Finite Group Databasebeta

← C61×#11544 #29514977

Subgroups — C61×#11544 #29514977

Order 15616.

380 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 98 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
1C61×#2484C211yesmaximal, characteristic
2C61×#1464C211yesmaximal, characteristic
3C61×#1458C211yesmaximal, characteristic
4C61×#1326C212yesmaximal
5C61×#1317C212yesmaximal
6C2×#117×C61C2211yescharacteristic
7C22×C4⋊C4×C61C411yescharacteristic
8C61×#432—21no—
9C61×#431—21no—
10C61×#400—21no—
11C61×#398—21no—
12C61×#387—21no—
13C61×#387—21no—
14C61×#385C411yescharacteristic
15C61×#385C2211yescharacteristic
16C61×#381C411yescharacteristic
17C61×#381C411yescharacteristic
18C61×#381C2211yescharacteristic
19C61×#324—21no—
20C61×#324—21no—
21C61×#323C2212yes—
22C61×#323C2212yes—
23C23×C4×C61C2×C411yescharacteristic
24C23×C4×C61C2×C411yescharacteristic
25C23×C4×C61C2×C411yescharacteristic
26#117×C61—41no—
27#117×C61—41no—
28C2×C4⋊C4×C61—21no—
29C2×C4⋊C4×C61—21no—
30C2×C4⋊C4×C61—21no—
31C2×C4⋊C4×C61—21no—
32C2×C4⋊C4×C61—41no—
33C2×C4⋊C4×C61—41no—
34C2×C4⋊C4×C61D411yescharacteristic
35C2×C4⋊C4×C61D411yescharacteristic
36C2×C22⋊C4×C61C2×C411yescharacteristic
37C2×C22⋊C4×C61C2×C411yescharacteristic
38C2×C22⋊C4×C61C2×C411yescharacteristic
39C2×C22⋊C4×C61C2311yescharacteristic
40C2×C42×C61D411yescharacteristic
41C2×C42×C61D411yescharacteristic
42C4⋊C8×C61—41no—
43C4⋊C8×C61—41no—
44C22⋊C8×C61—22no—
45C22⋊C8×C61—22no—
46#97×C61—41no—
47C4×C8×C61—41no—
48#95×C61—21no—
49#95×C61—21no—
50#95×C61—21no—
51#95×C61—21no—
52#95×C61—21no—
53#95×C61—21no—
54#95×C61—21no—
55#95×C61—21no—
56C24×C61C22×C411yescharacteristic
57C22×C4×C61—21no—
58C22×C4×C61—22no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—22no—
65C22×C4×C61—41no—
66C22×C4×C61—42no—
67C22×C4×C61—41no—
68C22×C4×C61—41no—
69C22×C4×C61—41no—
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C2×C8×C61—42no—
77C2×C8×C61—42no—
78C4⋊C4×C61—41no—
79C4⋊C4×C61—41no—
80C4⋊C4×C61—42no—
81C4⋊C4×C61—42no—
82C4⋊C4×C61—42no—
83C4⋊C4×C61—41no—
84C4⋊C4×C61—41no—
85C22⋊C4×C61—22no—
86C22⋊C4×C61—41no—
87C22⋊C4×C61—41no—
88C22⋊C4×C61—41no—
89C42×C61—21no—
90C42×C61—21no—
91C42×C61—21no—
92C42×C61—21no—
93C23×C61—21no—
94C23×C61—21no—
95C23×C61—41no—
96C23×C61—41no—
97C23×C61C2×C22⋊C411yescharacteristic
98C23×C61#13112yes—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—22no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—42no—
110C2×C4×C61—42no—
111C2×C4×C61—41no—
112C2×C4×C61—42no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—42no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—82no—
129C2×C4×C61#9911yescharacteristic
130C2×C4×C61#9911yescharacteristic
131C8×C61—82no—
132C8×C61—82no—
133#11544C6111yesmaximal, characteristic, direct product factor, Sylow
134C22×C61—21no—
135C22×C61—21no—
136C22×C61—22no—
137C22×C61—42no—
138C22×C61—42no—
139C22×C61—41no—
140C22×C61—41no—
141C22×C61#40811yescharacteristic
142C22×C61C2×#9911yescharacteristic
143C22×C61#41311yescharacteristic
144C4×C61—21no—
145C4×C61—21no—
146C4×C61—41no—
147C4×C61—41no—
148C4×C61—42no—
149C4×C61—41no—
150C4×C61—41no—
151C4×C61—41no—
152C4×C61—81no—
153C4×C61—81no—
154C4×C61—81no—
155#2484C2×C6111yescharacteristic
156#1464C2×C6111yescharacteristic
157#1458C2×C6111yescharacteristic
