Finite Group Databasebeta

← #29569240

Subgroups — #29569240

Order 15616.

362 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21453781C211yesmaximal, characteristic
2#21447377C211yesmaximal, characteristic
3#21447229C211yesmaximal, characteristic
4#21447229C211yesmaximal, characteristic
5#21443644C211yesmaximal, characteristic
6#21443644C211yesmaximal, characteristic
7C61×#1271C211yesmaximal, characteristic
8C2×#14519702—21no—
9C2×#14519702—21no—
10#16839695—21no—
11#16839694—21no—
12#16839682—21no—
13#16839668C2211yescharacteristic
14#16839668C2211yescharacteristic
15#16839666—21no—
16#16839661—21no—
17#16839648—21no—
18#16839632C2211yescharacteristic
19#16839525—21no—
20#16839525—21no—
21#16839524—21no—
22#16839524—21no—
23#16839517C2211yescharacteristic
24C61×#389C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×Dic122D411yescharacteristic
28C22×Dic122D411yescharacteristic
29C22×#92418—21no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61D411yescharacteristic
36C2×C4⋊Dic61D411yescharacteristic
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×C4×Dic61—21no—
40#14519702—42no—
41#14519702—42no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49C22×C8×C61—21no—
50C22×C8×C61—21no—
51C2×C4⋊C4×C61—21no—
52C2×C4⋊C4×C61D411yescharacteristic
53C2×C4⋊C4×C61D411yescharacteristic
54C2×C42×C61C2311yescharacteristic
55#95×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61—21no—
58C22×C4×C61C2×D411yescharacteristic
59C22×C4×C61C2×D411yescharacteristic
60C22×C4×C61C2×D411yescharacteristic
61C22×Dic61—21no—
62C22×Dic61—21no—
63C22×Dic61—21no—
64C22×Dic61—21no—
65C22×Dic61—41no—
66C2×Dic122—21no—
67C2×Dic122—21no—
68C2×Dic122—21no—
69C2×Dic122—41no—
70C2×Dic122—41no—
71C2×Dic122—41no—
72C2×Dic122—41no—
73C2×Dic122SD1612yes—
74C2×C8×C61—41no—
75C2×C8×C61—41no—
76C2×C8×C61—41no—
77C2×C8×C61—41no—
78C2×C8×C61—41no—
79C2×C8×C61—41no—
80C4⋊C4×C61—21no—
81C4⋊C4×C61—41no—
82C4⋊C4×C61—41no—
83C4⋊C4×C61—41no—
84C4⋊C4×C61Q1612yes—
85C42×C61—41no—
86C4⋊Dic61—41no—
87C4⋊Dic61—41no—
88C4⋊Dic61—42no—
89C4⋊Dic61—41no—
90C4⋊Dic61—41no—
91C4⋊Dic61—41no—
92C4⋊Dic61—41no—
93C4⋊Dic61—81no—
94C4⋊Dic61—81no—
95#11758196—81no—
96#11758196—81no—
97C4×Dic61—81no—
98C2×#92418—41no—
99C2×#92418—41no—
100C2×#92418—41no—
101C23×C61#12011yescharacteristic
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—22no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61C2×SD1611yescharacteristic
115C2×C4×C61C2×Q1611yescharacteristic
116C2×C4×C61#13511yescharacteristic
117C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
118C2×C4×C61#13711yescharacteristic
119C2×C4×C61#13711yescharacteristic
120C2×Dic61—22no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—81no—
133C2×Dic61—81no—
134C2×Dic61—81no—
135Dic122—42no—
136Dic122—42no—
137Dic122—81no—
138Dic122—81no—
139C8×C61—81no—
140C8×C61—81no—
141#92418—81no—
142#7816—611nomaximal, Sylow
143C22×C61#44811yescharacteristic
144C22×C61#44911yescharacteristic
145C22×C61#45111yescharacteristic
146C22×C61#45411yescharacteristic
147C22×C61#45511yescharacteristic
148C22×C61#45511yescharacteristic
149C22×C61#45811yescharacteristic
150C4×C61—21no—
151C4×C61—21no—
152C4×C61—21no—
153C4×C61—21no—
154C4×C61—21no—
155C4×C61—21no—
156C4×C61—42no—
157C4×C61—81no—
158Dic61—42no—
159Dic61—81no—
160Dic61—81no—
161Dic61—81no—
162Dic61—161no—
163#2806—611no—
164#2099—611no—
165#2072—611no—
166#2072—611no—
167#1272—611no—
168#1272—611no—
169#1271D6111yescharacteristic
170C2×C61#160811yescharacteristic
171C2×C61#161211yescharacteristic
