Finite Group Databasebeta

← C61×#10206 #29513639

Subgroups — C61×#10206 #29513639

Order 15616.

560 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3246C211yesmaximal, characteristic
2C61×#3229C211yesmaximal, characteristic, complemented
3C61×#3152C211yesmaximal, characteristic
4C61×#1988C211yesmaximal, characteristic, complemented
5C61×#1986C211yesmaximal, characteristic, complemented
6C61×#1502C211yesmaximal, characteristic
7C61×#1283C211yesmaximal, characteristic, complemented
8C2×#137×C61—22no—
9C61×#533C2211yescharacteristic
10C61×#532C2211yescharacteristic
11C2×C4⋊Q8×C61C2211yescharacteristic
12C61×#498—21no—
13C61×#497—22no—
14C61×#494—21no—
15C61×#492—21no—
16C61×#487—21no—
17C61×#483—22no—
18C61×#476—21no—
19C61×#475—22no—
20C61×#475—21no—
21C61×#465—22no—
22C61×#461—21no—
23C61×#460—21no—
24C61×#431C2211yescharacteristic
25C2×C4⋊C8×C61C2211yescharacteristic
26C4×M16×C61C2211yescharacteristic
27C4×C4⋊C4×C61C2211yescharacteristic
28C61×#340—22no—
29C61×#339—22no—
30C61×#327—22no—
31C2×#41×C61—21no—
32C22×Q8×C61—21no—
33#137×C61—44no—
34#137×C61—44no—
35C2×Q16×C61—24no—
36C2×SD16×C61—24no—
37C2×SD16×C61—22no—
38C2×M16×C61D412yes—
39C22×C8×C61D412yes—
40C4⋊Q8×C61—21no—
41C4⋊Q8×C61—21no—
42C4⋊Q8×C61—21no—
43C4⋊Q8×C61D412yes—
44C4⋊Q8×C61D411yescharacteristic
45C4⋊Q8×C61D411yescharacteristic
46C4⋊Q8×C61D411yescharacteristic
47#127×C61D411yescharacteristic
48#125×C61—21no—
49#124×C61—21no—
50C22⋊Q8×C61—21no—
51C22⋊Q8×C61—21no—
52#121×C61—21no—
53#121×C61—21no—
54C4×Q8×C61—21no—
55C4×Q8×C61—21no—
56C4×D4×C61—21no—
57C4×D4×C61—21no—
58#117×C61—21no—
59C2×C4⋊C4×C61—21no—
60C2×C4⋊C4×C61—21no—
61C2×C4⋊C4×C61—21no—
62C2×C42×C61—21no—
63C2×C42×C61C2311yescharacteristic
64#106×C61—22no—
65#106×C61—24no—
66C4⋊C8×C61—21no—
67C4⋊C8×C61—21no—
68C4⋊C8×C61—21no—
69#103×C61—22no—
70#103×C61—24no—
71#102×C61—22no—
72C22⋊C8×C61D412yes—
73#97×C61—21no—
74C4×C8×C61—21no—
75C4×C8×C61—21no—
76#95×C61—21no—
77#41×C61—42no—
78#41×C61—42no—
79C2×Q8×C61—21no—
80C2×Q8×C61—21no—
81C2×Q8×C61—21no—
82C2×Q8×C61—22no—
83C2×Q8×C61—41no—
84C2×Q8×C61—42no—
85C2×Q8×C61—42no—
86C2×D4×C61—21no—
87C2×D4×C61—21no—
88C2×D4×C61—21no—
89C2×D4×C61—41no—
90C22×C4×C61—41no—
91C22×C4×C61—41no—
92C22×C4×C61—41no—
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61C2×D411yescharacteristic
95C22×C4×C61C2×D411yescharacteristic
96Q16×C61—48no—
97SD16×C61—48no—
98SD16×C61—82no—
99M16×C61—22no—
100M16×C61SD1614yescomplemented
101C2×C8×C61—22no—
102C2×C8×C61—22no—
103C2×C8×C61—22no—
104C2×C8×C61—42no—
105C4⋊C4×C61—22no—
106C4⋊C4×C61—21no—
107C4⋊C4×C61—22no—
108C4⋊C4×C61—21no—
109C4⋊C4×C61—21no—
110C4⋊C4×C61—22no—
111C4⋊C4×C61—21no—
112C4⋊C4×C61—21no—
113C4⋊C4×C61—21no—
114C4⋊C4×C61—41no—
115C4⋊C4×C61—41no—
116C4⋊C4×C61—41no—
117C4⋊C4×C61—41no—
118C4⋊C4×C61—41no—
119C22⋊C4×C61—41no—
120C22⋊C4×C61—41no—
121C22⋊C4×C61—41no—
122C42×C61—41no—
123C42×C61—42no—
