Finite Group Databasebeta

← C59×#9291 #28421400

Subgroups — C59×#9291 #28421400

Order 15104.

494 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3226C211yesmaximal, characteristic
2C59×#2932C211yesmaximal, characteristic
3C59×#1960C211yesmaximal, characteristic, complemented
4C59×#1546C211yesmaximal, characteristic, complemented
5C59×#1517C211yesmaximal, characteristic
6C59×#1286C211yesmaximal, characteristic, complemented
7C59×#1275C211yesmaximal, characteristic, complemented
8C2×#131×C59—21no—
9C59×#532C2211yescharacteristic
10C2×C4⋊Q8×C59C2211yescharacteristic
11C59×#500C412yescomplemented
12C59×#486C412yescomplemented
13C59×#480—22no—
14C59×#474—22no—
15C59×#435—22no—
16C59×#435—22no—
17C59×#431C2211yescharacteristic
18C59×#431C2211yescharacteristic
19C59×#423C2211yescharacteristic
20C2×#103×C59—21no—
21C2×#103×C59—21no—
22C59×#408—21no—
23C2×#97×C59C2211yescharacteristic
24C59×#382C2211yescharacteristic
25C59×#332—22no—
26C59×#327—22no—
27C2×#41×C59—21no—
28C22×Q8×C59—21no—
29#131×C59—42no—
30#131×C59—42no—
31C2×M16×C59—22no—
32C2×M16×C59—21no—
33C22×C8×C59—22no—
34C22×C8×C59D411yescharacteristic
35C22×C8×C59D411yescharacteristic
36C4⋊Q8×C59—21no—
37C4⋊Q8×C59—21no—
38C4⋊Q8×C59—21no—
39C4⋊Q8×C59C2×C412yes—
40C4⋊Q8×C59C2×C411yescharacteristic
41#127×C59C2×C411yescharacteristic
42#124×C59—21no—
43#121×C59—21no—
44#121×C59D412yes—
45C4×D4×C59—21no—
46C4×D4×C59D412yes—
47C2×C4⋊C4×C59—21no—
48C2×C4⋊C4×C59—21no—
49C2×C4⋊C4×C59—21no—
50C2×C42×C59C2311yescharacteristic
51#107×C59—24no—
52C4⋊C8×C59—21no—
53C4⋊C8×C59—21no—
54C4⋊C8×C59—21no—
55C4⋊C8×C59D412yes—
56#103×C59—42no—
57#103×C59—42no—
58#102×C59—24no—
59C22⋊C8×C59—24no—
60C22⋊C8×C59—21no—
61C22⋊C8×C59—21no—
62#97×C59—21no—
63#97×C59—21no—
64C4×C8×C59—21no—
65C4×C8×C59C2×C412yes—
66#95×C59—21no—
67#95×C59—21no—
68#41×C59—41no—
69#41×C59—41no—
70#41×C59—41no—
71#41×C59—41no—
72C2×Q8×C59—21no—
73C2×Q8×C59—22no—
74C2×Q8×C59—41no—
75C2×Q8×C59—41no—
76C2×Q8×C59—41no—
77C2×Q8×C59—41no—
78C2×Q8×C59—41no—
79C2×D4×C59—22no—
80C2×D4×C59—21no—
81C2×D4×C59—21no—
82C2×D4×C59C22⋊C412yes—
83C22×C4×C59—22no—
84C22×C4×C59—41no—
85C22×C4×C59—41no—
86C22×C4×C59C2×D411yescharacteristic
87C22×C4×C59C2×D411yescharacteristic
88C22×C4×C59#4111yescharacteristic
89M16×C59—44no—
90M16×C59—41no—
91M16×C59—41no—
92C2×C8×C59—21no—
93C2×C8×C59—21no—
94C2×C8×C59—22no—
95C2×C8×C59—21no—
96C2×C8×C59—22no—
97C2×C8×C59—21no—
98C2×C8×C59—21no—
99C2×C8×C59—44no—
100C2×C8×C59—41no—
101C2×C8×C59D812yes—
102C4⋊C4×C59—21no—
103C4⋊C4×C59—22no—
104C4⋊C4×C59—22no—
105C4⋊C4×C59—41no—
106C4⋊C4×C59—41no—
107C4⋊C4×C59—41no—
108C4⋊C4×C59—41no—
109C4⋊C4×C59C22⋊C412yes—
110C22⋊C4×C59—22no—
111C22⋊C4×C59—22no—
112C42×C59C22×C411yescharacteristic
113C42×C59C2×D411yescharacteristic
114C42×C59C2×D411yescharacteristic
115C42×C59#4111yescharacteristic
116C23×C59—22no—
117C23×C59#12111yescharacteristic
118Q8×C59—41no—
119Q8×C59—41no—
