Finite Group Databasebeta

← C61×#9532 #29512965

Subgroups — C61×#9532 #29512965

Order 15616.

444 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3114C211yesmaximal, characteristic
2C61×#2967C211yesmaximal, characteristic, complemented
3C61×#1535C211yesmaximal, characteristic, complemented
4C61×#1490C211yesmaximal, characteristic, complemented
5C61×#1466C211yesmaximal, characteristic, complemented
6C61×#1308C211yesmaximal, characteristic, complemented
7C61×#1291C211yesmaximal, characteristic, complemented
8C61×#529C2211yescharacteristic
9C2×C4×D4×C61C2211yescharacteristic
10C61×#483C411yescharacteristic
11C61×#480C411yescharacteristic
12C61×#478—21no—
13C61×#463—21no—
14C61×#450C411yescharacteristic
15C61×#447C411yescharacteristic
16C61×#446—21no—
17C61×#442—21no—
18C61×#440—21no—
19C61×#436—21no—
20C61×#435—21no—
21C61×#435—21no—
22C61×#433—21no—
23C61×#432C2211yescharacteristic
24C61×#432C2211yescharacteristic
25C61×#432C2211yescharacteristic
26C61×#432C2211yescharacteristic
27C61×#405—21no—
28C4×M16×C61C2211yescharacteristic
29C61×#330—21no—
30C61×#329—21no—
31C61×D4⋊C8—21no—
32C61×D4⋊C8—21no—
33C61×#323—21no—
34C61×#323—21no—
35C22×D4×C61C2×C411yescharacteristic
36C23×C4×C61—21no—
37C2×SD16×C61—21no—
38C2×D8×C61—21no—
39C2×M16×C61—21no—
40C2×M16×C61—21no—
41C22×C8×C61—21no—
42#126×C61—21no—
43#125×C61D411yescharacteristic
44#124×C61D411yescharacteristic
45#123×C61—21no—
46C22⋊Q8×C61C2×C411yescharacteristic
47#121×C61C2×C411yescharacteristic
48C4×Q8×C61D411yescharacteristic
49C4×D4×C61—21no—
50C4×D4×C61—21no—
51C4×D4×C61—21no—
52C4×D4×C61—21no—
53C4×D4×C61—21no—
54C4×D4×C61D411yescharacteristic
55#117×C61—21no—
56C2×C4⋊C4×C61C2×C411yescharacteristic
57C2×C22⋊C4×C61—21no—
58C2×C42×C61C2311yescharacteristic
59#107×C61—21no—
60#106×C61—21no—
61C4⋊C8×C61—21no—
62C4⋊C8×C61—21no—
63C4⋊C8×C61—21no—
64C4⋊C8×C61—21no—
65C4⋊C8×C61—21no—
66C4⋊C8×C61—21no—
67#103×C61—21no—
68#102×C61—21no—
69#102×C61—21no—
70#102×C61—21no—
71C22⋊C8×C61—21no—
72C22⋊C8×C61—21no—
73C22⋊C8×C61—21no—
74C22⋊C8×C61—21no—
75C22⋊C8×C61C2×C411yescharacteristic
76C22⋊C8×C61C2×C411yescharacteristic
77C22⋊C8×C61D411yescharacteristic
78C22⋊C8×C61D411yescharacteristic
79#97×C61—21no—
80#97×C61—21no—
81#97×C61—21no—
82#97×C61—21no—
83#97×C61—21no—
84#97×C61—21no—
85C4×C8×C61—21no—
86C4×C8×C61D411yescharacteristic
87C4×C8×C61D411yescharacteristic
88C24×C61—21no—
89C2×Q8×C61C22⋊C411yescharacteristic
90C2×D4×C61—21no—
91C2×D4×C61—21no—
92C2×D4×C61—21no—
93C2×D4×C61—42no—
94C2×D4×C61C22⋊C411yescharacteristic
95C22×C4×C61—21no—
96C22×C4×C61—21no—
97C22×C4×C61—41no—
98C22×C4×C61—41no—
99C22×C4×C61—82no—
100C22×C4×C61C22×C411yescharacteristic
101C22×C4×C61C2×D411yescharacteristic
102C22×C4×C61#4111yescharacteristic
103SD16×C61—42no—
104D8×C61—42no—
105M16×C61—42no—
106M16×C61—42no—
107C2×C8×C61—21no—
108C2×C8×C61—21no—
109C2×C8×C61—21no—
110C2×C8×C61—21no—
111C2×C8×C61—21no—
112C2×C8×C61—21no—
113C2×C8×C61—42no—
114C2×C8×C61—41no—
115C2×C8×C61—41no—
116C4⋊C4×C61—21no—
117C4⋊C4×C61—21no—
118C4⋊C4×C61—21no—
119C4⋊C4×C61—21no—
120C4⋊C4×C61—21no—
121C4⋊C4×C61—21no—
122C4⋊C4×C61C22⋊C411yescharacteristic
