Finite Group Databasebeta

← #34078764

Subgroups — #34078764

Order 19328.

460 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 133 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×#18012747C211yesmaximal, characteristic
3#23752788C211yesmaximal, characteristic
4#23752786C211yesmaximal, characteristic
5#23752469C214yesmaximal, complemented
6#23752452C214yesmaximal, complemented
7#23752248C211yesmaximal, characteristic, complemented
8#23752222C211yesmaximal, characteristic, complemented
9#419×C151C211yesmaximal, characteristic, complemented
10C2×#14559004C2211yescharacteristic
11C22×Dic302C2211yescharacteristic
12C2×#14558994—24no—
13C2×#14558994C2212yes—
14C2×#14558994C2212yes—
15#18012747—24no—
16C2×#14558987C2212yes—
17C22×C151⋊C8C2211yescharacteristic
18C2×C8×D151C2212yes—
19#18012739—21no—
20#18012737—21no—
21#18012728—21no—
22#18012727—21no—
23#18012723—22no—
24#18012722—22no—
25#18012719C2214yes—
26#18012715C2214yes—
27#18012698C2211yescharacteristic
28#18012672C2212yes—
29#18012670C2212yes—
30#18012664C2214yes—
31C22×Q8×C151C2211yescharacteristic
32C2×M16×C151C2211yescharacteristic
33#117×C151C2211yescharacteristic
34#103×C151C2214yes—
35#14559004—22no—
36#14559004—22no—
37C2×Dic302—21no—
38C2×Dic302—22no—
39C2×Dic302—22no—
40C2×Dic302D411yescharacteristic
41C2×Dic302C2312yes—
42C2×D604D411yescharacteristic
43C2×C22⋊D151D412yes—
44C22×Dic151—21no—
45C2×C4×D151C2312yes—
46#14558994—24no—
47#14558994—24no—
48#14558987—24no—
49C2×C151⋊C8D414yes—
50C2×C151⋊C8C2311yescharacteristic
51C2×C151⋊C8C2311yescharacteristic
52C8×D151—24no—
53C4⋊Dic151—24no—
54C4⋊Dic151C2312yes—
55Dic151⋊C4—24no—
56C22⋊Dic151—21no—
57(C2×D151)⋊C4—24no—
58(C2×D151)⋊C4—24no—
59C4×Dic151—21no—
60C2×Q8×C151—21no—
61C2×Q8×C151—22no—
62C2×Q8×C151—22no—
63C2×Q8×C151C2312yes—
64C22×C4×C151—21no—
65C22×C4×C151C2311yescharacteristic
66M16×C151—22no—
67C2×C8×C151C2312yes—
68C4⋊C4×C151C2312yes—
69C22⋊C4×C151—21no—
70C42×C151—21no—
71C22×D151C2×D412yes—
72Dic302—22no—
73Dic302—22no—
74Dic302—22no—
75Dic302—42no—
76D604—22no—
77C22⋊D151—24no—
78C2×Dic151—22no—
79C2×Dic151—22no—
80C2×Dic151—42no—
81C2×Dic151C2×D412yes—
82C4×D151—22no—
83C4×D151—22no—
84C151⋊C8C2×D412yes—
85C151⋊C8C2×D412yes—
86C23×C151C2×D411yescharacteristic
87Q8×C151—22no—
88Q8×C151—22no—
89Q8×C151—42no—
90C2×C4×C151—22no—
91C2×C4×C151—22no—
92C2×C4×C151—42no—
93C2×C4×C151C2×D411yescharacteristic
94C2×C4×C151C2×D412yes—
95C2×C4×C151#4112yes—
96C2×C4×C151C2411yescharacteristic
97C8×C151—22no—
98C22×C151—22no—
99C22×C151#12112yes—
100C22×C151C22×D411yescharacteristic
101C2×D151—22no—
102C2×D151—24no—
103C4×C151—42no—
104C4×C151—42no—
105C4×C151#12112yes—
106C4×C151C22×D411yescharacteristic
107C4×C151C2×#4111yescharacteristic
108Dic151—22no—
109Dic151—42no—
110Dic151—42no—
111C2×C151—22no—
112C2×C151C2×#12111yescharacteristic
113C2×C151#57812yes—
