Finite Group Databasebeta

← C59×#34643 #28446752

Subgroups — C59×#34643 #28446752

Order 15104.

2234 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#529C212yesmaximal, complemented
2C59×#2664C214yesmaximal, complemented
3C59×#2663C214yesmaximal, complemented
4C59×#2662C214yesmaximal, complemented
5C59×#2661C214yesmaximal, complemented
6C59×#2399C211yesmaximal, characteristic, complemented
7C59×#2398C212yesmaximal, complemented
8C59×#2397C211yesmaximal, characteristic, complemented
9C59×#2392C214yesmaximal, complemented
10C59×#2293C214yesmaximal, complemented
11C4×#117×C59C211yesmaximal, characteristic, complemented
12C59×#529—216no—
13C2×#126×C59C2214yes—
14C2×#125×C59C2212yes—
15C2×#124×C59C2212yes—
16C2×#123×C59C2214yes—
17C2×C22⋊Q8×C59C2212yes—
18C2×#121×C59C2212yes—
19C2×C4×Q8×C59C2212yes—
20C2×C4×D4×C59C2214yes—
21C2×C4×D4×C59C2214yes—
22C2×C4×D4×C59C2212yes—
23C2×#117×C59C2212yes—
24C2×#117×C59C2214yes—
25C22×C42×C59C2211yescharacteristic
26C59×#400C2214yes—
27C59×#399C2214yes—
28C59×#398C2214yes—
29C59×#398C2214yes—
30C59×#397C2214yes—
31C59×#397C2214yes—
32C59×#396C2218yes—
33C59×#395C2214yes—
34C59×#394C2218yes—
35C59×#394C2214yes—
36C59×#394C2214yes—
37C59×#393C2214yes—
38C59×#392C2214yes—
39C59×#392C2214yes—
40C59×#390C2218yes—
41C59×#389C2218yes—
42C59×#388C2218yes—
43C59×#388C2218yes—
44C4×C4⋊C4×C59C2214yes—
45C4×C4⋊C4×C59C2214yes—
46C4×C22⋊C4×C59C2214yes—
47C4×C22⋊C4×C59C2218yes—
48C59×#376C2211yescharacteristic
49C59×#376C2211yescharacteristic
50C43×C59C2212yes—
51C22×Q8×C59C2312yes—
52C22×D4×C59C2314yes—
53C22×D4×C59C2314yes—
54C22×D4×C59C2312yes—
55C23×C4×C59C2314yes—
56C23×C4×C59C2311yescharacteristic
57C23×C4×C59C2312yes—
58#126×C59—216no—
59#125×C59—28no—
60#124×C59—28no—
61#123×C59—216no—
62C22⋊Q8×C59—28no—
63#121×C59—28no—
64C4×Q8×C59—28no—
65C4×D4×C59—216no—
66C4×D4×C59—28no—
67C4×D4×C59—216no—
68#117×C59—216no—
69#117×C59—28no—
70C2×C4⋊C4×C59C2314yes—
71C2×C4⋊C4×C59C2314yes—
72C2×C4⋊C4×C59C2314yes—
73C2×C4⋊C4×C59C2314yes—
74C2×C4⋊C4×C59C2314yes—
75C2×C4⋊C4×C59C2314yes—
76C2×C4⋊C4×C59C2312yes—
77C2×C4⋊C4×C59C2312yes—
78C2×C4⋊C4×C59C2318yes—
79C2×C22⋊C4×C59C2314yes—
80C2×C22⋊C4×C59C2314yes—
81C2×C22⋊C4×C59C2314yes—
82C2×C22⋊C4×C59C2318yes—
83C2×C22⋊C4×C59C2314yes—
84C2×C22⋊C4×C59C2314yes—
85C2×C22⋊C4×C59C2314yes—
86C2×C22⋊C4×C59C2318yes—
87C2×C22⋊C4×C59C2318yes—
88C2×C42×C59D418yescomplemented
89C2×C42×C59C2312yes—
90C2×C42×C59C2314yes—
91C2×C42×C59C2318yes—
92C2×C42×C59C2312yes—
93C2×C42×C59C2311yescharacteristic
94C2×C42×C59C2311yescharacteristic
95C2×C42×C59C2312yes—
96#95×C59C2314yes—
97#95×C59C2314yes—
98#95×C59C2318yes—
99#95×C59C2318yes—
