Finite Group Databasebeta

← #34055931

Subgroups — #34055931

Order 19072.

328 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 117 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#23750031C211yesmaximal, characteristic, complemented
3#23750031C211yesmaximal, characteristic, complemented
4#23749987C211yesmaximal, characteristic, complemented
5#23749987C211yesmaximal, characteristic, complemented
6#23749966C212yesmaximal, complemented
7#23749949C212yesmaximal
8#23749929C212yesmaximal, complemented
9#23749922C212yesmaximal, complemented
10#23749682C211yesmaximal, 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⋊#11924746C2212yes—
27#18011834C2212yes—
28#18011834C2212yes—
29#18011831C2212yes—
30#18011831C2212yes—
31C22⋊#11924746C2212yes—
32#18011822C2211yescharacteristic
33#18011822C2211yescharacteristic
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—22no—
80D596—22no—
81C22⋊D149—42no—
82C2×Dic149—21no—
83C2×Dic149—21no—
84C2×Dic149—21no—
85C4×D149—42no—
86#11924746—22no—
87#11924746—22no—
88C23×C149C2×D411yescharacteristic
89Q8×C149—42no—
90Q8×C149—42no—
91C2×C4×C149—22no—
92C2×C4×C149—22no—
93C2×C4×C149—22no—
94C2×C4×C149—41no—
95C2×C4×C149—41no—
96C2×C4×C149C2×D411yescharacteristic
97C2×C4×C149C2×D411yescharacteristic
98C2×C4×C149C2×D411yescharacteristic
99C2×C4×C149C2×D411yescharacteristic
100C2×C4×C149C2×D411yescharacteristic
101C2×C4×C149C2411yescharacteristic
102C22×C149—21no—
103C22×C149—21no—
104C22×C149—21no—
105C22×C149C22×D411yescharacteristic
106C2×D149—41no—
107C2×D149—41no—
108C2×D149—41no—
109C4×C149—21no—
110C4×C149—21no—
111C4×C149—21no—
112C4×C149—21no—
113C4×C149—21no—
114C4×C149—42no—
115C4×C149—42no—
116C4×C1492−1+412yes—
117Dic149—41no—
118Dic149—41no—
119Dic149—41no—
120C2×C149—41no—
121C2×C149#53611yescharacteristic
122C2×C149#57511yescharacteristic
123C2×C149#57511yescharacteristic
124D149—81no—
125C149#324011yescharacteristic, complemented, Sylow
126#3240—1491nomaximal, Sylow
127#533D14911yescharacteristic, complemented
128#529—1491no—
129#501—1491no—
130#501—1491no—
131#489—1491no—
132#489—1491no—
133#485—1492no—
134#482—1492no—
135#479—1492no—
136#478—1492no—
137#432—1491no—
138C4⋊Q8C2×D14911yescharacteristic
139C4⋊Q8C2×D14911yescharacteristic
140#126—2981no—
141#125—1491no—
142#125C2×D14912yes—
143#124—1491no—
144#123—2981no—
145C22⋊Q8—21no—
146C22⋊Q8—21no—
147C22⋊Q8—1491no—
148#121—1491no—
149C4×Q8—21no—
150C4×Q8—21no—
151C4×Q8—1491no—
152C4×D4—2981no—
153C4×D4—1491no—
154#117—2981no—
155#117C2×D14912yes—
156C2×C42C2×D14911yescharacteristic
157#107—1492no—
158#107—1492no—
159#106—1492no—
160#106—1492no—
161C4⋊C8—1492no—
162#103—1492no—
163#103—1492no—
164#102—1492no—
165#102—1492no—
166C22⋊C8—1492no—
167#97—1491no—
168#97—1491no—
169C2×Q8—21no—
170C2×Q8—21no—
171C2×Q8—1491no—
172C2×D4—2981no—
173C2×D4—1491no—
174C22×C4—2981no—
175C22×C4C22⋊D14911yescharacteristic
176C22×C4C22⋊D14911yescharacteristic
177C22×C4C22×D14911yescharacteristic
178C2×C8—1492no—
179C2×C8—1492no—
180C4⋊C4—22no—
181C4⋊C4—22no—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—2981no—
185C4⋊C4—2981no—
186C4⋊C4—2981no—
187C4⋊C4—2981no—
188C4⋊C4—1491no—
189C4⋊C4—1491no—
190C4⋊C4C22×D14912yes—
191C4⋊C4C22×D14912yes—
192C22⋊C4—22no—
193C22⋊C4—2981no—
194C22⋊C4—2981no—
195C22⋊C4—2981no—
196C22⋊C4—2981no—
197C22⋊C4—2981no—
198C42—22no—
199C42—2981no—
200C42C22⋊D14911yescharacteristic
201C42C22⋊D14911yescharacteristic
202C42C22×D14911yescharacteristic
203C42C22×D14911yescharacteristic
204C23—2981no—
205C23C2×C22⋊D14911yescharacteristic
206Q8—42no—
207Q8—42no—
208Q8—2982no—
209D4—2982no—
210D4—5962no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—2981no—
217C2×C4—2981no—
218C2×C4—2981no—
219C2×C4—5962no—
220C2×C4C2×C22⋊D14911yescharacteristic
221C2×C4C2×C22⋊D14911yescharacteristic
222C2×C4C2×C22⋊D14911yescharacteristic
223C2×C4C2×C22⋊D14911yescharacteristic
224C2×C4C2×C22⋊D14911yescharacteristic
225C2×C4C23×D14911yescharacteristic
226C8—2982no—
227C8—2982no—
228C22—21no—
229C22—21no—
230C22—21no—
231C22—5961no—
232C22—5961no—
233C22—5961no—
234C22C22×C22⋊D14911yescharacteristic
235C4—21no—
236C4—21no—
237C4—21no—
238C4—21no—
239C4—21no—
240C4—42no—
241C4—42no—
242C4—5961no—
243C4—5961no—
244C4—5961no—
245C4#1801195912yes—
246C2—41no—
247C2—11921no—
248C2#2375019911yescharacteristic
249C2#2375042311yescharacteristic
250C2#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#3240
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. #23750031C2semidirect
3. #23750031C2semidirect
4. #23749987C2semidirect
5. #23749987C2semidirect
6. #23749966C2semidirect
8. #23749929C2semidirect
9. #23749922C2semidirect
10. #23749682C2semidirect
11. #533×C149C2semidirect
125. C149#3240semidirect
127. #533D149semidirect

Maximal subgroups

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

subgroupindex
#237501592
#237500312
#237499872
#237499662
#237499492
#237499292
#237499222
#237496822
#533×C1492
#3240149