Finite Group Databasebeta

← C61×#12806 #29516239

Subgroups — C61×#12806 #29516239

Order 15616.

420 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#2930C211yesmaximal, characteristic
2C61×#2120C212yesmaximal
3C61×#1813C211yesmaximal, characteristic, complemented
4C61×#1812C211yesmaximal, characteristic, complemented
5C61×#1395C212yesmaximal, complemented
6C2×#131×C61C2211yescharacteristic
7C22×M16×C61C411yescharacteristic, complemented
8C61×#525C2211yescharacteristic
9C61×#436—21no—
10C61×#436—21no—
11C61×#435—21no—
12C61×#435—21no—
13C2×#108×C61—21no—
14C61×#427—21no—
15C61×#424C411yescharacteristic, complemented
16C61×#413C2212yes—
17C61×#410C2212yes—
18C61×#408C2211yescharacteristic
19C61×#407C411yescharacteristic, complemented
20C61×#405C411yescharacteristic, complemented
21C61×#352—22no—
22C61×AΣL(1,𝔽16)—22no—
23C61×#338—21no—
24C61×H(3,ℤ/4)—21no—
25C2×#41×C61C2311yescharacteristic
26C23×C4×C61C2×C411yescharacteristic
27#131×C61—41no—
28#131×C61—41no—
29C2×M16×C61—21no—
30C2×M16×C61—21no—
31C2×M16×C61—22no—
32C2×M16×C61—41no—
33C2×M16×C61—41no—
34C2×M16×C61C2×C411yescharacteristic
35C2×M16×C61C2×C411yescharacteristic
36C2×M16×C61D411yescharacteristic
37C2×M16×C61D411yescharacteristic
38C22×C8×C61C2×C411yescharacteristic
39C22×C8×C61C2×C411yescharacteristic
40C22×C8×C61D411yescharacteristic
41C22×C8×C61D411yescharacteristic
42#123×C61D411yescharacteristic
43#123×C61Q811yescharacteristic
44C22⋊Q8×C61—21no—
45#121×C61—21no—
46#120×C61D411yescharacteristic
47#120×C61Q811yescharacteristic
48C4×D4×C61—21no—
49C4×D4×C61—21no—
50#117×C61—22no—
51#117×C61C2×C411yescharacteristic
52#108×C61—41no—
53#108×C61—41no—
54#107×C61—41no—
55#106×C61—41no—
56C4⋊C8×C61—21no—
57C4⋊C8×C61—21no—
58#101×C61—22no—
59#100×C61—22no—
60#99×C61—22no—
61#99×C61—22no—
62C22⋊C8×C61—21no—
63C22⋊C8×C61—21no—
64C22⋊C8×C61—21no—
65C22⋊C8×C61—21no—
66#97×C61—21no—
67C4×C8×C61—21no—
68C24×C61C4⋊C411yescharacteristic
69#41×C61—41no—
70#41×C61—41no—
71C2×Q8×C61#4111yescharacteristic
72C2×D4×C61—21no—
73C2×D4×C61—21no—
74C2×D4×C61C2×D411yescharacteristic
75C2×D4×C61C2×Q811yescharacteristic
76C2×D4×C61#4111yescharacteristic
77C22×C4×C61—21no—
78C22×C4×C61—21no—
79C22×C4×C61—41no—
80C22×C4×C61—41no—
81C22×C4×C61C4⋊C411yescharacteristic
82C22×C4×C61C22×C411yescharacteristic
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85M16×C61—41no—
86M16×C61—41no—
87M16×C61—41no—
88M16×C61—42no—
89M16×C61—41no—
90M16×C61—41no—
91M16×C61—41no—
92M16×C61—42no—
93M16×C61—42no—
94C2×C8×C61—21no—
95C2×C8×C61—21no—
96C2×C8×C61—21no—
97C2×C8×C61—21no—
98C2×C8×C61—21no—
99C2×C8×C61—21no—
100C2×C8×C61—21no—
101C2×C8×C61—21no—
102C2×C8×C61—41no—
103C2×C8×C61—42no—
104C2×C8×C61C22⋊C411yescharacteristic
105C2×C8×C61C22⋊C411yescharacteristic
106C2×C8×C61C22⋊C411yescharacteristic
107C2×C8×C61C22⋊C411yescharacteristic
108C4⋊C4×C61—21no—
109C4⋊C4×C61—21no—
110C4⋊C4×C61—21no—
111C4⋊C4×C61—42no—
112C22⋊C4×C61—21no—
