Finite Group Databasebeta

← #29568698

Subgroups — #29568698

Order 15616.

450 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21445887C211yesmaximal, characteristic
2#21445799C211yesmaximal, characteristic
3#21443642C212yesmaximal, complemented
4#21443642C212yesmaximal, complemented
5C61×#2851C211yesmaximal, characteristic
6C2×C4⋊#92418—21no—
7C2×C22⋊#92418—21no—
8C2×C22⋊#92418—21no—
9#16839517—21no—
10#16839517C2212yes—
11#16839517C2212yes—
12C2×#125×C61C411yescharacteristic
13C22×C42×C61C2211yescharacteristic
14C61×#389C2211yescharacteristic
15C61×#389C2211yescharacteristic
16C61×#387—21no—
17C61×#387—21no—
18C61×#385—21no—
19C61×#385—21no—
20C61×#382C411yescharacteristic
21C61×#380C411yescharacteristic
22C61×#380C411yescharacteristic
23C22×#92418—22no—
24C22×#92418—22no—
25C4⋊#92418—42no—
26C22⋊#92418—42no—
27C22⋊#92418—42no—
28C23×C4×C61C2×C411yescharacteristic
29C23×C4×C61D411yescharacteristic
30C23×C4×C61D411yescharacteristic
31#125×C61—42no—
32C2×C4⋊C4×C61—21no—
33C2×C4⋊C4×C61—21no—
34C2×C4⋊C4×C61—21no—
35C2×C4⋊C4×C61—21no—
36C2×C4⋊C4×C61C2×C411yescharacteristic
37C2×C4⋊C4×C61C2×C411yescharacteristic
38C2×C4⋊C4×C61C2×C411yescharacteristic
39C2×C4⋊C4×C61C2×C411yescharacteristic
40C2×C22⋊C4×C61—21no—
41C2×C22⋊C4×C61—21no—
42C2×C42×C61—42no—
43C2×C42×C61C2×C411yescharacteristic
44C2×C42×C61D411yescharacteristic
45C2×C42×C61D411yescharacteristic
46C2×C42×C61C2311yescharacteristic
47#95×C61—21no—
48#95×C61—21no—
49#95×C61—21no—
50#95×C61—21no—
51#95×C61—21no—
52#95×C61—21no—
53C24×C61C22⋊C411yescharacteristic
54C22×C4×C61—22no—
55C22×C4×C61—22no—
56C22×C4×C61—22no—
57C22×C4×C61—22no—
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—41no—
65C22×C4×C61—41no—
66C22×C4×C61—41no—
67C22×C4×C61—41no—
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22×C411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C4⋊C4×C61—22no—
75C4⋊C4×C61—22no—
76C4⋊C4×C61—42no—
77C4⋊C4×C61—41no—
78C4⋊C4×C61—41no—
79C4⋊C4×C61—42no—
80C4⋊C4×C61—42no—
81C4⋊C4×C61—41no—
82C4⋊C4×C61—41no—
83C22⋊C4×C61—42no—
84C22⋊C4×C61—42no—
85C42×C61—22no—
86C42×C61—22no—
87C42×C61—41no—
88C42×C61—41no—
89C2×#92418—42no—
90C2×#92418—42no—
91C2×#92418—42no—
92C2×#92418—42no—
93C2×#92418—42no—
94C2×#92418—42no—
95C23×C61—21no—
96C23×C61—21no—
97C23×C61—21no—
98C23×C61—21no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61#10112yes—
102C23×C61C2×C22⋊C411yescharacteristic
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—44no—
118C2×C4×C61—44no—
119C2×C4×C61—42no—
120C2×C4×C61—42no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61#9912yes—
134C2×C4×C61#13112yes—
135C2×C4×C61#13512yes—
136C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C61#13711yescharacteristic
138#92418—82no—
139#92418—82no—
140#7731—611nomaximal, Sylow
141C22×C61—22no—
142C22×C61—22no—
143C22×C61—22no—
144C22×C61—41no—
145C22×C61—41no—
146C22×C61—41no—
147C22×C61—41no—
148C22×C61#40811yescharacteristic
149C22×C61C2×#9911yescharacteristic
150C22×C61C2×#10111yescharacteristic
151C22×C61#41611yescharacteristic
152C22×C61#41711yescharacteristic
153C22×C61#42111yescharacteristic
154C22×C61#42111yescharacteristic
155C4×C61—22no—
156C4×C61—21no—
157C4×C61—21no—
158C4×C61—22no—
159C4×C61—22no—
160C4×C61—41no—
161C4×C61—41no—
162C4×C61—81no—
163C4×C61—81no—
164C4×C61—81no—
165C4×C61—81no—
166#2851D6111yescharacteristic
167#1817—611no—
168#1797—611no—
169#1271—612no—
170#1271—612no—
171C2×C61—42no—
172C2×C61#147211yescharacteristic
173C2×C61#148211yescharacteristic
174C2×C61#149511yescharacteristic
175C2×C61#151311yescharacteristic
