Finite Group Databasebeta

← #34071137

Subgroups — #34071137

Order 19328.

236 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 41 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#23752924C211yesmaximal, characteristic, complemented
2#23752397C211yesmaximal, characteristic, complemented
3#23752387C211yesmaximal, characteristic, complemented
4#23752384C211yesmaximal, characteristic, complemented
5#23752010C211yesmaximal, characteristic, complemented
6#23752008C211yesmaximal, characteristic, complemented
7#355×C151C211yesmaximal, characteristic, complemented
8#18012787C2211yescharacteristic
9#18012772—21no—
10#18012767—21no—
11#18012765—21no—
12#18012737C2211yescharacteristic
13#18012728C2211yescharacteristic
14#18012725—21no—
15#18012712—21no—
16#18012711—21no—
17(C22⋊D151)⋊C4—21no—
18#18012696—21no—
19#18012695—21no—
20#18012667—21no—
21#18012665—21no—
22#18012665—21no—
23#18012658C2211yescharacteristic
24#124×C151C2211yescharacteristic
25#101×C151C2211yescharacteristic
26#101×C151C2211yescharacteristic
27#14559005—41no—
28#14559004—21no—
29#14559004—21no—
30#14559004—21no—
31C2×Dic302D411yescharacteristic
32Q8×D151—41no—
33C2×D604D411yescharacteristic
34C2×C22⋊D151—21no—
35C2×C22⋊D151—21no—
36C22×Dic151—21no—
37C2×C4×D151—21no—
38Dic604—41no—
39#14558993—41no—
40#14558993—41no—
41#14558992—41no—
42D1208—41no—
43#14558989—41no—
44#14558988—21no—
45Dic151⋊C4—21no—
46Dic151⋊C4—21no—
47Dic151⋊C4—21no—
48C22⋊Dic151—21no—
49(C2×D151)⋊C4—21no—
50(C2×D151)⋊C4—21no—
51(C2×D151)⋊C4—21no—
52C4×Dic151—21no—
53C4×Dic151D411yescharacteristic
54C4×Dic151D411yescharacteristic
55C2×Q8×C151C2311yescharacteristic
56C2×D4×C151D411yescharacteristic
57M16×C151—21no—
58M16×C151—21no—
59C22⋊C4×C151—21no—
60C22⋊C4×C151—21no—
61C42×C151D411yescharacteristic
62C22×D151—21no—
63Dic302—21no—
64Dic302—21no—
65Dic302—21no—
66Dic302—41no—
67D604—21no—
68D604—21no—
69D604—21no—
70D604—41no—
71C22⋊D151—42no—
72C22⋊D151—41no—
73C22⋊D151—81no—
74C2×Dic151—21no—
75C2×Dic151—21no—
76C2×Dic151—21no—
77C2×Dic151—42no—
78C4×D151—42no—
79C4×D151—41no—
80C4×D151—41no—
81C4×D151—41no—
82C151⋊C8—41no—
83C23×C151—21no—
84Q8×C151—41no—
85D4×C151—41no—
86C2×C4×C151—21no—
87C2×C4×C151C2×D411yescharacteristic
88C2×C4×C151C2×D411yescharacteristic
89C2×C4×C151C2×D411yescharacteristic
90C8×C151—41no—
91C8×C151—41no—
92C22×C151—41no—
93C22×C151—41no—
94C22×C151—41no—
95C22×C151#12011yescharacteristic
96C2×D151—41no—
97C2×D151—41no—
98C2×D151—41no—
99C2×D151—41no—
100C4×C151—21no—
101C4×C151—21no—
102C4×C151—21no—
103C4×C151—41no—
104Dic151—22no—
105Dic151—41no—
106Dic151—41no—
107Dic151—41no—
108C2×C151—21no—
109C2×C151—81no—
110C2×C151B(4,𝔽2)11yescharacteristic
111D151—81no—
