Finite Group Databasebeta

← #28477165

Subgroups — #28477165

Order 15104.

464 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21432463C211yesmaximal, characteristic
2#21423949C211yesmaximal, characteristic, complemented
3#21421918C212yesmaximal, complemented
4#21421916C212yesmaximal
5C4×C4⋊C8×C59C211yesmaximal, characteristic, complemented
6C2×#14273721—21no—
7C2×C4⋊(C59⋊C8)—21no—
8C2×#14273638—21no—
9#16837304C411yescharacteristic
10#16837304C411yescharacteristic
11#16837304C2211yescharacteristic
12#16837300C411yescharacteristic
13#16837300C411yescharacteristic
14#16837300C2211yescharacteristic
15#16837293—21no—
16#16837293—21no—
17#16837293—21no—
18#16837157C2212yes—
19C2×C4⋊C8×C59—21no—
20C2×C4×C8×C59—21no—
21C43×C59C2211yescharacteristic
22C59×#336C2212yes—
23C22×D236C2×C411yescharacteristic
24C22×C59⋊C8—22no—
25#14273721—42no—
26#14273721—42no—
27C2×C4⋊Dic59C2×C411yescharacteristic
28C2×C4⋊Dic59C2×C411yescharacteristic
29C2×C4⋊Dic59C2×C411yescharacteristic
30C2×Dic59⋊C4—21no—
31C2×Dic59⋊C4—21no—
32C2×Dic59⋊C4—21no—
33C2×(C2×D59)⋊C4—21no—
34C2×(C2×D59)⋊C4—21no—
35C2×(C2×D59)⋊C4—21no—
36C2×(C2×D59)⋊C4—21no—
37C2×(C2×D59)⋊C4—21no—
38C2×(C2×D59)⋊C4—21no—
39C4⋊(C59⋊C8)—24no—
40#14273638—42no—
41C59⋊#95—21no—
42C59⋊#95—21no—
43C59⋊#95—21no—
44C22×C8×C59—22no—
45C2×C42×C59C2×C411yescharacteristic
46C2×C42×C59C2×C411yescharacteristic
47C2×C42×C59D411yescharacteristic
48C2×C42×C59D411yescharacteristic
49C2×C42×C59D411yescharacteristic
50C2×C42×C59D411yescharacteristic
51C2×C42×C59C2311yescharacteristic
52C4⋊C8×C59—24no—
53C4×C8×C59—42no—
54C23×D59—21no—
55C22×C4×C59C22⋊C411yescharacteristic
56C22×C4×C59C22⋊C411yescharacteristic
57C22×C4×C59C22⋊C411yescharacteristic
58C22×C4×C59C22⋊C411yescharacteristic
59C22×C4×C59C22×C411yescharacteristic
60C22×C4×C59C2×D411yescharacteristic
61C22×C4×C59C2×D411yescharacteristic
62C22×Dic59—21no—
63C22×Dic59—21no—
64C22×Dic59—21no—
65C2×D236—22no—
66C2×D236—41no—
67C2×D236—41no—
68C2×C8×C59—24no—
69C2×C8×C59—42no—
70C2×C8×C59—42no—
71C42×C59—22no—
72C42×C59—22no—
73C42×C59—22no—
74C42×C59—21no—
75C42×C59—21no—
76C42×C59—41no—
77C42×C59—41no—
78C42×C59D812yes—
79C42×C59SD1612yes—
80(C2×D59)⋊C4—42no—
81(C2×D59)⋊C4—42no—
82(C2×D59)⋊C4—42no—
83(C2×D59)⋊C4—42no—
84(C2×D59)⋊C4—41no—
85(C2×D59)⋊C4—41no—
86(C2×D59)⋊C4—41no—
87(C2×D59)⋊C4—41no—
88C4⋊Dic59—22no—
89C4⋊Dic59—41no—
90C4⋊Dic59—41no—
91Dic59⋊C4—42no—
92Dic59⋊C4—42no—
93Dic59⋊C4—41no—
94Dic59⋊C4—41no—
95C2×C59⋊C8—24no—
96C2×C59⋊C8—42no—
97C2×C59⋊C8—42no—
98C23×C59C2×C22⋊C411yescharacteristic
99C22×D59—41no—
100C22×D59—41no—
101C22×D59—41no—
102C22×D59—41no—
103C22×D59—41no—
104C22×D59—41no—
105C22×D59—41no—
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—21no—
116C2×C4×C59—21no—
