Finite Group Databasebeta

← #28497933

Subgroups — #28497933

Order 15104.

392 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 89 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#21432789C211yesmaximal, characteristic
2#21425705C211yesmaximal, characteristic, complemented
3C22⋊C16×D59C211yesmaximal, characteristic, complemented
4#21422038C211yesmaximal, characteristic, complemented
5#21422021C211yesmaximal, characteristic, complemented
6#21422021C211yesmaximal, characteristic, complemented
7C59×#1323C211yesmaximal, characteristic, complemented
8C2×#14273735C411yescharacteristic
9C22×C8×D59C2211yescharacteristic
10#16837914C411yescharacteristic
11C2×#14273666—21no—
12C2×C16×D59—21no—
13#16837472—21no—
14#16837472—21no—
15#16837467—21no—
16#16837467—21no—
17#16837368C2211yescharacteristic
18#16837365C411yescharacteristic
19#16837358C411yescharacteristic
20C22⋊(C59⋊C16)C2211yescharacteristic
21C22⋊(C59⋊C16)C2211yescharacteristic
22(C2×D59)⋊C16—21no—
23(C2×D59)⋊C16—21no—
24C59×#424C2211yescharacteristic
25C59×C22⋊C16C2211yescharacteristic
26C59×C22⋊C16C2211yescharacteristic
27C2×#11745685C2×C411yescharacteristic
28C22×C4×D59C2×C411yescharacteristic
29#14273735—42no—
30C2×#11745664C2×C411yescharacteristic
31C2×#11745659—21no—
32C22×C59⋊C8C2×C411yescharacteristic
33C2×C8×D59—21no—
34C2×C8×D59—42no—
35C2×C8×D59D411yescharacteristic
36C2×C8×D59D411yescharacteristic
37C2×C8×D59D411yescharacteristic
38C2×C8×D59D411yescharacteristic
39#14273711—21no—
40#14273707C811yescharacteristic
41#14273707C811yescharacteristic
42#14273702C811yescharacteristic
43#14273702C811yescharacteristic
44#14273697—21no—
45C4×D236—21no—
46C4×D236—21no—
47#14273666—42no—
48C2×C59⋊C16—21no—
49C2×C59⋊C16—21no—
50C16×D59—42no—
51(C2×D59)⋊C8—21no—
52(C2×D59)⋊C8—21no—
53(C2×D59)⋊C8—21no—
54(C2×D59)⋊C8—21no—
55#14273638—21no—
56C4×C59⋊C8—21no—
57C2×M16×C59C2×C411yescharacteristic
58C22×C8×C59C2311yescharacteristic
59#117×C59C2×C411yescharacteristic
60C2×C16×C59—21no—
61C2×C16×C59—21no—
62C4⋊C8×C59—21no—
63C4⋊C8×C59—21no—
64C23×D59M1611yescharacteristic
65C22×C4×C59C22×C411yescharacteristic
66C2×C22⋊D59—21no—
67C22×Dic59M1611yescharacteristic
68#11745685—41no—
69#11745685—41no—
70C2×D236—21no—
71C2×D236—21no—
72C2×D236C2×C811yescharacteristic
73C2×C4×D59—21no—
74C2×C4×D59—41no—
75C2×C4×D59—41no—
76C2×C4×D59C22⋊C411yescharacteristic
77C2×C4×D59C22⋊C411yescharacteristic
78C2×C4×D59C2×C811yescharacteristic
79C2×C4×D59C2×C811yescharacteristic
80C2×Dic118C2×C811yescharacteristic
81M16×C59—41no—
82C2×C8×C59—21no—
83C2×C8×C59—41no—
84C2×C8×C59C2×D411yescharacteristic
85C2×C8×C59C2×D411yescharacteristic
86C4⋊C4×C59C2×C811yescharacteristic
87C4⋊C4×C59C2×C811yescharacteristic
88C22⋊C4×C59—21no—
89C42×C59—21no—
90(C2×D59)⋊C4—21no—
91(C2×D59)⋊C4—21no—
92(C2×D59)⋊C4—21no—
93(C2×D59)⋊C4—21no—
