Finite Group Databasebeta

← C61×#9761 #29513194

Subgroups — C61×#9761 #29513194

Order 15616.

440 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3167C211yesmaximal, characteristic
2C61×#1726C211yesmaximal, characteristic, complemented
3C61×#1568C211yesmaximal, characteristic, complemented
4C61×#1531C211yesmaximal, characteristic, complemented
5C61×#1530C211yesmaximal, characteristic
6C61×#1506C211yesmaximal, characteristic, complemented
7C61×#1505C211yesmaximal, characteristic
8C61×#533C2211yescharacteristic
9C61×#532C2211yescharacteristic
10C61×#498C411yescharacteristic, complemented
11C61×#492C411yescharacteristic, complemented
12C61×#487C411yescharacteristic, complemented
13C61×#486C411yescharacteristic, complemented
14C61×#465—21no—
15C61×#465—21no—
16C4×SD16×C61—21no—
17C4×SD16×C61—21no—
18C61×#432C2211yescharacteristic
19C61×#432C2211yescharacteristic
20C2×#97×C61—21no—
21C2×#97×C61C2211yescharacteristic
22C2×C4×C8×C61—21no—
23C2×C4×C8×C61C2211yescharacteristic
24C61×#376C2211yescharacteristic
25C61×#335—21no—
26C61×#334—21no—
27C61×#330—22no—
28C61×#329—22no—
29C61×#328—22no—
30C61×#327—22no—
31C2×#41×C61—21no—
32C2×SD16×C61—21no—
33C2×SD16×C61—21no—
34C22×C8×C61—21no—
35C22×C8×C61D411yescharacteristic
36C22×C8×C61D411yescharacteristic
37C4⋊Q8×C61C2×C411yescharacteristic
38C4⋊Q8×C61C2×C411yescharacteristic
39C4⋊Q8×C61C2×C411yescharacteristic
40#127×C61C2×C411yescharacteristic
41#125×C61—21no—
42#124×C61—21no—
43C22⋊Q8×C61—21no—
44C22⋊Q8×C61—21no—
45#121×C61—21no—
46#121×C61—21no—
47C4×Q8×C61—21no—
48C4×Q8×C61—21no—
49C4×D4×C61—21no—
50C4×D4×C61—21no—
51#117×C61—21no—
52C2×C42×C61—21no—
53C2×C42×C61C2311yescharacteristic
54#106×C61—21no—
55#106×C61—21no—
56C4⋊C8×C61—21no—
57C4⋊C8×C61—21no—
58#103×C61—21no—
59#103×C61—21no—
60#102×C61—21no—
61#102×C61—21no—
62C22⋊C8×C61—21no—
63C22⋊C8×C61—21no—
64#97×C61—24no—
65#97×C61—21no—
66#97×C61—21no—
67#97×C61—21no—
68#97×C61D412yes—
69C4×C8×C61—24no—
70C4×C8×C61C2×C411yescharacteristic
71C4×C8×C61C2×C411yescharacteristic
72C4×C8×C61D411yescharacteristic
73C4×C8×C61D411yescharacteristic
74#95×C61—21no—
75#95×C61D412yes—
76#41×C61—82no—
77C2×Q8×C61—21no—
78C2×Q8×C61—21no—
79C2×Q8×C61—21no—
80C2×D4×C61—21no—
81C2×D4×C61—21no—
82C2×D4×C61—21no—
83C2×D4×C61—41no—
84C22×C4×C61—22no—
85C22×C4×C61—41no—
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61C2×D411yescharacteristic
88C22×C4×C61#4111yescharacteristic
89SD16×C61—42no—
90SD16×C61—42no—
91C2×C8×C61—22no—
92C2×C8×C61—22no—
93C2×C8×C61—22no—
94C2×C8×C61—22no—
95C2×C8×C61—22no—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C2×C8×C61C22⋊C411yescharacteristic
99C2×C8×C61C22⋊C411yescharacteristic
100C2×C8×C61C22⋊C411yescharacteristic
101C2×C8×C61C22⋊C411yescharacteristic
102C4⋊C4×C61—21no—
103C4⋊C4×C61—21no—
104C4⋊C4×C61—21no—
105C4⋊C4×C61—21no—
106C4⋊C4×C61—21no—
107C4⋊C4×C61—21no—
108C4⋊C4×C61—41no—
109C4⋊C4×C61—41no—
110C22⋊C4×C61—41no—
111C22⋊C4×C61—41no—
112C22⋊C4×C61—41no—
