Finite Group Databasebeta

← C59×#10224 #28422333

Subgroups — C59×#10224 #28422333

Order 15104.

462 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3230C211yesmaximal, characteristic
2C59×#3209C211yesmaximal, characteristic
3C59×#3162C211yesmaximal, characteristic
4C59×#1993C211yesmaximal, characteristic
5C59×#1518C211yesmaximal, characteristic
6C59×#1518C211yesmaximal, characteristic
7C59×#1281C211yesmaximal, characteristic
8C59×#533C2211yescharacteristic
9C59×#533C2211yescharacteristic
10C2×C4⋊Q8×C59C2211yescharacteristic
11C59×#501—21no—
12C59×#501—21no—
13C59×#501—21no—
14C59×#501—21no—
15C59×#500—21no—
16C59×#494—21no—
17C59×#487—21no—
18C59×#487—21no—
19C59×#484—22no—
20C59×#477—22no—
21C59×#462—22no—
22C59×#451—22no—
23C59×#431C2211yescharacteristic
24C59×#431C2211yescharacteristic
25C59×#427—22no—
26C2×#97×C59C2211yescharacteristic
27C59×#382C2211yescharacteristic
28C59×#340—22no—
29C59×#328—22no—
30C59×#328—22no—
31C22×Q8×C59—21no—
32C2×Q16×C59—24no—
33C22×C8×C59D412yes—
34C4⋊Q8×C59—21no—
35C4⋊Q8×C59—21no—
36C4⋊Q8×C59—21no—
37C4⋊Q8×C59D412yes—
38C4⋊Q8×C59D411yescharacteristic
39C4⋊Q8×C59D411yescharacteristic
40C4⋊Q8×C59D411yescharacteristic
41C4⋊Q8×C59D411yescharacteristic
42#125×C59—21no—
43#125×C59—21no—
44C22⋊Q8×C59—21no—
45C22⋊Q8×C59—21no—
46C22⋊Q8×C59—21no—
47C22⋊Q8×C59—21no—
48C4×Q8×C59—21no—
49C4×Q8×C59—21no—
50C4×Q8×C59—21no—
51C4×Q8×C59—21no—
52#117×C59—21no—
53#117×C59—21no—
54C2×C4⋊C4×C59—21no—
55C2×C4⋊C4×C59—21no—
56C2×C4⋊C4×C59—21no—
57C2×C42×C59C2311yescharacteristic
58#107×C59—22no—
59#107×C59—22no—
60#107×C59—24no—
61#106×C59—22no—
62#106×C59—22no—
63C4⋊C8×C59—21no—
64C4⋊C8×C59—21no—
65#103×C59—24no—
66#103×C59—24no—
67C22⋊C8×C59D412yes—
68C22⋊C8×C59D412yes—
69#97×C59—21no—
70#97×C59—21no—
71C4×C8×C59—21no—
72C4×C8×C59—21no—
73#95×C59—21no—
74#95×C59—21no—
75C2×Q8×C59—21no—
76C2×Q8×C59—22no—
77C2×Q8×C59—21no—
78C2×Q8×C59—21no—
79C2×Q8×C59—21no—
80C2×Q8×C59—41no—
81C2×Q8×C59—82no—
82C22×C4×C59—41no—
83C22×C4×C59—41no—
84C22×C4×C59C2×D411yescharacteristic
85C22×C4×C59C2×D411yescharacteristic
86C22×C4×C59C2×D411yescharacteristic
87Q16×C59—84no—
88C2×C8×C59—22no—
89C2×C8×C59—22no—
90C2×C8×C59—22no—
91C2×C8×C59—22no—
92C2×C8×C59Q1614yescomplemented
93C4⋊C4×C59—21no—
94C4⋊C4×C59—22no—
95C4⋊C4×C59—21no—
96C4⋊C4×C59—21no—
97C4⋊C4×C59—21no—
98C4⋊C4×C59—21no—
99C4⋊C4×C59—21no—
100C4⋊C4×C59—22no—
101C4⋊C4×C59—21no—
102C4⋊C4×C59—21no—
103C4⋊C4×C59—41no—
104C4⋊C4×C59—41no—
105C4⋊C4×C59—41no—
106C4⋊C4×C59—41no—
107C4⋊C4×C59—41no—
108C4⋊C4×C59—41no—
109C4⋊C4×C59—42no—
110C22⋊C4×C59—41no—
111C22⋊C4×C59—41no—
112C42×C59—41no—
113C42×C59—41no—
114C42×C59C2×D411yescharacteristic
115C42×C59C2×D411yescharacteristic
116C42×C59C2×D411yescharacteristic
117C42×C59#4111yescharacteristic
118C23×C59#12711yescharacteristic
119Q8×C59—42no—
120Q8×C59—44no—
121Q8×C59—42no—
122Q8×C59—81no—
123Q8×C59—81no—
124Q8×C59—82no—
125C2×C4×C59—41no—
126C2×C4×C59—41no—
127C2×C4×C59—41no—
128C2×C4×C59—41no—
129C2×C4×C59—41no—
130C2×C4×C59—41no—
131C2×C4×C59—42no—
132C2×C4×C59—82no—
133C2×C4×C59—81no—
134C2×C4×C59—81no—
135C2×C4×C59—81no—
136C2×C4×C59#12011yescharacteristic
137C2×C4×C59#12011yescharacteristic
138C2×C4×C59#12011yescharacteristic
139C2×C4×C59#12111yescharacteristic
140C2×C4×C59#12111yescharacteristic
141C2×C4×C59#12111yescharacteristic
142C2×C4×C59C2×Q1612yes—
143C2×C4×C59#13712yes—
144C8×C59—24no—
145C8×C59—42no—
146C8×C59—42no—
147#10224C5911yesmaximal, characteristic, direct product factor, Sylow
148C22×C59—21no—
149C22×C59—21no—
150C22×C59#39211yescharacteristic
151C22×C59#49411yescharacteristic
152C22×C59#49711yescharacteristic
153C4×C59—21no—
154C4×C59—21no—
155C4×C59—21no—
156C4×C59—21no—
157C4×C59—82no—
158C4×C59—81no—
159C4×C59—81no—
160C4×C59—81no—
161C4×C59—81no—
162C4×C59—161no—
163C4×C59#45112yes—
