Finite Group Databasebeta

← #21435994

Subgroups — #21435994

Order 7552.

398 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838100C211yesmaximal, characteristic, complemented
2#16838063C211yesmaximal, characteristic, complemented
3#16837758C211yesmaximal, characteristic, complemented
4#16837742C211yesmaximal, characteristic, complemented
5#16837720C211yesmaximal, characteristic, complemented
6#16837711C211yesmaximal, characteristic, complemented
7#16837638C211yesmaximal, characteristic, complemented
8#16837634C211yesmaximal, characteristic, complemented
9#16837620C211yesmaximal, characteristic, complemented
10#16837550C211yesmaximal, characteristic, complemented
11#16837541C211yesmaximal, characteristic, complemented
12#16837487C211yesmaximal, characteristic, complemented
13C8×C22⋊D59C211yesmaximal, characteristic, complemented
14#16837397C211yesmaximal, characteristic, complemented
15C2×#103×C59C211yesmaximal, characteristic, complemented
16C2×#11745689C2211yescharacteristic
17C2×#11745671C2211yescharacteristic
18C2×#11745671C2211yescharacteristic
19C2×D472C2211yescharacteristic
20C2×C8×D59C2211yescharacteristic
21#14273722—21no—
22#14273718C2211yescharacteristic
23#14273716—21no—
24#14273716C2211yescharacteristic
25#14273712—21no—
26#14273703—21no—
27#14273703C2211yescharacteristic
28#14273702C2211yescharacteristic
29#14273701—21no—
30#14273701—21no—
31#14273701C2211yescharacteristic
32#14273701C2211yescharacteristic
33Q8×Dic59C2211yescharacteristic
34#14273689C2211yescharacteristic
35C4×C22⋊D59—21no—
36C4×C22⋊D59—21no—
37C4×C22⋊D59C2211yescharacteristic
38#14273685C2211yescharacteristic
39#14273661C2211yescharacteristic
40#14273658C2211yescharacteristic
41#14273658C2211yescharacteristic
42Dic59⋊C8C2211yescharacteristic
43#14273651C2211yescharacteristic
44#14273651C2211yescharacteristic
45#14273649C2211yescharacteristic
46#14273649C2211yescharacteristic
47#14273647C2211yescharacteristic
48#14273647C2211yescharacteristic
49C22⋊(C59⋊C8)C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51C8×Dic59C2211yescharacteristic
52C22×Q8×C59C2211yescharacteristic
53C22×C8×C59C2211yescharacteristic
54C2×C4⋊C4×C59C2211yescharacteristic
55#103×C59C2211yescharacteristic
56#103×C59C2211yescharacteristic
57#103×C59C2211yescharacteristic
58#103×C59C2211yescharacteristic
59C2×Q8×C59—21no—
60C2×Q8×C59—22no—
61C2×Q8×C59—41no—
62C2×Q8×C59C2311yescharacteristic
63C2×Q8×C59C2311yescharacteristic
64C22×C4×C59—21no—
65C22×C4×C59—21no—
66C22×C4×C59C2311yescharacteristic
67C2×C22⋊D59—21no—
68C2×C22⋊D59—21no—
69C2×C22⋊D59D411yescharacteristic
70#11745689—22no—
71#11745689—41no—
72C2×D236—21no—
73C2×D236—21no—
74C2×D236C2311yescharacteristic
75C2×D236C2311yescharacteristic
76C2×C4×D59—21no—
77C2×C4×D59—21no—
78C2×C4×D59C2311yescharacteristic
79C2×C8×C59—41no—
80C2×C8×C59C2311yescharacteristic
81C2×C8×C59C2311yescharacteristic
82C4⋊C4×C59—21no—
83C4⋊C4×C59C2311yescharacteristic
