Finite Group Databasebeta

← #28493246

Subgroups — #28493246

Order 15104.

370 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21425045C211yesmaximal, characteristic
2#21424852C211yesmaximal, characteristic
3#21424814C211yesmaximal, characteristic
4C2×#16837155C211yesmaximal, characteristic
5C2×#16837151C211yesmaximal, characteristic
6#21421979C211yesmaximal, characteristic
7C59×#1990C211yesmaximal, characteristic
8C2×#14273660—21no—
9C2×C4⋊(C59⋊C8)C2211yescharacteristic
10C2×C4⋊(C59⋊C8)C2211yescharacteristic
11C2×C4⋊(C59⋊C8)C2211yescharacteristic
12C2×Dic59⋊C8—21no—
13C4×C4⋊Dic59C2211yescharacteristic
14#16837164—21no—
15#16837164—21no—
16#16837164—21no—
17#16837156—21no—
18#16837155—22no—
19#16837151—22no—
20C2×C4⋊Q8×C59C2211yescharacteristic
21C2×C4×C8×C59C2211yescharacteristic
22C59×#384C2211yescharacteristic
23C59×#340—21no—
24C59×#340—21no—
25C22×C59⋊C8—21no—
26C22×C59⋊C8—21no—
27C22×C59⋊C8—21no—
28C2×C4⋊Dic59D411yescharacteristic
29C2×C4⋊Dic59D411yescharacteristic
30C2×C4×Dic59—21no—
31#14273660—42no—
32C4⋊(C59⋊C8)—21no—
33C4⋊(C59⋊C8)—21no—
34C4⋊(C59⋊C8)—21no—
35C4⋊(C59⋊C8)—21no—
36C4⋊(C59⋊C8)—21no—
37C4⋊(C59⋊C8)D412yes—
38Dic59⋊C8—42no—
39C59⋊#95—21no—
40C22×Q8×C59—21no—
41C22×C8×C59D411yescharacteristic
42C22×C8×C59D411yescharacteristic
43C4⋊Q8×C59—21no—
44C4⋊Q8×C59—21no—
45C4⋊Q8×C59—21no—
46C4⋊Q8×C59Q812yes—
47C2×C4⋊C4×C59—21no—
48C2×C4⋊C4×C59—21no—
49C2×C4⋊C4×C59—21no—
50C2×C4⋊C4×C59—21no—
51C2×C4⋊C4×C59—21no—
52C2×C42×C59C2311yescharacteristic
53C4×C8×C59—21no—
54C4×C8×C59—21no—
55C2×Q8×C59—22no—
56C2×Q8×C59—41no—
57C2×Q8×C59—81no—
58C2×Q8×C59—81no—
59C22×C4×C59—41no—
60C22×C4×C59—41no—
61C22×C4×C59C2×D411yescharacteristic
62C22×C4×C59C2×D411yescharacteristic
63C22×C4×C59#4111yescharacteristic
64C22×Dic59—21no—
65C22×Dic59—21no—
66C2×C8×C59—21no—
67C2×C8×C59—21no—
68C2×C8×C59—21no—
69C2×C8×C59—21no—
70C2×C8×C59—21no—
71C2×C8×C59Q1612yes—
72C4⋊C4×C59—22no—
73C4⋊C4×C59—22no—
74C4⋊C4×C59—41no—
75C4⋊C4×C59—41no—
76C4⋊C4×C59—41no—
77C4⋊C4×C59—41no—
78C4⋊C4×C59—41no—
79C4⋊C4×C59—41no—
80C4⋊C4×C59—81no—
81C42×C59C2×D411yescharacteristic
82C42×C59C2×Q811yescharacteristic
83C42×C59#4111yescharacteristic
84C42×C59#4111yescharacteristic
85C4⋊Dic59—21no—
86C4⋊Dic59—21no—
87C4⋊Dic59—21no—
88C4⋊Dic59Q1612yes—
89C4×Dic59—41no—
90C4×Dic59—41no—
91C2×C59⋊C8—22no—
92C2×C59⋊C8—41no—
93C2×C59⋊C8—41no—
94C2×C59⋊C8—41no—
95C2×C59⋊C8—41no—
96C2×C59⋊C8—41no—
97C2×C59⋊C8—41no—
98C2×C59⋊C8—41no—
99C2×C59⋊C8—41no—
100C23×C59#12111yescharacteristic
101Q8×C59—82no—
102Q8×C59—82no—
103C2×C4×C59—21no—
104C2×C4×C59—21no—
105C2×C4×C59—42no—
106C2×C4×C59—81no—
107C2×C4×C59—81no—
108C2×C4×C59—81no—
109C2×C4×C59—81no—
110C2×C4×C59—81no—
111C2×C4×C59#12111yescharacteristic
112C2×C4×C59#12111yescharacteristic
