Finite Group Databasebeta

← #29569244

Subgroups — #29569244

Order 15616.

410 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 87 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#21452850C211yesmaximal, characteristic
2#21447361C211yesmaximal, characteristic
3#21447297C211yesmaximal, characteristic
4#21447295C211yesmaximal, characteristic
5#21443644C211yesmaximal, characteristic
6#21443643C211yesmaximal, characteristic
7C61×#1271C211yesmaximal, characteristic
8C2×#14519776—21no—
9C2×#14519709—21no—
10C2×#14519709—21no—
11C2×#14519708—21no—
12C2×#14519702—21no—
13#16839695—21no—
14#16839683—21no—
15#16839682—21no—
16#16839668C2211yescharacteristic
17#16839660C2211yescharacteristic
18#16839648—21no—
19#16839645—21no—
20#16839632C2211yescharacteristic
21#16839525—21no—
22#16839524—21no—
23#16839517C2211yescharacteristic
24C61×#389C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×Dic122—21no—
28C22×Dic122D411yescharacteristic
29C22×#92418—21no—
30#14519776—42no—
31#14519776—42no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61D411yescharacteristic
37C2×C4⋊Dic61D411yescharacteristic
38C2×C4⋊Dic61D411yescharacteristic
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×C4×Dic61—21no—
43#14519709—42no—
44#14519709—42no—
45#14519708—42no—
46#14519702—42no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53C22×C8×C61—21no—
54C22×C8×C61—21no—
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61D411yescharacteristic
57C2×C4⋊C4×C61D411yescharacteristic
58C2×C42×C61C2311yescharacteristic
59#95×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61C2×D411yescharacteristic
63C22×C4×C61C2×D411yescharacteristic
64C22×C4×C61C2×D411yescharacteristic
65C22×Dic61—21no—
66C22×Dic61—21no—
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61—41no—
70C2×Dic122—21no—
71C2×Dic122—41no—
72C2×Dic122—41no—
73C2×Dic122—42no—
74C2×Dic122—81no—
75C2×Dic122—81no—
76C2×Dic122SD1612yes—
77C2×C8×C61—22no—
78C2×C8×C61—22no—
79C2×C8×C61—41no—
80C2×C8×C61—41no—
81C2×C8×C61—41no—
82C2×C8×C61—41no—
83C4⋊C4×C61—21no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—41no—
86C4⋊C4×C61—41no—
87C4⋊C4×C61SD1612yes—
88C42×C61—41no—
89C4⋊Dic61—21no—
90C4⋊Dic61—42no—
91C4⋊Dic61—41no—
92C4⋊Dic61—41no—
93C4⋊Dic61—41no—
94C4⋊Dic61—41no—
95C4⋊Dic61—41no—
96C4⋊Dic61—41no—
97C4⋊Dic61—41no—
98C4⋊Dic61—41no—
99C4⋊Dic61SD1612yes—
100#11758196—42no—
101#11758196—41no—
102#11758196—41no—
103#11758196—81no—
104C4×Dic61—42no—
105C2×#92418—22no—
106C2×#92418—41no—
107C2×#92418—41no—
108C23×C61#12011yescharacteristic
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—22no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61C2×SD1611yescharacteristic
122C2×C4×C61C2×SD1611yescharacteristic
123C2×C4×C61C2×SD1611yescharacteristic
124C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C61#13711yescharacteristic
126C2×C4×C61#13711yescharacteristic
127C2×Dic61—22no—
128C2×Dic61—22no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—81no—
140C2×Dic61—81no—
141C2×Dic61—81no—
142Dic122—42no—
143Dic122—81no—
144Dic122—84no—
145C8×C61—42no—
146C8×C61—42no—
147#92418—42no—
148#7817—611nomaximal, Sylow
149C22×C61#44811yescharacteristic
150C22×C61#44811yescharacteristic
151C22×C61#45011yescharacteristic
152C22×C61#45311yescharacteristic
153C22×C61#45611yescharacteristic
154C22×C61#45611yescharacteristic
155C22×C61#45811yescharacteristic
156C4×C61—21no—
157C4×C61—21no—
158C4×C61—21no—
159C4×C61—21no—
160C4×C61—21no—
161C4×C61—21no—
162C4×C61—42no—
163C4×C61—81no—
164Dic61—42no—
165Dic61—42no—
166Dic61—81no—
167Dic61—81no—
168Dic61—161no—
169#2734—611no—
170#2096—611no—
171#2084—611no—
172#2084—611no—
173#1272—611no—
174#1271—611no—
175#1271D6111yescharacteristic
176C2×C61#161111yescharacteristic
177C2×C61#161111yescharacteristic
