Finite Group Databasebeta

← #34081024

Subgroups — #34081024

Order 19328.

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

normal subgroups only

This group has 386 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#23752936C211yesmaximal, characteristic, complemented
2#23752866C211yesmaximal, characteristic
3#23752564C211yesmaximal, characteristic, complemented
4#23752555C212yesmaximal, complemented
5#23752454C212yesmaximal, complemented
6#23752423C211yesmaximal, characteristic, complemented
7#23752375C212yesmaximal, complemented
8C4×#14558992C211yesmaximal, characteristic, complemented
9#23752277C211yesmaximal, characteristic, complemented
10#23752205C212yesmaximal, complemented
11#474×C151C211yesmaximal, characteristic, complemented
12C2×#14559003C2212yes—
13C2×Dic604C2212yes—
14C2×#14558992C2211yescharacteristic
15C2×C8×D151C2212yes—
16#18012739C2211yescharacteristic
17#18012734—22no—
18#18012728—21no—
19#18012723—22no—
20#18012719C2212yes—
21#18012719C2212yes—
22#18012713—21no—
23Q8×Dic151—21no—
24C4×Dic302C2211yescharacteristic
25C4×D604C2211yescharacteristic
26#18012697C2212yes—
27C2×C4⋊Dic151—21no—
28#18012670C2211yescharacteristic
29#18012664C2212yes—
30#18012662C2211yescharacteristic
31#18012662C2212yes—
32#18012662C2212yes—
33#18012660C2211yescharacteristic
34(C2×D151)⋊C8C2212yes—
35C4×C151⋊C8C2211yescharacteristic
36C4⋊Q8×C151C2211yescharacteristic
37C4×D4×C151C2211yescharacteristic
38#107×C151C2212yes—
39C4⋊C8×C151C2211yescharacteristic
40#102×C151C2212yes—
41#14559003—24no—
42#14559003—42no—
43C2×Dic302C2311yescharacteristic
44C2×Dic302C2312yes—
45C2×D604D411yescharacteristic
46C2×C22⋊D151—22no—
47C22×Dic151—22no—
48C2×C4×D151C2312yes—
49Dic604—42no—
50#14558992—22no—
51C2×C151⋊C8C2311yescharacteristic
52C2×C151⋊C8C2311yescharacteristic
53C8×D151—42no—
54C4⋊Dic151—22no—
55C4⋊Dic151—22no—
56C4⋊Dic151—21no—
57C4⋊Dic151—21no—
58C4⋊Dic151D411yescharacteristic
59C4⋊Dic151C2311yescharacteristic
60Dic151⋊C4—21no—
61(C2×D151)⋊C4—22no—
62(C2×D151)⋊C4—22no—
63(C2×D151)⋊C4—22no—
64(C2×D151)⋊C4D412yes—
65C4×Dic151—22no—
66C4×Dic151—21no—
67C2×Q8×C151—21no—
68C2×D4×C151C2311yescharacteristic
69C22×C4×C151—21no—
70C2×C8×C151C2312yes—
71C4⋊C4×C151—21no—
72C4⋊C4×C151C2312yes—
73C4⋊C4×C151C2311yescharacteristic
74C22⋊C4×C151—21no—
75C42×C151C2311yescharacteristic
76C22×D151C2×D412yes—
77Dic302—21no—
78Dic302—22no—
79Dic302—21no—
80Dic302—22no—
81D604—22no—
82C22⋊D151—44no—
83C2×Dic151—21no—
84C2×Dic151—21no—
85C2×Dic151—22no—
86C2×Dic151—44no—
87C2×Dic151C2×D412yes—
88C4×D151—22no—
89C4×D151—22no—
90C151⋊C8—21no—
91C151⋊C8—21no—
92C23×C151—21no—
93Q8×C151—42no—
94D4×C151—21no—
95D4×C151#4112yes—
96C2×C4×C151—22no—
97C2×C4×C151—21no—
98C2×C4×C151—42no—
99C2×C4×C151C2×D411yescharacteristic
100C2×C4×C151C2×D411yescharacteristic
101C2×C4×C151C2411yescharacteristic
102C8×C151—22no—
103C22×C151—22no—
104C22×C151—41no—
105C22×C151—41no—
106C22×C151C22×D411yescharacteristic
107C2×D151—22no—
108C2×D151—22no—
109C2×D151—22no—
110C4×C151—21no—
111C4×C151—41no—
112C4×C151—42no—
113C4×C151#13512yes—
114C4×C151C2×#4111yescharacteristic
115C4×C151H(5,𝔽2)11yescharacteristic
116Dic151—22no—
117Dic151—42no—
118Dic151—41no—
119Dic151—41no—
120C2×C151—42no—
121C2×C151#54611yescharacteristic
