Finite Group Databasebeta

← C61×#11816 #29515249

Subgroups — C61×#11816 #29515249

Order 15616.

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

normal subgroups only

This group has 388 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×#2396C211yesmaximal, characteristic
2C61×#1822C211yesmaximal, characteristic
3C61×#1464C211yesmaximal, characteristic
4C61×#1354C212yesmaximal, complemented
5C61×#1353C212yesmaximal, complemented
6C2×C4×Q8×C61C411yescharacteristic
7C2×#117×C61C2211yescharacteristic
8C61×#432—21no—
9C61×#407—21no—
10C61×#400C2211yescharacteristic
11C61×#399C411yescharacteristic
12C61×#398—21no—
13C61×#396—21no—
14C61×#395C2211yescharacteristic
15C61×#393C411yescharacteristic
16C4×C4⋊C4×C61—21no—
17C4×C4⋊C4×C61C411yescharacteristic
18C4×C22⋊C4×C61—21no—
19C61×#343—21no—
20C61×#343C2212yes—
21C61×#324C2212yes—
22C61×#323—21no—
23C22×Q8×C61C2×C411yescharacteristic
24C23×C4×C61D411yescharacteristic
25C2×M16×C61—22no—
26C4×Q8×C61—41no—
27C4×Q8×C61—41no—
28#117×C61—41no—
29#117×C61—41no—
30C2×C4⋊C4×C61—21no—
31C2×C4⋊C4×C61—21no—
32C2×C4⋊C4×C61—21no—
33C2×C4⋊C4×C61—21no—
34C2×C4⋊C4×C61C2×C411yescharacteristic
35C2×C4⋊C4×C61D411yescharacteristic
36C2×C4⋊C4×C61C2311yescharacteristic
37C2×C22⋊C4×C61—21no—
38C2×C22⋊C4×C61—21no—
39C2×C22⋊C4×C61C2×C411yescharacteristic
40C2×C22⋊C4×C61D411yescharacteristic
41C2×C42×C61—21no—
42C2×C42×C61—21no—
43C2×C42×C61C2×C411yescharacteristic
44C2×C42×C61D411yescharacteristic
45C4⋊C8×C61—41no—
46C22⋊C8×C61—22no—
47C22⋊C8×C61—41no—
48C22⋊C8×C61—41no—
49#97×C61—41no—
50#95×C61—21no—
51#95×C61—21no—
52#95×C61—21no—
53#95×C61—21no—
54#95×C61C2×C411yescharacteristic
55#95×C61C2×C411yescharacteristic
56C24×C61C22⋊C411yescharacteristic
57C2×Q8×C61—42no—
58C2×Q8×C61—41no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—22no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—41no—
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22×C411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73M16×C61—42no—
74M16×C61—42no—
75C2×C8×C61—42no—
76C2×C8×C61—42no—
77C4⋊C4×C61—41no—
78C4⋊C4×C61—41no—
79C4⋊C4×C61—42no—
80C4⋊C4×C61—42no—
81C4⋊C4×C61—42no—
82C4⋊C4×C61—42no—
83C4⋊C4×C61—41no—
84C22⋊C4×C61—41no—
85C22⋊C4×C61—41no—
86C22⋊C4×C61—42no—
87C22⋊C4×C61—42no—
88C42×C61—21no—
89C42×C61—21no—
90C42×C61—21no—
91C42×C61—21no—
92C42×C61—42no—
93C42×C61—41no—
94C42×C61—41no—
95C23×C61—21no—
96C23×C61—21no—
97C23×C61—21no—
98C23×C61—41no—
99C23×C61—41no—
100C23×C61C2×C22⋊C411yescharacteristic
101Q8×C61—42no—
102Q8×C61—42no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—22no—
108C2×C4×C61—22no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—42no—
114C2×C4×C61—42no—
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—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61#9911yescharacteristic
130C2×C4×C61#9911yescharacteristic
131C2×C4×C61#13712yes—
132C8×C61—82no—
133C8×C61—82no—
134#11816C6111yesmaximal, characteristic, direct product factor, Sylow
135C22×C61—21no—
136C22×C61—21no—
137C22×C61—42no—
138C22×C61—41no—
139C22×C61—41no—
140C22×C61—41no—
141C22×C61—81no—
142C22×C61C2×#9911yescharacteristic
143C22×C61#41911yescharacteristic
144C22×C61#42111yescharacteristic
145C4×C61—22no—
146C4×C61—21no—
147C4×C61—21no—
148C4×C61—42no—
149C4×C61—41no—
150C4×C61—42no—
151C4×C61—41no—
152C4×C61—41no—
153C4×C61—41no—
154C4×C61—81no—
155C4×C61—81no—
156#2396C2×C6111yescharacteristic
157#1822C2×C6111yescharacteristic
158#1464C2×C6111yescharacteristic
