Finite Group Databasebeta

← #21436261

Subgroups — #21436261

Order 7552.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×Dic118C211yesmaximal, characteristic, complemented
2#16837772C211yesmaximal, characteristic, complemented
3#16837743C211yesmaximal, characteristic, complemented
4#16837737C211yesmaximal, characteristic, complemented
5#16837706C211yesmaximal, characteristic, complemented
6#16837646C211yesmaximal, characteristic, complemented
7#16837629C211yesmaximal, characteristic, complemented
8#16837607C211yesmaximal, characteristic, complemented
9#16837540C211yesmaximal, characteristic, complemented
10#16837540C211yesmaximal, characteristic, complemented
11#16837502C211yesmaximal, characteristic, complemented
12#16837474C211yesmaximal, characteristic, complemented
13#16837410C211yesmaximal, characteristic, complemented
14C2×#14273650C211yesmaximal, characteristic, complemented
15C59×#553C211yesmaximal, characteristic
16C22×Dic118C2211yescharacteristic
17C22×Dic118C2211yescharacteristic
18C2×#11745670C2211yescharacteristic
19C2×#11745670C2211yescharacteristic
20C2×#11745670C2211yescharacteristic
21C2×#11745664C2211yescharacteristic
22C22×C59⋊C8C2211yescharacteristic
23#14273727C2211yescharacteristic
24#14273726—21no—
25#14273706C2211yescharacteristic
26#14273706C2211yescharacteristic
27#14273704—21no—
28#14273704—21no—
29C4×Dic118C2211yescharacteristic
30D4×Dic59—21no—
31#14273660C2211yescharacteristic
32#14273660C2211yescharacteristic
33#14273658C2211yescharacteristic
34C4⋊(C59⋊C8)C2211yescharacteristic
35#14273650C2211yescharacteristic
36#14273650C2211yescharacteristic
37#14273650C2211yescharacteristic
38#14273650C2211yescharacteristic
39#14273650C2211yescharacteristic
40#14273650C2211yescharacteristic
41#14273650C2211yescharacteristic
42#14273650C2211yescharacteristic
43#14273650C2211yescharacteristic
44#14273648C2211yescharacteristic
45C22⋊(C59⋊C8)C2211yescharacteristic
46C22⋊(C59⋊C8)C2211yescharacteristic
47#14273638C2211yescharacteristic
48#126×C59—21no—
49#125×C59C2211yescharacteristic
50#123×C59—21no—
51#121×C59—21no—
52#121×C59C2211yescharacteristic
53#121×C59C2211yescharacteristic
54C4×D4×C59—21no—
55C4×D4×C59C2211yescharacteristic
56C4×D4×C59C2211yescharacteristic
57#117×C59C2211yescharacteristic
58C2×C4⋊C4×C59C2211yescharacteristic
59C2×D4×C59—21no—
60C2×D4×C59—21no—
61C2×D4×C59D411yescharacteristic
62C2×D4×C59C2311yescharacteristic
63C22×C4×C59—21no—
64C22×C4×C59—21no—
65C22×C4×C59C2311yescharacteristic
66C22×C4×C59C2311yescharacteristic
67C22×Dic59—21no—
68C22×Dic59—21no—
69C2×Dic118—22no—
70C2×Dic118—22no—
71C2×Dic118—21no—
72C2×Dic118—21no—
73C2×Dic118—41no—
74C2×Dic118—41no—
75C2×Dic118C2311yescharacteristic
76C2×Dic118C2311yescharacteristic
77C2×Dic118C2311yescharacteristic
78C4⋊C4×C59—21no—
79C4⋊C4×C59—21no—
80C4⋊C4×C59—21no—
81C4⋊C4×C59D411yescharacteristic
82C4⋊C4×C59C2311yescharacteristic
