Finite Group Databasebeta

← #21436207

Subgroups — #21436207

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#16838109C211yesmaximal, characteristic, complemented
2#16837761C211yesmaximal, characteristic, complemented
3#16837730C211yesmaximal, characteristic, complemented
4#16837718C211yesmaximal, characteristic, complemented
5#16837687C211yesmaximal, characteristic, complemented
6#16837658C211yesmaximal, characteristic, complemented
7#16837629C211yesmaximal, characteristic, complemented
8#16837621C211yesmaximal, characteristic, complemented
9#16837564C211yesmaximal, characteristic, complemented
10#16837558C211yesmaximal, characteristic, complemented
11#16837507C211yesmaximal, characteristic, complemented
12#16837474C211yesmaximal, characteristic, complemented
13#16837403C211yesmaximal, characteristic, complemented
14C2×#14273651C211yesmaximal, characteristic, complemented
15C59×#548C211yesmaximal, characteristic
16C2×#11745672C2211yescharacteristic
17C2×#11745672C2211yescharacteristic
18C2×#11745670C2211yescharacteristic
19C2×#11745664C2211yescharacteristic
20C22×C59⋊C8C2211yescharacteristic
21#14273727C2211yescharacteristic
22#14273718—21no—
23#14273706C2211yescharacteristic
24#14273706C2211yescharacteristic
25#14273704—21no—
26#14273704—21no—
27C4×Dic118C2211yescharacteristic
28D4×Dic59—21no—
29C2×C4⋊Dic59C2211yescharacteristic
30C2×C4⋊Dic59C2211yescharacteristic
31#14273658C2211yescharacteristic
32#14273658C2211yescharacteristic
33#14273658C2211yescharacteristic
34C4⋊(C59⋊C8)C2211yescharacteristic
35#14273651C2211yescharacteristic
36#14273651C2211yescharacteristic
37#14273651C2211yescharacteristic
38#14273651C2211yescharacteristic
39#14273651C2211yescharacteristic
40#14273651C2211yescharacteristic
41#14273650C2211yescharacteristic
42#14273648C2211yescharacteristic
43#14273648C2211yescharacteristic
44#14273648C2211yescharacteristic
45C22⋊(C59⋊C8)C2211yescharacteristic
46C22⋊(C59⋊C8)C2211yescharacteristic
47#14273638C2211yescharacteristic
48C2×#41×C59C2211yescharacteristic
49C22×Q8×C59C2211yescharacteristic
50#124×C59—21no—
51#124×C59C2211yescharacteristic
52C22⋊Q8×C59—21no—
53C22⋊Q8×C59C2211yescharacteristic
54#121×C59—21no—
55#121×C59C2211yescharacteristic
56C4×Q8×C59C2211yescharacteristic
57C4×D4×C59—21no—
58C4×D4×C59C2211yescharacteristic
59#41×C59—22no—
60#41×C59—41no—
61C2×Q8×C59—21no—
62C2×Q8×C59—22no—
63C2×Q8×C59—41no—
64C2×Q8×C59C2311yescharacteristic
65C2×Q8×C59C2311yescharacteristic
66C2×D4×C59—21no—
67C2×D4×C59—21no—
68C2×D4×C59D411yescharacteristic
69C2×D4×C59C2311yescharacteristic
70C22×C4×C59—21no—
71C22×C4×C59—21no—
72C22×C4×C59C2311yescharacteristic
73C22×C4×C59C2311yescharacteristic
74C22×Dic59—21no—
75C22×Dic59—21no—
76C2×Dic118—21no—
77C2×Dic118C2311yescharacteristic
78C4⋊C4×C59—21no—
79C4⋊C4×C59—21no—
80C4⋊C4×C59D411yescharacteristic
81C4⋊C4×C59C2311yescharacteristic
82C22⋊C4×C59—21no—
83C22⋊C4×C59—21no—
84C22⋊C4×C59—21no—
85C22⋊C4×C59—21no—
86C22⋊C4×C59D411yescharacteristic
87C22⋊C4×C59D411yescharacteristic
88C42×C59—21no—
89C42×C59C2311yescharacteristic
90C22⋊Dic59—21no—
91C22⋊Dic59—21no—
92#11745672—22no—
93#11745672—41no—
94#11745670—41no—
95C4⋊Dic59—21no—
96C4⋊Dic59—21no—
97C4⋊Dic59—21no—
98C4⋊Dic59C2311yescharacteristic
99C4⋊Dic59C2311yescharacteristic
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
114Q8×C59—21no—
115Q8×C59—21no—
116Q8×C59—21no—
117Q8×C59—42no—
118Q8×C59#4112yes—
119D4×C59—22no—
120D4×C59—21no—
121D4×C59—21no—
122D4×C59—42no—
123D4×C59—42no—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—21no—
