Finite Group Databasebeta

← #29581461

Subgroups — #29581461

Order 15616.

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

normal subgroups only

This group has 458 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#21457027C211yesmaximal, characteristic
2#21456361C211yesmaximal, characteristic
3#21451769C211yesmaximal, characteristic
4#21444422C211yesmaximal, characteristic
5#21444332C211yesmaximal, characteristic
6#21443711C211yesmaximal, characteristic
7C61×#1556C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9C2×#14519769C2211yescharacteristic
10#16840171—21no—
11#16840168—22no—
12#16840165—21no—
13#16840158—21no—
14#16840131—21no—
15#16840098—21no—
16#16840093—21no—
17#16840070—22no—
18#16839802—22no—
19C4×#11758194C2211yescharacteristic
20#16839700—22no—
21#16839700—22no—
22#16839669—21no—
23#16839669—21no—
24#16839608C2211yescharacteristic
25#16839503—22no—
26#16839500—22no—
27C2×C4⋊Q8×C61C2211yescharacteristic
28C61×#432C2211yescharacteristic
29C61×#432C2211yescharacteristic
30C61×#332—22no—
31C2×#11758194—21no—
32#14519777D411yescharacteristic
33#14519777D411yescharacteristic
34#14519769—21no—
35#14519769—21no—
36#14519769—21no—
37#14519769—21no—
38#14519769—21no—
39#14519756—21no—
40#14519756—21no—
41C4×Dic122—21no—
42C4×Dic122—21no—
43#14519736—21no—
44C2×C4⋊Dic61D411yescharacteristic
45C2×C4⋊Dic61D411yescharacteristic
46C2×#11758196—21no—
47C2×#11758196—21no—
48C2×C4×Dic61—21no—
49#14519711—22no—
50#14519710—24no—
51#14519709—22no—
52#14519708—24no—
53#14519702—22no—
54#14519702—22no—
55#14519688D412yes—
56C4×#92418—21no—
57#14519684—24no—
58#14519684—24no—
59#14519684—21no—
60#14519684D412yes—
61C22×Q8×C61—21no—
62C4⋊Q8×C61—21no—
63C4⋊Q8×C61—21no—
64C4⋊Q8×C61—21no—
65C4⋊Q8×C61—21no—
66C2×C4⋊C4×C61—21no—
67C2×C4⋊C4×C61D412yes—
68C2×C42×C61C2311yescharacteristic
69C4⋊C8×C61—21no—
70C4⋊C8×C61D412yes—
71C22⋊C8×C61—21no—
72C22⋊C8×C61—21no—
73#97×C61—21no—
74#97×C61—21no—
75C2×Q8×C61—44no—
76C2×Q8×C61—41no—
77C2×Q8×C61—41no—
78C22×C4×C61—22no—
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C22×Dic61—22no—
83C22×Dic61—21no—
84C22×Dic61—21no—
85C2×Dic122—21no—
86C2×Dic122—21no—
87C2×C8×C61—22no—
88C2×C8×C61—41no—
89C4⋊C4×C61—22no—
90C4⋊C4×C61—22no—
91C4⋊C4×C61—41no—
92C4⋊C4×C61—41no—
93C42×C61C2×D411yescharacteristic
94C42×C61C2×D411yescharacteristic
95C42×C61C2×D411yescharacteristic
96C42×C61#4111yescharacteristic
97C22⋊Dic61—41no—
98C4⋊Dic61—21no—
99C4⋊Dic61—21no—
100C4⋊Dic61—21no—
101C4⋊Dic61—21no—
102C4⋊Dic61—21no—
103C4⋊Dic61—21no—
104C4⋊Dic61—21no—
105C4⋊Dic61—21no—
106#11758196—41no—
107#11758196—41no—
108#11758196—41no—
109#11758196—41no—
110#11758196—41no—
111#11758196—41no—
112C4×Dic61—42no—
113C4×Dic61—41no—
114#11758194—24no—
115C2×#92418—22no—
116C23×C61#12011yescharacteristic
117Q8×C61—82no—
118Q8×C61—82no—
119C2×C4×C61—22no—
120C2×C4×C61—22no—
121C2×C4×C61—41no—
122C2×C4×C61—44no—
123C2×C4×C61—42no—
124C2×C4×C61#12011yescharacteristic
125C2×C4×C61#12011yescharacteristic
126C2×C4×C61#12111yescharacteristic
127C2×C4×C61#12111yescharacteristic
128C2×C4×C61#12111yescharacteristic
129C2×C4×C61#12711yescharacteristic
130C2×Dic61—42no—
131C2×Dic61—42no—
132C2×Dic61—42no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—42no—
138C2×Dic61—42no—
139Dic122—42no—
140Dic122—81no—
141C8×C61—42no—
142C8×C61—81no—
143#92418—24no—
144#10103—611nomaximal, Sylow
145C22×C61—21no—
146C22×C61—21no—
147C22×C61#39211yescharacteristic
148C22×C61#45612yes—
149C4×C61—21no—
150C4×C61—21no—
151C4×C61—21no—
152C4×C61—21no—
153C4×C61—21no—
154C4×C61—82no—
155C4×C61#45412yes—
156Dic61—82no—
157Dic61—81no—
158Dic61—81no—
159Dic61—81no—
160Dic61—81no—
161#3236—611no—
162#3165—611no—
163#2642—611no—
