Finite Group Databasebeta

← C61×#11890 #29515323

Subgroups — C61×#11890 #29515323

Order 15616.

416 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3050C211yesmaximal, characteristic
2C61×#2112C211yesmaximal, characteristic, complemented
3C61×#1808C211yesmaximal, characteristic, complemented
4C61×#1348C212yesmaximal, complemented
5C61×#1347C212yesmaximal, complemented
6C2×#135×C61C411yescharacteristic, complemented
7C23×C8×C61C2211yescharacteristic
8C61×#525—21no—
9C2×M32×C61—21no—
10C61×#467C411yescharacteristic, complemented
11C61×#467C2211yescharacteristic
12C61×#466C411yescharacteristic, complemented
13C61×#466C2211yescharacteristic
14C61×#465—21no—
15C61×#465—21no—
16C61×#427C411yescharacteristic, complemented
17C2×#107×C61—21no—
18C61×#416—21no—
19C61×#380—21no—
20C61×C22⋊C16—21no—
21C61×C22⋊C16C2212yes—
22C61×#340C2212yes—
23C2×#41×C61—21no—
24C23×C4×C61D411yescharacteristic
25#135×C61—42no—
26C2×Q16×C61C2×C411yescharacteristic
27C2×SD16×C61—21no—
28C2×D8×C61C2×C411yescharacteristic
29C22×C8×C61—42no—
30C22×C8×C61C2×C411yescharacteristic
31C22×C8×C61C2×C411yescharacteristic
32C22×C8×C61D411yescharacteristic
33C22×C8×C61D411yescharacteristic
34C22×C8×C61D411yescharacteristic
35C22×C8×C61C2311yescharacteristic
36#123×C61—41no—
37C22⋊Q8×C61—21no—
38C22⋊Q8×C61—21no—
39#121×C61—21no—
40#121×C61—21no—
41#120×C61—41no—
42C4×D4×C61—41no—
43C4×D4×C61—41no—
44#117×C61—21no—
45C2×C4⋊C4×C61—22no—
46C2×C22⋊C4×C61—41no—
47M32×C61—42no—
48C2×C16×C61—22no—
49#107×C61—42no—
50#107×C61C2×C411yescharacteristic
51#107×C61C2×C411yescharacteristic
52#106×C61—21no—
53#103×C61—21no—
54#103×C61—21no—
55#102×C61—21no—
56#102×C61—21no—
57#95×C61—41no—
58C24×C61D811yescharacteristic
59#41×C61—42no—
60#41×C61—42no—
61C2×Q8×C61—21no—
62C2×D4×C61—21no—
63C2×D4×C61—41no—
64C2×D4×C61—41no—
65C2×D4×C61—41no—
66C22×C4×C61—41no—
67C22×C4×C61—41no—
68C22×C4×C61—41no—
69C22×C4×C61—42no—
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61D811yescharacteristic
73C22×C4×C61SD1611yescharacteristic
74C22×C4×C61SD1611yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76Q16×C61—41no—
77SD16×C61—42no—
78D8×C61—41no—
79C2×C8×C61—22no—
80C2×C8×C61—22no—
81C2×C8×C61—22no—
82C2×C8×C61—41no—
83C2×C8×C61—41no—
84C2×C8×C61—41no—
85C2×C8×C61C22⋊C411yescharacteristic
86C2×C8×C61C22⋊C411yescharacteristic
87C2×C8×C61C22×C411yescharacteristic
88C2×C8×C61C2×D411yescharacteristic
89C4⋊C4×C61—21no—
90C4⋊C4×C61—21no—
91C4⋊C4×C61—42no—
92C4⋊C4×C61—42no—
93C4⋊C4×C61—41no—
94C4⋊C4×C61—41no—
95C22⋊C4×C61—41no—
96C22⋊C4×C61—41no—
97C22⋊C4×C61—41no—
98C22⋊C4×C61—41no—
99C22⋊C4×C61—41no—
100C22⋊C4×C61—82no—
101C42×C61—41no—
102C16×C61—42no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61—41no—
106C23×C61—41no—
107C23×C61—41no—
108C23×C61#10211yescharacteristic
109C23×C61#10211yescharacteristic
110C23×C61C2×D811yescharacteristic
111Q8×C61—41no—
112Q8×C61—41no—
113D4×C61—41no—
114D4×C61—41no—
115D4×C61—82no—
116D4×C61—82no—
117D4×C61—81no—
118D4×C61—81no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
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—82no—
132C2×C4×C61—82no—
133C2×C4×C61—82no—
134C2×C4×C61—82no—
135C2×C4×C61#10211yescharacteristic
136C2×C4×C61#10211yescharacteristic
137C2×C4×C61C2×C22⋊C411yescharacteristic
138C2×C4×C61C2×SD1611yescharacteristic
139C8×C61—21no—
140C8×C61—21no—
141C8×C61—21no—
142C8×C61#9912yes—
143#11890C6111yesmaximal, characteristic, direct product factor, Sylow
144C22×C61—21no—
145C22×C61—21no—
146C22×C61—21no—
147C22×C61—21no—
148C22×C61—21no—
149C22×C61—21no—
150C22×C61—21no—
151C22×C61—21no—
152C22×C61—42no—
153C22×C61—42no—
154C22×C61—81no—
155C22×C61—81no—
156C22×C61—81no—
157C22×C61C2×#10211yescharacteristic
158C22×C61#50911yescharacteristic
159C22×C61#51011yescharacteristic
160C4×C61—21no—
161C4×C61—21no—
162C4×C61—21no—
163C4×C61—81no—
164C4×C61—81no—
165C4×C61—81no—
166C4×C61—162no—
167C4×C61C2×#9911yescharacteristic
168C4×C61#42111yescharacteristic
169#3050C2×C6111yescharacteristic
170#2112C2×C6111yescharacteristic, complemented
171#1808C2×C6111yescharacteristic, complemented
172#1348C2×C6112yescomplemented
173#1347C2×C6112yescomplemented
174C2×C61—21no—
175C2×C61—21no—
176C2×C61—41no—
