Finite Group Databasebeta

← C59×#9267 #28421376

Subgroups — C59×#9267 #28421376

Order 15104.

492 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3206C211yesmaximal, characteristic
2C59×#2935C211yesmaximal, characteristic
3C59×#1997C211yesmaximal, characteristic, complemented
4C59×#1547C211yesmaximal, characteristic
5C2×C59×#333C211yesmaximal, characteristic, complemented
6C59×#1301C211yesmaximal, characteristic, complemented
7C59×#1283C211yesmaximal, characteristic, complemented
8C2×#131×C59—21no—
9C59×#532C2211yescharacteristic
10C2×C4⋊Q8×C59C2211yescharacteristic
11C59×#492—21no—
12C59×#487—21no—
13C59×#461—22no—
14C59×#448C414yes—
15C59×#436—21no—
16C59×#435—22no—
17C8×D4×C59—21no—
18C59×#431C2211yescharacteristic
19C59×#423C2211yescharacteristic
20C2×C4⋊C8×C59C2211yescharacteristic
21C2×C4⋊C8×C59C2211yescharacteristic
22C59×#408—21no—
23C4×M16×C59C2211yescharacteristic
24C59×#343—21no—
25C59×#343—21no—
26C59×#333—21no—
27C59×#333—21no—
28C59×#332—21no—
29C59×#331—21no—
30C2×#41×C59—21no—
31C22×Q8×C59C2×C412yes—
32C2×SD16×C59—24no—
33#131×C59—42no—
34#131×C59—42no—
35C2×M16×C59—22no—
36C2×M16×C59—21no—
37C2×M16×C59D411yescharacteristic
38C2×M16×C59D411yescharacteristic
39C22×C8×C59—22no—
40C22×C8×C59—21no—
41C22×C8×C59—21no—
42C4⋊Q8×C59—21no—
43C4⋊Q8×C59—21no—
44C4⋊Q8×C59—21no—
45C4⋊Q8×C59—21no—
46C4⋊Q8×C59D411yescharacteristic
47#127×C59D411yescharacteristic
48#124×C59—21no—
49#121×C59—21no—
50#121×C59C2×C412yes—
51C4×D4×C59—21no—
52C4×D4×C59D412yes—
53C2×C4⋊C4×C59—21no—
54C2×C4⋊C4×C59—21no—
55C2×C42×C59C2311yescharacteristic
56C4⋊C8×C59—21no—
57C4⋊C8×C59—21no—
58C4⋊C8×C59—21no—
59C4⋊C8×C59—21no—
60C4⋊C8×C59—21no—
61C4⋊C8×C59—21no—
62C4⋊C8×C59D411yescharacteristic
63C4⋊C8×C59D411yescharacteristic
64#103×C59—24no—
65C22⋊C8×C59—22no—
66C22⋊C8×C59—22no—
67C22⋊C8×C59C2×C412yes—
68#97×C59—21no—
69C4×C8×C59—21no—
70C4×C8×C59—21no—
71#41×C59—41no—
72#41×C59—41no—
73#41×C59—41no—
74#41×C59—41no—
75C2×Q8×C59—21no—
76C2×Q8×C59—22no—
77C2×Q8×C59—22no—
78C2×Q8×C59—82no—
79C2×D4×C59—22no—
80C2×D4×C59—21no—
81C2×D4×C59—21no—
82C2×D4×C59C22⋊C412yes—
83C22×C4×C59—22no—
84C22×C4×C59—22no—
85C22×C4×C59C22×C411yescharacteristic
86C22×C4×C59C2×D411yescharacteristic
87C22×C4×C59#4111yescharacteristic
88SD16×C59—84no—
89M16×C59—21no—
90M16×C59—21no—
91M16×C59—21no—
92M16×C59—44no—
93M16×C59—41no—
94M16×C59—41no—
95M16×C59SD1612yescomplemented
96C2×C8×C59—21no—
97C2×C8×C59—22no—
98C2×C8×C59—21no—
99C2×C8×C59—21no—
100C2×C8×C59—21no—
101C2×C8×C59—44no—
102C2×C8×C59—41no—
103C2×C8×C59—41no—
104C2×C8×C59—41no—
105C2×C8×C59—41no—
106C2×C8×C59—81no—
107C4⋊C4×C59—21no—
108C4⋊C4×C59—41no—
109C4⋊C4×C59—41no—
110C4⋊C4×C59—41no—
111C4⋊C4×C59—41no—
112C4⋊C4×C59C22⋊C412yes—
113C22⋊C4×C59—22no—
114C22⋊C4×C59—22no—
115C42×C59C2×D411yescharacteristic
116C42×C59C2×D411yescharacteristic
117C42×C59C2×D411yescharacteristic
118C42×C59#4111yescharacteristic
119C23×C59—22no—
120C23×C59C4×D411yescharacteristic
121Q8×C59—44no—
122Q8×C59—41no—
123Q8×C59—41no—
124Q8×C59—82no—
