Finite Group Databasebeta

← #21433813

Subgroups — #21433813

Order 7552.

452 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838200C211yesmaximal, characteristic, complemented
2C2×#14273747C211yesmaximal, characteristic, complemented
3C2×#14273734C211yesmaximal, characteristic, complemented
4#16837675C212yesmaximal, complemented
5#16837670C212yesmaximal, complemented
6#16837667C212yesmaximal, complemented
7#16837663C212yesmaximal, complemented
8C2×#14273662C211yesmaximal, characteristic, complemented
9#16837386C211yesmaximal, characteristic, complemented
10#16837384C211yesmaximal, characteristic, complemented
11C59×#575C211yesmaximal, characteristic, complemented
12C2×#11745685C2211yescharacteristic
13#14273758—21no—
14#14273757C2212yes—
15#14273753—21no—
16#14273752C2212yes—
17#14273747—22no—
18#14273747—21no—
19#14273747—21no—
20#14273747—21no—
21#14273747—21no—
22C2×#11745672C2211yescharacteristic, complemented
23C2×#11745670C2211yescharacteristic, complemented
24C2×#11745671C2211yescharacteristic, complemented
25C2×#11745669C2211yescharacteristic, complemented
26#14273734—21no—
27#14273734—21no—
28#14273734C2212yes—
29#14273734C2212yes—
30C2×#11745664—21no—
31C2×#11745664C2211yescharacteristic
32C2×#11745664C2211yescharacteristic
33C22×C59⋊C8—21no—
34C22×C59⋊C8C2211yescharacteristic
35#14273662C2212yescomplemented
36#14273662C2212yescomplemented
37#14273646C2212yescomplemented
38#14273645C2212yescomplemented
39#14273644C2212yescomplemented
40#14273643C2212yescomplemented
41C2×#41×C59C2211yescharacteristic
42C2×#41×C59C2211yescharacteristic
43#137×C59—21no—
44#137×C59C2212yes—
45AGL(1,ℤ/8)×C59—21no—
46AGL(1,ℤ/8)×C59C2212yes—
47#135×C59—22no—
48C2×M16×C59C2211yescharacteristic
49#41×C59—21no—
50#41×C59—21no—
51#41×C59—21no—
52#41×C59—21no—
53#41×C59—21no—
54#41×C59—21no—
55#41×C59D412yes—
56#41×C59C2312yes—
57C2×Q8×C59D411yescharacteristic
58C2×Q8×C59C2311yescharacteristic
59C2×D4×C59—21no—
60C2×D4×C59—21no—
61C2×D4×C59D411yescharacteristic
62C2×D4×C59C2311yescharacteristic
63C22×C4×C59—21no—
64C22×C4×C59—21no—
65C22×C4×C59C2311yescharacteristic
66C2×C22⋊D59—21no—
67#11745685—21no—
68#11745685—21no—
69#11745685—21no—
70#11745685—21no—
71C2×D236C2311yescharacteristic
72C2×C4×D59—21no—
73C2×Dic118C2311yescharacteristic
74Q16×C59—22no—
75SD16×C59—22no—
76SD16×C59—22no—
77D8×C59—22no—
78M16×C59—21no—
79M16×C59C2312yes—
80C2×C8×C59—21no—
81#11745672—22no—
82#11745672—21no—
83#11745672—21no—
84#11745671—22no—
85#11745671—21no—
86#11745671—21no—
87#11745670—22no—
88#11745670—21no—
89#11745670—21no—
90#11745669—22no—
91#11745669—21no—
92#11745669—21no—
93#11745664—21no—
94#11745664—21no—
95#11745664—22no—
96#11745664—22no—
97#11745664C2312yes—
98#11745664C2312yes—
99C2×C59⋊C8—21no—
100C2×C59⋊C8—21no—
101C2×C59⋊C8—22no—
102C2×C59⋊C8—22no—
103C2×C59⋊C8D411yescharacteristic
104C2×C59⋊C8D411yescharacteristic
