Finite Group Databasebeta

← #28505295

Subgroups — #28505295

Order 15104.

490 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837229C211yesmaximal, characteristic, complemented
2C2×#16837203C211yesmaximal, characteristic
3C2×#16837203C211yesmaximal, characteristic
4#21424829C211yesmaximal, characteristic, complemented
5#21422187C211yesmaximal, characteristic, complemented
6#21422174C211yesmaximal, characteristic, complemented
7C2×C4×D8×C59C211yesmaximal, characteristic
8C22×C59⋊C16C2211yescharacteristic
9C22×C59⋊C16C2211yescharacteristic
10C2×#14273661C2211yescharacteristic
11C2×#14273661C2211yescharacteristic
12#16837300—21no—
13#16837229—22no—
14#16837203—22no—
15#16837203C414yescomplemented
16#16837165—21no—
17C22×D8×C59C2211yescharacteristic
18C2×C4×D4×C59—21no—
19C4×D8×C59—22no—
20C4×D8×C59—22no—
21C2×#107×C59C2211yescharacteristic
22C2×#102×C59—21no—
23C2×C4×C8×C59C2211yescharacteristic
24C2×C4⋊Dic59—21no—
25C2×C4⋊Dic59—21no—
26C2×Dic59⋊C4—41no—
27C2×C59⋊C16—21no—
28C2×C59⋊C16—21no—
29C2×C59⋊C16—21no—
30C2×C59⋊C16—21no—
31C2×C59⋊C16—21no—
32C2×C59⋊C16C2×C412yescomplemented
33#14273661—21no—
34#14273661—21no—
35#14273661—21no—
36#14273661C2×C412yescomplemented
37C59⋊#95—41no—
38C22×D4×C59—21no—
39C23×C4×C59—41no—
40C2×D8×C59—21no—
41C2×D8×C59—21no—
42C2×D8×C59—21no—
43C2×D8×C59C2×C412yes—
44C2×D8×C59D412yes—
45C2×D8×C59Q812yes—
46C22×C8×C59D411yescharacteristic
47C22×C8×C59C2311yescharacteristic
48C4×D4×C59—24no—
49C4×D4×C59—42no—
50C2×C4⋊C4×C59—21no—
51C2×C22⋊C4×C59—41no—
52C2×C42×C59D411yescharacteristic
53#107×C59—21no—
54#107×C59D412yes—
55#102×C59—24no—
56C4×C8×C59—21no—
57C4×C8×C59—21no—
58C24×C59—41no—
59C2×D4×C59—22no—
60C2×D4×C59—22no—
61C2×D4×C59—22no—
62C2×D4×C59—41no—
63C2×D4×C59—41no—
64C2×D4×C59—41no—
65C22×C4×C59—44no—
66C22×C4×C59—41no—
67C22×C4×C59—82no—
68C22×C4×C59—82no—
69C22×C4×C59D811yescharacteristic
70C22×C4×C59D811yescharacteristic
71C22×C4×C59C2×D411yescharacteristic
72C22×Dic59—41no—
73C22×Dic59—41no—
74D8×C59—22no—
75D8×C59—22no—
76D8×C59—22no—
77D8×C59C4⋊C414yescomplemented
78C2×C8×C59—21no—
79C2×C8×C59—21no—
80C2×C8×C59—21no—
81C2×C8×C59C22×C411yescharacteristic
82C2×C8×C59C2×D411yescharacteristic
83C2×C8×C59C2×D411yescharacteristic
84C2×C8×C59C2×Q811yescharacteristic
85C2×C8×C59#4111yescharacteristic
86C2×C8×C59#4111yescharacteristic
87C4⋊C4×C59—22no—
88C4⋊C4×C59—41no—
89C22⋊C4×C59—44no—
90C42×C59—21no—
91C42×C59—21no—
92C4⋊Dic59—22no—
93C4⋊Dic59—41no—
94C4⋊Dic59—41no—
95C4⋊Dic59—41no—
96Dic59⋊C4—82no—
97C59⋊C16—22no—
98C59⋊C16—41no—
99C23×C59—42no—
100C23×C59—42no—
101C23×C59—42no—
102C23×C59—81no—
103C23×C59—81no—
104C23×C59—81no—
105C23×C59—81no—
106C23×C59C2×D811yescharacteristic
107D4×C59—24no—
108D4×C59—42no—
109D4×C59—42no—
110D4×C59—42no—
111C2×C4×C59—21no—
112C2×C4×C59—21no—
113C2×C4×C59—21no—
114C2×C4×C59—21no—
115C2×C4×C59—21no—
116C2×C4×C59—42no—
