Finite Group Databasebeta

← #34080182

Subgroups — #34080182

Order 19328.

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

normal subgroups only

This group has 396 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#23752824C211yesmaximal, characteristic, complemented
2#23752607C211yesmaximal, characteristic, complemented
3#23752584C211yesmaximal, characteristic, complemented
4#23752576C211yesmaximal, characteristic, complemented
5#23752566C211yesmaximal, characteristic, complemented
6#23752431C212yesmaximal, complemented
7#23752409C212yesmaximal, complemented
8#23752374C212yesmaximal, complemented
9#23752363C212yesmaximal, complemented
10#23752273C211yesmaximal, characteristic, complemented
11#535×C151C211yesmaximal, characteristic
12C2×#14558994C2212yescomplemented
13C2×#14558992C2212yes—
14C2×#14558992C2212yes—
15C2×#14558992C2212yescomplemented
16#18012739C2211yescharacteristic, complemented
17#18012732—22no—
18#18012731C2211yescharacteristic, complemented
19#18012729—22no—
20#18012718C2212yes—
21C4×Dic302C2212yescomplemented
22C4⋊(C151⋊C8)C2212yescomplemented
23#18012663C2212yescomplemented
24#18012660C2212yes—
25#18012660C2212yes—
26#18012660C2212yescomplemented
27C22⋊(C151⋊C8)C2212yes—
28#18012650C2211yescharacteristic, complemented
29C4×C151⋊C8C2211yescharacteristic, complemented
30C2×#41×C151C2211yescharacteristic
31C22×D4×C151C2211yescharacteristic
32#127×C151C2211yescharacteristic
33#127×C151C2211yescharacteristic
34#124×C151C2211yescharacteristic
35#124×C151C2211yescharacteristic
36#121×C151—22no—
37#120×C151—22no—
38#117×C151C2211yescharacteristic
39C2×Dic302C2312yes—
40#14558994—42no—
41#14558992—42no—
42#14558992—42no—
43#14558992—42no—
44C2×C151⋊C8C2312yes—
45C2×C151⋊C8C2312yes—
46C4⋊Dic151—22no—
47C4⋊Dic151C2312yes—
48Dic151⋊C4—22no—
49Dic151⋊C4—22no—
50Dic151⋊C4—22no—
51C22⋊Dic151—22no—
52C4×Dic151—22no—
53C24×C151—21no—
54#41×C151—42no—
55C2×Q8×C151C2311yescharacteristic
56C2×D4×C151—21no—
57C2×D4×C151—21no—
58C2×D4×C151—22no—
59C2×D4×C151—22no—
60C2×D4×C151—42no—
61C2×D4×C151C2311yescharacteristic
62C2×D4×C151C2311yescharacteristic
63C2×D4×C151C2311yescharacteristic
64C22×C4×C151—21no—
65C22×C4×C151C2311yescharacteristic
66C4⋊C4×C151D412yes—
67C22⋊C4×C151—22no—
68C22⋊C4×C151—22no—
69C22⋊C4×C151D412yes—
70C42×C151C2311yescharacteristic
71C42×C151C2311yescharacteristic
72Dic302—22no—
73Dic302—22no—
74C2×Dic151—22no—
75C2×Dic151—22no—
76C151⋊C8—22no—
77C151⋊C8—22no—
78C23×C151—21no—
79C23×C151—21no—
80C23×C151—21no—
81C23×C151—42no—
82C23×C151—82no—
83C23×C151C2×D411yescharacteristic
84Q8×C151—22no—
85D4×C151—22no—
86D4×C151—22no—
87D4×C151—22no—
88D4×C151—42no—
89D4×C151—42no—
90D4×C151—82no—
91D4×C151—82no—
92C2×C4×C151—22no—
93C2×C4×C151—21no—
94C2×C4×C151—42no—
95C2×C4×C151C2×D412yes—
96C2×C4×C151C2×D411yescharacteristic
97C2×C4×C151C2×D412yes—
98C2×C4×C151C2411yescharacteristic
99C22×C151—21no—
100C22×C151—22no—
101C22×C151—41no—
102C22×C151—41no—
103C22×C151—41no—
104C22×C151—42no—
105C22×C151—42no—
106C22×C151—42no—
107C22×C151—84no—
108C22×C151C22×D411yescharacteristic
109C4×C151—21no—
110C4×C151—22no—
111C4×C151—22no—
112C4×C151—41no—
113C4×C151H(5,𝔽2)12yes—
114Dic151—42no—
115Dic151—42no—
116C2×C151—41no—
117C2×C151—81no—
118C2×C151—81no—
119C2×C151—81no—
120C2×C151#53511yescharacteristic
121C2×C151#57712yes—
122C151#322211yescharacteristic, complemented, Sylow
