Finite Group Databasebeta

← #34080177

Subgroups — #34080177

Order 19328.

396 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 109 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#23752823C211yesmaximal, characteristic, complemented
2#23752780C211yesmaximal, characteristic
3#23752586C211yesmaximal, characteristic, complemented
4#23752577C211yesmaximal, characteristic, complemented
5#23752566C211yesmaximal, characteristic, complemented
6#23752436C212yesmaximal, complemented
7#23752410C212yesmaximal, complemented
8#23752373C212yesmaximal, complemented
9#23752361C212yesmaximal, complemented
10#23752274C211yesmaximal, characteristic, complemented
11#497×C151C211yesmaximal, characteristic, complemented
12C2×#14559005C2211yescharacteristic
13C2×D4×D151C2211yescharacteristic
14C2×#14558991C2212yes—
15C2×#14558991C2212yescomplemented
16#18012736C2211yescharacteristic
17#18012735C2211yescharacteristic
18#18012734—22no—
19#18012731C2211yescharacteristic, complemented
20#18012729—22no—
21#18012728C2211yescharacteristic
22#18012715C2212yes—
23#18012712—22no—
24#18012709—22no—
25Q8×Dic151C2212yescomplemented
26#18012696C2211yescharacteristic
27Dic151⋊C8C2212yescomplemented
28#18012663C2212yescomplemented
29#18012661C2212yes—
30#18012661C2212yescomplemented
31#18012660C2212yes—
32(C2×D151)⋊C8C2212yes—
33C4×C151⋊C8C2211yescharacteristic, complemented
34C2×Q16×C151C2212yescomplemented
35C2×SD16×C151C2212yes—
36C4⋊Q8×C151C2211yescharacteristic, complemented
37#124×C151C2211yescharacteristic
38#97×C151C2211yescharacteristic, complemented
39C23×D151—21no—
40#14559005—42no—
41C2×D604—21no—
42C2×D604—22no—
43C2×D604C2311yescharacteristic
44C2×D604C2311yescharacteristic
45C2×C22⋊D151—21no—
46C2×C22⋊D151—22no—
47D4×D151—42no—
48C2×C4×D151—21no—
49C2×C4×D151C2311yescharacteristic
50#14558991—42no—
51#14558991—42no—
52C2×C151⋊C8C2312yes—
53C4⋊Dic151—22no—
54C4⋊Dic151C2312yes—
55Dic151⋊C4—22no—
56Dic151⋊C4—22no—
57Dic151⋊C4D412yes—
58(C2×D151)⋊C4—22no—
59(C2×D151)⋊C4—22no—
60(C2×D151)⋊C4D412yes—
61C4×Dic151—22no—
62C4×Dic151C2311yescharacteristic
63C2×Q8×C151C2312yes—
64C2×Q8×C151C2311yescharacteristic
65C2×D4×C151C2311yescharacteristic
66Q16×C151—42no—
67SD16×C151—42no—
68C2×C8×C151C2312yes—
69C4⋊C4×C151—22no—
70C22⋊C4×C151—22no—
71C42×C151C2311yescharacteristic
72C22×D151—21no—
73C22×D151—21no—
74C22×D151—42no—
75C22×D151—82no—
76C22×D151C2×D411yescharacteristic
77D604—22no—
78D604—22no—
79D604—42no—
80D604—82no—
81C22⋊D151—42no—
82C22⋊D151—82no—
83C2×Dic151—22no—
84C2×Dic151C2×D412yes—
85C2×Dic151C2×D411yescharacteristic
86C4×D151—22no—
87C4×D151—42no—
88C151⋊C8—22no—
89C23×C151—21no—
90Q8×C151—22no—
91Q8×C151—22no—
92Q8×C151—22no—
93D4×C151—22no—
94C2×C4×C151—22no—
95C2×C4×C151—21no—
96C2×C4×C151C2×D412yes—
97C2×C4×C151C2411yescharacteristic
98C8×C151—22no—
99C22×C151—41no—
100C22×C151—42no—
101C22×C151C22×D411yescharacteristic
102C2×D151—21no—
103C2×D151—22no—
104C2×D151—41no—
105C2×D151—41no—
106C2×D151—42no—
107C2×D151—42no—
108C2×D151—84no—
109C4×C151—22no—
110C4×C151—42no—
111C4×C151—41no—
112C4×C151H(5,𝔽2)12yes—
113Dic151—21no—
114Dic151—22no—
115Dic151—42no—
116C2×C151—81no—
117C2×C151#53511yescharacteristic
118C2×C151#57712yes—
119D151—41no—
120D151—81no—
121D151—81no—
