Finite Group Databasebeta

← #21425381

Subgroups — #21425381

Order 7552.

266 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 63 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#16838200C211yesmaximal, characteristic
2#16837425C211yesmaximal, characteristic, complemented
3C2×#14273654C211yesmaximal, characteristic, complemented
4C2×#14273653C211yesmaximal, characteristic, complemented
5#16837384C211yesmaximal, characteristic, complemented
6C59⋊#338C211yesmaximal, characteristic, complemented
7C59×#413C211yesmaximal, characteristic, complemented
8C2×#11745685C2211yescharacteristic
9#14273758—21no—
10#14273757—21no—
11#14273753—21no—
12#14273752—21no—
13#14273747—22no—
14C2×#11745664C2211yescharacteristic
15C2×#11745664C2211yescharacteristic
16C2×C4×Dic59C2211yescharacteristic
17Dic59⋊C8—22no—
18#14273654—21no—
19#14273654—21no—
20#14273653—21no—
21#14273653—21no—
22#14273645—21no—
23#14273643—21no—
24C2×#41×C59C2211yescharacteristic
25C2×M16×C59C2211yescharacteristic
26C2×M16×C59C2211yescharacteristic
27#101×C59—21no—
28#100×C59—21no—
29#41×C59—21no—
30#41×C59—21no—
31#41×C59—21no—
32#41×C59—21no—
33C2×Q8×C59D411yescharacteristic
34C2×D4×C59—21no—
35C2×D4×C59D411yescharacteristic
36C22×C4×C59—21no—
37C22×C4×C59C2311yescharacteristic
38C2×C22⋊D59—21no—
39C22×Dic59—21no—
40#11745685—21no—
41#11745685—21no—
42#11745685—21no—
43#11745685—21no—
44C2×D236D411yescharacteristic
45C2×C4×D59—21no—
46C2×Dic118D411yescharacteristic
47M16×C59—21no—
48M16×C59—21no—
49M16×C59—21no—
50M16×C59—21no—
51C2×C8×C59—21no—
52C2×C8×C59—21no—
53#11745672—22no—
54#11745671—22no—
55#11745670—22no—
56#11745669—22no—
57C4×Dic59—21no—
58C4×Dic59D411yescharacteristic
59C4×Dic59D411yescharacteristic
60#11745664—21no—
61#11745664—21no—
62#11745664—21no—
63#11745664—21no—
64C2×C59⋊C8—21no—
65C2×C59⋊C8D412yes—
66C23×C59—21no—
67C23×C59#4111yescharacteristic
68C22×D59—21no—
69Q8×C59—21no—
70Q8×C59—21no—
71D4×C59—21no—
72D4×C59—21no—
73D4×C59—41no—
74D4×C59—41no—
75C2×C4×C59—21no—
76C2×C4×C59—41no—
77C2×C4×C59—41no—
78C2×C4×C59C2×D411yescharacteristic
79C2×C4×C59C2×D411yescharacteristic
80C2×C4×C59C2×D411yescharacteristic
81C2×C4×C59C2×D411yescharacteristic
82C2×C4×C59#4111yescharacteristic
83C2×C4×C59#4111yescharacteristic
84C22⋊D59—41no—
85C22⋊D59—41no—
86C2×Dic59—21no—
87C2×Dic59—21no—
88C2×Dic59—21no—
89C2×Dic59—42no—
90D236—21no—
91D236—21no—
92C4×D59—41no—
93C4×D59—41no—
94Dic118—21no—
95Dic118—21no—
96C8×C59—41no—
97C8×C59—41no—
98C59⋊C8—22no—
99C59⋊C8—41no—
100C22×C59—41no—
101C22×C59—41no—
102C22×C59—81no—
103C22×C59#12111yescharacteristic
104C22×C59#12311yescharacteristic
105C22×C59#12311yescharacteristic
106C2×D59—41no—
107C2×D59—81no—
108C4×C59—41no—
109C4×C59#12011yescharacteristic
110C4×C59#12111yescharacteristic
111C4×C59#12111yescharacteristic
112C4×C59#12411yescharacteristic
113Dic59—22no—
114Dic59—41no—
115Dic59—41no—
116#2050—591nomaximal, Sylow
