Finite Group Databasebeta

← #21436151

Subgroups — #21436151

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#16838094C211yesmaximal, characteristic
2Q8×C22⋊D59C211yesmaximal, characteristic
3#16837769C211yesmaximal, characteristic, complemented
4#16837741C211yesmaximal, characteristic, complemented
5#16837733C211yesmaximal, characteristic, complemented
6#16837707C211yesmaximal, characteristic, complemented
7#16837657C211yesmaximal, characteristic, complemented
8#16837641C211yesmaximal, characteristic, complemented
9#16837610C211yesmaximal, characteristic, complemented
10#16837556C211yesmaximal, characteristic, complemented
11#16837509C211yesmaximal, characteristic, complemented
12#16837470C211yesmaximal, characteristic
13#16837409C211yesmaximal, characteristic, complemented
14C2×#14273651C211yesmaximal, characteristic, complemented
15C59×#451C211yesmaximal, characteristic, complemented
16C2×Q8×D59C2211yescharacteristic
17C2×#11745672C2211yescharacteristic
18C2×#11745659C2211yescharacteristic
19C22×C59⋊C8C2211yescharacteristic
20#14273725—21no—
21#14273725C2211yescharacteristic
22#14273722—21no—
23#14273718—21no—
24#14273718C2211yescharacteristic
25#14273711—21no—
26#14273706—21no—
27#14273706C2211yescharacteristic
28#14273703—21no—
29#14273703C2211yescharacteristic
30#14273703C2211yescharacteristic
31Q8×Dic59C2211yescharacteristic
32Q8×Dic59C2211yescharacteristic
33C4×C22⋊D59—21no—
34C4×C22⋊D59C2211yescharacteristic
35#14273685C2211yescharacteristic
36#14273683—21no—
37C2×C4⋊Dic59C2211yescharacteristic
38#14273660C2211yescharacteristic
39#14273659C2211yescharacteristic
40#14273659C2211yescharacteristic
41Dic59⋊C8C2211yescharacteristic
42#14273652C2211yescharacteristic
43#14273652C2211yescharacteristic
44#14273651C2211yescharacteristic
45#14273651C2211yescharacteristic
46#14273651C2211yescharacteristic
47#14273651C2211yescharacteristic
48#14273651C2211yescharacteristic
49#14273650C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51#14273637C2211yescharacteristic
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×D59C2311yescharacteristic
73C2×Dic118—21no—
74C2×Dic118C2311yescharacteristic
75Q16×C59—22no—
76Q16×C59—41no—
77C2×C8×C59C2311yescharacteristic
78C2×C8×C59C2311yescharacteristic
79C4⋊C4×C59—21no—
80C4⋊C4×C59C2311yescharacteristic
81C22⋊C4×C59—21no—
82C22⋊Dic59—21no—
83C22⋊Dic59D411yescharacteristic
84#11745672—41no—
85(C2×D59)⋊C4—21no—
86(C2×D59)⋊C4—21no—
87(C2×D59)⋊C4—21no—
88(C2×D59)⋊C4D411yescharacteristic
89C4⋊Dic59—21no—
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⋊C4D411yescharacteristic
103C4×Dic59—21no—
104C4×Dic59—21no—
105C4×Dic59—21no—
106C4×Dic59C2311yescharacteristic
107C2×C59⋊C8—41no—
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110#11745659—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⋊D59—22no—
130C2×Dic59—21no—
131C2×Dic59—21no—
132C2×Dic59—21no—
133C2×Dic59—21no—
134C2×Dic59—42no—
135C2×Dic59C2×D411yescharacteristic
136C2×Dic59C2×D411yescharacteristic
137C2×Dic59C2×D411yescharacteristic
138C4×D59—21no—
139C4×D59—21no—
140C4×D59—42no—
141Dic118—21no—
142Dic118—21no—
143Dic118—42no—
144C8×C59—21no—
145C8×C59—21no—
146C59⋊C8—21no—
147C59⋊C8—21no—
148C22×C59—21no—
149C22×C59—21no—
150C22×C59#13712yes—
151C22×C59C22×D411yescharacteristic
152C2×D59—21no—
153C2×D59—21no—
154C2×D59—21no—
155C4×C59—22no—
156C4×C59—21no—
157C4×C59—41no—
158C4×C59—41no—
159C4×C59—41no—
160C4×C59C2×#4111yescharacteristic
161C4×C59H(5,𝔽2)11yescharacteristic
162Dic59—21no—
163Dic59—21no—
164Dic59—21no—