113C22⋊C4×C61—21no—
114C22⋊C4×C61—21no—
115C22⋊C4×C61—21no—
116C22⋊C4×C61—42no—
117C22⋊C4×C61C4⋊C411yescharacteristic
118C22⋊C4×C61C4⋊C411yescharacteristic
119C42×C61—21no—
120C42×C61—42no—
121C23×C61—21no—
122C23×C61—41no—
123C23×C61—81no—
124C23×C61C2×C4⋊C411yescharacteristic
125C23×C61#12111yescharacteristic
126C23×C61C22⋊Q811yescharacteristic
127Q8×C61—41no—
128D4×C61—41no—
129D4×C61—41no—
130D4×C61—41no—
131D4×C61—81no—
132D4×C61—81no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—42no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—82no—
147C2×C4×C61C2×C22⋊C411yescharacteristic
148C2×C4×C61#11711yescharacteristic
149C2×C4×C61#12111yescharacteristic
150C2×C4×C61C22⋊Q811yescharacteristic
151C8×C61—21no—
152C8×C61—21no—
153C8×C61—21no—
154C8×C61—41no—
155C8×C61—41no—
156C8×C61—82no—
157C8×C61#9911yescharacteristic
158C8×C61#9911yescharacteristic
159#12806C6111yesmaximal, characteristic, direct product factor, Sylow
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—41no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61—82no—
170C22×C61#38011yescharacteristic
171C4×C61—21no—
172C4×C61—21no—
173C4×C61—21no—
174C4×C61—41no—
175C4×C61—41no—
176C4×C61—41no—
177C4×C61—162no—
178C4×C61C2×#9911yescharacteristic
179C4×C61#41011yescharacteristic
180#2930C2×C6111yescharacteristic
181#2120C2×C6112yes—
182#1813C2×C6111yescharacteristic, complemented
183#1812C2×C6111yescharacteristic, complemented
184#1395C2×C6112yescomplemented
185C2×C61—21no—
186C2×C61—41no—
187C2×C61—41no—
188C2×C61—41no—
189C2×C61—81no—
190C2×C61#179911yescharacteristic
191C2×#131C22×C6111yescharacteristic
192C22×M16C4×C6111yescharacteristic, complemented
193#525C22×C6111yescharacteristic
194#436—21no—
195#436—21no—
196#435—21no—
197#435—21no—
198C2×#108—21no—
199#427—21no—
200#424C4×C6111yescharacteristic, complemented
201#413C22×C6112yes—
202#410C22×C6112yes—
203#408C22×C6111yescharacteristic
204#407C4×C6111yescharacteristic, complemented
205#405C4×C6111yescharacteristic, complemented
206#352—22no—
207AΣL(1,𝔽16)—22no—
208#338—21no—
209H(3,ℤ/4)—21no—
210C61#1280611yescharacteristic, direct product factor, Sylow
211C2×#41C23×C6111yescharacteristic
212C23×C4C2×C4×C6111yescharacteristic
213#131—41no—
214#131—41no—
215C2×M16—21no—
216C2×M16—21no—
217C2×M16—22no—
218C2×M16—41no—
219C2×M16—41no—
220C2×M16C2×C4×C6111yescharacteristic
221C2×M16C2×C4×C6111yescharacteristic
222C2×M16D4×C6111yescharacteristic
223C2×M16D4×C6111yescharacteristic
224C22×C8C2×C4×C6111yescharacteristic
225C22×C8C2×C4×C6111yescharacteristic
226C22×C8D4×C6111yescharacteristic
227C22×C8D4×C6111yescharacteristic
228#123D4×C6111yescharacteristic
229#123Q8×C6111yescharacteristic
230C22⋊Q8—21no—
231#121—21no—
232#120D4×C6111yescharacteristic
233#120Q8×C6111yescharacteristic
234C4×D4—21no—
235C4×D4—21no—
236#117—22no—
237#117C2×C4×C6111yescharacteristic
238#108—41no—
239#108—41no—
240#107—41no—
