Finite Group Databasebeta

← #28488488

Subgroups — #28488488

Order 15104.

578 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837748C211yesmaximal, characteristic
2#21425057C211yesmaximal, characteristic, complemented
3#21424903C211yesmaximal, characteristic
4#21424897C211yesmaximal, characteristic, complemented
5#21424255C211yesmaximal, characteristic, complemented
6C2×#16837124C211yesmaximal, characteristic, complemented
7C59×#1957C211yesmaximal, characteristic
8C2×#14273727C2211yescharacteristic
9#16837748—22no—
10#16837748C414yescomplemented
11C2×#14273660—22no—
12C2×#14273650—22no—
13C2×#14273648—22no—
14C2×#14273648—22no—
15C2×C4×C59⋊C8C2211yescharacteristic
16C2×C4×C59⋊C8C2211yescharacteristic
17#16837272C2211yescharacteristic
18#16837165—22no—
19#16837124—22no—
20C2×#127×C59C2211yescharacteristic
21C2×#102×C59—22no—
22C2×C4×C8×C59C2211yescharacteristic
23C59×#384C2211yescharacteristic
24C22×Dic118—21no—
25C22×C59⋊C8D412yes—
26C22×C59⋊C8D412yes—
27#14273727—21no—
28#14273727—21no—
29#14273727—21no—
30#14273727C2×C412yes—
31C2×C4⋊Dic59—21no—
32C2×C4⋊Dic59—21no—
33C2×C4⋊Dic59—21no—
34C2×C4⋊Dic59—21no—
35C2×C4⋊Dic59—21no—
36#14273660—44no—
37#14273650—44no—
38#14273648—28no—
39#14273648—44no—
40C4×C59⋊C8—21no—
41C4×C59⋊C8—21no—
42C4×C59⋊C8C2×C412yes—
43C4×C59⋊C8D412yes—
44C22×D4×C59—21no—
45C22×D4×C59—21no—
46C22×D4×C59—21no—
47C22×C8×C59D412yes—
48#127×C59—21no—
49#127×C59—21no—
50#127×C59—21no—
51#127×C59C2×C412yes—
52C2×C4⋊C4×C59—21no—
53C2×C4⋊C4×C59—21no—
54C2×C4⋊C4×C59—21no—
55C2×C42×C59C2311yescharacteristic
56#102×C59—44no—
57C4×C8×C59—21no—
58C4×C8×C59—21no—
59C24×C59—41no—
60C2×D4×C59—22no—
61C2×D4×C59—22no—
62C2×D4×C59—22no—
63C2×D4×C59—41no—
64C2×D4×C59—41no—
65C2×D4×C59—41no—
66C2×D4×C59—42no—
67C2×D4×C59—42no—
68C2×D4×C59—42no—
69C2×D4×C59—42no—
70C2×D4×C59—42no—
71C2×D4×C59—42no—
72C22×C4×C59—41no—
73C22×C4×C59C2×D411yescharacteristic
74C22×C4×C59C2×D411yescharacteristic
75C22×C4×C59C2×D411yescharacteristic
76C22×Dic59—41no—
77C22×Dic59—41no—
78C2×Dic118—22no—
79C2×Dic118—42no—
80C2×Dic118—42no—
81C2×Dic118—41no—
82C2×C8×C59—22no—
83C2×C8×C59—22no—
84C2×C8×C59—22no—
85C4⋊C4×C59—42no—
86C4⋊C4×C59—42no—
87C4⋊C4×C59—42no—
88C42×C59C22×C411yescharacteristic
89C42×C59C2×D411yescharacteristic
90C42×C59#4111yescharacteristic
91C42×C59#4111yescharacteristic
92C4⋊Dic59—22no—
93C4⋊Dic59—22no—
94C4⋊Dic59—41no—
95C4⋊Dic59—41no—
96C4⋊Dic59—42no—
97C4⋊Dic59—42no—
98C4⋊Dic59—42no—
99C2×C59⋊C8—22no—
100C2×C59⋊C8—22no—
101C2×C59⋊C8—22no—
102C2×C59⋊C8—22no—
103C2×C59⋊C8C22⋊C414yes—
104C2×C59⋊C8D814yes—
105C23×C59—42no—
106C23×C59—81no—
107C23×C59—81no—
108C23×C59—81no—
109C23×C59—81no—
110C23×C59—81no—
111C23×C59—81no—
112C23×C59#12711yescharacteristic
113D4×C59—44no—
114D4×C59—44no—
115D4×C59—44no—
116D4×C59—82no—
117D4×C59—82no—
118D4×C59—82no—
119C2×C4×C59—81no—
