Finite Group Databasebeta

← #29568977

Subgroups — #29568977

Order 15616.

392 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 83 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#21453772C211yesmaximal, characteristic
2#21447147C211yesmaximal, characteristic
3#21447066C211yesmaximal, characteristic
4#21446961C211yesmaximal, characteristic
5#21443644C211yesmaximal, characteristic
6#21443643C211yesmaximal, characteristic
7C61×#1271C211yesmaximal, characteristic
8C2×#14519777C2211yescharacteristic
9C2×#14519710—21no—
10C2×#14519702—21no—
11C2×#14519702—21no—
12C2×#14519702—21no—
13#16839701—21no—
14#16839701—21no—
15#16839683—21no—
16#16839668C2211yescharacteristic
17#16839661—21no—
18#16839660C2211yescharacteristic
19#16839649—21no—
20#16839648—21no—
21#16839525—21no—
22#16839524—21no—
23#16839517C2211yescharacteristic
24C61×#389C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×Dic122—21no—
28C22×Dic122D411yescharacteristic
29C22×#92418—21no—
30#14519777—42no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61D411yescharacteristic
36C2×C4⋊Dic61D411yescharacteristic
37C2×C4⋊Dic61D411yescharacteristic
38C2×#11758196—21no—
39C2×C4×Dic61—21no—
40#14519710—42no—
41#14519702—42no—
42#14519702—42no—
43#14519702—42no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52C22×C8×C61—21no—
53C22×C8×C61—21no—
54C2×C4⋊C4×C61—21no—
55C2×C4⋊C4×C61D411yescharacteristic
56C2×C4⋊C4×C61D411yescharacteristic
57C2×C42×C61C2311yescharacteristic
58#95×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61C2×D411yescharacteristic
62C22×C4×C61C2×D411yescharacteristic
63C22×C4×C61C2×D411yescharacteristic
64C22×Dic61—21no—
65C22×Dic61—21no—
66C22×Dic61—21no—
67C22×Dic61—21no—
68C22×Dic61—41no—
69C2×Dic122—22no—
70C2×Dic122—21no—
71C2×Dic122—21no—
72C2×Dic122—41no—
73C2×Dic122—41no—
74C2×Dic122—41no—
75C2×Dic122—41no—
76C2×Dic122—41no—
77C2×Dic122—41no—
78C2×Dic122—41no—
79C2×C8×C61—41no—
80C2×C8×C61—41no—
81C2×C8×C61—41no—
82C2×C8×C61—41no—
83C2×C8×C61—41no—
84C2×C8×C61—41no—
85C4⋊C4×C61—21no—
86C4⋊C4×C61—41no—
87C4⋊C4×C61—41no—
88C4⋊C4×C61—41no—
89C4⋊C4×C61Q1612yes—
90C42×C61—41no—
91C4⋊Dic61—22no—
92C4⋊Dic61—22no—
93C4⋊Dic61—21no—
94C4⋊Dic61—21no—
95C4⋊Dic61—41no—
96C4⋊Dic61—41no—
97C4⋊Dic61—41no—
98C4⋊Dic61—41no—
99C4⋊Dic61—81no—
100C4⋊Dic61—81no—
101#11758196—41no—
102#11758196—41no—
103C4×Dic61—81no—
104C2×#92418—22no—
105C2×#92418—41no—
106C2×#92418—41no—
107C23×C61#12011yescharacteristic
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—22no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61C2×Q1611yescharacteristic
121C2×C4×C61#13511yescharacteristic
122C2×C4×C61#13511yescharacteristic
123C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C61#13711yescharacteristic
125C2×C4×C61#13711yescharacteristic
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—42no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—81no—
140C2×Dic61—81no—
141Dic122—42no—
142Dic122—42no—
143Dic122—42no—
144Dic122—81no—
145Dic122—81no—
146Dic122—81no—
147C8×C61—81no—
148C8×C61—81no—
149#92418—42no—
150#7777—611nomaximal, Sylow
151C22×C61#44911yescharacteristic
152C22×C61#45111yescharacteristic
153C22×C61#45211yescharacteristic
154C22×C61#45411yescharacteristic
155C22×C61#45511yescharacteristic
156C22×C61#45611yescharacteristic
157C22×C61B(4,𝔽2)11yescharacteristic
158C4×C61—21no—
159C4×C61—21no—
160C4×C61—21no—
161C4×C61—21no—
162C4×C61—21no—
163C4×C61—21no—
164C4×C61—42no—
165C4×C61—81no—
166Dic61—82no—
167Dic61—81no—
168Dic61—81no—
169Dic61—81no—
170Dic61—81no—
171#2805—611no—
172#2057—611no—
173#2043—611no—
174#2024—611no—
175#1272—611no—
176#1271—611no—
177#1271D6111yescharacteristic
178C2×C61#159711yescharacteristic
179C2×C61#160511yescharacteristic
