Finite Group Databasebeta

← #21435965

Subgroups — #21435965

Order 7552.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838110C211yesmaximal, characteristic
2Q8×C22⋊D59C211yesmaximal, characteristic
3#16837751C211yesmaximal, characteristic, complemented
4#16837738C211yesmaximal, characteristic, complemented
5#16837736C211yesmaximal, characteristic, complemented
6#16837695C211yesmaximal, characteristic, complemented
7#16837641C211yesmaximal, characteristic, complemented
8#16837640C211yesmaximal, characteristic, complemented
9#16837610C211yesmaximal, characteristic, complemented
10#16837556C211yesmaximal, characteristic, complemented
11Q16×Dic59C211yesmaximal, characteristic, complemented
12(C22⋊D59)⋊C8C211yesmaximal, characteristic
13C2×#14273651C211yesmaximal, characteristic, complemented
14#103×D59C211yesmaximal, characteristic, complemented
15C59×#451C211yesmaximal, characteristic, complemented
16C2×Q8×D59C2211yescharacteristic
17C2×#11745672C2211yescharacteristic
18C22×C59⋊C8C2211yescharacteristic
19C2×C8×D59C2211yescharacteristic
20#14273726C2211yescharacteristic
21#14273725—21no—
22#14273725C2211yescharacteristic
23#14273717—21no—
24#14273707—21no—
25#14273706—21no—
26#14273706C2211yescharacteristic
27#14273704—21no—
28#14273703—21no—
29#14273703C2211yescharacteristic
30#14273703C2211yescharacteristic
31Q8×Dic59C2211yescharacteristic
32Q8×Dic59C2211yescharacteristic
33C4×C22⋊D59—21no—
34C4×C22⋊D59C2211yescharacteristic
35(C22⋊D59)⋊C4—21no—
36C2×C4⋊Dic59C2211yescharacteristic
37C4⋊C4×D59C2211yescharacteristic
38#14273661C2211yescharacteristic
39#14273661C2211yescharacteristic
40#14273660C2211yescharacteristic
41Dic59⋊C8C2211yescharacteristic
42#14273652C2211yescharacteristic
43#14273652C2211yescharacteristic
44#14273651C2211yescharacteristic
45#14273651C2211yescharacteristic
46#14273651C2211yescharacteristic
47#14273651C2211yescharacteristic
48#14273651C2211yescharacteristic
49#14273650C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51C8×Dic59C2211yescharacteristic
52C22×Q8×C59C2211yescharacteristic
53C2×Q16×C59C2211yescharacteristic
54C2×Q16×C59C2211yescharacteristic
55C22⋊Q8×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×Q8×C59C2311yescharacteristic
65C22×C4×C59—21no—
66C22×C4×C59C2311yescharacteristic
67C2×C22⋊D59D411yescharacteristic
68C22×Dic59—21no—
69Q8×D59—22no—
70Q8×D59—41no—
71C2×C4×D59—21no—
72C2×C4×D59—21no—
73C2×C4×D59C2311yescharacteristic
74C2×Dic118—21no—
75C2×Dic118—21no—
76C2×Dic118C2311yescharacteristic
77Q16×C59—22no—
78Q16×C59—41no—
79C2×C8×C59C2311yescharacteristic
80C2×C8×C59C2311yescharacteristic
81C4⋊C4×C59—21no—
82C4⋊C4×C59C2311yescharacteristic
83C22⋊C4×C59—21no—
84C22⋊Dic59—21no—
85C22⋊Dic59D411yescharacteristic
86#11745672—41no—
87(C2×D59)⋊C4—21no—
88(C2×D59)⋊C4—21no—
89(C2×D59)⋊C4D411yescharacteristic
90C4⋊Dic59—21no—
91C4⋊Dic59—21no—
92C4⋊Dic59—21no—
93C4⋊Dic59C2311yescharacteristic
94C4⋊Dic59C2311yescharacteristic
95C4⋊Dic59C2311yescharacteristic
96Dic59⋊C4—21no—
97Dic59⋊C4—21no—
98Dic59⋊C4—21no—
99Dic59⋊C4—21no—
100Dic59⋊C4—21no—
101Dic59⋊C4—21no—
102Dic59⋊C4—21no—
103Dic59⋊C4D411yescharacteristic
104C4×Dic59—21no—
105C4×Dic59—21no—
106C4×Dic59C2311yescharacteristic
107C2×C59⋊C8—41no—
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110C8×D59—41no—
111C23×C59C2×D411yescharacteristic
112C22×D59C2×D411yescharacteristic
113Q8×C59—21no—
114Q8×C59—21no—
115Q8×C59—21no—
116Q8×C59—21no—
117Q8×C59—21no—
118Q8×C59—42no—
119Q8×C59#4112yes—
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—42no—
127C2×C4×C59C2×D411yescharacteristic
128C2×C4×C59C2411yescharacteristic
129C22⋊D59Q1614yescomplemented
130C2×Dic59—21no—
131C2×Dic59—21no—
132C2×Dic59—21no—
133C2×Dic59—21no—
134C2×Dic59—81no—
135C2×Dic59C2×D411yescharacteristic
136C2×Dic59C2×D411yescharacteristic
137C2×Dic59C2×D411yescharacteristic
138C4×D59—21no—
139C4×D59—21no—
140C4×D59—42no—
141C4×D59—81no—
142Dic118—21no—
143Dic118—21no—
144Dic118—42no—
145Dic118—81no—
146C8×C59—21no—
147C8×C59—21no—
148C59⋊C8—21no—
149C59⋊C8—21no—
150C22×C59—21no—
151C22×C59—21no—
