Finite Group Databasebeta

← #28507226

Subgroups — #28507226

Order 15104.

350 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837530C211yesmaximal, characteristic
2#21425851C211yesmaximal, characteristic
3M32×Dic59C211yesmaximal, characteristic
4#21422180C211yesmaximal, characteristic
5#21422179C211yesmaximal, characteristic
6#21422179C211yesmaximal, characteristic
7C59×#1377C211yesmaximal, characteristic
8C2×C4×Dic118C411yescharacteristic
9C2×#14273667C2211yescharacteristic
10C2×#14273667C2211yescharacteristic
11#16837530—21no—
12#16837530—21no—
13#16837530—21no—
14#16837530—21no—
15C2×C4⋊(C59⋊C8)C411yescharacteristic
16C2×Dic59⋊C8C411yescharacteristic
17C2×Dic59⋊C8C411yescharacteristic
18C2×#14273637C2211yescharacteristic
19C2×C8×Dic59C2211yescharacteristic
20Dic59⋊C16—21no—
21Dic59⋊C16—21no—
22#16837177—21no—
23C16×Dic59—21no—
24C2×M32×C59C2211yescharacteristic
25C2×M32×C59C2211yescharacteristic
26C2×#97×C59C2211yescharacteristic
27C22×Dic118C811yescharacteristic
28C22×C59⋊C8C2×C411yescharacteristic
29C22×C59⋊C8C2×C411yescharacteristic
30C4×Dic118—21no—
31C4×Dic118—21no—
32C4×Dic118—21no—
33C4×Dic118—21no—
34C2×C4⋊Dic59C811yescharacteristic
35C2×Dic59⋊C4C811yescharacteristic
36C2×Dic59⋊C4C811yescharacteristic
37C2×C4×Dic59C2×C411yescharacteristic
38C2×C4×Dic59C2×C411yescharacteristic
39#14273667—21no—
40#14273667—21no—
41#14273667—21no—
42#14273667Q812yescomplemented
43C2×C59⋊C16—21no—
44C2×C59⋊C16—21no—
45C4⋊(C59⋊C8)—21no—
46C4⋊(C59⋊C8)—21no—
47Dic59⋊C8—21no—
48Dic59⋊C8—21no—
49Dic59⋊C8—21no—
50Dic59⋊C8—21no—
51#14273637—21no—
52#14273637—21no—
53C8×Dic59D411yescharacteristic
54C8×Dic59D411yescharacteristic
55C8×Dic59D411yescharacteristic
56C8×Dic59D411yescharacteristic
57C22×C8×C59C2×C411yescharacteristic
58C22×C8×C59C2311yescharacteristic
59C2×C42×C59C2×C411yescharacteristic
60M32×C59—21no—
61M32×C59—21no—
62M32×C59—21no—
63M32×C59Q812yescomplemented
64C2×C16×C59—21no—
65C2×C16×C59—21no—
66#97×C59—21no—
67#97×C59—21no—
68C22×C4×C59C2×C811yescharacteristic
69C22×C4×C59C2×C811yescharacteristic
70C22×C4×C59C22×C411yescharacteristic
71C22×Dic59C2×C811yescharacteristic
72C22×Dic59C2×C811yescharacteristic
73C22×Dic59C2×C811yescharacteristic
74C22×Dic59C2×C811yescharacteristic
75C2×Dic118—21no—
76C2×Dic118—21no—
77C2×Dic118—42no—
78C2×C8×C59—21no—
79C2×C8×C59—21no—
80C2×C8×C59—21no—
81C2×C8×C59C2×D411yescharacteristic
82C2×C8×C59C2×D411yescharacteristic
83C2×C8×C59C2×Q811yescharacteristic
84C2×C8×C59C2×Q811yescharacteristic
85C2×C8×C59#4111yescharacteristic
86C2×C8×C59#4111yescharacteristic
87C42×C59—21no—
88C42×C59—21no—
89C4⋊Dic59—21no—
90C4⋊Dic59—21no—
91Dic59⋊C4—21no—
92Dic59⋊C4—21no—
93Dic59⋊C4—21no—
94Dic59⋊C4—21no—
95C4×Dic59—21no—
96C4×Dic59—21no—
97C4×Dic59C22⋊C411yescharacteristic
98C4×Dic59C22⋊C411yescharacteristic
99C4×Dic59M1611yescharacteristic
