Finite Group Databasebeta

← #21436272

Subgroups — #21436272

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
1#16838102C211yesmaximal, characteristic
2Q8×D236C211yesmaximal, characteristic, complemented
3#16837771C211yesmaximal, characteristic, complemented
4#16837745C211yesmaximal, characteristic, complemented
5#16837739C211yesmaximal, characteristic, complemented
6#16837709C211yesmaximal, characteristic, complemented
7#16837647C211yesmaximal, characteristic, complemented
8#16837630C211yesmaximal, characteristic, complemented
9#16837607C211yesmaximal, characteristic, complemented
10#16837539C211yesmaximal, characteristic, complemented
11#16837539C211yesmaximal, characteristic, complemented
12#16837475C211yesmaximal, characteristic, complemented
13#16837409C211yesmaximal, characteristic, complemented
14#103×D59C211yesmaximal, characteristic, complemented
15C59×#440C211yesmaximal, characteristic, complemented
16C2×Q8×D59C2211yescharacteristic
17C2×Q8×D59C2211yescharacteristic
18C2×#11745670C2211yescharacteristic
19C2×#11745670C2211yescharacteristic
20C2×#11745659C2211yescharacteristic
21C2×C8×D59C2211yescharacteristic
22#14273727—21no—
23#14273727C2211yescharacteristic
24#14273720—21no—
25#14273719C2211yescharacteristic
26#14273710—21no—
27#14273707—21no—
28#14273707—21no—
29#14273707C2211yescharacteristic
30#14273707C2211yescharacteristic
31#14273700—21no—
32#14273698C2211yescharacteristic
33#14273698C2211yescharacteristic
34C4×D236—21no—
35C4×D236C2211yescharacteristic
36C4×C22⋊D59—21no—
37#14273685C2211yescharacteristic
38C4⋊C4×D59C2211yescharacteristic
39#14273660C2211yescharacteristic
40#14273658C2211yescharacteristic
41C4⋊(C59⋊C8)C2211yescharacteristic
42#14273652C2211yescharacteristic
43#14273652C2211yescharacteristic
44#14273652C2211yescharacteristic
45#14273652C2211yescharacteristic
46#14273651C2211yescharacteristic
47#14273651C2211yescharacteristic
48#14273650C2211yescharacteristic
49#14273650C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51(C2×D59)⋊C8C2211yescharacteristic
52C2×SD16×C59C2211yescharacteristic
53C4×Q8×C59C2211yescharacteristic
54C4×D4×C59C2211yescharacteristic
55#107×C59C2211yescharacteristic
56#103×C59C2211yescharacteristic
57#102×C59C2211yescharacteristic
58#97×C59C2211yescharacteristic
59C2×Q8×C59C2311yescharacteristic
60C2×D4×C59C2311yescharacteristic
61C22×C4×C59—21no—
62C2×C22⋊D59—21no—
63C2×C22⋊D59—21no—
64Q8×D59—22no—
65Q8×D59—22no—
66Q8×D59—41no—
67Q8×D59—41no—
68C2×D236D411yescharacteristic
69C2×C4×D59—21no—
70C2×C4×D59—21no—
71C2×C4×D59—21no—
72C2×C4×D59C2311yescharacteristic
73C2×C4×D59C2311yescharacteristic
74C2×Dic118—21no—
75C2×Dic118—21no—
76C2×Dic118C2311yescharacteristic
77C2×Dic118C2311yescharacteristic
78SD16×C59—22no—
79C2×C8×C59C2311yescharacteristic
80C2×C8×C59C2311yescharacteristic
81C4⋊C4×C59—21no—
82C4⋊C4×C59C2311yescharacteristic
83C4⋊C4×C59C2311yescharacteristic
84C22⋊C4×C59—21no—
85C42×C59—21no—
86C42×C59C2311yescharacteristic
87C22⋊Dic59—21no—
88C22⋊Dic59—21no—
89#11745670—41no—
90#11745670—41no—
91(C2×D59)⋊C4—21no—
92(C2×D59)⋊C4—21no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4D411yescharacteristic
95(C2×D59)⋊C4D411yescharacteristic
96C4⋊Dic59—21no—
97C4⋊Dic59—21no—
98C4⋊Dic59—21no—
99C4⋊Dic59—21no—
100C4⋊Dic59D411yescharacteristic
101C4⋊Dic59C2311yescharacteristic
102C4⋊Dic59C2311yescharacteristic
103Dic59⋊C4—21no—
104Dic59⋊C4—21no—
105Dic59⋊C4—21no—
106C4×Dic59—21no—
107C2×C59⋊C8C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109#11745659—41no—
110C8×D59—41no—
111C23×C59—21no—
112C22×D59C2×D411yescharacteristic
113C22×D59C2×D411yescharacteristic
114Q8×C59—21no—
115Q8×C59#4112yes—
116D4×C59—21no—
117D4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—81no—
122C2×C4×C59C2×D411yescharacteristic
123C2×C4×C59C2×D411yescharacteristic
124C2×C4×C59C2411yescharacteristic
125C22⋊D59—42no—
126C22⋊D59—81no—
127C2×Dic59—21no—
128C2×Dic59—21no—
129C2×Dic59—21no—
130C2×Dic59—21no—
131C2×Dic59C2×D411yescharacteristic
132C2×Dic59C2×D411yescharacteristic
133D236—22no—
134C4×D59—21no—
135C4×D59—21no—
136C4×D59—21no—
137C4×D59—21no—
138C4×D59—42no—
139C4×D59—42no—
140C4×D59—81no—
141Dic118—21no—
142Dic118—21no—
