Finite Group Databasebeta

← #28487663

Subgroups — #28487663

Order 15104.

720 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14273724C211yesmaximal, characteristic
2C4×C4⋊(C59⋊C8)C211yesmaximal, characteristic, complemented
3C2×#16837129C214yesmaximal, complemented
4C59×#1767C211yesmaximal, characteristic, complemented
5C2×#14273724C411yescharacteristic
6C2×C4×D236—21no—
7C2×C4×D236—21no—
8C2×C4×D236C2212yes—
9C2×C4⋊(C59⋊C8)—21no—
10C2×C4×C59⋊C8C2212yes—
11#16837304—21no—
12#16837304—21no—
13#16837304C412yes—
14#16837272C411yescharacteristic
15#16837157—21no—
16#16837129—28no—
17C2×C4⋊C8×C59C2212yes—
18C2×#97×C59—21no—
19C43×C59C2211yescharacteristic
20C59×#336—21no—
21C22×D236—21no—
22C22×D236—21no—
23C22×D236C2×C412yes—
24C22×C4×D59—22no—
25C22×C59⋊C8—22no—
26#14273724—24no—
27C4×D236—24no—
28C4×D236—24no—
29C4×D236—44no—
30C4×D236—42no—
31C4×D236—42no—
32C2×C4⋊Dic59—21no—
33C2×C4⋊Dic59—21no—
34C2×C4⋊Dic59C2×C412yes—
35C2×(C2×D59)⋊C4—22no—
36C2×(C2×D59)⋊C4—22no—
37C2×(C2×D59)⋊C4—22no—
38C4⋊(C59⋊C8)—24no—
39C4×C59⋊C8—24no—
40C22×C8×C59—22no—
41C2×C42×C59C2×C411yescharacteristic
42C2×C42×C59C2×C411yescharacteristic
43C2×C42×C59D411yescharacteristic
44C2×C42×C59D411yescharacteristic
45C2×C42×C59D411yescharacteristic
46C2×C42×C59D411yescharacteristic
47C2×C42×C59C2311yescharacteristic
48C4⋊C8×C59—22no—
49C4⋊C8×C59D414yescomplemented
50#97×C59—42no—
51C23×D59—22no—
52C22×C4×C59C22⋊C411yescharacteristic
53C22×C4×C59C22⋊C411yescharacteristic
54C22×C4×C59C22⋊C411yescharacteristic
55C22×C4×C59C22⋊C411yescharacteristic
56C22×C4×C59C22×C411yescharacteristic
57C22×C4×C59C2×D411yescharacteristic
58C22×C4×C59C2×D411yescharacteristic
59C22×Dic59—22no—
60C2×D236—24no—
61C2×D236—24no—
62C2×D236—24no—
63C2×D236—24no—
64C2×D236—22no—
65C2×D236—42no—
66C2×D236—42no—
67C2×D236—42no—
68C2×D236—42no—
69C2×D236M1614yes—
70C2×C4×D59—44no—
71C2×C4×D59—42no—
72C2×C4×D59—42no—
73C2×C4×D59—44no—
74C2×C8×C59—24no—
75C2×C8×C59—42no—
76C2×C8×C59—42no—
77C42×C59—22no—
78C42×C59—22no—
79C42×C59—22no—
80C42×C59—22no—
81C42×C59—41no—
82C42×C59D812yes—
83C42×C59SD1612yes—
84C42×C59C2×D412yes—
85C42×C59#4112yes—
86(C2×D59)⋊C4—44no—
87(C2×D59)⋊C4—44no—
88(C2×D59)⋊C4—42no—
89(C2×D59)⋊C4—42no—
90C4⋊Dic59—24no—
91C4⋊Dic59—42no—
92C4⋊Dic59—42no—
93C2×C59⋊C8—24no—
94C2×C59⋊C8—42no—
95C2×C59⋊C8—42no—
96C23×C59C2×C22⋊C411yescharacteristic
97C22×D59—24no—
98C22×D59—42no—
99C22×D59—42no—
100C22×D59—42no—
101C22×D59—42no—
102C22×D59—42no—
103C22×D59—42no—
104C2×C4×C59—21no—
105C2×C4×C59—21no—
106C2×C4×C59—21no—
107C2×C4×C59—21no—
108C2×C4×C59—21no—
109C2×C4×C59—21no—
110C2×C4×C59—21no—
111C2×C4×C59—21no—
112C2×C4×C59—21no—
113C2×C4×C59—21no—
114C2×C4×C59—21no—
115C2×C4×C59#10212yes—
116C2×C4×C59#10212yes—
