Finite Group Databasebeta

← #28486086

Subgroups — #28486086

Order 15104.

466 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 109 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
1#21433179C211yesmaximal, characteristic
2#21429305C211yesmaximal, characteristic
3#21424089C211yesmaximal, characteristic
4#21422777C211yesmaximal, characteristic
5#21421998C211yesmaximal, characteristic
6#21421997C211yesmaximal, characteristic
7C59×#1548C211yesmaximal, characteristic
8C2×C4×Dic118C2211yescharacteristic
9#16837532—22no—
10#16837529—22no—
11#16837456—22no—
12#16837455C2211yescharacteristic
13#16837426C2211yescharacteristic
14C2×#14273645—21no—
15#16837321C414yes—
16#16837307—21no—
17#16837298—22no—
18#16837271—21no—
19C4×C4⋊Dic59C2211yescharacteristic
20#16837170—21no—
21#16837151—22no—
22C2×C4⋊Q8×C59C2211yescharacteristic
23C59×#431C2211yescharacteristic
24C59×#423C2211yescharacteristic
25C59×#333—22no—
26C22×Dic118D411yescharacteristic
27C2×#11745664—21no—
28C4×Dic118—21no—
29C4×Dic118—21no—
30C4×Dic118—21no—
31C4×Dic118—21no—
32C2×C4⋊Dic59—21no—
33C2×C4⋊Dic59D411yescharacteristic
34C2×Dic59⋊C4—24no—
35C2×Dic59⋊C4C2×C412yes—
36C2×C4×Dic59—21no—
37C2×C4×Dic59D412yes—
38C4⋊(C59⋊C8)—21no—
39C4⋊(C59⋊C8)—21no—
40C4⋊(C59⋊C8)D412yes—
41Dic59⋊C8—24no—
42#14273645—42no—
43C22⋊(C59⋊C8)—21no—
44#14273637—24no—
45C4×C59⋊C8—21no—
46C59⋊#95—24no—
47C59⋊#95C2×C412yes—
48C22×Q8×C59C2×C412yes—
49C2×M16×C59—21no—
50C4⋊Q8×C59—21no—
51C4⋊Q8×C59—21no—
52C4⋊Q8×C59—21no—
53C4⋊Q8×C59—21no—
54C2×C4⋊C4×C59—21no—
55C2×C4⋊C4×C59—21no—
56C2×C42×C59C2311yescharacteristic
57C4⋊C8×C59—21no—
58C4⋊C8×C59—21no—
59C4⋊C8×C59D412yes—
60C22⋊C8×C59—21no—
61C4×C8×C59—21no—
62C2×Q8×C59—22no—
63C2×Q8×C59—22no—
64C2×Q8×C59—82no—
65C22×C4×C59—22no—
66C22×C4×C59C22×C411yescharacteristic
67C22×C4×C59C2×D411yescharacteristic
68C22×C4×C59C2×D411yescharacteristic
69C22×Dic59—22no—
70C22×Dic59C22⋊C412yes—
71C22×Dic59C22⋊C412yes—
72C2×Dic118—21no—
73C2×Dic118—21no—
74C2×Dic118—21no—
75C2×Dic118—21no—
76C2×Dic118—21no—
77C2×Dic118—21no—
78M16×C59—41no—
79M16×C59—41no—
80C2×C8×C59—22no—
81C2×C8×C59—41no—
82C4⋊C4×C59—41no—
83C4⋊C4×C59—41no—
84C4⋊C4×C59—41no—
85C4⋊C4×C59—41no—
86C42×C59C2×D411yescharacteristic
87C42×C59C2×D411yescharacteristic
88C42×C59#4111yescharacteristic
89C42×C59#4111yescharacteristic
90C4⋊Dic59—24no—
91C4⋊Dic59—21no—
92C4⋊Dic59—21no—
93Dic59⋊C4—22no—
94Dic59⋊C4—22no—
95Dic59⋊C4—84no—
96C4×Dic59—22no—
97C4×Dic59—22no—
98C4×Dic59—41no—
99C4×Dic59—41no—
100#11745664—41no—
101#11745664—41no—
102C2×C59⋊C8—22no—
103C2×C59⋊C8—41no—
104C23×C59C2×C22⋊C411yescharacteristic
105Q8×C59—82no—
106Q8×C59—82no—
107C2×C4×C59—22no—
108C2×C4×C59—41no—
109C2×C4×C59—44no—
110C2×C4×C59—42no—
111C2×C4×C59C4×D411yescharacteristic
112C2×C4×C59C4×D411yescharacteristic
113C2×C4×C59#12011yescharacteristic
114C2×C4×C59#12111yescharacteristic
115C2×C4×C59#12111yescharacteristic
116C2×C4×C59#12311yescharacteristic
117C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
118C2×C4×C59#13711yescharacteristic
119C2×C4×C59#13711yescharacteristic
120C2×C4×C59#13711yescharacteristic
121C2×Dic59—24no—
122C2×Dic59—22no—
123C2×Dic59—22no—
124C2×Dic59—22no—
125C2×Dic59—22no—
126C2×Dic59—42no—
127C2×Dic59—42no—
128C2×Dic59—42no—
129Dic118—41no—
130Dic118—41no—
131Dic118—41no—
132Dic118—41no—
133C8×C59—42no—
134C8×C59—81no—
135C59⋊C8—42no—
136C59⋊C8—81no—
137#9400—591nomaximal, Sylow
138C22×C59—21no—
139C22×C59—21no—
140C22×C59#38611yescharacteristic
141C22×C59#41711yescharacteristic
142C22×C59#41911yescharacteristic
143C4×C59—21no—
144C4×C59—21no—
145C4×C59—21no—
146C4×C59—82no—
147C4×C59#45612yes—
148C4×C59#46811yescharacteristic
149C4×C59#46811yescharacteristic
150C4×C59#47011yescharacteristic
151C4×C59#47011yescharacteristic
152Dic59—44no—
153Dic59—42no—
154Dic59—42no—
