Finite Group Databasebeta

← #29654915

Subgroups — #29654915

Order 15616.

906 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 906 conjugacy classes of subgroups — too many to draw. Only its 191 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#21459629C211yesmaximal, characteristic
2#21456965C212yesmaximal
3#21450804C211yesmaximal, characteristic
4#21444829C218yesmaximal
5#21444319C212yesmaximal
6C61×#1461C211yesmaximal, characteristic
7Q8×Dic122—22no—
8#16840491—22no—
9#16840488—24no—
10#16840393—21no—
11#16840393C2214yes—
12#16840319—22no—
13#16840319C2212yes—
14C2×#14519777C2211yescharacteristic
15C2×#14519775—21no—
16#16840240—21no—
17#16840160—22no—
18#16840113—22no—
19#16840093C2218yes—
20#16840048—24no—
21#16839692C2214yes—
22#16839667—21no—
23#16839660—22no—
24C4×C4⋊Dic61C2211yescharacteristic
25#16839500C2218yes—
26C2×C4×Q8×C61C2211yescharacteristic
27C61×#431C2212yes—
28C61×#324C2214yes—
29C22×Dic122—21no—
30#14519777—22no—
31#14519777—22no—
32#14519777—22no—
33#14519777—22no—
34#14519777D412yes—
35#14519777D412yes—
36#14519776—24no—
37#14519776—28no—
38#14519775—44no—
39#14519769—24no—
40#14519769—22no—
41#14519768—24no—
42#14519768—28no—
43#14519756—22no—
44#14519756—24no—
45#14519756C2314yes—
46Q8×Dic61—24no—
47Q8×Dic61—24no—
48C4×Dic122—24no—
49C4×Dic122—24no—
50C4×Dic122—22no—
51C4×Dic122D414yes—
52#14519736—24no—
53#14519736—22no—
54C2×C4⋊Dic61—21no—
55C2×C4⋊Dic61—21no—
56C2×C4⋊Dic61C2312yes—
57C2×#11758196—24no—
58C2×C4×Dic61—21no—
59#14519709—28no—
60#14519702—28no—
61#14519684—24no—
62#14519684C2312yes—
63C22×Q8×C61D411yescharacteristic
64C4×Q8×C61—22no—
65C4×Q8×C61—22no—
66C2×C4⋊C4×C61D411yescharacteristic
67C2×C4⋊C4×C61C2312yes—
68C2×C42×C61D412yes—
69C2×C42×C61C2311yescharacteristic
70C4⋊C8×C61—22no—
71C22⋊C8×C61C2314yes—
72C4×C8×C61—22no—
73C2×Q8×C61—22no—
74C2×Q8×C61—22no—
75C2×Q8×C61SD1614yes—
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61C2×D412yes—
78C22×C4×C61C2×D412yes—
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61C2411yescharacteristic
81C22×Dic61—22no—
82C22×Dic61—22no—
83C2×Dic122—22no—
84C2×Dic122—24no—
85C2×Dic122—42no—
86C2×Dic122—42no—
87C2×Dic122—42no—
88C2×Dic122C2×D414yes—
89C2×C8×C61—24no—
90C4⋊C4×C61—22no—
91C4⋊C4×C61—24no—
92C42×C61—22no—
93C42×C61—22no—
94C42×C61C2×D412yes—
95C42×C61C2×D412yes—
96C22⋊Dic61—24no—
97C4⋊Dic61—24no—
98C4⋊Dic61—24no—
99C4⋊Dic61—24no—
100C4⋊Dic61—24no—
101C4⋊Dic61—22no—
102C4⋊Dic61—22no—
103C4⋊Dic61—22no—
104C4⋊Dic61—24no—
105C4⋊Dic61—41no—
106C4⋊Dic61—41no—
107C4⋊Dic61C2×D414yes—
108#11758196—28no—
109#11758196—24no—
110#11758196—24no—
111#11758196—48no—
112C4×Dic61—28no—
113C4×Dic61—24no—
114C4×Dic61—42no—
115C23×C61C22×D411yescharacteristic
116Q8×C61—28no—
117C2×C4×C61—22no—
118C2×C4×C61—22no—
119C2×C4×C61—22no—
120C2×C4×C61—22no—
121C2×C4×C61—41no—
122C2×C4×C61—42no—
123C2×C4×C61#12011yescharacteristic
124C2×C4×C61#12012yes—
125C2×C4×C61#12011yescharacteristic
126C2×C4×C61C2×SD1614yes—
127C2×C4×C61C2×SD1612yes—
128C2×C4×C61#13712yes—
129C2×C4×C61C22×D412yes—
130C2×Dic61—24no—
131C2×Dic61—24no—
132C2×Dic61—24no—
133C2×Dic61—42no—
134C2×Dic61—42no—
135C2×Dic61—42no—
136C2×Dic61—42no—
137C2×Dic61—42no—
138Dic122—44no—
139Dic122—44no—
140Dic122—84no—
141Dic122—84no—
142C8×C61—44no—
143#18410—611nomaximal, Sylow
144C22×C61—21no—
145C22×C61—21no—
146C22×C61C2×#12011yescharacteristic
147C22×C61C22×SD1611yescharacteristic
148C22×C61C2×#13711yescharacteristic
149C4×C61—24no—
150C4×C61—21no—
151C4×C61—22no—
152C4×C61—42no—
153C4×C61#44814yes—
154C4×C61#45612yes—
155Dic61—44no—
156Dic61—44no—
157Dic61—44no—
158Dic61—82no—
159#3502—611no—
160#3229—612no—
161#2546—611no—