117C2×C4×C59#10412yes—
118C2×C4×C59C4×D412yes—
119C2×C4×C59#12112yes—
120C2×C4×C59#12411yescharacteristic
121C2×C4×C59#12711yescharacteristic
122C2×C4×C59C2×M1612yes—
123C2×C4×C59#13112yes—
124C2×C4×C59C2×D811yescharacteristic
125C2×C4×C59C2×SD1611yescharacteristic
126C2×C4×C59AGL(1,ℤ/8)12yes—
127C2×Dic59—42no—
128C2×Dic59—42no—
129C2×Dic59—42no—
130D236—28no—
131D236—48no—
132D236—48no—
133D236—44no—
134C4×D59—84no—
135C4×D59—84no—
136C8×C59—44no—
137C59⋊C8—44no—
138#9678—591nomaximal, Sylow
139C22×C59#39011yescharacteristic
140C22×C59#40711yescharacteristic
141C22×C59#40811yescharacteristic
142C22×C59C2×#10211yescharacteristic
143C22×C59#41811yescharacteristic
144C22×C59C2×#10411yescharacteristic
145C22×C59#42111yescharacteristic
146C2×D59—44no—
147C2×D59—44no—
148C2×D59—44no—
149C2×D59—82no—
150C2×D59—82no—
151C2×D59—82no—
152C2×D59—82no—
153C4×C59—21no—
154C4×C59—21no—
155C4×C59—22no—
156C4×C59—22no—
157C4×C59—22no—
158C4×C59—41no—
159C4×C59#43514yes—
160C4×C59#45912yes—
161C4×C59#46012yes—
162Dic59—82no—
163C4×#127—591no—
164#1767D5911yescharacteristic, complemented
165C4×C4⋊C8—591no—
166C2×D4⋊C8—594no—
167C2×C59#148611yescharacteristic
168C2×C59#149011yescharacteristic
169C2×C59#149211yescharacteristic
170C2×C59#149611yescharacteristic
171C2×C59#195511yescharacteristic
172C2×C59#198011yescharacteristic
173C2×C59#198211yescharacteristic
174D59—84no—
175C2×#127—591no—
176C2×C4×D4—592no—
177C2×C4×D4—1181no—
178C2×C4×D4—1181no—
179C2×C4⋊C8—1181no—
180C2×C4⋊C8C2×D5912yes—
181C2×#97—21no—
182C2×C4×C8—592no—
183#390—592no—
184#390—1181no—
185#390—1181no—
186#384—591no—
187C43C2×D5911yescharacteristic
188#336—21no—
189#336—1181no—
190D4⋊C8—1188no—
191C59#967811yescharacteristic, complemented, Sylow
192C22×D4—592no—
193C22×D4—1181no—
194C22×D4—1181no—
195C23×C4—1182no—
196C22×C8—22no—
197C22×C8—1182no—
198#127—1184no—
199C4×D4—1184no—
200C4×D4—1184no—
201C4×D4—2364no—
202C4×D4—2362no—
203C4×D4—2362no—
204C2×C4⋊C4—592no—
205C2×C4⋊C4—1181no—
206C2×C4⋊C4—1181no—
207C2×C22⋊C4—1182no—
208C2×C22⋊C4—1182no—
209C2×C22⋊C4—1182no—
210C2×C42C4×D5911yescharacteristic
211C2×C42C4×D5911yescharacteristic
212C2×C42D23611yescharacteristic
213C2×C42D23611yescharacteristic
214C2×C42C22⋊D5911yescharacteristic
215C2×C42C22⋊D5911yescharacteristic
216C2×C42C22×D5911yescharacteristic
217C4⋊C8—22no—
218C4⋊C8—1184no—
219C4⋊C8D23614yescomplemented
220#97—42no—
221C4×C8—1184no—
222C24—1182no—
223C2×D4—594no—
224C2×D4—1184no—
225C2×D4—1184no—
226C2×D4—1184no—
227C2×D4—1182no—
228C2×D4—1184no—
229C2×D4—2362no—
230C2×D4—2362no—
231C2×D4—2362no—
232C2×D4—2362no—
233C22×C4—1182no—
234C22×C4—2364no—
235C22×C4—2362no—
236C22×C4—2362no—
237C22×C4—2364no—
238C22×C4(C2×D59)⋊C411yescharacteristic
239C22×C4(C2×D59)⋊C411yescharacteristic
