Finite Group Databasebeta

← C59×#10268 #28422377

Subgroups — C59×#10268 #28422377

Order 15104.

658 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#492C211yesmaximal, characteristic
2C2×C59×#475C211yesmaximal, characteristic, complemented
3C2×C59×#460C211yesmaximal, characteristic
4C59×#1984C211yesmaximal, characteristic, complemented
5C2×C59×#332C211yesmaximal, characteristic, complemented
6C2×C59×#331C211yesmaximal, characteristic
7C59×#1277C211yesmaximal, characteristic, complemented
8C22×SD16×C59—21no—
9C22×SD16×C59—22no—
10C2×C4⋊Q8×C59C2211yescharacteristic
11C2×#127×C59C2211yescharacteristic
12C2×C4×Q8×C59C2211yescharacteristic
13C59×#492—22no—
14C59×#492—22no—
15C59×#475—22no—
16C59×#475—22no—
17C59×#460—22no—
18C59×#460—22no—
19C2×#106×C59—21no—
20C2×C4⋊C8×C59C2211yescharacteristic
21C2×C4⋊C8×C59C2211yescharacteristic
22C2×C4⋊C8×C59C2211yescharacteristic
23C2×#103×C59—21no—
24C2×#102×C59—21no—
25C2×C4×C8×C59C2211yescharacteristic
26C59×#336—22no—
27C59×#332—22no—
28C59×#331—22no—
29C22×Q8×C59—21no—
30C22×Q8×C59D411yescharacteristic
31C22×D4×C59—21no—
32C22×D4×C59—21no—
33C22×D4×C59—21no—
34C2×SD16×C59—24no—
35C2×SD16×C59—28no—
36C2×SD16×C59—44no—
37C2×SD16×C59—42no—
38C2×SD16×C59—42no—
39C2×SD16×C59—44no—
40C22×C8×C59—21no—
41C22×C8×C59—21no—
42C22×C8×C59—21no—
43C22×C8×C59D412yes—
44C4⋊Q8×C59—21no—
45C4⋊Q8×C59—21no—
46C4⋊Q8×C59—21no—
47C4⋊Q8×C59D412yes—
48#127×C59—21no—
49#127×C59—21no—
50#127×C59—21no—
51#127×C59D412yes—
52C4×Q8×C59—21no—
53C4×Q8×C59—21no—
54C4×Q8×C59—21no—
55C4×Q8×C59—21no—
56C2×C4⋊C4×C59—21no—
57C2×C4⋊C4×C59—21no—
58C2×C4⋊C4×C59—21no—
59C2×C4⋊C4×C59D411yescharacteristic
60C2×C42×C59—21no—
61C2×C42×C59C2311yescharacteristic
62#106×C59—24no—
63C4⋊C8×C59—21no—
64C4⋊C8×C59—21no—
65C4⋊C8×C59—21no—
66C4⋊C8×C59—21no—
67C4⋊C8×C59D412yes—
68C4⋊C8×C59D412yes—
69#103×C59—24no—
70#102×C59—24no—
71C4×C8×C59—21no—
72C4×C8×C59—21no—
73C24×C59—41no—
74C2×Q8×C59—21no—
75C2×Q8×C59—21no—
76C2×Q8×C59—21no—
77C2×Q8×C59—22no—
78C2×Q8×C59—21no—
79C2×Q8×C59—21no—
80C2×Q8×C59—41no—
81C2×Q8×C59—42no—
82C2×Q8×C59—42no—
83C2×Q8×C59SD1612yescomplemented
84C2×D4×C59—22no—
85C2×D4×C59—22no—
86C2×D4×C59—22no—
87C2×D4×C59—41no—
88C2×D4×C59—41no—
89C2×D4×C59—41no—
90C2×D4×C59—41no—
91C2×D4×C59—42no—
92C2×D4×C59—41no—
93C2×D4×C59—41no—
94C2×D4×C59—42no—
95C2×D4×C59—41no—
96C2×D4×C59—82no—
97C22×C4×C59—21no—
98C22×C4×C59—21no—
99C22×C4×C59—41no—
100C22×C4×C59C2×D411yescharacteristic
101C22×C4×C59C2×D411yescharacteristic
102C22×C4×C59#4111yescharacteristic
103SD16×C59—416no—
104SD16×C59—48no—
105C2×C8×C59—22no—
106C2×C8×C59—22no—
107C2×C8×C59—22no—
108C2×C8×C59—22no—
109C2×C8×C59—41no—
110C2×C8×C59—41no—
111C2×C8×C59—41no—
112C2×C8×C59—41no—
113C2×C8×C59—41no—
114C2×C8×C59—42no—
115C2×C8×C59SD1614yescomplemented
116C4⋊C4×C59—21no—
117C4⋊C4×C59—22no—
118C4⋊C4×C59—21no—
119C4⋊C4×C59—22no—
120C4⋊C4×C59—41no—
121C4⋊C4×C59—41no—
122C4⋊C4×C59—41no—
123C4⋊C4×C59—41no—
124C42×C59—41no—
125C42×C59—41no—
126C42×C59C2×D411yescharacteristic
127C42×C59C2×D411yescharacteristic
128C42×C59C2×D411yescharacteristic
129C42×C59C2×D411yescharacteristic
130C23×C59—42no—
131C23×C59—82no—
132C23×C59—81no—
133C23×C59—81no—
134C23×C59—82no—
135C23×C59#12111yescharacteristic
136Q8×C59—22no—
137Q8×C59—22no—