120Q8×C59—42no—
121Q8×C59—42no—
122Q8×C59—81no—
123Q8×C59—81no—
124D4×C59—42no—
125D4×C59—42no—
126D4×C59—42no—
127D4×C59—41no—
128D4×C59—41no—
129D4×C59—81no—
130C2×C4×C59—22no—
131C2×C4×C59—41no—
132C2×C4×C59—41no—
133C2×C4×C59—42no—
134C2×C4×C59—42no—
135C2×C4×C59—42no—
136C2×C4×C59—81no—
137C2×C4×C59—81no—
138C2×C4×C59—81no—
139C2×C4×C59—81no—
140C2×C4×C59—81no—
141C2×C4×C59C2×C22⋊C411yescharacteristic
142C2×C4×C59C4×D411yescharacteristic
143C2×C4×C59C4×D411yescharacteristic
144C2×C4×C59#12011yescharacteristic
145C2×C4×C59#12111yescharacteristic
146C2×C4×C59#12311yescharacteristic
147C2×C4×C59C2×D811yescharacteristic
148C2×C4×C59#13511yescharacteristic
149C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
151C8×C59—22no—
152C8×C59—42no—
153C8×C59—42no—
154C8×C59—41no—
155C8×C59—81no—
156#9291C5911yesmaximal, characteristic, direct product factor, Sylow
157C22×C59—21no—
158C22×C59—21no—
159C22×C59—42no—
160C22×C59—42no—
161C22×C59—42no—
162C22×C59#38611yescharacteristic
163C22×C59#45911yescharacteristic
164C22×C59#46311yescharacteristic
165C4×C59—21no—
166C4×C59—21no—
167C4×C59—21no—
168C4×C59—21no—
169C4×C59—42no—
170C4×C59—82no—
171C4×C59—161no—
172C4×C59C4×D811yescharacteristic
173C4×C59#44211yescharacteristic
174C4×C59#44711yescharacteristic
175C4×C59#44911yescharacteristic
176#3226C2×C5911yescharacteristic
177#2932C2×C5911yescharacteristic
178#1960C2×C5911yescharacteristic, complemented
179#1546C2×C5911yescharacteristic, complemented
180#1517C2×C5911yescharacteristic
181#1286C2×C5911yescharacteristic, complemented
182#1275C2×C5911yescharacteristic, complemented
183C2×C59—21no—
184C2×C59—21no—
185C2×C59—82no—
186C2×C59#187911yescharacteristic
187C2×C59#190211yescharacteristic
188C2×C59#190911yescharacteristic
189C2×#131—21no—
190#532C22×C5911yescharacteristic
191C2×C4⋊Q8C22×C5911yescharacteristic
192#500C4×C5912yescomplemented
193#486C4×C5912yescomplemented
194#480—22no—
195#474—22no—
196#435—22no—
197#435—22no—
198#431C22×C5911yescharacteristic
199#431C22×C5911yescharacteristic
200#423C22×C5911yescharacteristic
201C2×#103—21no—
202C2×#103—21no—
203#408—21no—
204C2×#97C22×C5911yescharacteristic
205#382C22×C5911yescharacteristic
206#332—22no—
207#327—22no—
208C59#929111yescharacteristic, direct product factor, Sylow
209C2×#41—21no—
210C22×Q8—21no—
211#131—42no—
212#131—42no—
213C2×M16—22no—
214C2×M16—21no—
215C22×C8—22no—
216C22×C8D4×C5911yescharacteristic
217C22×C8D4×C5911yescharacteristic
218C4⋊Q8—21no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8C2×C4×C5912yes—
222C4⋊Q8C2×C4×C5911yescharacteristic
223#127C2×C4×C5911yescharacteristic
224#124—21no—
225#121—21no—
226#121D4×C5912yes—
227C4×D4—21no—
228C4×D4D4×C5912yes—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C42C23×C5911yescharacteristic
233#107—24no—
234C4⋊C8—21no—
235C4⋊C8—21no—
236C4⋊C8—21no—
237C4⋊C8D4×C5912yes—
238#103—42no—
239#103—42no—
240#102—24no—
241C22⋊C8—24no—