122C151#322211yescharacteristic, complemented, Sylow
123#3222—1511nomaximal, Sylow
124#541—1511no—
125#535—1511no—
126#497D15111yescharacteristic, complemented
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×#41—1511no—
136C22×D4—1511no—
137C2×Q16C2×D15112yescomplemented
138C2×SD16—1512no—
139C2×SD16—1512no—
140C2×SD16C2×D15112yes—
141C4⋊Q8C2×D15111yescharacteristic, complemented
142#127—1511no—
143#127—1511no—
144#126—3022no—
145#125—3022no—
146#125—1511no—
147#124—1511no—
148#124C2×D15111yescharacteristic
149C22⋊Q8—1512no—
150#121—3022no—
151#120—3022no—
152C4×Q8—1512no—
153#117—1511no—
154C4⋊C8—1512no—
155#103—1512no—
156#102—1512no—
157#102—1512no—
158#102—1512no—
159C22⋊C8—1512no—
160#97C2×D15111yescharacteristic, complemented
161C4×C8—1511no—
162C24—3021no—
163#41—6042no—
164C2×Q8C22×D15111yescharacteristic
165C2×Q8C22×D15112yes—
166C2×D4—3021no—
167C2×D4—3021no—
168C2×D4—3022no—
169C2×D4—3022no—
170C2×D4—6042no—
171C2×D4—1511no—
172C2×D4—1511no—
173C2×D4C22×D15111yescharacteristic
174C22×C4—3021no—
175C22×C4—1511no—
176Q16—42no—
177SD16—42no—
178SD16—6042no—
179SD16—6042no—
180C2×C8—1512no—
181C2×C8C22×D15112yes—
182C4⋊C4—22no—
183C4⋊C4—3022no—
184C4⋊C4—3022no—
185C4⋊C4—3022no—
186C4⋊C4—1512no—
187C4⋊C4—1512no—
188C22⋊C4—22no—
189C22⋊C4—3022no—
190C22⋊C4—3022no—
191C22⋊C4—1512no—
192C42—3022no—
193C42—1511no—
194C42C22×D15111yescharacteristic
195C23—21no—
196C23—3021no—
197C23—3021no—
198C23—6042no—
199C23—1511no—
200C23—12082no—
201Q8—22no—
202Q8—22no—
203Q8—22no—
204D4—22no—
205D4—3022no—
206D4—3022no—
207D4—6042no—
208D4—6042no—
209D4—12082no—
210D4—12082no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—3022no—
214C2×C4—3022no—
215C2×C4—6042no—
216C2×C4—1512no—
217C2×C4—1511no—
218C2×C4D4×D15112yes—
219C2×C4C23×D15111yescharacteristic
220C8—22no—
221C8—3022no—
222C22—42no—
223C22—41no—
224C22—3022no—
225C22—3021no—
226C22—6042no—
227C22—6042no—
228C22—6041no—
229C22—6041no—
230C22—12084no—
231C22C2×D4×D15111yescharacteristic
232C4—22no—
233C4—41no—
234C4—42no—
235C4—3022no—
236C4—3021no—
237C4—6042no—
238C4#1801278412yes—
239C2—81no—
240C2—6041no—
241C2—12081no—
242C2—12081no—
243C2#2375277511yescharacteristic
244C2#2375302112yes—
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#497×C151C2
socleC22×C151C22×D4
prime radical#23752780C2
hypercenter#497D151
hypocenterC151#3222
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. #23752823C2semidirect
3. #23752586C2semidirect
4. #23752577C2semidirect
5. #23752566C2semidirect
6. #23752436C2semidirect
7. #23752410C2semidirect
8. #23752373C2semidirect
9. #23752361C2semidirect
10. #23752274C2semidirect
11. #497×C151C2semidirect
15. C2×#14558991C22semidirect
19. #18012731C22semidirect
25. Q8×Dic151C22semidirect
27. Dic151⋊C8C22semidirect
28. #18012663C22semidirect
30. #18012661C22semidirect
33. C4×C151⋊C8C22semidirect
34. C2×Q16×C151C22semidirect
36. C4⋊Q8×C151C22semidirect
38. #97×C151C22semidirect
122. C151#3222semidirect
126. #497D151semidirect
137. C2×Q16C2×D151semidirect
141. C4⋊Q8C2×D151semidirect
160. #97C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237528232
#237527802
#237525862
#237525772
#237525662
#237524362
#237524102
#237523732
#237523612
#237522742
#497×C1512
#3222151