Finite Group Databasebeta

← #28482806

Subgroups — #28482806

Order 15104.

380 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 93 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#21433232C211yesmaximal, characteristic
2#21422879C211yesmaximal, characteristic, complemented
3#21422580C211yesmaximal, characteristic
4#21422507C211yesmaximal, characteristic
5#21421989C211yesmaximal, characteristic, complemented
6#21421946C211yesmaximal, characteristic, complemented
7C59×#1843C211yesmaximal, characteristic, complemented
8#16837936C2211yescharacteristic
9#16837531—21no—
10#16837473—21no—
11#16837472—21no—
12C8×C22⋊D59—21no—
13#16837462—21no—
14#16837459C2211yescharacteristic
15#16837455C2211yescharacteristic
16#16837427—21no—
17C4×#11745664C2211yescharacteristic
18#16837154—21no—
19#16837152—21no—
20#16837138C411yescharacteristic
21#16837138C411yescharacteristic
22#16837135C411yescharacteristic
23#16837135C411yescharacteristic
24#16837132—21no—
25#16837129—21no—
26C2×C4⋊C8×C59—21no—
27C2×C4⋊C8×C59—21no—
28C2×C4⋊C8×C59C2211yescharacteristic
29C2×C4⋊C8×C59C2211yescharacteristic
30C59×#376C2211yescharacteristic
31C2×#11745664—21no—
32C2×#11745659—21no—
33C2×C8×D59—21no—
34#14273721—21no—
35#14273719Q811yescharacteristic
36#14273715Q811yescharacteristic
37#14273710—21no—
38#14273706C2×C411yescharacteristic
39#14273701C2×C411yescharacteristic
40C4×Dic118D411yescharacteristic
41C4×D236D411yescharacteristic
42C4×C22⋊D59—21no—
43#14273684—21no—
44C4⋊(C59⋊C8)—21no—
45C4⋊(C59⋊C8)D411yescharacteristic
46C4⋊(C59⋊C8)D411yescharacteristic
47Dic59⋊C8—21no—
48Dic59⋊C8—21no—
49C22⋊(C59⋊C8)—21no—
50C22⋊(C59⋊C8)C2×C411yescharacteristic
51C22⋊(C59⋊C8)C2×C411yescharacteristic
52(C2×D59)⋊C8—21no—
53(C2×D59)⋊C8—21no—
54#14273638—21no—
55#14273638—21no—
56#14273637—21no—
57C4×C59⋊C8—21no—
58C4×C59⋊C8—21no—
59C8×Dic59—21no—
60C22×C8×C59—21no—
61C22×C8×C59D411yescharacteristic
62C22×C8×C59D411yescharacteristic
63C2×C42×C59—21no—
64C2×C42×C59C2311yescharacteristic
65C4⋊C8×C59—21no—
66C4⋊C8×C59—21no—
67C4⋊C8×C59—21no—
68C4⋊C8×C59—21no—
69C4⋊C8×C59—42no—
70C4⋊C8×C59—42no—
71#95×C59—21no—
72#95×C59C2×C411yescharacteristic
73#95×C59C2×C411yescharacteristic
74C22×C4×C59—21no—
75C22×C4×C59—21no—
76C22×C4×C59C22×C411yescharacteristic
77C22×C4×C59C2×D411yescharacteristic
78C22×C4×C59#4111yescharacteristic
79C2×C22⋊D59—21no—
80C2×D236C4⋊C411yescharacteristic
81C2×C4×D59—21no—
82C2×Dic118C4⋊C411yescharacteristic
83C2×C8×C59—21no—
84C2×C8×C59—21no—
85C2×C8×C59—41no—
86C2×C8×C59—41no—
87C2×C8×C59—41no—
88C2×C8×C59—41no—
89C2×C8×C59—41no—
90C42×C59—22no—
91C42×C59—22no—
92C42×C59C2×D411yescharacteristic
93C42×C59C2×D411yescharacteristic
94C42×C59C2×Q811yescharacteristic
95C42×C59#4111yescharacteristic
96C22⋊Dic59—21no—
97(C2×D59)⋊C4—21no—
98(C2×D59)⋊C4—21no—
99(C2×D59)⋊C4—21no—
