Finite Group Databasebeta

← #21436383

Subgroups — #21436383

Order 7552.

386 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
1#16838116C211yesmaximal, characteristic
2Q8×C22⋊D59C211yesmaximal, characteristic, complemented
3#16837751C211yesmaximal, characteristic, complemented
4#16837744C211yesmaximal, characteristic, complemented
5#16837741C211yesmaximal, characteristic, complemented
6#16837695C211yesmaximal, characteristic, complemented
7#16837646C211yesmaximal, characteristic, complemented
8#16837645C211yesmaximal, characteristic, complemented
9#16837605C211yesmaximal, characteristic, complemented
10#16837539C211yesmaximal, characteristic, complemented
11SD16×Dic59C211yesmaximal, characteristic, complemented
12#16837477C211yesmaximal, characteristic, complemented
13#16837411C211yesmaximal, characteristic, complemented
14#16837409C211yesmaximal, characteristic, complemented
15C59×#448C211yesmaximal, characteristic, complemented
16C2×Q8×D59C2211yescharacteristic
17C2×#11745670C2211yescharacteristic
18C2×#11745664C2211yescharacteristic
19C2×#11745659C2211yescharacteristic
20#14273726C2211yescharacteristic
21#14273725—21no—
22#14273725C2211yescharacteristic
23#14273714—21no—
24#14273713—21no—
25#14273706—21no—
26#14273706C2211yescharacteristic
27#14273703—21no—
28#14273703C2211yescharacteristic
29#14273699—21no—
30#14273698C2211yescharacteristic
31Q8×Dic59C2211yescharacteristic
32D4×Dic59C2211yescharacteristic
33C4×C22⋊D59—21no—
34C4×C22⋊D59C2211yescharacteristic
35#14273686C2211yescharacteristic
36#14273685C2211yescharacteristic
37#14273683—21no—
38#14273661C2211yescharacteristic
39#14273660C2211yescharacteristic
40#14273659C2211yescharacteristic
41Dic59⋊C8C2211yescharacteristic
42#14273652C2211yescharacteristic
43#14273652C2211yescharacteristic
44#14273651C2211yescharacteristic
45#14273651C2211yescharacteristic
46#14273651C2211yescharacteristic
47#14273651C2211yescharacteristic
48#14273650C2211yescharacteristic
49#14273648C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51C8×Dic59C2211yescharacteristic
52C22×Q8×C59C2211yescharacteristic
53C2×SD16×C59C2211yescharacteristic
54C2×SD16×C59C2211yescharacteristic
55#121×C59C2211yescharacteristic
56#103×C59C2211yescharacteristic
57#103×C59C2211yescharacteristic
58C22⋊C8×C59C2211yescharacteristic
59C2×Q8×C59—21no—
60C2×Q8×C59—22no—
61C2×Q8×C59—41no—
62C2×Q8×C59C2311yescharacteristic
63C2×Q8×C59C2311yescharacteristic
64C2×D4×C59—21no—
65C2×D4×C59C2311yescharacteristic
66C22×C4×C59—21no—
67C22×C4×C59C2311yescharacteristic
68C2×C22⋊D59—21no—
69C2×C22⋊D59D411yescharacteristic
70C22×Dic59—21no—
71Q8×D59—22no—
72Q8×D59—41no—
73C2×C4×D59—21no—
74C2×C4×D59C2311yescharacteristic
75C2×Dic118—21no—
76C2×Dic118—21no—
77C2×Dic118C2311yescharacteristic
78SD16×C59—22no—
79SD16×C59—41no—
80C2×C8×C59C2311yescharacteristic
81C2×C8×C59C2311yescharacteristic
