Finite Group Databasebeta

← #21436149

Subgroups — #21436149

Order 7552.

376 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838092C211yesmaximal, characteristic
2D4×Dic118C211yesmaximal, characteristic
3#16837771C211yesmaximal, characteristic, complemented
4#16837744C211yesmaximal, characteristic, complemented
5#16837733C211yesmaximal, characteristic, complemented
6#16837710C211yesmaximal, characteristic, complemented
7#16837660C211yesmaximal, characteristic, complemented
8#16837643C211yesmaximal, characteristic, complemented
9#16837613C211yesmaximal, characteristic, complemented
10#16837560C211yesmaximal, characteristic, complemented
11#16837560C211yesmaximal, characteristic, complemented
12#16837510C211yesmaximal, characteristic, complemented
13#16837412C211yesmaximal, characteristic, complemented
14C2×#14273652C211yesmaximal, characteristic, complemented
15C59×#435C211yesmaximal, characteristic
16C22×Dic118C2211yescharacteristic
17C22×Dic118C2211yescharacteristic
18C2×Dic236C2211yescharacteristic
19C2×Dic236C2211yescharacteristic
20C2×Dic236C2211yescharacteristic
21#14273727C2211yescharacteristic
22#14273726—21no—
23#14273720—21no—
24#14273719C2211yescharacteristic
25#14273717—21no—
26#14273708—21no—
27#14273706C2211yescharacteristic
28#14273706C2211yescharacteristic
29#14273706C2211yescharacteristic
30#14273706C2211yescharacteristic
31#14273704—21no—
32#14273704—21no—
33C4×Dic118C2211yescharacteristic
34C4×Dic118C2211yescharacteristic
35D4×Dic59—21no—
36#14273686C2211yescharacteristic
37#14273683—21no—
38C2×C4⋊Dic59C2211yescharacteristic
39#14273661C2211yescharacteristic
40#14273659C2211yescharacteristic
41#14273659C2211yescharacteristic
42#14273652C2211yescharacteristic
43#14273652C2211yescharacteristic
44#14273652C2211yescharacteristic
45#14273652C2211yescharacteristic
46#14273652C2211yescharacteristic
47#14273652C2211yescharacteristic
48#14273652C2211yescharacteristic
49#14273652C2211yescharacteristic
50#14273652C2211yescharacteristic
51#14273652C2211yescharacteristic
52C2×M16×C59C2211yescharacteristic
53C22×C8×C59C2211yescharacteristic
54C4×D4×C59C2211yescharacteristic
55C4⋊C8×C59C2211yescharacteristic
56C22⋊C8×C59C2211yescharacteristic
57C22⋊C8×C59C2211yescharacteristic
58#97×C59C2211yescharacteristic
59C2×D4×C59D411yescharacteristic
60C22×C4×C59C2311yescharacteristic
61C22×C4×C59C2311yescharacteristic
62C22×Dic59—21no—
63C22×Dic59—21no—
64C22×Dic59—21no—
65C2×Dic118—22no—
66C2×Dic118—22no—
67C2×Dic118—21no—
68C2×Dic118—21no—
69C2×Dic118—41no—
70C2×Dic118—41no—
71C2×Dic118C2311yescharacteristic
72C2×Dic118C2311yescharacteristic
73C2×Dic118C2311yescharacteristic
74C2×Dic118C2311yescharacteristic
75M16×C59—41no—
76C2×C8×C59—41no—
77C2×C8×C59C2311yescharacteristic
78C2×C8×C59C2311yescharacteristic
79C2×C8×C59C2311yescharacteristic
80C2×C8×C59C2311yescharacteristic
81C4⋊C4×C59D411yescharacteristic