117C2×C4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59#10212yes—
121C2×C4×C59#10212yes—
122C2×C4×C59#10412yes—
123C2×C4×C59#10412yes—
124C2×C4×C59#13112yes—
125C2×C4×C59C2×D811yescharacteristic
126C2×C4×C59C2×SD1611yescharacteristic
127C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C59#13711yescharacteristic
129C2×Dic59—41no—
130C2×Dic59—41no—
131C2×Dic59—41no—
132C2×Dic59—41no—
133C2×Dic59—41no—
134C2×Dic59—41no—
135C2×Dic59—41no—
136C2×Dic59—41no—
137C2×Dic59—41no—
138D236—82no—
139C8×C59—44no—
140C59⋊C8—44no—
141#7686—591nomaximal, Sylow
142C22×C59#40811yescharacteristic
143C22×C59#41011yescharacteristic
144C22×C59#41311yescharacteristic
145C22×C59C2×#10211yescharacteristic
146C22×C59#41711yescharacteristic
147C22×C59C2×#10411yescharacteristic
148C22×C59C2×#10411yescharacteristic
149C2×D59—81no—
150C2×D59—81no—
151C2×D59—81no—
152C2×D59—81no—
153C2×D59—81no—
154C2×D59—81no—
155C2×D59—81no—
156C4×C59—22no—
157C4×C59—22no—
158C4×C59—22no—
159C4×C59—22no—
160C4×C59—21no—
161C4×C59—21no—
162C4×C59—21no—
163C4×C59—21no—
164C4×C59—22no—
165Dic59—81no—
166Dic59—81no—
167Dic59—81no—
168#2860—591no—
169#1767—591no—
170C4×C4⋊C8D5911yescharacteristic, complemented
171#1271—592no—
172#1270—592no—
173C2×C59#147311yescharacteristic
174C2×C59#148311yescharacteristic
175C2×C59#149211yescharacteristic
176C2×C59#150211yescharacteristic
177C2×C59#150911yescharacteristic
178C2×C59#152411yescharacteristic
179C2×C59#154711yescharacteristic
180D59—161no—
181C2×#126—1181no—
182C2×C4⋊C8—21no—
183C2×C4⋊C8—1181no—
184C2×#97—1181no—
185C2×C4×C8—21no—
186#390—591no—
187#390—591no—
188#390—591no—
189#389—591no—
190#389—591no—
191#389—591no—
192#388—1181no—
193#388—1181no—
194#388—1181no—
195C43C2×D5911yescharacteristic
196#336—592no—
197#336C2×D5912yes—
198C59#768611yescharacteristic, complemented, Sylow
199C22×D4—591no—
200C22×C8—22no—
201C22×C8—1182no—
202#126—2362no—
203#126—2362no—
204C2×C4⋊C4—591no—
205C2×C4⋊C4—591no—
206C2×C4⋊C4—591no—
207C2×C4⋊C4—1181no—
208C2×C4⋊C4—1181no—
209C2×C4⋊C4—1181no—
210C2×C22⋊C4—1181no—
211C2×C22⋊C4—1181no—
212C2×C22⋊C4—1181no—
213C2×C22⋊C4—1181no—
214C2×C22⋊C4—1181no—
215C2×C22⋊C4—1181no—
216C2×C42C4×D5911yescharacteristic
217C2×C42C4×D5911yescharacteristic
218C2×C42D23611yescharacteristic
219C2×C42D23611yescharacteristic
220C2×C42C22⋊D5911yescharacteristic
221C2×C42C22⋊D5911yescharacteristic
222C2×C42C22×D5911yescharacteristic
223C4⋊C8—24no—
224C4⋊C8—1184no—
225#97—2362no—
226C4×C8—42no—
227#95—1181no—
228#95—1181no—
229#95—1181no—
230C24—1181no—
231C2×D4—1182no—
232C2×D4—2361no—
233C2×D4—2361no—
234C22×C4—1181no—
235C22×C4—1181no—
236C22×C4—1181no—
237C22×C4(C2×D59)⋊C411yescharacteristic
238C22×C4(C2×D59)⋊C411yescharacteristic
239C22×C4(C2×D59)⋊C411yescharacteristic