177C2×C61—41no—
178C2×C61—161no—
179C2×C61#151911yescharacteristic
180C2×C61#213911yescharacteristic
181C2×C61#214511yescharacteristic
182C2×#135C4×C6111yescharacteristic, complemented
183C23×C8C22×C6111yescharacteristic
184#525—21no—
185C2×M32—21no—
186#467C4×C6111yescharacteristic, complemented
187#467C22×C6111yescharacteristic
188#466C4×C6111yescharacteristic, complemented
189#466C22×C6111yescharacteristic
190#465—21no—
191#465—21no—
192#427C4×C6111yescharacteristic, complemented
193C2×#107—21no—
194#416—21no—
195#380—21no—
196C22⋊C16—21no—
197C22⋊C16C22×C6112yes—
198#340C22×C6112yes—
199C61#1189011yescharacteristic, direct product factor, Sylow
200C2×#41—21no—
201C23×C4D4×C6111yescharacteristic
202#135—42no—
203C2×Q16C2×C4×C6111yescharacteristic
204C2×SD16—21no—
205C2×D8C2×C4×C6111yescharacteristic
206C22×C8—42no—
207C22×C8C2×C4×C6111yescharacteristic
208C22×C8C2×C4×C6111yescharacteristic
209C22×C8D4×C6111yescharacteristic
210C22×C8D4×C6111yescharacteristic
211C22×C8D4×C6111yescharacteristic
212C22×C8C23×C6111yescharacteristic
213#123—41no—
214C22⋊Q8—21no—
215C22⋊Q8—21no—
216#121—21no—
217#121—21no—
218#120—41no—
219C4×D4—41no—
220C4×D4—41no—
221#117—21no—
222C2×C4⋊C4—22no—
223C2×C22⋊C4—41no—
224M32—42no—
225C2×C16—22no—
226#107—42no—
227#107C2×C4×C6111yescharacteristic
228#107C2×C4×C6111yescharacteristic
229#106—21no—
230#103—21no—
231#103—21no—
232#102—21no—
233#102—21no—
234#95—41no—
235C24D8×C6111yescharacteristic
236#41—42no—
237#41—42no—
238C2×Q8—21no—
239C2×D4—21no—
240C2×D4—41no—
241C2×D4—41no—
242C2×D4—41no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—42no—
247C22×C4C22⋊C4×C6111yescharacteristic
248C22×C4C22⋊C4×C6111yescharacteristic
249C22×C4D8×C6111yescharacteristic
250C22×C4SD16×C6111yescharacteristic
251C22×C4SD16×C6111yescharacteristic
252C22×C4C2×D4×C6111yescharacteristic
253Q16—41no—
254SD16—42no—
255D8—41no—
256C2×C8—22no—
257C2×C8—22no—
258C2×C8—22no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8C22⋊C4×C6111yescharacteristic
263C2×C8C22⋊C4×C6111yescharacteristic
264C2×C8C22×C4×C6111yescharacteristic
265C2×C8C2×D4×C6111yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—42no—
269C4⋊C4—42no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—82no—
278C42—41no—
279C16—42no—
280C23—21no—
281C23—21no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23#102×C6111yescharacteristic
286C23#102×C6111yescharacteristic
287C23C2×D8×C6111yescharacteristic
288Q8—41no—
289Q8—41no—
290D4—41no—
291D4—41no—
292D4—82no—
293D4—82no—
294D4—81no—
295D4—81no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—82no—
309C2×C4—82no—
310C2×C4—82no—
311C2×C4—82no—
312C2×C4#102×C6111yescharacteristic
313C2×C4#102×C6111yescharacteristic
314C2×C4C2×C22⋊C4×C6111yescharacteristic
315C2×C4C2×SD16×C6111yescharacteristic
316C8—21no—
317C8—21no—
318C8—21no—
319C8#99×C6112yes—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—42no—
329C22—42no—
330C22—81no—
331C22—81no—
332C22—81no—
333C22C2×#102×C6111yescharacteristic
334C22C61×#50911yescharacteristic
335C22C61×#51011yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—81no—
340C4—81no—
341C4—81no—
342C4—162no—
343C4C2×#99×C6111yescharacteristic
344C4C61×#42111yescharacteristic
345C2—21no—
346C2—21no—
347C2—41no—
348C2—41no—
349C2—161no—
350C2C61×#151911yescharacteristic
351C2C61×#213911yescharacteristic
352C2C61×#214511yescharacteristic
subgroupG/H
center, socleC22×C61C2×#102
commutatorC2×C8C22×C4×C61
Frattini, cosocleC22×C8C23×C61
prime radicalC61×#3050C2
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C23×C4×C61 ◁ C23×C8×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#2112C2semidirect
3. C61×#1808C2semidirect
4. C61×#1348C2semidirect
5. C61×#1347C2semidirect
6. C2×#135×C61C4semidirect
10. C61×#467C4semidirect
12. C61×#466C4semidirect
16. C61×#427C4semidirect
143. #11890C61direct (N × H)
170. #2112C2×C61semidirect
171. #1808C2×C61semidirect
172. #1348C2×C61semidirect
173. #1347C2×C61semidirect
182. C2×#135C4×C61semidirect
186. #467C4×C61semidirect
188. #466C4×C61semidirect
192. #427C4×C61semidirect
199. C61#11890direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#30502
C61×#21122
C61×#18082
C61×#13482
C61×#13472
#1189061