Finite Group Databasebeta

← #28499581

Subgroups — #28499581

Order 15104.

382 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 69 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#21429787C211yesmaximal, characteristic
2#21424172C211yesmaximal, characteristic
3#21422407C211yesmaximal, characteristic
4#21422120C211yesmaximal, characteristic
5#21422097C211yesmaximal, characteristic
6#21422095C211yesmaximal, characteristic
7C59×#1352C211yesmaximal, characteristic
8C2×#14273718C411yescharacteristic, complemented
9C2×#14273683C2211yescharacteristic
10#16837452—21no—
11#16837340C411yescharacteristic, complemented
12#16837334C411yescharacteristic, complemented
13#16837327C2211yescharacteristic
14#16837298—21no—
15#16837290—21no—
16#16837288—21no—
17#16837277—21no—
18#16837263—21no—
19#16837247C411yescharacteristic, complemented
20#16837169C2211yescharacteristic
21#16837168—21no—
22#16837127—21no—
23#16837126C2211yescharacteristic
24C59×#399C2211yescharacteristic
25C59×#342C2211yescharacteristic
26C59×#323C2211yescharacteristic
27C23×Dic59D411yescharacteristic
28#14273718—41no—
29#14273718—41no—
30#14273683—41no—
31#14273683—41no—
32C2×C4⋊Dic59—21no—
33C2×C4⋊Dic59—21no—
34C2×C4⋊Dic59C2×C411yescharacteristic
35C2×Dic59⋊C4—21no—
36C2×Dic59⋊C4C2×C411yescharacteristic
37C2×Dic59⋊C4D411yescharacteristic
38C2×C22⋊Dic59—21no—
39C2×C22⋊Dic59—21no—
40C2×C22⋊Dic59D411yescharacteristic
41C2×C4×Dic59—21no—
42C2×C4×Dic59C2×C411yescharacteristic
43C2×C4×Dic59D411yescharacteristic
44Dic59⋊C8—41no—
45C22⋊(C59⋊C8)—21no—
46C8×Dic59—41no—
47C59⋊#95—21no—
48C59⋊#95—21no—
49C59⋊#95—21no—
50C59⋊#95—21no—
51C59⋊#95—21no—
52C59⋊#95—41no—
53C59⋊#95—41no—
54C59⋊#95C2×C411yescharacteristic
55C2×C4⋊C4×C59—21no—
56C2×C4⋊C4×C59C2×C411yescharacteristic
57C2×C22⋊C4×C59—21no—
58C2×C22⋊C4×C59—21no—
59C2×C22⋊C4×C59C2311yescharacteristic
60C22⋊C8×C59—21no—
61#95×C59C2×C411yescharacteristic
62C24×C59C2×D411yescharacteristic
63C22×C4×C59—21no—
64C22×C4×C59—21no—
65C22×C4×C59—41no—
66C22×C4×C59C22×C411yescharacteristic
67C22×C4×C59C2×D411yescharacteristic
68C22×Dic59—21no—
69C22×Dic59—21no—
70C22×Dic59—21no—
71C22×Dic59—21no—
72C22×Dic59—21no—
73C22×Dic59—21no—
74C22×Dic59—41no—
75C22×Dic59—41no—
76C22×Dic59C22⋊C411yescharacteristic
77C22×Dic59C22⋊C411yescharacteristic
78C22×Dic59C22⋊C411yescharacteristic
79C22×Dic59C22⋊C411yescharacteristic
80C2×C8×C59—41no—
81C4⋊C4×C59—42no—
82C4⋊C4×C59—41no—
83C22⋊C4×C59—41no—
84C22⋊C4×C59—42no—
85C22⋊C4×C59—41no—
86C22⋊C4×C59—41no—
87C22⋊Dic59—41no—
88C22⋊Dic59—41no—
89C22⋊Dic59—41no—
90C22⋊Dic59—41no—
91C22⋊Dic59—41no—
92C4⋊Dic59—42no—
93C4⋊Dic59—41no—
94C4⋊Dic59—41no—
95C4⋊Dic59—41no—
96Dic59⋊C4—41no—
97Dic59⋊C4—41no—
98Dic59⋊C4—42no—
99C4×Dic59—21no—
100C4×Dic59—21no—
