Finite Group Databasebeta

← #29592964

Subgroups — #29592964

Order 15616.

350 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 55 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#21453620C211yesmaximal, characteristic
2#21447161C211yesmaximal, characteristic
3#21444827C211yesmaximal, characteristic
4#21443849C211yesmaximal, characteristic
5#21443826C211yesmaximal, characteristic
6#21443764C211yesmaximal, characteristic
7C61×#1605C211yesmaximal, characteristic
8#16840090—21no—
9#16839805—21no—
10#16839695—21no—
11#16839692C2211yescharacteristic
12#16839681—21no—
13#16839659—21no—
14#16839658—21no—
15#16839647—21no—
16#16839645—21no—
17#16839631C2211yescharacteristic
18#16839531C2211yescharacteristic
19#16839521—21no—
20#16839499—21no—
21#16839488C2211yescharacteristic
22C61×#544C2211yescharacteristic
23C61×#451—21no—
24C61×#395C2211yescharacteristic
25C61×#328—21no—
26C61×#324C2211yescharacteristic
27C2×#11758194—21no—
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61D411yescharacteristic
30C2×C4⋊Dic61D411yescharacteristic
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×#11758196—21no—
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×C4×Dic61—21no—
37C2×C4×Dic61D411yescharacteristic
38#14519710—41no—
39#14519708—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
49C22×Q8×C61D411yescharacteristic
50C2×Q16×C61—41no—
51C4⋊Q8×C61—41no—
52#125×C61—41no—
53C22⋊Q8×C61—21no—
54C22⋊Q8×C61—21no—
55#117×C61—21no—
56C2×C4⋊C4×C61—21no—
57C2×C4⋊C4×C61C2311yescharacteristic
58#103×C61—41no—
59C22⋊C8×C61—21no—
60#95×C61—21no—
61#95×C61D411yescharacteristic
62C2×Q8×C61—21no—
63C2×Q8×C61—21no—
64C2×Q8×C61—41no—
65C2×Q8×C61—81no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75Q16×C61—82no—
76C2×C8×C61—41no—
77C4⋊C4×C61—21no—
78C4⋊C4×C61—21no—
79C4⋊C4×C61—21no—
80C4⋊C4×C61—21no—
81C4⋊C4×C61—41no—
82C4⋊C4×C61—41no—
83C4⋊C4×C61—41no—
84C4⋊C4×C61—81no—
85C22⋊C4×C61—41no—
86C42×C61—41no—
87C4⋊Dic61—24no—
88C4⋊Dic61—41no—
89C4⋊Dic61—41no—
90#11758196—41no—
91#11758196—41no—
92#11758196—81no—
93#11758196—81no—
94#11758196—81no—
95#11758196—81no—
96C4×Dic61—21no—
97C4×Dic61—21no—
98C4×Dic61—81no—
99#11758194—22no—
100#11758194—41no—
101C2×#92418—41no—
102C2×#92418—41no—
103C23×C61#12011yescharacteristic
104Q8×C61—42no—
105Q8×C61—81no—
106Q8×C61—81no—
107Q8×C61—81no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—22no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61#13511yescharacteristic
123C2×C4×C61#13711yescharacteristic
124C2×Dic61—22no—
125C2×Dic61—22no—
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—
136C8×C61—81no—
137#92418—42no—
138#92418—81no—
139#12240—611nomaximal, Sylow
140C22×C61—21no—
141C22×C61—21no—
142C22×C61#45211yescharacteristic
143C22×C61#45611yescharacteristic
144C22×C61B(4,𝔽2)11yescharacteristic
145C4×C61—21no—
146C4×C61—21no—
147C4×C61—42no—
148C4×C61—41no—
149C4×C61—41no—
150C4×C61—81no—
151C4×C61—81no—
152C4×C61—81no—
153Dic61—42no—
154Dic61—42no—
155Dic61—81no—
156Dic61—81no—
157#2792—611no—
158#2060—611no—
159#1611—611no—
160#1605D6111yescharacteristic
161#1354—611no—
162#1346—611no—
163#1325—611no—
164C2×C61—21no—
165C2×C61—21no—
166C2×C61#160311yescharacteristic
167C2×C61#220011yescharacteristic
