Finite Group Databasebeta

← #21433934

Subgroups — #21433934

Order 7552.

362 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 141 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#16838033C211yesmaximal, characteristic
2#16837880C211yesmaximal, characteristic
3#16837711C212yesmaximal, complemented
4#16837707C212yesmaximal, complemented
5#16837695C212yesmaximal, complemented
6#16837685C212yesmaximal, complemented
7#16837442C211yesmaximal, characteristic
8#16837440C211yesmaximal, characteristic
9#16837428C211yesmaximal, characteristic
10#16837411C211yesmaximal, characteristic
11C2×#103×C59C211yesmaximal, characteristic
12C2×#11745664C2211yescharacteristic
13#14273726—21no—
14#14273726C2212yes—
15#14273718—21no—
16#14273718C2212yes—
17#14273706—22no—
18Q8×Dic59—21no—
19Q8×Dic59—21no—
20Q8×Dic59C2212yes—
21Q8×Dic59C2212yes—
22#14273686—22no—
23#14273686C2211yescharacteristic
24#14273686C2211yescharacteristic
25#14273686C2211yescharacteristic
26#14273661C2211yescharacteristic
27#14273661C2211yescharacteristic
28#14273660C2212yes—
29#14273659C2211yescharacteristic
30#14273659C2211yescharacteristic
31#14273658C2212yes—
32Dic59⋊C8C2212yes—
33Dic59⋊C8C2212yes—
34#14273651C2212yes—
35#14273651C2212yes—
36C22×Q8×C59C2211yescharacteristic
37C22×C8×C59C2211yescharacteristic
38C2×C4⋊C4×C59C2211yescharacteristic
39#103×C59C2212yes—
40#103×C59C2212yes—
41C2×Q8×C59—21no—
42C2×Q8×C59—22no—
43C2×Q8×C59Q814yescomplemented
44C2×Q8×C59C2312yes—
45C22×C4×C59—21no—
46C22×C4×C59—21no—
47C22×C4×C59C2311yescharacteristic
48C2×Dic118—22no—
49C2×C8×C59—22no—
50C2×C8×C59C2311yescharacteristic
51C2×C8×C59C2311yescharacteristic
52C4⋊C4×C59—21no—
53C4⋊C4×C59C2312yes—
54C22⋊Dic59—21no—
55C22⋊Dic59—21no—
56C22⋊Dic59D412yes—
57C4⋊Dic59—22no—
58C4⋊Dic59—22no—
59C4⋊Dic59—22no—
60C4⋊Dic59D411yescharacteristic
61C4⋊Dic59D411yescharacteristic
62C4⋊Dic59C2311yescharacteristic
63C4⋊Dic59C2311yescharacteristic
64C4⋊Dic59C2311yescharacteristic
65C4⋊Dic59C2311yescharacteristic
66Dic59⋊C4—22no—
67Dic59⋊C4—22no—
68C4×Dic59—21no—
69C4×Dic59—21no—
70C4×Dic59—22no—
71C4×Dic59—22no—
72C4×Dic59C2312yes—
73#11745664—22no—
74C2×C59⋊C8C2312yes—
75C23×C59C2×D411yescharacteristic
76Q8×C59—24no—
77Q8×C59—22no—
78Q8×C59C2×Q814yes—
79C2×C4×C59—24no—
80C2×C4×C59—22no—
81C2×C4×C59—22no—
82C2×C4×C59—81no—
83C2×C4×C59C2×D411yescharacteristic
84C2×C4×C59C2×Q812yes—
85C2×C4×C59#4112yes—
86C2×C4×C59C2411yescharacteristic
87C2×Dic59—21no—
88C2×Dic59—21no—
89C2×Dic59—21no—
90C2×Dic59—21no—
91C2×Dic59C2×D412yes—
92C2×Dic59C2×D412yes—
93Dic118—82no—
94C8×C59—21no—
95C8×C59—21no—
96C59⋊C8—22no—
97C22×C59—21no—
98C22×C59—21no—
99C22×C59C22⋊Q812yes—
100C22×C59C22×D411yescharacteristic
101C4×C59—24no—
102C4×C59—42no—
103C4×C59C22⋊Q812yes—
104C4×C59C22×Q811yescharacteristic
105C4×C59C2×#4111yescharacteristic
