Finite Group Databasebeta

← C22×#41×#595 #17981035

Subgroups — C22×#41×#595 #17981035

Order 4352.

12878 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×#595C2148yesmaximal, direct product factor
2C22×Q8×#595C212yesmaximal, complemented
3C22×D4×#595C216yesmaximal, complemented
4C22×#10587677C213yesmaximal, complemented
5C23×C4×#595C213yesmaximal, complemented
6C22×#41×D17C211yesmaximal, characteristic
7C24×#595C2216yes—
8#41×#595C221256yesdirect product factor
9C2×Q8×#595C22148yescomplemented
10C2×D4×#595C221144yescomplemented
11C2×#10587677C22172yescomplemented
12C22×C4⋊#595C2216yes—
13C22×C22⋊#595C2216yes—
14C22×C4×#595C2211yescharacteristic
15C22×C4×#595C2213yes—
16C22×C4×#595C2216yes—
17C22×C4×#595C22172yescomplemented
18C22×#63256C411yescharacteristic, complemented
19C22×#63252C413yescomplemented
20C22×#63254C413yescomplemented
21C2×#41×D17C4124yescomplemented
22C2×#41×D17C22124yes—
23C22×Q8×D17C2211yescharacteristic
24C22×D4×D17C2213yes—
25C23×C4×D17C2213yes—
26C22×#41×C17C411yescharacteristic, complemented
27C24×D17C2313yes—
28C23×#595—248no—
29C23×#595C2316yes—
30C23×#595C23172yes—
31C23×#595C2312yes—
32C2×#41×C17C2×C4124yescomplemented
33C22×Q8×C17C2×C411yescharacteristic, complemented
34C22×D4×C17C2×C413yescomplemented
35C23×C4×C17C2×C413yescomplemented
36C22×C22⋊D17C2×C416yescomplemented
37C23×Dic17C2×C413yescomplemented
38#41×D17C2×C41192yescomplemented
39#41×D17C23164yes—
40C2×#63256C2×C4124yescomplemented
41C2×Q8×D17C2×C4112yescomplemented
42C2×Q8×D17C23112yes—
43C2×#63254C2×C4172yescomplemented
44C2×D4×D17C2×C4136yescomplemented
45C2×D4×D17C23136yes—
46C2×#63252C2×C4172yescomplemented
47C22×D68C2×C413yescomplemented
48C22×C4×D17C2×C4136yescomplemented
49C22×C4×D17C2×C413yescomplemented
50C22×C4×D17C2×C413yescomplemented
51C22×C4×D17C2311yescharacteristic
52C22×C4×D17C2313yes—
53C22×C4×D17C23136yes—
54C22×Dic34C2×C413yescomplemented
55C2×C22⋊#595C23172yes—
56Q8×#595C231128yescomplemented
57D4×#595C231384yescomplemented
58#10587677C231192yescomplemented
59C2×C4⋊#595C23172yes—
60C2×C4×#595C23112yes—
61C2×C4×#595C23136yes—
62C2×C4×#595C23172yes—
63C2×C4×#595C231192yescomplemented
64C24×C17C22×C413yes—
65C23×D17—224no—
66C23×D17C22×C413yes—
67C23×D17C22×C4118yes—
68C23×D17C24118yes—
69C23×D17C2411yescharacteristic
70C22×#595—224no—
71C22×#595—2288no—
72C22×#595#41116yesdirect product factor
73C22×#595C24136yes—
74C22×#595C24196yes—
75C22×#595C24112yes—
76#41×C17C22×C4164yescomplemented
77C2×Q8×C17C22×C4112yescomplemented
78C2×D4×C17C22×C4136yescomplemented
79C22×C4×C17C22×C413yes—
80C22×C4×C17C22×C411yescharacteristic
81C22×C4×C17C22×C4136yescomplemented
82C2×C22⋊D17C22×C4172yescomplemented
83C22×Dic17C22×C413yes—
84C22×Dic17C22×C411yescharacteristic
