Finite Group Databasebeta

← #34078762

Subgroups — #34078762

Order 19328.

460 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C22×#14558994C211yesmaximal, characteristic, complemented
2C2×#18012746C211yesmaximal, characteristic
3#23752783C211yesmaximal, characteristic
4#23752468C214yesmaximal, complemented
5#23752451C214yesmaximal, complemented
6#23752248C211yesmaximal, characteristic, complemented
7#23752221C211yesmaximal, characteristic, complemented
8#23752220C211yesmaximal, characteristic, complemented
9#536×C151C211yesmaximal, characteristic
10C22×Dic302C2211yescharacteristic
11C2×#14558994—24no—
12C2×#14558994C2212yes—
13C2×#14558994C2212yes—
14#18012746—24no—
15C2×#14558988C2212yes—
16C2×#14558988C2211yescharacteristic
17C22×C151⋊C8C2212yes—
18C22×C151⋊C8C2211yescharacteristic
19#18012737—21no—
20#18012726—21no—
21#18012720—22no—
22#18012718C2214yes—
23#18012698C2211yescharacteristic
24#18012672C2212yes—
25#18012670C2212yes—
26#18012663C2214yes—
27#18012662C2214yes—
28C2×#41×C151C2211yescharacteristic
29C22×Q8×C151C2211yescharacteristic
30C4⋊Q8×C151—21no—
31#124×C151—21no—
32#123×C151—22no—
33C22⋊Q8×C151C2214yes—
34#117×C151C2211yescharacteristic
35C2×Dic302—21no—
36C2×Dic302—22no—
37C2×Dic302—22no—
38C2×Dic302C2312yes—
39C22×Dic151—21no—
40#14558994—24no—
41#14558994—24no—
42#14558988—24no—
43#14558988—22no—
44C2×C151⋊C8—24no—
45C2×C151⋊C8D414yes—
46C2×C151⋊C8C2312yes—
47C2×C151⋊C8C2311yescharacteristic
48C2×C151⋊C8C2311yescharacteristic
49C4⋊Dic151C2312yes—
50Dic151⋊C4—24no—
51C22⋊Dic151—21no—
52C22⋊Dic151—24no—
53C4×Dic151—21no—
54#41×C151—22no—
55#41×C151—22no—
56C2×Q8×C151—21no—
57C2×Q8×C151—22no—
58C2×Q8×C151—22no—
59C2×Q8×C151D411yescharacteristic
60C2×Q8×C151C2312yes—
61C2×D4×C151D412yes—
62C2×D4×C151D411yescharacteristic
63C22×C4×C151—21no—
64C22×C4×C151C2312yes—
65C22×C4×C151C2311yescharacteristic
66C4⋊C4×C151—24no—
67C4⋊C4×C151C2312yes—
68C22⋊C4×C151—21no—
69C22⋊C4×C151—24no—
70C42×C151—21no—
71Dic302—22no—
72Dic302—22no—
73Dic302—42no—
74C2×Dic151—22no—
75C2×Dic151—22no—
76C2×Dic151—42no—
77C151⋊C8—22no—
78C151⋊C8C2×D412yes—
79C151⋊C8C2×D412yes—
80C23×C151C2×D412yes—
81C23×C151C2×D411yescharacteristic
82Q8×C151—22no—
83Q8×C151—22no—
84Q8×C151—22no—
85Q8×C151—42no—
86D4×C151—24no—
87D4×C151—22no—
88C2×C4×C151—22no—
89C2×C4×C151—22no—
90C2×C4×C151—22no—
91C2×C4×C151—22no—
92C2×C4×C151—42no—
93C2×C4×C151C2×D412yes—
94C2×C4×C151C2×D412yes—
95C2×C4×C151C2×D411yescharacteristic
96C2×C4×C151#4112yes—
97C2×C4×C151C2411yescharacteristic
98C22×C151—22no—
99C22×C151—22no—
100C22×C151—24no—
101C22×C151#12112yes—
102C22×C151C22×D411yescharacteristic
103C4×C151—22no—
104C4×C151—42no—
105C4×C151—42no—
106C4×C151#12112yes—
107C4×C151C22×D411yescharacteristic
108C4×C151C2×#4111yescharacteristic
109Dic151—42no—
110Dic151—42no—
111C2×C151—22no—
112C2×C151—42no—
