Finite Group Databasebeta

← C61×#12963 #29516396

Subgroups — C61×#12963 #29516396

Order 15616.

416 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#2978C211yesmaximal, characteristic
2C61×#2120C211yesmaximal, characteristic
3C61×#1891C211yesmaximal, characteristic
4C61×#1868C211yesmaximal, characteristic, complemented
5C61×#1858C211yesmaximal, characteristic, complemented
6C61×#1395C211yesmaximal, characteristic, complemented
7C61×#1392C211yesmaximal, characteristic, complemented
8C61×#568C2211yescharacteristic
9C61×#525C2211yescharacteristic
10C61×#436—21no—
11C61×#436—21no—
12C61×#435—21no—
13C61×#435—21no—
14C61×#433—21no—
15C61×#430—21no—
16C61×#424—21no—
17C61×#413C2211yescharacteristic
18C61×#413C2211yescharacteristic
19C61×#410C2211yescharacteristic
20C61×#408C2211yescharacteristic
21C61×#408C2211yescharacteristic
22C61×#407—21no—
23C61×#407—21no—
24C61×#352C412yes—
25C61×AΣL(1,𝔽16)C412yes—
26C61×#344—21no—
27C61×#344—21no—
28C61×#341—21no—
29C2×#41×C61C2311yescharacteristic
30C23×C4×C61D411yescharacteristic
31#131×C61—42no—
32C2×M16×C61—21no—
33C2×M16×C61—21no—
34C2×M16×C61—21no—
35C2×M16×C61—21no—
36C2×M16×C61—21no—
37C2×M16×C61—21no—
38C2×M16×C61—21no—
39C2×M16×C61D411yescharacteristic
40C2×M16×C61D411yescharacteristic
41C22×C8×C61D411yescharacteristic
42C22×C8×C61D411yescharacteristic
43#123×C61C2×C411yescharacteristic
44#123×C61Q811yescharacteristic
45C22⋊Q8×C61—21no—
46#121×C61—21no—
47#120×C61C2×C411yescharacteristic
48#120×C61Q811yescharacteristic
49C4×D4×C61—21no—
50C4×D4×C61—21no—
51#117×C61—21no—
52#117×C61D411yescharacteristic
53#108×C61—42no—
54C4⋊C8×C61—21no—
55C4⋊C8×C61—21no—
56C4⋊C8×C61—42no—
57#101×C61—21no—
58#101×C61—21no—
59#100×C61—21no—
60#100×C61C2×C412yes—
61#99×C61—21no—
62#99×C61C2×C412yes—
63C22⋊C8×C61—21no—
64C22⋊C8×C61—21no—
65C22⋊C8×C61—21no—
66C22⋊C8×C61—21no—
67C22⋊C8×C61—21no—
68C22⋊C8×C61—21no—
69C22⋊C8×C61—42no—
70#97×C61—21no—
71C4×C8×C61—21no—
72C24×C61C4⋊C411yescharacteristic
73#41×C61—41no—
74#41×C61—41no—
75C2×Q8×C61#4111yescharacteristic
76C2×D4×C61—21no—
77C2×D4×C61—21no—
78C2×D4×C61C22×C411yescharacteristic
79C2×D4×C61C2×Q811yescharacteristic
80C2×D4×C61#4111yescharacteristic
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61—41no—
84C22×C4×C61—41no—
85C22×C4×C61C4⋊C411yescharacteristic
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61C2×D411yescharacteristic
88C22×C4×C61C2×D411yescharacteristic
89M16×C61—22no—
90M16×C61—22no—
91M16×C61—41no—
92M16×C61—41no—
93M16×C61—41no—
94M16×C61—41no—
95M16×C61—41no—
96M16×C61—41no—
97M16×C61—41no—
98M16×C61—41no—
99M16×C61—81no—
100M16×C61—81no—
101C2×C8×C61—22no—
102C2×C8×C61—22no—
103C2×C8×C61—21no—
104C2×C8×C61—21no—
105C2×C8×C61—21no—
106C2×C8×C61—21no—
107C2×C8×C61—41no—
108C2×C8×C61—41no—
109C2×C8×C61—41no—
110C2×C8×C61—41no—