82C4⋊C4×C59C2311yescharacteristic
83C22⋊C4×C59—21no—
84C22⋊Dic59—21no—
85C22⋊Dic59—21no—
86C22⋊Dic59—21no—
87C22⋊Dic59—21no—
88C22⋊Dic59D411yescharacteristic
89#11745670—41no—
90(C2×D59)⋊C4—21no—
91(C2×D59)⋊C4—21no—
92(C2×D59)⋊C4D411yescharacteristic
93C4⋊Dic59—21no—
94C4⋊Dic59C2311yescharacteristic
95C4⋊Dic59C2311yescharacteristic
96C4⋊Dic59C2311yescharacteristic
97Dic59⋊C4—21no—
98Dic59⋊C4—21no—
99Dic59⋊C4—21no—
100Dic59⋊C4—21no—
101Dic59⋊C4—21no—
102Dic59⋊C4D411yescharacteristic
103C4×Dic59—21no—
104C4×Dic59—21no—
105C4×Dic59—21no—
106C4×Dic59C2311yescharacteristic
107#11745664—41no—
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110#11745659—41no—
111C23×C59—21no—
112C23×C59C2×D411yescharacteristic
113C22×D59C2×D411yescharacteristic
114Q8×C59—21no—
115Q8×C59—21no—
116Q8×C59—21no—
117Q8×C59—42no—
118Q8×C59#4112yes—
119D4×C59—21no—
120D4×C59—21no—
121D4×C59—81no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—42no—
128C2×C4×C59C2×D411yescharacteristic
129C2×C4×C59C2411yescharacteristic
130C22⋊D59—22no—
131C22⋊D59—81no—
132C2×Dic59—21no—
133C2×Dic59—21no—
134C2×Dic59—21no—
135C2×Dic59—21no—
136C2×Dic59—42no—
137C2×Dic59C2×D411yescharacteristic
138C2×Dic59C2×D411yescharacteristic
139C2×Dic59C2×D411yescharacteristic
140C4×D59—21no—
141C4×D59—21no—
142C4×D59—42no—
143Dic118—21no—
144Dic118—21no—
145Dic118—42no—
146Dic118—81no—
147C8×C59—21no—
148C8×C59—21no—
149C59⋊C8—21no—
150C59⋊C8—21no—
151C22×C59—21no—
152C22×C59—21no—
153C22×C59—21no—
154C22×C59—41no—
155C22×C59—41no—
156C22×C59—41no—
157C22×C59C22×D411yescharacteristic
158C2×D59—21no—
159C2×D59—21no—
160C2×D59—21no—
161C4×C59—22no—
162C4×C59—21no—
163C4×C59—41no—
164C4×C59—41no—
165C4×C59C2×#4111yescharacteristic
166C4×C59H(5,𝔽2)11yescharacteristic
167Dic59—21no—
168Dic59—21no—
169Dic59—41no—
170Dic59—41no—
171Dic59—41no—
172Dic59—41no—
173Dic59#13712yes—
174#3329—591nomaximal, Sylow
175C2×C59—41no—
176C2×C59—81no—
177C2×C59#54611yescharacteristic
178C2×C59C2×#13711yescharacteristic
179C2×C59#57711yescharacteristic
180D59—41no—
181#555—591no—
182D4×Q8—591no—
183#487—591no—
184#485—591no—
185#485—591no—
186#477—591no—
187#468—591no—
188#468—591no—
189#461—591no—
190#448—591no—
191#448D5911yescharacteristic, complemented
192C4×SD16—591no—
193#436—591no—
194#419—591no—
195#419—591no—
196C59#332911yescharacteristic, complemented, Sylow
197C22×Q8—591no—
198C22×Q8C2×D5911yescharacteristic
199C2×SD16—591no—
200C2×SD16C2×D5911yescharacteristic
201C2×SD16C2×D5911yescharacteristic
202C2×M16—591no—
203C2×M16—591no—
204C4⋊Q8—591no—
205C4⋊Q8—591no—
206C4⋊Q8—1181no—
207#124—1181no—
208#124—1181no—
209C22⋊Q8—591no—
210C22⋊Q8—591no—
211C22⋊Q8—1181no—
212C22⋊Q8—1181no—
213#121—591no—
214#121—1181no—
215#121C2×D5911yescharacteristic
216C4×Q8—591no—
217C4×D4—591no—
218C4×D4—591no—
219C4×D4—1181no—
220#117—591no—
221#117—591no—
222#117—1181no—