100#95×C59C2314yes—
101#95×C59C2314yes—
102C24×C59C2414yes—
103C24×C59C2411yescharacteristic
104C2×Q8×C59—24no—
105C2×Q8×C59—44no—
106C2×D4×C59—28no—
107C2×D4×C59—24no—
108C2×D4×C59—28no—
109C2×D4×C59—48no—
110C2×D4×C59—44no—
111C2×D4×C59—48no—
112C22×C4×C59—24no—
113C22×C4×C59—28no—
114C22×C4×C59—216no—
115C22×C4×C59—44no—
116C22×C4×C59C2×D414yes—
117C22×C4×C59C2×D418yes—
118C22×C4×C59C2414yes—
119C22×C4×C59C2414yes—
120C22×C4×C59C2414yes—
121C22×C4×C59C2414yes—
122C22×C4×C59C2412yes—
123C22×C4×C59C2412yes—
124C22×C4×C59C2411yescharacteristic
125C22×C4×C59C2414yes—
126C22×C4×C59C2411yescharacteristic
127C4⋊C4×C59—28no—
128C4⋊C4×C59—28no—
129C4⋊C4×C59—24no—
130C4⋊C4×C59—28no—
131C4⋊C4×C59—24no—
132C4⋊C4×C59—28no—
133C4⋊C4×C59—28no—
134C4⋊C4×C59—28no—
135C4⋊C4×C59—48no—
136C22⋊C4×C59—28no—
137C22⋊C4×C59—28no—
138C22⋊C4×C59—28no—
139C22⋊C4×C59—28no—
140C22⋊C4×C59—28no—
141C22⋊C4×C59—28no—
142C22⋊C4×C59—216no—
143C22⋊C4×C59—48no—
144C22⋊C4×C59—48no—
145C42×C59—28no—
146C42×C59—24no—
147C42×C59—48no—
148C42×C59C2×D414yes—
149C42×C59C2×D414yes—
150C42×C59C2×D418yes—
151C42×C59#4118yes—
152C23×C59—22no—
153C23×C59—24no—
154C23×C59—24no—
155C23×C59—28no—
156C23×C59—24no—
157C23×C59—28no—
158C23×C59—24no—
159C23×C59C22×D412yes—
160C23×C59C2511yescharacteristic
161Q8×C59—48no—
162D4×C59—48no—
163D4×C59—416no—
164D4×C59—416no—
165C2×C4×C59—22no—
166C2×C4×C59—24no—
167C2×C4×C59—28no—
168C2×C4×C59—24no—
169C2×C4×C59—28no—
170C2×C4×C59—24no—
171C2×C4×C59—24no—
172C2×C4×C59—24no—
173C2×C4×C59—24no—
174C2×C4×C59—28no—
175C2×C4×C59—28no—
176C2×C4×C59—24no—
177C2×C4×C59—28no—
178C2×C4×C59—24no—
179C2×C4×C59—48no—
180C2×C4×C59—416no—
181C2×C4×C59C22×D412yes—
182C2×C4×C59C22×D414yes—
183C2×C4×C59C22×D414yes—
184C2×C4×C59C22×D412yes—
185C2×C4×C59C2×#4118yes—
186C2×C4×C59C2×#4114yes—
187#34643C5911yesmaximal, characteristic, direct product factor, Sylow
188C22×C59—22no—
189C22×C59—24no—
190C22×C59—44no—
191C22×C59—44no—
192C22×C59—44no—
193C22×C59—44no—
194C22×C59—48no—
195C22×C59—48no—
196C22×C59C23×D411yescharacteristic
197C22×C59C22×#4112yes—
198C22×C59#58514yes—
199C4×C59—22no—
200C4×C59—24no—
201C4×C59—24no—
202C4×C59—28no—
203C4×C59—44no—
204C4×C59—44no—
205C4×C59—44no—
206C4×C59—44no—
207C4×C59#53214yes—
208C2×#529C2×C5912yescomplemented
209#2664C2×C5914yescomplemented
210#2663C2×C5914yescomplemented
211#2662C2×C5914yescomplemented
212#2661C2×C5914yescomplemented
213#2399C2×C5911yescharacteristic, complemented
214#2398C2×C5912yescomplemented
215#2397C2×C5911yescharacteristic, complemented
216#2392C2×C5914yescomplemented
217#2293C2×C5914yescomplemented
