Finite Group Databasebeta

← #21436915

Subgroups — #21436915

Order 7552.

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

normal subgroups only

This group has 350 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#16838138C211yesmaximal, characteristic
2#16838132C211yesmaximal, characteristic, complemented
3#16837760C212yesmaximal, complemented
4#16837694C211yesmaximal, characteristic, complemented
5#16837680C212yesmaximal, complemented
6#16837623C212yesmaximal, complemented
7#16837599C211yesmaximal, characteristic
8#16837532C211yesmaximal, characteristic, complemented
9#16837499C212yesmaximal, complemented
10C4×Dic236C211yesmaximal, characteristic, complemented
11C59×#486C211yesmaximal, characteristic
12C2×Dic236C2211yescharacteristic
13C2×#11745670C2212yes—
14#14273726—21no—
15#14273726C2212yes—
16#14273725—22no—
17#14273714—21no—
18#14273714C2212yes—
19#14273708—22no—
20C4×Dic118C2211yescharacteristic
21C4×Dic118C2211yescharacteristic
22C4×Dic118C2211yescharacteristic
23#14273692—21no—
24#14273692C2212yes—
25D4×Dic59—21no—
26D4×Dic59C2212yes—
27#14273661C2211yescharacteristic
28#14273660C2212yes—
29C4⋊(C59⋊C8)C2211yescharacteristic
30Dic59⋊C8C2212yes—
31#14273652C2211yescharacteristic
32#14273652C2211yescharacteristic
33#14273650C2212yes—
34#14273648C2212yes—
35#14273637C2212yes—
36C4⋊Q8×C59C2211yescharacteristic
37#127×C59C2211yescharacteristic
38#102×C59C2212yes—
39#102×C59C2212yes—
40C4×C8×C59C2211yescharacteristic
41C2×Q8×C59—21no—
42C2×D4×C59—21no—
43C2×D4×C59—21no—
44C2×D4×C59C2312yes—
45C22×Dic59—22no—
46C2×Dic118—22no—
47C2×Dic118D411yescharacteristic
48C2×Dic118C2311yescharacteristic
49C2×Dic118C2311yescharacteristic
50C2×C8×C59C2311yescharacteristic
51C2×C8×C59C2311yescharacteristic
52C4⋊C4×C59—21no—
53C4⋊C4×C59C2312yes—
54C42×C59C2311yescharacteristic
55C22⋊Dic59—22no—
56C22⋊Dic59—22no—
57C22⋊Dic59—22no—
58#11745670—24no—
59C4⋊Dic59D411yescharacteristic
60C4⋊Dic59C2311yescharacteristic
61C4⋊Dic59C2311yescharacteristic
62Dic59⋊C4—21no—
63Dic59⋊C4—21no—
64Dic59⋊C4—22no—
65Dic59⋊C4—22no—
66Dic59⋊C4D412yes—
67C4×Dic59—21no—
68C4×Dic59—21no—
69C4×Dic59—22no—
70C4×Dic59C2312yes—
71C2×C59⋊C8C2312yes—
72Dic236—22no—
73C23×C59—22no—
74Q8×C59—81no—
75D4×C59—22no—
76D4×C59—22no—
77D4×C59—42no—
78D4×C59—81no—
79C2×C4×C59—22no—
80C2×C4×C59C2×D411yescharacteristic
81C2×C4×C59C2×D411yescharacteristic
82C2×C4×C59C2411yescharacteristic
83C2×Dic59—21no—
84C2×Dic59—21no—
85C2×Dic59—21no—
86C2×Dic59—21no—
87C2×Dic59—82no—
88C2×Dic59C2×D412yes—
89C2×Dic59C2×D412yes—
90Dic118—22no—
91Dic118—21no—
92Dic118—21no—
93Dic118—21no—
94Dic118—82no—
95Dic118#4112yes—
96C8×C59—21no—
97C8×C59—21no—
98C59⋊C8—22no—
99C22×C59—42no—
100C22×C59—42no—
101C22×C59—42no—
102C22×C59C22×D411yescharacteristic
103C4×C59—21no—
104C4×C59—42no—
105C4×C59#13712yes—
106C4×C59C2×#4111yescharacteristic