106Dic59—22no—
107Dic59—22no—
108Dic59—41no—
109Dic59—41no—
110Dic59—41no—
111Dic59—41no—
112#3082—591nomaximal, Sylow
113C2×C59—22no—
114C2×C59C2×C22⋊Q811yescharacteristic
115C2×C59#57711yescharacteristic
116C2×C59#57811yescharacteristic
117#544—591no—
118#519—591no—
119#479—592no—
120#479—592no—
121#477—592no—
122#475—592no—
123#428—591no—
124#427—591no—
125#424—591no—
126#419—591no—
127C2×#103D5911yescharacteristic
128C59#308211yescharacteristic, complemented, Sylow
129C22×Q8C2×D5911yescharacteristic
130C2×M16—591no—
131C22×C8C2×D5911yescharacteristic
132C4⋊Q8—592no—
133C4⋊Q8—1181no—
134#125—592no—
135#125—1181no—
136C22⋊Q8—1182no—
137C4×Q8—592no—
138C4×Q8—592no—
139C4×Q8—1181no—
140C4×Q8—1181no—
141#117—591no—
142#117—591no—
143#117—591no—
144#117—1182no—
145C2×C4⋊C4C2×D5911yescharacteristic
146#107—591no—
147#107—591no—
148#107—592no—
149#106—591no—
150#106—591no—
151#106—592no—
152C4⋊C8—592no—
153C4⋊C8—592no—
154#103—592no—
155#103—592no—
156#103C2×D5912yes—
157#103C2×D5912yes—
158C2×Q8—21no—
159C2×Q8—22no—
160C2×Q8—1182no—
161C2×Q8Dic11814yescomplemented
162C2×Q8C22×D5912yes—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4C22×D5911yescharacteristic
166M16—1182no—
167C2×C8—22no—
168C2×C8—592no—
169C2×C8C22×D5911yescharacteristic
170C2×C8C22×D5911yescharacteristic
171C4⋊C4—21no—
172C4⋊C4—591no—
173C4⋊C4—591no—
174C4⋊C4—591no—
175C4⋊C4—591no—
176C4⋊C4—591no—
177C4⋊C4—591no—
178C4⋊C4—1182no—
179C4⋊C4—1182no—
180C4⋊C4—1182no—
181C4⋊C4—1182no—
182C4⋊C4—1182no—
183C4⋊C4C22×D5912yes—
184C22⋊C4—592no—
185C22⋊C4—1181no—
186C22⋊C4—1181no—
187C42—592no—
188C42—1182no—
189C42—1182no—
190C42—1181no—
191C42—1181no—
192C23D4×D5911yescharacteristic
193Q8—24no—
194Q8—22no—
195Q8—4722no—
196Q8C2×Dic11814yes—
197C2×C4—24no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—81no—
201C2×C4—592no—
202C2×C4—592no—
203C2×C4—1181no—
204C2×C4—1181no—
205C2×C4—1181no—
206C2×C4—1181no—
207C2×C4C2×Dic11812yes—
208C2×C4D4×D5911yescharacteristic
209C2×C4#1174568712yes—
210C2×C4C23×D5911yescharacteristic
211C8—21no—
212C8—21no—
213C8—1182no—
214C22—21no—
215C22—21no—
216C22#1427370412yes—
217C22C2×D4×D5911yescharacteristic
218C4—24no—
219C4—42no—
220C4—1182no—
221C4—1182no—
222C4—2361no—
223C4—2361no—
224C4—2361no—
225C4—2361no—
226C4#1427370412yes—
227C4C22×Dic11811yescharacteristic
228C4C2×#1174568711yescharacteristic
229C2—22no—
230C2C2×#1427370411yescharacteristic
231C2#1683820811yescharacteristic
232C2#1683821511yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC2×#103×C59C2
socleC22×C59C22×D4
hypercenterC2×#103D59
hypocenterC59#3082
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
3. #16837711C2semidirect
4. #16837707C2semidirect
5. #16837695C2semidirect
6. #16837685C2semidirect
43. C2×Q8×C59Q8semidirect
128. C59#3082semidirect
161. C2×Q8Dic118semidirect