123#3222—1511nomaximal, Sylow
124#541—1511no—
125#535D15111yescharacteristic
126#497—1511no—
127#492—1511no—
128#490—1511no—
129#488—1511no—
130#464—1512no—
131#460—1512no—
132#452—1512no—
133#450—1512no—
134#433—1511no—
135C2×#41C2×D15111yescharacteristic
136C22×D4C2×D15111yescharacteristic
137C2×Q16—1512no—
138C2×SD16—1512no—
139C2×SD16—1512no—
140C2×SD16—1512no—
141C4⋊Q8—1511no—
142#127C2×D15111yescharacteristic
143#127C2×D15111yescharacteristic
144#126—3022no—
145#125—3022no—
146#125—1511no—
147#124C2×D15111yescharacteristic
148#124C2×D15111yescharacteristic
149C22⋊Q8—1512no—
150#121—22no—
151#120—22no—
152C4×Q8—1512no—
153#117C2×D15111yescharacteristic
154C4⋊C8—1512no—
155#103—1512no—
156#102—1512no—
157#102—1512no—
158#102—1512no—
159C22⋊C8—1512no—
160#97—1511no—
161C4×C8—1511no—
162C24—21no—
163#41—42no—
164C2×Q8—1512no—
165C2×Q8C22×D15111yescharacteristic
166C2×D4—21no—
167C2×D4—21no—
168C2×D4—22no—
169C2×D4—22no—
170C2×D4—42no—
171C2×D4C22×D15111yescharacteristic
172C2×D4C22×D15111yescharacteristic
173C2×D4C22×D15111yescharacteristic
174C22×C4—21no—
175C22×C4C22×D15111yescharacteristic
176Q16—6042no—
177SD16—6042no—
178SD16—6042no—
179SD16—6042no—
180C2×C8—1512no—
181C2×C8—1512no—
182C4⋊C4—3022no—
183C4⋊C4—3022no—
184C4⋊C4—3022no—
185C4⋊C4—3022no—
186C4⋊C4—1512no—
187C4⋊C4C22⋊D15112yes—
188C22⋊C4—22no—
189C22⋊C4—22no—
190C22⋊C4—3022no—
191C22⋊C4C22⋊D15112yes—
192C42—3022no—
193C42C22×D15111yescharacteristic
194C42C22×D15111yescharacteristic
195C23—21no—
196C23—21no—
197C23—21no—
198C23—42no—
199C23—82no—
200C23C2×C22⋊D15111yescharacteristic
201Q8—22no—
202Q8—3022no—
203Q8—3022no—
204D4—22no—
205D4—22no—
206D4—22no—
207D4—42no—
208D4—42no—
209D4—82no—
210D4—82no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—42no—
214C2×C4—3022no—
215C2×C4—3022no—
216C2×C4C2×C22⋊D15112yes—
217C2×C4C2×C22⋊D15112yes—
218C2×C4C2×C22⋊D15111yescharacteristic
219C2×C4C23×D15111yescharacteristic
220C8—3022no—
221C8—3022no—
222C22—22no—
223C22—21no—
224C22—42no—
225C22—42no—
226C22—42no—
227C22—41no—
228C22—41no—
229C22—41no—
230C22—84no—
231C22C22×C22⋊D15111yescharacteristic
232C4—22no—
233C4—22no—
234C4—21no—
235C4—41no—
236C4—6042no—
237C4—6042no—
238C4#1801278412yes—
239C2—41no—
240C2—81no—
241C2—81no—
242C2—81no—
243C2#2375277911yescharacteristic
244C2#2375302312yes—
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting, prime radical#535×C151C2
socleC22×C151C22×D4
hypercenter#535D151
hypocenterC151#3222
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ #117 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #23752824C2semidirect
2. #23752607C2semidirect
3. #23752584C2semidirect
4. #23752576C2semidirect
5. #23752566C2semidirect
6. #23752431C2semidirect
7. #23752409C2semidirect
8. #23752374C2semidirect
9. #23752363C2semidirect
10. #23752273C2semidirect
12. C2×#14558994C22semidirect
15. C2×#14558992C22semidirect
16. #18012739C22semidirect
18. #18012731C22semidirect
21. C4×Dic302C22semidirect
22. C4⋊(C151⋊C8)C22semidirect
23. #18012663C22semidirect
26. #18012660C22semidirect
28. #18012650C22semidirect
29. C4×C151⋊C8C22semidirect
122. C151#3222semidirect

Maximal subgroups

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

subgroupindex
#237528242
#237526072
#237525842
#237525762
#237525662
#237524312
#237524092
#237523742
#237523632
#237522732
#535×C1512
#3222151