100C4×Dic59M1611yescharacteristic
101C2×C59⋊C8—21no—
102C2×C59⋊C8—21no—
103C2×C59⋊C8—21no—
104C2×C59⋊C8—21no—
105C2×C59⋊C8—21no—
106C2×C59⋊C8C22⋊C411yescharacteristic
107C2×C59⋊C8C22⋊C411yescharacteristic
108C16×C59—22no—
109C16×C59—41no—
110C59⋊C16—22no—
111C59⋊C16—41no—
112C23×C59C22×C811yescharacteristic
113C2×C4×C59—21no—
114C2×C4×C59—21no—
115C2×C4×C59—41no—
116C2×C4×C59—41no—
117C2×C4×C59C2×C22⋊C411yescharacteristic
118C2×C4×C59C4×Q811yescharacteristic
119C2×C4×C59C4×Q811yescharacteristic
120C2×C4×C59C2×M1611yescharacteristic
121C2×C4×C59#13111yescharacteristic
122C2×C4×C59#13111yescharacteristic
123C2×Dic59—22no—
124C2×Dic59—21no—
125C2×Dic59—21no—
126C2×Dic59—41no—
127C2×Dic59—41no—
128C2×Dic59—41no—
129C2×Dic59C22⋊C811yescharacteristic
130C2×Dic59C22⋊C811yescharacteristic
131C2×Dic59C22⋊C811yescharacteristic
132C2×Dic59C22⋊C811yescharacteristic
133Dic118—42no—
134Dic118—42no—
135C8×C59—41no—
136C8×C59C22⋊Q811yescharacteristic
137C8×C59C22⋊Q811yescharacteristic
138C8×C59#12411yescharacteristic
139C8×C59C4⋊Q811yescharacteristic
140C59⋊C8—21no—
141C59⋊C8—21no—
142C59⋊C8—41no—
143#13268—591nomaximal, Sylow
144C22×C59—21no—
145C22×C59—21no—
146C22×C59C2×C22⋊C811yescharacteristic
147C22×C59C8×Q811yescharacteristic
148C22×C59C8×Q811yescharacteristic
149C4×C59—41no—
150C4×C59—41no—
151C4×C59#39111yescharacteristic
152C4×C59#40811yescharacteristic
153C4×C59#44611yescharacteristic
154C4×C59#44611yescharacteristic
155Dic59—21no—
156Dic59—21no—
157Dic59—21no—
158Dic59—41no—
159Dic59—41no—
160Dic59#34912yes—
161C2×#446—591no—
162#2150—591no—
163C4×M32—591no—
164#1377—591no—
165#1377—591no—
166#1377—591no—
167#1377D5911yescharacteristic
168C2×C59—21no—
169C2×C59—21no—
170C2×C59#198411yescharacteristic
171C2×C59C2×#34911yescharacteristic
172C2×C59#211511yescharacteristic
173C2×C4×Q8—591no—
174C2×M32—591no—
175C2×M32—591no—
176C2×M32C2×D5911yescharacteristic
177C2×M32C2×D5911yescharacteristic
178#446—1181no—
179#446—1181no—
180#446—1181no—
181#446—1181no—
182C2×C4⋊C8—591no—
183C2×C4⋊C8—591no—
184C2×C4⋊C8—591no—
185C2×#97—591no—
186C2×#97C2×D5911yescharacteristic
187C2×C4×C8—591no—
188C4⋊C16—1181no—
189C4⋊C16—1181no—
190#346—1181no—
191C4×C16—1181no—
192C59#1326811yescharacteristic, complemented, Sylow
193C22×Q8—591no—
194C22×C8—591no—
195C22×C8—591no—
196C22×C8C4×D5911yescharacteristic
197C22×C8C22×D5911yescharacteristic
198C4×Q8—1181no—
199C4×Q8—1181no—
200C4×Q8—1181no—
201C4×Q8—1181no—
202C2×C4⋊C4—591no—
203C2×C4⋊C4—591no—
204C2×C4⋊C4—591no—
205C2×C42—591no—
206C2×C42—591no—
207C2×C42C4×D5911yescharacteristic
208M32—21no—
209M32—21no—
210M32—21no—
211M32—592no—
212M32—1181no—
213M32—1181no—
214M32—1181no—
215M32Dic11812yescomplemented
216C2×C16—21no—
217C2×C16—21no—
218C2×C16—1181no—
219C2×C16—1181no—
220C4⋊C8—1181no—
221C4⋊C8—1181no—
222C4⋊C8—1181no—
223C4⋊C8—1181no—
