Finite Group Databasebeta

← C59×#10552 #28422661

Subgroups — C59×#10552 #28422661

Order 15104.

386 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3141C211yesmaximal, characteristic
2C59×#1950C211yesmaximal, characteristic, complemented
3C59×#1548C211yesmaximal, characteristic, complemented
4C59×#1547C211yesmaximal, characteristic
5C2×C59×#332C211yesmaximal, characteristic, complemented
6C59×#1480C211yesmaximal, characteristic
7C59×#1283C211yesmaximal, characteristic, complemented
8C59×#532C2211yescharacteristic
9C2×C4⋊Q8×C59C2211yescharacteristic
10C59×#489—22no—
11C59×#487—21no—
12C59×#486—21no—
13C59×#431C2211yescharacteristic
14C2×#108×C59—21no—
15C59×#423C2211yescharacteristic
16C2×C4⋊C8×C59C2211yescharacteristic
17C2×C4⋊C8×C59C2211yescharacteristic
18C59×#417—21no—
19C59×#417—21no—
20C4×M16×C59C2211yescharacteristic
21C59×#341—21no—
22C59×#333—22no—
23C59×#332—21no—
24C59×#332—22no—
25C59×#331—21no—
26C59×D4⋊C8—22no—
27C2×#41×C59—21no—
28C22×Q8×C59—21no—
29C2×M16×C59—21no—
30C2×M16×C59D411yescharacteristic
31C2×M16×C59D411yescharacteristic
32C22×C8×C59—21no—
33C22×C8×C59—21no—
34C4⋊Q8×C59—21no—
35C4⋊Q8×C59—21no—
36C4⋊Q8×C59—21no—
37C4⋊Q8×C59D411yescharacteristic
38C4⋊Q8×C59D412yes—
39#127×C59D411yescharacteristic
40#124×C59—21no—
41#121×C59—21no—
42#121×C59—21no—
43C4×D4×C59—21no—
44C4×D4×C59—21no—
45C2×C4⋊C4×C59—21no—
46C2×C4⋊C4×C59—21no—
47C2×C42×C59C2311yescharacteristic
48#108×C59—42no—
49C4⋊C8×C59—21no—
50C4⋊C8×C59—21no—
51C4⋊C8×C59—21no—
52C4⋊C8×C59—21no—
53C4⋊C8×C59—21no—
54C4⋊C8×C59—21no—
55C4⋊C8×C59D412yes—
56#103×C59—22no—
57#103×C59—22no—
58#102×C59—22no—
59#102×C59—22no—
60C22⋊C8×C59—21no—
61#97×C59—21no—
62C4×C8×C59—21no—
63C4×C8×C59—21no—
64#41×C59—41no—
65#41×C59—41no—
66#41×C59—41no—
67#41×C59—41no—
68C2×Q8×C59—21no—
69C2×Q8×C59—22no—
70C2×Q8×C59—41no—
71C2×Q8×C59—81no—
72C2×Q8×C59—81no—
73C2×D4×C59—21no—
74C2×D4×C59—21no—
75C2×D4×C59—21no—
76C2×D4×C59—41no—
77C22×C4×C59—41no—
78C22×C4×C59—41no—
79C22×C4×C59C2×D411yescharacteristic
80C22×C4×C59#4111yescharacteristic
81C22×C4×C59#4111yescharacteristic
82M16×C59—21no—
83M16×C59—21no—
84M16×C59—21no—
85M16×C59—21no—
86M16×C59—41no—
87M16×C59—41no—
88C2×C8×C59—21no—
89C2×C8×C59—21no—
90C2×C8×C59—22no—
91C2×C8×C59—41no—
92C2×C8×C59—41no—
93C2×C8×C59—41no—
94C2×C8×C59—41no—
95C2×C8×C59—41no—
96C2×C8×C59—81no—
97C4⋊C4×C59—22no—
98C4⋊C4×C59—22no—
99C4⋊C4×C59—21no—
100C4⋊C4×C59—21no—
101C4⋊C4×C59—41no—
102C4⋊C4×C59—41no—
103C22⋊C4×C59—41no—
104C22⋊C4×C59—41no—
105C42×C59C2×D411yescharacteristic
106C42×C59C2×D411yescharacteristic
107C42×C59C2×D411yescharacteristic
108C42×C59#4111yescharacteristic
109C23×C59—41no—
110C23×C59#12411yescharacteristic
111Q8×C59—41no—
112Q8×C59—41no—
113Q8×C59—82no—
114Q8×C59—81no—
115Q8×C59—81no—
116D4×C59—41no—
117D4×C59—41no—
118D4×C59—41no—
119D4×C59—41no—
120D4×C59—81no—
121D4×C59—81no—
122D4×C59—81no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59—41no—
126C2×C4×C59—41no—
127C2×C4×C59—42no—
128C2×C4×C59—82no—
129C2×C4×C59—81no—
130C2×C4×C59—81no—
131C2×C4×C59#12011yescharacteristic
132C2×C4×C59#12111yescharacteristic
133C2×C4×C59#12111yescharacteristic
134C2×C4×C59#12111yescharacteristic
135C2×C4×C59#12311yescharacteristic
136C2×C4×C59#12311yescharacteristic
137C2×C4×C59#13511yescharacteristic
138C2×C4×C59#13511yescharacteristic
139C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C59#13711yescharacteristic
141C8×C59—41no—
142C8×C59—41no—
143C8×C59—42no—
144C8×C59—81no—
145C8×C59—81no—
146C8×C59—81no—
147#10552C5911yesmaximal, characteristic, direct product factor, Sylow
148C22×C59—21no—
149C22×C59—21no—
150C22×C59—81no—
151C22×C59—81no—
152C22×C59—81no—
153C22×C59#39411yescharacteristic
154C22×C59#48811yescharacteristic
155C22×C59#48911yescharacteristic
156C4×C59—21no—
157C4×C59—21no—
158C4×C59—21no—
159C4×C59—82no—
160C4×C59—81no—
161C4×C59#44911yescharacteristic
162C4×C59#45211yescharacteristic
163C4×C59#46311yescharacteristic
164C4×C59#46411yescharacteristic
165C4×C59#47111yescharacteristic
166C4×C59#47211yescharacteristic
167#3141C2×C5911yescharacteristic
168#1950C2×C5911yescharacteristic, complemented