111C2×C8×C61—41no—
112C4⋊C4×C61—21no—
113C4⋊C4×C61—21no—
114C4⋊C4×C61—21no—
115C4⋊C4×C61—41no—
116C22⋊C4×C61—21no—
117C22⋊C4×C61—21no—
118C22⋊C4×C61—21no—
119C22⋊C4×C61—21no—
120C22⋊C4×C61—22no—
121C22⋊C4×C61C4⋊C411yescharacteristic
122C22⋊C4×C61C4⋊C411yescharacteristic
123C42×C61—21no—
124C42×C61—41no—
125C23×C61—21no—
126C23×C61—41no—
127C23×C61—81no—
128C23×C61C2×C4⋊C411yescharacteristic
129C23×C61C4×D411yescharacteristic
130C23×C61C22⋊Q811yescharacteristic
131Q8×C61—41no—
132D4×C61—41no—
133D4×C61—41no—
134D4×C61—41no—
135D4×C61—81no—
136D4×C61—81no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—42no—
150C2×C4×C61—81no—
151C2×C4×C61C4×D411yescharacteristic
152C2×C4×C61#12011yescharacteristic
153C2×C4×C61C22⋊Q811yescharacteristic
154C2×C4×C61#12311yescharacteristic
155C8×C61—42no—
156C8×C61—42no—
157C8×C61—41no—
158C8×C61—41no—
159C8×C61—41no—
160C8×C61—41no—
161C8×C61—81no—
162#12963C6111yesmaximal, characteristic, direct product factor, Sylow
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61—41no—
171C22×C61—42no—
172C22×C61—41no—
173C22×C61—81no—
174C22×C61#38511yescharacteristic
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—41no—
179C4×C61—41no—
180C4×C61—41no—
181C4×C61—82no—
182C4×C61B(4,𝔽2)11yescharacteristic
183C4×C61#45811yescharacteristic
184#2978C2×C6111yescharacteristic
185#2120C2×C6111yescharacteristic
186#1891C2×C6111yescharacteristic
187#1868C2×C6111yescharacteristic, complemented
188#1858C2×C6111yescharacteristic, complemented
189#1395C2×C6111yescharacteristic, complemented
190#1392C2×C6111yescharacteristic, complemented
191C2×C61—21no—
192C2×C61—41no—
193C2×C61—41no—
194C2×C61—41no—
195C2×C61—81no—
196C2×C61#186711yescharacteristic
197#568C22×C6111yescharacteristic
198#525C22×C6111yescharacteristic
199#436—21no—
200#436—21no—
201#435—21no—
202#435—21no—
203#433—21no—
204#430—21no—
205#424—21no—
206#413C22×C6111yescharacteristic
207#413C22×C6111yescharacteristic
208#410C22×C6111yescharacteristic
209#408C22×C6111yescharacteristic
210#408C22×C6111yescharacteristic
211#407—21no—
212#407—21no—
213#352C4×C6112yes—
214AΣL(1,𝔽16)C4×C6112yes—
215#344—21no—
216#344—21no—
217#341—21no—
218C61#1296311yescharacteristic, direct product factor, Sylow
219C2×#41C23×C6111yescharacteristic
220C23×C4D4×C6111yescharacteristic
221#131—42no—
222C2×M16—21no—
223C2×M16—21no—
224C2×M16—21no—
225C2×M16—21no—
226C2×M16—21no—
227C2×M16—21no—
228C2×M16—21no—
229C2×M16D4×C6111yescharacteristic
230C2×M16D4×C6111yescharacteristic
231C22×C8D4×C6111yescharacteristic
232C22×C8D4×C6111yescharacteristic
233#123C2×C4×C6111yescharacteristic
234#123Q8×C6111yescharacteristic
235C22⋊Q8—21no—
236#121—21no—
237#120C2×C4×C6111yescharacteristic
238#120Q8×C6111yescharacteristic
239C4×D4—21no—
240C4×D4—21no—
241#117—21no—