112D151—81no—
113C151#220411yescharacteristic, complemented, Sylow
114#2204—1511nomaximal, Sylow
115#555—1511no—
116#456—1511no—
117#454—1511no—
118#454—1511no—
119#356—1511no—
120#355—1511no—
121#355D15111yescharacteristic, complemented
1222−1+4—1511no—
123#137—3021no—
124AGL(1,ℤ/8)—3021no—
125AGL(1,ℤ/8)—3021no—
126C4⋊Q8—1511no—
127#124—3021no—
128#124—1511no—
129#124C2×D15111yescharacteristic
130#121—3021no—
131#121—3021no—
132C4×D4—3021no—
133#117—3021no—
134#117—3021no—
135#104—3021no—
136#104—3021no—
137#104—3021no—
138#101—1511no—
139#101C2×D15111yescharacteristic
140#101C2×D15111yescharacteristic
141#41—3021no—
142#41—3021no—
143#41—3021no—
144#41—6041no—
145C2×Q8—6041no—
146C2×Q8—1511no—
147C2×Q8C22×D15111yescharacteristic
148C2×D4—3021no—
149C2×D4—3021no—
150C2×D4—1511no—
151C2×D4D60411yescharacteristic
152C22×C4—3021no—
153C22×C4—3021no—
154Q16—6041no—
155SD16—6041no—
156SD16—6041no—
157SD16—6041no—
158D8—6041no—
159D8—6041no—
160M16—21no—
161M16—21no—
162M16—3021no—
163C4⋊C4—3021no—
164C4⋊C4—3021no—
165C4⋊C4—3021no—
166C22⋊C4—21no—
167C22⋊C4—21no—
168C22⋊C4—3021no—
169C22⋊C4—3021no—
170C22⋊C4—3021no—
171C22⋊C4—3021no—
172C42—3021no—
173C42—1511no—
174C42—1511no—
175C42D60411yescharacteristic
176C23—21no—
177C23—3021no—
178Q8—41no—
179Q8—3021no—
180Q8—3021no—
181Q8—3021no—
182Q8—6041no—
183D4—41no—
184D4—3021no—
185D4—3021no—
186D4—3021no—
187D4—6041no—
188D4—6042no—
189D4—6041no—
190D4—12081no—
191C2×C4—21no—
192C2×C4—3021no—
193C2×C4—3021no—
194C2×C4—3021no—
195C2×C4—6041no—
196C2×C4—6041no—
197C2×C4—6041no—
198C2×C4—6042no—
199C2×C4—6042no—
200C2×C4D4×D15111yescharacteristic
201C2×C4D4×D15111yescharacteristic
202C2×C4C2×D60411yescharacteristic
203C8—41no—
204C8—41no—
205C8—6041no—
206C22—41no—
207C22—41no—
208C22—41no—
209C22—6041no—
210C22—6041no—
211C22—6041no—
212C22—6041no—
213C22#1801270911yescharacteristic
214C4—21no—
215C4—21no—
216C4—21no—
217C4—41no—
218C4—3022no—
219C4—6041no—
220C4—6041no—
221C4—6041no—
222C2—21no—
223C2—81no—
224C2—12081no—
225C2—12081no—
226C2#2375240011yescharacteristic
subgroupG/H
centerC2#23752400
commutator, cosocleC2×Q8×C151C23
FrattiniC2×Q8C22×D151
Fitting#355×C151C2
socleC2×C151B(4,𝔽2)
hypercenter#355D151
hypocenterC151#2204
LCSG ▷ C2×Q8×C151 ▷ C22×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
1. #23752924C2semidirect
2. #23752397C2semidirect
3. #23752387C2semidirect
4. #23752384C2semidirect
5. #23752010C2semidirect
6. #23752008C2semidirect
7. #355×C151C2semidirect
113. C151#2204semidirect
121. #355D151semidirect

Maximal subgroups

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

subgroupindex
#237529242
#237523972
#237523872
#237523842
#237520102
#237520082
#355×C1512
#2204151