113C2×C4×C59C22⋊Q811yescharacteristic
114C2×C4×C59C22⋊Q811yescharacteristic
115C2×C4×C59C22⋊Q811yescharacteristic
116C2×C4×C59#12611yescharacteristic
117C2×C4×C59C2×Q1611yescharacteristic
118C2×C4×C59C2×Q1611yescharacteristic
119C2×C4×C59#13511yescharacteristic
120C2×C4×C59#13511yescharacteristic
121C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
122C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C59#13711yescharacteristic
124C2×C4×C59#13711yescharacteristic
125C2×Dic59—22no—
126C2×Dic59—41no—
127C2×Dic59—41no—
128C2×Dic59—41no—
129C2×Dic59—41no—
130C2×Dic59—41no—
131C8×C59—22no—
132C8×C59—41no—
133C59⋊C8—42no—
134C59⋊C8—81no—
135C59⋊C8—81no—
136#10593—591nomaximal, Sylow
137C22×C59#39611yescharacteristic
138C22×C59#46211yescharacteristic
139C22×C59#46311yescharacteristic
140C22×C59#46711yescharacteristic
141C22×C59#46811yescharacteristic
142C22×C59#47111yescharacteristic
143C22×C59#47211yescharacteristic
144C4×C59—21no—
145C4×C59—21no—
146C4×C59—82no—
147C4×C59—161no—
148C4×C59#46211yescharacteristic
149C4×C59#46311yescharacteristic
150C4×C59#46711yescharacteristic
151C4×C59#46811yescharacteristic
152C4×C59#47711yescharacteristic
153C4×C59#47711yescharacteristic
154C4×C59#47911yescharacteristic
155C4×C59#47911yescharacteristic
156Dic59—42no—
157Dic59—81no—
158#1990D5911yescharacteristic
159#1987—591no—
160#1947—591no—
161#1939—591no—
162C2×#335—591no—
163C2×#333—591no—
164#1296—591no—
165C2×C59#167611yescharacteristic
166C2×C59#168311yescharacteristic
167C2×C59#169211yescharacteristic
168C2×C59#169711yescharacteristic
169C2×C59#206311yescharacteristic
170C2×C59#206811yescharacteristic
171C2×C59#206811yescharacteristic
172C2×C4⋊Q8C2×D5911yescharacteristic
173C2×#107—1181no—
174C2×C4⋊C8—591no—
175C2×C4⋊C8—591no—
176C2×C4⋊C8—591no—
177C2×C4⋊C8—1181no—
178C2×C4×C8C2×D5911yescharacteristic
179#384C2×D5911yescharacteristic
180C4×C4⋊C4—591no—
181#340—21no—
182#340—21no—
183#340—1181no—
184#340—1181no—
185#340—1181no—
186#336—1181no—
187#335—1182no—
188#333—1182no—
189C59#1059311yescharacteristic, complemented, Sylow
190C22×Q8—21no—
191C22×C8—1181no—
192C22×C8—1181no—
193C22×C8—1181no—
194C22×C8C22⋊D5911yescharacteristic
195C22×C8C22⋊D5911yescharacteristic
196C4⋊Q8—21no—
197C4⋊Q8—21no—
198C4⋊Q8—21no—
199C4⋊Q8Dic11812yes—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—591no—
206C2×C4⋊C4—591no—
207C2×C42—1181no—
208C2×C42C22×D5911yescharacteristic
209#107—2362no—
210C4⋊C8—592no—
211C4⋊C8—1181no—
212C4⋊C8—1181no—
213C4⋊C8—1181no—
214C4⋊C8—1181no—
215C4⋊C8—1181no—
216C4⋊C8—2362no—
217C4×C8—21no—
218C4×C8—21no—
219#95—1181no—
220C2×Q8—22no—
221C2×Q8—41no—
222C2×Q8—81no—
223C2×Q8—81no—
224C22×C4—41no—
225C22×C4—41no—
226C22×C4—1181no—
227C22×C4—1181no—
228C22×C4D4×D5911yescharacteristic
