Finite Group Databasebeta

← C4×#16837339 #28510519

Subgroups — C4×#16837339 #28510519

Order 15104.

1966 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837339C211yesmaximal, characteristic
2C2×C4×C4⋊Dic59C213yesmaximal, complemented
3C2×C4×(C2×D59)⋊C4C213yesmaximal
4#21422363C213yesmaximal, complemented
5#21422361C211yesmaximal, characteristic, complemented
6#21422342C213yesmaximal
7C4×#95×C59C211yesmaximal, characteristic, complemented
8C23×C4×D59C2211yescharacteristic
9C22×C4⋊Dic59C2213yes—
10C22×C4⋊Dic59C2213yes—
11C22×(C2×D59)⋊C4C2213yes—
12C22×(C2×D59)⋊C4C2213yes—
13C22×C4×Dic59C2213yes—
14#16837339C418yesdirect product factor
15C4×C4⋊Dic59—212no—
16C4×(C2×D59)⋊C4—212no—
17C2×C59⋊#95C2216yes—
18C2×C59⋊#95C2213yes—
19C2×C59⋊#95C2213yes—
20C22×C42×C59C2213yes—
21C2×#95×C59C2213yes—
22C2×#95×C59C2211yescharacteristic
23C24×D59C2311yescharacteristic
24C23×Dic59C2313yes—
25C23×Dic59C2311yescharacteristic
26C23×Dic59C2313yes—
27C22×C4×D59—26no—
28C22×C4×D59—26no—
29C22×C4×D59Q814yes—
30C2×C4⋊Dic59—26no—
31C2×C4⋊Dic59—26no—
32C2×C4⋊Dic59—26no—
33C2×C4⋊Dic59—212no—
34C2×C4⋊Dic59C2×C4112yescomplemented
35C2×(C2×D59)⋊C4—26no—
36C2×(C2×D59)⋊C4—26no—
37C2×(C2×D59)⋊C4—26no—
38C2×(C2×D59)⋊C4—26no—
39C2×(C2×D59)⋊C4—26no—
40C2×(C2×D59)⋊C4C2×C4112yes—
41C2×C4×Dic59—26no—
42C2×C4×Dic59—212no—
43C59⋊#95—26no—
44C59⋊#95—26no—
45C59⋊#95—212no—
46C23×C4×C59C2313yes—
47C23×C4×C59C2313yes—
48C23×C4×C59C2311yescharacteristic
49C2×C42×C59—212no—
50C2×C42×C59D4112yes—
51#95×C59—26no—
52#95×C59C2×C414yescomplemented
53C24×C59C2411yescharacteristic
54C23×D59—23no—
55C23×D59—23no—
56C23×D59—23no—
57C23×D59—23no—
58C23×D59C22×C412yes—
59C23×D59C2×Q812yes—
60C23×D59#4112yes—
61C22×C4×C59—26no—
62C22×C4×C59—26no—
63C22×C4×C59—26no—
64C22×C4×C59—26no—
65C22×C4×C59—23no—
66C22×C4×C59—23no—
67C22×C4×C59C22×C416yes—
68C22×C4×C59C2×D416yes—
69C22×C4×C59C2×D416yes—
70C22×C4×C59C2×D416yes—
71C22×C4×C59C2×Q812yes—
72C22×C4×C59#4116yes—
73C22×C4×C59#4116yes—
74C22×Dic59—23no—
75C22×Dic59—23no—
76C22×Dic59—23no—
77C22×Dic59—26no—
78C22×Dic59—26no—
79C22×Dic59—23no—
80C22×Dic59—23no—
81C22×Dic59—26no—
82C22×Dic59—26no—
83C22×Dic59—23no—
84C22×Dic59C22×C416yes—
85C22×Dic59C2×Q812yes—
86C22×Dic59#4116yes—
87C2×C4×D59—224no—
88C2×C4×D59—412no—
89C2×C4×D59—44no—
90C42×C59—224no—
91(C2×D59)⋊C4—224no—
92(C2×D59)⋊C4—224no—
93C4⋊Dic59—224no—
94C4⋊Dic59—224no—
95C4×Dic59—412no—
96C23×C59C23×C411yescharacteristic
97C23×C59C22×D413yes—
98C23×C59C22×Q811yescharacteristic
99C23×C59C2×#4111yescharacteristic
100C23×C59C2×#4113yes—
101C23×C59C2×#4113yes—
102C23×C59C2×#4113yes—
103C22×D59—26no—
104C22×D59—26no—
105C22×D59—26no—
106C22×D59—26no—
107C22×D59—26no—
108C22×D59—26no—
109C22×D59—43no—
110C22×D59—43no—
111C22×D59—46no—
112C22×D59—41no—
113C22×D59—43no—
