Finite Group Databasebeta

← #34060832

Subgroups — #34060832

Order 19072.

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

normal subgroups only

This group has 408 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×#18011970C212yesmaximal, complemented
2C2×#18011969C212yesmaximal, complemented
3#23750567C211yesmaximal, characteristic, complemented
4C4×C22⋊#10597010C211yesmaximal, characteristic, complemented
5C2×#18011884C211yesmaximal, characteristic
6C2×C4⋊#10597010—21no—
7C2×C22⋊#10597010C2212yes—
8C2×C22⋊#10597010C2212yes—
9C2×C4×#10597010—21no—
10#18011970—24no—
11#18011969—24no—
12(C2×#10597010)⋊C4—21no—
13(C2×#10597010)⋊C4—21no—
14C22×D596C2211yescharacteristic
15C22×C22⋊D149C411yescharacteristic, complemented
16C22×C22⋊D149C2211yescharacteristic
17C22×C4×D149C2211yescharacteristic
18#18011884—21no—
19#18011884—21no—
20#18011884—21no—
21#18011884—21no—
22C2×#14558715C411yescharacteristic, complemented
23C2×#14558713C411yescharacteristic, complemented
24C2×C22⋊C4×C149C411yescharacteristic, complemented
25C22×#10597010—22no—
26C22×#10597010—22no—
27C4⋊#10597010—42no—
28C22⋊#10597010—22no—
29C22⋊#10597010—22no—
30C22⋊#10597010—22no—
31C22⋊#10597010D414yescomplemented
32C4×#10597010—42no—
33C23×D149C2×C411yescharacteristic
34C23×D149C2311yescharacteristic
35C2×D596—22no—
36C2×D596—21no—
37C2×D596—21no—
38C2×D596—22no—
39C2×C22⋊D149—22no—
40C2×C22⋊D149—21no—
41C2×C22⋊D149—21no—
42C2×C22⋊D149—22no—
43C2×C22⋊D149—21no—
44C2×C22⋊D149—21no—
45C2×C22⋊D149—42no—
46C22×Dic149C2×C411yescharacteristic
47C22×Dic149C2×C411yescharacteristic
48C2×C4×D149—42no—
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—
62C2×#10597010—24no—
63C2×#10597010—42no—
64C2×#10597010—42no—
65C2×#10597010—42no—
66C2×#10597010—42no—
67C2×#10597010—42no—
68C22×D149—21no—
69C22×D149—22no—
70C22×D149—41no—
71C22×D149—41no—
72C22×D149—41no—
73C22×D149—41no—
74C22×D149C2×D411yescharacteristic
75C22×D149C2×D411yescharacteristic
76C22×D149C2×D412yes—
77C22×D149#4112yes—
78D596—42no—
79D596—41no—
80D596—41no—
81C22⋊D149—42no—
82C22⋊D149—42no—
83C22⋊D149—41no—
84C22⋊D149—41no—
85C22⋊D149—42no—
86C2×Dic149—22no—
87C2×Dic149—21no—
88C2×Dic149—22no—
89C2×Dic149C22⋊C411yescharacteristic
90C2×Dic149C22⋊C411yescharacteristic
91C4×D149—22no—
92C4×D149—22no—
93C4×D149—41no—
94C4×D149—41no—
95C23×C149—21no—
96C23×C149—22no—
97C23×C149—41no—
98C23×C149—41no—
99C23×C149C22×C411yescharacteristic
100C2×C4×C149—21no—
101C2×C4×C149—22no—
102C2×C4×C149—41no—
103C2×C4×C149C22⋊C411yescharacteristic
104C2×C4×C149C22⋊C411yescharacteristic
105C22×C149—21no—
106C22×C149—21no—
107C22×C149—41no—
108C22×C149—41no—
109C22×C149—41no—
110C22×C149—82no—
111C22×C149C2×C22⋊C411yescharacteristic
112C22×C149C4×D412yes—
113C2×D149—21no—
114C2×D149—21no—
115C2×D149—21no—
116C2×D149—21no—
117C2×D149—42no—
118C2×D149—42no—
119C2×D149—41no—
120C2×D149—41no—
121C2×D149—41no—
122C2×D149—82no—
123C2×D149#12112yes—
124C2×D149#12411yescharacteristic
125C2×D149#12711yescharacteristic
126#10597010—44no—
127#10597010—82no—
128C4×C149—21no—
129C4×C149—21no—
130C4×C149—41no—
131Dic149—21no—
132Dic149—41no—
133Dic149#9912yescomplemented
134C2×C149—22no—
135C2×C149—81no—
136C2×C149#39011yescharacteristic
137C2×C149C2×#9911yescharacteristic
138C2×C149#41011yescharacteristic
139D149—22no—
140D149—21no—
141D149—21no—
142D149—81no—
143C149#196411yescharacteristic, complemented, Sylow