165Dic59—41no—
166Dic59—41no—
167Dic59—41no—
168Dic59—41no—
169#3312—591nomaximal, Sylow
170C2×C59—22no—
171C2×C59#54611yescharacteristic
172C2×C59C2×#13711yescharacteristic
173C2×C59#57811yescharacteristic
174D59—41no—
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#451D5911yescharacteristic, complemented
186#441—591no—
187#435—591no—
188#419—591no—
189C2×#103—591no—
190C59#331211yescharacteristic, complemented, Sylow
191C22×Q8—591no—
192C22×Q8C2×D5911yescharacteristic
193C2×Q16—591no—
194C2×Q16C2×D5911yescharacteristic
195C2×Q16C2×D5911yescharacteristic
196C2×M16—591no—
197C22×C8—591no—
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—1181no—
208C22⋊Q8—1181no—
209C22⋊Q8C2×D5911yescharacteristic
210C4×Q8—591no—
211C4×Q8—591no—
212C4×D4—591no—
213C4×D4—1181no—
214#117—591no—
215#117—1181no—
216C2×C4⋊C4—591no—
217#107—591no—
218#106—591no—
219#106—591no—
220C4⋊C8—591no—
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#103C2×D5911yescharacteristic
230#103C2×D5911yescharacteristic
231C22⋊C8—591no—
232C22⋊C8C2×D5911yescharacteristic
233#97—591no—
234C2×Q8—21no—
235C2×Q8—22no—
236C2×Q8—41no—
237C2×Q8—591no—
238C2×Q8—1181no—
239C2×Q8—1182no—
240C2×Q8—2361no—
241C2×Q8C22×D5911yescharacteristic
242C2×Q8C22×D5911yescharacteristic
243C2×Q8C22×D5911yescharacteristic
244C2×D4—591no—
245C22×C4—21no—
246C22×C4—591no—
247C22×C4—1181no—
248C22×C4—1181no—
249C22×C4C22×D5911yescharacteristic
250Q16—22no—
251Q16—41no—
252Q16—2361no—
253M16—2361no—
254C2×C8—591no—
255C2×C8—591no—
256C2×C8—2361no—
257C2×C8C22×D5911yescharacteristic
258C2×C8C22×D5911yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—591no—
261C4⋊C4—591no—
262C4⋊C4—591no—
263C4⋊C4—591no—
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⋊C4C22×D5911yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—591no—
277C22⋊C4—591no—
278C22⋊C4—1181no—
279C22⋊C4—1181no—
280C22⋊C4—1181no—
281C22⋊C4—1181no—
282C42—591no—
283C42—1181no—
284C42—1181no—
285C42—1181no—
286C23—591no—
287C23D4×D5911yescharacteristic
288Q8—21no—
289Q8—21no—
290Q8—21no—
291Q8—21no—
292Q8—21no—
293Q8—42no—
294Q8—1181no—
295Q8—1181no—
296Q8—2362no—
297Q8#1174568712yes—
298D4—1182no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—42no—
306C2×C4—591no—
307C2×C4—591no—
308C2×C4—591no—
309C2×C4—1181no—
310C2×C4—1181no—
311C2×C4—1181no—
312C2×C4—1181no—
313C2×C4—1181no—
314C2×C4—1181no—
315C2×C4—2362no—
316C2×C4—2362no—
317C2×C4D4×D5911yescharacteristic
318C2×C4C23×D5911yescharacteristic
319C8—21no—
320C8—21no—
321C8—1181no—
322C8—1181no—
323C22—21no—
324C22—21no—
325C22—1181no—
326C22—1181no—
327C22—1181no—
328C22#1427375912yes—
329C22C2×D4×D5911yescharacteristic
330C4—21no—
331C4—22no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—1181no—
336C4—1181no—
337C4—1181no—
338C4—2361no—
339C4—2361no—
340C4—2361no—
341C4—2361no—
342C4C2×#1174568711yescharacteristic
343C4#1427377211yescharacteristic
344C2—22no—
345C2—2361no—
346C2#1683803911yescharacteristic
347C2C2×#1427375911yescharacteristic
348C2#1683821811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#451C2
socleC22×C59C22×D4
hypercenter#451D59
hypocenterC59#3312
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. #16837769C2semidirect
4. #16837741C2semidirect
5. #16837733C2semidirect
6. #16837707C2semidirect
7. #16837657C2semidirect
8. #16837641C2semidirect
9. #16837610C2semidirect
10. #16837556C2semidirect
11. #16837509C2semidirect
13. #16837409C2semidirect
14. C2×#14273651C2semidirect
15. C59×#451C2semidirect
185. #451D59semidirect
190. C59#3312semidirect