113C2×C151C2×#12111yescharacteristic
114C2×C151#57812yes—
115C151#305911yescharacteristic, complemented, Sylow
116#3059—1511nomaximal, Sylow
117C22×Q16—1511no—
118C2×#131—1511no—
119#536—1511no—
120#536D15111yescharacteristic
121#470—1514no—
122#467—1514no—
123#427—1511no—
124#419—1511no—
125#419—1511no—
126C2×#41C2×D15111yescharacteristic
127C22×Q8—1511no—
128C22×Q8C2×D15111yescharacteristic
129C2×Q16—3024no—
130C2×Q16—1512no—
131C2×Q16—1512no—
132#131—3024no—
133C2×M16—1511no—
134C2×M16—1512no—
135C22×C8—1512no—
136C22×C8—1511no—
137C4⋊Q8—21no—
138C4⋊Q8—3021no—
139#124—21no—
140#124—3021no—
141#123—22no—
142#123—3022no—
143C22⋊Q8—1514no—
144C22⋊Q8C2×D15114yes—
145#117—1511no—
146#117C2×D15111yescharacteristic
147#107—1512no—
148#106—1512no—
149#103—1514no—
150#103—1514no—
151#41—22no—
152#41—22no—
153C2×Q8—21no—
154C2×Q8—22no—
155C2×Q8—22no—
156C2×Q8—3021no—
157C2×Q8—3022no—
158C2×Q8—3022no—
159C2×Q8—1512no—
160C2×Q8C22⋊D15111yescharacteristic
161C2×Q8C22×D15112yes—
162C2×D4C22⋊D15112yes—
163C2×D4C22⋊D15111yescharacteristic
164C22×C4—21no—
165C22×C4—3021no—
166C22×C4C22×D15112yes—
167C22×C4C22×D15111yescharacteristic
168Q16—3024no—
169Q16—3024no—
170M16—3022no—
171M16—3024no—
172C2×C8—3024no—
173C2×C8—1512no—
174C2×C8—1514no—
175C2×C8—1511no—
176C2×C8—1511no—
177C4⋊C4—24no—
178C4⋊C4—3024no—
179C4⋊C4—1512no—
180C4⋊C4C22×D15112yes—
181C22⋊C4—21no—
182C22⋊C4—24no—
183C22⋊C4—3021no—
184C22⋊C4—3024no—
185C42—21no—
186C42—3021no—
187C23C2×C22⋊D15112yes—
188C23C2×C22⋊D15111yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—22no—
192Q8—42no—
193Q8—3022no—
194Q8—3022no—
195Q8—6042no—
196D4—24no—
197D4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—42no—
203C2×C4—3022no—
204C2×C4—3022no—
205C2×C4—6042no—
206C2×C4D4×D15112yes—
207C2×C4C2×C22⋊D15112yes—
208C2×C4C2×C22⋊D15111yescharacteristic
209C2×C4#1455900312yes—
210C2×C4C23×D15111yescharacteristic
211C8—3022no—
212C8—1512no—
213C8—1512no—
214C22—22no—
215C22—24no—
216C22—22no—
217C22#1801271112yes—
218C22C22×C22⋊D15111yescharacteristic
219C4—22no—
220C4—42no—
221C4—42no—
222C4—6042no—
223C4—6042no—
224C4#1801271112yes—
225C4C2×D4×D15111yescharacteristic
226C4C2×#1455900311yescharacteristic
227C2—22no—
228C2—42no—
229C2C2×#1801271111yescharacteristic
230C2#2375302712yes—
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#536×C151C2
socleC22×C151C22×D4
prime radicalC2×#41×C151C22
hypercenter#536D151
hypocenterC151#3059
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
1. C22×#14558994C2semidirect
4. #23752468C2semidirect
5. #23752451C2semidirect
6. #23752248C2semidirect
7. #23752221C2semidirect
8. #23752220C2semidirect
115. C151#3059semidirect

Maximal subgroups

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

subgroupindex
C22×#145589942
C2×#180127462
#237527832
#237524682
#237524512
#237522482
#237522212
#237522202
#536×C1512
#3059151