101C4×Dic59—21no—
102C4×Dic59—21no—
103C4×Dic59—42no—
104C2×C59⋊C8—41no—
105C23×C59—21no—
106C23×C59—21no—
107C23×C59—41no—
108C23×C59—41no—
109C23×C59C2×C22⋊C411yescharacteristic
110C23×C59#13511yescharacteristic
111C23×C59#13511yescharacteristic
112C2×C4×C59—22no—
113C2×C4×C59—21no—
114C2×C4×C59—21no—
115C2×C4×C59—41no—
116C2×C4×C59—41no—
117C2×C4×C59—41no—
118C2×C4×C59—41no—
119C2×C4×C59—41no—
120C2×C4×C59—41no—
121C2×C4×C59—41no—
122C2×C4×C59—81no—
123C2×C4×C59—81no—
124C2×C4×C59—81no—
125C2×Dic59—21no—
126C2×Dic59—21no—
127C2×Dic59—21no—
128C2×Dic59—21no—
129C2×Dic59—21no—
130C2×Dic59—21no—
131C2×Dic59—21no—
132C2×Dic59—41no—
133C2×Dic59—41no—
134C2×Dic59—41no—
135C2×Dic59—41no—
136C2×Dic59—41no—
137C2×Dic59—41no—
138C2×Dic59—41no—
139C2×Dic59—41no—
140C2×Dic59—41no—
141C2×Dic59—41no—
142C2×Dic59—41no—
143C2×Dic59—41no—
144C2×Dic59—81no—
145C2×Dic59—81no—
146C2×Dic59—81no—
147C2×Dic59#9911yescharacteristic
148C2×Dic59#9911yescharacteristic
149C8×C59—81no—
150C59⋊C8—81no—
151#11846—591nomaximal, Sylow
152C22×C59—21no—
153C22×C59—21no—
154C22×C59—21no—
155C22×C59—21no—
156C22×C59—41no—
157C22×C59—41no—
158C22×C59—41no—
159C22×C59—41no—
160C22×C59—81no—
161C22×C59C2×#9911yescharacteristic
162C22×C59#41611yescharacteristic
163C22×C59#42111yescharacteristic
164C4×C59—42no—
165C4×C59—41no—
166C4×C59—41no—
167C4×C59—81no—
168C4×C59—161no—
169Dic59—21no—
170Dic59—21no—
171Dic59—41no—
172Dic59—41no—
173Dic59—41no—
174Dic59—81no—
175Dic59—81no—
176Dic59—161no—
177#2611—591no—
178#1820—591no—
179#1458—591no—
180#1352—591no—
181#1352D5911yescharacteristic
182#1344—591no—
183#1344—591no—
184C2×C59—21no—
185C2×C59—21no—
186C2×C59—41no—
187C2×C59—41no—
188C2×C59#151611yescharacteristic
189C2×C59#212311yescharacteristic
190C2×C59#212611yescharacteristic
191C2×#125—591no—
192C2×#117—591no—
193#431—1181no—
194#400—591no—
195#399C2×D5911yescharacteristic
196#398—591no—
197#397—591no—
198#389—1181no—
199#388—1181no—
200#387—1181no—
201#385—1181no—
202#381—1181no—
203#376—591no—
204#342—591no—
205#342—1181no—
206#342C2×D5911yescharacteristic
207#324—1181no—
208#323—591no—
209#323C2×D5911yescharacteristic
210C59#1184611yescharacteristic, complemented, Sylow
211C23×C4—591no—
212#125—2361no—
213#125—2361no—
214#117—2361no—
215#117—2361no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—591no—
218C2×C4⋊C4—591no—
219C2×C4⋊C4—591no—
220C2×C4⋊C4—1181no—
221C2×C4⋊C4—1181no—
222C2×C4⋊C4—1181no—
223C2×C4⋊C4C4×D5911yescharacteristic
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—591no—
227C2×C22⋊C4—1181no—
228C2×C22⋊C4—1181no—
229C2×C22⋊C4C22×D5911yescharacteristic
230C2×C42—591no—
231C2×C42—591no—
232C2×C42—1181no—
233C4⋊C8—2361no—
234C22⋊C8—21no—
235C22⋊C8—1181no—
236C4×C8—2361no—
237#95—591no—
238#95—1181no—