113C42×C61—22no—
114C42×C61—22no—
115C42×C61—41no—
116C42×C61C22×C411yescharacteristic
117C42×C61C2×D411yescharacteristic
118C42×C61C2×D411yescharacteristic
119C42×C61#4111yescharacteristic
120C23×C61—41no—
121C23×C61#12111yescharacteristic
122Q8×C61—41no—
123Q8×C61—41no—
124Q8×C61—81no—
125Q8×C61—81no—
126D4×C61—41no—
127D4×C61—41no—
128D4×C61—81no—
129D4×C61—81no—
130D4×C61—82no—
131C2×C4×C61—22no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—24no—
135C2×C4×C61—41no—
136C2×C4×C61—42no—
137C2×C4×C61—42no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—82no—
142C2×C4×C61C2×C22⋊C411yescharacteristic
143C2×C4×C61C4×D411yescharacteristic
144C2×C4×C61C4×D411yescharacteristic
145C2×C4×C61#12111yescharacteristic
146C2×C4×C61#12411yescharacteristic
147C2×C4×C61#12711yescharacteristic
148C8×C61—24no—
149C8×C61—21no—
150C8×C61—21no—
151C8×C61—81no—
152C8×C61—81no—
153C8×C61#10412yes—
154C8×C61#10412yes—
155#9761C6111yesmaximal, characteristic, direct product factor, Sylow
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—81no—
159C22×C61—81no—
160C22×C61—81no—
161C22×C61#39011yescharacteristic
162C22×C61#47112yes—
163C4×C61—21no—
164C4×C61—21no—
165C4×C61—21no—
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—44no—
169C4×C61—81no—
170C4×C61—81no—
171C4×C61—81no—
172C4×C61C2×#10411yescharacteristic
173C4×C61C2×#10411yescharacteristic
174#3167C2×C6111yescharacteristic
175#1726C2×C6111yescharacteristic, complemented
176#1568C2×C6111yescharacteristic, complemented
177#1531C2×C6111yescharacteristic, complemented
178#1530C2×C6111yescharacteristic
179#1506C2×C6111yescharacteristic, complemented
180#1505C2×C6111yescharacteristic
181C2×C61—22no—
182C2×C61—161no—
183C2×C61#196211yescharacteristic
184C2×C61#197611yescharacteristic
185C2×C61#197711yescharacteristic
186#533C22×C6111yescharacteristic
187#532C22×C6111yescharacteristic
188#498C4×C6111yescharacteristic, complemented
189#492C4×C6111yescharacteristic, complemented
190#487C4×C6111yescharacteristic, complemented
191#486C4×C6111yescharacteristic, complemented
192#465—21no—
193#465—21no—
194C4×SD16—21no—
195C4×SD16—21no—
196#432C22×C6111yescharacteristic
197#432C22×C6111yescharacteristic
198C2×#97—21no—
199C2×#97C22×C6111yescharacteristic
200C2×C4×C8—21no—
201C2×C4×C8C22×C6111yescharacteristic
202#376C22×C6111yescharacteristic
203#335—21no—
204#334—21no—
205#330—22no—
206#329—22no—
207#328—22no—
208#327—22no—
209C61#976111yescharacteristic, direct product factor, Sylow
210C2×#41—21no—
211C2×SD16—21no—
212C2×SD16—21no—
213C22×C8—21no—
214C22×C8D4×C6111yescharacteristic
215C22×C8D4×C6111yescharacteristic
216C4⋊Q8C2×C4×C6111yescharacteristic
217C4⋊Q8C2×C4×C6111yescharacteristic
218C4⋊Q8C2×C4×C6111yescharacteristic
219#127C2×C4×C6111yescharacteristic
220#125—21no—
221#124—21no—
222C22⋊Q8—21no—
223C22⋊Q8—21no—
224#121—21no—
225#121—21no—
226C4×Q8—21no—
227C4×Q8—21no—
228C4×D4—21no—
229C4×D4—21no—
230#117—21no—
231C2×C42—21no—
