Finite Group Databasebeta

← #29568962

Subgroups — #29568962

Order 15616.

380 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 79 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#21453810C211yesmaximal, characteristic
2#21447152C211yesmaximal, characteristic
3#21447148C211yesmaximal, characteristic
4#21447066C211yesmaximal, characteristic
5#21443643C211yesmaximal, characteristic
6#21443641C211yesmaximal, characteristic
7C61×#1271C211yesmaximal, characteristic
8C2×#14519777C2211yescharacteristic
9C2×#14519711—21no—
10C2×#14519708—21no—
11C2×#14519702—21no—
12C2×#14519702—21no—
13#16839702—21no—
14#16839701—21no—
15#16839700—21no—
16#16839660C2211yescharacteristic
17#16839660C2211yescharacteristic
18#16839649—21no—
19#16839648—21no—
20#16839643—21no—
21#16839525—21no—
22#16839524—21no—
23#16839517C2211yescharacteristic
24C61×#389C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×Dic122—21no—
28C22×#92418—21no—
29#14519777—42no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61D411yescharacteristic
33C2×C4⋊Dic61D411yescharacteristic
34C2×C4⋊Dic61D411yescharacteristic
35C2×C4⋊Dic61D411yescharacteristic
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×C4×Dic61—21no—
39#14519711—42no—
40#14519708—42no—
41#14519702—42no—
42#14519702—42no—
43#14519684—21no—
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—41no—
71C2×Dic122—41no—
72C2×Dic122—41no—
73C2×Dic122—41no—
74C2×Dic122—41no—
75C2×C8×C61—22no—
76C2×C8×C61—41no—
77C2×C8×C61—41no—
78C2×C8×C61—41no—
79C2×C8×C61—41no—
80C2×C8×C61—41no—
81C4⋊C4×C61—21no—
82C4⋊C4×C61—21no—
83C4⋊C4×C61—41no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—41no—
86C42×C61—41no—
87C4⋊Dic61—22no—
88C4⋊Dic61—22no—
89C4⋊Dic61—21no—
90C4⋊Dic61—21no—
91C4⋊Dic61—21no—
92C4⋊Dic61—21no—
93C4⋊Dic61—41no—
94C4⋊Dic61—41no—
95C4⋊Dic61—41no—
96C4⋊Dic61—41no—
97#11758196—41no—
98#11758196—41no—
99#11758196—41no—
100#11758196—41no—
101C4×Dic61—81no—
102C2×#92418—22no—
103C2×#92418—41no—
104C2×#92418—41no—
105C23×C61#12011yescharacteristic
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—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61#13511yescharacteristic
119C2×C4×C61#13511yescharacteristic
120C2×C4×C61#13511yescharacteristic
121C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
122C2×C4×C61#13711yescharacteristic
123C2×C4×C61#13711yescharacteristic
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—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—42no—
137C2×Dic61—81no—
138C2×Dic61—81no—
139Dic122—42no—
140Dic122—42no—
141Dic122—81no—
142Dic122—81no—
143C8×C61—42no—
144C8×C61—81no—
145#92418—42no—
146#7775—611nomaximal, Sylow
147C22×C61#44911yescharacteristic
148C22×C61#45211yescharacteristic
149C22×C61#45211yescharacteristic
150C22×C61#45411yescharacteristic
151C22×C61#45611yescharacteristic
152C22×C61#45611yescharacteristic
153C22×C61B(4,𝔽2)11yescharacteristic
154C4×C61—21no—
155C4×C61—21no—
156C4×C61—21no—
157C4×C61—21no—
158C4×C61—21no—
159C4×C61—21no—
160C4×C61—81no—
161C4×C61—81no—
162Dic61—82no—
163Dic61—81no—
164Dic61—81no—
165Dic61—81no—
166Dic61—81no—
167#2810—611no—
168#2058—611no—
169#2057—611no—
170#2043—611no—
171#1271—611no—
172#1271—611no—
173#1271D6111yescharacteristic
174C2×C61#159711yescharacteristic
175C2×C61#160311yescharacteristic
176C2×C61#160311yescharacteristic
177C2×C61#163811yescharacteristic
178C2×C61#165011yescharacteristic
179C2×C61#165211yescharacteristic
180C2×C61#166311yescharacteristic