168C2×C61#220511yescharacteristic
169#544C2×D6111yescharacteristic
170#483—1221no—
171#451—21no—
172#428—1221no—
173#398—611no—
174#398—1221no—
175#395—1221no—
176#395C2×D6111yescharacteristic
177#389—1221no—
178#389—1221no—
179#387—1221no—
180#387—1221no—
181#384—611no—
182#343—611no—
183#339—1221no—
184#328—21no—
185#328—1221no—
186#324—611no—
187#324C2×D6111yescharacteristic
188C61#1224011yescharacteristic, complemented, Sylow
189C22×Q8C22⋊D6111yescharacteristic
190C2×Q16—41no—
191C2×M16—1221no—
192C4⋊Q8—41no—
193#125—41no—
194C22⋊Q8—21no—
195C22⋊Q8—21no—
196#117—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—611no—
199C2×C4⋊C4—611no—
200C2×C4⋊C4—1221no—
201C2×C4⋊C4—1221no—
202C2×C4⋊C4—1221no—
203C2×C4⋊C4—1221no—
204C2×C4⋊C4—1221no—
205C2×C4⋊C4—1221no—
206C2×C4⋊C4C22×D6111yescharacteristic
207C2×C42—611no—
208C2×C42—1221no—
209#107—2441no—
210#106—2441no—
211#106—2441no—
212#103—41no—
213#103—2441no—
214C22⋊C8—21no—
215C22⋊C8—1221no—
216#95—21no—
217#95—611no—
218#95—1221no—
219#95—1221no—
220#95—1221no—
221#95—1221no—
222#95—1221no—
223#95C22⋊D6111yescharacteristic
224C2×Q8—21no—
225C2×Q8—21no—
226C2×Q8—41no—
227C2×Q8—81no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—1221no—
231C22×C4—1221no—
232C22×C4—1221no—
233C22×C4—1221no—
234C22×C4D4×D6111yescharacteristic
235C22×C4D4×D6111yescharacteristic
236C22×C4C2×C22⋊D6111yescharacteristic
237Q16—82no—
238M16—1222no—
239M16—2441no—
240C2×C8—41no—
241C2×C8—2441no—
242C2×C8—2441no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—81no—
251C4⋊C4—1224no—
252C4⋊C4—4881no—
253C4⋊C4—4881no—
254C4⋊C4—4881no—
255C4⋊C4—4881no—
256C4⋊C4—2441no—
257C4⋊C4—2441no—
258C4⋊C4—2441no—
259C4⋊C4—2441no—
260C22⋊C4—41no—
261C42—41no—
262C42—1221no—
263C42—1221no—
264C42—4881no—
265C23#1451974511yescharacteristic
266Q8—42no—
267Q8—81no—
268Q8—81no—
269Q8—81no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—22no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—1222no—
285C2×C4—1222no—
286C2×C4—2441no—
287C2×C4—2441no—
288C2×C4—2441no—
289C2×C4—2441no—
290C2×C4—2441no—
291C2×C4—2441no—
292C2×C4—2441no—
293C2×C4—2441no—
294C2×C4—2441no—
295C2×C4—2441no—
296C2×C4#1451980011yescharacteristic
297C2×C4#1451980911yescharacteristic
298C8—81no—
299C8—4881no—
300C8—2442no—
301C22—21no—
302C22—21no—
303C22#1683992311yescharacteristic
304C22#1683994311yescharacteristic
305C22#1683994811yescharacteristic
306C4—21no—
307C4—21no—
308C4—42no—
309C4—41no—
310C4—41no—
311C4—81no—
312C4—81no—
313C4—81no—
314C4—4881no—
315C4—4881no—
316C4—2442no—
317C4—2442no—
318C2—21no—
319C2—21no—
320C2#2144478111yescharacteristic
321C2#2144782411yescharacteristic
322C2#2144784811yescharacteristic
subgroupG/H
centerC22#16839948
commutator, cosocleC2×C4⋊C4×C61C23
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1605C2
socleC22×C61B(4,𝔽2)
prime radicalC23×C61#120
hypercenter#1605D61
hypocenterC61#12240
LCSG ▷ C2×C4⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1605

Complements

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

NH ≅ G/Ntype
188. C61#12240semidirect

Maximal subgroups

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

subgroupindex
#214536202
#214471612
#214448272
#214438492
#214438262
#214437642
C61×#16052
#1224061