105C2×C59⋊C8D411yescharacteristic
106C2×C59⋊C8D411yescharacteristic
107C2×C59⋊C8C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109C23×C59—21no—
110C23×C59—21no—
111C23×C59#4111yescharacteristic
112C22×D59—21no—
113Q8×C59—21no—
114Q8×C59—21no—
115Q8×C59—21no—
116Q8×C59C2×D412yes—
117D4×C59—22no—
118D4×C59—22no—
119D4×C59—21no—
120D4×C59—21no—
121D4×C59—21no—
122D4×C59—41no—
123D4×C59—41no—
124D4×C59C2×D412yes—
125C2×C4×C59—21no—
126C2×C4×C59—22no—
127C2×C4×C59—22no—
128C2×C4×C59—21no—
129C2×C4×C59—41no—
130C2×C4×C59—41no—
131C2×C4×C59C2×D411yescharacteristic
132C2×C4×C59C2×D411yescharacteristic
133C2×C4×C59C2×D411yescharacteristic
134C2×C4×C59C2×D411yescharacteristic
135C2×C4×C59#4111yescharacteristic
136C2×C4×C59C2411yescharacteristic
137C22⋊D59—41no—
138C22⋊D59—41no—
139C2×Dic59—21no—
140D236—21no—
141D236—21no—
142C4×D59—41no—
143C4×D59—41no—
144Dic118—21no—
145Dic118—21no—
146C8×C59—22no—
147C59⋊C8—22no—
148C59⋊C8—22no—
149C59⋊C8C2×D411yescharacteristic
150C59⋊C8C2×D411yescharacteristic
151C59⋊C8C2×D411yescharacteristic
152C59⋊C8C2×D411yescharacteristic
153C22×C59—22no—
154C22×C59—41no—
155C22×C59—42no—
156C22×C59—41no—
157C22×C59—81no—
158C22×C59#12111yescharacteristic
159C22×C59#12111yescharacteristic
160C22×C59C2×#4111yescharacteristic
161C2×D59—41no—
162C2×D59—81no—
163C4×C59—22no—
164C4×C59—41no—
165C4×C59#12111yescharacteristic
166C4×C59#12111yescharacteristic
167C4×C59C22×D411yescharacteristic
168C4×C59C22×D411yescharacteristic
169Dic59—41no—
170#3067—591nomaximal, Sylow
171C2×C59—21no—
172C2×C59—21no—
173C2×C59—21no—
174C2×C59—42no—
175C2×C59—81no—
176C2×C59C2×#12111yescharacteristic
177D59—81no—
178#575—591no—
179#575D5911yescharacteristic, complemented
180C2×#135—591no—
181C2×#131—591no—
182#473—592no—
183#472—592no—
184#471—592no—
185#471—592no—
186C2×#108—591no—
187#413—591no—
188#413—591no—
189C59#306711yescharacteristic, complemented, Sylow
190C2×#41—591no—
191C2×#41C2×D5911yescharacteristic
192C2×#41C2×D5911yescharacteristic
193#137—21no—
194#137—592no—
195#137—1181no—
196#137C2×D5912yes—
197AGL(1,ℤ/8)—21no—
198AGL(1,ℤ/8)—592no—
199AGL(1,ℤ/8)—1181no—
200AGL(1,ℤ/8)C2×D5912yes—
201#135—22no—
202#135—1181no—
203#135—1181no—
204#135—1181no—
205#135—1181no—
206#135—1182no—
207C2×Q16—591no—
208C2×SD16—591no—
209C2×SD16—591no—
210C2×D8—591no—
211#131—592no—
212#131—592no—
213#131—1181no—
214#131—1181no—
215C2×M16—591no—
216C2×M16—591no—
217C2×M16—1181no—
218C2×M16C2×D5911yescharacteristic
219C22×C8—591no—
220C22×C8—1181no—
221#108—592no—
222#108—592no—
223#101—592no—
224#101—592no—
225#100—592no—
226#100—592no—
227#41—21no—
228#41—21no—
229#41—21no—
230#41—21no—
231#41—21no—
232#41—21no—
233#41—1181no—
234#41—1181no—
235#41—1181no—
236#41—1181no—
237#41C22⋊D5912yes—
238#41C22×D5912yes—
239C2×Q8—591no—
240C2×Q8C22⋊D5911yescharacteristic
241C2×Q8C22×D5911yescharacteristic