176C2×C61#151611yescharacteristic
177C2×C61#153411yescharacteristic
178C2×C61#155211yescharacteristic
179C2×#125Dic6111yescharacteristic
180C22×C42C2×D6111yescharacteristic
181C2×C4⋊C8—1221no—
182C2×C22⋊C8—1221no—
183C2×C22⋊C8—1221no—
184#389C2×D6111yescharacteristic
185#389C2×D6111yescharacteristic
186#387—21no—
187#387—21no—
188#385—21no—
189#385—21no—
190#382Dic6111yescharacteristic
191#380Dic6111yescharacteristic
192#380Dic6111yescharacteristic
193#336—612no—
194#336—612no—
195#336—1221no—
196C61#773111yescharacteristic, complemented, Sylow
197C23×C4C2×Dic6111yescharacteristic
198C23×C4C22⋊D6111yescharacteristic
199C23×C4C22⋊D6111yescharacteristic
200C22×C8—1222no—
201C22×C8—1222no—
202#125—42no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4C2×Dic6111yescharacteristic
208C2×C4⋊C4C2×Dic6111yescharacteristic
209C2×C4⋊C4C2×Dic6111yescharacteristic
210C2×C4⋊C4C2×Dic6111yescharacteristic
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C42—42no—
214C2×C42C2×Dic6111yescharacteristic
215C2×C42C22⋊D6111yescharacteristic
216C2×C42C22⋊D6111yescharacteristic
217C2×C42C22×D6111yescharacteristic
218C4⋊C8—2442no—
219C22⋊C8—2442no—
220C22⋊C8—2442no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227C24C22⋊Dic6111yescharacteristic
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4C22⋊Dic6111yescharacteristic
243C22×C4C22⋊Dic6111yescharacteristic
244C22×C4C22⋊Dic6111yescharacteristic
245C22×C4C22×Dic6111yescharacteristic
246C22×C4C2×C22⋊D6111yescharacteristic
247C22×C4C2×C22⋊D6111yescharacteristic
248C2×C8—2442no—
249C2×C8—2442no—
250C2×C8—2442no—
251C2×C8—2442no—
252C2×C8—2442no—
253C2×C8—2442no—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—42no—
259C4⋊C4—42no—
260C4⋊C4—42no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C22⋊C4—42no—
264C22⋊C4—42no—
265C42—22no—
266C42—22no—
267C42—41no—
268C42—41no—
269C23—21no—
270C23—21no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23#1451969612yes—
276C23C2×C22⋊Dic6111yescharacteristic
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
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—44no—
292C2×C4—44no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4#1451969212yes—
308C2×C4#1451978412yes—
309C2×C4#1451979712yes—
310C2×C4#1451980211yescharacteristic
311C2×C4#1451980711yescharacteristic
312C8—4882no—
313C8—4882no—
314C22—22no—
315C22—22no—
316C22—22no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22#1683972911yescharacteristic
322C22C2×#1451969211yescharacteristic
323C22C2×#1451969611yescharacteristic
324C22#1683975811yescharacteristic
325C22#1683976311yescharacteristic
326C22#1683977911yescharacteristic
327C22#1683977911yescharacteristic
328C4—21no—
329C4—21no—
330C4—22no—
331C4—22no—
332C4—22no—
333C4—41no—
334C4—41no—
335C4—81no—
336C4—81no—
337C4—81no—
338C4—81no—
339C2—42no—
340C2#2144418311yescharacteristic
341C2#2144422711yescharacteristic
342C2#2144428411yescharacteristic
343C2#2144436211yescharacteristic
344C2#2144437511yescharacteristic
345C2#2144444611yescharacteristic
346C2#2144451911yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2851C2
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#2851D61
hypocenterC61#7731
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2851

Complements

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

NH ≅ G/Ntype
3. #21443642C2semidirect
4. #21443642C2semidirect
196. C61#7731semidirect

Maximal subgroups

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

subgroupindex
#214458872
#214457992
#214436422
C61×#28512
#773161