Finite Group Databasebeta

← #28486857

Subgroups — #28486857

Order 15104.

356 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21424815C211yesmaximal, characteristic
2#21423965C211yesmaximal, characteristic
3#21421937C211yesmaximal, characteristic
4#21421937C211yesmaximal, characteristic
5#21421931C211yesmaximal, characteristic
6C59⋊#1273C211yesmaximal, characteristic
7C4×#107×C59C211yesmaximal, characteristic
8C2×C4⋊(C59⋊C8)—21no—
9C2×C4⋊(C59⋊C8)C2211yescharacteristic
10C2×C4⋊(C59⋊C8)C2211yescharacteristic
11C2×#14273638—21no—
12C2×C4×C59⋊C8C2211yescharacteristic
13C2×C4×C59⋊C8C2211yescharacteristic
14#16837157—21no—
15#16837157—21no—
16C2×#107×C59C411yescharacteristic
17C2×#107×C59C411yescharacteristic
18C2×C4×C8×C59C2211yescharacteristic
19C4×C4⋊C4×C59C2211yescharacteristic
20C4×C4⋊C4×C59C2211yescharacteristic
21C59×#340C411yescharacteristic
22C59×#340C411yescharacteristic
23C22×C59⋊C8—21no—
24C22×C59⋊C8—21no—
25C22×C59⋊C8—21no—
26C22×C59⋊C8D411yescharacteristic
27C22×C59⋊C8D411yescharacteristic
28C4⋊(C59⋊C8)—21no—
29C4⋊(C59⋊C8)—21no—
30C4⋊(C59⋊C8)—21no—
31C4⋊(C59⋊C8)—42no—
32C4⋊(C59⋊C8)Q812yes—
33#14273638—42no—
34C4×C59⋊C8—21no—
35C4×C59⋊C8—21no—
36C4×C59⋊C8—21no—
37C4×C59⋊C8—21no—
38C22×C8×C59C2×C411yescharacteristic
39C22×C8×C59C2×C411yescharacteristic
40C2×C4⋊C4×C59C2×C411yescharacteristic
41C2×C4⋊C4×C59C2×C411yescharacteristic
42C2×C4⋊C4×C59C2×C411yescharacteristic
43C2×C4⋊C4×C59C2×C411yescharacteristic
44C2×C42×C59—21no—
45C2×C42×C59—21no—
46C2×C42×C59C2311yescharacteristic
47#107×C59—22no—
48#107×C59—22no—
49C4×C8×C59—21no—
50C4×C8×C59—21no—
51#95×C59—21no—
52#95×C59—21no—
53C22×C4×C59—21no—
54C22×C4×C59—21no—
55C22×C4×C59—21no—
56C22×C4×C59—21no—
57C22×C4×C59C22×C411yescharacteristic
58C22×C4×C59C2×D411yescharacteristic
59C22×C4×C59#4111yescharacteristic
60C2×C8×C59—21no—
61C2×C8×C59—21no—
62C2×C8×C59—21no—
63C2×C8×C59—21no—
64C2×C8×C59—21no—
65C2×C8×C59M1612yes—
66C4⋊C4×C59—21no—
67C4⋊C4×C59—21no—
68C4⋊C4×C59—21no—
69C4⋊C4×C59—21no—
70C4⋊C4×C59—21no—
71C4⋊C4×C59—21no—
72C4⋊C4×C59—21no—
73C4⋊C4×C59M1612yes—
74C42×C59—41no—
75C42×C59—41no—
76C42×C59—41no—
77C42×C59—41no—
78C42×C59C2×Q811yescharacteristic
79C42×C59#4111yescharacteristic
80C42×C59#4111yescharacteristic
81C42×C59#4111yescharacteristic
82C2×C59⋊C8—21no—
83C2×C59⋊C8—21no—
84C2×C59⋊C8—22no—
85C2×C59⋊C8—22no—
86C2×C59⋊C8—21no—
87C2×C59⋊C8—21no—
88C2×C59⋊C8—21no—
89C2×C59⋊C8—41no—
90C2×C59⋊C8—41no—
91C2×C59⋊C8—41no—
92C2×C59⋊C8—41no—
93C2×C59⋊C8—41no—
94C2×C59⋊C8—41no—
95C2×C59⋊C8—41no—
96C2×C59⋊C8Q1612yes—
97C23×C59C4×D411yescharacteristic
98C2×C4×C59—21no—
99C2×C4×C59—21no—
100C2×C4×C59—22no—
101C2×C4×C59—41no—
102C2×C4×C59—41no—
103C2×C4×C59—41no—
104C2×C4×C59—41no—
105C2×C4×C59—41no—
106C2×C4×C59—41no—
107C2×C4×C59—41no—
108C2×C4×C59—41no—
