Finite Group Databasebeta

← #21436463

Subgroups — #21436463

Order 7552.

342 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 115 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#16838090C212yesmaximal
2#16837746C212yesmaximal, complemented
3#16837734C212yesmaximal, complemented
4#16837706C212yesmaximal, complemented
5#16837644C211yesmaximal, characteristic, complemented
6#16837644C211yesmaximal, characteristic, complemented
7C4×Dic236C211yesmaximal, characteristic, complemented
8C8×D236C211yesmaximal, characteristic
9#16837439C211yesmaximal, characteristic, complemented
10#107×D59C211yesmaximal, characteristic, complemented
11C59×#499C211yesmaximal, characteristic, complemented
12C2×Dic236C2211yescharacteristic
13C2×C8×D59C2211yescharacteristic
14C2×C8×D59C2211yescharacteristic
15#14273722—22no—
16#14273718—22no—
17#14273712—22no—
18#14273707C2212yes—
19#14273707C2212yes—
20C4×Dic118C2212yes—
21C4×D236C2211yescharacteristic
22#14273685—22no—
23#14273685C2212yes—
24C4⋊C4×D59C2212yes—
25#14273661C2211yescharacteristic
26#14273660C2212yes—
27#14273658C2212yes—
28C4⋊(C59⋊C8)C2211yescharacteristic
29#14273652C2212yes—
30#14273650C2212yes—
31#14273650C2212yes—
32(C2×D59)⋊C8C2211yescharacteristic
33(C2×D59)⋊C8C2211yescharacteristic
34#125×C59C2212yes—
35#107×C59C2211yescharacteristic
36#107×C59C2211yescharacteristic
37#106×C59C2212yes—
38C4×C8×C59C2211yescharacteristic
39C2×D236D411yescharacteristic
40C2×C4×D59—22no—
41C2×C4×D59C2311yescharacteristic
42C2×C4×D59C2311yescharacteristic
43C2×Dic118C2312yes—
44C2×C8×C59C2311yescharacteristic
45C2×C8×C59C2311yescharacteristic
46C4⋊C4×C59—22no—
47C4⋊C4×C59—22no—
48C4⋊C4×C59C2312yes—
49C4⋊C4×C59C2312yes—
50C42×C59C2311yescharacteristic
51(C2×D59)⋊C4—22no—
52(C2×D59)⋊C4—22no—
53(C2×D59)⋊C4—22no—
54(C2×D59)⋊C4D411yescharacteristic
55(C2×D59)⋊C4D411yescharacteristic
56C4⋊Dic59—22no—
57C4⋊Dic59—22no—
58C4⋊Dic59D411yescharacteristic
59C4⋊Dic59C2312yes—
60Dic59⋊C4—22no—
61Dic59⋊C4—22no—
62C4×Dic59—22no—
63C4×Dic59—22no—
64C2×C59⋊C8C2311yescharacteristic
65C2×C59⋊C8C2311yescharacteristic
66Dic236—22no—
67C8×D59—22no—
68C8×D59—22no—
69C22×D59C2×D411yescharacteristic
70C22×D59C2×D411yescharacteristic
71C2×C4×C59—22no—
72C2×C4×C59—22no—
73C2×C4×C59C2×D411yescharacteristic
74C2×C4×C59C2×D411yescharacteristic
75C2×C4×C59C2411yescharacteristic
76C2×Dic59—22no—
77C2×Dic59—22no—
78C2×Dic59C2×D411yescharacteristic
79C2×Dic59C2×D411yescharacteristic
80D236—22no—
81C4×D59—21no—
82C4×D59—21no—
83C4×D59—21no—
84C4×D59—21no—
85C4×D59—44no—
86Dic118—22no—
87Dic118—22no—
88C8×C59—21no—
89C8×C59#4112yes—
90C59⋊C8—21no—
91C59⋊C8—21no—
92C22×C59C22×D411yescharacteristic
93C2×D59—21no—
94C2×D59—21no—
95C2×D59—21no—
96C2×D59—21no—
97C2×D59—21no—
98C2×D59#13512yes—
99C4×C59—21no—
100C4×C59—21no—
101C4×C59—42no—
102C4×C59—42no—
103C4×C59C2×#4111yescharacteristic
104C4×C592−1+411yescharacteristic
105Dic59—21no—