114C22×D59C4×Q814yes—
115C2×C4×C59—212no—
116C2×C4×C59—26no—
117C2×C4×C59—26no—
118C2×C4×C59—212no—
119C2×C4×C59—26no—
120C2×C4×C59—26no—
121C2×C4×C59—26no—
122C2×C4×C59—46no—
123C2×C4×C59—46no—
124C2×C4×C59C4×D4112yes—
125C2×C4×C59C22⋊Q8112yes—
126C2×C4×C59#123112yes—
127C2×C4×C59#12714yes—
128C2×Dic59—212no—
129C2×Dic59—26no—
130C2×Dic59—26no—
131C2×Dic59—212no—
132C2×Dic59—26no—
133C2×Dic59—43no—
134C2×Dic59—46no—
135C2×Dic59—43no—
136C2×Dic59—43no—
137C2×Dic59—43no—
138C2×Dic59—41no—
139C2×Dic59—43no—
140C2×Dic59—46no—
141C4×D59—416no—
142C4×#399—591nomaximal, Sylow
143C22×C59C2×C4×D413yes—
144C22×C59C2×C4×Q811yescharacteristic
145C22×C59C4×#4113yes—
146C22×C59C2×C22⋊Q813yes—
147C22×C59C2×#12313yes—
148C22×C59#52513yes—
149C22×C59#52513yes—
150C22×C59#52916yes—
151C22×C59#52913yes—
152C22×C59C2×#12711yescharacteristic
153C22×C59#53213yes—
154C22×C59#53313yes—
155C2×D59—212no—
156C2×D59—42no—
157C2×D59—42no—
158C2×D59—46no—
159C2×D59—46no—
160C2×D59—42no—
161C2×D59—46no—
162C4×C59—212no—
163C4×C59—46no—
164C4×C59#39918yescomplemented
165Dic59—46no—
166Dic59—42no—
167Dic59—46no—
168C2×#399—591no—
169C2×C4×C4⋊C4—593no—
170C2×C4×C22⋊C4—593no—
171#1445—593no—
172#1444—591no—
173#1439—593no—
174C4×#95D5911yescharacteristic, complemented
175C2×C59C4×#12313yes—
176C2×C59C4×C22⋊Q813yes—
177C2×C59C4×#12711yescharacteristic
178C2×C59C2×#39911yescharacteristic
179C2×C59#239513yes—
180C2×C59#239613yes—
181C2×C59#239711yescharacteristic
182D59—44no—
183C24×C4—591no—
184C22×C4⋊C4—593no—
185C22×C4⋊C4—593no—
186C22×C22⋊C4—593no—
187C22×C22⋊C4—593no—
188C22×C42—593no—
189C22×C42C2×D5913yes—
190#399—598no—
191C4×C4⋊C4—11812no—
192C4×C22⋊C4—11812no—
193C2×#95—596no—
194C2×#95—593no—
195C2×#95—593no—
196C2×#95C2×D5913yes—
197C2×#95C2×D5911yescharacteristic
198C59C4×#39911yescharacteristic, complemented, Sylow
199C25—591no—
200C23×C4—593no—
201C23×C4—593no—
202C23×C4—591no—
203C23×C4—594no—
204C23×C4—1186no—
205C23×C4—1186no—
206C23×C4C22×D5913yes—
207C23×C4C22×D5913yes—
208C23×C4C22×D5911yescharacteristic
209C2×C4⋊C4—5912no—
210C2×C4⋊C4—11812no—
211C2×C4⋊C4—1186no—
212C2×C4⋊C4—1186no—
213C2×C4⋊C4—1186no—
214C2×C22⋊C4—5912no—
215C2×C22⋊C4—1186no—
216C2×C22⋊C4—1186no—
217C2×C22⋊C4—1186no—
218C2×C22⋊C4—1186no—
219C2×C22⋊C4—1186no—
220C2×C42—212no—
221C2×C42—1186no—
222C2×C42—11812no—
223C2×C42D236112yes—
224#95—26no—
225#95—1186no—
226#95—1186no—
227#95—11812no—
228#95C4×D5914yescomplemented
229C24—592no—
230C24—592no—
231C24—592no—
232C24—1183no—
233C24—1183no—
234C24—1183no—
235C24—1183no—
236C24C23×D5911yescharacteristic
237C22×C4—26no—
238C22×C4—26no—
239C22×C4—23no—
240C22×C4—23no—
241C22×C4—26no—
242C22×C4—26no—
243C22×C4—596no—
244C22×C4—592no—
245C22×C4—596no—
246C22×C4—1183no—
247C22×C4—1183no—
248C22×C4—1183no—
249C22×C4—1186no—