162#1611—618no—
163#1503—612no—
164#1461D6111yescharacteristic
165C2×C61—21no—
166C2×C61—21no—
167C2×C61C2×#44811yescharacteristic
168C2×C61C2×#45611yescharacteristic
169C2×C61#302811yescharacteristic
170Q82—1222no—
171#557—1224no—
172#557—1222no—
173#544—614no—
174#544—1221no—
175#533—612no—
176#533—1222no—
177C2×C4⋊Q8—611no—
178C2×C4⋊Q8—1221no—
179#519—1221no—
180C2×C4×Q8C2×D6111yescharacteristic
181#498—1222no—
182#487—1222no—
183#483—618no—
184#475—1224no—
185#431C2×D6112yes—
186#398—614no—
187#391—1221no—
188#389—1222no—
189C4×C4⋊C4—611no—
190#328—618no—
191#324C2×D6114yes—
192C61#1841011yescharacteristic, complemented, Sylow
193C22×Q8—1221no—
194C22×Q8D24411yescharacteristic
195C4⋊Q8—612no—
196C4⋊Q8—612no—
197C4⋊Q8—1222no—
198C4⋊Q8—1222no—
199C4⋊Q8—1228no—
200C4⋊Q8—1224no—
201C4⋊Q8—1222no—
202C4⋊Q8—1222no—
203C4⋊Q8—2444no—
204#125—1224no—
205#125—1228no—
206#125—1224no—
207#125—1222no—
208C22⋊Q8—614no—
209C22⋊Q8—1222no—
210C22⋊Q8—1224no—
211C4×Q8—22no—
212C4×Q8—22no—
213C4×Q8—614no—
214C4×Q8—1224no—
215C4×Q8—1224no—
216C4×Q8—1224no—
217C4×Q8—1224no—
218C4×Q8—1222no—
219#117—1222no—
220#117—1224no—
221C2×C4⋊C4—612no—
222C2×C4⋊C4—1221no—
223C2×C4⋊C4—1221no—
224C2×C4⋊C4—1224no—
225C2×C4⋊C4D24411yescharacteristic
226C2×C4⋊C4C22×D6112yes—
227C2×C42—1221no—
228C2×C42D24412yes—
229C2×C42C22×D6111yescharacteristic
230#106—1228no—
231C4⋊C8—22no—
232#103—1228no—
233C22⋊C8C22×D6114yes—
234C4×C8—22no—
235#95—612no—
236#95—1224no—
237C2×Q8—22no—
238C2×Q8—22no—
239C2×Q8—614no—
240C2×Q8—1224no—
241C2×Q8—1222no—
242C2×Q8—2442no—
243C2×Q8—2442no—
244C2×Q8—2442no—
245C2×Q8#1175819014yes—
246C22×C4—1222no—
247C22×C4—1222no—
248C22×C4C2×D24411yescharacteristic
249C22×C4C2×D24412yes—
250C22×C4C2×D24412yes—
251C22×C4C2×D24411yescharacteristic
252C22×C4C23×D6111yescharacteristic
253C2×C8—24no—
254C4⋊C4—24no—
255C4⋊C4—22no—
256C4⋊C4—614no—
257C4⋊C4—1224no—
258C4⋊C4—1228no—
259C4⋊C4—1224no—
260C4⋊C4—1224no—
261C4⋊C4—1224no—
262C4⋊C4—1224no—
263C4⋊C4—1224no—
264C4⋊C4—1222no—
265C4⋊C4—1222no—
266C4⋊C4—1222no—
267C4⋊C4—1224no—
268C4⋊C4—2441no—
269C4⋊C4—2441no—
270C4⋊C4—2448no—
271C22⋊C4—1224no—
272C42—22no—
273C42—22no—
274C42—1228no—
275C42—1224no—
276C42—2442no—
277C42D4×D6112yes—
278C42D4×D6112yes—
279C23C22×D24411yescharacteristic
280Q8—28no—
281Q8—4884no—
282Q8—4884no—
283Q8—2444no—
284Q8—2444no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—1224no—
292C2×C4—1224no—
293C2×C4—1224no—
294C2×C4—2442no—
295C2×C4—2442no—
296C2×C4—2442no—
297C2×C4—2442no—
298C2×C4—2442no—
299C2×C4#1451974711yescharacteristic
300C2×C4#1451974711yescharacteristic
301C2×C4#1451974712yes—
302C2×C4C2×#1175819014yes—
303C2×C4C2×#1175819012yes—
304C2×C4#1451981012yes—
305C2×C4C2×D4×D6112yes—
306C8—44no—
307C22—21no—
308C22—21no—
309C22C2×#1451974711yescharacteristic
310C22C22×#1175819011yescharacteristic
311C22C2×#1451981011yescharacteristic
312C4—21no—
313C4—22no—
314C4—24no—
315C4—42no—
316C4—4882no—
317C4—2444no—
318C4—2444no—
319C4—2444no—
320C4#1683990314yes—
321C4#1683994712yes—
322C2—21no—
323C2—21no—
324C2C2×#1683990311yescharacteristic
325C2C2×#1683994711yescharacteristic
326C2#2145522611yescharacteristic
subgroupG/H
centerC22C2×#14519747
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1461C2
socleC22×C61C2×#120
prime radicalC23×C61C22×D4
hypercenter#1461D61
hypocenterC61#18410
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1461

Complements

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

NH ≅ G/Ntype
192. C61#18410semidirect

Maximal subgroups

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

subgroupindex
#214596292
#214569652
#214508042
#214448292
#214443192
C61×#14612
#1841061