Finite Group Databasebeta

← #28493192

Subgroups — #28493192

Order 15104.

374 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 97 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#21432368C211yesmaximal, characteristic
2#21424264C211yesmaximal, characteristic
3#21424230C211yesmaximal, characteristic
4#21424229C211yesmaximal, characteristic
5#21421978C211yesmaximal, characteristic
6#21421978C211yesmaximal, characteristic
7C59×#1295C211yesmaximal, characteristic
8C2×#14273661—21no—
9C2×#14273659—21no—
10C2×#14273638C2211yescharacteristic
11#16837344—21no—
12#16837344—21no—
13#16837341—21no—
14#16837323—21no—
15#16837323—21no—
16#16837322—21no—
17#16837272C2211yescharacteristic
18#16837268C2211yescharacteristic
19#16837268C2211yescharacteristic
20#16837165—21no—
21#16837165—21no—
22#16837164—21no—
23#16837164—21no—
24C2×#97×C59C2211yescharacteristic
25C2×#97×C59C2211yescharacteristic
26C59×#382C2211yescharacteristic
27C22×Dic118—21no—
28C22×C59⋊C8—21no—
29C2×C4⋊Dic59—21no—
30C2×C4⋊Dic59—21no—
31C2×C4⋊Dic59—21no—
32C2×C4⋊Dic59—21no—
33C2×C4⋊Dic59D411yescharacteristic
34C2×C4⋊Dic59D411yescharacteristic
35C2×C4⋊Dic59D411yescharacteristic
36C2×C4⋊Dic59D411yescharacteristic
37C2×Dic59⋊C4—21no—
38C2×Dic59⋊C4—21no—
39#14273661—42no—
40#14273659—42no—
41#14273638—21no—
42#14273638Q812yescomplemented
43C59⋊#95—21no—
44C59⋊#95—21no—
45C59⋊#95—21no—
46C59⋊#95—21no—
47C59⋊#95—21no—
48C59⋊#95—21no—
49C59⋊#95—21no—
50C59⋊#95—21no—
51C22×C8×C59—21no—
52C22×C8×C59—21no—
53C2×C4⋊C4×C59D411yescharacteristic
54C2×C4⋊C4×C59D411yescharacteristic
55C2×C42×C59C2311yescharacteristic
56#97×C59—21no—
57#97×C59—21no—
58#97×C59Q812yescomplemented
59#97×C59Q812yescomplemented
60#95×C59—21no—
61#95×C59—21no—
62C22×C4×C59—21no—
63C22×C4×C59—21no—
64C22×C4×C59C2×D411yescharacteristic
65C22×C4×C59C2×D411yescharacteristic
66C22×C4×C59C2×D411yescharacteristic
67C22×Dic59—21no—
68C22×Dic59—21no—
69C22×Dic59—21no—
70C22×Dic59—21no—
71C22×Dic59—41no—
72C2×Dic118—81no—
73C2×Dic118—81no—
74C2×Dic118—81no—
75C2×C8×C59—22no—
76C2×C8×C59—22no—
77C2×C8×C59—22no—
78C2×C8×C59—22no—
79C2×C8×C59—41no—
80C2×C8×C59—41no—
81C4⋊C4×C59—41no—
82C4⋊C4×C59—41no—
83C42×C59C2×Q811yescharacteristic
84C42×C59C2×Q811yescharacteristic
85C42×C59C2×Q811yescharacteristic
86C42×C59#4111yescharacteristic
87C4⋊Dic59—41no—
88C4⋊Dic59—41no—
89C4⋊Dic59—41no—
90C4⋊Dic59—41no—
91C4⋊Dic59—41no—
92C4⋊Dic59—41no—
93C4⋊Dic59—42no—
94C4⋊Dic59—42no—
95C4⋊Dic59—81no—
96Dic59⋊C4—81no—
97Dic59⋊C4—81no—
98C2×C59⋊C8—22no—
99C2×C59⋊C8—41no—
100C2×C59⋊C8—41no—
101C23×C59#12011yescharacteristic
102C2×C4×C59—21no—
103C2×C4×C59—21no—
104C2×C4×C59—21no—
105C2×C4×C59—21no—
106C2×C4×C59—21no—
107C2×C4×C59—21no—
108C2×C4×C59—41no—
109C2×C4×C59—41no—
110C2×C4×C59—41no—
111C2×C4×C59—41no—
112C2×C4×C59—41no—
113C2×C4×C59—41no—
114C2×C4×C59C22⋊Q811yescharacteristic
115C2×C4×C59C22⋊Q811yescharacteristic
116C2×C4×C59C22⋊Q811yescharacteristic
117C2×C4×C59C4⋊Q811yescharacteristic
118C2×C4×C59C4⋊Q811yescharacteristic
119C2×C4×C59C4⋊Q811yescharacteristic
120C2×Dic59—41no—
121C2×Dic59—41no—
122C2×Dic59—41no—
123C2×Dic59—41no—
124C2×Dic59—41no—
125C2×Dic59—41no—
126C2×Dic59—41no—
127C2×Dic59—41no—
128C2×Dic59—41no—
129C2×Dic59—41no—
130C2×Dic59—41no—
131C2×Dic59—41no—
132C2×Dic59—81no—
133C2×Dic59—81no—
134C2×Dic59—81no—
135Dic118—84no—
136C8×C59—24no—
137C8×C59—42no—
138C59⋊C8—42no—
139#10584—591nomaximal, Sylow
140C22×C59#39511yescharacteristic
141C22×C59#45311yescharacteristic
142C22×C59#45411yescharacteristic
143C22×C59#45411yescharacteristic
144C22×C59#45511yescharacteristic
145C22×C59#45511yescharacteristic
146C22×C59#45611yescharacteristic
147C4×C59—21no—
148C4×C59—21no—
149C4×C59—21no—
150C4×C59—21no—
151C4×C59—21no—
152C4×C59—21no—
153C4×C59—81no—
154C4×C59—81no—
155Dic59—81no—
156Dic59—81no—
157Dic59—81no—
158Dic59—81no—
159Dic59—161no—
160#2844—591no—
161#1847—591no—
162#1836—591no—
163#1836—591no—
164#1295—591no—
165#1295—591no—