109C2×C4×C59—41no—
110C2×C4×C59—41no—
111C2×C4×C59—41no—
112C2×C4×C59#11711yescharacteristic
113C2×C4×C59C4×Q811yescharacteristic
114C2×C4×C59C22⋊Q811yescharacteristic
115C2×C4×C59#12311yescharacteristic
116C2×C4×C59#12511yescharacteristic
117C2×C4×C59#12611yescharacteristic
118C2×C4×C59C2×M1611yescharacteristic
119C2×C4×C59C2×M1611yescharacteristic
120C2×C4×C59#13111yescharacteristic
121C2×C4×C59#13111yescharacteristic
122C2×C4×C59C2×Q1611yescharacteristic
123C2×C4×C59#13511yescharacteristic
124C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
126C8×C59—22no—
127C8×C59—41no—
128C59⋊C8—22no—
129C59⋊C8—42no—
130C59⋊C8—42no—
131C59⋊C8—41no—
132C59⋊C8—81no—
133#9540—591nomaximal, Sylow
134C22×C59#38711yescharacteristic
135C22×C59#43511yescharacteristic
136C22×C59#43611yescharacteristic
137C22×C59C4×Q1611yescharacteristic
138C22×C59#44211yescharacteristic
139C22×C59#44311yescharacteristic
140C22×C59#44411yescharacteristic
141C4×C59—21no—
142C4×C59—21no—
143C4×C59—42no—
144C4×C59—81no—
145C4×C59—81no—
146C4×C59—81no—
147C4×C59#43211yescharacteristic
148C4×C59#43311yescharacteristic
149C4×C59#44611yescharacteristic
150C4×C59#44611yescharacteristic
151C4×C59#47711yescharacteristic
152C4×C59#47811yescharacteristic
153C4×C59#48211yescharacteristic
154C4×C59#48411yescharacteristic
155#1939—591no—
156C4×#107D5911yescharacteristic
157#1770—591no—
158#1279—591no—
159#1279—591no—
160#1277—591no—
161#1273—591no—
162C2×C59#158411yescharacteristic
163C2×C59#158611yescharacteristic
164C2×C59#159111yescharacteristic
165C2×C59#159411yescharacteristic
166C2×C59#191711yescharacteristic
167C2×C59#192111yescharacteristic
168C2×C59#192211yescharacteristic
169C2×#107Dic5911yescharacteristic
170C2×#107Dic5911yescharacteristic
171C2×C4⋊C8—591no—
172C2×C4⋊C8—591no—
173C2×C4⋊C8—1181no—
174C2×#97—1181no—
175C2×C4×C8—591no—
176C2×C4×C8—591no—
177C2×C4×C8C2×D5911yescharacteristic
178C4×C4⋊C4C2×D5911yescharacteristic
179C4×C4⋊C4C2×D5911yescharacteristic
180#340Dic5911yescharacteristic
181#340Dic5911yescharacteristic
182#336—1181no—
183#336—1181no—
184C59#954011yescharacteristic, complemented, Sylow
185C22×C8—591no—
186C22×C8—591no—
187C22×C8—1181no—
188C22×C8—1181no—
189C22×C8—1181no—
190C22×C8C2×Dic5911yescharacteristic
191C22×C8C2×Dic5911yescharacteristic
192C2×C4⋊C4C2×Dic5911yescharacteristic
193C2×C4⋊C4C2×Dic5911yescharacteristic
194C2×C4⋊C4C2×Dic5911yescharacteristic
195C2×C4⋊C4C2×Dic5911yescharacteristic
196C2×C42—21no—
197C2×C42—21no—
198C2×C42C22×D5911yescharacteristic
199#107—22no—
200#107—22no—
201C4⋊C8—592no—
202C4⋊C8—1181no—
203C4⋊C8—1181no—
204C4⋊C8—1181no—
205C4⋊C8—2362no—
206#97—2362no—
207C4×C8—21no—
208C4×C8—21no—
209C4×C8—1181no—
210C4×C8—1181no—
211C4×C8—1181no—
212C4×C8—1181no—
213#95—21no—
214#95—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4D4×D5911yescharacteristic
