Finite Group Databasebeta

← #21425013

Subgroups — #21425013

Order 7552.

336 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 85 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#16837948C211yesmaximal, characteristic
2C2×#14273655C211yesmaximal, characteristic, complemented
3C2×#14273654C211yesmaximal, characteristic, complemented
4C2×#14273653C211yesmaximal, characteristic, complemented
5M16×Dic59C211yesmaximal, characteristic, complemented
6C4×Dic59⋊C4C211yesmaximal, characteristic, complemented
7C2×#104×C59C211yesmaximal, characteristic, complemented
8C2×#11745685C2211yescharacteristic
9C2×#11745664C2211yescharacteristic
10#14273725C411yescharacteristic, complemented
11#14273723C411yescharacteristic, complemented
12#14273716C411yescharacteristic, complemented
13#14273714C411yescharacteristic, complemented
14#14273699—21no—
15#14273699—21no—
16C4×C22⋊D59—21no—
17C4×C22⋊D59—21no—
18C2×Dic59⋊C4—21no—
19C2×C4×Dic59C2211yescharacteristic
20C2×C4×Dic59C2211yescharacteristic
21#14273655—22no—
22#14273654—22no—
23#14273653—22no—
24#14273637—21no—
25C8×Dic59—21no—
26C59⋊#95—21no—
27C2×#41×C59C2211yescharacteristic
28C2×M16×C59C2211yescharacteristic
29C2×C42×C59C2211yescharacteristic
30#104×C59—22no—
31#41×C59—21no—
32#41×C59—21no—
33#41×C59—21no—
34#41×C59—21no—
35C2×Q8×C59C2×C411yescharacteristic
36C2×D4×C59—21no—
37C2×D4×C59C2×C411yescharacteristic
38C22×C4×C59—21no—
39C22×C4×C59—21no—
40C22×C4×C59C2311yescharacteristic
41C2×C22⋊D59—21no—
42C2×C22⋊D59—21no—
43C2×C22⋊D59—21no—
44C22×Dic59—21no—
45C22×Dic59D411yescharacteristic
46C22×Dic59D411yescharacteristic
47#11745685—21no—
48#11745685—21no—
49#11745685—21no—
50#11745685—21no—
51C2×D236C2×C411yescharacteristic
52C2×C4×D59—21no—
53C2×Dic118C2×C411yescharacteristic
54M16×C59—21no—
55M16×C59D412yescomplemented
56C2×C8×C59—21no—
57C42×C59—21no—
58C42×C59—21no—
59C22⋊Dic59—21no—
60C22⋊Dic59—21no—
61(C2×D59)⋊C4—21no—
62(C2×D59)⋊C4—21no—
63Dic59⋊C4—24no—
64Dic59⋊C4—21no—
65Dic59⋊C4—21no—
66C4×Dic59—21no—
67C4×Dic59—21no—
68C4×Dic59C2×C411yescharacteristic
69C4×Dic59C2×C411yescharacteristic
70C4×Dic59D411yescharacteristic
71C4×Dic59D411yescharacteristic
72#11745664—21no—
73#11745664D412yescomplemented
74C2×C59⋊C8—21no—
75C23×C59—21no—
76C23×C59C2×D411yescharacteristic
77C22×D59—21no—
78Q8×C59—21no—
79Q8×C59—21no—
80D4×C59—21no—
81D4×C59—21no—
82D4×C59—41no—
83D4×C59—41no—
84C2×C4×C59—22no—
85C2×C4×C59—21no—
86C2×C4×C59—41no—
87C2×C4×C59—41no—
88C2×C4×C59—41no—
89C2×C4×C59—41no—
90C2×C4×C59C22×C411yescharacteristic
91C2×C4×C59C2×D411yescharacteristic
92C2×C4×C59C2×D411yescharacteristic
93C2×C4×C59C2×D411yescharacteristic
94C2×C4×C59#4111yescharacteristic
95C2×C4×C59#4111yescharacteristic
96C22⋊D59—42no—
97C22⋊D59—41no—
98C22⋊D59—41no—
99C22⋊D59—42no—
100C2×Dic59—22no—
101C2×Dic59—22no—
102C2×Dic59—21no—
103C2×Dic59—41no—
104C2×Dic59—41no—
105C2×Dic59—41no—
106C2×Dic59C22⋊C411yescharacteristic
107C2×Dic59C22⋊C411yescharacteristic
108C2×Dic59C22⋊C411yescharacteristic
109C2×Dic59C22⋊C411yescharacteristic
110D236—21no—
111D236—21no—
112C4×D59—41no—
113C4×D59—41no—
114Dic118—21no—
115Dic118—21no—
116C8×C59—22no—
117C59⋊C8—22no—
118C22×C59—21no—
119C22×C59—21no—
120C22×C59—41no—
121C22×C59—41no—
122C22×C59—41no—
123C22×C59C2×C22⋊C411yescharacteristic
124C22×C59#12411yescharacteristic
125C22×C59#12711yescharacteristic
126C2×D59—41no—
127C2×D59—41no—
128C2×D59—41no—
129C4×C59—42no—
130C4×C59—41no—
131C4×C59C4×D411yescharacteristic
132C4×C59C4×D411yescharacteristic
133C4×C59#12111yescharacteristic
134C4×C59#12111yescharacteristic
135Dic59—21no—
136Dic59—21no—
137Dic59—21no—
138Dic59—42no—