166#1295D5911yescharacteristic
167C2×C59#165711yescharacteristic
168C2×C59#165911yescharacteristic
169C2×C59#166411yescharacteristic
170C2×C59#166411yescharacteristic
171C2×C59#206011yescharacteristic
172C2×C59#206111yescharacteristic
173C2×C59#206111yescharacteristic
174C2×#107—1181no—
175C2×#106—1181no—
176C2×#97—591no—
177C2×#97C2×D5911yescharacteristic
178C2×#97C2×D5911yescharacteristic
179#400—1181no—
180#400—1181no—
181#400—1181no—
182#395—1181no—
183#395—1181no—
184#395—1181no—
185#384—591no—
186#382—591no—
187#382—591no—
188#382C2×D5911yescharacteristic
189#340—1181no—
190#340—1181no—
191#340—1181no—
192#340—1181no—
193C59#1058411yescharacteristic, complemented, Sylow
194C22×Q8—1181no—
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—1181no—
198C2×C4⋊C4—591no—
199C2×C4⋊C4—591no—
200C2×C4⋊C4—591no—
201C2×C4⋊C4—591no—
202C2×C4⋊C4—1181no—
203C2×C4⋊C4—1181no—
204C2×C4⋊C4—1181no—
205C2×C4⋊C4—1181no—
206C2×C4⋊C4—1181no—
207C2×C4⋊C4—1181no—
208C2×C4⋊C4D23611yescharacteristic
209C2×C4⋊C4D23611yescharacteristic
210C2×C42C22×D5911yescharacteristic
211#107—2362no—
212#106—2362no—
213#97—21no—
214#97—21no—
215#97—592no—
216#97—1181no—
217#97Dic11812yescomplemented
218#97Dic11812yescomplemented
219#95—21no—
220#95—21no—
221#95—1181no—
222#95—1181no—
223#95—1181no—
224#95—1181no—
225#95—1181no—
226#95—1181no—
227#95—1181no—
228#95—1181no—
229C2×Q8—4721no—
230C2×Q8—4721no—
231C2×Q8—4721no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—1181no—
235C22×C4—1181no—
236C22×C4—1181no—
237C22×C4—1181no—
238C22×C4—2361no—
239C22×C4C2×D23611yescharacteristic
240C22×C4D4×D5911yescharacteristic
241C22×C4D4×D5911yescharacteristic
242C2×C8—22no—
243C2×C8—22no—
244C2×C8—22no—
245C2×C8—22no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—1182no—
249C2×C8—2361no—
250C2×C8—2361no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—4721no—
254C4⋊C4—4721no—
255C4⋊C4—4721no—
256C4⋊C4—2361no—
257C4⋊C4—2361no—
258C4⋊C4—2362no—
259C4⋊C4—2362no—
260C4⋊C4—2361no—
261C4⋊C4—2361no—
262C4⋊C4—2361no—
263C4⋊C4—2361no—
264C42C2×Dic11811yescharacteristic
265C42C2×Dic11811yescharacteristic
266C42#1174568711yescharacteristic
267C42Q8×D5911yescharacteristic
268C23#1427369711yescharacteristic
269Q8—4724no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—4721no—
283C2×C4—4721no—
284C2×C4—4721no—
285C2×C4—2361no—
286C2×C4—2361no—
287C2×C4—2361no—
288C2×C4—2361no—
289C2×C4—2361no—
290C2×C4—2361no—
291C2×C4—2361no—
292C2×C4—2361no—
293C2×C4—2361no—
294C2×C4—2361no—
295C2×C4—2361no—
296C2×C4—2361no—
297C2×C4#1427370411yescharacteristic
298C2×C4#1427370411yescharacteristic
299C2×C4#1427370711yescharacteristic
300C2×C4#1427372611yescharacteristic
301C2×C4#1427372611yescharacteristic
302C2×C4#1427372711yescharacteristic
303C8—24no—
304C8—42no—
305C8—2362no—
306C22#1683732311yescharacteristic
307C22#1683757111yescharacteristic
308C22#1683757611yescharacteristic
309C22#1683757711yescharacteristic
310C22#1683758111yescharacteristic
311C22#1683758211yescharacteristic
312C22#1683758611yescharacteristic
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—81no—
320C4—81no—
321C4—9441no—
322C4—4721no—
323C4—4721no—
324C4—4721no—
325C4—4721no—
326C2#2142339611yescharacteristic
327C2#2142340411yescharacteristic
328C2#2142343111yescharacteristic
329C2#2142343311yescharacteristic
330C2#2142544011yescharacteristic
331C2#2142544511yescharacteristic
332C2#2142544711yescharacteristic
subgroupG/H
centerC23#14273697
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1295C2
socle, prime radicalC23×C59#120
hypercenter#1295D59
hypocenterC59#10584
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
42. #14273638Q8semidirect
58. #97×C59Q8semidirect
59. #97×C59Q8semidirect
193. C59#10584semidirect
217. #97Dic118semidirect
218. #97Dic118semidirect

Maximal subgroups

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

subgroupindex
#214323682
#214242642
#214242302
#214242292
#214219782
C59×#12952
#1058459