Finite Group Databasebeta

← #34055870

Subgroups — #34055870

Order 19072.

332 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 121 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
1#23750159C211yesmaximal, characteristic
2#23750024C212yesmaximal, complemented
3#23749982C212yesmaximal, complemented
4#23749966C212yesmaximal, complemented
5#23749949C212yesmaximal
6#23749917C211yesmaximal, characteristic, complemented
7#23749912C211yesmaximal, characteristic, complemented
8#23749907C211yesmaximal, characteristic, complemented
9#23749902C211yesmaximal, characteristic, complemented
10#23749678C211yesmaximal, characteristic, complemented
11#533×C149C211yesmaximal, characteristic, complemented
12#18011905—21no—
13#18011903C2211yescharacteristic
14#18011899C2211yescharacteristic
15#18011894—21no—
16#18011890C2211yescharacteristic
17#18011885C2211yescharacteristic
18C4×Dic298C2211yescharacteristic
19C4×D596C2211yescharacteristic
20C4×C22⋊D149—21no—
21#18011868—21no—
22#18011844C2212yes—
23#18011844C2212yes—
24#18011842C2212yes—
25#18011842C2212yes—
26C4⋊#11924746C2211yescharacteristic
27C4⋊#11924746C2211yescharacteristic
28#18011834C2212yes—
29#18011834C2212yes—
30#18011831C2212yes—
31#18011831C2212yes—
32C22⋊#11924746C2212yes—
33C4×#11924746C2212yes—
34C4⋊Q8×C149C2211yescharacteristic
35C4⋊Q8×C149C2211yescharacteristic
36#125×C149C2212yes—
37C22⋊Q8×C149—21no—
38C22⋊Q8×C149—21no—
39C4×Q8×C149—21no—
40C4×Q8×C149—21no—
41#117×C149C2212yes—
42C2×C42×C149C2211yescharacteristic
43C2×Dic298C2311yescharacteristic
44C2×D596C2311yescharacteristic
45C2×C22⋊D149—21no—
46C2×C4×D149—21no—
47C2×#11924746C2312yes—
48C2×#11924746C2312yes—
49C4⋊Dic149C2311yescharacteristic
50C4⋊Dic149C2311yescharacteristic
51#14558715—21no—
52#14558715—21no—
53#14558715—21no—
54#14558715—21no—
55C22⋊Dic149—21no—
56#14558713—21no—
57#14558713—21no—
58#14558713—21no—
59#14558713—21no—
60C4×Dic149—21no—
61C2×Q8×C149—21no—
62C2×Q8×C149—21no—
63C22×C4×C149D411yescharacteristic
64C22×C4×C149D411yescharacteristic
65C22×C4×C149C2311yescharacteristic
66C4⋊C4×C149—22no—
67C4⋊C4×C149—22no—
68C4⋊C4×C149—21no—
69C4⋊C4×C149—21no—
70C4⋊C4×C149C2312yes—
71C4⋊C4×C149C2312yes—
72C22⋊C4×C149—22no—
73C42×C149—22no—
74C42×C149D411yescharacteristic
75C42×C149D411yescharacteristic
76C42×C149C2311yescharacteristic
77C42×C149C2311yescharacteristic
78C22×D149—21no—
79Dic298—21no—
80Dic298—21no—
81D596—21no—
82D596—21no—
83C22⋊D149—42no—
84C2×Dic149—21no—
85C2×Dic149—21no—
86C2×Dic149—21no—
87C4×D149—42no—
88#11924746—22no—
89#11924746—22no—
90C23×C149C2×D411yescharacteristic
91Q8×C149—42no—
92Q8×C149—42no—
93C2×C4×C149—22no—
94C2×C4×C149—21no—
95C2×C4×C149—21no—
96C2×C4×C149—22no—
97C2×C4×C149—22no—
98C2×C4×C149—41no—
99C2×C4×C149C2×D411yescharacteristic
100C2×C4×C149C2×D411yescharacteristic
101C2×C4×C149C2×D411yescharacteristic
102C2×C4×C149C2×D411yescharacteristic
103C2×C4×C149C2×D411yescharacteristic
104C2×C4×C149C2411yescharacteristic
105C22×C149—21no—
106C22×C149—21no—
107C22×C149—21no—
108C22×C149C22×D411yescharacteristic
109C2×D149—41no—
110C2×D149—41no—
111C2×D149—41no—
112C4×C149—21no—
113C4×C149—21no—
114C4×C149—21no—
115C4×C149—21no—
116C4×C149—42no—
117C4×C149—42no—
118C4×C149#13512yes—
119C4×C1492−1+411yescharacteristic
120C4×C1492−1+411yescharacteristic
121Dic149—41no—
122Dic149—41no—
123Dic149—41no—
124C2×C149—41no—
125C2×C149#53611yescharacteristic
