Finite Group Databasebeta

← #29593071

Subgroups — #29593071

Order 15616.

342 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 57 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#21451057C211yesmaximal, characteristic
2#21447161C211yesmaximal, characteristic
3#21444861C211yesmaximal, characteristic
4#21443847C211yesmaximal, characteristic
5#21443846C211yesmaximal, characteristic
6#21443764C211yesmaximal, characteristic
7C61×#1617C211yesmaximal, characteristic
8#16840095—21no—
9#16839805—21no—
10#16839704—21no—
11#16839701C2211yescharacteristic
12#16839659—21no—
13#16839657—21no—
14#16839631C2211yescharacteristic
15#16839626—21no—
16#16839626—21no—
17#16839613—21no—
18#16839531C2211yescharacteristic
19#16839521—21no—
20#16839499—21no—
21#16839488C2211yescharacteristic
22C61×#544C2211yescharacteristic
23C61×#484—21no—
24C61×#400C2211yescharacteristic
25C61×#328—21no—
26C61×#324C2211yescharacteristic
27C2×#11758194—21no—
28C2×C4⋊Dic61D411yescharacteristic
29C2×C4⋊Dic61D411yescharacteristic
30C2×#11758196—21no—
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×#11758196—21no—
34C2×#11758196—21no—
35C2×C4×Dic61—21no—
36C2×C4×Dic61—21no—
37C2×C4×Dic61D411yescharacteristic
38#14519710—41no—
39#14519710—41no—
40#14519708—41no—
41#14519701—41no—
42C22⋊#92418—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684D411yescharacteristic
49C4⋊Q8×C61—41no—
50#125×C61—41no—
51C22⋊Q8×C61—21no—
52C22⋊Q8×C61—21no—
53#117×C61—21no—
54C2×C4⋊C4×C61D411yescharacteristic
55C2×C4⋊C4×C61C2311yescharacteristic
56#107×C61—41no—
57#103×C61—41no—
58C22⋊C8×C61—21no—
59#95×C61—21no—
60#95×C61—21no—
61#95×C61D411yescharacteristic
62C2×Q8×C61—21no—
63C2×Q8×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61C2×D411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—21no—
73C2×C8×C61—41no—
74C4⋊C4×C61—21no—
75C4⋊C4×C61—21no—
76C4⋊C4×C61—21no—
77C4⋊C4×C61—21no—
78C4⋊C4×C61—41no—
79C4⋊C4×C61—41no—
80C4⋊C4×C61—41no—
81C4⋊C4×C61—41no—
82C22⋊C4×C61—41no—
83C42×C61—41no—
84C4⋊Dic61—41no—
85C4⋊Dic61—41no—
86#11758196—42no—
87#11758196—42no—
88#11758196—42no—
89#11758196—42no—
90#11758196—81no—
91C4×Dic61—21no—
92C4×Dic61—42no—
93C4×Dic61—42no—
94C4×Dic61Q1612yes—
95#11758194—22no—
96#11758194—41no—
97C2×#92418—41no—
98C2×#92418—41no—
99C23×C61#12011yescharacteristic
100Q8×C61—81no—
101Q8×C61—81no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61C2×Q1611yescharacteristic
117C2×C4×C61#13711yescharacteristic
118C2×Dic61—22no—
119C2×Dic61—22no—
120C2×Dic61—22no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C8×C61—81no—
131#92418—42no—
132#92418—81no—
133#12257—611nomaximal, Sylow
134C22×C61—21no—
135C22×C61—21no—
136C22×C61#45111yescharacteristic
137C22×C61#45611yescharacteristic
138C22×C61B(4,𝔽2)11yescharacteristic
139C4×C61—21no—
140C4×C61—21no—
141C4×C61—41no—
142C4×C61—41no—
143C4×C61—81no—
144C4×C61—81no—
145C4×C61—81no—
146C4×C61—81no—
147Dic61—24no—
148Dic61—81no—
149Dic61—81no—
150Dic61—81no—
151#2571—611no—
152#2060—611no—
153#1617—611no—
154#1617D6111yescharacteristic
155#1353—611no—
156#1353—611no—
157#1325—611no—
158C2×C61—21no—
159C2×C61—21no—