123C4⋊C4×C61C22⋊C411yescharacteristic
124C22⋊C4×C61—21no—
125C22⋊C4×C61—21no—
126C22⋊C4×C61—21no—
127C22⋊C4×C61—21no—
128C22⋊C4×C61—21no—
129C22⋊C4×C61—41no—
130C22⋊C4×C61—41no—
131C42×C61—21no—
132C42×C61C2×D411yescharacteristic
133C42×C61C2×D411yescharacteristic
134C42×C61C2×D411yescharacteristic
135C42×C61#4111yescharacteristic
136C23×C61—22no—
137C23×C61—21no—
138C23×C61—41no—
139C23×C61—41no—
140C23×C61—81no—
141C23×C61—81no—
142C23×C61C4×D411yescharacteristic
143Q8×C61—41no—
144D4×C61—22no—
145D4×C61—22no—
146D4×C61—41no—
147D4×C61—41no—
148D4×C61—41no—
149D4×C61—81no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—82no—
160C2×C4×C61—82no—
161C2×C4×C61—81no—
162C2×C4×C61C2×C22⋊C411yescharacteristic
163C2×C4×C61C4×D411yescharacteristic
164C2×C4×C61#12011yescharacteristic
165C2×C4×C61#12111yescharacteristic
166C2×C4×C61#12111yescharacteristic
167C2×C4×C61#12311yescharacteristic
168C8×C61—22no—
169C8×C61—41no—
170C8×C61—41no—
171C8×C61—41no—
172C8×C61—41no—
173C8×C61—41no—
174C8×C61—81no—
175C8×C61—81no—
176#9532C6111yesmaximal, characteristic, direct product factor, Sylow
177C22×C61—21no—
178C22×C61—21no—
179C22×C61—21no—
180C22×C61—42no—
181C22×C61—41no—
182C22×C61—41no—
183C22×C61—41no—
184C22×C61—82no—
185C22×C61—82no—
186C22×C61—81no—
187C22×C61—81no—
188C22×C61#38611yescharacteristic
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—21no—
192C4×C61—21no—
193C4×C61—21no—
194C4×C61—21no—
195C4×C61—41no—
196C4×C61—41no—
197C4×C61—41no—
198C4×C61—81no—
199#3114C2×C6111yescharacteristic
200#2967C2×C6111yescharacteristic, complemented
201#1535C2×C6111yescharacteristic, complemented
202#1490C2×C6111yescharacteristic, complemented
203#1466C2×C6111yescharacteristic, complemented
204#1308C2×C6111yescharacteristic, complemented
205#1291C2×C6111yescharacteristic, complemented
206C2×C61—41no—
207C2×C61—81no—
208C2×C61—82no—
209C2×C61#189111yescharacteristic
210C2×C61#190311yescharacteristic
211C2×C61#190611yescharacteristic
212#529C22×C6111yescharacteristic
213C2×C4×D4C22×C6111yescharacteristic
214#483C4×C6111yescharacteristic
215#480C4×C6111yescharacteristic
216#478—21no—
217#463—21no—
218#450C4×C6111yescharacteristic
219#447C4×C6111yescharacteristic
220#446—21no—
221#442—21no—
222#440—21no—
223#436—21no—
224#435—21no—
225#435—21no—
226#433—21no—
227#432C22×C6111yescharacteristic
228#432C22×C6111yescharacteristic
229#432C22×C6111yescharacteristic
230#432C22×C6111yescharacteristic
231#405—21no—
232C4×M16C22×C6111yescharacteristic
233#330—21no—
234#329—21no—
235D4⋊C8—21no—
236D4⋊C8—21no—
237#323—21no—
238#323—21no—
239C61#953211yescharacteristic, direct product factor, Sylow
240C22×D4C2×C4×C6111yescharacteristic
241C23×C4—21no—
242C2×SD16—21no—
243C2×D8—21no—
244C2×M16—21no—
245C2×M16—21no—
246C22×C8—21no—
247#126—21no—
248#125D4×C6111yescharacteristic
249#124D4×C6111yescharacteristic
250#123—21no—
251C22⋊Q8C2×C4×C6111yescharacteristic
252#121C2×C4×C6111yescharacteristic
253C4×Q8D4×C6111yescharacteristic
254C4×D4—21no—
255C4×D4—21no—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4—21no—
259C4×D4D4×C6111yescharacteristic
260#117—21no—
261C2×C4⋊C4C2×C4×C6111yescharacteristic