180C2×C61#160611yescharacteristic
181C2×C61#163611yescharacteristic
182C2×C61#164411yescharacteristic
183C2×C61#165011yescharacteristic
184C2×C61#166411yescharacteristic
185C2×C4⋊Q8—611no—
186C2×#107—1221no—
187C2×#103—1221no—
188C2×#103—1221no—
189C2×#103—1221no—
190#400—1221no—
191#400—1221no—
192#395—1221no—
193#391—611no—
194#389—611no—
195#389—1221no—
196#389C2×D6111yescharacteristic
197#387—1221no—
198#387—1221no—
199#340—1221no—
200#340—1221no—
201#336—611no—
202#336C2×D6111yescharacteristic
203#336C2×D6111yescharacteristic
204C61#777711yescharacteristic, complemented, Sylow
205C22×Q8—611no—
206C22×Q8—1221no—
207C22×C8—21no—
208C22×C8—21no—
209C22×C8—1221no—
210C4⋊Q8—2442no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—611no—
213C2×C4⋊C4—611no—
214C2×C4⋊C4—611no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4—1221no—
217C2×C4⋊C4—1221no—
218C2×C4⋊C4—1221no—
219C2×C4⋊C4—1221no—
220C2×C4⋊C4D24411yescharacteristic
221C2×C4⋊C4D24411yescharacteristic
222C2×C42—1221no—
223C2×C42C22×D6111yescharacteristic
224#107—2442no—
225#103—2442no—
226#103—2442no—
227#103—2442no—
228#95—21no—
229#95—1221no—
230#95—1221no—
231#95—1221no—
232#95—1221no—
233#95—1221no—
234#95—1221no—
235#95—1221no—
236#95—1221no—
237C2×Q8—1222no—
238C2×Q8—1221no—
239C2×Q8—1221no—
240C2×Q8—2441no—
241C2×Q8—2441no—
242C2×Q8—2441no—
243C2×Q8—2441no—
244C2×Q8—2441no—
245C2×Q8—2441no—
246C2×Q8—2441no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—1221no—
250C22×C4—1221no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4—2441no—
254C22×C4C2×D24411yescharacteristic
255C22×C4D4×D6111yescharacteristic
256C22×C4D4×D6111yescharacteristic
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—1222no—
264C2×C8—2441no—
265C2×C8—2441no—
266C4⋊C4—21no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—1222no—
271C4⋊C4—1222no—
272C4⋊C4—1221no—
273C4⋊C4—1221no—
274C4⋊C4—4881no—
275C4⋊C4—4881no—
276C4⋊C4—2441no—
277C4⋊C4—2441no—
278C4⋊C4—2441no—
279C4⋊C4—2441no—
280C4⋊C4—2441no—
281C4⋊C4—2441no—
282C4⋊C4Dic24412yes—
283C42—41no—
284C42—4881no—
285C23#1451974711yescharacteristic
286Q8—4881no—
287Q8—4881no—
288Q8—4881no—
289Q8—2442no—
290Q8—2442no—
291Q8—2442no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—22no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—4881no—
305C2×C4—4881no—
306C2×C4—2441no—
307C2×C4—2441no—
308C2×C4—2441no—
309C2×C4—2441no—
310C2×C4—2441no—
311C2×C4—2441no—
312C2×C4—2442no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4C2×Dic24411yescharacteristic
320C2×C4#1451979811yescharacteristic
321C2×C4#1451979811yescharacteristic
322C2×C4#1451980111yescharacteristic
323C2×C4#1451980911yescharacteristic
324C2×C4#1451981011yescharacteristic
325C8—81no—
326C8—81no—
327C8—2442no—
328C22#1683990811yescharacteristic
329C22#1683992011yescharacteristic
330C22#1683992711yescharacteristic
331C22#1683993611yescharacteristic
332C22#1683994111yescharacteristic
333C22#1683994711yescharacteristic
334C22#1683995011yescharacteristic
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—42no—
342C4—81no—
343C4—4881no—
344C4—4882no—
345C4—4881no—
346C4—4881no—
347C4—4881no—
348C2#2144474911yescharacteristic
349C2#2144479511yescharacteristic
350C2#2144480211yescharacteristic
351C2#2144498011yescharacteristic
352C2#2144503611yescharacteristic
353C2#2144507611yescharacteristic
354C2#2144515511yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1271C2
socle, prime radicalC23×C61#120
hypercenter#1271D61
hypocenterC61#7777
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
204. C61#7777semidirect

Maximal subgroups

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

subgroupindex
#214537722
#214471472
#214470662
#214469612
#214436442
#214436432
C61×#12712
#777761