82C22⋊C4×C59D411yescharacteristic
83C22⋊C4×C59D411yescharacteristic
84C42×C59C2311yescharacteristic
85C22⋊Dic59—21no—
86C22⋊Dic59—21no—
87C22⋊Dic59—21no—
88C22⋊Dic59—21no—
89C22⋊Dic59—21no—
90C4⋊Dic59—21no—
91C4⋊Dic59—21no—
92C4⋊Dic59—21no—
93C4⋊Dic59C2311yescharacteristic
94C4⋊Dic59C2311yescharacteristic
95C4⋊Dic59C2311yescharacteristic
96C4⋊Dic59C2311yescharacteristic
97Dic59⋊C4—21no—
98Dic59⋊C4—21no—
99Dic59⋊C4—21no—
100Dic59⋊C4—21no—
101Dic59⋊C4—21no—
102Dic59⋊C4—21no—
103Dic59⋊C4—21no—
104Dic59⋊C4—21no—
105C4×Dic59—21no—
106C4×Dic59—21no—
107C4×Dic59—21no—
108Dic236—22no—
109Dic236—41no—
110Dic236—41no—
111C23×C59C2×D411yescharacteristic
112C23×C59C2×D411yescharacteristic
113D4×C59—22no—
114C2×C4×C59—21no—
115C2×C4×C59—21no—
116C2×C4×C59—21no—
117C2×C4×C59—21no—
118C2×C4×C59C2×D411yescharacteristic
119C2×C4×C59C2×D411yescharacteristic
120C2×C4×C59C2×D411yescharacteristic
121C2×C4×C59C2×D411yescharacteristic
122C2×C4×C59C2411yescharacteristic
123C2×Dic59—21no—
124C2×Dic59—21no—
125C2×Dic59—21no—
126C2×Dic59—21no—
127C2×Dic59—21no—
128C2×Dic59—21no—
129C2×Dic59—21no—
130C2×Dic59—21no—
131C2×Dic59—42no—
132C2×Dic59—42no—
133C2×Dic59—42no—
134Dic118—21no—
135Dic118—21no—
136Dic118—21no—
137Dic118—21no—
138Dic118—21no—
139Dic118—21no—
140Dic118—21no—
141Dic118—42no—
142Dic118—42no—
143Dic118#4112yes—
144C8×C59—21no—
145C8×C59—21no—
146C8×C59—21no—
147C8×C59—21no—
148C22×C59—21no—
149C22×C59—21no—
150C22×C59—21no—
151C22×C59—21no—
152C22×C59—21no—
153C22×C59#13712yes—
154C22×C59C22×D411yescharacteristic
155C4×C59—21no—
156C4×C59—21no—
157C4×C59—21no—
158C4×C59—21no—
159C4×C59C2×#4111yescharacteristic
160C4×C59H(5,𝔽2)11yescharacteristic
161Dic59—22no—
162Dic59—41no—
163Dic59—41no—
164Dic59—41no—
165Dic59—41no—
166Dic59—41no—
167Dic59—41no—
168Dic59—41no—
169#3312—591nomaximal, Sylow
170C2×C59—22no—
171C2×C59—41no—
172C2×C59#54611yescharacteristic
173C2×C59C2×#13711yescharacteristic
174C2×C59#57811yescharacteristic
175#552—591no—
176D4×Q8—591no—
177#491—591no—
178#485—591no—
179#483—591no—
180#479—591no—
181#470—591no—
182#467—591no—
183#462—591no—
184#451—591no—
185#451—591no—
186#441—591no—
187#435D5911yescharacteristic
188#419—591no—
189C2×#103—591no—
190C59#331211yescharacteristic, complemented, Sylow
191C22×Q8—591no—
192C22×Q8—591no—
193C2×Q16—591no—
194C2×Q16—591no—
195C2×Q16—591no—
196C2×M16C2×D5911yescharacteristic
197C22×C8C2×D5911yescharacteristic
198C4⋊Q8—591no—
199C4⋊Q8—1181no—
200#126—1181no—
201#125—591no—
202#125—1181no—
203#123—1181no—
204C22⋊Q8—591no—
205C22⋊Q8—591no—
206C22⋊Q8—591no—
207C22⋊Q8—591no—
208C22⋊Q8—1181no—
209C22⋊Q8—1181no—
210C4×Q8—591no—
211C4×Q8—591no—
212C4×D4—1181no—
213C4×D4C2×D5911yescharacteristic
214#117—591no—
215#117—1181no—
216C2×C4⋊C4—591no—
217#107—591no—
218#106—591no—
219#106—591no—
220C4⋊C8C2×D5911yescharacteristic
221#103—591no—
222#103—591no—
223#103—591no—