125D4×C59—42no—
126D4×C59—42no—
127D4×C59—42no—
128D4×C59—41no—
129D4×C59—41no—
130D4×C59—41no—
131D4×C59—41no—
132C2×C4×C59—21no—
133C2×C4×C59—21no—
134C2×C4×C59—22no—
135C2×C4×C59—41no—
136C2×C4×C59—42no—
137C2×C4×C59—42no—
138C2×C4×C59—42no—
139C2×C4×C59—82no—
140C2×C4×C59C2×C22⋊C411yescharacteristic
141C2×C4×C59C4×D411yescharacteristic
142C2×C4×C59#12011yescharacteristic
143C2×C4×C59#12111yescharacteristic
144C2×C4×C59#12111yescharacteristic
145C2×C4×C59#12311yescharacteristic
146C2×C4×C59C2×SD1611yescharacteristic
147C2×C4×C59#13511yescharacteristic
148C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C59#13711yescharacteristic
150C8×C59—22no—
151C8×C59—42no—
152C8×C59—41no—
153C8×C59—41no—
154C8×C59—41no—
155C8×C59—81no—
156C8×C59—81no—
157#9267C5911yesmaximal, characteristic, direct product factor, Sylow
158C22×C59—21no—
159C22×C59—21no—
160C22×C59—42no—
161C22×C59—42no—
162C22×C59—42no—
163C22×C59#38611yescharacteristic
164C22×C59C4×SD1611yescharacteristic
165C22×C59#44011yescharacteristic
166C4×C59—21no—
167C4×C59—21no—
168C4×C59—21no—
169C4×C59—42no—
170C4×C59—82no—
171C4×C59#45011yescharacteristic
172C4×C59#45211yescharacteristic
173C4×C59#46111yescharacteristic
174C4×C59#46311yescharacteristic
175C4×C59#47111yescharacteristic
176C4×C59#47311yescharacteristic
177#3206C2×C5911yescharacteristic
178#2935C2×C5911yescharacteristic
179#1997C2×C5911yescharacteristic, complemented
180#1547C2×C5911yescharacteristic
181C2×#333C2×C5911yescharacteristic, complemented
182#1301C2×C5911yescharacteristic, complemented
183#1283C2×C5911yescharacteristic, complemented
184C2×C59—21no—
185C2×C59—21no—
186C2×C59—82no—
187C2×C59#187711yescharacteristic
188C2×C59#190811yescharacteristic
189C2×C59#191411yescharacteristic
190C2×#131—21no—
191#532C22×C5911yescharacteristic
192C2×C4⋊Q8C22×C5911yescharacteristic
193#492—21no—
194#487—21no—
195#461—22no—
196#448C4×C5914yes—
197#436—21no—
198#435—22no—
199C8×D4—21no—
200#431C22×C5911yescharacteristic
201#423C22×C5911yescharacteristic
202C2×C4⋊C8C22×C5911yescharacteristic
203C2×C4⋊C8C22×C5911yescharacteristic
204#408—21no—
205C4×M16C22×C5911yescharacteristic
206#343—21no—
207#343—21no—
208#333—21no—
209#333—21no—
210#332—21no—
211#331—21no—
212C59#926711yescharacteristic, direct product factor, Sylow
213C2×#41—21no—
214C22×Q8C2×C4×C5912yes—
215C2×SD16—24no—
216#131—42no—
217#131—42no—
218C2×M16—22no—
219C2×M16—21no—
220C2×M16D4×C5911yescharacteristic
221C2×M16D4×C5911yescharacteristic
222C22×C8—22no—
223C22×C8—21no—
224C22×C8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8D4×C5911yescharacteristic
230#127D4×C5911yescharacteristic
231#124—21no—
232#121—21no—
233#121C2×C4×C5912yes—
234C4×D4—21no—
235C4×D4D4×C5912yes—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C42C23×C5911yescharacteristic
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8D4×C5911yescharacteristic
246C4⋊C8D4×C5911yescharacteristic
247#103—24no—
248C22⋊C8—22no—
249C22⋊C8—22no—
250C22⋊C8C2×C4×C5912yes—
251#97—21no—