107C4×C592−1+411yescharacteristic
108Dic59—22no—
109Dic59—22no—
110Dic59—22no—
111Dic59—41no—
112Dic59—41no—
113Dic59—41no—
114#3375—591nomaximal, Sylow
115C2×C59—82no—
116C2×C59#54811yescharacteristic
117C2×C59C2×#13711yescharacteristic
118C2×C59#57611yescharacteristic
119#559—591no—
120Q82—591no—
121#489—592no—
122#486D5911yescharacteristic
123#477—591no—
124#474—592no—
125#464—592no—
126#460—591no—
127#446—591no—
128#440—592no—
129C4×Q16—591no—
130C59#337511yescharacteristic, complemented, Sylow
131C2×Q16—591no—
132C2×SD16—592no—
133C4⋊Q8—592no—
134C4⋊Q8—1181no—
135C4⋊Q8—1182no—
136C4⋊Q8C2×D5911yescharacteristic
137#127C2×D5911yescharacteristic
138#124—592no—
139#124—1181no—
140#123—1182no—
141C4×Q8—591no—
142C4×Q8—592no—
143C4×Q8—591no—
144C4×Q8—591no—
145C4×Q8—1181no—
146C4×D4—592no—
147C4×D4—1181no—
148#107—591no—
149#107—592no—
150C4⋊C8—592no—
151C4⋊C8—591no—
152#103—591no—
153#103—591no—
154#103—592no—
155#102—592no—
156#102C2×D5912yes—
157#102C2×D5912yes—
158#97—592no—
159C4×C8C2×D5911yescharacteristic
160C2×Q8—21no—
161C2×Q8—591no—
162C2×Q8—591no—
163C2×Q8—591no—
164C2×Q8—1182no—
165C2×D4—21no—
166C2×D4—21no—
167C2×D4C22×D5912yes—
168C22×C4—1182no—
169Q16—1182no—
170SD16—1184no—
171C2×C8—592no—
172C2×C8C22×D5911yescharacteristic
173C2×C8C22×D5911yescharacteristic
174C4⋊C4—21no—
175C4⋊C4—591no—
176C4⋊C4—592no—
177C4⋊C4—591no—
178C4⋊C4—591no—
179C4⋊C4—1182no—
180C4⋊C4—1182no—
181C4⋊C4—1181no—
182C4⋊C4—1181no—
183C4⋊C4C22×D5912yes—
184C22⋊C4—1182no—
185C22⋊C4—1182no—
186C22⋊C4—1182no—
187C42—592no—
188C42—1182no—
189C42—1181no—
190C42—1181no—
191C42C22×D5911yescharacteristic
192C23—22no—
193Q8—81no—
194Q8—592no—
195Q8—1182no—
196Q8—1181no—
197Q8—1181no—
198Q8—1181no—
199Q8—4722no—
200D4—22no—
201D4—22no—
202D4—42no—
203D4—81no—
204C2×C4—22no—
205C2×C4—592no—
206C2×C4—592no—
207C2×C4—1181no—
208C2×C4—1181no—
209C2×C4—1181no—
210C2×C4—1181no—
211C2×C4—4722no—
212C2×C4D4×D5911yescharacteristic
213C2×C4D4×D5911yescharacteristic
214C2×C4C23×D5911yescharacteristic
215C8—21no—
216C8—21no—
217C8—1182no—
218C22—42no—
219C22—42no—
220C22—42no—
221C22C2×D4×D5911yescharacteristic
222C4—21no—
223C4—42no—
224C4—1182no—
225C4—1182no—
226C4—1182no—
227C4—2361no—
228C4—2361no—
229C4—2361no—
230C4#1427375612yes—
231C4#41×D5911yescharacteristic
232C4#1427377411yescharacteristic
233C2—82no—
234C2#1683806011yescharacteristic
235C2C2×#1427375611yescharacteristic
236C2#1683820311yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#486C2
socleC22×C59C22×D4
hypercenter#486D59
hypocenterC59#3375
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
2. #16838132C2semidirect
3. #16837760C2semidirect
4. #16837694C2semidirect
5. #16837680C2semidirect
6. #16837623C2semidirect
8. #16837532C2semidirect
9. #16837499C2semidirect
10. C4×Dic236C2semidirect
130. C59#3375semidirect