178C2×C61#161311yescharacteristic
179C2×C61#162311yescharacteristic
180C2×C61#165111yescharacteristic
181C2×C61#165111yescharacteristic
182C2×C61#166011yescharacteristic
183C2×C4⋊Q8—1221no—
184C2×#106—1221no—
185C2×#106—1221no—
186C2×#106—1221no—
187C2×#103—1221no—
188#398—1221no—
189#395—1221no—
190#395—1221no—
191#391—611no—
192#389—611no—
193#389C2×D6111yescharacteristic
194#387—1221no—
195#387—1221no—
196#384—611no—
197#340—1221no—
198#340—1221no—
199#336—611no—
200#336C2×D6111yescharacteristic
201#336C2×D6111yescharacteristic
202C61#781711yescharacteristic, complemented, Sylow
203C22×Q8—611no—
204C22×Q8—1221no—
205C22×C8—21no—
206C22×C8—21no—
207C22×C8—1221no—
208C4⋊Q8—2442no—
209C4⋊Q8—2442no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—611no—
212C2×C4⋊C4—611no—
213C2×C4⋊C4—611no—
214C2×C4⋊C4—1221no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4—1221no—
217C2×C4⋊C4—1221no—
218C2×C4⋊C4—1221no—
219C2×C4⋊C4—1221no—
220C2×C4⋊C4—1221no—
221C2×C4⋊C4D24411yescharacteristic
222C2×C4⋊C4D24411yescharacteristic
223C2×C42—1221no—
224C2×C42C22×D6111yescharacteristic
225#106—2442no—
226#106—2442no—
227#106—2442no—
228#103—2442no—
229#95—21no—
230#95—1221no—
231#95—1221no—
232#95—1221no—
233#95—1221no—
234#95—1221no—
235#95—1221no—
236C2×Q8—612no—
237C2×Q8—1221no—
238C2×Q8—4881no—
239C2×Q8—4881no—
240C2×Q8—2441no—
241C2×Q8—2441no—
242C2×Q8—2442no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—1221no—
246C22×C4—1221no—
247C22×C4—1221no—
248C22×C4—1221no—
249C22×C4—2441no—
250C22×C4C2×D24411yescharacteristic
251C22×C4D4×D6111yescharacteristic
252C22×C4D4×D6111yescharacteristic
253C2×C8—22no—
254C2×C8—22no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—1222no—
260C2×C8—2441no—
261C2×C8—2441no—
262C4⋊C4—21no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—612no—
267C4⋊C4—1221no—
268C4⋊C4—4881no—
269C4⋊C4—2441no—
270C4⋊C4—2441no—
271C4⋊C4—2441no—
272C4⋊C4—2441no—
273C4⋊C4—2442no—
274C4⋊C4—2442no—
275C4⋊C4—2441no—
276C4⋊C4—2441no—
277C4⋊C4—2441no—
278C4⋊C4—2441no—
279C4⋊C4—2441no—
280C4⋊C4—2441no—
281C4⋊C4#1175819012yes—
282C42—41no—
283C42—2442no—
284C23#1451974711yescharacteristic
285Q8—4881no—
286Q8—4884no—
287Q8—2442no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—22no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—1222no—
301C2×C4—1222no—
302C2×C4—4881no—
303C2×C4—4881no—
304C2×C4—4881no—
305C2×C4—2441no—
306C2×C4—2441no—
307C2×C4—2441no—
308C2×C4—2441no—
309C2×C4—2441no—
310C2×C4—2441no—
311C2×C4—2441no—
312C2×C4—2441no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4SD16×D6111yescharacteristic
316C2×C4SD16×D6111yescharacteristic
317C2×C4C2×#1175819011yescharacteristic
318C2×C4#1451980111yescharacteristic
319C2×C4#1451980911yescharacteristic
320C2×C4#1451981011yescharacteristic
321C8—42no—
322C8—42no—
323C8—2442no—
324C22#1683990211yescharacteristic
325C22#1683990311yescharacteristic
326C22#1683991411yescharacteristic
327C22#1683993111yescharacteristic
328C22#1683994611yescharacteristic
329C22#1683994711yescharacteristic
330C22#1683995311yescharacteristic
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—42no—
338C4—81no—
339C4—9761no—
340C4—4881no—
341C4—4881no—
342C4—2442no—
343C4—2442no—
344C2#2144482811yescharacteristic
345C2#2144482911yescharacteristic
346C2#2144484011yescharacteristic
347C2#2144489911yescharacteristic
348C2#2144508311yescharacteristic
349C2#2144508411yescharacteristic
350C2#2144513211yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1271C2
socle, prime radicalC23×C61#120
hypercenter#1271D61
hypocenterC61#7817
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
202. C61#7817semidirect

Maximal subgroups

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

subgroupindex
#214528502
#214473612
#214472972
#214472952
#214436442
#214436432
C61×#12712
#781761