Finite Group Databasebeta

← #28486098

Subgroups — #28486098

Order 15104.

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

normal subgroups only

This group has 486 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#21429084C211yesmaximal, characteristic
3#21424089C211yesmaximal, characteristic
4#21422769C211yesmaximal, characteristic
5#21422767C211yesmaximal, characteristic
6#21421999C211yesmaximal, characteristic
7C59×#1303C211yesmaximal, characteristic
8C2×#14273727—21no—
9C2×#14273727C2211yescharacteristic
10C2×C4×Dic118C2211yescharacteristic
11#16837532—22no—
12#16837529—22no—
13#16837456—22no—
14#16837455C2211yescharacteristic
15#16837426C2211yescharacteristic
16C2×#14273645—21no—
17#16837334C414yes—
18#16837308—21no—
19#16837301—22no—
20#16837170—21no—
21#16837149—22no—
22#16837147—22no—
23C59×#431C2211yescharacteristic
24C59×#423C2211yescharacteristic
25C4×C4⋊C4×C59C2211yescharacteristic
26C22×Dic118—21no—
27C22×Dic118D411yescharacteristic
28C2×#11745664—21no—
29#14273727—21no—
30#14273727—21no—
31#14273727—21no—
32#14273727—21no—
33#14273727—42no—
34#14273727—42no—
35C4×Dic118—21no—
36C4×Dic118—21no—
37C4×Dic118—21no—
38C4×Dic118—21no—
39C2×C4⋊Dic59—21no—
40C2×C4⋊Dic59—24no—
41C2×C4⋊Dic59C2×C412yes—
42C2×C4⋊Dic59D411yescharacteristic
43C2×Dic59⋊C4C2×C412yes—
44C2×C4×Dic59D412yes—
45C4⋊(C59⋊C8)—21no—
46C4⋊(C59⋊C8)—21no—
47C4⋊(C59⋊C8)D412yes—
48Dic59⋊C8—24no—
49#14273645—42no—
50C22⋊(C59⋊C8)—21no—
51#14273637—24no—
52C4×C59⋊C8—21no—
53C59⋊#95—24no—
54C2×M16×C59—21no—
55C2×C4⋊C4×C59—21no—
56C2×C42×C59—21no—
57C2×C42×C59C2311yescharacteristic
58C4⋊C8×C59—21no—
59C4⋊C8×C59—21no—
60C4⋊C8×C59D412yes—
61C22⋊C8×C59—21no—
62C4×C8×C59—21no—
63#95×C59C2×C412yes—
64C22×C4×C59—22no—
65C22×C4×C59C22×C411yescharacteristic
66C22×C4×C59C2×D411yescharacteristic
67C22×C4×C59C2×D411yescharacteristic
68C22×Dic59—22no—
69C22×Dic59C22⋊C412yes—
70C22×Dic59C22⋊C412yes—
71C2×Dic118—21no—
72C2×Dic118—21no—
73C2×Dic118—21no—
74C2×Dic118—21no—
75C2×Dic118—21no—
76C2×Dic118—21no—
77C2×Dic118—41no—
78C2×Dic118—41no—
79C2×Dic118—41no—
80C2×Dic118—41no—
81C2×Dic118—41no—
82C2×Dic118—41no—
83M16×C59—41no—
84M16×C59—41no—
85C2×C8×C59—22no—
86C2×C8×C59—41no—
87C4⋊C4×C59—24no—
88C42×C59—41no—
89C42×C59—41no—
90C42×C59C2×D411yescharacteristic
91C42×C59C2×D411yescharacteristic
92C42×C59#4111yescharacteristic
93C42×C59#4111yescharacteristic
94C4⋊Dic59—21no—
95C4⋊Dic59—21no—
96C4⋊Dic59—22no—
97C4⋊Dic59—22no—
98C4⋊Dic59—48no—
99C4⋊Dic59—41no—
100C4⋊Dic59—41no—
101Dic59⋊C4—22no—
102Dic59⋊C4—22no—
103C4×Dic59—22no—
104C4×Dic59—22no—
105#11745664—41no—
106#11745664—41no—
107C2×C59⋊C8—22no—