126C2×C149C2×#13511yescharacteristic
127C2×C149#57511yescharacteristic
128D149—81no—
129C149#323311yescharacteristic, complemented, Sylow
130#3233—1491nomaximal, Sylow
131#533D14911yescharacteristic, complemented
132#529—1491no—
133#499—1492no—
134#488—1492no—
135#485—1492no—
136#482—1492no—
137#477—1491no—
138#476—1491no—
139#475—1491no—
140#474—1491no—
141#431—1491no—
142C4⋊Q8C2×D14911yescharacteristic
143C4⋊Q8C2×D14911yescharacteristic
144#126—2981no—
145#125—1491no—
146#125C2×D14912yes—
147#124—1491no—
148#123—2981no—
149C22⋊Q8—21no—
150C22⋊Q8—21no—
151C22⋊Q8—1491no—
152#121—1491no—
153C4×Q8—21no—
154C4×Q8—21no—
155C4×Q8—1491no—
156C4×D4—2981no—
157C4×D4—1491no—
158#117—2981no—
159#117C2×D14912yes—
160C2×C42C2×D14911yescharacteristic
161#107—1492no—
162#107—1492no—
163#106—1492no—
164#106—1492no—
165C4⋊C8—1491no—
166C4⋊C8—1491no—
167#103—1492no—
168#103—1492no—
169#102—1492no—
170#102—1492no—
171C22⋊C8—1492no—
172C4×C8—1492no—
173C2×Q8—21no—
174C2×Q8—21no—
175C2×Q8—1491no—
176C2×D4—2981no—
177C2×D4—1491no—
178C22×C4—2981no—
179C22×C4C22⋊D14911yescharacteristic
180C22×C4C22⋊D14911yescharacteristic
181C22×C4C22×D14911yescharacteristic
182C2×C8—1492no—
183C2×C8—1492no—
184C4⋊C4—22no—
185C4⋊C4—22no—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—2981no—
189C4⋊C4—2981no—
190C4⋊C4—2981no—
191C4⋊C4—2981no—
192C4⋊C4—1491no—
193C4⋊C4—1491no—
194C4⋊C4C22×D14912yes—
195C4⋊C4C22×D14912yes—
196C22⋊C4—22no—
197C22⋊C4—2981no—
198C22⋊C4—2981no—
199C22⋊C4—2981no—
200C22⋊C4—2981no—
201C22⋊C4—2981no—
202C42—22no—
203C42—2981no—
204C42C22⋊D14911yescharacteristic
205C42C22⋊D14911yescharacteristic
206C42C22×D14911yescharacteristic
207C42C22×D14911yescharacteristic
208C23—2981no—
209C23C2×C22⋊D14911yescharacteristic
210Q8—42no—
211Q8—42no—
212Q8—2981no—
213Q8—2981no—
214D4—2981no—
215D4—2981no—
216D4—5962no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—41no—
223C2×C4—2981no—
224C2×C4—2981no—
225C2×C4—2981no—
226C2×C4—5962no—
227C2×C4C2×C22⋊D14911yescharacteristic
228C2×C4C2×C22⋊D14911yescharacteristic
229C2×C4C2×C22⋊D14911yescharacteristic
230C2×C4C2×C22⋊D14911yescharacteristic
231C2×C4C2×C22⋊D14911yescharacteristic
232C2×C4C23×D14911yescharacteristic
233C8—2982no—
234C8—2982no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—5961no—
239C22—5961no—
240C22—5961no—
241C22C22×C22⋊D14911yescharacteristic
242C4—21no—
243C4—21no—
244C4—21no—
245C4—21no—
246C4—42no—
247C4—42no—
248C4—5961no—
249C4—5961no—
250C4—5961no—
251C4#1801193112yes—
252C4#1801195911yescharacteristic
253C4#1801195911yescharacteristic
254C2—41no—
255C2—11921no—
256C2#2375019911yescharacteristic
257C2C2×#1801193111yescharacteristic
258C2#2375042311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#533×C149C2
socleC22×C149C22×D4
prime radical#18011885C22
hypercenter#533D149
hypocenterC149#3233
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #23750024C2semidirect
3. #23749982C2semidirect
4. #23749966C2semidirect
6. #23749917C2semidirect
7. #23749912C2semidirect
8. #23749907C2semidirect
9. #23749902C2semidirect
10. #23749678C2semidirect
11. #533×C149C2semidirect
129. C149#3233semidirect
131. #533D149semidirect

Maximal subgroups

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

subgroupindex
#237501592
#237500242
#237499822
#237499662
#237499492
#237499172
#237499122
#237499072
#237499022
#237496782
#533×C1492
#3233149