Finite Group Databasebeta

← #21436530

Subgroups — #21436530

Order 7552.

376 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838092C211yesmaximal, characteristic, complemented
2#16837808C211yesmaximal, characteristic, complemented
3#16837737C211yesmaximal, characteristic, complemented
4#16837732C211yesmaximal, characteristic, complemented
5#16837723C211yesmaximal, characteristic, complemented
6#16837713C211yesmaximal, characteristic, complemented
7#16837702C211yesmaximal, characteristic, complemented
8#16837694C211yesmaximal, characteristic, complemented
9#16837646C211yesmaximal, characteristic, complemented
10#16837629C211yesmaximal, characteristic, complemented
11#16837502C211yesmaximal, characteristic, complemented
12#16837474C211yesmaximal, characteristic, complemented
13#16837442C211yesmaximal, characteristic, complemented
14C2×#14273660C211yesmaximal, characteristic, complemented
15C59×#547C211yesmaximal, characteristic
16C2×#11745670C2211yescharacteristic
17C2×#11745664C2211yescharacteristic
18C22×C59⋊C8C2211yescharacteristic
19#14273720—21no—
20#14273719C2211yescharacteristic
21#14273717—21no—
22#14273708—21no—
23#14273706C2211yescharacteristic
24#14273706C2211yescharacteristic
25C4×Dic118C2211yescharacteristic
26#14273686C2211yescharacteristic
27#14273683—21no—
28C2×C4⋊Dic59C2211yescharacteristic
29#14273660C2211yescharacteristic
30#14273660C2211yescharacteristic
31#14273660C2211yescharacteristic
32#14273660C2211yescharacteristic
33#14273660C2211yescharacteristic
34#14273660C2211yescharacteristic
35#14273658C2211yescharacteristic
36#14273658C2211yescharacteristic
37#14273658C2211yescharacteristic
38C4⋊(C59⋊C8)C2211yescharacteristic
39#14273650C2211yescharacteristic
40#14273650C2211yescharacteristic
41#14273650C2211yescharacteristic
42#14273648C2211yescharacteristic
43#14273648C2211yescharacteristic
44#14273648C2211yescharacteristic
45C22⋊(C59⋊C8)C2211yescharacteristic
46C22⋊(C59⋊C8)C2211yescharacteristic
47#14273638C2211yescharacteristic
48C2×#41×C59—21no—
49C4⋊Q8×C59C2211yescharacteristic
50#123×C59—21no—
51#123×C59—21no—
52C22⋊Q8×C59—21no—
53#121×C59C2211yescharacteristic
54#121×C59C2211yescharacteristic
55C4×D4×C59C2211yescharacteristic
56C4×D4×C59C2211yescharacteristic
57C2×C4⋊C4×C59C2211yescharacteristic
58C2×C4⋊C4×C59C2211yescharacteristic
59#41×C59—44no—
60C2×Q8×C59—21no—
61C2×D4×C59—21no—
62C2×D4×C59—21no—
63C2×D4×C59D411yescharacteristic
64C2×D4×C59C2311yescharacteristic
65C22×C4×C59—21no—
66C22×C4×C59—21no—
67C22×C4×C59—21no—
68C22×C4×C59C2311yescharacteristic
69C22×C4×C59C2311yescharacteristic
70C22×Dic59—21no—
71C2×Dic118C2311yescharacteristic
72C4⋊C4×C59—21no—
73C4⋊C4×C59—21no—
74C4⋊C4×C59—21no—
75C4⋊C4×C59D411yescharacteristic
76C4⋊C4×C59C2311yescharacteristic
77C4⋊C4×C59C2311yescharacteristic