169#1548C2×C5911yescharacteristic, complemented
170#1547C2×C5911yescharacteristic
171C2×#332C2×C5911yescharacteristic, complemented
172#1480C2×C5911yescharacteristic
173#1283C2×C5911yescharacteristic, complemented
174C2×C59—21no—
175C2×C59—21no—
176C2×C59—161no—
177C2×C59#204211yescharacteristic
178C2×C59#204911yescharacteristic
179C2×C59#205111yescharacteristic
180#532C22×C5911yescharacteristic
181C2×C4⋊Q8C22×C5911yescharacteristic
182#489—22no—
183#487—21no—
184#486—21no—
185#431C22×C5911yescharacteristic
186C2×#108—21no—
187#423C22×C5911yescharacteristic
188C2×C4⋊C8C22×C5911yescharacteristic
189C2×C4⋊C8C22×C5911yescharacteristic
190#417—21no—
191#417—21no—
192C4×M16C22×C5911yescharacteristic
193#341—21no—
194#333—22no—
195#332—21no—
196#332—22no—
197#331—21no—
198D4⋊C8—22no—
199C59#1055211yescharacteristic, direct product factor, Sylow
200C2×#41—21no—
201C22×Q8—21no—
202C2×M16—21no—
203C2×M16D4×C5911yescharacteristic
204C2×M16D4×C5911yescharacteristic
205C22×C8—21no—
206C22×C8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8D4×C5912yes—
211C4⋊Q8D4×C5911yescharacteristic
212#127D4×C5911yescharacteristic
213#124—21no—
214#121—21no—
215#121—21no—
216C4×D4—21no—
217C4×D4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C42C23×C5911yescharacteristic
221#108—42no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8D4×C5912yes—
229#103—22no—
230#103—22no—
231#102—22no—
232#102—22no—
233C22⋊C8—21no—
234#97—21no—
235C4×C8—21no—
236C4×C8—21no—
237#41—41no—
238#41—41no—
239#41—41no—
240#41—41no—
241C2×Q8—21no—
242C2×Q8—22no—
243C2×Q8—41no—
244C2×Q8—81no—
245C2×Q8—81no—
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—21no—
249C2×D4—41no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4C2×D4×C5911yescharacteristic
253C22×C4#41×C5911yescharacteristic
254C22×C4#41×C5911yescharacteristic
255M16—21no—
256M16—21no—
257M16—21no—
258M16—21no—
259M16—41no—
260M16—41no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8—22no—
264C2×C8—41no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—81no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—41no—
278C42C2×D4×C5911yescharacteristic
279C42C2×D4×C5911yescharacteristic
280C42C2×D4×C5911yescharacteristic
281C42#41×C5911yescharacteristic
282C23—41no—
283C23#124×C5911yescharacteristic
284Q8—41no—
285Q8—41no—
286Q8—82no—
287Q8—81no—
288Q8—81no—
289D4—41no—
290D4—41no—
291D4—41no—
292D4—41no—
293D4—81no—
294D4—81no—
295D4—81no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—82no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4#120×C5911yescharacteristic
305C2×C4#121×C5911yescharacteristic
306C2×C4#121×C5911yescharacteristic
307C2×C4#121×C5911yescharacteristic
308C2×C4#123×C5911yescharacteristic
309C2×C4#123×C5911yescharacteristic
310C2×C4#135×C5911yescharacteristic
311C2×C4#135×C5911yescharacteristic
312C2×C4AGL(1,ℤ/8)×C5911yescharacteristic
313C2×C4#137×C5911yescharacteristic
314C8—41no—
315C8—41no—
316C8—42no—
317C8—81no—
318C8—81no—
319C8—81no—
320C22—21no—
321C22—21no—
322C22—81no—
323C22—81no—
324C22—81no—
325C22C59×#39411yescharacteristic
326C22C59×#48811yescharacteristic
327C22C59×#48911yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—81no—
332C4—82no—
333C4C59×#44911yescharacteristic
334C4C59×#45211yescharacteristic
335C4C59×#46311yescharacteristic
336C4C59×#46411yescharacteristic
337C4C59×#47111yescharacteristic
338C4C59×#47211yescharacteristic
339C2—21no—
340C2—21no—
341C2—161no—
342C2C59×#204211yescharacteristic
343C2C59×#204911yescharacteristic
344C2C59×#205111yescharacteristic
subgroupG/H
center, socleC22×C59#394
commutator, Frattini, cosocleC2×C42C23×C59
prime radicalC59×#532C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C59 ◁ C2×C42×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C59×#1950C2semidirect
3. C59×#1548C2semidirect
5. C2×C59×#332C2semidirect
7. C59×#1283C2semidirect
147. #10552C59direct (N × H)
168. #1950C2×C59semidirect
169. #1548C2×C59semidirect
171. C2×#332C2×C59semidirect
173. #1283C2×C59semidirect
199. C59#10552direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#31412
C59×#19502
C59×#15482
C59×#15472
C2×C59×#3322
C59×#14802
C59×#12832
#1055259