242#117D4×C6111yescharacteristic
243#108—42no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—42no—
247#101—21no—
248#101—21no—
249#100—21no—
250#100C2×C4×C6112yes—
251#99—21no—
252#99C2×C4×C6112yes—
253C22⋊C8—21no—
254C22⋊C8—21no—
255C22⋊C8—21no—
256C22⋊C8—21no—
257C22⋊C8—21no—
258C22⋊C8—21no—
259C22⋊C8—42no—
260#97—21no—
261C4×C8—21no—
262C24C4⋊C4×C6111yescharacteristic
263#41—41no—
264#41—41no—
265C2×Q8#41×C6111yescharacteristic
266C2×D4—21no—
267C2×D4—21no—
268C2×D4C22×C4×C6111yescharacteristic
269C2×D4C2×Q8×C6111yescharacteristic
270C2×D4#41×C6111yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4C4⋊C4×C6111yescharacteristic
276C22×C4C2×D4×C6111yescharacteristic
277C22×C4C2×D4×C6111yescharacteristic
278C22×C4C2×D4×C6111yescharacteristic
279M16—22no—
280M16—22no—
281M16—41no—
282M16—41no—
283M16—41no—
284M16—41no—
285M16—41no—
286M16—41no—
287M16—41no—
288M16—41no—
289M16—81no—
290M16—81no—
291C2×C8—22no—
292C2×C8—22no—
293C2×C8—21no—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—41no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—41no—
306C22⋊C4—21no—
307C22⋊C4—21no—
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—22no—
311C22⋊C4C4⋊C4×C6111yescharacteristic
312C22⋊C4C4⋊C4×C6111yescharacteristic
313C42—21no—
314C42—41no—
315C23—21no—
316C23—41no—
317C23—81no—
318C23C2×C4⋊C4×C6111yescharacteristic
319C23C4×D4×C6111yescharacteristic
320C23C22⋊Q8×C6111yescharacteristic
321Q8—41no—
322D4—41no—
323D4—41no—
324D4—41no—
325D4—81no—
326D4—81no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—81no—
341C2×C4C4×D4×C6111yescharacteristic
342C2×C4#120×C6111yescharacteristic
343C2×C4C22⋊Q8×C6111yescharacteristic
344C2×C4#123×C6111yescharacteristic
345C8—42no—
346C8—42no—
347C8—41no—
348C8—41no—
349C8—41no—
350C8—41no—
351C8—81no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—42no—
361C22—41no—
362C22—81no—
363C22C61×#38511yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—82no—
371C4C61×B(4,𝔽2)11yescharacteristic
372C4C61×#45811yescharacteristic
373C2—21no—
374C2—41no—
375C2—41no—
376C2—41no—
377C2—81no—
378C2C61×#186711yescharacteristic
subgroupG/H
centerC4×C61B(4,𝔽2)
commutatorC2×D4C22×C4×C61
Frattini, cosocleC2×#41C23×C61
socleC2×C61#1867
prime radicalC61×#525C22
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C61 ◁ C2×C4×C61 ◁ C2×#41×C61 ◁ G

Complements

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

NH ≅ G/Ntype
4. C61×#1868C2semidirect
5. C61×#1858C2semidirect
6. C61×#1395C2semidirect
7. C61×#1392C2semidirect
162. #12963C61direct (N × H)
187. #1868C2×C61semidirect
188. #1858C2×C61semidirect
189. #1395C2×C61semidirect
190. #1392C2×C61semidirect
218. C61#12963direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#29782
C61×#21202
C61×#18912
C61×#18682
C61×#18582
C61×#13952
C61×#13922
#1296361