Finite Group Databasebeta

← C59×#3350 #21421668

Subgroups — C59×#3350 #21421668

Order 7552.

348 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#556C211yesmaximal, characteristic, complemented
2C59×#553C211yesmaximal, characteristic
3C59×#501C211yesmaximal, characteristic, complemented
4C59×#485C211yesmaximal, characteristic, complemented
5C59×#483C211yesmaximal, characteristic, complemented
6C59×#482C211yesmaximal, characteristic, complemented
7C59×#482C211yesmaximal, characteristic, complemented
8C59×#479C211yesmaximal, characteristic, complemented
9C59×#476C211yesmaximal, characteristic, complemented
10C59×#468C211yesmaximal, characteristic, complemented
11C59×#465C211yesmaximal, characteristic, complemented
12C59×#440C211yesmaximal, characteristic, complemented
13C59×#435C211yesmaximal, characteristic, complemented
14C59×#428C211yesmaximal, characteristic, complemented
15C59×#427C211yesmaximal, characteristic, complemented
16C2×SD16×C59C2211yescharacteristic
17C2×M16×C59C2211yescharacteristic
18C22×C8×C59C2211yescharacteristic
19C4⋊Q8×C59C2211yescharacteristic
20#126×C59—21no—
21#126×C59—21no—
22#126×C59—21no—
23#125×C59C2211yescharacteristic
24#124×C59—21no—
25#123×C59—21no—
26C22⋊Q8×C59C2211yescharacteristic
27C22⋊Q8×C59C2211yescharacteristic
28#121×C59—21no—
29#121×C59C2211yescharacteristic
30#121×C59C2211yescharacteristic
31C4×Q8×C59—21no—
32C4×Q8×C59C2211yescharacteristic
33C4×D4×C59—21no—
34C4×D4×C59C2211yescharacteristic
35C4×D4×C59C2211yescharacteristic
36#117×C59C2211yescharacteristic
37#117×C59C2211yescharacteristic
38#117×C59C2211yescharacteristic
39C2×C4⋊C4×C59C2211yescharacteristic
40#107×C59C2211yescharacteristic
41#107×C59C2211yescharacteristic
42#107×C59C2211yescharacteristic
43#107×C59C2211yescharacteristic
44#106×C59C2211yescharacteristic
45#106×C59C2211yescharacteristic
46#106×C59C2211yescharacteristic
47#106×C59C2211yescharacteristic
48#106×C59C2211yescharacteristic
49C4⋊C8×C59C2211yescharacteristic
50#103×C59C2211yescharacteristic
51#103×C59C2211yescharacteristic
52#103×C59C2211yescharacteristic
53#102×C59C2211yescharacteristic
54#102×C59C2211yescharacteristic
55#102×C59C2211yescharacteristic
56C22⋊C8×C59C2211yescharacteristic
57C22⋊C8×C59C2211yescharacteristic
58#97×C59C2211yescharacteristic
59C2×Q8×C59—21no—
60C2×Q8×C59C2311yescharacteristic
61C2×D4×C59—21no—
62C2×D4×C59—21no—
63C2×D4×C59D411yescharacteristic
64C2×D4×C59C2311yescharacteristic
65C22×C4×C59—21no—
66C22×C4×C59—21no—
67C22×C4×C59C2311yescharacteristic
68C22×C4×C59C2311yescharacteristic
69SD16×C59—22no—
70M16×C59—22no—
71C2×C8×C59—22no—
72C2×C8×C59C2311yescharacteristic
73C2×C8×C59C2311yescharacteristic
74C2×C8×C59C2311yescharacteristic
75C2×C8×C59C2311yescharacteristic
76C4⋊C4×C59—21no—
77C4⋊C4×C59—21no—
78C4⋊C4×C59—21no—
79C4⋊C4×C59—21no—
80C4⋊C4×C59—21no—
81C4⋊C4×C59—21no—
82C4⋊C4×C59—21no—
83C4⋊C4×C59D411yescharacteristic
84C4⋊C4×C59C2311yescharacteristic
85C4⋊C4×C59C2311yescharacteristic
86C4⋊C4×C59C2311yescharacteristic
87C4⋊C4×C59C2311yescharacteristic
88C4⋊C4×C59C2311yescharacteristic
89C4⋊C4×C59C2311yescharacteristic
90C22⋊C4×C59—21no—
91C22⋊C4×C59—21no—
92C22⋊C4×C59—21no—
93C22⋊C4×C59—21no—
94C22⋊C4×C59—21no—
95C22⋊C4×C59—21no—
96C22⋊C4×C59—21no—
97C22⋊C4×C59—21no—
