Finite Group Databasebeta

← #21434228

Subgroups — #21434228

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#16837734C212yesmaximal
4#16837684C211yesmaximal, characteristic, complemented
5#16837613C211yesmaximal, characteristic, complemented
6#16837612C211yesmaximal, characteristic, complemented
7#16837559C212yesmaximal
8#16837508C212yesmaximal, complemented
9#16837506C212yesmaximal, complemented
10#16837458C211yesmaximal, characteristic
11C59×#475C211yesmaximal, characteristic, complemented
12C2×Q8×D59C2211yescharacteristic
13C2×Dic236C2212yes—
14C2×#11745672C2212yes—
15#14273727C2211yescharacteristic
16#14273718—21no—
17#14273707C2212yes—
18#14273703—21no—
19Q8×Dic59—21no—
20Q8×Dic59C2211yescharacteristic
21C4×Dic118—21no—
22C4×Dic118C2211yescharacteristic
23#14273692—21no—
24#14273692C2212yes—
25#14273692C2211yescharacteristic
26#14273685—21no—
27C4⋊C4×D59—21no—
28C4⋊C4×D59C2211yescharacteristic
29C42×D59—21no—
30C42×D59C2211yescharacteristic
31#14273658C2212yes—
32C4⋊(C59⋊C8)C2211yescharacteristic
33#14273652C2212yes—
34#14273650C2212yes—
35#14273650C2212yes—
36(C2×D59)⋊C8C2212yes—
37#14273637C2212yes—
38C4⋊Q8×C59C2211yescharacteristic
39C4×Q8×C59C2211yescharacteristic
40#106×C59C2212yes—
41C4⋊C8×C59C2211yescharacteristic
42#103×C59C2212yes—
43C2×Q8×C59—21no—
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×Dic118C2312yes—
54C2×Dic118C2311yescharacteristic
55C2×C8×C59C2312yes—
56C4⋊C4×C59—21no—
57C4⋊C4×C59—21no—
58C4⋊C4×C59C2312yes—
59C4⋊C4×C59C2311yescharacteristic
60C42×C59—21no—
61C42×C59C2311yescharacteristic
62#11745672—24no—
63(C2×D59)⋊C4—22no—
64C4⋊Dic59—21no—
65C4⋊Dic59—21no—
66C4⋊Dic59—21no—
67C4⋊Dic59—22no—
68C4⋊Dic59C2311yescharacteristic
69Dic59⋊C4—21no—
70Dic59⋊C4—21no—
71Dic59⋊C4—21no—
72Dic59⋊C4—22no—
73C4×Dic59—21no—
74C4×Dic59—21no—
75C4×Dic59—21no—
76C4×Dic59—22no—
77C4×Dic59D411yescharacteristic
78C4×Dic59D411yescharacteristic
79C4×Dic59C2311yescharacteristic
80C2×C59⋊C8C2312yes—
81Dic236—24no—
82C22×D59C2×D411yescharacteristic
83Q8×C59—21no—
84Q8×C59—42no—
85Q8×C59#4112yes—
86C2×C4×C59—21no—
87C2×C4×C59—21no—
88C2×C4×C59—22no—
89C2×C4×C59C2×D411yescharacteristic
90C2×C4×C59C2×D411yescharacteristic
91C2×C4×C59C2411yescharacteristic
92C2×Dic59—21no—
93C2×Dic59—21no—
94C2×Dic59—22no—
95C2×Dic59C2×D411yescharacteristic
96C2×Dic59C2×D411yescharacteristic
97C2×Dic59C2×D411yescharacteristic
98C4×D59—24no—
99C4×D59—22no—
100C4×D59—22no—
101C4×D59—21no—
102C4×D59—21no—
103C4×D59—42no—
104Dic118—24no—
105Dic118—21no—
106Dic118—22no—
107Dic118—22no—
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—41no—
118C4×C59—42no—
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#475D5911yescharacteristic, complemented
138#462—591no—
139#462—591no—
140#451—592no—
141#441—592no—
142#441—592no—
143#432—591no—
144C59#311311yescharacteristic, complemented, Sylow
145C22×Q8—591no—
146C2×Q16—592no—
147C2×Q16—592no—
148C4⋊Q8—591no—
149C4⋊Q8C2×D5911yescharacteristic
150#125—1181no—
151C22⋊Q8—592no—
152C22⋊Q8—1181no—
153C4×Q8—591no—
154C4×Q8—591no—
155C4×Q8—592no—
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#106C2×D5912yes—
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—21no—
177C2×Q8—591no—
178C2×Q8—592no—
179C2×Q8—1181no—
180C2×Q8—1182no—
181C2×Q8—1182no—
182C2×Q8C22×D5911yescharacteristic
183C22×C4—591no—
184C22×C4—591no—
185C22×C4—591no—
186C22×C4—1181no—
187C22×C4—1181no—
188Q16—1184no—
189Q16—1184no—
190C2×C8—592no—
191C2×C8C22×D5912yes—
192C4⋊C4—21no—
193C4⋊C4—21no—
194C4⋊C4—591no—
195C4⋊C4—1181no—
196C4⋊C4—1181no—
197C4⋊C4—1181no—
198C4⋊C4—1182no—
199C4⋊C4—1182no—
200C4⋊C4—1181no—
201C4⋊C4—1181no—
202C4⋊C4—1181no—
203C4⋊C4C22×D5911yescharacteristic
204C4⋊C4C22×D5912yes—
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—42no—
218Q8—592no—
219Q8—1184no—
220Q8—1181no—
221Q8—1182no—
222Q8—1182no—
223Q8#1174568912yes—
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—41no—
251C4—42no—
252C4—1181no—
253C4—1182no—
254C4—1181no—
255C4—1181no—
256C4—2362no—
257C4—2361no—
258C4#1427375612yes—
259C4#41×D5911yescharacteristic
260C4C2×#1174568911yescharacteristic
261C2—1182no—
262C2#1683791511yescharacteristic
263C2#137×D5911yescharacteristic
264C2C2×#1427375611yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#475C2
socleC22×C59C22×D4
hypercenter#475D59
hypocenterC59#3113
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
4. #16837684C2semidirect
5. #16837613C2semidirect
6. #16837612C2semidirect
8. #16837508C2semidirect
9. #16837506C2semidirect
11. C59×#475C2semidirect
137. #475D59semidirect
144. C59#3113semidirect