85C22×Dic17C22×C4136yescomplemented
86#63256C22×C4164yescomplemented
87Q8×D17C22×C4148yescomplemented
88Q8×D17C24116yes—
89#63254C22×C41192yescomplemented
90D4×D17C22×C41144yescomplemented
91D4×D17C24148yes—
92#63252C22×C41192yescomplemented
93C2×D68C22×C4136yescomplemented
94C2×C4×D17C22×C416yes—
95C2×C4×D17C22×C4118yes—
96C2×C4×D17C22×C41144yescomplemented
97C2×C4×D17C22×C4136yescomplemented
98C2×C4×D17C22×C4136yescomplemented
99C2×C4×D17C2416yes—
100C2×C4×D17C24118yes—
101C2×C4×D17C24148yes—
102C2×Dic34C22×C4136yescomplemented
103C22⋊#595C24196yes—
104C4⋊#595C24196yes—
105C4×#595C24116yes—
106C4×#595C24148yes—
107C4×#595C24196yes—
108C22×C4×#41—171nomaximal, Sylow
109C23×C17—212no—
110C23×C17C23×C4118yes—
111C23×C17C23×C411yescharacteristic
112C22×D17—212no—
113C22×D17—272no—
114C22×D17—272no—
115C22×D17C23×C4118yes—
116C22×D17C23×C4136yes—
117C22×D17C23×C413yes—
118C22×D17C2×#4118yes—
119C22×D17C25112yes—
120C22×D17C2513yes—
121C2×#595—272no—
122C2×#595—2192no—
123C2×#595C2×#41148yesdirect product factor
124C2×#595C25124yes—
125C2×#595C2518yes—
126Q8×C17C23×C4116yescomplemented
127D4×C17C23×C4148yescomplemented
128C2×C4×C17C23×C4118yes—
129C2×C4×C17C23×C416yes—
130C2×C4×C17C23×C4148yescomplemented
131C22⋊D17C23×C4196yescomplemented
132C2×Dic17C23×C4118yes—
133C2×Dic17C23×C416yes—
134C2×Dic17C23×C4148yescomplemented
135D68C23×C4148yescomplemented
136C4×D17C23×C4112yes—
137C4×D17C23×C4136yes—
138C4×D17C23×C4148yescomplemented
139C4×D17C23×C4148yescomplemented
140C4×D17C2514yes—
141C4×D17C25112yes—
142Dic34C23×C4148yescomplemented
143C23×#41—171no—
144C2×C4×#41—1748no—
145C22×C4×Q8—172no—
146C22×C4×D4—176no—
147C22×#117—173no—
148C23×C42—173no—
149C22×C17—236no—
150C22×C17C4×#4114yescomplemented
151C22×C17C24×C4112yes—
152C22×C17C24×C413yes—
153C2×D17—236no—
154C2×D17—224no—
155C2×D17—272no—
156C2×D17C4×#41112yescomplemented
157C2×D17C24×C4112yes—
158C2×D17C24×C413yes—
159C2×D17C22×#41112yes—
160C2×D17C2611yescharacteristic
161#595—224no—
162#595C22×#41116yesdirect product factor
163C4×C17C24×C4112yes—
164C4×C17C24×C414yes—
165Dic17C24×C4112yes—
166Dic17C24×C414yes—
167C22×#41—1724no—
168C22×#41—1724no—
169C22×#41—171no—
170C22×#41—173no—
171C22×#41—173no—
172C22×#41#59511yescharacteristic, direct product factor
173C23×Q8—171no—
174C23×D4—173no—
175C24×C4—173no—
176C24×C4—176no—
177C4×#41—17256no—
178C2×C4×Q8—1748no—
179C2×C4×D4—17144no—
180C2×#117—1772no—
181C22×C4⋊C4—176no—
182C22×C22⋊C4—176no—
183C22×C42—171no—
184C22×C42—173no—
185C22×C42—176no—
186C22×C42—1772no—
187C2×C17—212no—
188C2×C17C2×C4×#4116yescomplemented
189C2×C17C25×C411yescharacteristic
190D17—212no—
191D17C2×C4×#4116yescomplemented
192D17C23×#4112yes—
193C25—173no—
194C2×#41—1764no—
195C2×#41—17192no—
