Finite Group Databasebeta

← #28476643

Subgroups — #28476643

Order 15104.

550 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21426579C211yesmaximal, characteristic
2C4×C22⋊(C59⋊C8)C211yesmaximal, characteristic
3#21421920C212yesmaximal, complemented
4#21421918C212yesmaximal, complemented
5C4×C22⋊C8×C59C211yesmaximal, characteristic
6C2×#14273686C411yescharacteristic
7C2×#14273686C411yescharacteristic
8C2×C22⋊(C59⋊C8)—21no—
9C2×C4×C59⋊C8—21no—
10#16837300C411yescharacteristic
11#16837300C411yescharacteristic
12#16837300C2211yescharacteristic
13#16837300C2211yescharacteristic
14#16837275—21no—
15#16837275—21no—
16C4×Dic59⋊C4—21no—
17C4×Dic59⋊C4—21no—
18#16837157C2212yes—
19C22×C42×C59C2211yescharacteristic
20C2×C22⋊C8×C59—21no—
21C2×C4×C8×C59—21no—
22C59×#336C2212yes—
23C22×C59⋊C8—22no—
24#14273686—22no—
25#14273686—42no—
26#14273686C814yescomplemented
27C2×C4⋊Dic59C2×C411yescharacteristic
28C2×C4⋊Dic59C2×C411yescharacteristic
29C2×C4⋊Dic59C2×C411yescharacteristic
30C2×C4⋊Dic59C2×C411yescharacteristic
31C2×Dic59⋊C4—21no—
32C2×Dic59⋊C4—21no—
33C2×Dic59⋊C4—21no—
34C2×Dic59⋊C4—21no—
35C2×C22⋊Dic59—21no—
36C2×C22⋊Dic59—21no—
37C2×C4×Dic59—21no—
38C2×C4×Dic59—21no—
39C22⋊(C59⋊C8)—24no—
40C4×C59⋊C8—42no—
41C59⋊#95—21no—
42C59⋊#95—21no—
43C59⋊#95—21no—
44C59⋊#95—21no—
45C23×C4×C59C2×C411yescharacteristic
46C23×C4×C59D411yescharacteristic
47C23×C4×C59D411yescharacteristic
48C22×C8×C59—22no—
49C2×C42×C59—42no—
50C2×C42×C59C2×C411yescharacteristic
51C2×C42×C59D411yescharacteristic
52C2×C42×C59D411yescharacteristic
53C2×C42×C59C2311yescharacteristic
54C22⋊C8×C59—24no—
55C4×C8×C59—42no—
56C24×C59C22⋊C411yescharacteristic
57C22×C4×C59—22no—
58C22×C4×C59—22no—
59C22×C4×C59—22no—
60C22×C4×C59—22no—
61C22×C4×C59—22no—
62C22×C4×C59—22no—
63C22×C4×C59—41no—
64C22×C4×C59—41no—
65C22×C4×C59C22⋊C411yescharacteristic
66C22×C4×C59C22⋊C411yescharacteristic
67C22×C4×C59C22⋊C411yescharacteristic
68C22×C4×C59C2×C812yes—
69C22×C4×C59M1612yes—
70C22×C4×C59C22×C411yescharacteristic
71C22×C4×C59C2×D411yescharacteristic
72C22×C4×C59C2×D411yescharacteristic
73C22×Dic59—21no—
74C22×Dic59—21no—
75C22×Dic59—21no—
76C22×Dic59—21no—
77C2×C8×C59—24no—
78C2×C8×C59—42no—
79C2×C8×C59—42no—
80C42×C59—22no—
81C42×C59—22no—
82C42×C59—41no—
83C42×C59—41no—
84C22⋊Dic59—24no—
85C22⋊Dic59—42no—
86C4⋊Dic59—21no—
87C4⋊Dic59—21no—
88C4⋊Dic59—41no—
89C4⋊Dic59—41no—
90C4⋊Dic59C2×C812yes—
91C4⋊Dic59C2×C812yes—
92Dic59⋊C4—42no—
93Dic59⋊C4—42no—
94Dic59⋊C4—42no—
95Dic59⋊C4—42no—
96C4×Dic59—24no—
97C4×Dic59—42no—
98C2×C59⋊C8—24no—
99C2×C59⋊C8—42no—
100C2×C59⋊C8—42no—
101C23×C59—21no—
102C23×C59—21no—
103C23×C59—21no—
104C23×C59—21no—
105C23×C59—21no—
106C23×C59—21no—
107C23×C59C22⋊C812yes—
108C23×C59C2×C22⋊C411yescharacteristic
