Finite Group Databasebeta

← C61×#12273 #29515706

Subgroups — C61×#12273 #29515706

Order 15616.

364 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 70 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×#2586C211yesmaximal, characteristic
2C61×#2028C211yesmaximal, characteristic
3C61×#1611C211yesmaximal, characteristic
4C61×#1605C211yesmaximal, characteristic
5C61×#1354C211yesmaximal, characteristic
6C61×#1346C211yesmaximal, characteristic
7C61×#1319C211yesmaximal, characteristic
8C61×#544C2211yescharacteristic
9C61×#483—21no—
10C61×#451—21no—
11C61×#419—21no—
12C61×#398C2211yescharacteristic
13C61×#395—21no—
14C61×#395C2211yescharacteristic
15C61×#391—21no—
16C61×#391C2211yescharacteristic
17C61×#389—21no—
18C61×#387—21no—
19C61×#387—21no—
20C4×C4⋊C4×C61—21no—
21C61×#343C2211yescharacteristic
22C61×#339—21no—
23C61×#328—21no—
24C61×#328—21no—
25C61×#324C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×Q8×C61D411yescharacteristic
28C22×Q8×C61D411yescharacteristic
29C2×Q16×C61—41no—
30C2×M16×C61—21no—
31C4⋊Q8×C61—41no—
32#125×C61—41no—
33C22⋊Q8×C61—21no—
34C22⋊Q8×C61—21no—
35#117×C61—21no—
36C2×C4⋊C4×C61—21no—
37C2×C4⋊C4×C61—21no—
38C2×C4⋊C4×C61—21no—
39C2×C4⋊C4×C61—21no—
40C2×C4⋊C4×C61—21no—
41C2×C4⋊C4×C61D411yescharacteristic
42C2×C4⋊C4×C61C2311yescharacteristic
43C2×C42×C61—21no—
44C2×C42×C61—21no—
45C2×C42×C61D411yescharacteristic
46#106×C61—41no—
47#103×C61—41no—
48#103×C61—41no—
49#103×C61—41no—
50#103×C61—41no—
51C22⋊C8×C61—21no—
52C22⋊C8×C61—21no—
53#95×C61—21no—
54#95×C61—21no—
55#95×C61—21no—
56#95×C61—21no—
57#95×C61—21no—
58#95×C61—21no—
59#95×C61—21no—
60#95×C61D411yescharacteristic
61#95×C61D411yescharacteristic
62C2×Q8×C61—21no—
63C2×Q8×C61—21no—
64C2×Q8×C61—21no—
65C2×Q8×C61—21no—
66C2×Q8×C61—42no—
67C2×Q8×C61—41no—
68C2×Q8×C61—41no—
69C2×Q8×C61—41no—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61—21no—
74C22×C4×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79Q16×C61—82no—
80M16×C61—41no—
81M16×C61—41no—
82C2×C8×C61—41no—
83C2×C8×C61—41no—
84C2×C8×C61—41no—
85C4⋊C4×C61—24no—
86C4⋊C4×C61—21no—
87C4⋊C4×C61—21no—
88C4⋊C4×C61—21no—
89C4⋊C4×C61—21no—
90C4⋊C4×C61—41no—
91C4⋊C4×C61—42no—
92C4⋊C4×C61—41no—
93C4⋊C4×C61—41no—
94C4⋊C4×C61—41no—
95C4⋊C4×C61—41no—
96C4⋊C4×C61—41no—
97C4⋊C4×C61—81no—
98C4⋊C4×C61—81no—
99C22⋊C4×C61—41no—
100C42×C61—42no—
101C42×C61—41no—
102C42×C61—41no—
103C42×C61—81no—
104C23×C61#12011yescharacteristic
105Q8×C61—42no—
106Q8×C61—42no—
107Q8×C61—81no—
108Q8×C61—81no—
109Q8×C61—81no—
110Q8×C61—81no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—22no—
114C2×C4×C61—22no—
115C2×C4×C61—22no—
116C2×C4×C61—22no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
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—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61#13511yescharacteristic
138C2×C4×C61#13711yescharacteristic
139C8×C61—81no—
140C8×C61—81no—
141C8×C61—81no—
142#12273C6111yesmaximal, characteristic, direct product factor, Sylow
143C22×C61—21no—
144C22×C61—21no—
145C22×C61#45211yescharacteristic
146C22×C61#45511yescharacteristic
147C22×C61B(4,𝔽2)11yescharacteristic
148C4×C61—21no—
149C4×C61—21no—
150C4×C61—42no—
151C4×C61—42no—
152C4×C61—42no—
153C4×C61—41no—