224C4⋊C8—1181no—
225C4⋊C8—1181no—
226#97—21no—
227#97—21no—
228#97—1181no—
229#97—1181no—
230C4×C8—591no—
231C4×C8—591no—
232C4×C8—591no—
233C4×C8—591no—
234C2×Q8—1181no—
235C2×Q8—1181no—
236C2×Q8—2362no—
237C22×C4—591no—
238C22×C4—591no—
239C22×C4—591no—
240C22×C4—591no—
241C22×C4C8×D5911yescharacteristic
242C22×C4C8×D5911yescharacteristic
243C22×C4C2×C4×D5911yescharacteristic
244C2×C8—21no—
245C2×C8—21no—
246C2×C8—21no—
247C2×C8—591no—
248C2×C8—591no—
249C2×C8—1181no—
250C2×C8—1181no—
251C2×C8—1181no—
252C2×C8—1181no—
253C2×C8—1181no—
254C2×C8C2×Dic11811yescharacteristic
255C2×C8#1174568511yescharacteristic
256C2×C8D4×D5911yescharacteristic
257C2×C8D4×D5911yescharacteristic
258C2×C8#1174568711yescharacteristic
259C2×C8Q8×D5911yescharacteristic
260C4⋊C4—1181no—
261C4⋊C4—1181no—
262C4⋊C4—1181no—
263C4⋊C4—1181no—
264C4⋊C4—1181no—
265C4⋊C4—1181no—
266C42—21no—
267C42—21no—
268C42—591no—
269C42—591no—
270C42—591no—
271C42—591no—
272C42—1181no—
273C42—1181no—
274C16—22no—
275C16—41no—
276C16—1182no—
277C16—2361no—
278C23C2×C8×D5911yescharacteristic
279Q8—2362no—
280Q8—2362no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—591no—
286C2×C4—591no—
287C2×C4—591no—
288C2×C4—591no—
289C2×C4—1182no—
290C2×C4—1181no—
291C2×C4—1181no—
292C2×C4—2361no—
293C2×C4—2361no—
294C2×C4—2361no—
295C2×C4C22⋊C4×D5911yescharacteristic
296C2×C4#1427369211yescharacteristic
297C2×C4C4×Dic11811yescharacteristic
298C2×C4M16×D5911yescharacteristic
299C2×C4#1427373311yescharacteristic
300C2×C4#1427373511yescharacteristic
301C8—41no—
302C8—1181no—
303C8—1181no—
304C8—2361no—
305C8#1427370411yescharacteristic
306C8#1427370511yescharacteristic
307C8#1427371311yescharacteristic
308C8#1427372611yescharacteristic
309C22—21no—
310C22—21no—
311C22C22⋊C8×D5911yescharacteristic
312C22#1683752611yescharacteristic
313C22C8×Dic11811yescharacteristic
314C4—41no—
315C4—41no—
316C4—592no—
317C4—1181no—
318C4—1181no—
319C4—1181no—
320C4—2361no—
321C4—2361no—
322C4#1683730611yescharacteristic
323C4#1683736711yescharacteristic
324C4#1683753011yescharacteristic
325C4#1683753111yescharacteristic
326C2—21no—
327C2—21no—
328C2#2142503011yescharacteristic
329C2#349×D5911yescharacteristic
330C2#2142571511yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D59
commutator, prime radicalC23×C59C22×C8
FrattiniC22×C8C22×D59
FittingC59×#1377C2
socleC22×C59C2×C22⋊C8
cosocleC22×C8×C59C23
hypercenter#1377D59
hypocenterC59#13268
LCSG ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1377

Complements

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

NH ≅ G/Ntype
42. #14273667Q8semidirect
63. M32×C59Q8semidirect
192. C59#13268semidirect
215. M32Dic118semidirect

Maximal subgroups

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

subgroupindex
C2×#168375302
#214258512
M32×Dic592
#214221802
#214221792
C59×#13772
#1326859