Finite Group Databasebeta

← #21425747

Subgroups — #21425747

Order 7552.

266 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 65 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#16837966C211yesmaximal, characteristic
2#16837376C211yesmaximal, characteristic, complemented
3#16837190C214yesmaximal, complemented
4C59×#413C211yesmaximal, characteristic, complemented
5C22×D236C411yescharacteristic, complemented
6#14273723—21no—
7#14273716—21no—
8#14273701—21no—
9#14273701—21no—
10#14273695C412yescomplemented
11#14273695C2212yes—
12#14273686—21no—
13#14273686C411yescharacteristic, complemented
14#14273642—21no—
15#14273642C2212yes—
16C2×#41×C59C2211yescharacteristic
17C2×M16×C59—21no—
18#101×C59—21no—
19#100×C59C2212yes—
20C23×D59C2×C412yes—
21#41×C59—41no—
22#41×C59—41no—
23C2×Q8×C59D411yescharacteristic
24C2×D4×C59C2×C411yescharacteristic
25C2×D4×C59D411yescharacteristic
26C2×D4×C59C2311yescharacteristic
27C22×C4×C59C2×C411yescharacteristic
28C22×C4×C59D411yescharacteristic
29C22×C4×C59D411yescharacteristic
30C2×C22⋊D59—22no—
31C2×C22⋊D59—22no—
32C2×D236—21no—
33C2×D236—21no—
34C2×D236—41no—
35C2×D236—41no—
36M16×C59—22no—
37M16×C59—41no—
38C2×C8×C59—41no—
39C22⋊Dic59—22no—
40C22⋊Dic59C2×C412yes—
41(C2×D59)⋊C4—22no—
42(C2×D59)⋊C4—22no—
43C4⋊Dic59—21no—
44C4⋊Dic59—41no—
45C4×Dic59—21no—
46C4×Dic59—41no—
47C23×C59C22⋊C411yescharacteristic
48C23×C59C22×C411yescharacteristic
49C23×C59C2×D411yescharacteristic
50C22×D59—22no—
51C22×D59—42no—
52C22×D59—82no—
53Q8×C59—41no—
54D4×C59—41no—
55D4×C59—41no—
56D4×C59—41no—
57C2×C4×C59—21no—
58C2×C4×C59—21no—
59C2×C4×C59—21no—
60C2×C4×C59—21no—
61C2×C4×C59—21no—
62C2×C4×C59—21no—
63C2×C4×C59C22⋊C411yescharacteristic
64C2×C4×C59C22⋊C411yescharacteristic
65C2×C4×C59C22⋊C411yescharacteristic
66C2×C4×C59C2×D411yescharacteristic
67C22⋊D59—82no—
68C22⋊D59—82no—
69C2×Dic59—22no—
70C2×Dic59—42no—
71D236—42no—
72D236—41no—
73D236—41no—
74C8×C59—42no—
75C22×C59—21no—
76C22×C59—21no—
77C22×C59—21no—
78C22×C59—41no—
79C22×C59—41no—
80C22×C59—41no—
81C22×C59C2×C22⋊C411yescharacteristic
82C2×D59—42no—
83C2×D59—42no—
84C2×D59—42no—
85C2×D59—84no—
86C4×C59—21no—
87C4×C59—21no—
88C4×C59—21no—
89C4×C59#9911yescharacteristic
90C4×C59#9911yescharacteristic
91Dic59—42no—
92Dic59—82no—
93#2122—591nomaximal, Sylow
94C2×C59—21no—
95C2×C59—41no—
96C2×C59—41no—
97C2×C59—41no—
98C2×C59C2×#9911yescharacteristic
99D59—82no—
100#535—591no—
101#413D5911yescharacteristic, complemented
102#410—591no—
103AΣL(1,𝔽16)—594no—
104C59#212211yescharacteristic, complemented, Sylow
105C2×#41C2×D5911yescharacteristic
106C22×D4—591no—
107C2×M16—21no—
108#127—1181no—
109#124—1181no—
110#121—1181no—
111#121—1181no—
112#120—592no—
113#120—592no—
114#117—591no—
115#117—1181no—
116#101—21no—
117#100C2×D5912yes—
118#99—592no—
119#99—1181no—
120C24—592no—
121#41—41no—
122#41—41no—
123C2×Q8C22⋊D5911yescharacteristic
124C2×D4—1182no—
125C2×D4—1182no—
126C2×D4—1181no—
127C2×D4—1181no—
128C2×D4—2361no—
129C2×D4—2361no—
130C2×D4C4×D5911yescharacteristic
131C2×D4D23611yescharacteristic
132C2×D4C22×D5911yescharacteristic
133C22×C4C4×D5911yescharacteristic
134C22×C4D23611yescharacteristic
135C22×C4C22⋊D5911yescharacteristic
136M16—22no—
137M16—41no—
138C2×C8—41no—
139C4⋊C4—1181no—
140C4⋊C4—2361no—
141C22⋊C4—592no—
142C22⋊C4—1182no—
143C22⋊C4—1182no—
144C22⋊C4—1182no—
145C42—1181no—
146C42—2361no—
147C23—1182no—
148C23—4722no—
149C23—2362no—
150C23(C2×D59)⋊C411yescharacteristic
151C23C2×C4×D5911yescharacteristic
152C23C2×D23611yescharacteristic
153Q8—41no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—4722no—
158D4—4722no—
159D4—2362no—
160D4—2361no—
161D4—2361no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—1182no—
169C2×C4—2362no—
170C2×C4(C2×D59)⋊C411yescharacteristic
171C2×C4(C2×D59)⋊C411yescharacteristic
172C2×C4(C2×D59)⋊C411yescharacteristic
173C2×C4C2×C22⋊D5911yescharacteristic
174C8—42no—
175C22—21no—
176C22—21no—
177C22—21no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—4724no—
182C22—2362no—
183C22—2362no—
184C22—2362no—
185C22C2×(C2×D59)⋊C411yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—4722no—
190C4—2362no—
191C4#1427364111yescharacteristic
192C4#1427364111yescharacteristic
193C2—21no—
194C2—41no—
195C2—41no—
196C2—41no—
197C2—4722no—
198C2C2×#1427364111yescharacteristic
subgroupG/H
centerC2C2×#14273641
commutatorC23×C59C22×C4
FrattiniC2×D4C22×D59
FittingC59×#413C2
socleC2×C59C2×#99
hypercenter#413D59
hypocenterC59#2122
LCSG ▷ C23×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #16837376C2semidirect
3. #16837190C2semidirect
4. C59×#413C2semidirect
5. C22×D236C4semidirect
10. #14273695C4semidirect
13. #14273686C4semidirect
101. #413D59semidirect
104. C59#2122semidirect