232C2×C42C23×C6111yescharacteristic
233#106—21no—
234#106—21no—
235C4⋊C8—21no—
236C4⋊C8—21no—
237#103—21no—
238#103—21no—
239#102—21no—
240#102—21no—
241C22⋊C8—21no—
242C22⋊C8—21no—
243#97—24no—
244#97—21no—
245#97—21no—
246#97—21no—
247#97D4×C6112yes—
248C4×C8—24no—
249C4×C8C2×C4×C6111yescharacteristic
250C4×C8C2×C4×C6111yescharacteristic
251C4×C8D4×C6111yescharacteristic
252C4×C8D4×C6111yescharacteristic
253#95—21no—
254#95D4×C6112yes—
255#41—82no—
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—41no—
263C22×C4—22no—
264C22×C4—41no—
265C22×C4C2×D4×C6111yescharacteristic
266C22×C4C2×D4×C6111yescharacteristic
267C22×C4#41×C6111yescharacteristic
268SD16—42no—
269SD16—42no—
270C2×C8—22no—
271C2×C8—22no—
272C2×C8—22no—
273C2×C8—22no—
274C2×C8—22no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8C22⋊C4×C6111yescharacteristic
278C2×C8C22⋊C4×C6111yescharacteristic
279C2×C8C22⋊C4×C6111yescharacteristic
280C2×C8C22⋊C4×C6111yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C42—22no—
293C42—22no—
294C42—41no—
295C42C22×C4×C6111yescharacteristic
296C42C2×D4×C6111yescharacteristic
297C42C2×D4×C6111yescharacteristic
298C42#41×C6111yescharacteristic
299C23—41no—
300C23#121×C6111yescharacteristic
301Q8—41no—
302Q8—41no—
303Q8—81no—
304Q8—81no—
305D4—41no—
306D4—41no—
307D4—81no—
308D4—81no—
309D4—82no—
310C2×C4—22no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—24no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—82no—
321C2×C4C2×C22⋊C4×C6111yescharacteristic
322C2×C4C4×D4×C6111yescharacteristic
323C2×C4C4×D4×C6111yescharacteristic
324C2×C4#121×C6111yescharacteristic
325C2×C4#124×C6111yescharacteristic
326C2×C4#127×C6111yescharacteristic
327C8—24no—
328C8—21no—
329C8—21no—
330C8—81no—
331C8—81no—
332C8#104×C6112yes—
333C8#104×C6112yes—
334C22—21no—
335C22—21no—
336C22—81no—
337C22—81no—
338C22—81no—
339C22C61×#39011yescharacteristic
340C22C61×#47112yes—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—44no—
347C4—81no—
348C4—81no—
349C4—81no—
350C4C2×#104×C6111yescharacteristic
351C4C2×#104×C6111yescharacteristic
352C2—22no—
353C2—161no—
354C2C61×#196211yescharacteristic
355C2C61×#197611yescharacteristic
356C2C61×#197711yescharacteristic
subgroupG/H
center, socleC22×C61#390
commutatorC42C22×C4×C61
Frattini, cosocleC2×C42C23×C61
prime radicalC61×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#1726C2semidirect
3. C61×#1568C2semidirect
4. C61×#1531C2semidirect
6. C61×#1506C2semidirect
10. C61×#498C4semidirect
11. C61×#492C4semidirect
12. C61×#487C4semidirect
13. C61×#486C4semidirect
155. #9761C61direct (N × H)
175. #1726C2×C61semidirect
176. #1568C2×C61semidirect
177. #1531C2×C61semidirect
179. #1506C2×C61semidirect
188. #498C4×C61semidirect
189. #492C4×C61semidirect
190. #487C4×C61semidirect
191. #486C4×C61semidirect
209. C61#9761direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#31672
C61×#17262
C61×#15682
C61×#15312
C61×#15302
C61×#15062
C61×#15052
#976161