Finite Group Databasebeta

← #34080187

Subgroups — #34080187

Order 19328.

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

normal subgroups only

This group has 364 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#23752788C211yesmaximal, characteristic
2#23752604C211yesmaximal, characteristic, complemented
3#23752591C211yesmaximal, characteristic, complemented
4#23752582C211yesmaximal, characteristic, complemented
5#23752569C211yesmaximal, characteristic, complemented
6#23752434C212yesmaximal, complemented
7#23752422C212yesmaximal, complemented
8#23752372C212yesmaximal
9#23752367C212yesmaximal, complemented
10#23752273C211yesmaximal, characteristic, complemented
11#541×C151C211yesmaximal, characteristic, complemented
12C2×#14559004C2211yescharacteristic
13C22×Dic302C2211yescharacteristic
14C2×#14558994C2212yes—
15C2×#14558994C2212yes—
16C2×#14558994C2212yes—
17C2×#14558991C2212yes—
18#18012739C2211yescharacteristic
19#18012739C2211yescharacteristic
20#18012727C2211yescharacteristic
21#18012727C2211yescharacteristic
22#18012723—22no—
23#18012719—22no—
24C4⋊(C151⋊C8)C2212yes—
25#18012662C2212yes—
26#18012662C2212yes—
27#18012662C2212yes—
28#18012659C2212yes—
29C22⋊(C151⋊C8)C2212yes—
30#18012650C2211yescharacteristic
31C4×C151⋊C8C2211yescharacteristic
32C4⋊Q8×C151C2211yescharacteristic
33#126×C151—22no—
34#125×C151—22no—
35#125×C151C2211yescharacteristic
36C22⋊Q8×C151C2212yes—
37C4×Q8×C151C2212yes—
38#117×C151C2211yescharacteristic
39#14559004—42no—
40C2×Dic302—21no—
41C2×Dic302—42no—
42C2×Dic302C2311yescharacteristic
43C2×Dic302C2311yescharacteristic
44C2×Dic302C2311yescharacteristic
45C2×D604C2311yescharacteristic
46C2×C22⋊D151—21no—
47C22×Dic151—21no—
48C2×C4×D151—21no—
49#14558994—42no—
50#14558994—42no—
51#14558994—42no—
52#14558991—42no—
53C2×C151⋊C8C2312yes—
54C2×C151⋊C8C2312yes—
55C4⋊Dic151—22no—
56C4⋊Dic151—22no—
57(C2×D151)⋊C4—22no—
58(C2×D151)⋊C4—22no—
59C2×Q8×C151C2312yes—
60C22×C4×C151C2311yescharacteristic
61C4⋊C4×C151—22no—
62C4⋊C4×C151—22no—
63C4⋊C4×C151—22no—
64C4⋊C4×C151—22no—
65C4⋊C4×C151D412yes—
66C4⋊C4×C151C2312yes—
67C22⋊C4×C151—22no—
68C22⋊C4×C151D412yes—
69C42×C151—22no—
70C42×C151C2311yescharacteristic
71C42×C151C2311yescharacteristic
72C22×D151—21no—
73Dic302—22no—
74Dic302—22no—
75Dic302—22no—
76Dic302—42no—
77D604—22no—
78C22⋊D151—42no—
79C2×Dic151—21no—
80C2×Dic151—21no—
81C2×Dic151—21no—
82C2×Dic151—42no—
83C4×D151—42no—
84C151⋊C8—22no—
85C151⋊C8—22no—
86C23×C151C2×D411yescharacteristic
87Q8×C151—22no—
88Q8×C151—22no—
89C2×C4×C151—22no—
90C2×C4×C151—22no—
91C2×C4×C151—22no—
92C2×C4×C151C2×D412yes—
93C2×C4×C151C2×D412yes—
94C2×C4×C151C2×D411yescharacteristic
95C2×C4×C151C2411yescharacteristic
96C22×C151—21no—
97C22×C151—22no—
98C22×C151C22×D411yescharacteristic
99C2×D151—41no—
100C2×D151—42no—
101C4×C151—21no—
102C4×C151—22no—
103C4×C151—22no—
104C4×C151—42no—
105C4×C151—42no—
106C4×C151H(5,𝔽2)12yes—
107Dic151—41no—
108Dic151—41no—
109Dic151—41no—