78C4⋊C4×C59C2311yescharacteristic
79C22⋊C4×C59—21no—
80C22⋊C4×C59—21no—
81C22⋊C4×C59—21no—
82C22⋊C4×C59D411yescharacteristic
83C22⋊C4×C59D411yescharacteristic
84C42×C59C2311yescharacteristic
85C22⋊Dic59—21no—
86C22⋊Dic59—21no—
87C22⋊Dic59—21no—
88#11745670—22no—
89C4⋊Dic59—21no—
90C4⋊Dic59C2311yescharacteristic
91C4⋊Dic59C2311yescharacteristic
92C4⋊Dic59C2311yescharacteristic
93Dic59⋊C4—21no—
94Dic59⋊C4—21no—
95Dic59⋊C4—21no—
96Dic59⋊C4—21no—
97Dic59⋊C4—21no—
98C4×Dic59—21no—
99C4×Dic59—21no—
100#11745664—22no—
101C2×C59⋊C8—22no—
102C2×C59⋊C8C2311yescharacteristic
103C2×C59⋊C8C2311yescharacteristic
104C2×C59⋊C8C2311yescharacteristic
105C2×C59⋊C8C2311yescharacteristic
106C23×C59—21no—
107C23×C59C2×D411yescharacteristic
108C23×C59C2×D411yescharacteristic
109Q8×C59—42no—
110D4×C59—22no—
111D4×C59—21no—
112D4×C59—21no—
113D4×C59—42no—
114D4×C59—42no—
115C2×C4×C59—21no—
116C2×C4×C59—21no—
117C2×C4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—42no—
123C2×C4×C59—42no—
124C2×C4×C59—42no—
125C2×C4×C59C2×D411yescharacteristic
126C2×C4×C59C2×D411yescharacteristic
127C2×C4×C59C2×D411yescharacteristic
128C2×C4×C59C2×D411yescharacteristic
129C2×C4×C59C2411yescharacteristic
130C2×Dic59—21no—
131C2×Dic59—21no—
132C2×Dic59—21no—
133C2×Dic59—21no—
134C2×Dic59—42no—
135Dic118—21no—
136Dic118—21no—
137C59⋊C8—21no—
138C59⋊C8—21no—
139C59⋊C8—21no—
140C59⋊C8#4112yescomplemented
141C22×C59—21no—
142C22×C59—21no—
143C22×C59—21no—
144C22×C59—21no—
145C22×C59—21no—
146C22×C59—41no—
147C22×C59—41no—
148C22×C59—41no—
149C22×C59AGL(1,ℤ/8)12yes—
150C22×C59C22×D411yescharacteristic
151C4×C59—21no—
152C4×C59—21no—
153C4×C59—21no—
154C4×C59—21no—
155C4×C59—41no—
156C4×C59—41no—
157C4×C59—41no—
158C4×C59C2×#4111yescharacteristic
159C4×C592−1+411yescharacteristic
160Dic59—41no—
161Dic59—41no—
162Dic59—41no—
163Dic59—41no—
164#3343—591nomaximal, Sylow
165C2×C59—22no—
166C2×C59—41no—
167C2×C59—81no—
168C2×C59#54711yescharacteristic
169C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
170C2×C59#57811yescharacteristic
171#552—591no—
172#547D5911yescharacteristic
173#501—591no—
174#484—591no—
175#483—591no—
176#482—591no—
177#480—591no—
178#478—591no—
179#477—591no—
180#468—591no—
181#465—591no—
182#440—591no—
183#435—591no—
184#428—591no—
185C2×#107—591no—
186C59#334311yescharacteristic, complemented, Sylow
187C2×#41—21no—
188C2×SD16—591no—
189C2×M16—591no—
190C22×C8—591no—
191C4⋊Q8C2×D5911yescharacteristic
192#126—1181no—
193#125—591no—
194#125—1181no—
195#123—21no—
196#123—21no—
197#123—1181no—
198C22⋊Q8—21no—
199C22⋊Q8—591no—
200C22⋊Q8—591no—
201#121C2×D5911yescharacteristic
202#121C2×D5911yescharacteristic
203C4×Q8—591no—
204C4×D4C2×D5911yescharacteristic
205C4×D4C2×D5911yescharacteristic
206#117—591no—
207#117—1181no—
208C2×C4⋊C4—591no—
209C2×C4⋊C4C2×D5911yescharacteristic
