Finite Group Databasebeta

← #34069026

Subgroups — #34069026

Order 19328.

612 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 101 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×#14559003C211yesmaximal, characteristic
2C2×#18012654C211yesmaximal, characteristic, complemented
3C2×#18012653C212yesmaximal, complemented
4#23752073C212yesmaximal, complemented
5C2×#99×C151C211yesmaximal, characteristic, complemented
6C2×#14559003—22no—
7C2×#14559003—22no—
8C2×#14559003—24no—
9C2×#14559003—24no—
10C22×Dic302C411yescharacteristic, complemented
11C22×C22⋊D151C411yescharacteristic, complemented
12C22×C22⋊D151C2211yescharacteristic
13C23×Dic151C411yescharacteristic, complemented
14C23×Dic151C2211yescharacteristic
15C22×C4×D151C411yescharacteristic, complemented
16C2×C22⋊Dic151C2212yes—
17#18012654—22no—
18#18012653—24no—
19C151⋊#95—24no—
20C22×D4×C151C2211yescharacteristic
21C2×C22⋊C4×C151C2212yes—
22#99×C151—22no—
23C23×D151C2×C411yescharacteristic
24#14559003—216no—
25#14559003—216no—
26C2×Dic302—22no—
27C2×Dic302—22no—
28C2×Dic302—22no—
29C2×C22⋊D151—22no—
30C2×C22⋊D151—22no—
31C2×C22⋊D151—22no—
32C2×C22⋊D151—22no—
33C2×C22⋊D151—21no—
34C2×C22⋊D151—21no—
35C2×C22⋊D151D414yes—
36C22×Dic151—22no—
37C22×Dic151—22no—
38C22×Dic151—22no—
39C22×Dic151—22no—
40C22×Dic151—21no—
41C22×Dic151—21no—
42C22×Dic151—22no—
43C22×Dic151C2×C411yescharacteristic
44C22×Dic151C2×C411yescharacteristic
45C22×Dic151C2×C411yescharacteristic
46C22×Dic151D414yes—
47C2×C4×D151—22no—
48C2×C4×D151—22no—
49C2×C4×D151—22no—
50C22⋊Dic151—22no—
51C22⋊Dic151—22no—
52C24×C151C2×C411yescharacteristic
53C24×C151C2311yescharacteristic
54C2×D4×C151—22no—
55C2×D4×C151—22no—
56C2×D4×C151D412yes—
57C2×D4×C151D412yes—
58C22×C4×C151—22no—
59C22×C4×C151C2×C411yescharacteristic
60C22⋊C4×C151—22no—
61C22⋊C4×C151—22no—
62C22×D151—21no—
63C22×D151—21no—
64C22×D151—42no—
65C22×D151C22⋊C412yes—
66Dic302—28no—
67C22⋊D151—28no—
68C22⋊D151—24no—
69C22⋊D151—24no—
70C2×Dic151—28no—
71C2×Dic151—21no—
72C2×Dic151—21no—
73C2×Dic151—21no—
74C2×Dic151—21no—
75C2×Dic151—21no—
76C2×Dic151—21no—
77C2×Dic151—24no—
78C2×Dic151—24no—
79C2×Dic151—44no—
80C2×Dic151—42no—
81C2×Dic151C22⋊C412yes—
82C2×Dic151C22⋊C412yes—
83C2×Dic151C22⋊C412yes—
84C4×D151—28no—
85C23×C151—21no—
86C23×C151—21no—
87C23×C151—42no—
88C23×C151—42no—
89C23×C151C22⋊C412yes—
90C23×C151C22×C411yescharacteristic
91C23×C151C2×D412yes—
92C23×C151C2×D412yes—
93C23×C151C2×D411yescharacteristic
94C23×C151C2×D411yescharacteristic
95D4×C151—24no—
96D4×C151—24no—
97C2×C4×C151—21no—
98C2×C4×C151—21no—
99C2×C4×C151—44no—
100C2×C4×C151—42no—
101C2×C4×C151C22⋊C412yes—
102C22×C151—24no—
103C22×C151—22no—
104C22×C151—22no—
105C22×C151—42no—
106C22×C151—41no—
107C22×C151—41no—
108C22×C151—42no—
109C22×C151—42no—
110C22×C151—42no—
111C22×C151C2×C22⋊C411yescharacteristic
112C22×C151C2×C22⋊C411yescharacteristic
113C22×C151C2×C22⋊C411yescharacteristic
114C22×C151#12012yes—
115C22×C151#12012yes—
116C2×D151—22no—
117C2×D151—42no—
118C2×D151—42no—
119C2×D151—42no—
120C4×C151—22no—
121C4×C151—82no—
122Dic151—22no—
123Dic151—22no—
124Dic151—22no—
125Dic151—82no—
126C2×C151—22no—
127C2×C151—22no—
128C2×C151—21no—
129C2×C151—21no—
130C2×C151—42no—
131C2×C151#37911yescharacteristic
132C2×C151#41012yes—