250C22×C4—1186no—
251C22×C4—1183no—
252C22×C4—1186no—
253C22×C4—1183no—
254C22×C4—1183no—
255C22×C4—1186no—
256C22×C4—11824no—
257C22×C4—23612no—
258C22×C4—2364no—
259C22×C4C2×C4×D5916yes—
260C22×C4C2×D23616yes—
261C22×C4C2×D23616yes—
262C22×C4C2×D23616yes—
263C22×C4#1174568516yes—
264C22×C4#1174568716yes—
265C22×C4Q8×D5912yes—
266C4⋊C4—11824no—
267C4⋊C4—11824no—
268C22⋊C4—11824no—
269C22⋊C4—11824no—
270C42—224no—
271C42—23612no—
272C23—594no—
273C23—1186no—
274C23—1186no—
275C23—1186no—
276C23—1186no—
277C23—1186no—
278C23—1186no—
279C23—2363no—
280C23—2363no—
281C23—2366no—
282C23—2361no—
283C23—2363no—
284C23C22×C4×D5911yescharacteristic
285C23C22×D23613yes—
286C23C2×Q8×D5911yescharacteristic
287C23#41×D5913yes—
288C23#41×D5911yescharacteristic
289C23C2×#1174568713yes—
290C23C2×#1174568513yes—
291C2×C4—26no—
292C2×C4—26no—
293C2×C4—212no—
294C2×C4—212no—
295C2×C4—26no—
296C2×C4—26no—
297C2×C4—26no—
298C2×C4—46no—
299C2×C4—46no—
300C2×C4—1186no—
301C2×C4—1186no—
302C2×C4—11812no—
303C2×C4—1186no—
304C2×C4—11812no—
305C2×C4—2363no—
306C2×C4—2366no—
307C2×C4—2363no—
308C2×C4—2363no—
309C2×C4—2363no—
310C2×C4—2361no—
311C2×C4—2363no—
312C2×C4—2366no—
313C2×C4—23616no—
314C2×C4C4×D236112yes—
315C2×C4#14273707112yes—
316C2×C4#14273711112yes—
317C2×C4#1427372414yes—
318C22—11812no—
319C22—2362no—
320C22—2366no—
321C22—2366no—
322C22—2362no—
323C22—2366no—
324C22—2362no—
325C22C2×C4×D23613yes—
326C22C4×Q8×D5911yescharacteristic
327C22C4×#1174568713yes—
328C22C2×#1427370713yes—
329C22C2×#1427371113yes—
330C22#1683791413yes—
331C22#1683791413yes—
332C22#1683793216yes—
333C22#1683793413yes—
334C22C2×#1427372411yescharacteristic
335C22#1683795213yes—
336C22#1683795613yes—
337C4—212no—
338C4—46no—
339C4—2362no—
340C4—2366no—
341C4—2366no—
342C4#1683733918yesdirect product factor
343C2—2364no—
344C2C4×#1427371113yes—
345C2C4×#1427370713yes—
346C2C4×#1427372411yescharacteristic
347C2C2×#1683733911yescharacteristic
348C2#2142735613yes—
349C2#2142736813yes—
350C2#2142737711yescharacteristic
subgroupG/H
centerC23×C4C22×D59
commutatorC23×C59C23×C4
FrattiniC24C23×D59
FittingC4×#95×C59C2
socle, cosocleC24×C59C24
prime radicalC24×D59C23
hypercenterC4×#95D59
hypocenterC59C4×#399
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23×C4 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
2. C2×C4×C4⋊Dic59C2semidirect
4. #21422363C2semidirect
5. #21422361C2semidirect
7. C4×#95×C59C2semidirect
14. #16837339C4direct (N × H)
34. C2×C4⋊Dic59C2×C4semidirect
52. #95×C59C2×C4semidirect
164. C4×C59#399semidirect
174. C4×#95D59semidirect
198. C59C4×#399semidirect
228. #95C4×D59semidirect
342. C4#16837339direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168373392
C2×C4×C4⋊Dic592
C2×C4×(C2×D59)⋊C42
#214223632
#214223612
#214223422
C4×#95×C592
C4×#39959