Finite Group Databasebeta

← #21425194

Subgroups — #21425194

Order 7552.

370 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C22×#11745672C211yesmaximal, characteristic
2C2×#14273725C211yesmaximal, characteristic
3C2×#14273652C211yesmaximal, characteristic
4C2×#14273651C211yesmaximal, characteristic
5#16837309C211yesmaximal, characteristic
6#16837156C211yesmaximal, characteristic
7C22×Q16×C59C211yesmaximal, characteristic
8C22×Dic118C2211yescharacteristic
9C2×#11745672—22no—
10C2×#11745672—22no—
11C2×#11745672—22no—
12C22×C59⋊C8C2211yescharacteristic
13#14273725—22no—
14#14273725—22no—
15C2×C4⋊Dic59C2211yescharacteristic
16C2×Dic59⋊C4—22no—
17C2×C4×Dic59C2211yescharacteristic
18#14273652—22no—
19#14273651—22no—
20C59⋊#95—22no—
21C22×Q8×C59C2211yescharacteristic
22C22×Q8×C59C2211yescharacteristic
23C2×Q16×C59—22no—
24C2×Q16×C59—22no—
25C2×Q16×C59—22no—
26C22×C8×C59C2211yescharacteristic
27C2×Q8×C59—21no—
28C2×Q8×C59—21no—
29C2×Q8×C59—21no—
30C2×Q8×C59—21no—
31C2×Q8×C59—21no—
32C2×Q8×C59—21no—
33C2×Q8×C59—21no—
34C2×Q8×C59—21no—
35C2×Q8×C59—21no—
36C2×Q8×C59—21no—
37C2×Q8×C59D412yes—
38C2×Q8×C59D412yes—
39C22×C4×C59—21no—
40C22×C4×C59—21no—
41C22×C4×C59C2311yescharacteristic
42C22×Dic59—21no—
43C22×Dic59—21no—
44C22×Dic59D412yes—
45C2×Dic118—21no—
46C2×Dic118—21no—
47C2×Dic118—21no—
48C2×Dic118—21no—
49C2×Dic118—21no—
50C2×Dic118D412yes—
51Q16×C59—28no—
52C2×C8×C59—21no—
53C2×C8×C59—21no—
54C2×C8×C59D412yes—
55#11745672—28no—
56C4⋊Dic59—21no—
57C4⋊Dic59—21no—
58Dic59⋊C4—28no—
59C4×Dic59—21no—
60C4×Dic59—21no—
61C2×C59⋊C8—21no—
62C2×C59⋊C8—21no—
63C2×C59⋊C8D412yes—
64C23×C59C2×D411yescharacteristic
65Q8×C59—22no—
66Q8×C59—22no—
67Q8×C59—22no—
68Q8×C59—22no—
69Q8×C59—41no—
70Q8×C59—41no—
71Q8×C59—41no—
72Q8×C59—41no—
73C2×C4×C59—22no—
74C2×C4×C59—22no—
75C2×C4×C59—41no—
76C2×C4×C59—41no—
77C2×C4×C59—41no—
78C2×C4×C59—41no—
79C2×C4×C59C2×D411yescharacteristic
80C2×C4×C59C2×D411yescharacteristic
81C2×C4×C59C2×D411yescharacteristic
82C2×C4×C59C2×D411yescharacteristic
83C2×C4×C59C2×D411yescharacteristic
84C2×C4×C59#4111yescharacteristic
85C2×Dic59—22no—
86C2×Dic59—22no—
87C2×Dic59—22no—
88C2×Dic59—41no—
89C2×Dic59—41no—
90C2×Dic59—41no—
91C2×Dic59—42no—
92C2×Dic59Q1614yescomplemented
93Dic118—22no—
94Dic118—22no—
95Dic118—41no—
96Dic118—41no—
97C8×C59—22no—
98C59⋊C8—22no—
99C22×C59#12011yescharacteristic
100C22×C59#12111yescharacteristic
101C22×C59#12711yescharacteristic
102C22×C59C2×Q1612yes—
103C22×C59#13712yes—
104C4×C59—42no—
105C4×C59—42no—
106C4×C59#12011yescharacteristic
107C4×C59#12011yescharacteristic
108C4×C59#12111yescharacteristic
109C4×C59#12111yescharacteristic
110Dic59—24no—
111Dic59—42no—
112Dic59—81no—
113#2016—591nomaximal, Sylow