164C4×C59#46212yes—
165#3230C2×C5911yescharacteristic
166#3209C2×C5911yescharacteristic
167#3162C2×C5911yescharacteristic
168#1993C2×C5911yescharacteristic
169#1518C2×C5911yescharacteristic
170#1518C2×C5911yescharacteristic
171#1281C2×C5911yescharacteristic
172C2×C59—21no—
173C2×C59—21no—
174C2×C59#200811yescharacteristic
175C2×C59#200911yescharacteristic
176C2×C59#201611yescharacteristic
177#533C22×C5911yescharacteristic
178#533C22×C5911yescharacteristic
179C2×C4⋊Q8C22×C5911yescharacteristic
180#501—21no—
181#501—21no—
182#501—21no—
183#501—21no—
184#500—21no—
185#494—21no—
186#487—21no—
187#487—21no—
188#484—22no—
189#477—22no—
190#462—22no—
191#451—22no—
192#431C22×C5911yescharacteristic
193#431C22×C5911yescharacteristic
194#427—22no—
195C2×#97C22×C5911yescharacteristic
196#382C22×C5911yescharacteristic
197#340—22no—
198#328—22no—
199#328—22no—
200C59#1022411yescharacteristic, direct product factor, Sylow
201C22×Q8—21no—
202C2×Q16—24no—
203C22×C8D4×C5912yes—
204C4⋊Q8—21no—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8D4×C5912yes—
208C4⋊Q8D4×C5911yescharacteristic
209C4⋊Q8D4×C5911yescharacteristic
210C4⋊Q8D4×C5911yescharacteristic
211C4⋊Q8D4×C5911yescharacteristic
212#125—21no—
213#125—21no—
214C22⋊Q8—21no—
215C22⋊Q8—21no—
216C22⋊Q8—21no—
217C22⋊Q8—21no—
218C4×Q8—21no—
219C4×Q8—21no—
220C4×Q8—21no—
221C4×Q8—21no—
222#117—21no—
223#117—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C42C23×C5911yescharacteristic
228#107—22no—
229#107—22no—
230#107—24no—
231#106—22no—
232#106—22no—
233C4⋊C8—21no—
234C4⋊C8—21no—
235#103—24no—
236#103—24no—
237C22⋊C8D4×C5912yes—
238C22⋊C8D4×C5912yes—
239#97—21no—
240#97—21no—
241C4×C8—21no—
242C4×C8—21no—
243#95—21no—
244#95—21no—
245C2×Q8—21no—
246C2×Q8—22no—
247C2×Q8—21no—
248C2×Q8—21no—
249C2×Q8—21no—
250C2×Q8—41no—
251C2×Q8—82no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4C2×D4×C5911yescharacteristic
255C22×C4C2×D4×C5911yescharacteristic
256C22×C4C2×D4×C5911yescharacteristic
257Q16—84no—
258C2×C8—22no—
259C2×C8—22no—
260C2×C8—22no—
261C2×C8—22no—
262C2×C8Q16×C5914yescomplemented
263C4⋊C4—21no—
264C4⋊C4—22no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—22no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—42no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C42—41no—
283C42—41no—
284C42C2×D4×C5911yescharacteristic
285C42C2×D4×C5911yescharacteristic
286C42C2×D4×C5911yescharacteristic
287C42#41×C5911yescharacteristic
288C23#127×C5911yescharacteristic
289Q8—42no—
290Q8—44no—
291Q8—42no—
292Q8—81no—
293Q8—81no—
294Q8—82no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—82no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4#120×C5911yescharacteristic
307C2×C4#120×C5911yescharacteristic
308C2×C4#120×C5911yescharacteristic
309C2×C4#121×C5911yescharacteristic
310C2×C4#121×C5911yescharacteristic
311C2×C4#121×C5911yescharacteristic
312C2×C4C2×Q16×C5912yes—
313C2×C4#137×C5912yes—
314C8—24no—
315C8—42no—
316C8—42no—
317C22—21no—
318C22—21no—
319C22C59×#39211yescharacteristic
320C22C59×#49411yescharacteristic
321C22C59×#49711yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—82no—
327C4—81no—
328C4—81no—
329C4—81no—
330C4—81no—
331C4—161no—
332C4C59×#45112yes—
333C4C59×#46212yes—
334C2—21no—
335C2—21no—
336C2C59×#200811yescharacteristic
337C2C59×#200911yescharacteristic
338C2C59×#201611yescharacteristic
subgroupG/H
center, socleC22×C59#392
commutator, Frattini, cosocleC2×C42C23×C59
prime radicalC23×C59#127
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
92. C2×C8×C59Q16semidirect
147. #10224C59direct (N × H)
200. C59#10224direct (N × H)
262. C2×C8Q16×C59semidirect

Maximal subgroups

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

subgroupindex
C59×#32302
C59×#32092
C59×#31622
C59×#19932
C59×#15182
C59×#12812
#1022459