122C2×C151C2×#13511yescharacteristic
123C2×C151#57811yescharacteristic
124D151—42no—
125C151#330211yescharacteristic, complemented, Sylow
126#3302—1511nomaximal, Sylow
127#556—1511no—
128#547—1511no—
129#487—1511no—
130#485—1512no—
131#474D15111yescharacteristic, complemented
132#467—1512no—
133#462—1511no—
134#452—1512no—
135C4×SD16—1511no—
136C8×D4—1511no—
137#416—1512no—
138C2×#41—1512no—
139C2×Q16—1512no—
140C2×SD16—1511no—
141C22×C8—1512no—
142C4⋊Q8—1511no—
143C4⋊Q8C2×D15111yescharacteristic
144#126—3022no—
145#124—3021no—
146#123—3022no—
147C22⋊Q8—1512no—
148C22⋊Q8—1512no—
149#121—3021no—
150C4×Q8—3021no—
151C4×Q8—1511no—
152C4×D4—1511no—
153C4×D4C2×D15111yescharacteristic
154#117—1512no—
155C2×C4⋊C4—3021no—
156#107C2×D15112yes—
157#106—1511no—
158C4⋊C8C2×D15111yescharacteristic
159#103—1512no—
160#103—1512no—
161#103—1511no—
162#103—1512no—
163#102—1511no—
164#102C2×D15112yes—
165C22⋊C8—1512no—
166C4×C8—1511no—
167#41—3024no—
168#41—6042no—
169C2×Q8—21no—
170C2×Q8—1512no—
171C2×Q8—1511no—
172C2×D4—3022no—
173C2×D4—1511no—
174C2×D4C22×D15111yescharacteristic
175C22×C4—21no—
176C22×C4—3022no—
177C22×C4—1512no—
178Q16—6042no—
179SD16—3022no—
180C2×C8—6042no—
181C2×C8—1511no—
182C2×C8—1511no—
183C2×C8C22×D15112yes—
184C4⋊C4—21no—
185C4⋊C4—3022no—
186C4⋊C4—3022no—
187C4⋊C4—3021no—
188C4⋊C4—3021no—
189C4⋊C4—3021no—
190C4⋊C4—1511no—
191C4⋊C4—1511no—
192C4⋊C4C22×D15112yes—
193C4⋊C4C22×D15111yescharacteristic
194C22⋊C4—21no—
195C22⋊C4—3022no—
196C22⋊C4—3022no—
197C22⋊C4—3022no—
198C22⋊C4—1512no—
199C42—3022no—
200C42—3021no—
201C42C22×D15111yescharacteristic
202C23—21no—
203C23—1512no—
204Q8—42no—
205Q8—3021no—
206Q8—3022no—
207Q8—3021no—
208Q8—3022no—
209D4—21no—
210D4—3022no—
211D4—6044no—
212D4#1455900512yes—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—42no—
216C2×C4—3022no—
217C2×C4—3022no—
218C2×C4—3021no—
219C2×C4—3021no—
220C2×C4—3022no—
221C2×C4—6044no—
222C2×C4—1512no—
223C2×C4D4×D15111yescharacteristic
224C2×C4D4×D15111yescharacteristic
225C2×C4C23×D15111yescharacteristic
226C8—22no—
227C8—3021no—
228C8—3021no—
229C22—22no—
230C22—41no—
231C22—41no—
232C22—3022no—
233C22—3022no—
234C22—3022no—
235C22C2×D4×D15111yescharacteristic
236C4—21no—
237C4—41no—
238C4—42no—
239C4—3022no—
240C4—6041no—
241C4—6042no—
242C4—6041no—
243C4#1801275812yes—
244C4C2×#1455900511yescharacteristic
245C4#1801278511yescharacteristic
246C2—42no—
247C2—6042no—
248C2#2375285311yescharacteristic
249C2C2×#1801275811yescharacteristic
250C2#2375302811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#474×C151C2
socleC22×C151C22×D4
prime radical#23752866C2
hypercenter#474D151
hypocenterC151#3302
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #23752936C2semidirect
3. #23752564C2semidirect
4. #23752555C2semidirect
5. #23752454C2semidirect
6. #23752423C2semidirect
7. #23752375C2semidirect
8. C4×#14558992C2semidirect
9. #23752277C2semidirect
10. #23752205C2semidirect
11. #474×C151C2semidirect
125. C151#3302semidirect
131. #474D151semidirect

Maximal subgroups

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

subgroupindex
#237529362
#237528662
#237525642
#237525552
#237524542
#237524232
#237523752
C4×#145589922
#237522772
#237522052
#474×C1512
#3302151