154C4×C61—41no—
155C4×C61—42no—
156C4×C61—81no—
157C4×C61—81no—
158C4×C61—81no—
159C4×C61—81no—
160#2586C2×C6111yescharacteristic
161#2028C2×C6111yescharacteristic
162#1611C2×C6111yescharacteristic
163#1605C2×C6111yescharacteristic
164#1354C2×C6111yescharacteristic
165#1346C2×C6111yescharacteristic
166#1319C2×C6111yescharacteristic
167C2×C61—21no—
168C2×C61—21no—
169C2×C61#160611yescharacteristic
170C2×C61#219711yescharacteristic
171C2×C61#220511yescharacteristic
172#544C22×C6111yescharacteristic
173#483—21no—
174#451—21no—
175#419—21no—
176#398C22×C6111yescharacteristic
177#395—21no—
178#395C22×C6111yescharacteristic
179#391—21no—
180#391C22×C6111yescharacteristic
181#389—21no—
182#387—21no—
183#387—21no—
184C4×C4⋊C4—21no—
185#343C22×C6111yescharacteristic
186#339—21no—
187#328—21no—
188#328—21no—
189#324C22×C6111yescharacteristic
190#324C22×C6111yescharacteristic
191C61#1227311yescharacteristic, direct product factor, Sylow
192C22×Q8D4×C6111yescharacteristic
193C22×Q8D4×C6111yescharacteristic
194C2×Q16—41no—
195C2×M16—21no—
196C4⋊Q8—41no—
197#125—41no—
198C22⋊Q8—21no—
199C22⋊Q8—21no—
200#117—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4D4×C6111yescharacteristic
207C2×C4⋊C4C23×C6111yescharacteristic
208C2×C42—21no—
209C2×C42—21no—
210C2×C42D4×C6111yescharacteristic
211#106—41no—
212#103—41no—
213#103—41no—
214#103—41no—
215#103—41no—
216C22⋊C8—21no—
217C22⋊C8—21no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95D4×C6111yescharacteristic
226#95D4×C6111yescharacteristic
227C2×Q8—21no—
228C2×Q8—21no—
229C2×Q8—21no—
230C2×Q8—21no—
231C2×Q8—42no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×Q8—41no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4C2×D4×C6111yescharacteristic
242C22×C4C2×D4×C6111yescharacteristic
243C22×C4C2×D4×C6111yescharacteristic
244Q16—82no—
245M16—41no—
246M16—41no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—41no—
250C4⋊C4—24no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—42no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—81no—
263C4⋊C4—81no—
264C22⋊C4—41no—
265C42—41no—
266C42—42no—
267C42—41no—
268C42—81no—
269C23#120×C6111yescharacteristic
270Q8—42no—
271Q8—42no—
272Q8—81no—
273Q8—81no—
274Q8—81no—
275Q8—81no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4#135×C6111yescharacteristic
303C2×C4#137×C6111yescharacteristic
304C8—81no—
305C8—81no—
306C8—81no—
307C22—21no—
308C22—21no—
309C22C61×#45211yescharacteristic
310C22C61×#45511yescharacteristic
311C22C61×B(4,𝔽2)11yescharacteristic
312C4—21no—
313C4—21no—
314C4—42no—
315C4—42no—
316C4—42no—
317C4—41no—
318C4—41no—
319C4—42no—
320C4—81no—
321C4—81no—
322C4—81no—
323C4—81no—
324C2—21no—
325C2—21no—
326C2C61×#160611yescharacteristic
327C2C61×#219711yescharacteristic
328C2C61×#220511yescharacteristic
subgroupG/H
center, socleC22×C61B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C61
prime radicalC23×C61#120
LCSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C23×C61 ◁ C2×C4⋊C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
142. #12273C61direct (N × H)
191. C61#12273direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#25862
C61×#20282
C61×#16112
C61×#16052
C61×#13542
C61×#13462
C61×#13192
#1227361