106Dic59—21no—
107Dic59—42no—
108Dic59—42no—
109#3336—591nomaximal, Sylow
110C2×C59#54711yescharacteristic
111C2×C59C2×#13511yescharacteristic
112C2×C59#57811yescharacteristic
113D59—22no—
114D59—41no—
115#552—592no—
116#499D5911yescharacteristic, complemented
117#485—592no—
118#483—592no—
119#479—592no—
120#467—591no—
121#467—591no—
122C4×Q16—591no—
123C8×D4—591no—
124#427—591no—
125C2×#107—591no—
126C59#333611yescharacteristic, complemented, Sylow
127C2×Q16—591no—
128C22×C8—591no—
129C22×C8—591no—
130#126—1182no—
131#125—1182no—
132#125C2×D5912yes—
133#123—1182no—
134C22⋊Q8—592no—
135C22⋊Q8—592no—
136C4×Q8—592no—
137C4×D4—591no—
138#117—592no—
139#117—1182no—
140C2×C4⋊C4—592no—
141#107—591no—
142#107—592no—
143#107C2×D5911yescharacteristic
144#107C2×D5911yescharacteristic
145#106—592no—
146#106C2×D5912yes—
147C4⋊C8—591no—
148#103—592no—
149#103—592no—
150#103—592no—
151C22⋊C8—591no—
152C22⋊C8—591no—
153C4×C8C2×D5911yescharacteristic
154C2×Q8—592no—
155C2×D4—591no—
156C22×C4—591no—
157C22×C4—591no—
158C22×C4—1182no—
159Q16—1182no—
160C2×C8—591no—
161C2×C8—591no—
162C2×C8—1182no—
163C2×C8—1182no—
164C2×C8C22×D5911yescharacteristic
165C2×C8C22×D5911yescharacteristic
166C4⋊C4—22no—
167C4⋊C4—22no—
168C4⋊C4—591no—
169C4⋊C4—592no—
170C4⋊C4—1182no—
171C4⋊C4—1182no—
172C4⋊C4—1182no—
173C4⋊C4—1182no—
174C4⋊C4C22×D5912yes—
175C4⋊C4C22×D5912yes—
176C22⋊C4—591no—
177C22⋊C4—591no—
178C22⋊C4—1182no—
179C22⋊C4—1182no—
180C22⋊C4—1182no—
181C42—1182no—
182C42—1182no—
183C42C22×D5911yescharacteristic
184C23—591no—
185C23—591no—
186Q8—1182no—
187Q8—1182no—
188D4—1182no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—591no—
192C2×C4—591no—
193C2×C4—1181no—
194C2×C4—1181no—
195C2×C4—1181no—
196C2×C4—1181no—
197C2×C4—1182no—
198C2×C4—1182no—
199C2×C4—2364no—
200C2×C4D4×D5911yescharacteristic
201C2×C4D4×D5911yescharacteristic
202C2×C4C23×D5911yescharacteristic
203C8—21no—
204C8—1181no—
205C8—1181no—
206C8#1174568912yes—
207C22—592no—
208C22—1181no—
209C22—1181no—
210C22—1181no—
211C22—1181no—
212C22—1181no—
213C22C2×D4×D5911yescharacteristic
214C4—21no—
215C4—21no—
216C4—42no—
217C4—42no—
218C4—1181no—
219C4—1181no—
220C4—2362no—
221C4—2362no—
222C4C2×#1174568911yescharacteristic
223C4#1427377511yescharacteristic
224C2—1182no—
225C2—2361no—
226C2#1683805511yescharacteristic
227C2#135×D5911yescharacteristic
228C2#1683821611yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#499C2
socleC22×C59C22×D4
hypercenter#499D59
hypocenterC59#3336
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #499

Complements

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

NH ≅ G/Ntype
2. #16837746C2semidirect
3. #16837734C2semidirect
4. #16837706C2semidirect
5. #16837644C2semidirect
6. #16837644C2semidirect
7. C4×Dic236C2semidirect
9. #16837439C2semidirect
10. #107×D59C2semidirect
11. C59×#499C2semidirect
116. #499D59semidirect
126. C59#3336semidirect