252C4×C8—21no—
253C4×C8—21no—
254#41—41no—
255#41—41no—
256#41—41no—
257#41—41no—
258C2×Q8—21no—
259C2×Q8—22no—
260C2×Q8—22no—
261C2×Q8—82no—
262C2×D4—22no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4C22⋊C4×C5912yes—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4C22×C4×C5911yescharacteristic
269C22×C4C2×D4×C5911yescharacteristic
270C22×C4#41×C5911yescharacteristic
271SD16—84no—
272M16—21no—
273M16—21no—
274M16—21no—
275M16—44no—
276M16—41no—
277M16—41no—
278M16SD16×C5912yescomplemented
279C2×C8—21no—
280C2×C8—22no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—44no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—81no—
290C4⋊C4—21no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4C22⋊C4×C5912yes—
296C22⋊C4—22no—
297C22⋊C4—22no—
298C42C2×D4×C5911yescharacteristic
299C42C2×D4×C5911yescharacteristic
300C42C2×D4×C5911yescharacteristic
301C42#41×C5911yescharacteristic
302C23—22no—
303C23C4×D4×C5911yescharacteristic
304Q8—44no—
305Q8—41no—
306Q8—41no—
307Q8—82no—
308D4—42no—
309D4—42no—
310D4—42no—
311D4—41no—
312D4—41no—
313D4—41no—
314D4—41no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—22no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—82no—
323C2×C4C2×C22⋊C4×C5911yescharacteristic
324C2×C4C4×D4×C5911yescharacteristic
325C2×C4#120×C5911yescharacteristic
326C2×C4#121×C5911yescharacteristic
327C2×C4#121×C5911yescharacteristic
328C2×C4#123×C5911yescharacteristic
329C2×C4C2×SD16×C5911yescharacteristic
330C2×C4#135×C5911yescharacteristic
331C2×C4AGL(1,ℤ/8)×C5911yescharacteristic
332C2×C4#137×C5911yescharacteristic
333C8—22no—
334C8—42no—
335C8—41no—
336C8—41no—
337C8—41no—
338C8—81no—
339C8—81no—
340C22—21no—
341C22—21no—
342C22—42no—
343C22—42no—
344C22—42no—
345C22C59×#38611yescharacteristic
346C22C4×SD16×C5911yescharacteristic
347C22C59×#44011yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—42no—
352C4—82no—
353C4C59×#45011yescharacteristic
354C4C59×#45211yescharacteristic
355C4C59×#46111yescharacteristic
356C4C59×#46311yescharacteristic
357C4C59×#47111yescharacteristic
358C4C59×#47311yescharacteristic
359C2—21no—
360C2—21no—
361C2—82no—
362C2C59×#187711yescharacteristic
363C2C59×#190811yescharacteristic
364C2C59×#191411yescharacteristic
subgroupG/H
center, socleC22×C59#386
commutatorC22×C4C22×C4×C59
Frattini, cosocleC2×C42C23×C59
prime radicalC59×#532C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C59 ◁ C2×C42×C59 ◁ G

Complements

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

NH ≅ G/Ntype
3. C59×#1997C2semidirect
5. C2×C59×#333C2semidirect
6. C59×#1301C2semidirect
7. C59×#1283C2semidirect
95. M16×C59SD16semidirect
157. #9267C59direct (N × H)
179. #1997C2×C59semidirect
181. C2×#333C2×C59semidirect
182. #1301C2×C59semidirect
183. #1283C2×C59semidirect
212. C59#9267direct (N × H)
278. M16SD16×C59semidirect

Maximal subgroups

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

subgroupindex
C59×#32062
C59×#29352
C59×#19972
C59×#15472
C2×C59×#3332
C59×#13012
C59×#12832
#926759