117C2×C4×C59—88no—
118C2×C4×C59—81no—
119C2×C4×C59—81no—
120C2×C4×C59SD3212yes—
121C2×C4×C59C4×D411yescharacteristic
122C2×C4×C59#12011yescharacteristic
123C2×C4×C59C22⋊Q811yescharacteristic
124C2×C4×C59#13511yescharacteristic
125C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C59#13711yescharacteristic
127C2×Dic59—42no—
128C2×Dic59—81no—
129C2×Dic59—81no—
130C2×Dic59—81no—
131C2×Dic59—81no—
132C2×Dic59—81no—
133C8×C59—41no—
134C8×C59C2×C4⋊C411yescharacteristic
135C8×C59C4×D411yescharacteristic
136C8×C59C22⋊Q811yescharacteristic
137C8×C59#12311yescharacteristic
138#12937—591nomaximal, Sylow
139C22×C59—44no—
140C22×C59—82no—
141C22×C59—82no—
142C22×C59—82no—
143C22×C59—82no—
144C22×C59—82no—
145C22×C59—82no—
146C22×C59C4×D811yescharacteristic
147C22×C59#44711yescharacteristic
148C22×C59#47411yescharacteristic
149C22×C59C2×SD3211yescharacteristic
150C22×C59#50811yescharacteristic
151C22×C59#50911yescharacteristic
152C22×C59#50911yescharacteristic
153C4×C59—22no—
154C4×C59—41no—
155C4×C59—82no—
156C4×C59#38511yescharacteristic
157C4×C59#44011yescharacteristic
158C4×C59#45211yescharacteristic
159C4×C59#47811yescharacteristic
160Dic59—82no—
161Dic59—161no—
162C2×C4×D8D5911yescharacteristic
163C2×#367—591no—
164C2×#357—591no—
165C2×#357—591no—
166#1942—591no—
167#1380—591no—
168#1374—591no—
169C2×C59—84no—
170C2×C59#186211yescharacteristic
171C2×C59C4×SD3211yescharacteristic
172C2×C59#217711yescharacteristic
173C2×C59#218611yescharacteristic
174C2×C59#218711yescharacteristic
175C2×C59#222611yescharacteristic
176C2×C59#222811yescharacteristic
177C22×D8C2×D5911yescharacteristic
178C2×C4×D4—21no—
179C22×C16—591no—
180C22×C16—591no—
181C4×D8—22no—
182C4×D8—22no—
183C2×#107—591no—
184C2×#107—591no—
185C2×#107C2×D5911yescharacteristic
186C2×#102—21no—
187C2×C4×C8C2×D5911yescharacteristic
188#389—1181no—
189#367—1182no—
190#357—594no—
191#357—1182no—
192#340—1181no—
193C59#1293711yescharacteristic, complemented, Sylow
194C22×D4—21no—
195C23×C4—41no—
196C2×D8—21no—
197C2×D8—21no—
198C2×D8—21no—
199C2×D8Dic11812yes—
200C2×D8C4×D5912yes—
201C2×D8C22⋊D5912yes—
202C22×C8C22⋊D5911yescharacteristic
203C22×C8C22×D5911yescharacteristic
204C4×D4—24no—
205C4×D4—42no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—1181no—
208C2×C4⋊C4—1181no—
209C2×C4⋊C4—2361no—
210C2×C22⋊C4—41no—
211C2×C42C22⋊D5911yescharacteristic
212C2×C16—592no—
213C2×C16—1181no—
214C2×C16—1181no—
215C2×C16—1181no—
216C2×C16—1181no—
217C2×C16—1181no—
218#107—21no—
219#107—592no—
220#107—1181no—
221#107—1181no—
222#107—1181no—
223#107C22⋊D5912yes—
224#102—24no—
225C4×C8—21no—
226C4×C8—21no—
227#95—2361no—
228C24—41no—
229C2×D4—22no—
230C2×D4—22no—
231C2×D4—22no—
232C2×D4—41no—
233C2×D4—41no—
234C2×D4—41no—
235C22×C4—44no—
236C22×C4—41no—
237C22×C4—82no—
238C22×C4—82no—
239C22×C4—2361no—
240C22×C4—2361no—
241C22×C4#1174566911yescharacteristic