210C2×C4⋊C4C2×D5911yescharacteristic
211#107—591no—
212#107—591no—
213#107—591no—
214#107—591no—
215#107—591no—
216#107—591no—
217#106—591no—
218#106—591no—
219#106—591no—
220C4⋊C8—591no—
221#103—591no—
222#103—591no—
223#103—591no—
224#102—591no—
225#102—591no—
226#102—591no—
227C22⋊C8—591no—
228C22⋊C8—591no—
229#97—591no—
230#41—44no—
231C2×Q8—21no—
232C2×Q8—591no—
233C2×D4—21no—
234C2×D4—21no—
235C2×D4C22⋊D5911yescharacteristic
236C2×D4C22×D5911yescharacteristic
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—1181no—
241C22×C4C22×D5911yescharacteristic
242C22×C4C22×D5911yescharacteristic
243SD16—1182no—
244M16—1182no—
245C2×C8—591no—
246C2×C8—591no—
247C2×C8—591no—
248C2×C8—591no—
249C2×C8—1182no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—591no—
254C4⋊C4—591no—
255C4⋊C4—591no—
256C4⋊C4—1181no—
257C4⋊C4—1181no—
258C4⋊C4—1181no—
259C4⋊C4—1181no—
260C4⋊C4—1181no—
261C4⋊C4—1181no—
262C4⋊C4C22⋊D5911yescharacteristic
263C4⋊C4C22×D5911yescharacteristic
264C4⋊C4C22×D5911yescharacteristic
265C4⋊C4C22×D5911yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—1181no—
270C22⋊C4—1181no—
271C22⋊C4—1181no—
272C22⋊C4C22⋊D5911yescharacteristic
273C22⋊C4C22⋊D5911yescharacteristic
274C42—1181no—
275C42—1181no—
276C42C22×D5911yescharacteristic
277C23—21no—
278C23C2×C22⋊D5911yescharacteristic
279C23C2×C22⋊D5911yescharacteristic
280Q8—42no—
281Q8—1181no—
282Q8—1181no—
283D4—22no—
284D4—21no—
285D4—21no—
286D4—42no—
287D4—42no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—1181no—
299C2×C4—1181no—
300C2×C4—1181no—
301C2×C4—1181no—
302C2×C4—2362no—
303C2×C4C2×C22⋊D5911yescharacteristic
304C2×C4C2×C22⋊D5911yescharacteristic
305C2×C4C2×C22⋊D5911yescharacteristic
306C2×C4C2×C22⋊D5911yescharacteristic
307C2×C4C23×D5911yescharacteristic
308C8—592no—
309C8—1181no—
310C8—1181no—
311C8—1181no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22#1427375312yes—
321C22C22×C22⋊D5911yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—2361no—
330C4—2361no—
331C4—2361no—
332C4—2361no—
333C4#41×D5911yescharacteristic
334C4#1427377411yescharacteristic
335C2—22no—
336C2—41no—
337C2—81no—
338C2#1683805111yescharacteristic
339C2C2×#1427375311yescharacteristic
340C2#1683821711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#547C2
socleC22×C59C22×D4
hypercenter#547D59
hypocenterC59#3343
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #16838092C2semidirect
2. #16837808C2semidirect
3. #16837737C2semidirect
4. #16837732C2semidirect
5. #16837723C2semidirect
6. #16837713C2semidirect
7. #16837702C2semidirect
8. #16837694C2semidirect
9. #16837646C2semidirect
10. #16837629C2semidirect
11. #16837502C2semidirect
12. #16837474C2semidirect
13. #16837442C2semidirect
14. C2×#14273660C2semidirect
140. C59⋊C8#41semidirect
186. C59#3343semidirect