262C2×C22⋊C4—21no—
263C2×C42C23×C6111yescharacteristic
264#107—21no—
265#106—21no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8—21no—
272#103—21no—
273#102—21no—
274#102—21no—
275#102—21no—
276C22⋊C8—21no—
277C22⋊C8—21no—
278C22⋊C8—21no—
279C22⋊C8—21no—
280C22⋊C8C2×C4×C6111yescharacteristic
281C22⋊C8C2×C4×C6111yescharacteristic
282C22⋊C8D4×C6111yescharacteristic
283C22⋊C8D4×C6111yescharacteristic
284#97—21no—
285#97—21no—
286#97—21no—
287#97—21no—
288#97—21no—
289#97—21no—
290C4×C8—21no—
291C4×C8D4×C6111yescharacteristic
292C4×C8D4×C6111yescharacteristic
293C24—21no—
294C2×Q8C22⋊C4×C6111yescharacteristic
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—42no—
299C2×D4C22⋊C4×C6111yescharacteristic
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—82no—
305C22×C4C22×C4×C6111yescharacteristic
306C22×C4C2×D4×C6111yescharacteristic
307C22×C4#41×C6111yescharacteristic
308SD16—42no—
309D8—42no—
310M16—42no—
311M16—42no—
312C2×C8—21no—
313C2×C8—21no—
314C2×C8—21no—
315C2×C8—21no—
316C2×C8—21no—
317C2×C8—21no—
318C2×C8—42no—
319C2×C8—41no—
320C2×C8—41no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4C22⋊C4×C6111yescharacteristic
328C4⋊C4C22⋊C4×C6111yescharacteristic
329C22⋊C4—21no—
330C22⋊C4—21no—
331C22⋊C4—21no—
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C42—21no—
337C42C2×D4×C6111yescharacteristic
338C42C2×D4×C6111yescharacteristic
339C42C2×D4×C6111yescharacteristic
340C42#41×C6111yescharacteristic
341C23—22no—
342C23—21no—
343C23—41no—
344C23—41no—
345C23—81no—
346C23—81no—
347C23C4×D4×C6111yescharacteristic
348Q8—41no—
349D4—22no—
350D4—22no—
351D4—41no—
352D4—41no—
353D4—41no—
354D4—81no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—82no—
365C2×C4—82no—
366C2×C4—81no—
367C2×C4C2×C22⋊C4×C6111yescharacteristic
368C2×C4C4×D4×C6111yescharacteristic
369C2×C4#120×C6111yescharacteristic
370C2×C4#121×C6111yescharacteristic
371C2×C4#121×C6111yescharacteristic
372C2×C4#123×C6111yescharacteristic
373C8—22no—
374C8—41no—
375C8—41no—
376C8—41no—
377C8—41no—
378C8—41no—
379C8—81no—
380C8—81no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—42no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—82no—
389C22—82no—
390C22—81no—
391C22—81no—
392C22C61×#38611yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—41no—
400C4—41no—
401C4—41no—
402C4—81no—
403C2—41no—
404C2—81no—
405C2—82no—
406C2C61×#189111yescharacteristic
407C2C61×#190311yescharacteristic
408C2C61×#190611yescharacteristic
subgroupG/H
center, socleC22×C61#386
commutatorC22×C4C22×C4×C61
Frattini, cosocleC2×C42C23×C61
prime radicalC61×#447C4
LCSG ▷ C22×C4 ▷ 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×#2967C2semidirect
3. C61×#1535C2semidirect
4. C61×#1490C2semidirect
5. C61×#1466C2semidirect
6. C61×#1308C2semidirect
7. C61×#1291C2semidirect
176. #9532C61direct (N × H)
200. #2967C2×C61semidirect
201. #1535C2×C61semidirect
202. #1490C2×C61semidirect
203. #1466C2×C61semidirect
204. #1308C2×C61semidirect
205. #1291C2×C61semidirect
239. C61#9532direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#31142
C61×#29672
C61×#15352
C61×#14902
C61×#14662
C61×#13082
C61×#12912
#953261