Finite Group Databasebeta

← #34060126

Subgroups — #34060126

Order 19072.

340 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 68 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×#18011968C211yesmaximal, characteristic, complemented
2#23750567C211yesmaximal, characteristic, complemented
3#23750477C212yesmaximal, complemented
4#23750476C212yesmaximal, complemented
5#121×D149C211yesmaximal, characteristic
6C22×#11924753—21no—
7C2×C4⋊#10597010—21no—
8C2×C22⋊#10597010—21no—
9#18011968—21no—
10#18011968C2212yescomplemented
11(C2×#10597010)⋊C4C2212yescomplemented
12C2×D4×D149—21no—
13C2×D4×D149C411yescharacteristic, complemented
14C22×C4×D149C2211yescharacteristic
15#18011886C2211yescharacteristic
16#18011885C411yescharacteristic, complemented
17#18011884—21no—
18#18011883—21no—
19#18011882C2211yescharacteristic
20C4⋊C4×D149C411yescharacteristic, complemented
21C22⋊C4×D149—21no—
22#121×C149C411yescharacteristic, complemented
23C22×#10597010—22no—
24C2×#11924753—22no—
25C2×#11924753—42no—
26C4⋊#10597010—42no—
27C22⋊#10597010—42no—
28C23×D149—21no—
29C23×D149D411yescharacteristic
30C2×D596—21no—
31C2×D596C2×C411yescharacteristic
32C2×C22⋊D149—21no—
33C2×C22⋊D149—21no—
34C2×C22⋊D149—21no—
35D4×D149—42no—
36D4×D149—42no—
37D4×D149—42no—
38C22×Dic149D411yescharacteristic
39C2×C4×D149—21no—
40C2×C4×D149—42no—
41C2×C4×D149C2×C411yescharacteristic
42C2×C4×D149D411yescharacteristic
43C2×C4×D149D411yescharacteristic
44C2×C4×D149C2311yescharacteristic
45C4⋊Dic149C2×C411yescharacteristic
46#14558715—21no—
47C22⋊Dic149—21no—
48#14558713—21no—
49#14558713—21no—
50C2×D4×C149—21no—
51C2×D4×C149C2×C411yescharacteristic
52C22×C4×C149C2×C411yescharacteristic
53C4⋊C4×C149C2×C411yescharacteristic
54C22⋊C4×C149—21no—
55C2×#10597010—42no—
56C2×#10597010—42no—
57C2×#10597010—42no—
58#11924753—42no—
59C22×D149—21no—
60C22×D149—41no—
61C22×D149—41no—
62C22×D149—42no—
63C22×D149—42no—
64C22×D149—42no—
65C22×D149C22⋊C411yescharacteristic
66C22×D149D812yes—
67C22×D149SD1612yes—
68C22×D149C2×D411yescharacteristic
69D596—41no—
70D596—41no—
71D596—41no—
72C22⋊D149—42no—
73C22⋊D149—41no—
74C22⋊D149—41no—
75C22⋊D149—42no—
76C2×Dic149—22no—
77C2×Dic149—21no—
78C2×Dic149C22⋊C411yescharacteristic
79C2×Dic149C2×D411yescharacteristic
80C4×D149—22no—
81C4×D149—22no—
82C4×D149—41no—
83C4×D149—41no—
84C4×D149—42no—
85C23×C149—21no—
86C23×C149C22⋊C411yescharacteristic
87D4×C149—41no—
88D4×C149—42no—
89C2×C4×C149—21no—
90C2×C4×C149—41no—
91C2×C4×C149C22⋊C411yescharacteristic
92C2×C4×C149C22×C411yescharacteristic
93C22×C149—21no—
94C22×C149—21no—
95C22×C149—41no—
96C22×C149—41no—
97C22×C149—41no—
98C22×C149#10212yes—
99C22×C149C2×C22⋊C411yescharacteristic
100C2×D149—21no—
101C2×D149—21no—
102C2×D149—21no—
103C2×D149—21no—
104C2×D149—42no—
105C2×D149—42no—
106C2×D149—41no—
107C2×D149—41no—
108C2×D149—41no—
109C2×D149—84no—
110C2×D149#10212yes—
111C2×D149C2×D811yescharacteristic
112C2×D149C2×SD1611yescharacteristic
113#10597010—82no—
114C4×C149—21no—
115C4×C149—21no—
116C4×C149—41no—
117Dic149—21no—
118Dic149—41no—
119Dic149#9912yes—
120C2×C149—22no—
121C2×C149—81no—
122C2×C149C2×#9911yescharacteristic
123C2×C149C2×#10211yescharacteristic