218C4×#117C2×C5911yescharacteristic, complemented
219C2×C59—42no—
220C2×C59—84no—
221C2×C59C2×#53211yescharacteristic
222C2×C59#344912yes—
223C2×C59#345514yes—
224#529—216no—
225C2×#126C22×C5914yes—
226C2×#125C22×C5912yes—
227C2×#124C22×C5912yes—
228C2×#123C22×C5914yes—
229C2×C22⋊Q8C22×C5912yes—
230C2×#121C22×C5912yes—
231C2×C4×Q8C22×C5912yes—
232C2×C4×D4C22×C5914yes—
233C2×C4×D4C22×C5914yes—
234C2×C4×D4C22×C5912yes—
235C2×#117C22×C5912yes—
236C2×#117C22×C5914yes—
237C22×C42C22×C5911yescharacteristic
238#400C22×C5914yes—
239#399C22×C5914yes—
240#398C22×C5914yes—
241#398C22×C5914yes—
242#397C22×C5914yes—
243#397C22×C5914yes—
244#396C22×C5918yes—
245#395C22×C5914yes—
246#394C22×C5918yes—
247#394C22×C5914yes—
248#394C22×C5914yes—
249#393C22×C5914yes—
250#392C22×C5914yes—
251#392C22×C5914yes—
252#390C22×C5918yes—
253#389C22×C5918yes—
254#388C22×C5918yes—
255#388C22×C5918yes—
256C4×C4⋊C4C22×C5914yes—
257C4×C4⋊C4C22×C5914yes—
258C4×C22⋊C4C22×C5918yes—
259C4×C22⋊C4C22×C5914yes—
260#376C22×C5911yescharacteristic
261#376C22×C5911yescharacteristic
262C43C22×C5912yes—
263C59#3464311yescharacteristic, direct product factor, Sylow
264C22×Q8C23×C5912yes—
265C22×D4C23×C5914yes—
266C22×D4C23×C5912yes—
267C22×D4C23×C5914yes—
268C23×C4C23×C5914yes—
269C23×C4C23×C5911yescharacteristic
270C23×C4C23×C5912yes—
271#126—216no—
272#125—28no—
273#124—28no—
274#123—216no—
275C22⋊Q8—28no—
276#121—28no—
277C4×Q8—28no—
278C4×D4—216no—
279C4×D4—28no—
280C4×D4—216no—
281#117—216no—
282#117—28no—
283C2×C4⋊C4C23×C5914yes—
284C2×C4⋊C4C23×C5914yes—
285C2×C4⋊C4C23×C5914yes—
286C2×C4⋊C4C23×C5912yes—
287C2×C4⋊C4C23×C5914yes—
288C2×C4⋊C4C23×C5914yes—
289C2×C4⋊C4C23×C5912yes—
290C2×C4⋊C4C23×C5914yes—
291C2×C4⋊C4C23×C5918yes—
292C2×C22⋊C4C23×C5914yes—
293C2×C22⋊C4C23×C5914yes—
294C2×C22⋊C4C23×C5914yes—
295C2×C22⋊C4C23×C5914yes—
296C2×C22⋊C4C23×C5914yes—
297C2×C22⋊C4C23×C5914yes—
298C2×C22⋊C4C23×C5918yes—
299C2×C22⋊C4C23×C5918yes—
300C2×C22⋊C4C23×C5918yes—
301C2×C42D4×C5918yescomplemented
302C2×C42C23×C5914yes—
303C2×C42C23×C5912yes—
304C2×C42C23×C5918yes—
305C2×C42C23×C5911yescharacteristic
306C2×C42C23×C5911yescharacteristic
307C2×C42C23×C5912yes—
308C2×C42C23×C5912yes—
309#95C23×C5914yes—
310#95C23×C5914yes—
311#95C23×C5918yes—
312#95C23×C5918yes—
313#95C23×C5914yes—
314#95C23×C5914yes—
315C24C24×C5914yes—
316C24C24×C5911yescharacteristic
317C2×Q8—24no—
318C2×Q8—44no—
319C2×D4—28no—
320C2×D4—24no—
321C2×D4—28no—
322C2×D4—48no—
323C2×D4—44no—
324C2×D4—48no—
325C22×C4—24no—
326C22×C4—28no—
327C22×C4—216no—
328C22×C4—44no—
329C22×C4C2×D4×C5914yes—
330C22×C4C2×D4×C5918yes—
331C22×C4C24×C5914yes—
332C22×C4C24×C5914yes—
333C22×C4C24×C5914yes—