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—591no—
245C2×D4—1181no—
246C2×D4C22⋊D5911yescharacteristic
247C2×D4C22×D5911yescharacteristic
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—1181no—
251C22×C4C22×D5911yescharacteristic
252Q16—22no—
253Q16—1181no—
254Q16—1181no—
255Q16—1182no—
256SD16—22no—
257SD16—22no—
258SD16—1181no—
259SD16—1181no—
260SD16—1181no—
261SD16—1181no—
262SD16—1182no—
263SD16—1182no—
264D8—22no—
265D8—1181no—
266D8—1181no—
267D8—1182no—
268M16—21no—
269M16—592no—
270M16—592no—
271M16—1182no—
272M16—1182no—
273M16—1181no—
274M16—1181no—
275M16C22×D5912yes—
276C2×C8—21no—
277C2×C8—591no—
278C2×C8—591no—
279C2×C8—591no—
280C2×C8—591no—
281C2×C8—591no—
282C2×C8—591no—
283C2×C8—1182no—
284C2×C8—1182no—
285C2×C8—1181no—
286C2×C8—1181no—
287C23—21no—
288C23—21no—
289C23—1181no—
290C23#1174568711yescharacteristic
291Q8—21no—
292Q8—21no—
293Q8—21no—
294Q8—1181no—
295Q8—1181no—
296Q8C2×C22⋊D5912yes—
297D4—22no—
298D4—22no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—41no—
303D4—41no—
304D4—1181no—
305D4—1181no—
306D4—2361no—
307D4—2361no—
308D4C2×C22⋊D5912yes—
309C2×C4—21no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—21no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—1181no—
316C2×C4—2361no—
317C2×C4—2361no—
318C2×C4D4×D5911yescharacteristic
319C2×C4D4×D5911yescharacteristic
320C2×C4#1174568711yescharacteristic
321C2×C4C2×C22⋊D5911yescharacteristic
322C2×C4C2×C22⋊D5911yescharacteristic
323C2×C4C23×D5911yescharacteristic
324C8—22no—
325C8—591no—
326C8—591no—
327C8—591no—
328C8—591no—
329C8—1182no—
330C8—1182no—
331C22—22no—
332C22—41no—
333C22—42no—
334C22—41no—
335C22—81no—
336C22—4721no—
337C22—2361no—
338C22#1427369911yescharacteristic
339C22#1427369911yescharacteristic
340C22C2×#1174568711yescharacteristic
341C4—22no—
342C4—41no—
343C4—2361no—
344C4#1427369911yescharacteristic
345C4#1427369911yescharacteristic
346C4C2×D4×D5911yescharacteristic
347C4C22×C22⋊D5911yescharacteristic
348C2—21no—
349C2—21no—
350C2—21no—
351C2—42no—
352C2—81no—
353C2—4721no—
354C2C2×#1427369911yescharacteristic
subgroupG/H
centerC4#14273699
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#575C2
socleC2×C59C2×#121
hypercenter#575D59
hypocenterC59#3067
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #16838200C2semidirect
2. C2×#14273747C2semidirect
3. C2×#14273734C2semidirect
4. #16837675C2semidirect
5. #16837670C2semidirect
6. #16837667C2semidirect
7. #16837663C2semidirect
8. C2×#14273662C2semidirect
9. #16837386C2semidirect
10. #16837384C2semidirect
11. C59×#575C2semidirect
22. C2×#11745672C22semidirect
23. C2×#11745670C22semidirect
24. C2×#11745671C22semidirect
25. C2×#11745669C22semidirect
35. #14273662C22semidirect
36. #14273662C22semidirect
37. #14273646C22semidirect
38. #14273645C22semidirect
39. #14273644C22semidirect
40. #14273643C22semidirect
179. #575D59semidirect
189. C59#3067semidirect