Finite Group Databasebeta

← C59×#11844 #28423953

Subgroups — C59×#11844 #28423953

Order 15104.

432 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#2610C211yesmaximal, characteristic
2C59×#1820C211yesmaximal, characteristic, complemented
3C59×#1458C211yesmaximal, characteristic, complemented
4C59×#1351C212yesmaximal, complemented
5C59×#1343C212yesmaximal
6C2×#124×C59C411yescharacteristic, complemented
7C2×#117×C59C2211yescharacteristic
8C59×#431—21no—
9C59×#395C411yescharacteristic, complemented
10C59×#394C411yescharacteristic, complemented
11C59×#393C2211yescharacteristic
12C59×#392C2211yescharacteristic
13C59×#390—21no—
14C59×#388—21no—
15C59×#388—21no—
16C59×#386—21no—
17C59×#381—21no—
18C59×#376C411yescharacteristic, complemented
19C59×#342—21no—
20C59×#342C2212yes—
21C59×#324—21no—
22C59×#323C2212yes—
23C22×Q8×C59C2×C411yescharacteristic
24C22×D4×C59—21no—
25C22×D4×C59C2×C411yescharacteristic
26C23×C4×C59D411yescharacteristic
27#124×C59—41no—
28#124×C59—41no—
29#117×C59—41no—
30#117×C59—41no—
31C2×C4⋊C4×C59—21no—
32C2×C4⋊C4×C59C2×C411yescharacteristic
33C2×C4⋊C4×C59D411yescharacteristic
34C2×C22⋊C4×C59—21no—
35C2×C22⋊C4×C59—21no—
36C2×C22⋊C4×C59—21no—
37C2×C22⋊C4×C59—21no—
38C2×C22⋊C4×C59—22no—
39C2×C22⋊C4×C59—21no—
40C2×C22⋊C4×C59—21no—
41C2×C22⋊C4×C59D411yescharacteristic
42C2×C22⋊C4×C59C2311yescharacteristic
43C2×C42×C59—21no—
44C2×C42×C59C2×C411yescharacteristic
45C2×C42×C59D411yescharacteristic
46C4⋊C8×C59—41no—
47C22⋊C8×C59—22no—
48C4×C8×C59—41no—
49#95×C59—21no—
50#95×C59—21no—
51#95×C59—21no—
52#95×C59—41no—
53#95×C59—41no—
54#95×C59C2×C411yescharacteristic
55#95×C59C2×C411yescharacteristic
56C24×C59—21no—
57C24×C59C2×D411yescharacteristic
58C2×Q8×C59—41no—
59C2×Q8×C59—81no—
60C2×D4×C59—42no—
61C2×D4×C59—41no—
62C2×D4×C59—42no—
63C2×D4×C59—81no—
64C2×D4×C59—81no—
65C22×C4×C59—21no—
66C22×C4×C59—22no—
67C22×C4×C59—21no—
68C22×C4×C59—21no—
69C22×C4×C59—21no—
70C22×C4×C59—21no—
71C22×C4×C59—41no—
72C22×C4×C59—42no—
73C22×C4×C59C22⋊C411yescharacteristic
74C22×C4×C59C22⋊C411yescharacteristic
75C22×C4×C59C22⋊C411yescharacteristic
76C22×C4×C59C22⋊C411yescharacteristic
77C22×C4×C59C22×C411yescharacteristic
78C22×C4×C59C2×D411yescharacteristic
79C2×C8×C59—42no—
80C4⋊C4×C59—41no—
81C4⋊C4×C59—41no—
82C4⋊C4×C59—81no—
83C22⋊C4×C59—41no—
84C22⋊C4×C59—41no—
85C22⋊C4×C59—42no—
86C22⋊C4×C59—42no—
87C22⋊C4×C59—42no—
88C22⋊C4×C59—41no—
89C22⋊C4×C59—41no—
90C22⋊C4×C59—42no—
91C22⋊C4×C59—42no—
92C22⋊C4×C59—81no—
93C22⋊C4×C59—81no—
94C42×C59—21no—
95C42×C59—21no—
96C42×C59—21no—
97C42×C59—21no—
98C42×C59—42no—
99C23×C59—21no—
100C23×C59—21no—
101C23×C59—41no—
102C23×C59—41no—
103C23×C59—41no—
104C23×C59—41no—
105C23×C59—41no—
106C23×C59—41no—