108C2×C59⋊C8—41no—
109C23×C59C2×C22⋊C411yescharacteristic
110C2×C4×C59—22no—
111C2×C4×C59—24no—
112C2×C4×C59—41no—
113C2×C4×C59—42no—
114C2×C4×C59—42no—
115C2×C4×C59C4×D411yescharacteristic
116C2×C4×C59C4×D411yescharacteristic
117C2×C4×C59#12011yescharacteristic
118C2×C4×C59#12111yescharacteristic
119C2×C4×C59#12111yescharacteristic
120C2×C4×C59#12311yescharacteristic
121C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
122C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C59#13711yescharacteristic
125C2×Dic59—22no—
126C2×Dic59—22no—
127C2×Dic59—22no—
128C2×Dic59—22no—
129C2×Dic59—42no—
130C2×Dic59—42no—
131C2×Dic59—42no—
132C2×Dic59—42no—
133Dic118—41no—
134Dic118—41no—
135Dic118—41no—
136Dic118—41no—
137Dic118—81no—
138Dic118—81no—
139Dic118—81no—
140Dic118—81no—
141C8×C59—42no—
142C8×C59—81no—
143C59⋊C8—42no—
144C59⋊C8—81no—
145#9402—591nomaximal, Sylow
146C22×C59—21no—
147C22×C59—21no—
148C22×C59#38611yescharacteristic
149C22×C59#41711yescharacteristic
150C22×C59#41811yescharacteristic
151C4×C59—21no—
152C4×C59—21no—
153C4×C59—21no—
154C4×C59—44no—
155C4×C59#45612yes—
156C4×C59#46811yescharacteristic
157C4×C59#46811yescharacteristic
158C4×C59#46911yescharacteristic
159C4×C59#46911yescharacteristic
160Dic59—42no—
161Dic59—42no—
162Dic59—82no—
163#2983—591no—
164#2546—591no—
165#1801—591no—
166#1546—591no—
167#1546—591no—
168#1303—591no—
169#1303D5911yescharacteristic
170C2×C59—21no—
171C2×C59—21no—
172C2×C59#188611yescharacteristic
173C2×C59#189511yescharacteristic
174C2×C59#191511yescharacteristic
175C2×C4⋊Q8—591no—
176C2×C4⋊Q8—1181no—
177C2×C4×Q8—591no—
178#446—1182no—
179#446—1182no—
180#432—1182no—
181#431—591no—
182#431C2×D5911yescharacteristic
183#423—591no—
184#423C2×D5911yescharacteristic
185C2×#101—1181no—
186#398—594no—
187#391—1181no—
188#389—1182no—
189C4×C4⋊C4C2×D5911yescharacteristic
190#343—1181no—
191#332—1182no—
192#332—1182no—
193C59#940211yescharacteristic, complemented, Sylow
194C22×Q8—591no—
195C22×Q8—1181no—
196C2×M16—21no—
197C2×M16—1181no—
198C4⋊Q8—1181no—
199C4⋊Q8—1181no—
200C4⋊Q8—1181no—
201C4⋊Q8—1181no—
202C4⋊Q8—2362no—
203C4⋊Q8—2362no—
204C4×Q8—1181no—
205C4×Q8—1181no—
206C4×Q8—1181no—
207C4×Q8—1181no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—592no—
210C2×C4⋊C4—591no—
211C2×C4⋊C4—592no—
212C2×C4⋊C4—1184no—
213C2×C4⋊C4—1181no—
214C2×C42—21no—
215C2×C42—592no—
216C2×C42C22×D5911yescharacteristic
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—592no—
220C4⋊C8—1184no—
221C4⋊C8—1181no—
222C4⋊C8—1181no—
223C4⋊C8D23612yes—
224#101—2362no—
225C22⋊C8—21no—
226C22⋊C8—1181no—
227#97—1184no—
228C4×C8—21no—
229C4×C8—1181no—