84C4⋊C4×C59C2311yescharacteristic
85C22⋊Dic59D411yescharacteristic
86#11745671—22no—
87#11745671—41no—
88(C2×D59)⋊C4—21no—
89(C2×D59)⋊C4—21no—
90(C2×D59)⋊C4—21no—
91(C2×D59)⋊C4—21no—
92(C2×D59)⋊C4—21no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4—21no—
95(C2×D59)⋊C4—21no—
96(C2×D59)⋊C4D411yescharacteristic
97C4⋊Dic59—21no—
98C4⋊Dic59—21no—
99C4⋊Dic59C2311yescharacteristic
100C4⋊Dic59C2311yescharacteristic
101Dic59⋊C4—21no—
102Dic59⋊C4—21no—
103Dic59⋊C4D411yescharacteristic
104C4×Dic59—21no—
105C4×Dic59—21no—
106C4×Dic59C2311yescharacteristic
107C2×C59⋊C8C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109D472—41no—
110C8×D59—41no—
111C23×C59C2×D411yescharacteristic
112C22×D59—21no—
113C22×D59—21no—
114C22×D59C2×D411yescharacteristic
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×C59—81no—
128C2×C4×C59C2×D411yescharacteristic
129C2×C4×C59C2411yescharacteristic
130C22⋊D59—22no—
131C22⋊D59—42no—
132C22⋊D59—42no—
133C2×Dic59—21no—
134C2×Dic59—21no—
135C2×Dic59C2×D411yescharacteristic
136C2×Dic59C2×D411yescharacteristic
137C2×Dic59C2×D411yescharacteristic
138D236—21no—
139D236—21no—
140D236—21no—
141D236—21no—
142D236—42no—
143D236—81no—
144C4×D59—21no—
145C4×D59—21no—
146C4×D59—42no—
147C4×D59—81no—
148C8×C59—21no—
149C8×C59—21no—
150C59⋊C8—21no—
151C59⋊C8—21no—
152C22×C59—21no—
153C22×C59—21no—
154C22×C59#13512yes—
155C22×C59C22×D411yescharacteristic
156C2×D59—21no—
157C2×D59—21no—
158C2×D59—21no—
159C2×D59—41no—
160C2×D59—41no—
161C2×D59—41no—
162C2×D59—41no—
163C2×D59—41no—
164C2×D59—41no—
165C4×C59—22no—
166C4×C59—21no—
167C4×C59—41no—
168C4×C59—41no—
169C4×C59—41no—
170C4×C59C2×#4111yescharacteristic
171C4×C59H(5,𝔽2)11yescharacteristic
172Dic59—21no—
173Dic59—21no—
174Dic59—21no—
175Dic59—41no—
176Dic59—41no—
177#3301—591nomaximal, Sylow
178C2×C59—22no—
179C2×C59#54611yescharacteristic
180C2×C59C2×#13511yescharacteristic
181C2×C59#57711yescharacteristic
182D59—41no—
183D59—81no—
184D59—81no—
185#553—591no—
186#548—591no—
187#488—591no—
188#485—591no—
189#481—591no—
190#479—591no—
191#466—591no—
192#465—591no—
193#463—591no—
194#449—591no—
195#448—591no—
196C4×SD16—591no—
197C8×D4—591no—
198#416—591no—
199C2×#103D5911yescharacteristic, complemented
200C59#330111yescharacteristic, complemented, Sylow
201C2×#41—591no—
202C22×Q8C2×D5911yescharacteristic
203C2×SD16—591no—
204C2×SD16—591no—
205C2×D8—591no—
206C22×C8—591no—
207C22×C8C2×D5911yescharacteristic
208#126—1181no—
209#125—591no—
210#124—591no—
211#124—1181no—
212#123—1181no—
213C22⋊Q8—591no—
214C22⋊Q8—1181no—
215#121—591no—
216#121—591no—
217#121—591no—
218#121—1181no—
219#121—1181no—
220C4×Q8—591no—
221C4×D4—591no—
222C4×D4—591no—
223C4×D4—1181no—
224C4×D4—1181no—
225#117—591no—
226C2×C4⋊C4C2×D5911yescharacteristic
227#107—591no—
228#106—591no—
229#106—591no—
230C4⋊C8—591no—
231#103—591no—
232#103—591no—
233#103C2×D5911yescharacteristic
234#103C2×D5911yescharacteristic
235#103C2×D5911yescharacteristic