124C42×C61C2×D411yescharacteristic
125C42×C61C2×D411yescharacteristic
126C42×C61C2×D411yescharacteristic
127C42×C61#4111yescharacteristic
128C23×C61—41no—
129C23×C61#12711yescharacteristic
130Q8×C61—42no—
131Q8×C61—44no—
132Q8×C61—42no—
133Q8×C61—41no—
134Q8×C61—41no—
135Q8×C61—82no—
136D4×C61—42no—
137D4×C61—41no—
138D4×C61—41no—
139D4×C61—81no—
140D4×C61—81no—
141D4×C61—81no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—41no—
145C2×C4×C61—42no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—42no—
150C2×C4×C61—81no—
151C2×C4×C61—81no—
152C2×C4×C61—81no—
153C2×C4×C61—81no—
154C2×C4×C61—82no—
155C2×C4×C61#12011yescharacteristic
156C2×C4×C61#12011yescharacteristic
157C2×C4×C61#12011yescharacteristic
158C2×C4×C61#12111yescharacteristic
159C2×C4×C61#12111yescharacteristic
160C2×C4×C61#12111yescharacteristic
161C2×C4×C61C2×SD1612yes—
162C2×C4×C61AGL(1,ℤ/8)12yes—
163C8×C61—24no—
164C8×C61—42no—
165C8×C61—42no—
166#10206C6111yesmaximal, characteristic, direct product factor, Sylow
167C22×C61—21no—
168C22×C61—21no—
169C22×C61—81no—
170C22×C61—81no—
171C22×C61—81no—
172C22×C61#39211yescharacteristic
173C22×C61#49211yescharacteristic
174C22×C61#49611yescharacteristic
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—82no—
179C4×C61—81no—
180C4×C61—81no—
181C4×C61—81no—
182C4×C61—82no—
183C4×C61#45012yes—
184C4×C61#45511yescharacteristic
185C4×C61#45611yescharacteristic
186C4×C61#46012yes—
187#3246C2×C6111yescharacteristic
188#3229C2×C6111yescharacteristic, complemented
189#3152C2×C6111yescharacteristic
190#1988C2×C6111yescharacteristic, complemented
191#1986C2×C6111yescharacteristic, complemented
192#1502C2×C6111yescharacteristic
193#1283C2×C6111yescharacteristic, complemented
194C2×C61—21no—
195C2×C61—21no—
196C2×C61—161no—
197C2×C61#200711yescharacteristic
198C2×C61#200911yescharacteristic
199C2×C61#201411yescharacteristic
200C2×#137—22no—
201#533C22×C6111yescharacteristic
202#532C22×C6111yescharacteristic
203C2×C4⋊Q8C22×C6111yescharacteristic
204#498—21no—
205#497—22no—
206#494—21no—
207#492—21no—
208#487—21no—
209#483—22no—
210#476—21no—
211#475—22no—
212#475—21no—
213#465—22no—
214#461—21no—
215#460—21no—
216#431C22×C6111yescharacteristic
217C2×C4⋊C8C22×C6111yescharacteristic
218C4×M16C22×C6111yescharacteristic
219C4×C4⋊C4C22×C6111yescharacteristic
220#340—22no—
221#339—22no—
222#327—22no—
223C61#1020611yescharacteristic, direct product factor, Sylow
224C2×#41—21no—
225C22×Q8—21no—
226#137—44no—
227#137—44no—
228C2×Q16—24no—
229C2×SD16—24no—
230C2×SD16—22no—
231C2×M16D4×C6112yes—
232C22×C8D4×C6112yes—
233C4⋊Q8—21no—
234C4⋊Q8—21no—
235C4⋊Q8—21no—
236C4⋊Q8D4×C6112yes—
237C4⋊Q8D4×C6111yescharacteristic
238C4⋊Q8D4×C6111yescharacteristic
239C4⋊Q8D4×C6111yescharacteristic
240#127D4×C6111yescharacteristic
241#125—21no—
242#124—21no—
243C22⋊Q8—21no—
244C22⋊Q8—21no—
245#121—21no—
246#121—21no—
247C4×Q8—21no—