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#103C2×D5911yescharacteristic
235#103C2×D5911yescharacteristic
236#102—591no—
237C22⋊C8—591no—
238C22⋊C8C2×D5911yescharacteristic
239C4×C8—591no—
240C2×Q8—21no—
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8—591no—
244C2×Q8—1181no—
245C2×Q8—1181no—
246C2×Q8—1182no—
247C2×Q8—2361no—
248C2×Q8C22×D5911yescharacteristic
249C2×Q8C22×D5911yescharacteristic
250C2×D4—21no—
251C2×D4—591no—
252C2×D4—1181no—
253C2×D4C22×D5911yescharacteristic
254C22×C4—21no—
255C22×C4—591no—
256C22×C4—1181no—
257C22×C4—1181no—
258C22×C4C22×D5911yescharacteristic
259SD16—22no—
260SD16—41no—
261SD16—2361no—
262M16—2361no—
263M16—2361no—
264C2×C8—591no—
265C2×C8—591no—
266C2×C8C22×D5911yescharacteristic
267C2×C8C22×D5911yescharacteristic
268C4⋊C4—591no—
269C4⋊C4—591no—
270C4⋊C4—591no—
271C4⋊C4—591no—
272C4⋊C4—1181no—
273C4⋊C4—1181no—
274C4⋊C4—1181no—
275C4⋊C4—1181no—
276C4⋊C4—1181no—
277C4⋊C4—1181no—
278C4⋊C4C22×D5911yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—591no—
281C22⋊C4—591no—
282C22⋊C4—1181no—
283C22⋊C4—1181no—
284C22⋊C4—1181no—
285C22⋊C4—1181no—
286C22⋊C4—1181no—
287C22⋊C4—1181no—
288C42—591no—
289C42—1181no—
290C42—1181no—
291C42—1181no—
292C23—21no—
293C23—591no—
294C23D4×D5911yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—42no—
299Q8—1181no—
300Q8—1181no—
301Q8—4721no—
302Q8—2362no—
303Q8#1174568712yes—
304D4—21no—
305D4—21no—
306D4—81no—
307D4—1182no—
308D4—4721no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—591no—
316C2×C4—591no—
317C2×C4—591no—
318C2×C4—1181no—
319C2×C4—1181no—
320C2×C4—1181no—
321C2×C4—1181no—
322C2×C4—1181no—
323C2×C4—1181no—
324C2×C4—2362no—
325C2×C4—2362no—
326C2×C4D4×D5911yescharacteristic
327C2×C4C23×D5911yescharacteristic
328C8—21no—
329C8—21no—
330C8—1181no—
331C8—1181no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—1181no—
339C22—1181no—
340C22—1181no—
341C22C2×D4×D5911yescharacteristic
342C4—21no—
343C4—22no—
344C4—41no—
345C4—41no—
346C4—592no—
347C4—1181no—
348C4—1181no—
349C4—2361no—
350C4—2361no—
351C4—2361no—
352C4—2361no—
353C4C2×#1174568711yescharacteristic
354C4#1427377211yescharacteristic
355C2—41no—
356C2—81no—
357C2—2361no—
358C2#1683803911yescharacteristic
359C2#137×D5911yescharacteristic
360C2#1683820811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#448C2
socleC22×C59C22×D4
hypercenter#448D59
hypocenterC59#3329
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
2. Q8×C22⋊D59C2semidirect
3. #16837751C2semidirect
4. #16837744C2semidirect
5. #16837741C2semidirect
6. #16837695C2semidirect
7. #16837646C2semidirect
8. #16837645C2semidirect
9. #16837605C2semidirect
10. #16837539C2semidirect
11. SD16×Dic59C2semidirect
12. #16837477C2semidirect
13. #16837411C2semidirect
14. #16837409C2semidirect
15. C59×#448C2semidirect
191. #448D59semidirect
196. C59#3329semidirect