Finite Group Databasebeta

← #21434779

Subgroups — #21434779

Order 7552.

374 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838023C211yesmaximal, characteristic, complemented
2#16838007C211yesmaximal, characteristic, complemented
3#16837811C211yesmaximal, characteristic, complemented
4#16837791C211yesmaximal, characteristic, complemented
5#16837757C211yesmaximal, characteristic, complemented
6#16837749C211yesmaximal, characteristic, complemented
7#16837655C211yesmaximal, characteristic, complemented
8#16837648C211yesmaximal, characteristic, complemented
9#16837638C211yesmaximal, characteristic, complemented
10#16837631C211yesmaximal, characteristic, complemented
11#16837515C211yesmaximal, characteristic, complemented
12#16837504C211yesmaximal, characteristic, complemented
13C4×#11745660C211yesmaximal, characteristic, complemented
14C4×D472C211yesmaximal, characteristic, complemented
15C59×#405C211yesmaximal, characteristic, complemented
16C2×#11745660C2211yescharacteristic
17C2×#11745660C2211yescharacteristic
18C2×D472C2211yescharacteristic
19C2×D472C2211yescharacteristic
20#14273727C2211yescharacteristic
21#14273724C2211yescharacteristic
22#14273722—21no—
23#14273719C2211yescharacteristic
24#14273715C2211yescharacteristic
25#14273713—21no—
26#14273712—21no—
27#14273712—21no—
28#14273709—21no—
29#14273706C2211yescharacteristic
30#14273705—21no—
31#14273701C2211yescharacteristic
32#14273701C2211yescharacteristic
33#14273701C2211yescharacteristic
34#14273700—21no—
35#14273700—21no—
36C4×Dic118C2211yescharacteristic
37C4×D236C2211yescharacteristic
38C4×D236C2211yescharacteristic
39C4×D236C2211yescharacteristic
40#14273661C2211yescharacteristic
41#14273661C2211yescharacteristic
42#14273659C2211yescharacteristic
43#14273659C2211yescharacteristic
44#14273652C2211yescharacteristic
45#14273652C2211yescharacteristic
46#14273649C2211yescharacteristic
47#14273649C2211yescharacteristic
48#14273649C2211yescharacteristic
49#14273649C2211yescharacteristic
50#14273649C2211yescharacteristic
51#14273649C2211yescharacteristic
52C2×M16×C59C2211yescharacteristic
53C22×C8×C59C2211yescharacteristic
54#117×C59C2211yescharacteristic
55#97×C59C2211yescharacteristic
56#97×C59C2211yescharacteristic
57C4×C8×C59C2211yescharacteristic
58C4×C8×C59C2211yescharacteristic
59C22×C4×C59C2311yescharacteristic
60C2×C22⋊D59—21no—
61C2×C22⋊D59—21no—
62C2×C22⋊D59—21no—
63C2×D236—21no—
64C2×D236—21no—
65C2×D236C2311yescharacteristic
66C2×D236C2311yescharacteristic
67C2×D236C2311yescharacteristic
68C2×C4×D59—21no—
69C2×C4×D59—21no—
70C2×C4×D59—21no—
71C2×Dic118—21no—
72C2×Dic118C2311yescharacteristic
73M16×C59—22no—
74C2×C8×C59—22no—
75C2×C8×C59C2311yescharacteristic
76C2×C8×C59C2311yescharacteristic
77C2×C8×C59C2311yescharacteristic
78C2×C8×C59C2311yescharacteristic
79C4⋊C4×C59D411yescharacteristic
80C4⋊C4×C59D411yescharacteristic
81C22⋊C4×C59D411yescharacteristic
82C22⋊C4×C59D411yescharacteristic
83C42×C59C2311yescharacteristic
