Finite Group Databasebeta

← #34080911

Subgroups — #34080911

Order 19328.

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

normal subgroups only

This group has 444 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#23753028C212yesmaximal, complemented
2#23753027C212yesmaximal, complemented
3#23752591C211yesmaximal, characteristic, complemented
4#23752486C212yesmaximal, complemented
5#23752485C212yesmaximal, complemented
6#23752396C212yesmaximal, complemented
7#23752394C211yesmaximal, characteristic, complemented
8#23752326C212yesmaximal, complemented
9#456×C151C211yesmaximal, characteristic, complemented
10#18012787C2211yescharacteristic
11#18012786C2212yes—
12#18012772C2212yes—
13#18012771—22no—
14#18012770—22no—
15#18012770C2212yes—
16#18012769—22no—
17#18012769C2212yes—
18#18012768—22no—
19#18012760—22no—
20#18012759—22no—
21#18012759C2212yes—
22C2×#14558994—22no—
23C2×#14558994C2212yes—
24C2×#14558994C2212yes—
25Q16×D151—22no—
26#18012747C2212yes—
27#18012746C2212yes—
28#18012739C2211yescharacteristic
29#18012674C2212yes—
30#18012667C2212yes—
31#18012658C2211yescharacteristic
32#18012657C2212yes—
33C4×C151⋊C8C2211yescharacteristic
342−1+4×C151C2211yescharacteristic
35#137×C151C2212yes—
36C4⋊Q8×C151C2211yescharacteristic
37#104×C151C2212yes—
38#101×C151C2211yescharacteristic
39#14559005—22no—
40#14559004—22no—
41#14559004—41no—
42#14559004C2312yes—
43#14559003—22no—
44#14559003—42no—
45C2×Dic302—22no—
46C2×Dic302C2312yes—
47Q8×D151—22no—
48Q8×D151—22no—
49Dic604—22no—
50#14558994—22no—
51#14558994—22no—
52#14558994—22no—
53#14558994—22no—
54#14558994—22no—
55#14558994—22no—
56#14558994D412yes—
57#14558993—22no—
58#14558992—22no—
59#14558992D412yes—
60#14558991—22no—
61#14558991D412yes—
62#14558989D412yes—
63#14558988—22no—
64#14558988C2312yes—
65#14558987—22no—
66C2×C151⋊C8—22no—
67C2×C151⋊C8C2312yes—
68C8×D151—22no—
69C4⋊Dic151—41no—
70#41×C151—22no—
71#41×C151—41no—
72#41×C151C2312yes—
73C2×Q8×C151—22no—
74C2×Q8×C151C2311yescharacteristic
75C2×Q8×C151C2311yescharacteristic
76Q16×C151—22no—
77SD16×C151—22no—
78M16×C151C2312yes—
79C4⋊C4×C151—41no—
80C42×C151C2311yescharacteristic
81Dic302—22no—
82Dic302—22no—
83Dic302—41no—
84Dic302—42no—
85Dic302C2×D412yes—
86D604—41no—
87D604C2×D412yes—
88C22⋊D151—22no—
89C22⋊D151—42no—
90C2×Dic151—22no—
91C2×Dic151—42no—
92C4×D151—22no—
93C4×D151—42no—
94C4×D151—42no—
95C151⋊C8—22no—
96C151⋊C8C2×D412yes—
97C151⋊C8C2×D412yes—
98Q8×C151—22no—
99Q8×C151—22no—
100Q8×C151—41no—
101Q8×C151C2×D412yes—
102D4×C151—22no—
103D4×C151—41no—
104D4×C151C2×D412yes—
105C2×C4×C151—21no—
106C2×C4×C151—22no—
107C2×C4×C151—21no—
108C2×C4×C151—21no—
109C2×C4×C151—42no—
110C2×C4×C151C2411yescharacteristic
111C8×C151—22no—
112C22×C151—22no—
113C22×C151H(5,𝔽2)11yescharacteristic
114C2×D151—22no—
115C4×C151—22no—
116C4×C151—22no—
117C4×C151—41no—
118C4×C151—41no—
119C4×C151C22×D412yes—
120Dic151—22no—
121Dic151—42no—
122C2×C151—21no—
123C2×C151—42no—
124C2×C151D4211yescharacteristic
125D151—42no—