229C22×C4#1174568711yescharacteristic
230C22×C4C2×C22⋊D5911yescharacteristic
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—1182no—
237C2×C8—2361no—
238C2×C8—2361no—
239C2×C8—2361no—
240C2×C8—2361no—
241C2×C8—2361no—
242C2×C8—2361no—
243C2×C8—2361no—
244C2×C8—2361no—
245C2×C8#1174567212yes—
246C4⋊C4—22no—
247C4⋊C4—22no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—81no—
255C4⋊C4—592no—
256C4⋊C4—1181no—
257C4⋊C4—1181no—
258C4⋊C4—1181no—
259C42—2361no—
260C42—2361no—
261C42C2×Dic11811yescharacteristic
262C42#1174568511yescharacteristic
263C42D4×D5911yescharacteristic
264C42#1174568711yescharacteristic
265C23#1427369811yescharacteristic
266Q8—82no—
267Q8—82no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—42no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—81no—
276C2×C4—1182no—
277C2×C4—2361no—
278C2×C4—2361no—
279C2×C4—2361no—
280C2×C4—2361no—
281C2×C4—2361no—
282C2×C4#1427369911yescharacteristic
283C2×C4#1427370011yescharacteristic
284C2×C4#1427370411yescharacteristic
285C2×C4#1427370411yescharacteristic
286C2×C4#1427370611yescharacteristic
287C2×C4#1427372011yescharacteristic
288C2×C4Q16×D5911yescharacteristic
289C2×C4C2×#1174567211yescharacteristic
290C2×C4#1427374711yescharacteristic
291C2×C4#1427375011yescharacteristic
292C2×C4#1427375211yescharacteristic
293C2×C4#1427375411yescharacteristic
294C2×C4#1427375611yescharacteristic
295C2×C4#1427375811yescharacteristic
296C8—22no—
297C8—41no—
298C8—4721no—
299C8—4721no—
300C8—2362no—
301C22#1683732511yescharacteristic
302C22#1683760911yescharacteristic
303C22#1683761411yescharacteristic
304C22#1683764011yescharacteristic
305C22#1683764511yescharacteristic
306C22#1683766211yescharacteristic
307C22#1683766911yescharacteristic
308C4—21no—
309C4—21no—
310C4—82no—
311C4—161no—
312C4—4721no—
313C4—2362no—
314C4#1683761111yescharacteristic
315C4#1683762011yescharacteristic
316C4#1683764111yescharacteristic
317C4#1683765011yescharacteristic
318C4#1683769511yescharacteristic
319C4#1683769711yescharacteristic
320C4#1683770911yescharacteristic
321C4#1683771111yescharacteristic
322C2#2142349711yescharacteristic
323C2#2142354411yescharacteristic
324C2#2142359911yescharacteristic
325C2#2142362611yescharacteristic
326C2#2142545411yescharacteristic
327C2#2142548911yescharacteristic
328C2#2142549111yescharacteristic
subgroupG/H
centerC23#14273698
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1990C2
socle, prime radicalC23×C59#121
hypercenter#1990D59
hypocenterC59#10593
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
189. C59#10593semidirect

Maximal subgroups

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

subgroupindex
#214250452
#214248522
#214248142
C2×#168371552
C2×#168371512
#214219792
C59×#19902
#1059359