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—21no—
116C2×C4×C59—21no—
117C2×C4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59—24no—
120C2×C4×C59—24no—
121C2×C4×C59—44no—
122C2×C4×C59—44no—
123C2×C4×C59C22⋊C812yes—
124C2×C4×C59#9912yes—
125C2×C4×C59#10112yes—
126C2×C4×C59#10412yes—
127C2×C4×C59#10412yes—
128C2×C4×C59C22×C811yescharacteristic
129C2×C4×C59C2×M1611yescharacteristic
130C2×C4×C59#13512yes—
131C2×C4×C59#13512yes—
132C2×Dic59—22no—
133C2×Dic59—22no—
134C2×Dic59—41no—
135C2×Dic59—41no—
136C2×Dic59—41no—
137C2×Dic59—41no—
138C2×Dic59—41no—
139C2×Dic59—41no—
140C2×Dic59—41no—
141C2×Dic59—41no—
142C2×Dic59—41no—
143C2×Dic59—41no—
144C8×C59—44no—
145C59⋊C8—44no—
146#7564—591nomaximal, Sylow
147C22×C59—22no—
148C22×C59—22no—
149C22×C59—22no—
150C22×C59—41no—
151C22×C59—41no—
152C22×C59—41no—
153C22×C59—41no—
154C22×C59C2×C22⋊C811yescharacteristic
155C22×C59C2×#9911yescharacteristic
156C22×C59C2×#10111yescharacteristic
157C22×C59#41611yescharacteristic
158C22×C59#41611yescharacteristic
159C22×C59C2×#10411yescharacteristic
160C22×C59C2×#10411yescharacteristic
161C4×C59—21no—
162C4×C59—21no—
163C4×C59—22no—
164C4×C59—22no—
165C4×C59—22no—
166C4×C59—22no—
167C4×C59#32414yes—
168Dic59—42no—
169Dic59—42no—
170Dic59—81no—
171Dic59—81no—
172#2296—591no—
173C4×C22⋊C8—591no—
174C4×C22⋊C8D5911yescharacteristic
175#1271—592no—
176#1271—592no—
177C2×C59—42no—
178C2×C59C2×#32411yescharacteristic
179C2×C59#147611yescharacteristic
180C2×C59#147611yescharacteristic
181C2×C59#150111yescharacteristic
182C2×C59#150111yescharacteristic
183C2×C59#152611yescharacteristic
184C2×C59#154411yescharacteristic
185C2×#117—591no—
186C2×#117—591no—
187C22×C42C2×D5911yescharacteristic
188C2×C22⋊C8—21no—
189C2×C22⋊C8—1181no—
190C2×C4×C8—21no—
191C2×C4×C8—1181no—
192#389—591no—
193#389—591no—
194#389—591no—
195#389—591no—
196#385—1181no—
197#385—1181no—
198C4×C4⋊C4—1181no—
199C4×C4⋊C4—1181no—
200#336—592no—
201#336C2×D5912yes—
202C59#756411yescharacteristic, complemented, Sylow
203C23×C4C4×D5911yescharacteristic
204C23×C4D23611yescharacteristic
205C23×C4C22⋊D5911yescharacteristic
206C22×C8—22no—
207C22×C8—1182no—
208#117—594no—
209#117—1182no—
210#117—2362no—
211C2×C4⋊C4—591no—
212C2×C4⋊C4—591no—
213C2×C4⋊C4—591no—
214C2×C4⋊C4—591no—
215C2×C4⋊C4—1181no—
216C2×C4⋊C4—1181no—
217C2×C4⋊C4—1181no—
218C2×C4⋊C4—1181no—
219C2×C22⋊C4—1181no—
220C2×C22⋊C4—1181no—
221C2×C42—42no—
222C2×C42—1181no—
223C2×C42—1181no—
224C2×C42C4×D5911yescharacteristic
225C2×C42D23611yescharacteristic
226C2×C42C22⋊D5911yescharacteristic
227C2×C42C22×D5911yescharacteristic
228C22⋊C8—24no—
229C22⋊C8—1184no—
230C4×C8—42no—
231C4×C8—2362no—
232#95—1181no—
233#95—1181no—
234#95—1181no—
235#95—1181no—
236C24(C2×D59)⋊C411yescharacteristic