94C4⋊Dic59—21no—
95C4⋊Dic59—21no—
96#11745664—41no—
97C2×C59⋊C8—22no—
98C2×C59⋊C8—21no—
99C2×C59⋊C8C22⋊C411yescharacteristic
100C2×C59⋊C8C22⋊C411yescharacteristic
101#11745659—42no—
102C8×D59—22no—
103C8×D59—22no—
104C8×D59—41no—
105C8×D59—41no—
106C8×D59—42no—
107C16×C59—41no—
108C16×C59—41no—
109C59⋊C16—41no—
110C59⋊C16—41no—
111C23×C59C2×M1611yescharacteristic
112C22×D59—22no—
113C22×D59—21no—
114C22×D59—41no—
115C22×D59—41no—
116C22×D59C22⋊C811yescharacteristic
117C22×D59C22⋊C811yescharacteristic
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59C2×C22⋊C411yescharacteristic
123C2×C4×C59C22×C811yescharacteristic
124C22⋊D59—42no—
125C2×Dic59—21no—
126C2×Dic59—41no—
127C2×Dic59C22⋊C811yescharacteristic
128C2×Dic59C22⋊C811yescharacteristic
129D236—41no—
130D236—42no—
131D236—42no—
132C4×D59—21no—
133C4×D59—21no—
134C4×D59—21no—
135C4×D59—21no—
136C4×D59—41no—
137C4×D59—41no—
138C4×D59—41no—
139C4×D59—41no—
140Dic118—41no—
141C8×C59—21no—
142C8×C59—21no—
143C8×C59—41no—
144C59⋊C8—21no—
145C59⋊C8—41no—
146C59⋊C8#9912yes—
147#11470—591nomaximal, Sylow
148C22×C59—21no—
149C22×C59—21no—
150C22×C59—21no—
151C22×C59C2×C22⋊C811yescharacteristic
152C2×D59—21no—
153C2×D59—21no—
154C2×D59—21no—
155C2×D59—21no—
156C2×D59—21no—
157C2×D59—44no—
158C2×D59—41no—
159C2×D59—41no—
160C2×D59—41no—
161C2×D59#35012yes—
162C4×C59—21no—
163C4×C59—41no—
164C4×C59—41no—
165C4×C59C2×#9911yescharacteristic
166C4×C59#41311yescharacteristic
167Dic59—21no—
168Dic59—21no—
169Dic59—41no—
170#2929—591no—
171#2112—591no—
172C2×C22⋊C16—591no—
173#1323—591no—
174#1323D5911yescharacteristic, complemented
175#1315—591no—
176#1315—591no—
177C2×C59—41no—
178C2×C59#145911yescharacteristic
179C2×C59C2×#35011yescharacteristic
180C2×C59#211711yescharacteristic
181D59—22no—
182D59—41no—
183D59—81no—
184C2×#131—591no—
185C23×C8—591no—
186#525—591no—
187C2×M32—1181no—
188C22×C16—1181no—
189#435—1181no—
190#435—1181no—
191C8×D4—1181no—
192C8×D4—1181no—
193#424C2×D5911yescharacteristic
194#408—591no—
195#407—591no—
196#405—591no—
197C22⋊C16—591no—
198C22⋊C16—591no—
199C22⋊C16—1181no—
200C22⋊C16—1181no—
201C22⋊C16C2×D5911yescharacteristic
202C22⋊C16C2×D5911yescharacteristic
203C59#1147011yescharacteristic, complemented, Sylow
204C2×#41—591no—
205C23×C4—591no—
206#131—2362no—
207C2×M16—591no—
208C2×M16—1181no—
209C2×M16C4×D5911yescharacteristic
210C22×C8—591no—
211C22×C8—591no—
212C22×C8—591no—
213C22×C8—591no—
214C22×C8—591no—
215C22×C8—1181no—
216C22×C8—2362no—
217C22×C8C22×D5911yescharacteristic
218#123—1181no—
219C22⋊Q8—591no—
220C22⋊Q8—591no—
221#121—591no—
222#121—591no—
223#120—1181no—
224C4×D4—1181no—
225C4×D4—1181no—
226#117C4×D5911yescharacteristic
227M32—2362no—
228C2×C16—21no—
229C2×C16—21no—
230C2×C16—1181no—
231C2×C16—1181no—
232C2×C16—2362no—
233C4⋊C8—21no—
234C4⋊C8—21no—