110C2×C151—41no—
111C2×C151#53511yescharacteristic
112C2×C151#57812yes—
113D151—81no—
114C151#322311yescharacteristic, complemented, Sylow
115#3223—1511nomaximal, Sylow
116#541D15111yescharacteristic, complemented
117#536—1511no—
118#497—1511no—
119#494—1511no—
120#491—1511no—
121#488—1511no—
122#464—1512no—
123#462—1512no—
124#452—1512no—
125#451—1512no—
126#433—1511no—
127C2×#41—1511no—
128C22×Q8—1511no—
129C2×Q16—1512no—
130C2×Q16—1512no—
131C2×Q16—1512no—
132C2×SD16—1512no—
133C4⋊Q8—1511no—
134C4⋊Q8—1511no—
135C4⋊Q8C2×D15111yescharacteristic
136#126—22no—
137#125—22no—
138#125C2×D15111yescharacteristic
139#124—1511no—
140#124—1511no—
141#123—3022no—
142C22⋊Q8—3022no—
143C22⋊Q8C2×D15112yes—
144C4×Q8C2×D15112yes—
145#117C2×D15111yescharacteristic
146C4⋊C8—1512no—
147#103—1512no—
148#103—1512no—
149#103—1512no—
150#102—1512no—
151C22⋊C8—1512no—
152#97—1511no—
153C4×C8—1511no—
154#41—6042no—
155C2×Q8—3021no—
156C2×Q8—6042no—
157C2×Q8—1511no—
158C2×Q8—1511no—
159C2×Q8—1511no—
160C2×Q8C22×D15112yes—
161C2×D4—3021no—
162C2×D4—1511no—
163C22×C4—3021no—
164C22×C4—3021no—
165C22×C4C22×D15111yescharacteristic
166Q16—6042no—
167Q16—6042no—
168Q16—6042no—
169SD16—6042no—
170C2×C8—1512no—
171C2×C8—1512no—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—3022no—
177C4⋊C4—3022no—
178C4⋊C4C22⋊D15112yes—
179C4⋊C4C22×D15112yes—
180C22⋊C4—22no—
181C22⋊C4—3022no—
182C22⋊C4—3022no—
183C22⋊C4C22⋊D15112yes—
184C42—22no—
185C42C22×D15111yescharacteristic
186C42C22×D15111yescharacteristic
187C23—3021no—
188C23C2×C22⋊D15111yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—3022no—
192Q8—3022no—
193Q8—3022no—
194Q8—6042no—
195D4—3022no—
196D4—6042no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—3021no—
201C2×C4—3021no—
202C2×C4—3021no—
203C2×C4—6042no—
204C2×C4—6042no—
205C2×C4C2×C22⋊D15112yes—
206C2×C4C2×C22⋊D15112yes—
207C2×C4C2×C22⋊D15111yescharacteristic
208C2×C4C23×D15111yescharacteristic
209C8—3022no—
210C8—3022no—
211C22—22no—
212C22—21no—
213C22—6042no—
214C22—6041no—
215C22C22×C22⋊D15111yescharacteristic
216C4—22no—
217C4—22no—
218C4—21no—
219C4—42no—
220C4—42no—
221C4—6041no—
222C4—6041no—
223C4—6041no—
224C4#1801278512yes—
225C2—41no—
226C2—12081no—
227C2#2375277611yescharacteristic
228C2#2375302712yes—
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#541×C151C2
socleC22×C151C22×D4
prime radicalC2×#14559004C22
hypercenter#541D151
hypocenterC151#3223
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
2. #23752604C2semidirect
3. #23752591C2semidirect
4. #23752582C2semidirect
5. #23752569C2semidirect
6. #23752434C2semidirect
7. #23752422C2semidirect
9. #23752367C2semidirect
10. #23752273C2semidirect
11. #541×C151C2semidirect
114. C151#3223semidirect
116. #541D151semidirect

Maximal subgroups

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

subgroupindex
#237527882
#237526042
#237525912
#237525822
#237525692
#237524342
#237524222
#237523722
#237523672
#237522732
#541×C1512
#3223151