83C4⋊C4×C59C2311yescharacteristic
84C4⋊C4×C59C2311yescharacteristic
85C22⋊C4×C59—21no—
86C22⋊C4×C59—21no—
87C22⋊C4×C59—21no—
88C22⋊C4×C59—21no—
89C22⋊C4×C59D411yescharacteristic
90C22⋊C4×C59D411yescharacteristic
91C42×C59—21no—
92C42×C59C2311yescharacteristic
93C22⋊Dic59—21no—
94C22⋊Dic59—21no—
95#11745670—22no—
96#11745670—41no—
97#11745670—41no—
98C4⋊Dic59—21no—
99C4⋊Dic59—21no—
100C4⋊Dic59C2311yescharacteristic
101Dic59⋊C4—21no—
102Dic59⋊C4—21no—
103Dic59⋊C4—21no—
104C4×Dic59—21no—
105#11745664—41no—
106C2×C59⋊C8—41no—
107C2×C59⋊C8C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110C2×C59⋊C8C2311yescharacteristic
111C23×C59—21no—
112C23×C59C2×D411yescharacteristic
113C23×C59C2×D411yescharacteristic
114D4×C59—22no—
115D4×C59—21no—
116D4×C59—21no—
117D4×C59—42no—
118D4×C59—81no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—81no—
127C2×C4×C59—81no—
128C2×C4×C59C2×D411yescharacteristic
129C2×C4×C59C2×D411yescharacteristic
130C2×C4×C59C2×D411yescharacteristic
131C2×C4×C59C2×D411yescharacteristic
132C2×C4×C59C2411yescharacteristic
133C2×Dic59—21no—
134C2×Dic59—21no—
135C2×Dic59—21no—
136C2×Dic59—21no—
137C2×Dic59—42no—
138C2×Dic59—42no—
139Dic118—21no—
140Dic118—21no—
141Dic118—21no—
142Dic118—21no—
143Dic118—21no—
144Dic118—42no—
145Dic118—42no—
146Dic118#4112yes—
147C59⋊C8—21no—
148C59⋊C8—21no—
149C59⋊C8—21no—
150C59⋊C8—21no—
151C22×C59—21no—
152C22×C59—21no—
153C22×C59—21no—
154C22×C59—21no—
155C22×C59—21no—
156C22×C59—41no—
157C22×C59—41no—
158C22×C59—41no—
159C22×C59#13712yes—
160C22×C59C22×D411yescharacteristic
161C4×C59—21no—
162C4×C59—21no—
163C4×C59—21no—
164C4×C59—21no—
165C4×C59—41no—
166C4×C59—41no—
167C4×C59—41no—
168C4×C59C2×#4111yescharacteristic
169C4×C59H(5,𝔽2)11yescharacteristic
170Dic59—22no—
171Dic59—41no—
172Dic59—41no—
173Dic59—41no—
174#3320—591nomaximal, Sylow
175C2×C59—22no—
176C2×C59—41no—
177C2×C59—81no—
178C2×C59#54611yescharacteristic
179C2×C59C2×#13711yescharacteristic
180C2×C59#57711yescharacteristic
181#553D5911yescharacteristic
182D4×Q8—591no—
183#491—591no—
184#485—591no—
185#484—591no—
186#479—591no—
187#468—591no—
188#465—591no—
189#461—591no—
190#448—591no—
191#448—591no—
192#440—591no—
193#435—591no—
194#419—591no—
195C2×#103—591no—
196C59#332011yescharacteristic, complemented, Sylow
197C22×Q8—591no—
198C22×Q8—591no—
199C2×SD16—591no—
200C2×SD16—591no—
201C2×SD16—591no—
202C2×M16—591no—
203C22×C8—591no—
204C4⋊Q8—591no—
205C4⋊Q8—1181no—
206#126—21no—
207#125C2×D5911yescharacteristic
208#123—21no—
209C22⋊Q8—591no—
210C22⋊Q8—591no—
211C22⋊Q8—1181no—
212C22⋊Q8—1181no—
213#121—21no—
214#121C2×D5911yescharacteristic
215#121C2×D5911yescharacteristic
216C4×Q8—591no—
217C4×D4—21no—
218C4×D4—1181no—
219C4×D4C2×D5911yescharacteristic
220C4×D4C2×D5911yescharacteristic
221#117C2×D5911yescharacteristic
222C2×C4⋊C4C2×D5911yescharacteristic
223#107—591no—