107C23×C59—41no—
108C23×C59—41no—
109C23×C59—41no—
110C23×C59C2×C22⋊C411yescharacteristic
111C23×C59#13512yes—
112Q8×C59—82no—
113D4×C59—84no—
114D4×C59—82no—
115C2×C4×C59—21no—
116C2×C4×C59—21no—
117C2×C4×C59—22no—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59—42no—
126C2×C4×C59—42no—
127C2×C4×C59—41no—
128C2×C4×C59—41no—
129C2×C4×C59—41no—
130C2×C4×C59—41no—
131C2×C4×C59—41no—
132C2×C4×C59—41no—
133C2×C4×C59—41no—
134C2×C4×C59—41no—
135C2×C4×C59—41no—
136C2×C4×C59—41no—
137C2×C4×C59—41no—
138C2×C4×C59—41no—
139C2×C4×C59—82no—
140C2×C4×C59—82no—
141C2×C4×C59—82no—
142C2×C4×C59#9911yescharacteristic
143C2×C4×C59#9911yescharacteristic
144C8×C59—82no—
145#11844C5911yesmaximal, characteristic, direct product factor, Sylow
146C22×C59—21no—
147C22×C59—21no—
148C22×C59—22no—
149C22×C59—42no—
150C22×C59—41no—
151C22×C59—41no—
152C22×C59—81no—
153C22×C59—81no—
154C22×C59—81no—
155C22×C59—81no—
156C22×C59—81no—
157C22×C59—81no—
158C22×C59—81no—
159C22×C59—81no—
160C22×C59C2×#9911yescharacteristic
161C22×C59#41611yescharacteristic
162C22×C59#42111yescharacteristic
163C4×C59—21no—
164C4×C59—21no—
165C4×C59—42no—
166C4×C59—41no—
167C4×C59—41no—
168C4×C59—41no—
169C4×C59—41no—
170C4×C59—41no—
171C4×C59—81no—
172C4×C59—81no—
173C4×C59—162no—
174#2610C2×C5911yescharacteristic
175#1820C2×C5911yescharacteristic, complemented
176#1458C2×C5911yescharacteristic, complemented
177#1351C2×C5912yescomplemented
178#1343C2×C5912yes—
179C2×C59—21no—
180C2×C59—21no—
181C2×C59—42no—
182C2×C59—161no—
183C2×C59#151611yescharacteristic
184C2×C59#212211yescharacteristic
185C2×C59#212611yescharacteristic
186C2×#124C4×C5911yescharacteristic, complemented
187C2×#117C22×C5911yescharacteristic
188#431—21no—
189#395C4×C5911yescharacteristic, complemented
190#394C4×C5911yescharacteristic, complemented
191#393C22×C5911yescharacteristic
192#392C22×C5911yescharacteristic
193#390—21no—
194#388—21no—
195#388—21no—
196#386—21no—
197#381—21no—
198#376C4×C5911yescharacteristic, complemented
199#342—21no—
200#342C22×C5912yes—
201#324—21no—
202#323C22×C5912yes—
203C59#1184411yescharacteristic, direct product factor, Sylow
204C22×Q8C2×C4×C5911yescharacteristic
205C22×D4—21no—
206C22×D4C2×C4×C5911yescharacteristic
207C23×C4D4×C5911yescharacteristic
208#124—41no—
209#124—41no—
210#117—41no—
211#117—41no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4C2×C4×C5911yescharacteristic
214C2×C4⋊C4D4×C5911yescharacteristic
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—22no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4D4×C5911yescharacteristic
223C2×C22⋊C4C23×C5911yescharacteristic
224C2×C42—21no—
225C2×C42C2×C4×C5911yescharacteristic
226C2×C42D4×C5911yescharacteristic
227C4⋊C8—41no—