98C22⋊C4×C59D411yescharacteristic
99C22⋊C4×C59D411yescharacteristic
100C42×C59—21no—
101C42×C59—21no—
102C42×C59—21no—
103C42×C59—21no—
104C42×C59C2311yescharacteristic
105C23×C59—21no—
106C23×C59C2×D411yescharacteristic
107C23×C59C2×D411yescharacteristic
108Q8×C59—21no—
109Q8×C59—21no—
110Q8×C59—42no—
111D4×C59—21no—
112D4×C59—21no—
113D4×C59—41no—
114D4×C59—42no—
115D4×C59—81no—
116C2×C4×C59—21no—
117C2×C4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
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—21no—
127C2×C4×C59—81no—
128C2×C4×C59—81no—
129C2×C4×C59C2×D411yescharacteristic
130C2×C4×C59C2×D411yescharacteristic
131C2×C4×C59C2×D411yescharacteristic
132C2×C4×C59C2×D411yescharacteristic
133C2×C4×C59C2411yescharacteristic
134C8×C59—21no—
135C8×C59—21no—
136C8×C59—21no—
137C8×C59#4112yes—
138C22×C59—21no—
139C22×C59—21no—
140C22×C59—21no—
141C22×C59—21no—
142C22×C59—21no—
143C22×C59—21no—
144C22×C59—41no—
145C22×C59—41no—
146C22×C59—41no—
147C22×C59C22×D411yescharacteristic
148C4×C59—21no—
149C4×C59—21no—
150C4×C59—21no—
151C4×C59—21no—
152C4×C59—41no—
153C4×C59—41no—
154C4×C59—41no—
155C4×C59—41no—
156C4×C59—41no—
157C4×C59—41no—
158C4×C59—41no—
159C4×C59C2×#4111yescharacteristic
160C4×C592−1+411yescharacteristic
161#3350C5911yesmaximal, characteristic, direct product factor, Sylow
162C2×C59—41no—
163C2×C59—41no—
164C2×C59—81no—
165C2×C59#54711yescharacteristic
166C2×C59#57511yescharacteristic
167C2×C59#57711yescharacteristic
168#556C2×C5911yescharacteristic, complemented
169#553C2×C5911yescharacteristic
170#501C2×C5911yescharacteristic, complemented
171#485C2×C5911yescharacteristic, complemented
172#483C2×C5911yescharacteristic, complemented
173#482C2×C5911yescharacteristic, complemented
174#482C2×C5911yescharacteristic, complemented
175#479C2×C5911yescharacteristic, complemented
176#476C2×C5911yescharacteristic, complemented
177#468C2×C5911yescharacteristic, complemented
178#465C2×C5911yescharacteristic, complemented
179#440C2×C5911yescharacteristic, complemented
180#435C2×C5911yescharacteristic, complemented
181#428C2×C5911yescharacteristic, complemented
182#427C2×C5911yescharacteristic, complemented
183C59#335011yescharacteristic, direct product factor, Sylow
184C2×SD16C22×C5911yescharacteristic
185C2×M16C22×C5911yescharacteristic
186C22×C8C22×C5911yescharacteristic
187C4⋊Q8C22×C5911yescharacteristic
188#126—21no—
189#126—21no—
190#126—21no—
191#125C22×C5911yescharacteristic
192#124—21no—
193#123—21no—
194C22⋊Q8C22×C5911yescharacteristic
195C22⋊Q8C22×C5911yescharacteristic
196#121—21no—
197#121C22×C5911yescharacteristic
198#121C22×C5911yescharacteristic
199C4×Q8—21no—
200C4×Q8C22×C5911yescharacteristic
201C4×D4—21no—
202C4×D4C22×C5911yescharacteristic
203C4×D4C22×C5911yescharacteristic
204#117C22×C5911yescharacteristic
205#117C22×C5911yescharacteristic
206#117C22×C5911yescharacteristic
207C2×C4⋊C4C22×C5911yescharacteristic
208#107C22×C5911yescharacteristic
209#107C22×C5911yescharacteristic
210#107C22×C5911yescharacteristic
211#107C22×C5911yescharacteristic
212#106C22×C5911yescharacteristic
213#106C22×C5911yescharacteristic
214#106C22×C5911yescharacteristic
215#106C22×C5911yescharacteristic
216#106C22×C5911yescharacteristic
217C4⋊C8C22×C5911yescharacteristic