138Q8×C59—41no—
139Q8×C59—41no—
140Q8×C59—44no—
141Q8×C59—81no—
142Q8×C59—81no—
143D4×C59—42no—
144D4×C59—44no—
145D4×C59—42no—
146D4×C59—82no—
147D4×C59—82no—
148D4×C59—81no—
149D4×C59—81no—
150D4×C59—81no—
151D4×C59—81no—
152C2×C4×C59—22no—
153C2×C4×C59—22no—
154C2×C4×C59—41no—
155C2×C4×C59—41no—
156C2×C4×C59—41no—
157C2×C4×C59—42no—
158C2×C4×C59—42no—
159C2×C4×C59—82no—
160C2×C4×C59#12011yescharacteristic
161C2×C4×C59#12011yescharacteristic
162C2×C4×C59#12011yescharacteristic
163C2×C4×C59#12111yescharacteristic
164C2×C4×C59#12111yescharacteristic
165C2×C4×C59#12711yescharacteristic
166C2×C4×C59C2×SD1611yescharacteristic
167C2×C4×C59C2×SD1612yes—
168C2×C4×C59#13511yescharacteristic
169C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C59AGL(1,ℤ/8)12yes—
171C2×C4×C59#13711yescharacteristic
172C8×C59—24no—
173C8×C59—42no—
174C8×C59—42no—
175C8×C59—81no—
176#10268C5911yesmaximal, characteristic, direct product factor, Sylow
177C22×C59—82no—
178C22×C59—82no—
179C22×C59—82no—
180C22×C59—162no—
181C22×C59—162no—
182C22×C59#39211yescharacteristic
183C22×C59#46012yes—
184C22×C59#46511yescharacteristic
185C22×C59#46811yescharacteristic
186C22×C59#47112yes—
187C4×C59—21no—
188C4×C59—21no—
189C4×C59—42no—
190C4×C59—82no—
191C4×C59—81no—
192C4×C59#44811yescharacteristic
193C4×C59#44911yescharacteristic
194C4×C59#45011yescharacteristic
195C4×C59#45012yes—
196C4×C59#45211yescharacteristic
197C4×C59#49211yescharacteristic
198C4×C59#49611yescharacteristic
199C2×#492C2×C5911yescharacteristic
200C2×#475C2×C5911yescharacteristic, complemented
201C2×#460C2×C5911yescharacteristic
202#1984C2×C5911yescharacteristic, complemented
203C2×#332C2×C5911yescharacteristic, complemented
204C2×#331C2×C5911yescharacteristic
205#1277C2×C5911yescharacteristic, complemented
206C2×C59—162no—
207C2×C59#166612yes—
208C2×C59#168612yes—
209C2×C59#200011yescharacteristic
210C2×C59#201411yescharacteristic
211C2×C59#201911yescharacteristic
212C22×SD16—21no—
213C22×SD16—22no—
214C2×C4⋊Q8C22×C5911yescharacteristic
215C2×#127C22×C5911yescharacteristic
216C2×C4×Q8C22×C5911yescharacteristic
217#492—22no—
218#492—22no—
219#475—22no—
220#475—22no—
221#460—22no—
222#460—22no—
223C2×#106—21no—
224C2×C4⋊C8C22×C5911yescharacteristic
225C2×C4⋊C8C22×C5911yescharacteristic
226C2×C4⋊C8C22×C5911yescharacteristic
227C2×#103—21no—
228C2×#102—21no—
229C2×C4×C8C22×C5911yescharacteristic
230#336—22no—
231#332—22no—
232#331—22no—
233C59#1026811yescharacteristic, direct product factor, Sylow
234C22×Q8—21no—
235C22×Q8D4×C5911yescharacteristic
236C22×D4—21no—
237C22×D4—21no—
238C22×D4—21no—
239C2×SD16—24no—
240C2×SD16—28no—
241C2×SD16—44no—
242C2×SD16—42no—
243C2×SD16—42no—
244C2×SD16—44no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—21no—
248C22×C8D4×C5912yes—
249C4⋊Q8—21no—
250C4⋊Q8—21no—
251C4⋊Q8—21no—
252C4⋊Q8D4×C5912yes—
253#127—21no—
254#127—21no—
255#127—21no—
256#127D4×C5912yes—
257C4×Q8—21no—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4D4×C5911yescharacteristic
265C2×C42—21no—
266C2×C42C23×C5911yescharacteristic
267#106—24no—
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8—21no—
272C4⋊C8D4×C5912yes—
273C4⋊C8D4×C5912yes—
274#103—24no—
275#102—24no—
276C4×C8—21no—
277C4×C8—21no—
278C24—41no—
279C2×Q8—21no—
