Finite Group Databasebeta

← #21425374

Subgroups — #21425374

Order 7552.

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

normal subgroups only

This group has 254 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
1C2×#14273758C211yesmaximal, characteristic
2#16837450C211yesmaximal, characteristic, complemented
3#16837420C211yesmaximal, characteristic
4#16837384C211yesmaximal, characteristic
5C2×#14273646C211yesmaximal, characteristic, complemented
6#16837172C211yesmaximal, characteristic, complemented
7C59×#419C211yesmaximal, characteristic, complemented
8C2×#11745685C2211yescharacteristic
9#14273758—22no—
10#14273758—22no—
11C2×#11745672—21no—
12C2×#11745671—21no—
13C2×#11745664C2211yescharacteristic
14C2×#11745664C2211yescharacteristic
15C2×#11745664C2211yescharacteristic
16#14273662—22no—
17#14273655—22no—
18#14273646—22no—
19#14273645—21no—
20#14273643—21no—
21C22×Q8×C59C2211yescharacteristic
22C2×M16×C59C2211yescharacteristic
23#117×C59C2211yescharacteristic
24#103×C59—22no—
25C2×Q8×C59—21no—
26C2×Q8×C59—21no—
27C2×Q8×C59—21no—
28C2×Q8×C59—21no—
29C2×Q8×C59—21no—
30C2×Q8×C59D412yes—
31C22×C4×C59—21no—
32C22×C4×C59C2311yescharacteristic
33C2×C22⋊D59—21no—
34#11745685—21no—
35#11745685—21no—
36#11745685—21no—
37#11745685—21no—
38C2×D236D411yescharacteristic
39C2×C4×D59—21no—
40C2×Dic118D411yescharacteristic
41M16×C59—21no—
42M16×C59—21no—
43C2×C8×C59—21no—
44C4⋊C4×C59—21no—
45C22⋊C4×C59—21no—
46C42×C59—21no—
47#11745672—24no—
48#11745671—24no—
49#11745664—21no—
50#11745664—21no—
51#11745664—21no—
52#11745664—21no—
53#11745664D412yes—
54#11745664D412yes—
55C2×C59⋊C8—21no—
56C2×C59⋊C8—21no—
57C2×C59⋊C8—21no—
58C23×C59#4111yescharacteristic
59C22×D59—21no—
60Q8×C59—22no—
61Q8×C59—22no—
62Q8×C59—41no—
63Q8×C59—41no—
64C2×C4×C59—22no—
65C2×C4×C59—41no—
66C2×C4×C59—41no—
67C2×C4×C59—41no—
68C2×C4×C59C2×D411yescharacteristic
69C2×C4×C59C2×D411yescharacteristic
70C2×C4×C59C2×D411yescharacteristic
71C2×C4×C59C2×D411yescharacteristic
72C2×C4×C59#4111yescharacteristic
73C2×C4×C59#4111yescharacteristic
74C22⋊D59—41no—
75C22⋊D59—41no—
76C2×Dic59—21no—
77D236—21no—
78D236—21no—
79C4×D59—41no—
80C4×D59—41no—
81Dic118—21no—
82Dic118—21no—
83C8×C59—41no—
84C59⋊C8—22no—
85C59⋊C8—22no—
86C59⋊C8—41no—
87C22×C59—41no—
88C22×C59#12111yescharacteristic
89C22×C59#12311yescharacteristic
90C22×C59#12411yescharacteristic
91C2×D59—41no—
92C2×D59—81no—
93C4×C59—42no—
94C4×C59—81no—
95C4×C59#12011yescharacteristic
96C4×C59#12111yescharacteristic
97C4×C59#12111yescharacteristic
98C4×C59#12311yescharacteristic
99Dic59—41no—
100#2049—591nomaximal, Sylow
101C2×C59—21no—
102C2×C59—21no—
103C2×C59—21no—
104C2×C59#39411yescharacteristic
105D59—81no—
106C2×#137—591no—
107#430—591no—
108#421—591no—
109#419D5911yescharacteristic, complemented
110#413—591no—
111C2×#101—591no—
112#344—591no—
113C59#204911yescharacteristic, complemented, Sylow
114C2×#41—591no—
115C22×Q8C2×D5911yescharacteristic
116#137—1182no—
117#137—1182no—
118C2×Q16—1181no—
119C2×SD16—1181no—
120C2×M16—591no—
121C2×M16—591no—
122C2×M16—591no—
123C2×M16C2×D5911yescharacteristic
124#117C2×D5911yescharacteristic
125#108—1182no—
126#104—1182no—
127#103—22no—
128#101—1181no—
129#101—1182no—
130#100—1181no—
131#41—1181no—
132#41—1181no—
133#41—1181no—
134#41—1181no—
135C2×Q8—21no—
136C2×Q8—21no—
137C2×Q8—21no—
138C2×Q8—21no—
139C2×Q8—21no—
140C2×Q8—591no—
141C2×Q8C22⋊D5912yes—
142C2×D4—591no—
143C2×D4—1181no—
144C22×C4—21no—
145C22×C4—1181no—
146C22×C4C22×D5911yescharacteristic
147Q16—1184no—
148SD16—1184no—
149M16—21no—
150M16—21no—
151M16—592no—
152M16—592no—
153M16—1181no—
154M16—1181no—
155M16—1181no—
156M16—1181no—
157C2×C8—21no—
158C2×C8—1181no—
159C2×C8—1181no—
160C2×C8—1181no—
161C4⋊C4—21no—
162C22⋊C4—21no—
163C42—21no—
164C23—1181no—
165C23#1174568711yescharacteristic
166Q8—22no—
167Q8—22no—
168Q8—41no—
169Q8—41no—
170Q8—1181no—
171Q8—1181no—
172D4—1181no—
173D4—1181no—
174D4—2361no—
175D4—2361no—
176C2×C4—22no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—1181no—
181C2×C4—2361no—
182C2×C4—2361no—
183C2×C4#1174568511yescharacteristic
184C2×C4#1174568511yescharacteristic
185C2×C4D4×D5911yescharacteristic
186C2×C4D4×D5911yescharacteristic
187C2×C4D4×D5911yescharacteristic
188C2×C4C2×C22⋊D5911yescharacteristic
189C8—41no—
190C8—1182no—
191C8—1182no—
192C8—2361no—
193C22—41no—
194C22—4721no—
195C22—2361no—
196C22#1427369911yescharacteristic
197C22#1427370911yescharacteristic
198C22#1427371311yescharacteristic
199C4—42no—
200C4—81no—
201C4—2361no—
202C4#1427369511yescharacteristic
203C4#1427370011yescharacteristic
204C4#1427370011yescharacteristic
205C4#1427371011yescharacteristic
206C2—21no—
207C2—21no—
208C2—21no—
209C2—4721no—
210C2#1683731711yescharacteristic
subgroupG/H
centerC2#16837317
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC59×#419C2
socleC2×C59#394
hypercenter#419D59
hypocenterC59#2049
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
2. #16837450C2semidirect
5. C2×#14273646C2semidirect
6. #16837172C2semidirect
7. C59×#419C2semidirect
109. #419D59semidirect
113. C59#2049semidirect