239#95—1181no—
240#95—1181no—
241#95—1181no—
242#95—1181no—
243#95—2361no—
244#95—2361no—
245#95C4×D5911yescharacteristic
246C24D4×D5911yescharacteristic
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—41no—
250C22×C4—591no—
251C22×C4—591no—
252C22×C4—591no—
253C22×C4—591no—
254C22×C4—1181no—
255C22×C4—1181no—
256C22×C4—1181no—
257C22×C4—1181no—
258C22×C4—1181no—
259C22×C4—1181no—
260C22×C4—2361no—
261C22×C4—2361no—
262C22×C4C2×C4×D5911yescharacteristic
263C22×C4D4×D5911yescharacteristic
264C2×C8—41no—
265C2×C8—2361no—
266C4⋊C4—41no—
267C4⋊C4—42no—
268C4⋊C4—2361no—
269C4⋊C4—2361no—
270C4⋊C4—2361no—
271C4⋊C4—2361no—
272C4⋊C4—2361no—
273C4⋊C4—2362no—
274C4⋊C4—2362no—
275C22⋊C4—41no—
276C22⋊C4—42no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—2361no—
280C22⋊C4—2361no—
281C22⋊C4—2361no—
282C22⋊C4—2361no—
283C22⋊C4—2361no—
284C42—1181no—
285C42—1181no—
286C42—1181no—
287C42—1181no—
288C42—2362no—
289C23—21no—
290C23—21no—
291C23—41no—
292C23—41no—
293C23C22⋊C4×D5911yescharacteristic
294C23#1427374811yescharacteristic
295C23#1427375011yescharacteristic
296C2×C4—22no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—591no—
310C2×C4—591no—
311C2×C4—1181no—
312C2×C4—1181no—
313C2×C4—1181no—
314C2×C4—1181no—
315C2×C4—1181no—
316C2×C4—1181no—
317C2×C4—1181no—
318C2×C4—4721no—
319C2×C4—4721no—
320C2×C4—4721no—
321C2×C4—2361no—
322C2×C4—2361no—
323C2×C4—2361no—
324C2×C4—2361no—
325C2×C4—2361no—
326C2×C4—2361no—
327C2×C4—2361no—
328C2×C4—2361no—
329C2×C4—2361no—
330C2×C4—2361no—
331C2×C4—2361no—
332C2×C4—2361no—
333C8—81no—
334C8—4721no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—81no—
344C22#99×D5911yescharacteristic
345C22#1683739711yescharacteristic
346C22#1683741711yescharacteristic
347C4—42no—
348C4—41no—
349C4—41no—
350C4—81no—
351C4—161no—
352C4—1181no—
353C4—1181no—
354C4—9441no—
355C4—4721no—
356C4—4721no—
357C4—2361no—
358C4—2361no—
359C4—2361no—
360C2—21no—
361C2—21no—
362C2—41no—
363C2—41no—
364C2#2142265111yescharacteristic
365C2#2142574811yescharacteristic
366C2#2142575811yescharacteristic
subgroupG/H
centerC22#99×D59
commutatorC22×C4×C59C22×C4
FrattiniC2×C22⋊C4C22×D59
FittingC59×#1352C2
socleC22×C59C2×#99
prime radicalC24×C59C2×D4
cosocleC2×C22⋊C4×C59C23
hypercenter#1352D59
hypocenterC59#11846
LCSG ▷ C22×C4×C59 ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1352

Complements

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

NH ≅ G/Ntype
8. C2×#14273718C4semidirect
11. #16837340C4semidirect
12. #16837334C4semidirect
19. #16837247C4semidirect
210. C59#11846semidirect

Maximal subgroups

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

subgroupindex
#214297872
#214241722
#214224072
#214221202
#214220972
#214220952
C59×#13522
#1184659