164#1556D6111yescharacteristic
165#1528—611no—
166#1506—611no—
167#1300—611no—
168C2×C61—22no—
169C2×C61#200311yescharacteristic
170C2×C61#200511yescharacteristic
171C2×C61#200911yescharacteristic
172#533—611no—
173C2×C4⋊Q8C2×D6111yescharacteristic
174C2×#125—611no—
175#501—1221no—
176#501—1222no—
177#500—1221no—
178#498—1221no—
179#491—1221no—
180#484—1221no—
181#483—1221no—
182#479—1222no—
183#432C2×D6111yescharacteristic
184#432C2×D6111yescharacteristic
185#428—1222no—
186C4×M16—611no—
187#400—1222no—
188#400—1222no—
189#391—1221no—
190#391—1221no—
191#376—611no—
192#332—22no—
193#330—1222no—
194#328—1222no—
195C61#1010311yescharacteristic, complemented, Sylow
196C22×Q8—21no—
197C2×M16—1221no—
198C4⋊Q8—21no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—611no—
203C4⋊Q8—611no—
204#125—1221no—
205#125—1221no—
206#125—1221no—
207#125—1221no—
208#125—1221no—
209C22⋊Q8—1221no—
210C22⋊Q8—1221no—
211C4×Q8—1221no—
212C4×Q8—1221no—
213#117—1221no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—611no—
216C2×C4⋊C4—611no—
217C2×C4⋊C4—1221no—
218C2×C4⋊C4—1221no—
219C2×C4⋊C4D24412yes—
220C2×C42—1221no—
221C2×C42C22×D6111yescharacteristic
222#107—1224no—
223#107—1222no—
224#106—1224no—
225#106—1222no—
226C4⋊C8—21no—
227C4⋊C8C22⋊D6112yes—
228#103—1222no—
229#103—1222no—
230C22⋊C8—21no—
231C22⋊C8—21no—
232#97—21no—
233#97—21no—
234#97—612no—
235C4×C8—1221no—
236#95—612no—
237#95—1224no—
238#95—1224no—
239#95—1221no—
240C2×Q8—44no—
241C2×Q8—41no—
242C2×Q8—41no—
243C2×Q8—1221no—
244C2×Q8—1221no—
245C22×C4—22no—
246C22×C4—1222no—
247C22×C4—1221no—
248C22×C4—1221no—
249C22×C4C2×D24411yescharacteristic
250C22×C4D4×D6111yescharacteristic
251C22×C4D4×D6111yescharacteristic
252M16—1224no—
253C2×C8—22no—
254C2×C8—41no—
255C2×C8—1222no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—1221no—
261C4⋊C4—1221no—
262C4⋊C4—1221no—
263C4⋊C4—1221no—
264C4⋊C4—1221no—
265C4⋊C4—1221no—
266C4⋊C4—1221no—
267C4⋊C4—1221no—
268C4⋊C4—2441no—
269C4⋊C4—2441no—
270C4⋊C4—2441no—
271C4⋊C4—2441no—
272C4⋊C4—2441no—
273C4⋊C4—2441no—
274C22⋊C4—2441no—
275C42—2442no—
276C42—2441no—
277C42#1175822211yescharacteristic
278C42D4×D6111yescharacteristic
279C42D4×D6111yescharacteristic
280C42C2×C22⋊D6111yescharacteristic
281C23#1451974711yescharacteristic
282Q8—82no—
283Q8—82no—
284Q8—4881no—
285Q8—2442no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—41no—
289C2×C4—44no—
290C2×C4—42no—
291C2×C4—2442no—
292C2×C4—2442no—
293C2×C4—2442no—
294C2×C4—2442no—
295C2×C4—2442no—
296C2×C4—2441no—
297C2×C4—2441no—
298C2×C4—2441no—
299C2×C4—2441no—
300C2×C4#1451974511yescharacteristic
301C2×C4#1451974711yescharacteristic
302C2×C4#1451975011yescharacteristic
303C2×C4#1451975011yescharacteristic
304C2×C4#1451975111yescharacteristic
305C2×C4#1451977311yescharacteristic
306C8—42no—
307C8—81no—
308C8—1224no—
309C22—21no—
310C22—21no—
311C22#1683967111yescharacteristic
312C22#1683994712yes—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—82no—
319C4—4882no—
320C4—4881no—
321C4—4881no—
322C4—4881no—
323C4—4881no—
324C4#1683993312yes—
325C2—22no—
326C2#2144684211yescharacteristic
327C2#2144685711yescharacteristic
328C2#2144688111yescharacteristic
subgroupG/H
centerC22#16839671
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1556C2
socleC22×C61#392
prime radicalC23×C61#120
hypercenter#1556D61
hypocenterC61#10103
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1556

Complements

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

NH ≅ G/Ntype
195. C61#10103semidirect

Maximal subgroups

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

subgroupindex
#214570272
#214563612
#214517692
#214444222
#214443322
#214437112
C61×#15562
#1010361