143Dic118—21no—
144Dic118—21no—
145Dic118—42no—
146Dic118—42no—
147C8×C59—21no—
148C8×C59—21no—
149C59⋊C8—21no—
150C59⋊C8—21no—
151C22×C59—41no—
152C22×C59—41no—
153C22×C59—41no—
154C22×C59C22×D411yescharacteristic
155C2×D59—21no—
156C2×D59—21no—
157C2×D59—21no—
158C2×D59—21no—
159C2×D59—21no—
160C2×D59#13712yes—
161C4×C59—22no—
162C4×C59—21no—
163C4×C59—21no—
164C4×C59—41no—
165C4×C59—41no—
166C4×C59C2×#4111yescharacteristic
167C4×C59H(5,𝔽2)11yescharacteristic
168Dic59—21no—
169Dic59—21no—
170Dic59—41no—
171Dic59—41no—
172Dic59—41no—
173Dic59—41no—
174#3320—591nomaximal, Sylow
175C2×C59—81no—
176C2×C59#54611yescharacteristic
177C2×C59C2×#13711yescharacteristic
178C2×C59#57711yescharacteristic
179D59—22no—
180D59—41no—
181#553—591no—
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#440D5911yescharacteristic, complemented
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×SD16C2×D5911yescharacteristic
202C2×M16—591no—
203C22×C8—591no—
204C4⋊Q8—591no—
205C4⋊Q8—1181no—
206#126—1181no—
207#125—591no—
208#123—1181no—
209C22⋊Q8—591no—
210C22⋊Q8—591no—
211C22⋊Q8—1181no—
212C22⋊Q8—1181no—
213#121—591no—
214#121—591no—
215#121—1181no—
216C4×Q8C2×D5911yescharacteristic
217C4×D4—591no—
218C4×D4—1181no—
219C4×D4—1181no—
220C4×D4C2×D5911yescharacteristic
221#117—591no—
222C2×C4⋊C4—591no—
223#107—591no—
224#107C2×D5911yescharacteristic
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#103C2×D5911yescharacteristic
236#102C2×D5911yescharacteristic
237C22⋊C8—591no—
238C22⋊C8—591no—
239#97C2×D5911yescharacteristic
240C2×Q8—591no—
241C2×Q8—591no—
242C2×Q8—1181no—
243C2×Q8—1181no—
244C2×Q8—1182no—
245C2×Q8—1182no—
246C2×Q8—2361no—
247C2×Q8—2361no—
248C2×Q8C22×D5911yescharacteristic
249C2×D4—591no—
250C2×D4—1181no—
251C2×D4—1181no—
252C2×D4C22×D5911yescharacteristic
253C22×C4—21no—
254C22×C4—591no—
255C22×C4—591no—
256C22×C4—1181no—
257C22×C4—1181no—
258C22×C4—1181no—
259SD16—22no—
260SD16—2361no—
261SD16—2361no—
262M16—2361no—
263C2×C8—591no—
264C2×C8—591no—
265C2×C8—2361no—
266C2×C8C22×D5911yescharacteristic
267C2×C8C22×D5911yescharacteristic
268C4⋊C4—21no—
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⋊C4—1181no—
279C4⋊C4C22×D5911yescharacteristic
280C4⋊C4C22×D5911yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—591no—
283C22⋊C4—591no—
284C22⋊C4—1181no—
285C22⋊C4—1181no—
286C22⋊C4—1181no—
287C22⋊C4—1181no—
288C22⋊C4—1181no—
289C42—21no—
290C42—1181no—
291C42C22×D5911yescharacteristic
292C23—21no—
293C23—591no—
294C23—591no—
295Q8—21no—
296Q8—1181no—
297Q8—1181no—
298Q8—1181no—
299Q8—1181no—
300Q8—2362no—
301Q8—2362no—
302Q8#1174568512yes—
303D4—21no—
304D4—21no—
305D4—1182no—
306D4—4721no—
307D4—2362no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
312C2×C4—591no—
313C2×C4—591no—
314C2×C4—1181no—
315C2×C4—1181no—
316C2×C4—1181no—
317C2×C4—1181no—
318C2×C4—1181no—
319C2×C4—1181no—
320C2×C4—1181no—
321C2×C4—1181no—
322C2×C4—4721no—
323C2×C4—2362no—
324C2×C4—2362no—
325C2×C4D4×D5911yescharacteristic
326C2×C4D4×D5911yescharacteristic
327C2×C4C23×D5911yescharacteristic
328C8—21no—
329C8—21no—
330C8—1181no—
331C8—1181no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—592no—
336C22—1181no—
337C22—1181no—
338C22—1181no—
339C22—1181no—
340C22—1181no—
341C22C2×D4×D5911yescharacteristic
342C4—21no—
343C4—21no—
344C4—22no—
345C4—41no—
346C4—41no—
347C4—1181no—
348C4—1181no—
349C4—2361no—
350C4—2361no—
351C4—2361no—
352C4—2361no—
353C4C2×#1174568511yescharacteristic
354C4#1427377311yescharacteristic
355C2—81no—
356C2—1182no—
357C2—2361no—
358C2#1683804811yescharacteristic
359C2#137×D5911yescharacteristic
360C2#1683821211yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#440C2
socleC22×C59C22×D4
hypercenter#440D59
hypocenterC59#3320
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. Q8×D236C2semidirect
3. #16837771C2semidirect
4. #16837745C2semidirect
5. #16837739C2semidirect
6. #16837709C2semidirect
7. #16837647C2semidirect
8. #16837630C2semidirect
9. #16837607C2semidirect
10. #16837539C2semidirect
11. #16837539C2semidirect
12. #16837475C2semidirect
13. #16837409C2semidirect
14. #103×D59C2semidirect
15. C59×#440C2semidirect
192. #440D59semidirect
196. C59#3320semidirect