139Dic59—41no—
140Dic59#10412yescomplemented
141#1980—591nomaximal, Sylow
142C2×C59—21no—
143C2×C59—21no—
144C2×C59—81no—
145C2×C59#39011yescharacteristic
146C2×C59C2×#10411yescharacteristic
147C2×C59#42111yescharacteristic
148D59—81no—
149#532—591no—
150C2×#104—591no—
151C2×#104—591no—
152C2×#104—591no—
153C2×#104D5911yescharacteristic, complemented
154C4×M16—591no—
155C4×C4⋊C4—591no—
156C59#198011yescharacteristic, complemented, Sylow
157C2×#41—591no—
158C2×#41C2×D5911yescharacteristic
159C2×M16—591no—
160C2×M16C2×D5911yescharacteristic
161C4⋊Q8—591no—
162#127—591no—
163#124—591no—
164#124—591no—
165#121—1181no—
166#121—1181no—
167C4×D4—1181no—
168C4×D4—1181no—
169C2×C4⋊C4—1181no—
170C2×C42—591no—
171C2×C42—591no—
172C2×C42C2×D5911yescharacteristic
173#104—22no—
174#104—1182no—
175#104—1182no—
176#104—1182no—
177#97—1181no—
178C4×C8—1181no—
179#95—1181no—
180#41—21no—
181#41—21no—
182#41—21no—
183#41—21no—
184#41—1181no—
185#41—1181no—
186#41—1181no—
187#41—1181no—
188C2×Q8—591no—
189C2×Q8C4×D5911yescharacteristic
190C2×D4—21no—
191C2×D4—591no—
192C2×D4—1181no—
193C2×D4—1181no—
194C2×D4—1181no—
195C2×D4C4×D5911yescharacteristic
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—591no—
199C22×C4—591no—
200C22×C4—1181no—
201C22×C4—1181no—
202C22×C4C22×D5911yescharacteristic
203M16—21no—
204M16—592no—
205M16—1181no—
206M16C22⋊D5912yescomplemented
207C2×C8—21no—
208C2×C8—1181no—
209C4⋊C4—1181no—
210C4⋊C4—1181no—
211C4⋊C4—1184no—
212C22⋊C4—1181no—
213C22⋊C4—1181no—
214C22⋊C4—1181no—
215C22⋊C4—1181no—
216C42—21no—
217C42—21no—
218C42—591no—
219C42—591no—
220C42—591no—
221C42—591no—
222C42—1181no—
223C42—1181no—
224C23—21no—
225C23—1181no—
226C23D4×D5911yescharacteristic
227Q8—21no—
228Q8—21no—
229Q8—1181no—
230Q8—1181no—
231D4—21no—
232D4—21no—
233D4—41no—
234D4—41no—
235D4—1181no—
236D4—1181no—
237D4—2362no—
238D4—2362no—
239D4—2361no—
240D4—2361no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—591no—
248C2×C4—591no—
249C2×C4—591no—
250C2×C4—591no—
251C2×C4—1182no—
252C2×C4—1182no—
253C2×C4—1181no—
254C2×C4—2361no—
255C2×C4—2361no—
256C2×C4—2361no—
257C2×C4—2361no—
258C2×C4—2361no—
259C2×C4C2×C4×D5911yescharacteristic
260C2×C4#1174568511yescharacteristic
261C2×C4D4×D5911yescharacteristic
262C2×C4D4×D5911yescharacteristic
263C2×C4#1174568711yescharacteristic
264C2×C4C2×C22⋊D5911yescharacteristic
265C8—22no—
266C8—1182no—
267C22—21no—
268C22—21no—
269C22—41no—
270C22—41no—
271C22—41no—
272C22—2361no—
273C22—2361no—
274C22—2361no—
275C22C22⋊C4×D5911yescharacteristic
276C22#1427371311yescharacteristic
277C22#1427372311yescharacteristic
278C4—42no—
279C4—41no—
280C4—592no—
281C4—1181no—
282C4—1181no—
283C4—1181no—
284C4—2362no—
285C4—2361no—
286C4(C22⋊D59)⋊C411yescharacteristic
287C4C4×C22⋊D5911yescharacteristic
288C4#1427369911yescharacteristic
289C4#1427370011yescharacteristic
290C2—21no—
291C2—21no—
292C2—81no—
293C2—4721no—
294C2#1683730211yescharacteristic
295C2#104×D5911yescharacteristic
296C2#1683741711yescharacteristic
subgroupG/H
centerC2×C4D4×D59
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC2×#104×C59C2
socleC22×C59C2×C22⋊C4
hypercenterC2×#104D59
hypocenterC59#1980
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×#14273655C2semidirect
3. C2×#14273654C2semidirect
4. C2×#14273653C2semidirect
5. M16×Dic59C2semidirect
6. C4×Dic59⋊C4C2semidirect
7. C2×#104×C59C2semidirect
10. #14273725C4semidirect
11. #14273723C4semidirect
12. #14273716C4semidirect
13. #14273714C4semidirect
55. M16×C59D4semidirect
73. #11745664D4semidirect
140. Dic59#104semidirect
153. C2×#104D59semidirect
156. C59#1980semidirect
206. M16C22⋊D59semidirect