160C2×C61#160511yescharacteristic
161C2×C61#219811yescharacteristic
162C2×C61#220411yescharacteristic
163#544C2×D6111yescharacteristic
164#484—21no—
165#484—1221no—
166#428—1221no—
167#400—611no—
168#400—1221no—
169#400C2×D6111yescharacteristic
170#389—1221no—
171#389—1221no—
172#384—611no—
173#382—1221no—
174#382—1221no—
175C4×C4⋊C4—1221no—
176#343—611no—
177#339—1221no—
178#328—21no—
179#328—1221no—
180#324—611no—
181#324C2×D6111yescharacteristic
182C61#1225711yescharacteristic, complemented, Sylow
183C2×M16—1221no—
184C4⋊Q8—41no—
185#125—41no—
186C22⋊Q8—21no—
187C22⋊Q8—21no—
188#117—21no—
189C2×C4⋊C4—611no—
190C2×C4⋊C4—611no—
191C2×C4⋊C4—1221no—
192C2×C4⋊C4—1221no—
193C2×C4⋊C4—1221no—
194C2×C4⋊C4—1221no—
195C2×C4⋊C4—1221no—
196C2×C4⋊C4C22⋊D6111yescharacteristic
197C2×C4⋊C4C22×D6111yescharacteristic
198C2×C42—611no—
199C2×C42—1221no—
200C2×C42—1221no—
201#107—41no—
202#107—2441no—
203#107—2441no—
204#106—2441no—
205#103—41no—
206#103—2441no—
207C22⋊C8—21no—
208C22⋊C8—1221no—
209#95—21no—
210#95—21no—
211#95—611no—
212#95—1221no—
213#95—1221no—
214#95—1221no—
215#95—1221no—
216#95—1221no—
217#95C22⋊D6111yescharacteristic
218C2×Q8—21no—
219C2×Q8—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—1221no—
223C22×C4—1221no—
224C22×C4—1221no—
225C22×C4—1221no—
226C22×C4D4×D6111yescharacteristic
227C22×C4D4×D6111yescharacteristic
228C22×C4C2×C22⋊D6111yescharacteristic
229M16—1222no—
230M16—2441no—
231C2×C8—41no—
232C2×C8—2441no—
233C2×C8—2441no—
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—4881no—
243C4⋊C4—2441no—
244C4⋊C4—2441no—
245C4⋊C4—2442no—
246C4⋊C4—2442no—
247C4⋊C4—2442no—
248C4⋊C4—2442no—
249C22⋊C4—41no—
250C42—41no—
251C42—612no—
252C42—1221no—
253C42—2442no—
254C42—2442no—
255C23#1451974511yescharacteristic
256Q8—81no—
257Q8—81no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—1222no—
273C2×C4—1222no—
274C2×C4—1222no—
275C2×C4—2441no—
276C2×C4—2441no—
277C2×C4—2441no—
278C2×C4—2441no—
279C2×C4—2441no—
280C2×C4—2441no—
281C2×C4—2441no—
282C2×C4—2441no—
283C2×C4—2441no—
284C2×C4Q16×D6111yescharacteristic
285C2×C4#1451980911yescharacteristic
286C8—81no—
287C8—4881no—
288C8—2442no—
289C22—21no—
290C22—21no—
291C22#1683991611yescharacteristic
292C22#1683994311yescharacteristic
293C22#1683994811yescharacteristic
294C4—21no—
295C4—21no—
296C4—41no—
297C4—41no—
298C4—81no—
299C4—81no—
300C4—81no—
301C4—81no—
302C4—1224no—
303C4—4881no—
304C4—4881no—
305C4—4881no—
306C2—21no—
307C2—21no—
308C2#2144479111yescharacteristic
309C2#2144781311yescharacteristic
310C2#2144784311yescharacteristic
subgroupG/H
centerC22#16839948
commutator, cosocleC2×C4⋊C4×C61C23
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1617C2
socleC22×C61B(4,𝔽2)
prime radicalC23×C61#120
hypercenter#1617D61
hypocenterC61#12257
LCSG ▷ C2×C4⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1617

Complements

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

NH ≅ G/Ntype
182. C61#12257semidirect

Maximal subgroups

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

subgroupindex
#214510572
#214471612
#214448612
#214438472
#214438462
#214437642
C61×#16172
#1225761