158#1326C2×C6112yes—
159#1317C2×C6112yes—
160C2×C61—21no—
161C2×C61—21no—
162C2×C61—42no—
163C2×C61#146811yescharacteristic
164C2×C61#212011yescharacteristic
165C2×C61#212311yescharacteristic
166C2×#117C22×C6111yescharacteristic
167C22×C4⋊C4C4×C6111yescharacteristic
168#432—21no—
169#431—21no—
170#400—21no—
171#398—21no—
172#387—21no—
173#387—21no—
174#385C4×C6111yescharacteristic
175#385C22×C6111yescharacteristic
176#381C4×C6111yescharacteristic
177#381C4×C6111yescharacteristic
178#381C22×C6111yescharacteristic
179#324—21no—
180#324—21no—
181#323C22×C6112yes—
182#323C22×C6112yes—
183C61#1154411yescharacteristic, direct product factor, Sylow
184C23×C4C2×C4×C6111yescharacteristic
185C23×C4C2×C4×C6111yescharacteristic
186C23×C4C2×C4×C6111yescharacteristic
187#117—41no—
188#117—41no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—41no—
194C2×C4⋊C4—41no—
195C2×C4⋊C4D4×C6111yescharacteristic
196C2×C4⋊C4D4×C6111yescharacteristic
197C2×C22⋊C4C2×C4×C6111yescharacteristic
198C2×C22⋊C4C2×C4×C6111yescharacteristic
199C2×C22⋊C4C2×C4×C6111yescharacteristic
200C2×C22⋊C4C23×C6111yescharacteristic
201C2×C42D4×C6111yescharacteristic
202C2×C42D4×C6111yescharacteristic
203C4⋊C8—41no—
204C4⋊C8—41no—
205C22⋊C8—22no—
206C22⋊C8—22no—
207#97—41no—
208C4×C8—41no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217C24C22×C4×C6111yescharacteristic
218C22×C4—21no—
219C22×C4—22no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—22no—
226C22×C4—41no—
227C22×C4—42no—
228C22×C4—41no—
229C22×C4—41no—
230C22×C4—41no—
231C22×C4C22⋊C4×C6111yescharacteristic
232C22×C4C22⋊C4×C6111yescharacteristic
233C22×C4C22⋊C4×C6111yescharacteristic
234C22×C4C22⋊C4×C6111yescharacteristic
235C22×C4C2×D4×C6111yescharacteristic
236C22×C4C2×D4×C6111yescharacteristic
237C2×C8—42no—
238C2×C8—42no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—42no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C22⋊C4—22no—
247C22⋊C4—41no—
248C22⋊C4—41no—
249C22⋊C4—41no—
250C42—21no—
251C42—21no—
252C42—21no—
253C42—21no—
254C23—21no—
255C23—21no—
256C23—41no—
257C23—41no—
258C23C2×C22⋊C4×C6111yescharacteristic
259C23#131×C6112yes—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—41no—
273C2×C4—42no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—82no—
290C2×C4#99×C6111yescharacteristic
291C2×C4#99×C6111yescharacteristic
292C8—82no—
293C8—82no—
294C22—21no—
295C22—21no—
296C22—22no—
297C22—42no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22C61×#40811yescharacteristic
302C22C2×#99×C6111yescharacteristic
303C22C61×#41311yescharacteristic
304C4—21no—
305C4—21no—
306C4—41no—
307C4—41no—
308C4—42no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—81no—
313C4—81no—
314C4—81no—
315C2—21no—
316C2—21no—
317C2—42no—
318C2C61×#146811yescharacteristic
319C2C61×#212011yescharacteristic
320C2C61×#212311yescharacteristic
subgroupG/H
center, socleC22×C61C2×#99
commutatorC24C22×C4×C61
Frattini, cosocleC2×C22⋊C4C23×C61
prime radicalC24×C61C22×C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C22×C4×C61 ◁ C2×#117×C61 ◁ G

Complements

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

NH ≅ G/Ntype
133. #11544C61direct (N × H)
183. C61#11544direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#24842
C61×#14642
C61×#14582
C61×#13262
C61×#13172
#1154461