224#103—591no—
225#103—591no—
226#103—591no—
227#103—591no—
228#103—591no—
229#103—591no—
230#103—591no—
231C22⋊C8C2×D5911yescharacteristic
232C22⋊C8C2×D5911yescharacteristic
233#97C2×D5911yescharacteristic
234C2×Q8—591no—
235C2×Q8—591no—
236C2×Q8—591no—
237C2×Q8—591no—
238C2×Q8—1182no—
239C2×Q8—1182no—
240C2×Q8—1181no—
241C2×Q8—1181no—
242C2×Q8—2361no—
243C2×Q8—2361no—
244C2×D4D23611yescharacteristic
245C22×C4—1181no—
246C22×C4—1181no—
247C22×C4—1181no—
248C22×C4C22×D5911yescharacteristic
249C22×C4C22×D5911yescharacteristic
250Q16—1182no—
251Q16—2361no—
252Q16—2361no—
253M16—41no—
254C2×C8—41no—
255C2×C8C22×D5911yescharacteristic
256C2×C8C22×D5911yescharacteristic
257C2×C8C22×D5911yescharacteristic
258C2×C8C22×D5911yescharacteristic
259C4⋊C4—591no—
260C4⋊C4—591no—
261C4⋊C4—591no—
262C4⋊C4—591no—
263C4⋊C4—1181no—
264C4⋊C4—1181no—
265C4⋊C4—1181no—
266C4⋊C4—1181no—
267C4⋊C4—1181no—
268C4⋊C4—1181no—
269C4⋊C4—1181no—
270C4⋊C4—1181no—
271C4⋊C4—1181no—
272C4⋊C4—1181no—
273C4⋊C4—1181no—
274C4⋊C4D23611yescharacteristic
275C22⋊C4—1181no—
276C22⋊C4—1181no—
277C22⋊C4—1181no—
278C22⋊C4—1181no—
279C22⋊C4—1181no—
280C22⋊C4D23611yescharacteristic
281C22⋊C4D23611yescharacteristic
282C42—1181no—
283C42—1181no—
284C42—1181no—
285C42C22×D5911yescharacteristic
286C23C2×D23611yescharacteristic
287C23C2×D23611yescharacteristic
288Q8—592no—
289Q8—1181no—
290Q8—1181no—
291Q8—1181no—
292Q8—1181no—
293Q8—1181no—
294Q8—1181no—
295Q8—1181no—
296Q8—2362no—
297Q8—2362no—
298D4—22no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—1181no—
304C2×C4—1181no—
305C2×C4—1181no—
306C2×C4—1181no—
307C2×C4—1181no—
308C2×C4—1181no—
309C2×C4—1181no—
310C2×C4—1181no—
311C2×C4—2362no—
312C2×C4—2362no—
313C2×C4—2362no—
314C2×C4C2×D23611yescharacteristic
315C2×C4C2×D23611yescharacteristic
316C2×C4C2×D23611yescharacteristic
317C2×C4C2×D23611yescharacteristic
318C2×C4C23×D5911yescharacteristic
319C8—21no—
320C8—21no—
321C8—21no—
322C8—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22#1427376012yes—
329C22C22×D23611yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—1182no—
335C4—2361no—
336C4—2361no—
337C4—2361no—
338C4—2361no—
339C4—2361no—
340C4—2361no—
341C4—2361no—
342C4#41×D5911yescharacteristic
343C4#1427377211yescharacteristic
344C2—22no—
345C2—41no—
346C2#1683804711yescharacteristic
347C2C2×#1427376011yescharacteristic
348C2#1683821911yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#435C2
socleC22×C59C22×D4
hypercenter#435D59
hypocenterC59#3312
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
3. #16837771C2semidirect
4. #16837744C2semidirect
5. #16837733C2semidirect
6. #16837710C2semidirect
7. #16837660C2semidirect
8. #16837643C2semidirect
9. #16837613C2semidirect
10. #16837560C2semidirect
11. #16837560C2semidirect
12. #16837510C2semidirect
13. #16837412C2semidirect
14. C2×#14273652C2semidirect
190. C59#3312semidirect