248C4×Q8—21no—
249C4×D4—21no—
250C4×D4—21no—
251#117—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C42—21no—
256C2×C42C23×C6111yescharacteristic
257#106—22no—
258#106—24no—
259C4⋊C8—21no—
260C4⋊C8—21no—
261C4⋊C8—21no—
262#103—22no—
263#103—24no—
264#102—22no—
265C22⋊C8D4×C6112yes—
266#97—21no—
267C4×C8—21no—
268C4×C8—21no—
269#95—21no—
270#41—42no—
271#41—42no—
272C2×Q8—21no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×Q8—22no—
276C2×Q8—41no—
277C2×Q8—42no—
278C2×Q8—42no—
279C2×D4—21no—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—41no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4C2×D4×C6111yescharacteristic
287C22×C4C2×D4×C6111yescharacteristic
288C22×C4C2×D4×C6111yescharacteristic
289Q16—48no—
290SD16—48no—
291SD16—82no—
292M16—22no—
293M16SD16×C6114yescomplemented
294C2×C8—22no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8—42no—
298C4⋊C4—22no—
299C4⋊C4—21no—
300C4⋊C4—22no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—22no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C42—41no—
316C42—42no—
317C42C2×D4×C6111yescharacteristic
318C42C2×D4×C6111yescharacteristic
319C42C2×D4×C6111yescharacteristic
320C42#41×C6111yescharacteristic
321C23—41no—
322C23#127×C6111yescharacteristic
323Q8—42no—
324Q8—44no—
325Q8—42no—
326Q8—41no—
327Q8—41no—
328Q8—82no—
329D4—42no—
330D4—41no—
331D4—41no—
332D4—81no—
333D4—81no—
334D4—81no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—82no—
348C2×C4#120×C6111yescharacteristic
349C2×C4#120×C6111yescharacteristic
350C2×C4#120×C6111yescharacteristic
351C2×C4#121×C6111yescharacteristic
352C2×C4#121×C6111yescharacteristic
353C2×C4#121×C6111yescharacteristic
354C2×C4C2×SD16×C6112yes—
355C2×C4AGL(1,ℤ/8)×C6112yes—
356C8—24no—
357C8—42no—
358C8—42no—
359C22—21no—
360C22—21no—
361C22—81no—
362C22—81no—
363C22—81no—
364C22C61×#39211yescharacteristic
365C22C61×#49211yescharacteristic
366C22C61×#49611yescharacteristic
367C4—21no—
368C4—21no—
369C4—21no—
370C4—82no—
371C4—81no—
372C4—81no—
373C4—81no—
374C4—82no—
375C4C61×#45012yes—
376C4C61×#45511yescharacteristic
377C4C61×#45611yescharacteristic
378C4C61×#46012yes—
379C2—21no—
380C2—21no—
381C2—161no—
382C2C61×#200711yescharacteristic
383C2C61×#200911yescharacteristic
384C2C61×#201411yescharacteristic
subgroupG/H
center, socleC22×C61#392
commutator, Frattini, cosocleC2×C42C23×C61
prime radicalC61×#532C22
LCSG ▷ C2×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×#3229C2semidirect
4. C61×#1988C2semidirect
5. C61×#1986C2semidirect
7. C61×#1283C2semidirect
100. M16×C61SD16semidirect
166. #10206C61direct (N × H)
188. #3229C2×C61semidirect
190. #1988C2×C61semidirect
191. #1986C2×C61semidirect
193. #1283C2×C61semidirect
223. C61#10206direct (N × H)
293. M16SD16×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#32462
C61×#32292
C61×#31522
C61×#19882
C61×#19862
C61×#15022
C61×#12832
#1020661