131C2×C4×C59—42no—
132C2×C4×C59—42no—
133C2×C4×C59C2×D411yescharacteristic
134C2×C4×C59C2×D411yescharacteristic
135C2×C4×C59C2×D411yescharacteristic
136C2×C4×C59C2×D411yescharacteristic
137C2×C4×C59C2411yescharacteristic
138C2×Dic59—21no—
139C2×Dic59—21no—
140C2×Dic59—21no—
141C2×Dic59—21no—
142C2×Dic59—81no—
143C2×Dic59—81no—
144Dic118—21no—
145Dic118—21no—
146Dic118—81no—
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—22no—
164C4×C59—21no—
165C4×C59—21no—
166C4×C59—41no—
167C4×C59—41no—
168C4×C59C2×#4111yescharacteristic
169C4×C59H(5,𝔽2)11yescharacteristic
170Dic59—41no—
171Dic59—41no—
172Dic59—41no—
173Dic59—41no—
174#3316—591nomaximal, Sylow
175C2×C59—22no—
176C2×C59—41no—
177C2×C59—81no—
178C2×C59#54611yescharacteristic
179C2×C59C2×#13711yescharacteristic
180C2×C59#57711yescharacteristic
181#554—591no—
182#548D5911yescharacteristic
183#489—591no—
184#483—591no—
185#481—591no—
186#475—591no—
187#470—591no—
188#465—591no—
189#464—591no—
190#452—591no—
191#451—591no—
192#441—591no—
193#435—591no—
194#417—591no—
195C2×#103—591no—
196C59#331611yescharacteristic, complemented, Sylow
197C2×#41C2×D5911yescharacteristic
198C22×Q8C2×D5911yescharacteristic
199C2×Q16—591no—
200C2×Q16—591no—
201C2×SD16—591no—
202C2×M16—591no—
203C22×C8—591no—
204C4⋊Q8—591no—
205#125—1181no—
206#124—21no—
207#124C2×D5911yescharacteristic
208C22⋊Q8—21no—
209C22⋊Q8—591no—
210C22⋊Q8—591no—
211C22⋊Q8—1181no—
212C22⋊Q8—1181no—
213C22⋊Q8C2×D5911yescharacteristic
214#121—21no—
215#121C2×D5911yescharacteristic
216C4×Q8—591no—
217C4×Q8C2×D5911yescharacteristic
218C4×D4—21no—
219C4×D4—1181no—
220C4×D4C2×D5911yescharacteristic
221C2×C4⋊C4—591no—
222C2×C4⋊C4—591no—
223#106—591no—
224#106—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#102—591no—
235#102—591no—
236#102—591no—
237C22⋊C8—591no—
238C22⋊C8—591no—
239#97—591no—
240#41—22no—
241#41—41no—
242C2×Q8—21no—
243C2×Q8—22no—
244C2×Q8—41no—
245C2×Q8—591no—
246C2×Q8—1181no—
247C2×Q8C22×D5911yescharacteristic
248C2×Q8C22×D5911yescharacteristic
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
259Q16—1182no—
260Q16—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—591no—
271C4⋊C4—591no—
272C4⋊C4—591no—
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—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—21no—
296Q8—21no—
297Q8—21no—
298Q8—42no—
299Q8—1181no—
300Q8—1181no—
301Q8—4721no—
302Q8#1174568712yes—
303D4—22no—
304D4—21no—
305D4—21no—
306D4—42no—
307D4—42no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—1181no—
318C2×C4—1181no—
319C2×C4—1181no—
320C2×C4—1181no—
321C2×C4—4721no—
322C2×C4—4721no—
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—22no—
347C4—41no—
348C4—41no—
349C4—2361no—
350C4—2361no—
351C4—2361no—
352C4—2361no—
353C4C2×#1174568711yescharacteristic
354C4#1427377211yescharacteristic
355C2—22no—
356C2—41no—
357C2—81no—
358C2#1683804611yescharacteristic
359C2C2×#1427375711yescharacteristic
360C2#1683821011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#548C2
socleC22×C59C22×D4
hypercenter#548D59
hypocenterC59#3316
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #16838109C2semidirect
2. #16837761C2semidirect
3. #16837730C2semidirect
4. #16837718C2semidirect
5. #16837687C2semidirect
6. #16837658C2semidirect
7. #16837629C2semidirect
8. #16837621C2semidirect
9. #16837564C2semidirect
10. #16837558C2semidirect
11. #16837507C2semidirect
12. #16837474C2semidirect
13. #16837403C2semidirect
14. C2×#14273651C2semidirect
196. C59#3316semidirect