159#1354C2×C6112yescomplemented
160#1353C2×C6112yescomplemented
161C2×C61—21no—
162C2×C61—21no—
163C2×C61—81no—
164C2×C61#151111yescharacteristic
165C2×C61#212011yescharacteristic
166C2×C61#213211yescharacteristic
167C2×C4×Q8C4×C6111yescharacteristic
168C2×#117C22×C6111yescharacteristic
169#432—21no—
170#407—21no—
171#400C22×C6111yescharacteristic
172#399C4×C6111yescharacteristic
173#398—21no—
174#396—21no—
175#395C22×C6111yescharacteristic
176#393C4×C6111yescharacteristic
177C4×C4⋊C4—21no—
178C4×C4⋊C4C4×C6111yescharacteristic
179C4×C22⋊C4—21no—
180#343—21no—
181#343C22×C6112yes—
182#324C22×C6112yes—
183#323—21no—
184C61#1181611yescharacteristic, direct product factor, Sylow
185C22×Q8C2×C4×C6111yescharacteristic
186C23×C4D4×C6111yescharacteristic
187C2×M16—22no—
188C4×Q8—41no—
189C4×Q8—41no—
190#117—41no—
191#117—41no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4C2×C4×C6111yescharacteristic
197C2×C4⋊C4D4×C6111yescharacteristic
198C2×C4⋊C4C23×C6111yescharacteristic
199C2×C22⋊C4—21no—
200C2×C22⋊C4—21no—
201C2×C22⋊C4C2×C4×C6111yescharacteristic
202C2×C22⋊C4D4×C6111yescharacteristic
203C2×C42—21no—
204C2×C42—21no—
205C2×C42C2×C4×C6111yescharacteristic
206C2×C42D4×C6111yescharacteristic
207C4⋊C8—41no—
208C22⋊C8—22no—
209C22⋊C8—41no—
210C22⋊C8—41no—
211#97—41no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95C2×C4×C6111yescharacteristic
217#95C2×C4×C6111yescharacteristic
218C24C22⋊C4×C6111yescharacteristic
219C2×Q8—42no—
220C2×Q8—41no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—22no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—41no—
229C22×C4C22⋊C4×C6111yescharacteristic
230C22×C4C22⋊C4×C6111yescharacteristic
231C22×C4C22⋊C4×C6111yescharacteristic
232C22×C4C22×C4×C6111yescharacteristic
233C22×C4C2×D4×C6111yescharacteristic
234C22×C4C2×D4×C6111yescharacteristic
235M16—42no—
236M16—42no—
237C2×C8—42no—
238C2×C8—42no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C4⋊C4—42no—
245C4⋊C4—42no—
246C22⋊C4—41no—
247C22⋊C4—41no—
248C22⋊C4—42no—
249C22⋊C4—42no—
250C42—21no—
251C42—21no—
252C42—21no—
253C42—21no—
254C42—42no—
255C42—41no—
256C42—41no—
257C23—21no—
258C23—21no—
259C23—21no—
260C23—41no—
261C23—41no—
262C23C2×C22⋊C4×C6111yescharacteristic
263Q8—42no—
264Q8—42no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
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—41no—
290C2×C4—41no—
291C2×C4#99×C6111yescharacteristic
292C2×C4#99×C6111yescharacteristic
293C2×C4#137×C6112yes—
294C8—82no—
295C8—82no—
296C22—21no—
297C22—21no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22—41no—
302C22—81no—
303C22C2×#99×C6111yescharacteristic
304C22C61×#41911yescharacteristic
305C22C61×#42111yescharacteristic
306C4—22no—
307C4—21no—
308C4—21no—
309C4—42no—
310C4—41no—
311C4—42no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—81no—
316C4—81no—
317C2—21no—
318C2—21no—
319C2—81no—
320C2C61×#151111yescharacteristic
321C2C61×#212011yescharacteristic
322C2C61×#213211yescharacteristic
subgroupG/H
center, socleC22×C61C2×#99
commutatorC22×C4C22×C4×C61
Frattini, cosocleC2×C4⋊C4C23×C61
prime radicalC24×C61C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ 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
4. C61×#1354C2semidirect
5. C61×#1353C2semidirect
134. #11816C61direct (N × H)
159. #1354C2×C61semidirect
160. #1353C2×C61semidirect
184. C61#11816direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#23962
C61×#18222
C61×#14642
C61×#13542
C61×#13532
#1181661