172C2×C61#161711yescharacteristic
173C2×C61#162611yescharacteristic
174C2×C61#164411yescharacteristic
175C2×C61#164511yescharacteristic
176C2×C61#166211yescharacteristic
177C2×#103—1221no—
178C2×#103—1221no—
179#398—1221no—
180#398—1221no—
181#395—1221no—
182#391—611no—
183#391—611no—
184#391—1221no—
185#389—1221no—
186#389C2×D6111yescharacteristic
187#387—1221no—
188#384—611no—
189#340—1221no—
190#340—1221no—
191#340—1221no—
192#340—1221no—
193#336—611no—
194#336C2×D6111yescharacteristic
195#336C2×D6111yescharacteristic
196C61#781611yescharacteristic, complemented, Sylow
197C22×Q8—611no—
198C22×Q8—611no—
199C22×C8—21no—
200C22×C8—21no—
201C22×C8—1221no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—611no—
204C2×C4⋊C4—611no—
205C2×C4⋊C4—1221no—
206C2×C4⋊C4—1221no—
207C2×C4⋊C4—1221no—
208C2×C4⋊C4—1221no—
209C2×C4⋊C4—1221no—
210C2×C4⋊C4—1221no—
211C2×C4⋊C4—1221no—
212C2×C4⋊C4D24411yescharacteristic
213C2×C4⋊C4D24411yescharacteristic
214C2×C42—1221no—
215C2×C42C22×D6111yescharacteristic
216#103—2442no—
217#103—2442no—
218#95—21no—
219#95—1221no—
220#95—1221no—
221#95—1221no—
222#95—1221no—
223#95—1221no—
224#95—1221no—
225#95—1221no—
226C2×Q8—612no—
227C2×Q8—1221no—
228C2×Q8—1221no—
229C2×Q8—1221no—
230C2×Q8—2441no—
231C2×Q8—2441no—
232C2×Q8—2441no—
233C2×Q8—2441no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—1221no—
237C22×C4—1221no—
238C22×C4—1221no—
239C22×C4—1221no—
240C22×C4—2441no—
241C22×C4C2×D24411yescharacteristic
242C22×C4D4×D6111yescharacteristic
243C22×C4D4×D6111yescharacteristic
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—41no—
250C2×C8—2441no—
251C2×C8—2441no—
252C2×C8—2441no—
253C4⋊C4—21no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—4881no—
258C4⋊C4—4881no—
259C4⋊C4—4881no—
260C4⋊C4—4881no—
261C4⋊C4—2442no—
262C4⋊C4—2441no—
263C4⋊C4—2441no—
264C4⋊C4—2441no—
265C4⋊C4—2441no—
266C4⋊C4—2441no—
267C4⋊C4—2441no—
268C4⋊C4Dic24412yes—
269C42—41no—
270C42—4881no—
271C23#1451974711yescharacteristic
272Q8—4881no—
273Q8—4881no—
274Q8—2442no—
275Q8—2442no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—1222no—
289C2×C4—4881no—
290C2×C4—4881no—
291C2×C4—4881no—
292C2×C4—2441no—
293C2×C4—2441no—
294C2×C4—2441no—
295C2×C4—2441no—
296C2×C4—2441no—
297C2×C4—2441no—
298C2×C4—2441no—
299C2×C4—2441no—
300C2×C4—2441no—
301C2×C4—2441no—
302C2×C4—2441no—
303C2×C4SD16×D6111yescharacteristic
304C2×C4C2×Dic24411yescharacteristic
305C2×C4#1451979811yescharacteristic
306C2×C4#1451980111yescharacteristic
307C2×C4#1451980911yescharacteristic
308C2×C4#1451981011yescharacteristic
309C8—81no—
310C8—81no—
311C8—4881no—
312C22#1683990211yescharacteristic
313C22#1683990811yescharacteristic
314C22#1683992011yescharacteristic
315C22#1683993711yescharacteristic
316C22#1683994111yescharacteristic
317C22#1683994111yescharacteristic
318C22#1683995311yescharacteristic
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—42no—
326C4—81no—
327C4—9761no—
328C4—4881no—
329C4—4881no—
330C4—4881no—
331C4—2442no—
332C2#2144481111yescharacteristic
333C2#2144483411yescharacteristic
334C2#2144486311yescharacteristic
335C2#2144491611yescharacteristic
336C2#2144503611yescharacteristic
337C2#2144504311yescharacteristic
338C2#2144514311yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1271C2
socle, prime radicalC23×C61#120
hypercenter#1271D61
hypocenterC61#7816
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
196. C61#7816semidirect

Maximal subgroups

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

subgroupindex
#214537812
#214473772
#214472292
#214436442
C61×#12712
#781661