Finite Group Databasebeta

← #21424149

Subgroups — #21424149

Order 7552.

256 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 81 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×#14273735C211yesmaximal, characteristic
2C2×#14273662C211yesmaximal, characteristic, complemented
3#16837438C211yesmaximal, characteristic, complemented
4#16837420C211yesmaximal, characteristic
5#16837418C211yesmaximal, characteristic
6#16837174C211yesmaximal, characteristic, complemented
7C59×#344C211yesmaximal, characteristic, complemented
8C2×#11745685C2211yescharacteristic
9#14273735—21no—
10#14273735—21no—
11#14273735C412yescomplemented
12#14273735C412yescomplemented
13C2×#11745664C2211yescharacteristic
14C2×#11745659—21no—
15C22×C59⋊C8C2211yescharacteristic
16C2×C8×D59—21no—
17#14273686C2211yescharacteristic
18#14273662—21no—
19#14273662—21no—
20#14273660—21no—
21#14273658—21no—
22#14273655—22no—
23#14273653—22no—
24C2×M16×C59C2211yescharacteristic
25C2×M16×C59C2211yescharacteristic
26#117×C59C2211yescharacteristic
27C22×C4×C59C2311yescharacteristic
28C2×C22⋊D59—21no—
29#11745685—21no—
30#11745685—21no—
31#11745685C2×C412yes—
32#11745685D412yes—
33C2×D236Q811yescharacteristic
34C2×C4×D59—21no—
35C2×Dic118Q811yescharacteristic
36M16×C59—21no—
37M16×C59—21no—
38M16×C59—21no—
39M16×C59C2×C412yes—
40C2×C8×C59—21no—
41C2×C8×C59—21no—
42C4⋊C4×C59—21no—
43C22⋊C4×C59—21no—
44C42×C59—21no—
45C22⋊Dic59—21no—
46C4⋊Dic59—21no—
47C4×Dic59—21no—
48#11745664—21no—
49#11745664—21no—
50C2×C59⋊C8—21no—
51C2×C59⋊C8C2×C411yescharacteristic
52C2×C59⋊C8C2×C411yescharacteristic
53C2×C59⋊C8D411yescharacteristic
54C2×C59⋊C8D411yescharacteristic
55C2×C59⋊C8D411yescharacteristic
56C2×C59⋊C8D411yescharacteristic
57#11745659—22no—
58#11745659—22no—
59C8×D59—22no—
60C8×D59—22no—
61C23×C59#4111yescharacteristic
62C22×D59—21no—
63C2×C4×C59—41no—
64C2×C4×C59C22×C411yescharacteristic
65C2×C4×C59C2×D411yescharacteristic
66C2×C4×C59C2×D411yescharacteristic
67C2×C4×C59C2×D411yescharacteristic
68C2×C4×C59C2×Q811yescharacteristic
69C2×C4×C59#4111yescharacteristic
70C22⋊D59—22no—
71C22⋊D59—22no—
72C2×Dic59—21no—
73C2×Dic59—41no—
74D236—21no—
75D236C4⋊C412yes—
76C4×D59—22no—
77C4×D59—22no—
78Dic118—21no—
79Dic118C4⋊C412yes—
80C8×C59—22no—
81C8×C59—41no—
82C59⋊C8—41no—
83C59⋊C8C22⋊C411yescharacteristic
84C59⋊C8C22⋊C411yescharacteristic
85C59⋊C8C22⋊C411yescharacteristic
86C59⋊C8C22⋊C411yescharacteristic
87C22×C59—41no—
88C22×C59#11711yescharacteristic
89C22×C59#12111yescharacteristic
90C22×C59C22⋊Q811yescharacteristic
91C2×D59—22no—
92C2×D59—42no—
93C4×C59—81no—
94C4×C59C2×C22⋊C411yescharacteristic
95C4×C59C2×C4⋊C411yescharacteristic
96C4×C59#12111yescharacteristic
97C4×C59C22⋊Q811yescharacteristic
98Dic59—22no—
99Dic59—81no—
100#1814—591nomaximal, Sylow
101C2×C59—21no—
102C2×C59—21no—
103C2×C59—21no—
104C2×C59#38011yescharacteristic
105D59—42no—
106C2×#131—591no—
107C2×#108—591no—
108#427—591no—
109#421—591no—
110#421—591no—
111#344—591no—
112#344D5911yescharacteristic, complemented
113C59#181411yescharacteristic, complemented, Sylow
114C2×#41—591no—
115#131—592no—
116#131—592no—
117#131—1181no—
118#131—1181no—
119C2×M16—591no—
120C2×M16—1181no—
121C2×M16C2×D5911yescharacteristic
122C2×M16C2×D5911yescharacteristic
123C22×C8—591no—
124C22×C8—1181no—
125#117—591no—
126#117C2×D5911yescharacteristic
127#108—1181no—
128#108—1181no—
129#107—1181no—
130#106—1181no—
131#104—1182no—
132#104—1182no—
133#41—592no—
134#41—592no—
135#41—1181no—
136#41—1181no—
137C2×Q8—591no—
138C2×D4—591no—
139C2×D4—1181no—
140C22×C4—1181no—
141C22×C4C22×D5911yescharacteristic
142M16—21no—
143M16—21no—
144M16—21no—
145M16—1182no—
146M16—1182no—
147M16—1181no—
148M16—1181no—
149M16C4×D5912yes—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—591no—
153C2×C8—591no—
154C2×C8—591no—
155C2×C8—591no—
156C2×C8—591no—
157C2×C8—591no—
158C2×C8—1182no—
159C2×C8—1182no—
160C2×C8—1181no—
161C4⋊C4—21no—
162C4⋊C4—1181no—
163C22⋊C4—21no—
164C22⋊C4—1181no—
165C42—21no—
166C42—1181no—
167C23—1181no—
168C23#1174568511yescharacteristic
169Q8—592no—
170Q8—1181no—
171D4—592no—
172D4—1182no—
173D4—1182no—
174D4—1181no—
175C2×C4—41no—
176C2×C4—1181no—
177C2×C4—1182no—
178C2×C4—1182no—
179C2×C4—2361no—
180C2×C4C2×C4×D5911yescharacteristic
181C2×C4#1174568511yescharacteristic
182C2×C4D4×D5911yescharacteristic
183C2×C4D4×D5911yescharacteristic
184C2×C4D4×D5911yescharacteristic
185C2×C4Q8×D5911yescharacteristic
186C8—22no—
187C8—41no—
188C8—591no—
189C8—591no—
190C8—591no—
191C8—591no—
192C8—2361no—
193C22—41no—
194C22—1182no—
195C22—2362no—
196C22#1427368411yescharacteristic
197C22#1427370011yescharacteristic
198C22#1427370511yescharacteristic
199C4—81no—
200C4—1182no—
201C4—4721no—
202C4C22⋊C4×D5911yescharacteristic
203C4C4⋊C4×D5911yescharacteristic
204C4#1427370011yescharacteristic
205C4#1427370511yescharacteristic
206C2—21no—
207C2—21no—
208C2—21no—
209C2—2362no—
210C2#1683726111yescharacteristic
subgroupG/H
centerC4#14273700
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#344C2
socleC2×C59#380
hypercenter#344D59
hypocenterC59#1814
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C4 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
2. C2×#14273662C2semidirect
3. #16837438C2semidirect
6. #16837174C2semidirect
7. C59×#344C2semidirect
11. #14273735C4semidirect
12. #14273735C4semidirect
112. #344D59semidirect
113. C59#1814semidirect