235C22⋊C8—1181no—
236C22⋊C8—1181no—
237C22⋊C8—1181no—
238C22⋊C8—1181no—
239#97—1181no—
240C4×C8—1181no—
241C24—591no—
242#41—2361no—
243#41—2361no—
244C2×Q8—591no—
245C2×D4—591no—
246C2×D4—1181no—
247C2×D4—1181no—
248C2×D4—1181no—
249C22×C4—591no—
250C22×C4—591no—
251C22×C4—591no—
252C22×C4—591no—
253C22×C4—591no—
254C22×C4—1181no—
255C22×C4—2361no—
256C22×C4—2361no—
257C22×C4C2×C4×D5911yescharacteristic
258M16—41no—
259M16—2362no—
260M16—2361no—
261C2×C8—21no—
262C2×C8—41no—
263C2×C8—591no—
264C2×C8—591no—
265C2×C8—1182no—
266C2×C8—1182no—
267C2×C8—1182no—
268C2×C8—1181no—
269C2×C8—2361no—
270C2×C8—2361no—
271C2×C8—2362no—
272C2×C8D4×D5911yescharacteristic
273C2×C8D4×D5911yescharacteristic
274C4⋊C4—1181no—
275C4⋊C4—1181no—
276C4⋊C4C8×D5911yescharacteristic
277C4⋊C4C8×D5911yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—1181no—
280C22⋊C4—1181no—
281C22⋊C4—1181no—
282C22⋊C4—1181no—
283C42—21no—
284C16—41no—
285C16—41no—
286C16—2361no—
287C16—2361no—
288C23—591no—
289C23—591no—
290C23—1182no—
291C23—1181no—
292C23—2361no—
293C23—2361no—
294C23M16×D5911yescharacteristic
295Q8—2361no—
296D4—2361no—
297D4—2362no—
298D4—2362no—
299D4—2362no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—591no—
305C2×C4—591no—
306C2×C4—1181no—
307C2×C4—1181no—
308C2×C4—1181no—
309C2×C4—1181no—
310C2×C4—1181no—
311C2×C4—2361no—
312C2×C4—2361no—
313C2×C4—2361no—
314C2×C4—2361no—
315C2×C4—2361no—
316C2×C4C22⋊C4×D5911yescharacteristic
317C2×C4C2×C8×D5911yescharacteristic
318C8—21no—
319C8—21no—
320C8—41no—
321C8—592no—
322C8—1181no—
323C8—2361no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—592no—
328C22—1181no—
329C22—1181no—
330C22—1181no—
331C22—1181no—
332C22—1181no—
333C22—2364no—
334C22—2361no—
335C22—2361no—
336C22—2361no—
337C22C22⋊C8×D5911yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—1181no—
342C4—1181no—
343C4—2361no—
344C4#99×D5911yescharacteristic
345C4#1683738511yescharacteristic
346C2—41no—
347C2—1182no—
348C2—4721no—
349C2—2361no—
350C2#2142241311yescharacteristic
351C2#350×D5911yescharacteristic
352C2#2142572211yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D59
commutatorC2×C4×C59C22×C8
FrattiniC22×C8C22×D59
FittingC59×#1323C2
socleC22×C59C2×C22⋊C8
prime radical#16837914C4
cosocleC22×C8×C59C23
hypercenter#1323D59
hypocenterC59#11470
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1323

Complements

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

NH ≅ G/Ntype
2. #21425705C2semidirect
3. C22⋊C16×D59C2semidirect
4. #21422038C2semidirect
5. #21422021C2semidirect
6. #21422021C2semidirect
7. C59×#1323C2semidirect
174. #1323D59semidirect
203. C59#11470semidirect

Maximal subgroups

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

subgroupindex
#214327892
#214257052
C22⋊C16×D592
#214220382
#214220212
C59×#13232
#1147059