120C2×C4×C59—81no—
121C2×C4×C59—81no—
122C2×C4×C59C2×C22⋊C411yescharacteristic
123C2×C4×C59C4×D411yescharacteristic
124C2×C4×C59C4×D411yescharacteristic
125C2×C4×C59#12111yescharacteristic
126C2×C4×C59#12111yescharacteristic
127C2×C4×C59#12411yescharacteristic
128C2×C4×C59C2×D812yes—
129C2×C4×C59#13512yes—
130C2×C4×C59AGL(1,ℤ/8)12yes—
131C2×C4×C59AGL(1,ℤ/8)12yes—
132C2×C4×C59#13712yes—
133C2×C4×C59#13712yes—
134C2×Dic59—42no—
135C2×Dic59—81no—
136C2×Dic59—81no—
137C2×Dic59—81no—
138C2×Dic59—81no—
139C2×Dic59—81no—
140Dic118—44no—
141Dic118—82no—
142C8×C59—42no—
143C59⋊C8—24no—
144C59⋊C8—24no—
145#9830—591nomaximal, Sylow
146C22×C59—82no—
147C22×C59—82no—
148C22×C59—82no—
149C22×C59—161no—
150C22×C59—161no—
151C22×C59—161no—
152C22×C59—161no—
153C22×C59#39011yescharacteristic
154C22×C59#49311yescharacteristic
155C22×C59#49511yescharacteristic
156C22×C59#49611yescharacteristic
157C22×C59#49611yescharacteristic
158C22×C59#49711yescharacteristic
159C22×C59#49711yescharacteristic
160C4×C59—161no—
161C4×C59#41712yes—
162C4×C59C4×D812yes—
163C4×C59#44012yes—
164C4×C59#46612yes—
165C4×C59#46812yes—
166C4×C59#48912yes—
167Dic59—82no—
168Dic59—161no—
169C2×#486—591no—
170#1990—591no—
171#1957—591no—
172#1957D5911yescharacteristic
173#1956—591no—
174#1845—591no—
175C2×#322—591no—
176C2×C59—162no—
177C2×C59#171911yescharacteristic
178C2×C59#172011yescharacteristic
179C2×C59#172111yescharacteristic
180C2×C59#172211yescharacteristic
181C2×C59#195911yescharacteristic
182C2×C59#197011yescharacteristic
183C2×C59#197311yescharacteristic
184C2×C4⋊Q8—591no—
185C2×#127C2×D5911yescharacteristic
186#486—594no—
187#486—1182no—
188C2×#107—1182no—
189C2×#103—1182no—
190C2×#102—22no—
191C2×#102—1182no—
192C2×#102—1182no—
193C2×C4×C8—591no—
194C2×C4×C8—591no—
195C2×C4×C8C2×D5911yescharacteristic
196#384—591no—
197#384C2×D5911yescharacteristic
198#340—1182no—
199#322—1182no—
200C59#983011yescharacteristic, complemented, Sylow
201C22×Q8—1181no—
202C22×D4—21no—
203C22×D4—21no—
204C22×D4—21no—
205C22×C8—592no—
206C22×C8—592no—
207C22×C8C22⋊D5912yes—
208C4⋊Q8—592no—
209C4⋊Q8—1181no—
210C4⋊Q8—1181no—
211C4⋊Q8—1181no—
212#127—21no—
213#127—21no—
214#127—21no—
215#127C4×D5912yes—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—1181no—
220C2×C4⋊C4—1181no—
221C2×C4⋊C4—1181no—
222C2×C4⋊C4—1181no—
223C2×C4⋊C4—1181no—
224C2×C42C22×D5911yescharacteristic
225#107—2364no—
226#103—2364no—
227#102—44no—
228#102—1188no—
229#102—2364no—
230C4×C8—21no—
231C4×C8—21no—
232C4×C8—592no—
233C4×C8—592no—
234C4×C8—1181no—
235C4×C8—1181no—
236C24—41no—
237C2×Q8—1182no—
238C2×Q8—2362no—
239C2×Q8—2362no—
240C2×Q8—2361no—
241C2×D4—22no—
242C2×D4—22no—
243C2×D4—22no—
244C2×D4—41no—
245C2×D4—41no—
246C2×D4—41no—
247C2×D4—42no—
248C2×D4—42no—
249C2×D4—42no—
250C2×D4—42no—
251C2×D4—42no—
252C2×D4—42no—
253C22×C4—41no—