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—22no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—41no—
286C2×Q8—42no—
287C2×Q8—42no—
288C2×Q8SD16×C5912yescomplemented
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—22no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—42no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—42no—
300C2×D4—41no—
301C2×D4—82no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—41no—
305C22×C4C2×D4×C5911yescharacteristic
306C22×C4C2×D4×C5911yescharacteristic
307C22×C4#41×C5911yescharacteristic
308SD16—416no—
309SD16—48no—
310C2×C8—22no—
311C2×C8—22no—
312C2×C8—22no—
313C2×C8—22no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—42no—
320C2×C8SD16×C5914yescomplemented
321C4⋊C4—21no—
322C4⋊C4—22no—
323C4⋊C4—21no—
324C4⋊C4—22no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C42—41no—
330C42—41no—
331C42C2×D4×C5911yescharacteristic
332C42C2×D4×C5911yescharacteristic
333C42C2×D4×C5911yescharacteristic
334C42C2×D4×C5911yescharacteristic
335C23—42no—
336C23—82no—
337C23—81no—
338C23—81no—
339C23—82no—
340C23#121×C5911yescharacteristic
341Q8—22no—
342Q8—22no—
343Q8—41no—
344Q8—41no—
345Q8—44no—
346Q8—81no—
347Q8—81no—
348D4—42no—
349D4—44no—
350D4—42no—
351D4—82no—
352D4—82no—
353D4—81no—
354D4—81no—
355D4—81no—
356D4—81no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—82no—
365C2×C4#120×C5911yescharacteristic
366C2×C4#120×C5911yescharacteristic
367C2×C4#120×C5911yescharacteristic
368C2×C4#121×C5911yescharacteristic
369C2×C4#121×C5911yescharacteristic
370C2×C4#127×C5911yescharacteristic
371C2×C4C2×SD16×C5911yescharacteristic
372C2×C4C2×SD16×C5912yes—
373C2×C4#135×C5911yescharacteristic
374C2×C4AGL(1,ℤ/8)×C5911yescharacteristic
375C2×C4AGL(1,ℤ/8)×C5912yes—
376C2×C4#137×C5911yescharacteristic
377C8—24no—
378C8—42no—
379C8—42no—
380C8—81no—
381C22—82no—
382C22—82no—
383C22—82no—
384C22—162no—
385C22—162no—
386C22C59×#39211yescharacteristic
387C22C59×#46012yes—
388C22C59×#46511yescharacteristic
389C22C59×#46811yescharacteristic
390C22C59×#47112yes—
391C4—21no—
392C4—21no—
393C4—42no—
394C4—82no—
395C4—81no—
396C4C59×#44811yescharacteristic
397C4C59×#44911yescharacteristic
398C4C59×#45011yescharacteristic
399C4C59×#45012yes—
400C4C59×#45211yescharacteristic
401C4C59×#49211yescharacteristic
402C4C59×#49611yescharacteristic
403C2—162no—
404C2C59×#166612yes—
405C2C59×#168612yes—
406C2C59×#200011yescharacteristic
407C2C59×#201411yescharacteristic
408C2C59×#201911yescharacteristic
subgroupG/H
center, socleC23×C59#121
commutator, Frattini, cosocleC2×C42C23×C59
prime radicalC2×#127×C59C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C59 ◁ C2×C42×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C59×#475C2semidirect
4. C59×#1984C2semidirect
5. C2×C59×#332C2semidirect
7. C59×#1277C2semidirect
83. C2×Q8×C59SD16semidirect
115. C2×C8×C59SD16semidirect
176. #10268C59direct (N × H)
200. C2×#475C2×C59semidirect
202. #1984C2×C59semidirect
203. C2×#332C2×C59semidirect
205. #1277C2×C59semidirect
233. C59#10268direct (N × H)
288. C2×Q8SD16×C59semidirect
320. C2×C8SD16×C59semidirect

Maximal subgroups

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

subgroupindex
C2×C59×#4922
C2×C59×#4752
C2×C59×#4602
C59×#19842
C2×C59×#3322
C2×C59×#3312
C59×#12772
#1026859