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—1181no—
246C22×C4—1181no—
247C22×C4—1181no—
248C22×C4—1181no—
249C22×C4C8×D5912yes—
250C22×C4#1174565912yes—
251C22×C4(C2×D59)⋊C411yescharacteristic
252C22×C4(C2×D59)⋊C411yescharacteristic
253C22×C4(C2×D59)⋊C411yescharacteristic
254C22×C4C2×C4×D5911yescharacteristic
255C22×C4C2×D23611yescharacteristic
256C22×C4C2×C22⋊D5911yescharacteristic
257C2×C8—24no—
258C2×C8—42no—
259C2×C8—42no—
260C2×C8—1184no—
261C2×C8—2362no—
262C2×C8—2362no—
263C4⋊C4—592no—
264C4⋊C4—592no—
265C4⋊C4—1181no—
266C4⋊C4—1181no—
267C4⋊C4—2361no—
268C4⋊C4—2361no—
269C4⋊C4—2362no—
270C4⋊C4—2362no—
271C4⋊C4—2362no—
272C4⋊C4—2362no—
273C22⋊C4—1184no—
274C22⋊C4—2362no—
275C42—22no—
276C42—22no—
277C42—41no—
278C42—41no—
279C42—1184no—
280C42—2362no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23(C2×D59)⋊C812yes—
288C23C2×(C2×D59)⋊C411yescharacteristic
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—24no—
300C2×C4—24no—
301C2×C4—44no—
302C2×C4—44no—
303C2×C4—1182no—
304C2×C4—1182no—
305C2×C4—2361no—
306C2×C4—2361no—
307C2×C4—2361no—
308C2×C4—2361no—
309C2×C4—2361no—
310C2×C4—2361no—
311C2×C4—2361no—
312C2×C4—2361no—
313C2×C4—2361no—
314C2×C4—2361no—
315C2×C4(C2×D59)⋊C812yes—
316C2×C4#1427364112yes—
317C2×C4#1427364512yes—
318C2×C4#1427365312yes—
319C2×C4#1427365512yes—
320C2×C4C2×C8×D5911yescharacteristic
321C2×C4C2×#1174565911yescharacteristic
322C2×C4#1427374712yes—
323C2×C4#1427374912yes—
324C8—44no—
325C8—2364no—
326C22—22no—
327C22—22no—
328C22—22no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22C2×(C2×D59)⋊C811yescharacteristic
334C22C2×#1427364111yescharacteristic
335C22C2×#1427364511yescharacteristic
336C22#1683739611yescharacteristic
337C22#1683739911yescharacteristic
338C22C2×#1427365311yescharacteristic
339C22C2×#1427365511yescharacteristic
340C4—21no—
341C4—21no—
342C4—22no—
343C4—22no—
344C4—22no—
345C4—22no—
346C4—4721no—
347C4—4721no—
348C4—2362no—
349C4—2362no—
350C4#1683712714yes—
351C2—42no—
352C2C2×#1683712711yescharacteristic
353C2#2142247611yescharacteristic
354C2#2142247911yescharacteristic
355C2#2142258511yescharacteristic
356C2#2142258811yescharacteristic
357C2#2142269011yescharacteristic
358C2#2142276011yescharacteristic
subgroupG/H
centerC22×C4(C2×D59)⋊C4
commutatorC2×C4×C59C22×C8
FrattiniC2×C42C22×D59
FittingC4×C22⋊C8×C59C2
socleC23×C59C2×C22⋊C4
prime radicalC24×C59C22⋊C4
cosocleC2×C42×C59C23
hypercenterC4×C22⋊C8D59
hypocenterC59#7564
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
3. #21421920C2semidirect
4. #21421918C2semidirect
26. #14273686C8semidirect
202. C59#7564semidirect

Maximal subgroups

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

subgroupindex
#214265792
C4×C22⋊(C59⋊C8)2
#214219202
#214219182
C4×C22⋊C8×C592
#756459