126C151#329311yescharacteristic, complemented, Sylow
127#3293—1511nomaximal, Sylow
128#578—1512no—
129#578—1512no—
130#494—1511no—
131#473—1512no—
132#473—1512no—
133#456—1511no—
134#456—1512no—
135#456D15111yescharacteristic, complemented
136#443—1512no—
1372−1+4—1512no—
1382−1+4—1511no—
1392−1+4C2×D15111yescharacteristic
140#137—3022no—
141#137—3022no—
142#137—3022no—
143#137—3022no—
144#137—1512no—
145#137—1512no—
146#137—1512no—
147#137C2×D15112yes—
148#135—3022no—
149#135—3022no—
150#135—1512no—
151C2×Q16—3022no—
152C2×Q16—3022no—
153C2×Q16—1512no—
154C2×Q16—1512no—
155#131—1512no—
156#131—1512no—
157C4⋊Q8—1511no—
158C4⋊Q8C2×D15111yescharacteristic
159#108—1512no—
160#104—1512no—
161#104C2×D15112yes—
162#101—1511no—
163#101—1512no—
164#101C2×D15111yescharacteristic
165C4×C8—1511no—
166#41—22no—
167#41—41no—
168#41—3022no—
169#41—3022no—
170#41—3022no—
171#41—6041no—
172#41—6042no—
173#41—1512no—
174#41C22×D15112yes—
175C2×Q8—22no—
176C2×Q8—3022no—
177C2×Q8—3022no—
178C2×Q8—3022no—
179C2×Q8—1512no—
180C2×Q8C22×D15111yescharacteristic
181C2×Q8C22×D15111yescharacteristic
182Q16—22no—
183Q16—3022no—
184Q16—3022no—
185Q16—3022no—
186Q16—3022no—
187Q16—3022no—
188Q16—3022no—
189Q16—3022no—
190Q16—1512no—
191SD16—22no—
192SD16—3022no—
193SD16—3022no—
194SD16—3022no—
195SD16—1512no—
196SD16—1512no—
197D8—1512no—
198M16—3022no—
199M16—3022no—
200M16—1512no—
201M16C22×D15112yes—
202C2×C8—3022no—
203C2×C8—3022no—
204C2×C8—1512no—
205C4⋊C4—41no—
206C4⋊C4—6041no—
207C42C22×D15111yescharacteristic
208Q8—22no—
209Q8—22no—
210Q8—41no—
211Q8—3022no—
212Q8—3022no—
213Q8—6042no—
214Q8—6041no—
215Q8—1512no—
216Q8D4×D15112yes—
217D4—22no—
218D4—41no—
219D4—3022no—
220D4—6041no—
221D4—6042no—
222D4—1512no—
223D4D4×D15112yes—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—42no—
229C2×C4—3022no—
230C2×C4—3022no—
231C2×C4—6042no—
232C2×C4—6042no—
233C2×C4—6042no—
234C2×C4C23×D15111yescharacteristic
235C8—22no—
236C8—3022no—
237C8—1512no—
238C8—1512no—
239C22—22no—
240C22—3022no—
241C22#1801278411yescharacteristic
242C4—22no—
243C4—22no—
244C4—41no—
245C4—41no—
246C4—3022no—
247C4—6042no—
248C4C2×D4×D15112yes—
249C2—21no—
250C2—42no—
251C2—6042no—
252C2#2375284411yescharacteristic
subgroupG/H
centerC2#23752844
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#456×C151C2
socleC2×C151D42
hypercenter#456D151
hypocenterC151#3293
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ #456

Complements

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

NH ≅ G/Ntype
1. #23753028C2semidirect
2. #23753027C2semidirect
3. #23752591C2semidirect
4. #23752486C2semidirect
5. #23752485C2semidirect
6. #23752396C2semidirect
7. #23752394C2semidirect
8. #23752326C2semidirect
9. #456×C151C2semidirect
126. C151#3293semidirect
135. #456D151semidirect

Maximal subgroups

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

subgroupindex
#237530282
#237530272
#237525912
#237524862
#237524852
#237523962
#237523942
#237523262
#456×C1512
#3293151