334C22×C4C24×C5914yes—
335C22×C4C24×C5912yes—
336C22×C4C24×C5912yes—
337C22×C4C24×C5911yescharacteristic
338C22×C4C24×C5914yes—
339C22×C4C24×C5911yescharacteristic
340C4⋊C4—28no—
341C4⋊C4—28no—
342C4⋊C4—24no—
343C4⋊C4—28no—
344C4⋊C4—24no—
345C4⋊C4—28no—
346C4⋊C4—28no—
347C4⋊C4—28no—
348C4⋊C4—48no—
349C22⋊C4—28no—
350C22⋊C4—28no—
351C22⋊C4—28no—
352C22⋊C4—28no—
353C22⋊C4—28no—
354C22⋊C4—28no—
355C22⋊C4—216no—
356C22⋊C4—48no—
357C22⋊C4—48no—
358C42—28no—
359C42—24no—
360C42—48no—
361C42C2×D4×C5914yes—
362C42C2×D4×C5914yes—
363C42C2×D4×C5918yes—
364C42#41×C5918yes—
365C23—22no—
366C23—24no—
367C23—24no—
368C23—28no—
369C23—24no—
370C23—28no—
371C23—24no—
372C23C22×D4×C5912yes—
373C23C25×C5911yescharacteristic
374Q8—48no—
375D4—48no—
376D4—416no—
377D4—416no—
378C2×C4—22no—
379C2×C4—24no—
380C2×C4—28no—
381C2×C4—24no—
382C2×C4—28no—
383C2×C4—24no—
384C2×C4—24no—
385C2×C4—24no—
386C2×C4—24no—
387C2×C4—28no—
388C2×C4—28no—
389C2×C4—24no—
390C2×C4—28no—
391C2×C4—24no—
392C2×C4—48no—
393C2×C4—416no—
394C2×C4C22×D4×C5912yes—
395C2×C4C22×D4×C5914yes—
396C2×C4C22×D4×C5914yes—
397C2×C4C22×D4×C5912yes—
398C2×C4C2×#41×C5918yes—
399C2×C4C2×#41×C5914yes—
400C22—22no—
401C22—24no—
402C22—44no—
403C22—44no—
404C22—44no—
405C22—44no—
406C22—48no—
407C22—48no—
408C22C23×D4×C5911yescharacteristic
409C22C22×#41×C5912yes—
410C22C59×#58514yes—
411C4—22no—
412C4—24no—
413C4—24no—
414C4—28no—
415C4—44no—
416C4—44no—
417C4—44no—
418C4—44no—
419C4C59×#53214yes—
420C2—42no—
421C2—84no—
422C2C2×C59×#53211yescharacteristic
423C2C59×#344912yes—
424C2C59×#345514yes—
subgroupG/H
centerC22×C4×C59C24
commutator, Frattini, cosocleC23C25×C59
socleC23×C59C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C59×#529C2semidirect
2. C59×#2664C2semidirect
3. C59×#2663C2semidirect
4. C59×#2662C2semidirect
5. C59×#2661C2semidirect
6. C59×#2399C2semidirect
7. C59×#2398C2semidirect
8. C59×#2397C2semidirect
9. C59×#2392C2semidirect
10. C59×#2293C2semidirect
11. C4×#117×C59C2semidirect
88. C2×C42×C59D4semidirect
187. #34643C59direct (N × H)
208. C2×#529C2×C59semidirect
209. #2664C2×C59semidirect
210. #2663C2×C59semidirect
211. #2662C2×C59semidirect
212. #2661C2×C59semidirect
213. #2399C2×C59semidirect
214. #2398C2×C59semidirect
215. #2397C2×C59semidirect
216. #2392C2×C59semidirect
217. #2293C2×C59semidirect
218. C4×#117C2×C59semidirect
263. C59#34643direct (N × H)
301. C2×C42D4×C59semidirect

Maximal subgroups

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

subgroupindex
C2×C59×#5292
C59×#26642
C59×#26632
C59×#26622
C59×#26612
C59×#23992
C59×#23982
C59×#23972
C59×#23922
C59×#22932
C4×#117×C592
#3464359