240C22×C4(C2×D59)⋊C411yescharacteristic
241C22×C4(C2×D59)⋊C411yescharacteristic
242C22×C4C2×C4×D5911yescharacteristic
243C22×C4C2×D23611yescharacteristic
244C22×C4C2×C22⋊D5911yescharacteristic
245C2×C8—24no—
246C2×C8—42no—
247C2×C8—42no—
248C2×C8—1184no—
249C2×C8—2362no—
250C2×C8—2362no—
251C4⋊C4—1184no—
252C4⋊C4—2362no—
253C4⋊C4—2362no—
254C22⋊C4—2364no—
255C22⋊C4—2364no—
256C22⋊C4—2362no—
257C22⋊C4—2362no—
258C42—22no—
259C42—22no—
260C42—22no—
261C42—22no—
262C42—41no—
263C42#1174566912yes—
264C42#1174567112yes—
265C42C2×D23612yes—
266C42#1174568512yes—
267C23—1184no—
268C23—2362no—
269C23—2362no—
270C23—2362no—
271C23—2362no—
272C23—2362no—
273C23—2362no—
274C23C2×(C2×D59)⋊C411yescharacteristic
275D4—1188no—
276D4—2368no—
277D4—2368no—
278D4—2364no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—4724no—
291C2×C4—4724no—
292C2×C4—2362no—
293C2×C4—2362no—
294C2×C4—2362no—
295C2×C4#1427364712yes—
296C2×C4#1427364712yes—
297C2×C4#1427365312yes—
298C2×C4C4×D23612yes—
299C2×C4#1427370112yes—
300C2×C4#1427371511yescharacteristic
301C2×C4#1427372411yescharacteristic
302C2×C4M16×D5912yes—
303C2×C4#1427373512yes—
304C2×C4C2×#1174566911yescharacteristic
305C2×C4C2×#1174567111yescharacteristic
306C2×C4#1427375212yes—
307C8—44no—
308C8—2364no—
309C22—4722no—
310C22—4722no—
311C22—4722no—
312C22—4722no—
313C22—2364no—
314C22—2364no—
315C22—2364no—
316C22#1683730411yescharacteristic
317C22#1683736511yescharacteristic
318C22#1683737011yescharacteristic
319C22C2×#1427364711yescharacteristic
320C22#1683740611yescharacteristic
321C22C2×#1427365311yescharacteristic
322C22#1683741811yescharacteristic
323C4—21no—
324C4—21no—
325C4—22no—
326C4—22no—
327C4—22no—
328C4—41no—
329C4—4722no—
330C4#1683747514yes—
331C4#1683759712yes—
332C4#1683760212yes—
333C2—4724no—
334C2#2142252011yescharacteristic
335C2#2142253811yescharacteristic
336C2#2142254611yescharacteristic
337C2#2142256411yescharacteristic
338C2#2142489411yescharacteristic
339C2#2142501511yescharacteristic
340C2#2142502311yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D59
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#1767C2
socleC23×C59C2×C22⋊C4
prime radicalC2×#14273724C4
cosocleC2×C42×C59C23
hypercenter#1767D59
hypocenterC59#9678
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C43 ◁ #1767

Complements

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

NH ≅ G/Ntype
2. C4×C4⋊(C59⋊C8)C2semidirect
3. C2×#16837129C2semidirect
4. C59×#1767C2semidirect
49. C4⋊C8×C59D4semidirect
164. #1767D59semidirect
191. C59#9678semidirect
219. C4⋊C8D236semidirect

Maximal subgroups

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

subgroupindex
C4×#142737242
C4×C4⋊(C59⋊C8)2
C2×#168371292
C59×#17672
#967859