144#1964—1491nomaximal, Sylow
145C2×#121—1491no—
146C2×#99—1492no—
147C2×#99—1492no—
148#380—1491no—
149C4×C22⋊C4—1491no—
150C22×D4—1491no—
151C22×D4—1491no—
152C22×D4—1491no—
153C23×C4—1491no—
154#121—2981no—
155#121—2981no—
156#121—2981no—
157#121—2981no—
158C2×C4⋊C4—2981no—
159C2×C4⋊C4—1491no—
160C2×C22⋊C4—1492no—
161C2×C22⋊C4—1491no—
162C2×C22⋊C4—1492no—
163C2×C22⋊C4#1059701011yescharacteristic, complemented
164C2×C42—2981no—
165#99—2984no—
166#99—2984no—
167#95—2981no—
168#95—2981no—
169C24—1491no—
170C24—1491no—
171C24C2×#1059701011yescharacteristic
172C2×D4—2982no—
173C2×D4—2981no—
174C2×D4—2981no—
175C2×D4—2982no—
176C2×D4—2982no—
177C2×D4—2981no—
178C2×D4—2981no—
179C2×D4—2982no—
180C2×D4—2981no—
181C2×D4—2981no—
182C2×D4—5962no—
183C22×C4—2982no—
184C22×C4—2982no—
185C22×C4—5962no—
186C22×C4—1491no—
187C22×C4—1491no—
188C22×C4—1491no—
189C22×C4—1491no—
190C22×C4—1491no—
191C22×C4—1491no—
192C22×C4C2×#1059701011yescharacteristic
193C22×C4C2×#1059701011yescharacteristic
194C4⋊C4—2981no—
195C4⋊C4—2981no—
196C4⋊C4—5962no—
197C22⋊C4—21no—
198C22⋊C4—21no—
199C22⋊C4—2982no—
200C22⋊C4—2981no—
201C22⋊C4—2981no—
202C22⋊C4—2982no—
203C22⋊C4—2982no—
204C22⋊C4—1494no—
205C42—5962no—
206C23—21no—
207C23—22no—
208C23—41no—
209C23—41no—
210C23—2981no—
211C23—2982no—
212C23—5961no—
213C23—5961no—
214C23—5961no—
215C23—5961no—
216C23—1491no—
217C23—1491no—
218C23—1492no—
219C23—1492no—
220C23C22×#1059701011yescharacteristic
221D4—5962no—
222D4—5961no—
223D4—5961no—
224D4—5962no—
225D4—5962no—
226D4—5961no—
227D4—5961no—
228D4—5962no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—41no—
232C2×C4—2982no—
233C2×C4—2982no—
234C2×C4—2982no—
235C2×C4—2984no—
236C2×C4—2981no—
237C2×C4—2982no—
238C2×C4—5961no—
239C2×C4—5961no—
240C2×C4—5962no—
241C2×C4—5962no—
242C2×C4—5962no—
243C2×C4—5962no—
244C2×C4—5962no—
245C2×C4—1491no—
246C2×C4—1491no—
247C2×C4C22⋊#1059701011yescharacteristic
248C2×C4C22⋊#1059701011yescharacteristic
249C22—21no—
250C22—21no—
251C22—41no—
252C22—41no—
253C22—41no—
254C22—82no—
255C22—2981no—
256C22—2981no—
257C22—2981no—
258C22—2981no—
259C22—5962no—
260C22—5962no—
261C22—5961no—
262C22—5961no—
263C22—5961no—
264C22—1492no—
265C22—1491no—
266C22—1491no—
267C22—11922no—
268C22C2×C22⋊#1059701011yescharacteristic
269C22D4×#1059701012yes—
270C4—21no—
271C4—21no—
272C4—41no—
273C4—2981no—
274C4—5964no—
275C4—5961no—
276C4—1492no—
277C4—11922no—
278C2—22no—
279C2—81no—
280C2—2982no—
281C2—2981no—
282C2—2981no—
283C2—11921no—
284C2#2375057711yescharacteristic
285C2D149⋊#9911yescharacteristic
286C2#2375060411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC23×C149C22×C4
FrattiniC23C22×#10597010
FittingC2×C22⋊C4×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC2×#18011884C2
cosocleC23×D149C23
hypercenterC2×C22⋊C4#10597010
hypocenterC149#1964
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×#18011970C2semidirect
2. C2×#18011969C2semidirect
3. #23750567C2semidirect
4. C4×C22⋊#10597010C2semidirect
15. C22×C22⋊D149C4semidirect
22. C2×#14558715C4semidirect
23. C2×#14558713C4semidirect
24. C2×C22⋊C4×C149C4semidirect
31. C22⋊#10597010D4semidirect
133. Dic149#99semidirect
143. C149#1964semidirect
163. C2×C22⋊C4#10597010semidirect

Maximal subgroups

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

subgroupindex
C2×#180119702
C2×#180119692
#237505672
C4×C22⋊#105970102
C2×#180118842
#1964149