100(C2×D59)⋊C4—21no—
101C4⋊Dic59C4⋊C411yescharacteristic
102C4⋊Dic59C4⋊C411yescharacteristic
103Dic59⋊C4—21no—
104Dic59⋊C4—21no—
105Dic59⋊C4—21no—
106Dic59⋊C4—21no—
107C4×Dic59—21no—
108#11745664—22no—
109#11745664—41no—
110C2×C59⋊C8—21no—
111C2×C59⋊C8—21no—
112C2×C59⋊C8—21no—
113C2×C59⋊C8—21no—
114C2×C59⋊C8—41no—
115#11745659—81no—
116C8×D59—81no—
117C23×C59C4×D411yescharacteristic
118C22×D59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—22no—
124C2×C4×C59—22no—
125C2×C4×C59—41no—
126C2×C4×C59—41no—
127C2×C4×C59—41no—
128C2×C4×C59—41no—
129C2×C4×C59—41no—
130C2×C4×C59C2×C4⋊C411yescharacteristic
131C2×C4×C59C4×D411yescharacteristic
132C2×C4×C59#12011yescharacteristic
133C2×C4×C59C22⋊Q811yescharacteristic
134C2×C4×C59C22⋊Q811yescharacteristic
135C2×C4×C59#12311yescharacteristic
136C22⋊D59—41no—
137C22⋊D59—41no—
138C2×Dic59—21no—
139C2×Dic59—21no—
140C2×Dic59—21no—
141D236—41no—
142C4×D59—41no—
143C4×D59—41no—
144Dic118—41no—
145C8×C59—41no—
146C8×C59—41no—
147C8×C59—81no—
148C59⋊C8—41no—
149C59⋊C8—41no—
150C59⋊C8—42no—
151C59⋊C8—41no—
152C59⋊C8—41no—
153#8876—591nomaximal, Sylow
154C22×C59—21no—
155C22×C59—21no—
156C22×C59#38511yescharacteristic
157C22×C59#44311yescharacteristic
158C22×C59#44411yescharacteristic
159C2×D59—41no—
160C2×D59—41no—
161C2×D59—41no—
162C4×C59—21no—
163C4×C59—21no—
164C4×C59—21no—
165C4×C59—21no—
166C4×C59—21no—
167C4×C59—42no—
168C4×C59—42no—
169C4×C59#45311yescharacteristic
170C4×C59#45611yescharacteristic
171Dic59—41no—
172Dic59—41no—
173Dic59—41no—
174#2992—591no—
175#1843D5911yescharacteristic, complemented
176#1573—591no—
177#1500—591no—
178#1483—591no—
179#1300—591no—
180#1283—591no—
181C2×C59—21no—
182C2×C59—21no—
183C2×C59#185911yescharacteristic
184C2×C59#186611yescharacteristic
185C2×C59#186811yescharacteristic
186D59—81no—
187#529—591no—
188#446—1181no—
189#435—1181no—
190#435—1181no—
191C8×D4—1181no—
192#433—1181no—
193#432—591no—
194#431—591no—
195#424—1181no—
196C2×C4⋊C8—21no—
197C2×C4⋊C8—21no—
198C2×C4⋊C8C2×D5911yescharacteristic
199C2×C4⋊C8C2×D5911yescharacteristic
200C4×M16—591no—
201#376C2×D5911yescharacteristic
202#335—1181no—
203#334—1181no—
204#328—591no—
205#328—591no—
206#327—591no—
207#327—591no—
208Q8⋊C8—1181no—
209D4⋊C8—1181no—
210C59#887611yescharacteristic, complemented, Sylow
211C2×M16—1181no—
212C2×M16—1181no—
213C22×C8—21no—
214C22×C8—1181no—
215C22×C8C22⋊D5911yescharacteristic
216C22×C8C22⋊D5911yescharacteristic
217#126—1181no—
218#125—591no—
219#124—591no—
220#123—1181no—
221C22⋊Q8—591no—
222#121—591no—
223C4×Q8—591no—
224C4×D4—591no—
225C4×D4—1181no—
226#117—1181no—
227C2×C42—21no—
228C2×C42C22×D5911yescharacteristic
229C4⋊C8—21no—
230C4⋊C8—21no—
231C4⋊C8—21no—
232C4⋊C8—21no—
233C4⋊C8—42no—
234C4⋊C8—42no—
235C4⋊C8—591no—
236C4⋊C8—591no—
237C4⋊C8—1181no—