228C22⋊C8—22no—
229C4×C8—41no—
230#95—21no—
231#95—21no—
232#95—21no—
233#95—41no—
234#95—41no—
235#95C2×C4×C5911yescharacteristic
236#95C2×C4×C5911yescharacteristic
237C24—21no—
238C24C2×D4×C5911yescharacteristic
239C2×Q8—41no—
240C2×Q8—81no—
241C2×D4—41no—
242C2×D4—42no—
243C2×D4—42no—
244C2×D4—81no—
245C2×D4—81no—
246C22×C4—21no—
247C22×C4—22no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—41no—
253C22×C4—42no—
254C22×C4C22⋊C4×C5911yescharacteristic
255C22×C4C22⋊C4×C5911yescharacteristic
256C22×C4C22⋊C4×C5911yescharacteristic
257C22×C4C22⋊C4×C5911yescharacteristic
258C22×C4C22×C4×C5911yescharacteristic
259C22×C4C2×D4×C5911yescharacteristic
260C2×C8—42no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—81no—
264C22⋊C4—41no—
265C22⋊C4—41no—
266C22⋊C4—42no—
267C22⋊C4—42no—
268C22⋊C4—42no—
269C22⋊C4—41no—
270C22⋊C4—41no—
271C22⋊C4—42no—
272C22⋊C4—42no—
273C22⋊C4—81no—
274C22⋊C4—81no—
275C42—21no—
276C42—21no—
277C42—21no—
278C42—21no—
279C42—42no—
280C23—21no—
281C23—21no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23C2×C22⋊C4×C5911yescharacteristic
292C23#135×C5912yes—
293Q8—82no—
294D4—84no—
295D4—82no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—22no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—82no—
321C2×C4—82no—
322C2×C4—82no—
323C2×C4#99×C5911yescharacteristic
324C2×C4#99×C5911yescharacteristic
325C8—82no—
326C22—21no—
327C22—21no—
328C22—22no—
329C22—42no—
330C22—41no—
331C22—41no—
332C22—81no—
333C22—81no—
334C22—81no—
335C22—81no—
336C22—81no—
337C22—81no—
338C22—81no—
339C22—81no—
340C22C2×#99×C5911yescharacteristic
341C22C59×#41611yescharacteristic
342C22C59×#42111yescharacteristic
343C4—21no—
344C4—21no—
345C4—42no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4—81no—
352C4—81no—
353C4—162no—
354C2—21no—
355C2—21no—
356C2—42no—
357C2—161no—
358C2C59×#151611yescharacteristic
359C2C59×#212211yescharacteristic
360C2C59×#212611yescharacteristic
subgroupG/H
center, socleC22×C59C2×#99
commutatorC22×C4C22×C4×C59
Frattini, cosocleC2×C22⋊C4C23×C59
prime radicalC59×#392C22
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C59 ◁ C22×C4×C59 ◁ C2×#117×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C59×#1820C2semidirect
3. C59×#1458C2semidirect
4. C59×#1351C2semidirect
6. C2×#124×C59C4semidirect
9. C59×#395C4semidirect
10. C59×#394C4semidirect
18. C59×#376C4semidirect
145. #11844C59direct (N × H)
175. #1820C2×C59semidirect
176. #1458C2×C59semidirect
177. #1351C2×C59semidirect
186. C2×#124C4×C59semidirect
189. #395C4×C59semidirect
190. #394C4×C59semidirect
198. #376C4×C59semidirect
203. C59#11844direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#26102
C59×#18202
C59×#14582
C59×#13512
C59×#13432
#1184459