196C2×#41—1724no—
197C2×#41—1772no—
198C2×#41—1772no—
199C2×#41C2×#595124yesdirect product factor
200C22×Q8—1712no—
201C22×Q8—1712no—
202C22×Q8—173no—
203C22×Q8C2×#59511yescharacteristic, complemented
204C22×D4—176no—
205C22×D4—1736no—
206C22×D4—1736no—
207C22×D4—173no—
208C22×D4C2×#59513yescomplemented
209C23×C4—172no—
210C23×C4—173no—
211C23×C4—173no—
212C23×C4—173no—
213C23×C4—173no—
214C23×C4—171no—
215C23×C4—1736no—
216C23×C4—1736no—
217C23×C4—176no—
218C23×C4—1772no—
219C23×C4—3448no—
220C23×C4C2×#59513yescomplemented
221C4×Q8—17128no—
222C4×D4—17384no—
223#117—17192no—
224C2×C4⋊C4—1772no—
225C2×C22⋊C4—1772no—
226C2×C42—1736no—
227C2×C42—1772no—
228C2×C42—17192no—
229C2×C42—1712no—
230C17C22×C4×#4111yescharacteristic, complemented, Sylow
231C24—171no—
232C24—1718no—
233C24—173no—
234C24—1718no—
235C24—3424no—
236C24C22×#59513yes—
237#41—1764no—
238#41—17192no—
239#41—17192no—
240#41C22×#595164yesdirect product factor
241C2×Q8—1748no—
242C2×Q8—1716no—
243C2×Q8—1736no—
244C2×Q8C22×#595112yescomplemented
245C2×D4—1772no—
246C2×D4—17144no—
247C2×D4—1748no—
248C2×D4—1736no—
249C2×D4C22×#595136yescomplemented
250C22×C4—1716no—
251C22×C4—1712no—
252C22×C4—171no—
253C22×C4—173no—
254C22×C4—1736no—
255C22×C4—176no—
256C22×C4—1718no—
257C22×C4—1736no—
258C22×C4—1736no—
259C22×C4—176no—
260C22×C4—1718no—
261C22×C4—17144no—
262C22×C4—1748no—
263C22×C4—1736no—
264C22×C4—1796no—
265C22×C4—34288no—
266C22×C4—3424no—
267C22×C4C22×#59513yes—
268C22×C4C22×#59511yescharacteristic
269C22×C4C22×#595136yescomplemented
270C4⋊C4—1796no—
271C22⋊C4—1796no—
272C42—1716no—
273C42—1748no—
274C42—1796no—
275C23—212no—
276C23—178no—
277C23—173no—
278C23—173no—
279C23—1712no—
280C23—1736no—
281C23—1718no—
282C23—3472no—
283C23—3472no—
284C23—3412no—
285C23C23×#595118yes—
286C23C23×#59511yescharacteristic
287Q8—1748no—
288Q8C23×#595116yescomplemented
289D4—1796no—
290D4—1748no—
291D4C23×#595148yescomplemented
292C2×C4—178no—
293C2×C4—1748no—
294C2×C4—176no—
295C2×C4—1718no—
296C2×C4—1748no—
297C2×C4—174no—
298C2×C4—1712no—
299C2×C4—1712no—
300C2×C4—1736no—
301C2×C4—1748no—
302C2×C4—1748no—
303C2×C4—1724no—
304C2×C4—34192no—
305C2×C4—3472no—
306C2×C4C23×#59516yes—
307C2×C4C23×#595118yes—
308C2×C4C23×#595148yescomplemented
309C22—236no—
310C22—1712no—
311C22—1712no—
312C22—171no—
313C22—173no—
314C22—1712no—
315C22—3424no—
316C22—3472no—
317C22—3436no—
318C22#41×#59514yesdirect product factor
319C22C24×#595112yes—
320C22C24×#59513yes—
321C4—1716no—
322C4—174no—
323C4—1712no—
324C4—3424no—
325C4C24×#59514yes—
326C4C24×#595112yes—
327C2—212no—
328C2—172no—
329C2—176no—
330C2—3412no—
331C2C2×#41×#59516yesdirect product factor
332C2C25×#59511yescharacteristic
subgroupG/H
centerC22×C4C22×#595
commutatorC2×C17C25×C4
