Finite Group Databasebeta

← #21434225

Subgroups — #21434225

Order 7552.

380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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#16837957C211yesmaximal, characteristic
2C4×Q8×D59C211yesmaximal, characteristic
3#16837731C212yesmaximal
4#16837688C211yesmaximal, characteristic, complemented
5#16837687C211yesmaximal, characteristic, complemented
6#16837609C211yesmaximal, characteristic, complemented
7#16837556C212yesmaximal
8#16837509C212yesmaximal, complemented
9#16837506C212yesmaximal, complemented
10#16837458C211yesmaximal, characteristic
11C59×#462C211yesmaximal, characteristic, complemented
12C2×Q8×D59C2211yescharacteristic
13C2×#11745672C2212yes—
14#14273727C2211yescharacteristic
15#14273718—21no—
16#14273707—21no—
17#14273703C2212yes—
18Q8×Dic59C2212yes—
19Q8×Dic59C2211yescharacteristic
20C4×Dic118—21no—
21C4×Dic118C2211yescharacteristic
22#14273692—21no—
23#14273692—21no—
24#14273692C2211yescharacteristic
25#14273685—21no—
26C4⋊C4×D59—21no—
27C4⋊C4×D59C2211yescharacteristic
28C42×D59—21no—
29C42×D59C2211yescharacteristic
30#14273659C2212yes—
31#14273658C2212yes—
32C4⋊(C59⋊C8)C2211yescharacteristic
33#14273652C2212yes—
34#14273651C2212yes—
35#14273651C2212yes—
36(C2×D59)⋊C8C2212yes—
37#14273637C2212yes—
38C2×Q16×C59C2212yes—
39C4⋊Q8×C59C2211yescharacteristic
40C4×Q8×C59C2211yescharacteristic
41C4⋊C8×C59C2211yescharacteristic
42#103×C59C2212yes—
43C2×Q8×C59C2312yes—
44C2×Q8×C59C2311yescharacteristic
45Q8×D59—22no—
46Q8×D59—22no—
47C2×C4×D59—21no—
48C2×C4×D59—21no—
49C2×C4×D59D411yescharacteristic
50C2×C4×D59D411yescharacteristic
51C2×C4×D59C2311yescharacteristic
52C2×Dic118—21no—
53C2×Dic118—21no—
54C2×Dic118C2311yescharacteristic
55Q16×C59—24no—
56C2×C8×C59C2312yes—
57C4⋊C4×C59—21no—
58C4⋊C4×C59—21no—
59C4⋊C4×C59—21no—
60C4⋊C4×C59C2311yescharacteristic
61C42×C59—21no—
62C42×C59C2311yescharacteristic
63#11745672—24no—
64(C2×D59)⋊C4—22no—
65C4⋊Dic59—21no—
66C4⋊Dic59—21no—
67C4⋊Dic59—22no—
68C4⋊Dic59C2311yescharacteristic
69C4⋊Dic59C2312yes—
70Dic59⋊C4—21no—
71Dic59⋊C4—21no—
72Dic59⋊C4—21no—
73Dic59⋊C4—22no—
74C4×Dic59—21no—
75C4×Dic59—21no—
76C4×Dic59—21no—
77C4×Dic59—22no—
78C4×Dic59D411yescharacteristic
79C4×Dic59D411yescharacteristic
80C4×Dic59C2311yescharacteristic
81C2×C59⋊C8C2312yes—
82C22×D59C2×D411yescharacteristic
83Q8×C59—21no—
84Q8×C59—22no—
85Q8×C59—22no—
86Q8×C59#4112yes—
87C2×C4×C59—21no—
88C2×C4×C59—21no—
89C2×C4×C59—22no—
90C2×C4×C59C2×D411yescharacteristic
91C2×C4×C59C2×D411yescharacteristic
92C2×C4×C59C2411yescharacteristic
93C2×Dic59—21no—
94C2×Dic59—21no—
95C2×Dic59—22no—
96C2×Dic59C2×D411yescharacteristic
97C2×Dic59C2×D411yescharacteristic
98C2×Dic59C2×D411yescharacteristic
99C4×D59—24no—
100C4×D59—22no—
101C4×D59—22no—
102C4×D59—21no—
103C4×D59—21no—
104C4×D59—42no—
105Dic118—24no—
106Dic118—21no—
107Dic118—42no—
108Dic118#4112yes—
109C8×C59—22no—
110C59⋊C8—22no—
111C22×C59C22×D411yescharacteristic
112C2×D59—21no—
113C2×D59—21no—
114C2×D59#13712yes—
115C4×C59—22no—
116C4×C59—21no—
117C4×C59—42no—
118C4×C59—41no—
119C4×C59#13712yes—