181C2×C4⋊Q8—611no—
182C2×#107—1221no—
183C2×#106—1221no—
184C2×#103—1221no—
185C2×#103—1221no—
186#400—1221no—
187#400—1221no—
188#400—1221no—
189#389—611no—
190#389—611no—
191#389C2×D6111yescharacteristic
192#387—1221no—
193#387—1221no—
194#387—1221no—
195#340—1221no—
196#340—1221no—
197#336—611no—
198#336C2×D6111yescharacteristic
199#336C2×D6111yescharacteristic
200C61#777511yescharacteristic, complemented, Sylow
201C22×Q8—1221no—
202C22×C8—21no—
203C22×C8—21no—
204C22×C8—1221no—
205C4⋊Q8—2442no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—611no—
208C2×C4⋊C4—611no—
209C2×C4⋊C4—611no—
210C2×C4⋊C4—611no—
211C2×C4⋊C4—1221no—
212C2×C4⋊C4—1221no—
213C2×C4⋊C4—1221no—
214C2×C4⋊C4—1221no—
215C2×C4⋊C4D24411yescharacteristic
216C2×C4⋊C4D24411yescharacteristic
217C2×C42—1221no—
218C2×C42C22×D6111yescharacteristic
219#107—2442no—
220#106—2442no—
221#103—2442no—
222#103—2442no—
223#95—21no—
224#95—1221no—
225#95—1221no—
226#95—1221no—
227#95—1221no—
228#95—1221no—
229#95—1221no—
230#95—1221no—
231#95—1221no—
232#95—1221no—
233C2×Q8—1222no—
234C2×Q8—2441no—
235C2×Q8—2441no—
236C2×Q8—2441no—
237C2×Q8—2441no—
238C2×Q8—2441no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—1221no—
242C22×C4—1221no—
243C22×C4—1221no—
244C22×C4—1221no—
245C22×C4—2441no—
246C22×C4C2×D24411yescharacteristic
247C22×C4D4×D6111yescharacteristic
248C22×C4D4×D6111yescharacteristic
249C2×C8—22no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—41no—
254C2×C8—41no—
255C2×C8—1222no—
256C2×C8—2441no—
257C2×C8—2441no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—1222no—
264C4⋊C4—1222no—
265C4⋊C4—1221no—
266C4⋊C4—1221no—
267C4⋊C4—1221no—
268C4⋊C4—1221no—
269C4⋊C4—2441no—
270C4⋊C4—2441no—
271C4⋊C4—2441no—
272C4⋊C4—2441no—
273C4⋊C4—2441no—
274C4⋊C4—2441no—
275C4⋊C4—2441no—
276C4⋊C4—2441no—
277C42—41no—
278C42—4881no—
279C23#1451974711yescharacteristic
280Q8—4881no—
281Q8—4881no—
282Q8—2442no—
283Q8—2442no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—4881no—
297C2×C4—4881no—
298C2×C4—2441no—
299C2×C4—2441no—
300C2×C4—2441no—
301C2×C4—2441no—
302C2×C4—2441no—
303C2×C4—2441no—
304C2×C4—2442no—
305C2×C4—2441no—
306C2×C4—2441no—
307C2×C4—2441no—
308C2×C4—2441no—
309C2×C4—2441no—
310C2×C4—2441no—
311C2×C4#1451979611yescharacteristic
312C2×C4#1451979911yescharacteristic
313C2×C4#1451980011yescharacteristic
314C2×C4#1451980411yescharacteristic
315C2×C4#1451980611yescharacteristic
316C2×C4#1451981011yescharacteristic
317C8—42no—
318C8—81no—
319C8—2442no—
320C22#1683991011yescharacteristic
321C22#1683992511yescharacteristic
322C22#1683992611yescharacteristic
323C22#1683993611yescharacteristic
324C22#1683994611yescharacteristic
325C22#1683994711yescharacteristic
326C22#1683995011yescharacteristic
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—81no—
334C4—81no—
335C4—4882no—
336C4—4881no—
337C4—4881no—
338C4—4881no—
339C4—4881no—
340C2#2144475111yescharacteristic
341C2#2144478311yescharacteristic
342C2#2144478411yescharacteristic
343C2#2144499311yescharacteristic
344C2#2144507811yescharacteristic
345C2#2144509011yescharacteristic
346C2#2144514911yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1271C2
socle, prime radicalC23×C61#120
hypercenter#1271D61
hypocenterC61#7775
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
200. C61#7775semidirect

Maximal subgroups

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

subgroupindex
#214538102
#214471522
#214471482
#214470662
#214436432
#214436412
C61×#12712
#777561