254C22×C4—2361no—
255C22×C4—2361no—
256C22×C4D4×D5911yescharacteristic
257C22×C4D4×D5911yescharacteristic
258C22×C4C2×C22⋊D5911yescharacteristic
259C2×C8—22no—
260C2×C8—22no—
261C2×C8—22no—
262C2×C8—594no—
263C2×C8—594no—
264C2×C8—1182no—
265C2×C8—1182no—
266C2×C8—1182no—
267C2×C8—1182no—
268C4⋊C4—42no—
269C4⋊C4—42no—
270C4⋊C4—42no—
271C4⋊C4—1182no—
272C4⋊C4—1182no—
273C4⋊C4—2362no—
274C4⋊C4—2362no—
275C4⋊C4—2362no—
276C4⋊C4—2361no—
277C4⋊C4—2361no—
278C42C2×C4×D5911yescharacteristic
279C42#1174568511yescharacteristic
280C42D4×D5911yescharacteristic
281C42#1174568711yescharacteristic
282C23—42no—
283C23—81no—
284C23—81no—
285C23—81no—
286C23—81no—
287C23—81no—
288C23—81no—
289C23#1427372311yescharacteristic
290Q8—4722no—
291Q8—2364no—
292D4—44no—
293D4—44no—
294D4—44no—
295D4—82no—
296D4—82no—
297D4—82no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—4721no—
302C2×C4—4721no—
303C2×C4—4721no—
304C2×C4—4721no—
305C2×C4—4721no—
306C2×C4—2362no—
307C2×C4C22⋊C4×D5911yescharacteristic
308C2×C4(C22⋊D59)⋊C411yescharacteristic
309C2×C4C4×C22⋊D5911yescharacteristic
310C2×C4#1427369911yescharacteristic
311C2×C4#1427370011yescharacteristic
312C2×C4#1427371311yescharacteristic
313C2×C4D8×D5912yes—
314C2×C4#1427374812yes—
315C2×C4#1427375112yes—
316C2×C4#1427375312yes—
317C2×C4#1427375612yes—
318C2×C4#1427375712yes—
319C8—42no—
320C8—1184no—
321C8—1184no—
322C22—82no—
323C22—82no—
324C22—82no—
325C22—161no—
326C22—161no—
327C22—161no—
328C22—161no—
329C22#1683730211yescharacteristic
330C22#1683777711yescharacteristic
331C22#1683778311yescharacteristic
332C22#1683778911yescharacteristic
333C22#1683779011yescharacteristic
334C22#1683779311yescharacteristic
335C22#1683779711yescharacteristic
336C4—161no—
337C4—9441no—
338C4—4722no—
339C4#1683740012yes—
340C4#1683748212yes—
341C4#1683750212yes—
342C4#1683763712yes—
343C4#1683764612yes—
344C4#1683776012yes—
345C2—162no—
346C2#2142374711yescharacteristic
347C2#2142375811yescharacteristic
348C2#2142376111yescharacteristic
349C2#2142376911yescharacteristic
350C2#2142491111yescharacteristic
351C2#2142495911yescharacteristic
352C2#2142497611yescharacteristic
subgroupG/H
centerC23#14273723
commutatorC42×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#1957C2
socleC23×C59#127
prime radicalC2×#127×C59C22
cosocleC2×C42×C59C23
hypercenter#1957D59
hypocenterC59#9830
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1957

Complements

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

NH ≅ G/Ntype
2. #21425057C2semidirect
4. #21424897C2semidirect
5. #21424255C2semidirect
6. C2×#16837124C2semidirect
10. #16837748C4semidirect
200. C59#9830semidirect

Maximal subgroups

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

subgroupindex
C2×#168377482
#214250572
#214249032
#214248972
#214242552
C2×#168371242
C59×#19572
#983059