152C22×C59C2×Q1612yes—
153C22×C59C22×D411yescharacteristic
154C2×D59—21no—
155C2×D59—21no—
156C2×D59C2×Q1612yes—
157C4×C59—22no—
158C4×C59—21no—
159C4×C59—41no—
160C4×C59—41no—
161C4×C59—41no—
162C4×C59C2×#4111yescharacteristic
163C4×C59H(5,𝔽2)11yescharacteristic
164Dic59—21no—
165Dic59—21no—
166Dic59—41no—
167Dic59—41no—
168Dic59—41no—
169Dic59—41no—
170Dic59C2×Q1612yes—
171#3299—591nomaximal, Sylow
172C2×C59—22no—
173C2×C59#54611yescharacteristic
174C2×C59C22×Q1611yescharacteristic
175C2×C59#57711yescharacteristic
176D59—22no—
177#554—591no—
178D4×Q8—591no—
179#487—591no—
180#484—591no—
181#484—591no—
182#477—591no—
183#467—591no—
184#467—591no—
185#462—591no—
186#451—591no—
187#451D5911yescharacteristic, complemented
188C4×Q16—591no—
189C8×D4—591no—
190C2×#103—591no—
191C2×#103—591no—
192C59#329911yescharacteristic, complemented, Sylow
193C22×Q8—591no—
194C22×Q8C2×D5911yescharacteristic
195C2×Q16—591no—
196C2×Q16C2×D5911yescharacteristic
197C2×Q16C2×D5911yescharacteristic
198C22×C8—591no—
199C22×C8—591no—
200C4⋊Q8—591no—
201C4⋊Q8—591no—
202C4⋊Q8—1181no—
203#125—1181no—
204C22⋊Q8—591no—
205C22⋊Q8—591no—
206C22⋊Q8—591no—
207C22⋊Q8—1181no—
208C22⋊Q8—1181no—
209C22⋊Q8—1181no—
210C22⋊Q8—1181no—
211C22⋊Q8C2×D5911yescharacteristic
212C4×Q8—591no—
213C4×Q8—591no—
214C4×D4—591no—
215C4×D4—1181no—
216C4×D4—1181no—
217C2×C4⋊C4—591no—
218C2×C4⋊C4—591no—
219#107—591no—
220#107—591no—
221#107—591no—
222C4⋊C8—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—
231#103C2×D5911yescharacteristic
232#103C2×D5911yescharacteristic
233C22⋊C8—591no—
234C22⋊C8C2×D5911yescharacteristic
235C4×C8—591no—
236C2×Q8—21no—
237C2×Q8—22no—
238C2×Q8—41no—
239C2×Q8—591no—
240C2×Q8—1181no—
241C2×Q8—1181no—
242C2×Q8—1182no—
243C2×Q8—2361no—
244C2×Q8C22×D5911yescharacteristic
245C2×Q8C22×D5911yescharacteristic
246C2×Q8C22×D5911yescharacteristic
247C2×D4—591no—
248C22×C4—21no—
249C22×C4—591no—
250C22×C4—1181no—
251C22×C4—1181no—
252C22×C4—1181no—
253C22×C4C22×D5911yescharacteristic
254Q16—22no—
255Q16—41no—
256Q16—2361no—
257C2×C8—591no—
258C2×C8—591no—
259C2×C8—2361no—
260C2×C8—2361no—
261C2×C8C22×D5911yescharacteristic
262C2×C8C22×D5911yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—591no—
265C4⋊C4—591no—
266C4⋊C4—591no—
267C4⋊C4—591no—
268C4⋊C4—1181no—
269C4⋊C4—1181no—
270C4⋊C4—1181no—
271C4⋊C4—1181no—
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—
285C42—591no—
286C42—1181no—
287C42—1181no—
288C23—591no—
289C23D4×D5911yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—21no—
293Q8—21no—
294Q8—21no—
295Q8—42no—
296Q8—1181no—
297Q8—1181no—
298Q8—4721no—
299Q8—2362no—
300Q8#1174568712yes—
301D4—594no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—42no—
309C2×C4—591no—
310C2×C4—591no—
311C2×C4—591no—
312C2×C4—1181no—
313C2×C4—1181no—
314C2×C4—1181no—
315C2×C4—1181no—
316C2×C4—1181no—
317C2×C4—1181no—
318C2×C4—4721no—
319C2×C4—4721no—
320C2×C4—2362no—
321C2×C4D4×D5911yescharacteristic
322C2×C4C23×D5911yescharacteristic
323C8—21no—
324C8—21no—
325C8—1181no—
326C8—1181no—
327C22—21no—
328C22—21no—
329C22—592no—
330C22—1181no—
331C22—1181no—
332C22Q16×D5912yes—
333C22C2×D4×D5911yescharacteristic
334C4—21no—
335C4—22no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—592no—
340C4—1181no—
341C4—1181no—
342C4—2361no—
343C4—2361no—
344C4—2361no—
345C4—2361no—
346C4C2×#1174568711yescharacteristic
347C4#1427377211yescharacteristic
348C2—22no—
349C2—1182no—
350C2#1683803911yescharacteristic
351C2C2×Q16×D5911yescharacteristic
352C2#1683821111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#451C2
socleC22×C59C22×D4
hypercenter#451D59
hypocenterC59#3299
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
3. #16837751C2semidirect
4. #16837738C2semidirect
5. #16837736C2semidirect
6. #16837695C2semidirect
7. #16837641C2semidirect
8. #16837640C2semidirect
9. #16837610C2semidirect
10. #16837556C2semidirect
11. Q16×Dic59C2semidirect
13. C2×#14273651C2semidirect
14. #103×D59C2semidirect
15. C59×#451C2semidirect
129. C22⋊D59Q16semidirect
187. #451D59semidirect
192. C59#3299semidirect