—1492no—
151C2×C22⋊C4—1492no—
152C2×C42—2982no—
153C2×C42—1491no—
154#99—1492no—
155#99—1492no—
156#99—1491no—
157#99—1492no—
158#99#1059701011yescharacteristic, direct product factor
159#95—2982no—
160C24—1491no—
161C24—1491no—
162C2×D4—2982no—
163C2×D4—2982no—
164C2×D4—1491no—
165C2×D4—1491no—
166C2×D4—1491no—
167C2×D4C2×#1059701011yescharacteristic
168C22×C4—2982no—
169C22×C4—2982no—
170C22×C4—2981no—
171C22×C4—2981no—
172C22×C4—5962no—
173C22×C4—5962no—
174C22×C4—1491no—
175C22×C4—1492no—
176C22×C4—1491no—
177C22×C4—1491no—
178C22×C4—1491no—
179C22×C4—1491no—
180C22×C4—1492no—
181C4⋊C4—2982no—
182C22⋊C4—2982no—
183C22⋊C4—2982no—
184C22⋊C4—2982no—
185C22⋊C4—2982no—
186C22⋊C4—1494no—
187C22⋊C4—1492no—
188C22⋊C4C2×#1059701012yescomplemented
189C42—2981no—
190C42—2981no—
191C42—5964no—
192C23—2981no—
193C23—2981no—
194C23—5961no—
195C23—5961no—
196C23—5961no—
197C23—5961no—
198C23—1491no—
199C23—1492no—
200C23—1491no—
201C23—1491no—
202C23—1492no—
203C23C4×#1059701011yescharacteristic, complemented
204C23C22×#1059701011yescharacteristic
205D4—22no—
206D4—2982no—
207D4—2982no—
208D4—2982no—
209C2×C4—22no—
210C2×C4—2981no—
211C2×C4—2981no—
212C2×C4—2984no—
213C2×C4—2982no—
214C2×C4—2981no—
215C2×C4—2981no—
216C2×C4—2984no—
217C2×C4—2982no—
218C2×C4—5962no—
219C2×C4—5962no—
220C2×C4—5962no—
221C2×C4—5961no—
222C2×C4—5962no—
223C2×C4—5962no—
224C2×C4—5962no—
225C2×C4—5962no—
226C2×C4—5961no—
227C2×C4—5961no—
228C2×C4—1491no—
229C2×C4—1492no—
230C2×C4—1491no—
231C2×C4—1491no—
232C2×C4C4×#1059701011yescharacteristic, complemented
233C22—21no—
234C22—41no—
235C22—41no—
236C22—2982no—
237C22—2981no—
238C22—2982no—
239C22—2981no—
240C22—2981no—
241C22—5962no—
242C22—5961no—
243C22—5961no—
244C22—5962no—
245C22—5961no—
246C22—5961no—
247C22—1492no—
248C22—1491no—
249C22—1491no—
250C22C2×C4×#1059701011yescharacteristic
251C22D4×#1059701012yes—
252C4—21no—
253C4—42no—
254C4—2981no—
255C4—2982no—
256C4—2981no—
257C4—5962no—
258C4—5964no—
259C4—5961no—
260C4—5961no—
261C4—1492no—
262C2—22no—
263C2—21no—
264C2—41no—
265C2—2982no—
266C2—2981no—
267C2—5961no—
268C2—1491no—
269C2—1491no—
270C2C22⋊C4×#1059701011yescharacteristic
subgroupG/H
centerC2C22⋊C4×#10597010
commutatorC22×C149C2×C42
FrattiniC23C22×#10597010
Fitting#99×C149C4
socleC2×C149C4×C22⋊C4
prime radicalC2×D4×D149C22
cosocleC23×D149C23
hypercenter#99#10597010
hypocenterC149C4×#99
LCSG ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
3. C22⋊C4×#10597010C2semidirect
4. #23750502C2semidirect
6. C23×#10597010C4semidirect
10. C2×C4⋊#10597010C4semidirect
11. C2×C22⋊#10597010C4semidirect
15. C2×C4×#10597010C4semidirect
16. #18011970C4semidirect
17. #18011969C4semidirect
21. #18011826C4semidirect
22. #18011825C4semidirect
23. #99×C149C4semidirect
39. C22⋊#10597010C2×C4semidirect
52. C22⋊Dic149C2×C4semidirect
55. C22⋊C4×C149C2×C4semidirect
78. C22×D149C42semidirect
87. C2×Dic149C42semidirect
92. C23×C149C42semidirect
96. C2×C4×C149C42semidirect
121. #10597010#99direct (N × H)
135. C149C4×#99semidirect
158. #99#10597010direct (N × H)
188. C22⋊C4C2×#10597010semidirect
203. C23C4×#10597010semidirect
232. C2×C4C4×#10597010semidirect

Maximal subgroups

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

subgroupindex
C2×D4×#105970102
D149⋊#992
C22⋊C4×#105970102
#237505022
#99×D1492
C4×#99149