220C22×C4#1174568711yescharacteristic
221C22×C4C22×Dic5911yescharacteristic
222C2×C8—21no—
223C2×C8—21no—
224C2×C8—21no—
225C2×C8—21no—
226C2×C8—21no—
227C2×C8—592no—
228C2×C8—1181no—
229C2×C8—1181no—
230C2×C8—1182no—
231C2×C8—1182no—
232C2×C8—1181no—
233C2×C8—1181no—
234C2×C8—1181no—
235C2×C8—2361no—
236C2×C8—2361no—
237C2×C8—2361no—
238C2×C8—2361no—
239C2×C8—2361no—
240C2×C8—2361no—
241C2×C8—2361no—
242C2×C8#1174566412yes—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4#1174566412yes—
251C42—41no—
252C42—41no—
253C42—41no—
254C42—41no—
255C42#1174568511yescharacteristic
256C42#1174568511yescharacteristic
257C42Q8×D5911yescharacteristic
258C42#1174568911yescharacteristic
259C23D4×Dic5911yescharacteristic
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4#1427368611yescharacteristic
275C2×C4Q8×Dic5911yescharacteristic
276C2×C4#1427370511yescharacteristic
277C2×C4#1427371211yescharacteristic
278C2×C4#1427371711yescharacteristic
279C2×C4#1427372211yescharacteristic
280C2×C4C2×#1174566411yescharacteristic
281C2×C4C2×#1174566411yescharacteristic
282C2×C4#1427373411yescharacteristic
283C2×C4#1427373411yescharacteristic
284C2×C4Q16×D5911yescharacteristic
285C2×C4#1427375011yescharacteristic
286C2×C4#1427375111yescharacteristic
287C2×C4#1427375111yescharacteristic
288C8—22no—
289C8—41no—
290C8—1182no—
291C8—4721no—
292C8—2362no—
293C8—2362no—
294C8—2361no—
295C22#1683728811yescharacteristic
296C22#1683747411yescharacteristic
297C22#1683748011yescharacteristic
298C22Q16×Dic5911yescharacteristic
299C22#1683751411yescharacteristic
300C22#1683751911yescharacteristic
301C22#1683752411yescharacteristic
302C4—21no—
303C4—21no—
304C4—42no—
305C4—81no—
306C4—81no—
307C4—81no—
308C4#1683745911yescharacteristic
309C4#1683746311yescharacteristic
310C4#1683753311yescharacteristic
311C4#1683753311yescharacteristic
312C4#1683769611yescharacteristic
313C4#1683770511yescharacteristic
314C4#1683772911yescharacteristic
315C4#1683773911yescharacteristic
316C2#2142294711yescharacteristic
317C2#2142296111yescharacteristic
318C2#2142299311yescharacteristic
319C2#2142301011yescharacteristic
320C2#2142466211yescharacteristic
321C2#2142469011yescharacteristic
322C2#2142469711yescharacteristic
subgroupG/H
centerC22×C4D4×D59
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC4×#107×C59C2
socle, prime radicalC23×C59C4×D4
cosocleC2×C42×C59C23
hypercenterC4×#107D59
hypocenterC59#9540
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#107

Complements

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

NH ≅ G/Ntype
184. C59#9540semidirect

Maximal subgroups

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

subgroupindex
#214248152
#214239652
#214219372
#214219312
C59⋊#12732
C4×#107×C592
#954059