218#103C22×C5911yescharacteristic
219#103C22×C5911yescharacteristic
220#103C22×C5911yescharacteristic
221#102C22×C5911yescharacteristic
222#102C22×C5911yescharacteristic
223#102C22×C5911yescharacteristic
224C22⋊C8C22×C5911yescharacteristic
225C22⋊C8C22×C5911yescharacteristic
226#97C22×C5911yescharacteristic
227C2×Q8—21no—
228C2×Q8C23×C5911yescharacteristic
229C2×D4—21no—
230C2×D4—21no—
231C2×D4D4×C5911yescharacteristic
232C2×D4C23×C5911yescharacteristic
233C22×C4—21no—
234C22×C4—21no—
235C22×C4C23×C5911yescharacteristic
236C22×C4C23×C5911yescharacteristic
237SD16—22no—
238M16—22no—
239C2×C8—22no—
240C2×C8C23×C5911yescharacteristic
241C2×C8C23×C5911yescharacteristic
242C2×C8C23×C5911yescharacteristic
243C2×C8C23×C5911yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4D4×C5911yescharacteristic
252C4⋊C4C23×C5911yescharacteristic
253C4⋊C4C23×C5911yescharacteristic
254C4⋊C4C23×C5911yescharacteristic
255C4⋊C4C23×C5911yescharacteristic
256C4⋊C4C23×C5911yescharacteristic
257C4⋊C4C23×C5911yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4—21no—
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4D4×C5911yescharacteristic
267C22⋊C4D4×C5911yescharacteristic
268C42—21no—
269C42—21no—
270C42—21no—
271C42—21no—
272C42C23×C5911yescharacteristic
273C23—21no—
274C23C2×D4×C5911yescharacteristic
275C23C2×D4×C5911yescharacteristic
276Q8—21no—
277Q8—21no—
278Q8—42no—
279D4—21no—
280D4—21no—
281D4—41no—
282D4—42no—
283D4—81no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4C2×D4×C5911yescharacteristic
298C2×C4C2×D4×C5911yescharacteristic
299C2×C4C2×D4×C5911yescharacteristic
300C2×C4C2×D4×C5911yescharacteristic
301C2×C4C24×C5911yescharacteristic
302C8—21no—
303C8—21no—
304C8—21no—
305C8#41×C5912yes—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22C22×D4×C5911yescharacteristic
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4C2×#41×C5911yescharacteristic
328C42−1+4×C5911yescharacteristic
329C2—41no—
330C2—41no—
331C2—81no—
332C2C59×#54711yescharacteristic
333C2C59×#57511yescharacteristic
334C2C59×#57711yescharacteristic
subgroupG/H
center, socleC22×C59C22×D4
commutator, Frattini, cosocleC2×C4C24×C59
prime radicalC59×#553C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C59 ◁ C4×D4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C59×#556C2semidirect
3. C59×#501C2semidirect
4. C59×#485C2semidirect
5. C59×#483C2semidirect
6. C59×#482C2semidirect
7. C59×#482C2semidirect
8. C59×#479C2semidirect
9. C59×#476C2semidirect
10. C59×#468C2semidirect
11. C59×#465C2semidirect
12. C59×#440C2semidirect
13. C59×#435C2semidirect
14. C59×#428C2semidirect
15. C59×#427C2semidirect
161. #3350C59direct (N × H)
168. #556C2×C59semidirect
170. #501C2×C59semidirect
171. #485C2×C59semidirect
172. #483C2×C59semidirect
173. #482C2×C59semidirect
174. #482C2×C59semidirect
175. #479C2×C59semidirect
176. #476C2×C59semidirect
177. #468C2×C59semidirect
178. #465C2×C59semidirect
179. #440C2×C59semidirect
180. #435C2×C59semidirect
181. #428C2×C59semidirect
182. #427C2×C59semidirect
183. C59#3350direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C59×#5562
C59×#5532
C59×#5012
C59×#4852
C59×#4832
C59×#4822
C59×#4792
C59×#4762
C59×#4682
C59×#4652
C59×#4402
C59×#4352
C59×#4282
C59×#4272
#335059