114D151—42no—
115C151#305911yescharacteristic, complemented, Sylow
116#3059—1511nomaximal, Sylow
117C22×Q16—1511no—
118C2×#131—1511no—
119#536—1511no—
120#536—1511no—
121#470—1514no—
122#467—1514no—
123#427—1511no—
124#419—1511no—
125#419D15111yescharacteristic, complemented
126C2×#41—1511no—
127C22×Q8—1511no—
128C22×Q8C2×D15111yescharacteristic
129C2×Q16—3024no—
130C2×Q16—1512no—
131C2×Q16—1512no—
132#131—3024no—
133C2×M16—1512no—
134C2×M16C2×D15111yescharacteristic
135C22×C8—1512no—
136C22×C8—1511no—
137C4⋊Q8—3021no—
138C4⋊Q8—3021no—
139#124—3021no—
140#124—3021no—
141#123—3022no—
142#123—3022no—
143C22⋊Q8—1514no—
144C22⋊Q8—1514no—
145#117—1511no—
146#117C2×D15111yescharacteristic
147#107—1512no—
148#106—1512no—
149#103—1514no—
150#103C2×D15114yes—
151#41—3022no—
152#41—3022no—
153C2×Q8—21no—
154C2×Q8—22no—
155C2×Q8—22no—
156C2×Q8—3021no—
157C2×Q8—3022no—
158C2×Q8—3022no—
159C2×Q8—1512no—
160C2×Q8—1511no—
161C2×Q8C22×D15112yes—
162C2×D4—1512no—
163C2×D4—1511no—
164C22×C4—21no—
165C22×C4—3021no—
166C22×C4—1512no—
167C22×C4C22×D15111yescharacteristic
168Q16—3024no—
169Q16—3024no—
170M16—22no—
171M16—3024no—
172C2×C8—3024no—
173C2×C8—1514no—
174C2×C8—1511no—
175C2×C8—1511no—
176C2×C8C22×D15112yes—
177C4⋊C4—3024no—
178C4⋊C4—3024no—
179C4⋊C4—1512no—
180C4⋊C4C22×D15112yes—
181C22⋊C4—21no—
182C22⋊C4—3024no—
183C22⋊C4—3024no—
184C22⋊C4—3021no—
185C42—21no—
186C42—3021no—
187C23—1512no—
188C23D4×D15111yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—42no—
192Q8—3022no—
193Q8—3022no—
194Q8—3022no—
195Q8—6042no—
196D4—3024no—
197D4—3022no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—42no—
201C2×C4—3022no—
202C2×C4—3022no—
203C2×C4—3022no—
204C2×C4—3022no—
205C2×C4—6042no—
206C2×C4—1512no—
207C2×C4D4×D15111yescharacteristic
208C2×C4D4×D15112yes—
209C2×C4#1455900412yes—
210C2×C4C23×D15111yescharacteristic
211C8—22no—
212C8—1512no—
213C8—1512no—
214C22—22no—
215C22—3024no—
216C22—3022no—
217C22#1801271212yes—
218C22C2×D4×D15111yescharacteristic
219C4—42no—
220C4—42no—
221C4—3022no—
222C4—6042no—
223C4—6042no—
224C4#1801271212yes—
225C4C2×D4×D15111yescharacteristic
226C4C2×#1455900411yescharacteristic
227C2—22no—
228C2—6042no—
229C2C2×#1801271211yescharacteristic
230C2#2375302812yes—
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#419×C151C2
socleC22×C151C22×D4
prime radicalC2×#14559004C22
hypercenter#419D151
hypocenterC151#3059
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
1. C22×#14558994C2semidirect
5. #23752469C2semidirect
6. #23752452C2semidirect
7. #23752248C2semidirect
8. #23752222C2semidirect
9. #419×C151C2semidirect
115. C151#3059semidirect
125. #419D151semidirect

Maximal subgroups

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

subgroupindex
C22×#145589942
C2×#180127472
#237527882
#237527862
#237524692
#237524522
#237522482
#237522222
#419×C1512
#3059151