238C4⋊C8—1181no—
239C4⋊C8—1181no—
240C22⋊C8—591no—
241C22⋊C8—591no—
242C22⋊C8—1181no—
243C22⋊C8—1181no—
244C22⋊C8—1181no—
245#97—1181no—
246#97—1181no—
247#97—1181no—
248C4×C8—1181no—
249C4×C8—1181no—
250C4×C8—1181no—
251#95—21no—
252#95C4×D5911yescharacteristic
253#95C4×D5911yescharacteristic
254C2×Q8—591no—
255C2×D4—591no—
256C2×D4—1181no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—1181no—
260C22×C4C2×C4×D5911yescharacteristic
261C22×C4#1174568511yescharacteristic
262C22×C4C2×C22⋊D5911yescharacteristic
263M16—1182no—
264M16—4721no—
265M16—2361no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8—1181no—
274C2×C8—1181no—
275C2×C8—1181no—
276C2×C8—1181no—
277C2×C8—4721no—
278C2×C8—2361no—
279C4⋊C4—591no—
280C4⋊C4—591no—
281C4⋊C4—1181no—
282C4⋊C4—1181no—
283C4⋊C4—1181no—
284C4⋊C4—1181no—
285C22⋊C4—1181no—
286C22⋊C4—1181no—
287C22⋊C4—1181no—
288C22⋊C4—1181no—
289C22⋊C4—1181no—
290C42—22no—
291C42—22no—
292C42—1181no—
293C42D4×D5911yescharacteristic
294C42D4×D5911yescharacteristic
295C42Q8×D5911yescharacteristic
296C42#1174568911yescharacteristic
297C23—1181no—
298C23C4×C22⋊D5911yescharacteristic
299Q8—2361no—
300D4—2361no—
301D4—2361no—
302D4—2361no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—1181no—
315C2×C4—1181no—
316C2×C4—1181no—
317C2×C4—2361no—
318C2×C4—2361no—
319C2×C4C4⋊C4×D5911yescharacteristic
320C2×C4#1427368911yescharacteristic
321C2×C4#1427369511yescharacteristic
322C2×C4#1427370311yescharacteristic
323C2×C4#1427370511yescharacteristic
324C2×C4#1427371211yescharacteristic
325C8—41no—
326C8—41no—
327C8—81no—
328C8—2361no—
329C8—2361no—
330C8—2362no—
331C8—2361no—
332C8—2361no—
333C22—21no—
334C22—21no—
335C22—2361no—
336C22—2361no—
337C22—2361no—
338C22#1683727311yescharacteristic
339C22#1683751711yescharacteristic
340C22#1683752211yescharacteristic
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—42no—
347C4—42no—
348C4—2361no—
349C4—2361no—
350C4—2361no—
351C4#1683756911yescharacteristic
352C4#1683758411yescharacteristic
353C2—21no—
354C2—21no—
355C2—4721no—
356C2#2142432111yescharacteristic
357C2#2142437011yescharacteristic
358C2#2142438011yescharacteristic
subgroupG/H
centerC2×C4#14273695
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#1843C2
socleC22×C59#385
prime radical#14273701C2×C4
cosocleC2×C42×C59C23
hypercenter#1843D59
hypocenterC59#8876
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1843

Complements

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

NH ≅ G/Ntype
2. #21422879C2semidirect
5. #21421989C2semidirect
6. #21421946C2semidirect
7. C59×#1843C2semidirect
175. #1843D59semidirect
210. C59#8876semidirect

Maximal subgroups

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

subgroupindex
#214332322
#214228792
#214225802
#214225072
#214219892
#214219462
C59×#18432
#887659