133D151—42no—
134C151#178211yescharacteristic, complemented, Sylow
135#1782—1511nomaximal, Sylow
136C22×#41—1511no—
137C2×#99—1511no—
138C2×#99—1512no—
139C2×#99D15111yescharacteristic, complemented
140#381—1512no—
141C2×#41—3024no—
142C2×#41—3022no—
143C2×#41—3022no—
144C2×#41—3024no—
145C22×Q8—1511no—
146C22×D4—1511no—
147C22×D4—1511no—
148C22×D4C2×D15111yescharacteristic
149C23×C4—1511no—
150C23×C4—1511no—
151C23×C4—1511no—
152C2×C22⋊C4—1512no—
153C2×C22⋊C4C2×D15112yes—
154#99—22no—
155#99—3024no—
156#99—3022no—
157#95—3024no—
158C24—1511no—
159C24C4×D15111yescharacteristic
160C24C22×D15111yescharacteristic
161#41—30216no—
162#41—30216no—
163C2×Q8—3022no—
164C2×Q8—3022no—
165C2×Q8—3022no—
166C2×D4—22no—
167C2×D4—22no—
168C2×D4—3022no—
169C2×D4—3022no—
170C2×D4—3022no—
171C2×D4—3021no—
172C2×D4—3021no—
173C2×D4—3022no—
174C2×D4—1514no—
175C2×D4C22⋊D15112yes—
176C2×D4D60412yes—
177C22×C4—22no—
178C22×C4—3022no—
179C22×C4—3022no—
180C22×C4—3022no—
181C22×C4—3022no—
182C22×C4—3021no—
183C22×C4—3021no—
184C22×C4—3022no—
185C22×C4—3022no—
186C22×C4—3022no—
187C22×C4—3022no—
188C22×C4—1511no—
189C22×C4—1511no—
190C22×C4—1511no—
191C22×C4—1514no—
192C22×C4C4×D15111yescharacteristic
193C22⋊C4—22no—
194C22⋊C4—22no—
195C22⋊C4—3022no—
196C22⋊C4—3022no—
197C23—21no—
198C23—21no—
199C23—42no—
200C23—42no—
201C23—3021no—
202C23—3021no—
203C23—6042no—
204C23—1512no—
205C23(C2×D151)⋊C412yes—
206C23C2×C4×D15111yescharacteristic
207C23D4×D15112yes—
208C23D4×D15112yes—
209C23C2×C22⋊D15111yescharacteristic
210C23C2×D60411yescharacteristic
211Q8—3028no—
212D4—24no—
213D4—24no—
214D4—3028no—
215D4—3024no—
216D4—3024no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—44no—
220C2×C4—42no—
221C2×C4—3028no—
222C2×C4—3028no—
223C2×C4—3021no—
224C2×C4—3021no—
225C2×C4—3021no—
226C2×C4—3021no—
227C2×C4—3021no—
228C2×C4—3021no—
229C2×C4—3024no—
230C2×C4—3024no—
231C2×C4—6044no—
232C2×C4—6042no—
233C2×C4—1512no—
234C2×C4—1512no—
235C2×C4—1512no—
236C2×C4(C2×D151)⋊C412yes—
237C22—24no—
238C22—22no—
239C22—22no—
240C22—42no—
241C22—41no—
242C22—41no—
243C22—42no—
244C22—42no—
245C22—42no—
246C22—3022no—
247C22—6042no—
248C22—6042no—
249C22—6042no—
250C22C22⋊C4×D15111yescharacteristic
251C22C22⋊C4×D15111yescharacteristic
252C22C2×(C2×D151)⋊C411yescharacteristic
253C22#1801270712yes—
254C22#1801270912yes—
255C4—22no—
256C4—82no—
257C4—3022no—
258C4—3022no—
259C4—3022no—
260C4—12082no—
261C2—22no—
262C2—22no—
263C2—21no—
264C2—21no—
265C2—42no—
266C2—6042no—
267C2#2375206711yescharacteristic
268C2#2375218412yes—
subgroupG/H
centerC22C22⋊C4×D151
commutatorC23×C151C22×C4
FrattiniC24C22×D151
FittingC2×#99×C151C2
socleC22×C151C2×C22⋊C4
prime radicalC22×#14559003C2
cosocleC24×C151C23
hypercenterC2×#99D151
hypocenterC151#1782
LCSG ▷ C23×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. C2×#18012654C2semidirect
3. C2×#18012653C2semidirect
4. #23752073C2semidirect
5. C2×#99×C151C2semidirect
10. C22×Dic302C4semidirect
11. C22×C22⋊D151C4semidirect
13. C23×Dic151C4semidirect
15. C22×C4×D151C4semidirect
134. C151#1782semidirect
139. C2×#99D151semidirect

Maximal subgroups

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

subgroupindex
C22×#145590032
C2×#180126542
C2×#180126532
#237520732
C2×#99×C1512
#1782151