124C2×C149#42111yescharacteristic
125D149—21no—
126D149—22no—
127D149—21no—
128D149—81no—
129C149#151911yescharacteristic, complemented, Sylow
130#1519—1491nomaximal, Sylow
131C2×#121—1491no—
132C2×C22⋊C8—1491no—
133#380—1491no—
134#327—1492no—
135#327—1492no—
136C22×D4—2981no—
137C22×D4—1491no—
138C23×C4—1491no—
139C22×C8—2981no—
140#121—2981no—
141#121—2981no—
142#121—1491no—
143#121—1491no—
144#121—1491no—
145#121#1059701011yescharacteristic, complemented
146C2×C4⋊C4—2981no—
147C2×C4⋊C4—1491no—
148C2×C22⋊C4—2981no—
149C2×C22⋊C4—2981no—
150C22⋊C8—2981no—
151C22⋊C8—1492no—
152#95—1492no—
153C24—2981no—
154C24—1491no—
155C2×D4—21no—
156C2×D4—2981no—
157C2×D4—2981no—
158C2×D4—2981no—
159C2×D4—2981no—
160C2×D4—5962no—
161C2×D4—5962no—
162C2×D4—5962no—
163C2×D4—1491no—
164C2×D4C2×#1059701011yescharacteristic
165C22×C4—2981no—
166C22×C4—2982no—
167C22×C4—5962no—
168C22×C4—1491no—
169C22×C4—1491no—
170C22×C4—1491no—
171C22×C4—1491no—
172C22×C4—1491no—
173C22×C4C2×#1059701011yescharacteristic
174C2×C8—2982no—
175C2×C8—5962no—
176C4⋊C4—2981no—
177C4⋊C4—5962no—
178C4⋊C4—1491no—
179C4⋊C4C2×#1059701011yescharacteristic
180C22⋊C4—21no—
181C22⋊C4—2981no—
182C22⋊C4—2981no—
183C22⋊C4—2981no—
184C22⋊C4—5962no—
185C23—21no—
186C23—2981no—
187C23—5961no—
188C23—5961no—
189C23—5962no—
190C23—5962no—
191C23—5962no—
192C23—1491no—
193C23—1491no—
194C23—1492no—
195C23—1492no—
196C23C22⋊#1059701011yescharacteristic
197D4—41no—
198D4—42no—
199D4—5961no—
200D4—5961no—
201D4—5961no—
202D4—5961no—
203D4—5961no—
204D4—5962no—
205D4—5962no—
206C2×C4—21no—
207C2×C4—41no—
208C2×C4—2982no—
209C2×C4—2982no—
210C2×C4—2982no—
211C2×C4—2981no—
212C2×C4—5961no—
213C2×C4—5961no—
214C2×C4—5962no—
215C2×C4—5962no—
216C2×C4—5962no—
217C2×C4—5962no—
218C2×C4—1491no—
219C2×C4—1491no—
220C2×C4C22⋊#1059701011yescharacteristic
221C2×C4C22×#1059701011yescharacteristic
222C8—5962no—
223C22—21no—
224C22—21no—
225C22—41no—
226C22—41no—
227C22—41no—
228C22—2981no—
229C22—2981no—
230C22—2981no—
231C22—2981no—
232C22—5962no—
233C22—5962no—
234C22—5961no—
235C22—5961no—
236C22—5961no—
237C22—1491no—
238C22—1492no—
239C22—1491no—
240C22—11924no—
241C22#1801197312yes—
242C22C2×C22⋊#1059701011yescharacteristic
243C4—21no—
244C4—21no—
245C4—41no—
246C4—2981no—
247C4—5961no—
248C4—1492no—
249C4—11922no—
250C2—22no—
251C2—81no—
252C2—2981no—
253C2—2982no—
254C2—2981no—
255C2—11921no—
256C2D149⋊#9911yescharacteristic
257C2C2×#1801197311yescharacteristic
258C2#2375062211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#121×C149C4
socleC22×C149C2×C22⋊C4
prime radical#121×D149C2
cosocleC2×C4×D149C23
hypercenter#121#10597010
hypocenterC149#1519
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#18011968C2semidirect
2. #23750567C2semidirect
3. #23750477C2semidirect
4. #23750476C2semidirect
10. #18011968C22semidirect
11. (C2×#10597010)⋊C4C22semidirect
13. C2×D4×D149C4semidirect
16. #18011885C4semidirect
20. C4⋊C4×D149C4semidirect
22. #121×C149C4semidirect
129. C149#1519semidirect
145. #121#10597010semidirect

Maximal subgroups

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

subgroupindex
C2×#180119682
#237505672
#237504772
#237504762
#121×D1492
#1519149