120C4×C59C2×#4111yescharacteristic
121C4×C59C2×#4111yescharacteristic
122Dic59—21no—
123Dic59—22no—
124Dic59—21no—
125Dic59—21no—
126Dic59—42no—
127Dic59—41no—
128#3113—591nomaximal, Sylow
129C2×C59#52511yescharacteristic
130C2×C59C2×#13711yescharacteristic
131C2×C59C2×#13711yescharacteristic
132D59—22no—
133#533—591no—
134C2×C4×Q8—591no—
135#483—592no—
136#475—591no—
137#475—591no—
138#462—591no—
139#462D5911yescharacteristic, complemented
140#451—592no—
141#441—592no—
142#441—592no—
143#432—591no—
144C59#311311yescharacteristic, complemented, Sylow
145C22×Q8—591no—
146C2×Q16—592no—
147C2×Q16C2×D5912yes—
148C4⋊Q8—591no—
149C4⋊Q8C2×D5911yescharacteristic
150#125—1181no—
151C22⋊Q8—592no—
152C22⋊Q8—1181no—
153C4×Q8—591no—
154C4×Q8—592no—
155C4×Q8—591no—
156C4×Q8—591no—
157C4×Q8—1181no—
158C4×Q8—1181no—
159C4×Q8—1181no—
160C4×Q8C2×D5911yescharacteristic
161#117—1181no—
162C2×C4⋊C4—591no—
163C2×C4⋊C4—1181no—
164C2×C42—591no—
165C2×C42—1181no—
166#106—592no—
167#106—592no—
168C4⋊C8—591no—
169C4⋊C8C2×D5911yescharacteristic
170#103—592no—
171#103—592no—
172#103—592no—
173#103C2×D5912yes—
174C22⋊C8—592no—
175#97—592no—
176C2×Q8—591no—
177C2×Q8—1181no—
178C2×Q8—1182no—
179C2×Q8—1182no—
180C2×Q8—1181no—
181C2×Q8C22×D5912yes—
182C2×Q8C22×D5911yescharacteristic
183C22×C4—591no—
184C22×C4—591no—
185C22×C4—591no—
186C22×C4—1181no—
187C22×C4—1181no—
188Q16—24no—
189Q16—1184no—
190C2×C8—592no—
191C2×C8C22×D5912yes—
192C4⋊C4—21no—
193C4⋊C4—21no—
194C4⋊C4—21no—
195C4⋊C4—591no—
196C4⋊C4—592no—
197C4⋊C4—1181no—
198C4⋊C4—1181no—
199C4⋊C4—1181no—
200C4⋊C4—1182no—
201C4⋊C4—1182no—
202C4⋊C4—1181no—
203C4⋊C4—1181no—
204C4⋊C4C22×D5911yescharacteristic
205C22⋊C4—1182no—
206C42—21no—
207C42—591no—
208C42—591no—
209C42—591no—
210C42—1181no—
211C42—1181no—
212C42—1182no—
213C42—1181no—
214C42C22×D5911yescharacteristic
215C23—591no—
216Q8—21no—
217Q8—22no—
218Q8—22no—
219Q8—592no—
220Q8—1184no—
221Q8—1181no—
222Q8—2362no—
223Q8#1174568712yes—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—591no—
228C2×C4—591no—
229C2×C4—591no—
230C2×C4—1182no—
231C2×C4—1184no—
232C2×C4—1181no—
233C2×C4—1182no—
234C2×C4—1181no—
235C2×C4—1181no—
236C2×C4—1181no—
237C2×C4—1182no—
238C2×C4—2362no—
239C2×C4D4×D5911yescharacteristic
240C2×C4D4×D5911yescharacteristic
241C2×C4C23×D5911yescharacteristic
242C8—22no—
243C8—1182no—
244C22—592no—
245C22—1181no—
246C22—1181no—
247C22C2×D4×D5911yescharacteristic
248C4—22no—
249C4—21no—
250C4—42no—
251C4—41no—
252C4—1181no—
253C4—1182no—
254C4—1181no—
255C4—1181no—
256C4—2361no—
257C4—2362no—
258C4#1427375912yes—
259C4#41×D5911yescharacteristic
260C4C2×#1174568711yescharacteristic
261C2—1182no—
262C2#1683791211yescharacteristic
263C2#137×D5911yescharacteristic
264C2C2×#1427375911yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#462C2
socleC22×C59C22×D4
hypercenter#462D59
hypocenterC59#3113
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
4. #16837688C2semidirect
5. #16837687C2semidirect
6. #16837609C2semidirect
8. #16837509C2semidirect
9. #16837506C2semidirect
11. C59×#462C2semidirect
139. #462D59semidirect
144. C59#3113semidirect