240C22×C4(C2×D59)⋊C411yescharacteristic
241C22×C4C2×C4×D5911yescharacteristic
242C22×C4C2×D23611yescharacteristic
243C22×C4C2×C22⋊D5911yescharacteristic
244C2×C8—24no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—1184no—
248C2×C8—2362no—
249C2×C8—2362no—
250C4⋊C4—1182no—
251C4⋊C4—2361no—
252C4⋊C4—2361no—
253C4⋊C4—2362no—
254C4⋊C4—2362no—
255C4⋊C4—2361no—
256C4⋊C4—2361no—
257C22⋊C4—2362no—
258C22⋊C4—2362no—
259C22⋊C4—2362no—
260C22⋊C4—2362no—
261C22⋊C4—2361no—
262C22⋊C4—2361no—
263C22⋊C4—2361no—
264C22⋊C4—2361no—
265C42—22no—
266C42—22no—
267C42—22no—
268C42—21no—
269C42—21no—
270C42—41no—
271C42—41no—
272C42#1174566012yes—
273C42D47212yes—
274C23—2361no—
275C23—2361no—
276C23—2361no—
277C23—2361no—
278C23—2361no—
279C23—2361no—
280C23—2361no—
281C23C2×(C2×D59)⋊C411yescharacteristic
282D4—4722no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
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—2361no—
298C2×C4—2361no—
299C2×C4—2361no—
300C2×C4—2361no—
301C2×C4—2361no—
302C2×C4—2361no—
303C2×C4—2361no—
304C2×C4—2361no—
305C2×C4—2361no—
306C2×C4#1427364912yes—
307C2×C4#1427364912yes—
308C2×C4#1427365312yes—
309C2×C4#1427365512yes—
310C2×C4#1427373312yes—
311C2×C4C2×D47211yescharacteristic
312C2×C4C2×#1174566011yescharacteristic
313C2×C4#1427375311yescharacteristic
314C2×C4#1427375811yescharacteristic
315C8—44no—
316C8—2364no—
317C22—4721no—
318C22—4721no—
319C22—4721no—
320C22—4721no—
321C22—4721no—
322C22—4721no—
323C22—4721no—
324C22#1683736811yescharacteristic
325C22#1683737511yescharacteristic
326C22#1683738411yescharacteristic
327C22C2×#1427364911yescharacteristic
328C22#1683740111yescharacteristic
329C22C2×#1427365311yescharacteristic
330C22C2×#1427365511yescharacteristic
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—22no—
336C4—22no—
337C4—22no—
338C4—22no—
339C4—22no—
340C4—4721no—
341C4—4721no—
342C4—4721no—
343C2—9441no—
344C2#2142246311yescharacteristic
345C2#2142250711yescharacteristic
346C2#2142254811yescharacteristic
347C2#2142259211yescharacteristic
348C2#2142261911yescharacteristic
349C2#2142268511yescharacteristic
350C2#2142277111yescharacteristic
subgroupG/H
centerC23C2×(C2×D59)⋊C4
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC4×C4⋊C8×C59C2
socleC23×C59C2×C22⋊C4
prime radicalC22×D236C2×C4
cosocleC2×C42×C59C23
hypercenterC4×C4⋊C8D59
hypocenterC59#7686
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C43 ◁ C4×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #21423949C2semidirect
3. #21421918C2semidirect
5. C4×C4⋊C8×C59C2semidirect
170. C4×C4⋊C8D59semidirect
198. C59#7686semidirect

Maximal subgroups

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

subgroupindex
#214324632
#214239492
#214219182
#214219162
C4×C4⋊C8×C592
#768659