FrattiniC2C25×#595
FittingC22×#41×C17C4
socleC23×C17C23×C4
prime radicalC22×#41×D17C2
cosocleC2×D17C26
hypercenterC22×#41#595
hypocenterC17C22×C4×#41
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C2×#41×#595C2direct (N × H)
2. C22×Q8×#595C2semidirect
3. C22×D4×#595C2semidirect
4. C22×#10587677C2semidirect
5. C23×C4×#595C2semidirect
8. #41×#595C22direct (N × H)
9. C2×Q8×#595C22semidirect
10. C2×D4×#595C22semidirect
11. C2×#10587677C22semidirect
17. C22×C4×#595C22semidirect
18. C22×#63256C4semidirect
19. C22×#63252C4semidirect
20. C22×#63254C4semidirect
21. C2×#41×D17C4semidirect
26. C22×#41×C17C4semidirect
32. C2×#41×C17C2×C4semidirect
33. C22×Q8×C17C2×C4semidirect
34. C22×D4×C17C2×C4semidirect
35. C23×C4×C17C2×C4semidirect
36. C22×C22⋊D17C2×C4semidirect
37. C23×Dic17C2×C4semidirect
38. #41×D17C2×C4semidirect
40. C2×#63256C2×C4semidirect
41. C2×Q8×D17C2×C4semidirect
43. C2×#63254C2×C4semidirect
44. C2×D4×D17C2×C4semidirect
46. C2×#63252C2×C4semidirect
47. C22×D68C2×C4semidirect
48. C22×C4×D17C2×C4semidirect
49. C22×C4×D17C2×C4semidirect
50. C22×C4×D17C2×C4semidirect
54. C22×Dic34C2×C4semidirect
56. Q8×#595C23semidirect
57. D4×#595C23semidirect
58. #10587677C23semidirect
63. C2×C4×#595C23semidirect
72. C22×#595#41direct (N × H)
76. #41×C17C22×C4semidirect
77. C2×Q8×C17C22×C4semidirect
78. C2×D4×C17C22×C4semidirect
81. C22×C4×C17C22×C4semidirect
82. C2×C22⋊D17C22×C4semidirect
85. C22×Dic17C22×C4semidirect
86. #63256C22×C4semidirect
87. Q8×D17C22×C4semidirect
89. #63254C22×C4semidirect
90. D4×D17C22×C4semidirect
92. #63252C22×C4semidirect
93. C2×D68C22×C4semidirect
96. C2×C4×D17C22×C4semidirect
97. C2×C4×D17C22×C4semidirect
98. C2×C4×D17C22×C4semidirect
102. C2×Dic34C22×C4semidirect
123. C2×#595C2×#41direct (N × H)
126. Q8×C17C23×C4semidirect
127. D4×C17C23×C4semidirect
130. C2×C4×C17C23×C4semidirect
131. C22⋊D17C23×C4semidirect
134. C2×Dic17C23×C4semidirect
135. D68C23×C4semidirect
138. C4×D17C23×C4semidirect
139. C4×D17C23×C4semidirect
142. Dic34C23×C4semidirect
150. C22×C17C4×#41semidirect
156. C2×D17C4×#41semidirect
162. #595C22×#41direct (N × H)
172. C22×#41#595direct (N × H)
188. C2×C17C2×C4×#41semidirect
191. D17C2×C4×#41semidirect
199. C2×#41C2×#595direct (N × H)
203. C22×Q8C2×#595semidirect
208. C22×D4C2×#595semidirect
220. C23×C4C2×#595semidirect
230. C17C22×C4×#41semidirect
240. #41C22×#595direct (N × H)
244. C2×Q8C22×#595semidirect
249. C2×D4C22×#595semidirect
269. C22×C4C22×#595semidirect
288. Q8C23×#595semidirect
291. D4C23×#595semidirect
308. C2×C4C23×#595semidirect
318. C22#41×#595direct (N × H)
331. C2C2×#41×#595direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#41×#5952
C22×Q8×#5952
C22×D4×#5952
C22×#105876772
C23×C4×#5952
C22×#41×D172
C22×C4×#4117