230#95—1184no—
231#95C4×D5912yes—
232C2×Q8—1181no—
233C2×Q8—1181no—
234C2×Q8—1181no—
235C2×Q8—1181no—
236C2×Q8—1181no—
237C2×Q8—1181no—
238C2×Q8—2361no—
239C2×Q8—2361no—
240C2×Q8—2361no—
241C2×Q8—2361no—
242C2×Q8—2361no—
243C2×Q8—2361no—
244C22×C4—22no—
245C22×C4—592no—
246C22×C4—592no—
247C22×C4—1182no—
248C22×C4C2×C4×D5911yescharacteristic
249C22×C4D4×D5911yescharacteristic
250C22×C4D4×D5911yescharacteristic
251M16—41no—
252M16—41no—
253M16—2361no—
254M16—2361no—
255C2×C8—22no—
256C2×C8—41no—
257C2×C8—1182no—
258C2×C8—2361no—
259C4⋊C4—24no—
260C4⋊C4—1182no—
261C4⋊C4—1182no—
262C4⋊C4—1181no—
263C4⋊C4—1181no—
264C4⋊C4—1182no—
265C4⋊C4—1182no—
266C4⋊C4—2368no—
267C4⋊C4—2361no—
268C4⋊C4—2361no—
269C42—41no—
270C42—41no—
271C42—1182no—
272C42—1182no—
273C42C2×D23611yescharacteristic
274C42#1174568511yescharacteristic
275C42D4×D5911yescharacteristic
276C42#1174568911yescharacteristic
277C23C22⋊C4×D5911yescharacteristic
278Q8—4721no—
279Q8—4721no—
280Q8—4721no—
281Q8—4721no—
282Q8—2361no—
283Q8—2361no—
284Q8—2361no—
285Q8—2361no—
286C2×C4—22no—
287C2×C4—24no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—1182no—
292C2×C4—1182no—
293C2×C4—1182no—
294C2×C4—1182no—
295C2×C4—2362no—
296C2×C4—2362no—
297C2×C4—2362no—
298C2×C4—2362no—
299C2×C4#1427368911yescharacteristic
300C2×C4C4×D23611yescharacteristic
301C2×C4#1427369711yescharacteristic
302C2×C4#1427370011yescharacteristic
303C2×C4#1427370211yescharacteristic
304C2×C4#1427371211yescharacteristic
305C2×C4#1427375111yescharacteristic
306C2×C4#1427375411yescharacteristic
307C2×C4#1427375411yescharacteristic
308C2×C4#1427375911yescharacteristic
309C8—42no—
310C8—81no—
311C8—4721no—
312C8—2362no—
313C22—21no—
314C22—21no—
315C22#1683728011yescharacteristic
316C22#1683740211yescharacteristic
317C22#1683740511yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—44no—
322C4—4722no—
323C4—2362no—
324C4—2362no—
325C4#1683758612yes—
326C4#1683764911yescharacteristic
327C4#1683765111yescharacteristic
328C4#1683765411yescharacteristic
329C4#1683765611yescharacteristic
330C2—21no—
331C2—21no—
332C2#2142448811yescharacteristic
333C2#2142453311yescharacteristic
334C2#2142464711yescharacteristic
subgroupG/H
centerC22#16837280
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#1303C2
socleC22×C59#386
prime radicalC23×C59C2×C22⋊C4
cosocleC2×C42×C59C23
hypercenter#1303D59
hypocenterC59#9402
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
193. C59#9402semidirect

Maximal subgroups

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

subgroupindex
#214331792
#214290842
#214240892
#214227692
#214227672
#214219992
C59×#13032
#940259