114C2×C59#39211yescharacteristic
115C2×C59#45112yes—
116C2×C59#46212yes—
117C2×C59#49411yescharacteristic
118C2×C59#49711yescharacteristic
119C22×Q16—591no—
120C22×Q16D5911yescharacteristic
121C2×C4⋊Q8—591no—
122C2×#103—591no—
123C2×#103—591no—
124#391—591no—
125#336—591no—
126C59#201611yescharacteristic, complemented, Sylow
127C22×Q8—591no—
128C22×Q8C2×D5911yescharacteristic
129C22×Q8C2×D5911yescharacteristic
130C2×Q16—22no—
131C2×Q16—22no—
132C2×Q16—22no—
133C2×Q16—1182no—
134C2×Q16—1182no—
135C2×Q16—1182no—
136C22×C8—591no—
137C22×C8C2×D5911yescharacteristic
138C4⋊Q8—1182no—
139C4⋊Q8—1182no—
140C2×C4⋊C4—591no—
141C2×C4⋊C4—1182no—
142C2×C42—591no—
143#103—1182no—
144#103—1182no—
145#95—1182no—
146C2×Q8—21no—
147C2×Q8—21no—
148C2×Q8—21no—
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—21no—
152C2×Q8—21no—
153C2×Q8—21no—
154C2×Q8—21no—
155C2×Q8—21no—
156C2×Q8—592no—
157C2×Q8—1181no—
158C2×Q8—1181no—
159C2×Q8—1181no—
160C2×Q8—1181no—
161C2×Q8—1181no—
162C2×Q8C22⋊D5912yes—
163C2×Q8C22⋊D5912yes—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—592no—
167C22×C4—1181no—
168C22×C4—1181no—
169C22×C4C22×D5911yescharacteristic
170Q16—28no—
171Q16—1188no—
172C2×C8—21no—
173C2×C8—21no—
174C2×C8—592no—
175C2×C8—1181no—
176C2×C8—1181no—
177C2×C8C22⋊D5912yes—
178C4⋊C4—1188no—
179C4⋊C4—1181no—
180C4⋊C4—1181no—
181C42—1181no—
182C42—1181no—
183C23D4×D5911yescharacteristic
184Q8—22no—
185Q8—22no—
186Q8—22no—
187Q8—22no—
188Q8—41no—
189Q8—41no—
190Q8—41no—
191Q8—41no—
192Q8—1182no—
193Q8—1182no—
194Q8—2361no—
195Q8—2361no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—594no—
203C2×C4—1182no—
204C2×C4—1182no—
205C2×C4—1182no—
206C2×C4—2361no—
207C2×C4—2362no—
208C2×C4—2361no—
209C2×C4—2361no—
210C2×C4D4×D5911yescharacteristic
211C2×C4D4×D5911yescharacteristic
212C2×C4#1174568711yescharacteristic
213C2×C4C2×C22⋊D5911yescharacteristic
214C2×C4C2×C22⋊D5911yescharacteristic
215C2×C4C2×C22⋊D5911yescharacteristic
216C8—22no—
217C8—1182no—
218C22#1427369511yescharacteristic
219C22#1427369911yescharacteristic
220C22#1427372311yescharacteristic
221C22Q16×D5912yes—
222C22#1427375912yes—
223C4—42no—
224C4—42no—
225C4—1184no—
226C4—4721no—
227C4—2362no—
228C4#1427369511yescharacteristic
229C4#1427369611yescharacteristic
230C4#1427369811yescharacteristic
231C4#1427369911yescharacteristic
232C2#1683731011yescharacteristic
233C2#1683755612yes—
234C2#1683761012yes—
235C2#1683778011yescharacteristic
236C2#1683779511yescharacteristic
subgroupG/H
centerC23D4×D59
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC22×Q16×C59C2
socleC23×C59C2×D4
hypercenterC22×Q16D59
hypocenterC59#2016
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
92. C2×Dic59Q16semidirect
126. C59#2016semidirect