84C42×C59C2311yescharacteristic
85C22⋊Dic59—21no—
86(C2×D59)⋊C4—21no—
87(C2×D59)⋊C4—21no—
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—
94C4⋊Dic59—21no—
95C4⋊Dic59C2311yescharacteristic
96C4⋊Dic59C2311yescharacteristic
97C4⋊Dic59C2311yescharacteristic
98C4⋊Dic59C2311yescharacteristic
99Dic59⋊C4—21no—
100Dic59⋊C4—21no—
101Dic59⋊C4—21no—
102Dic59⋊C4—21no—
103C4×Dic59—21no—
104D472—22no—
105D472—22no—
106#11745660—22no—
107#11745660—22no—
108C23×C59C2×D411yescharacteristic
109C22×D59—21no—
110C22×D59—21no—
111C22×D59—21no—
112C2×C4×C59—21no—
113C2×C4×C59—21no—
114C2×C4×C59C2×D411yescharacteristic
115C2×C4×C59C2×D411yescharacteristic
116C2×C4×C59C2×D411yescharacteristic
117C2×C4×C59C2×D411yescharacteristic
118C2×C4×C59C2×D411yescharacteristic
119C2×C4×C59C2411yescharacteristic
120C22⋊D59—81no—
121C22⋊D59—81no—
122C22⋊D59—81no—
123C2×Dic59—21no—
124C2×Dic59—21no—
125C2×Dic59—21no—
126C2×Dic59—21no—
127C2×Dic59—21no—
128D236—21no—
129D236—21no—
130D236—21no—
131D236—21no—
132D236—21no—
133D236—21no—
134D236—81no—
135D236—81no—
136C4×D59—81no—
137C4×D59—81no—
138C4×D59—81no—
139Dic118—21no—
140Dic118—21no—
141Dic118—81no—
142C8×C59—21no—
143C8×C59—21no—
144C8×C59#4112yes—
145C8×C59#4112yes—
146C22×C59—21no—
147C22×C59—21no—
148C22×C59—21no—
149C22×C59C22×D411yescharacteristic
150C2×D59—41no—
151C2×D59—41no—
152C2×D59—41no—
153C2×D59—41no—
154C2×D59—41no—
155C2×D59—41no—
156C2×D59—41no—
157C2×D59—41no—
158C2×D59—41no—
159C4×C59—21no—
160C4×C59—21no—
161C4×C59—21no—
162C4×C59—21no—
163C4×C59—21no—
164C4×C59C2×#4111yescharacteristic
165C4×C59C2×#4111yescharacteristic
166Dic59—41no—
167Dic59—41no—
168Dic59—41no—
169Dic59—41no—
170Dic59—41no—
171#3179—591nomaximal, Sylow
172C2×C59—41no—
173C2×C59#53211yescharacteristic
174C2×C59#57611yescharacteristic
175C2×C59#57711yescharacteristic
176D59—81no—
177D59—81no—
178D59—81no—
179#542—591no—
180#540—591no—
181#501—591no—
182#496—591no—
183#488—591no—
184#486—591no—
185#469—591no—
186#468—591no—
187#466—591no—
188#465—591no—
189#442—591no—
190#440—591no—
191C4×SD16—591no—
192C4×D8—591no—
193#405D5911yescharacteristic, complemented
194C59#317911yescharacteristic, complemented, Sylow
195C2×SD16—591no—
196C2×SD16—591no—
197C2×D8—591no—
198C2×D8—591no—
199C2×M16C2×D5911yescharacteristic
200C22×C8C2×D5911yescharacteristic
201C4⋊Q8—591no—
202#127—591no—
203#126—1181no—
204#125—591no—
205#124—591no—
206#124—1181no—
207#123—1181no—
208#123—1181no—
209#123—1181no—
210C22⋊Q8—591no—
211C22⋊Q8—1181no—
212#121—591no—
213#121—591no—
214#121—591no—
215#121—1181no—
216#121—1181no—
217C4×Q8—591no—
218C4×D4—591no—
219C4×D4—591no—
220C4×D4—591no—
221#117C2×D5911yescharacteristic
222#107—591no—
223#107—591no—
224#106—591no—
225#106—591no—
226#103—591no—
227#103—591no—
228#102—591no—
229#102—591no—
230#102—591no—
231#102—591no—
232#102—591no—
233#102—591no—
234#97C2×D5911yescharacteristic
235#97C2×D5911yescharacteristic
236C4×C8C2×D5911yescharacteristic
237C4×C8C2×D5911yescharacteristic