242C22⋊C8—21no—
243C22⋊C8—21no—
244#97—21no—
245#97—21no—
246C4×C8—21no—
247C4×C8C2×C4×C5912yes—
248#95—21no—
249#95—21no—
250#41—41no—
251#41—41no—
252#41—41no—
253#41—41no—
254C2×Q8—21no—
255C2×Q8—22no—
256C2×Q8—41no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×Q8—41no—
260C2×Q8—41no—
261C2×D4—22no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4C22⋊C4×C5912yes—
265C22×C4—22no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4C2×D4×C5911yescharacteristic
269C22×C4C2×D4×C5911yescharacteristic
270C22×C4#41×C5911yescharacteristic
271M16—44no—
272M16—41no—
273M16—41no—
274C2×C8—21no—
275C2×C8—21no—
276C2×C8—22no—
277C2×C8—21no—
278C2×C8—22no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—44no—
282C2×C8—41no—
283C2×C8D8×C5912yes—
284C4⋊C4—21no—
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4C22⋊C4×C5912yes—
292C22⋊C4—22no—
293C22⋊C4—22no—
294C42C22×C4×C5911yescharacteristic
295C42C2×D4×C5911yescharacteristic
296C42C2×D4×C5911yescharacteristic
297C42#41×C5911yescharacteristic
298C23—22no—
299C23#121×C5911yescharacteristic
300Q8—41no—
301Q8—41no—
302Q8—42no—
303Q8—42no—
304Q8—81no—
305Q8—81no—
306D4—42no—
307D4—42no—
308D4—42no—
309D4—41no—
310D4—41no—
311D4—81no—
312C2×C4—22no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4C2×C22⋊C4×C5911yescharacteristic
324C2×C4C4×D4×C5911yescharacteristic
325C2×C4C4×D4×C5911yescharacteristic
326C2×C4#120×C5911yescharacteristic
327C2×C4#121×C5911yescharacteristic
328C2×C4#123×C5911yescharacteristic
329C2×C4C2×D8×C5911yescharacteristic
330C2×C4#135×C5911yescharacteristic
331C2×C4AGL(1,ℤ/8)×C5911yescharacteristic
332C2×C4AGL(1,ℤ/8)×C5911yescharacteristic
333C8—22no—
334C8—42no—
335C8—42no—
336C8—41no—
337C8—81no—
338C22—21no—
339C22—21no—
340C22—42no—
341C22—42no—
342C22—42no—
343C22C59×#38611yescharacteristic
344C22C59×#45911yescharacteristic
345C22C59×#46311yescharacteristic
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—42no—
351C4—82no—
352C4—161no—
353C4C4×D8×C5911yescharacteristic
354C4C59×#44211yescharacteristic
355C4C59×#44711yescharacteristic
356C4C59×#44911yescharacteristic
357C2—21no—
358C2—21no—
359C2—82no—
360C2C59×#187911yescharacteristic
361C2C59×#190211yescharacteristic
362C2C59×#190911yescharacteristic
subgroupG/H
center, socleC22×C59#386
commutatorC42C22×C4×C59
Frattini, cosocleC2×C42C23×C59
prime radicalC59×#532C22
LCSG ▷ C42 ▷ 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×#1960C2semidirect
4. C59×#1546C2semidirect
6. C59×#1286C2semidirect
7. C59×#1275C2semidirect
11. C59×#500C4semidirect
12. C59×#486C4semidirect
156. #9291C59direct (N × H)
178. #1960C2×C59semidirect
179. #1546C2×C59semidirect
181. #1286C2×C59semidirect
182. #1275C2×C59semidirect
192. #500C4×C59semidirect
193. #486C4×C59semidirect
208. C59#9291direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#32262
C59×#29322
C59×#19602
C59×#15462
C59×#15172
C59×#12862
C59×#12752
#929159