236#103C2×D5911yescharacteristic
237#102—591no—
238#102—591no—
239#102—591no—
240#102—591no—
241C22⋊C8—591no—
242C22⋊C8—591no—
243C4×C8—591no—
244#41—1182no—
245#41—2361no—
246C2×Q8—21no—
247C2×Q8—22no—
248C2×Q8—41no—
249C2×Q8C22×D5911yescharacteristic
250C2×Q8C22×D5911yescharacteristic
251C2×D4—591no—
252C2×D4—591no—
253C2×D4—591no—
254C2×D4—1181no—
255C2×D4—1181no—
256C2×D4—1181no—
257C2×D4—1181no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—591no—
261C22×C4—1181no—
262C22×C4—1181no—
263C22×C4C22×D5911yescharacteristic
264SD16—1182no—
265SD16—2361no—
266D8—2361no—
267C2×C8—41no—
268C2×C8—591no—
269C2×C8—591no—
270C2×C8—2361no—
271C2×C8C22×D5911yescharacteristic
272C2×C8C22×D5911yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—591no—
275C4⋊C4—591no—
276C4⋊C4—591no—
277C4⋊C4—1181no—
278C4⋊C4—1181no—
279C4⋊C4—1181no—
280C4⋊C4—1181no—
281C4⋊C4C22×D5911yescharacteristic
282C4⋊C4C22×D5911yescharacteristic
283C22⋊C4—591no—
284C22⋊C4—591no—
285C22⋊C4—1181no—
286C22⋊C4—1181no—
287C22⋊C4—1181no—
288C22⋊C4—1181no—
289C22⋊C4—1181no—
290C22⋊C4—1181no—
291C22⋊C4—1181no—
292C22⋊C4—1181no—
293C42—591no—
294C42—1181no—
295C42—1181no—
296C23—591no—
297C23—1181no—
298C23—1181no—
299C23D4×D5911yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—42no—
304Q8#1174568512yes—
305D4—1182no—
306D4—1181no—
307D4—1181no—
308D4—1181no—
309D4—1181no—
310D4—4721no—
311D4—2362no—
312D4—2362no—
313D4—2362no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—42no—
321C2×C4—81no—
322C2×C4—591no—
323C2×C4—591no—
324C2×C4—591no—
325C2×C4—1181no—
326C2×C4—1181no—
327C2×C4—1181no—
328C2×C4—1181no—
329C2×C4—4721no—
330C2×C4—2362no—
331C2×C4D4×D5911yescharacteristic
332C2×C4C23×D5911yescharacteristic
333C8—21no—
334C8—21no—
335C8—1181no—
336C8—1181no—
337C22—21no—
338C22—21no—
339C22—1181no—
340C22—1181no—
341C22—1181no—
342C22—2361no—
343C22—2361no—
344C22—2361no—
345C22—2361no—
346C22—2361no—
347C22—2361no—
348C22#1427375012yes—
349C22C2×D4×D5911yescharacteristic
350C4—21no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—1181no—
356C4—1181no—
357C4—1181no—
358C4—2361no—
359C4—2361no—
360C4C2×#1174568511yescharacteristic
361C4#1427377211yescharacteristic
362C2—22no—
363C2—4721no—
364C2—4721no—
365C2—2361no—
366C2#1683804211yescharacteristic
367C2C2×#1427375011yescharacteristic
368C2#1683820811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC2×#103×C59C2
socleC22×C59C22×D4
hypercenterC2×#103D59
hypocenterC59#3301
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. #16838100C2semidirect
2. #16838063C2semidirect
3. #16837758C2semidirect
4. #16837742C2semidirect
5. #16837720C2semidirect
6. #16837711C2semidirect
7. #16837638C2semidirect
8. #16837634C2semidirect
9. #16837620C2semidirect
10. #16837550C2semidirect
11. #16837541C2semidirect
12. #16837487C2semidirect
13. C8×C22⋊D59C2semidirect
14. #16837397C2semidirect
15. C2×#103×C59C2semidirect
199. C2×#103D59semidirect
200. C59#3301semidirect