155#2983—591no—
156#2567—591no—
157#1801—591no—
158#1548—591no—
159#1548D5911yescharacteristic
160#1303—591no—
161#1303—591no—
162C2×C59—21no—
163C2×C59—21no—
164C2×C59#188611yescharacteristic
165C2×C59#189411yescharacteristic
166C2×C59#191411yescharacteristic
167C2×C4⋊Q8C2×D5911yescharacteristic
168C2×C4×Q8—591no—
169#446—1182no—
170#446—1182no—
171#432—1182no—
172#431—591no—
173#431C2×D5911yescharacteristic
174#423—591no—
175#423C2×D5911yescharacteristic
176C2×#101—1181no—
177#395—594no—
178#391—1181no—
179#389—1182no—
180#384—1181no—
181C4×C4⋊C4—591no—
182#343—1181no—
183#333—22no—
184#333—1182no—
185C59#940011yescharacteristic, complemented, Sylow
186C22×Q8—591no—
187C22×Q8C4×D5912yes—
188C2×M16—21no—
189C2×M16—1181no—
190C4⋊Q8—21no—
191C4⋊Q8—21no—
192C4⋊Q8—21no—
193C4⋊Q8—21no—
194C4×Q8—1181no—
195C4×Q8—1181no—
196C4×Q8—1181no—
197C4×Q8—1181no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—592no—
201C2×C4⋊C4—591no—
202C2×C4⋊C4—1181no—
203C2×C4⋊C4—1184no—
204C2×C42—592no—
205C2×C42—1181no—
206C2×C42C22×D5911yescharacteristic
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—592no—
210C4⋊C8—1184no—
211C4⋊C8—1181no—
212C4⋊C8—1181no—
213C4⋊C8C22⋊D5912yes—
214#101—2362no—
215C22⋊C8—21no—
216C22⋊C8—1181no—
217#97—1184no—
218C4×C8—21no—
219C4×C8—1181no—
220#95—592no—
221#95—1184no—
222C2×Q8—22no—
223C2×Q8—22no—
224C2×Q8—82no—
225C2×Q8—1181no—
226C2×Q8—1181no—
227C2×Q8—1181no—
228C2×Q8—1181no—
229C2×Q8—1181no—
230C2×Q8—1181no—
231C22×C4—22no—
232C22×C4—592no—
233C22×C4—592no—
234C22×C4—1182no—
235C22×C4C2×C4×D5911yescharacteristic
236C22×C4D4×D5911yescharacteristic
237C22×C4D4×D5911yescharacteristic
238M16—41no—
239M16—41no—
240M16—2361no—
241M16—2361no—
242C2×C8—22no—
243C2×C8—41no—
244C2×C8—1182no—
245C2×C8—2361no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—1184no—
251C4⋊C4—1182no—
252C4⋊C4—1182no—
253C4⋊C4—1181no—
254C4⋊C4—1181no—
255C4⋊C4—4724no—
256C42—1182no—
257C42—1182no—
258C42—2361no—
259C42—2361no—
260C42#1174568511yescharacteristic
261C42D4×D5911yescharacteristic
262C42#1174568711yescharacteristic
263C42C2×C22⋊D5911yescharacteristic
264C23C22⋊C4×D5911yescharacteristic
265Q8—82no—
266Q8—82no—
267Q8—2361no—
268Q8—2361no—
269Q8—2361no—
270Q8—2361no—
271C2×C4—22no—
272C2×C4—41no—
273C2×C4—44no—
274C2×C4—42no—
275C2×C4—1184no—
276C2×C4—1182no—
277C2×C4—1182no—
278C2×C4—1182no—
279C2×C4—1182no—
280C2×C4—2362no—
281C2×C4—2362no—
282C2×C4—2362no—
283C2×C4(C22⋊D59)⋊C411yescharacteristic
284C2×C4C4×C22⋊D5911yescharacteristic
285C2×C4#1427369511yescharacteristic
286C2×C4#1427369811yescharacteristic
287C2×C4#1427370011yescharacteristic
288C2×C4#1427370911yescharacteristic
289C2×C4#1427375411yescharacteristic
290C2×C4#1427375611yescharacteristic
291C2×C4#1427375911yescharacteristic
292C2×C4#1427375911yescharacteristic
293C8—42no—
294C8—81no—
295C8—4721no—
296C8—2362no—
297C22—21no—
298C22—21no—
299C22#1683727811yescharacteristic
300C22#1683740211yescharacteristic
301C22#1683740911yescharacteristic
302C4—21no—
303C4—21no—
304C4—21no—
305C4—82no—
306C4—2364no—
307C4—2362no—
308C4—2362no—
309C4#1683758312yes—
310C4#1683764511yescharacteristic
311C4#1683765111yescharacteristic
312C4#1683765711yescharacteristic
313C4#1683765911yescharacteristic
314C2—21no—
315C2—21no—
316C2#2142448611yescharacteristic
317C2#2142452611yescharacteristic
318C2#2142464011yescharacteristic
subgroupG/H
centerC22#16837278
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#1548C2
socleC22×C59#386
prime radicalC23×C59C2×C22⋊C4
cosocleC2×C42×C59C23
hypercenter#1548D59
hypocenterC59#9400
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
185. C59#9400semidirect

Maximal subgroups

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

subgroupindex
#214331792
#214293052
#214240892
#214227772
#214219982
#214219972
C59×#15482
#940059