224#107—591no—
225#106—591no—
226C4⋊C8—591no—
227#103—591no—
228#103—591no—
229#103—591no—
230#103—591no—
231#103—591no—
232#103—591no—
233#103—591no—
234#103—591no—
235#103—591no—
236#102—591no—
237C22⋊C8—591no—
238C22⋊C8—591no—
239#97—591no—
240C2×Q8—591no—
241C2×Q8—591no—
242C2×Q8—591no—
243C2×Q8—1182no—
244C2×Q8—1182no—
245C2×Q8—1181no—
246C2×Q8—1181no—
247C2×Q8—2361no—
248C2×Q8—2361no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4C22⋊D5911yescharacteristic
252C2×D4C22×D5911yescharacteristic
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—1181no—
256C22×C4—1181no—
257C22×C4C22×D5911yescharacteristic
258C22×C4C22×D5911yescharacteristic
259SD16—1182no—
260SD16—2361no—
261SD16—2361no—
262M16—2361no—
263C2×C8—591no—
264C2×C8—591no—
265C2×C8—591no—
266C2×C8—591no—
267C2×C8—2361no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—591no—
272C4⋊C4—1181no—
273C4⋊C4—1181no—
274C4⋊C4—1181no—
275C4⋊C4—1181no—
276C4⋊C4—1181no—
277C4⋊C4C22⋊D5911yescharacteristic
278C4⋊C4C22×D5911yescharacteristic
279C4⋊C4C22×D5911yescharacteristic
280C4⋊C4C22×D5911yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—1181no—
286C22⋊C4—1181no—
287C22⋊C4C22⋊D5911yescharacteristic
288C22⋊C4C22⋊D5911yescharacteristic
289C42—21no—
290C42—1181no—
291C42C22×D5911yescharacteristic
292C23—21no—
293C23C2×C22⋊D5911yescharacteristic
294C23C2×C22⋊D5911yescharacteristic
295Q8—592no—
296Q8—1181no—
297Q8—1181no—
298Q8—1181no—
299Q8—1181no—
300Q8—1181no—
301Q8—2362no—
302Q8—2362no—
303D4—22no—
304D4—21no—
305D4—21no—
306D4—42no—
307D4—81no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—1181no—
318C2×C4—1181no—
319C2×C4—1181no—
320C2×C4—1181no—
321C2×C4—2362no—
322C2×C4—2362no—
323C2×C4C2×C22⋊D5911yescharacteristic
324C2×C4C2×C22⋊D5911yescharacteristic
325C2×C4C2×C22⋊D5911yescharacteristic
326C2×C4C2×C22⋊D5911yescharacteristic
327C2×C4C23×D5911yescharacteristic
328C8—1181no—
329C8—1181no—
330C8—1181no—
331C8—1181no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22#1427375712yes—
341C22C22×C22⋊D5911yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—1182no—
350C4—2361no—
351C4—2361no—
352C4—2361no—
353C4#41×D5911yescharacteristic
354C4#1427377311yescharacteristic
355C2—22no—
356C2—41no—
357C2—81no—
358C2#1683804011yescharacteristic
359C2C2×#1427375711yescharacteristic
360C2#1683821311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#553C2
socleC22×C59C22×D4
hypercenter#553D59
hypocenterC59#3320
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. D4×Dic118C2semidirect
2. #16837772C2semidirect
3. #16837743C2semidirect
4. #16837737C2semidirect
5. #16837706C2semidirect
6. #16837646C2semidirect
7. #16837629C2semidirect
8. #16837607C2semidirect
9. #16837540C2semidirect
10. #16837540C2semidirect
11. #16837502C2semidirect
12. #16837474C2semidirect
13. #16837410C2semidirect
14. C2×#14273650C2semidirect
196. C59#3320semidirect