238C2×Q8—591no—
239C2×Q8—1181no—
240C2×D4—591no—
241C2×D4—591no—
242C2×D4—591no—
243C2×D4—1181no—
244C2×D4—1181no—
245C2×D4—1181no—
246C2×D4—1181no—
247C2×D4—1181no—
248C22×C4—1181no—
249C22×C4—1181no—
250C22×C4—1181no—
251C22×C4C22×D5911yescharacteristic
252SD16—1182no—
253SD16—1182no—
254D8—1182no—
255D8—1182no—
256M16—22no—
257C2×C8—22no—
258C2×C8C22×D5911yescharacteristic
259C2×C8C22×D5911yescharacteristic
260C2×C8C22×D5911yescharacteristic
261C2×C8C22×D5911yescharacteristic
262C4⋊C4—591no—
263C4⋊C4—591no—
264C4⋊C4—591no—
265C4⋊C4—591no—
266C4⋊C4—1181no—
267C4⋊C4—1181no—
268C4⋊C4—1181no—
269C4⋊C4—1181no—
270C4⋊C4—1181no—
271C4⋊C4D23611yescharacteristic
272C4⋊C4D23611yescharacteristic
273C22⋊C4—1181no—
274C22⋊C4—1181no—
275C22⋊C4—1181no—
276C22⋊C4—1181no—
277C22⋊C4—1181no—
278C22⋊C4—1181no—
279C22⋊C4—1181no—
280C22⋊C4—1181no—
281C22⋊C4—1181no—
282C22⋊C4D23611yescharacteristic
283C22⋊C4D23611yescharacteristic
284C42—1181no—
285C42C22×D5911yescharacteristic
286C42C22×D5911yescharacteristic
287C23—1181no—
288C23—1181no—
289C23—1181no—
290C23C2×D23611yescharacteristic
291Q8—1181no—
292Q8—1181no—
293Q8—4721no—
294D4—1181no—
295D4—1181no—
296D4—1181no—
297D4—1181no—
298D4—1181no—
299D4—1181no—
300D4—4721no—
301D4—4721no—
302D4—4721no—
303D4—4721no—
304D4—4721no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—1181no—
308C2×C4—1181no—
309C2×C4—1181no—
310C2×C4—1181no—
311C2×C4—1181no—
312C2×C4—4721no—
313C2×C4—4721no—
314C2×C4—4721no—
315C2×C4C2×D23611yescharacteristic
316C2×C4C2×D23611yescharacteristic
317C2×C4C2×D23611yescharacteristic
318C2×C4C2×D23611yescharacteristic
319C2×C4C2×D23611yescharacteristic
320C2×C4C23×D5911yescharacteristic
321C8—21no—
322C8—21no—
323C8#1174568512yes—
324C8#1174568512yes—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—2361no—
329C22—2361no—
330C22—2361no—
331C22—2361no—
332C22—2361no—
333C22—2361no—
334C22—2361no—
335C22—2361no—
336C22—2361no—
337C22C22×D23611yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—2361no—
344C4—2361no—
345C4—2361no—
346C4—2361no—
347C4—2361no—
348C4C2×#1174568511yescharacteristic
349C4C2×#1174568511yescharacteristic
350C2—41no—
351C2—4721no—
352C2—4721no—
353C2—4721no—
354C2#1683795211yescharacteristic
355C2#1683820711yescharacteristic
356C2#1683821411yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#405C2
socleC22×C59C22×D4
hypercenter#405D59
hypocenterC59#3179
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ #117 ◁ #405

Complements

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

NH ≅ G/Ntype
1. #16838023C2semidirect
2. #16838007C2semidirect
3. #16837811C2semidirect
4. #16837791C2semidirect
5. #16837757C2semidirect
6. #16837749C2semidirect
7. #16837655C2semidirect
8. #16837648C2semidirect
9. #16837638C2semidirect
10. #16837631C2semidirect
11. #16837515C2semidirect
12. #16837504C2semidirect
13. C4×#11745660C2semidirect
14. C4×D472C2semidirect
15. C59×#405C2semidirect
193. #405D59semidirect
194. C59#3179semidirect