242C22×C4#1174566911yescharacteristic
243C22×C4C2×C22⋊D5911yescharacteristic
244D8—22no—
245D8—22no—
246D8—22no—
247D8Dic59⋊C414yescomplemented
248C2×C8—21no—
249C2×C8—21no—
250C2×C8—21no—
251C2×C8C2×Dic11811yescharacteristic
252C2×C8C2×C4×D5911yescharacteristic
253C2×C8#1174568511yescharacteristic
254C2×C8#1174568511yescharacteristic
255C2×C8C2×C22⋊D5911yescharacteristic
256C2×C8C2×C22⋊D5911yescharacteristic
257C4⋊C4—22no—
258C4⋊C4—41no—
259C4⋊C4—1182no—
260C4⋊C4—4722no—
261C4⋊C4—2361no—
262C4⋊C4—2361no—
263C4⋊C4—2361no—
264C22⋊C4—44no—
265C42—21no—
266C42—21no—
267C16—1182no—
268C16—2361no—
269C23—42no—
270C23—42no—
271C23—42no—
272C23—81no—
273C23—81no—
274C23—81no—
275C23—81no—
276C23C2×#1174566911yescharacteristic
277D4—24no—
278D4—42no—
279D4—42no—
280D4—42no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—42no—
287C2×C4—88no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4—4721no—
291C2×C4—4721no—
292C2×C4—4721no—
293C2×C4—4721no—
294C2×C4—4721no—
295C2×C4—2362no—
296C2×C4#1427367112yes—
297C2×C4C4×C22⋊D5911yescharacteristic
298C2×C4#1427369611yescharacteristic
299C2×C4#1427370611yescharacteristic
300C2×C4#1427374711yescharacteristic
301C2×C4#1427375311yescharacteristic
302C2×C4#1427375711yescharacteristic
303C8—41no—
304C8C2×Dic59⋊C411yescharacteristic
305C8C4×C22⋊D5911yescharacteristic
306C8#1427370611yescharacteristic
307C8#1427371011yescharacteristic
308C22—44no—
309C22—82no—
310C22—82no—
311C22—82no—
312C22—82no—
313C22—82no—
314C22—82no—
315C22C4×#1174566911yescharacteristic
316C22#1683753611yescharacteristic
317C22#1683768211yescharacteristic
318C22C2×#1427367111yescharacteristic
319C22#1683783211yescharacteristic
320C22#1683783711yescharacteristic
321C22#1683783811yescharacteristic
322C4—22no—
323C4—41no—
324C4—82no—
325C4—9441no—
326C4—4722no—
327C4#1683727511yescharacteristic
328C4#1683750211yescharacteristic
329C4#1683756411yescharacteristic
330C4#1683770211yescharacteristic
331C2—84no—
332C2#2142434311yescharacteristic
333C2C4×#1427367111yescharacteristic
334C2#2142597011yescharacteristic
335C2#2142601911yescharacteristic
336C2#2142602511yescharacteristic
337C2#2142624311yescharacteristic
338C2#2142625311yescharacteristic
subgroupG/H
centerC23C2×#11745669
commutatorC2×C8×C59C22×C4
FrattiniC22×C8C22×D59
FittingC2×C4×D8×C59C2
socleC23×C59C2×D8
prime radicalC22×D8×C59C22
cosocleC22×C8×C59C23
hypercenterC2×C4×D8D59
hypocenterC59#12937
LCSG ▷ C2×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#16837229C2semidirect
4. #21424829C2semidirect
5. #21422187C2semidirect
6. #21422174C2semidirect
15. #16837203C4semidirect
32. C2×C59⋊C16C2×C4semidirect
36. #14273661C2×C4semidirect
77. D8×C59C4⋊C4semidirect
193. C59#12937semidirect
247. D8Dic59⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#168372292
C2×#168372032
#214248292
#214221872
#214221742
C2×C4×D8×C592
#1293759