117C2×C59—21no—
118C2×C59—21no—
119C2×C59—21no—
120C2×C59—81no—
121C2×C59#39411yescharacteristic
122D59—81no—
123#575—591no—
124#423—591no—
125C2×#104—591no—
126C2×#104—591no—
127#413—591no—
128#413D5911yescharacteristic, complemented
129#338—591no—
130C59#205011yescharacteristic, complemented, Sylow
131C2×#41—591no—
132C2×#41C2×D5911yescharacteristic
133#137—1181no—
134#137—1181no—
135AGL(1,ℤ/8)—1181no—
136AGL(1,ℤ/8)—1181no—
137#135—1182no—
138C2×M16—591no—
139C2×M16—591no—
140C2×M16C2×D5911yescharacteristic
141C2×M16C2×D5911yescharacteristic
142C2×C42—591no—
143C4⋊C8—1182no—
144#104—1181no—
145#104—1181no—
146#104—1181no—
147#104—1181no—
148#101—21no—
149#101—1181no—
150#100—21no—
151#100—1181no—
152#41—21no—
153#41—21no—
154#41—21no—
155#41—21no—
156#41—1181no—
157#41—1181no—
158#41—1181no—
159#41—1181no—
160C2×Q8—591no—
161C2×Q8C22⋊D5911yescharacteristic
162C2×D4—21no—
163C2×D4—591no—
164C2×D4—1181no—
165C2×D4C22⋊D5911yescharacteristic
166C22×C4—21no—
167C22×C4—1181no—
168C22×C4—1181no—
169C22×C4C22×D5911yescharacteristic
170Q16—1182no—
171SD16—1182no—
172SD16—1182no—
173D8—1182no—
174M16—21no—
175M16—21no—
176M16—21no—
177M16—21no—
178M16—1181no—
179M16—1181no—
180M16—1181no—
181M16—1181no—
182C2×C8—21no—
183C2×C8—21no—
184C2×C8—592no—
185C2×C8—1181no—
186C42—591no—
187C42—591no—
188C42—1181no—
189C23—21no—
190C23—1181no—
191C23#1174568511yescharacteristic
192Q8—21no—
193Q8—21no—
194Q8—1181no—
195Q8—1181no—
196D4—21no—
197D4—21no—
198D4—41no—
199D4—41no—
200D4—1181no—
201D4—1181no—
202D4—2361no—
203D4—2361no—
204C2×C4—21no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—1181no—
208C2×C4—1181no—
209C2×C4—1181no—
210C2×C4—2362no—
211C2×C4—2361no—
212C2×C4—2361no—
213C2×C4#1174568511yescharacteristic
214C2×C4D4×D5911yescharacteristic
215C2×C4D4×D5911yescharacteristic
216C2×C4D4×D5911yescharacteristic
217C2×C4#1174568711yescharacteristic
218C2×C4C2×C22⋊D5911yescharacteristic
219C8—41no—
220C8—41no—
221C8—1182no—
222C8—2361no—
223C22—41no—
224C22—41no—
225C22—81no—
226C22—4721no—
227C22—2361no—
228C22#1427370011yescharacteristic
229C22#1427370911yescharacteristic
230C22#1427371011yescharacteristic
231C4—41no—
232C4—1182no—
233C4—2361no—
234C4—2361no—
235C4#1427369511yescharacteristic
236C4#1427369911yescharacteristic
237C4#1427370011yescharacteristic
238C4#1427371311yescharacteristic
239C2—21no—
240C2—21no—
241C2—21no—
242C2—81no—
243C2—4721no—
244C2#1683731711yescharacteristic
subgroupG/H
centerC4#14273713
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC59×#413C2
socleC2×C59#394
hypercenter#413D59
hypocenterC59#2050
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C4 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #16837425C2semidirect
3. C2×#14273654C2semidirect
4. C2×#14273653C2semidirect
5. #16837384C2semidirect
6. C59⋊#338C2semidirect
7. C59×#413C2semidirect
128. #413D59semidirect
130. C59#2050semidirect