241#106—41no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244#101—22no—
245#100—22no—
246#99—22no—
247#99—22no—
248C22⋊C8—21no—
249C22⋊C8—21no—
250C22⋊C8—21no—
251C22⋊C8—21no—
252#97—21no—
253C4×C8—21no—
254C24C4⋊C4×C6111yescharacteristic
255#41—41no—
256#41—41no—
257C2×Q8#41×C6111yescharacteristic
258C2×D4—21no—
259C2×D4—21no—
260C2×D4C2×D4×C6111yescharacteristic
261C2×D4C2×Q8×C6111yescharacteristic
262C2×D4#41×C6111yescharacteristic
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4C4⋊C4×C6111yescharacteristic
268C22×C4C22×C4×C6111yescharacteristic
269C22×C4C2×D4×C6111yescharacteristic
270C22×C4C2×D4×C6111yescharacteristic
271M16—41no—
272M16—41no—
273M16—41no—
274M16—42no—
275M16—41no—
276M16—41no—
277M16—41no—
278M16—42no—
279M16—42no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—21no—
287C2×C8—21no—
288C2×C8—41no—
289C2×C8—42no—
290C2×C8C22⋊C4×C6111yescharacteristic
291C2×C8C22⋊C4×C6111yescharacteristic
292C2×C8C22⋊C4×C6111yescharacteristic
293C2×C8C22⋊C4×C6111yescharacteristic
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—42no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—42no—
303C22⋊C4C4⋊C4×C6111yescharacteristic
304C22⋊C4C4⋊C4×C6111yescharacteristic
305C42—21no—
306C42—42no—
307C23—21no—
308C23—41no—
309C23—81no—
310C23C2×C4⋊C4×C6111yescharacteristic
311C23#121×C6111yescharacteristic
312C23C22⋊Q8×C6111yescharacteristic
313Q8—41no—
314D4—41no—
315D4—41no—
316D4—41no—
317D4—81no—
318D4—81no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—82no—
333C2×C4C2×C22⋊C4×C6111yescharacteristic
334C2×C4#117×C6111yescharacteristic
335C2×C4#121×C6111yescharacteristic
336C2×C4C22⋊Q8×C6111yescharacteristic
337C8—21no—
338C8—21no—
339C8—21no—
340C8—41no—
341C8—41no—
342C8—82no—
343C8#99×C6111yescharacteristic
344C8#99×C6111yescharacteristic
345C22—21no—
346C22—21no—
347C22—21no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—82no—
355C22C61×#38011yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—162no—
363C4C2×#99×C6111yescharacteristic
364C4C61×#41011yescharacteristic
365C2—21no—
366C2—41no—
367C2—41no—
368C2—41no—
369C2—81no—
370C2C61×#179911yescharacteristic
subgroupG/H
centerC4×C61#410
commutatorC22×C4C22×C4×C61
Frattini, cosocleC2×#41C23×C61
socleC2×C61#1799
prime radicalC61×#525C22
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C61 ◁ C2×C8×C61 ◁ C2×#131×C61 ◁ G

Complements

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

NH ≅ G/Ntype
3. C61×#1813C2semidirect
4. C61×#1812C2semidirect
5. C61×#1395C2semidirect
7. C22×M16×C61C4semidirect
15. C61×#424C4semidirect
19. C61×#407C4semidirect
20. C61×#405C4semidirect
159. #12806C61direct (N × H)
182. #1813C2×C61semidirect
183. #1812C2×C61semidirect
184. #1395C2×C61semidirect
192. C22×M16C4×C61semidirect
200. #424C4×C61semidirect
204. #407C4×C61semidirect
205. #405C4×C61semidirect
210. C61#12806direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#29302
C61×#21202
C61×#18132
C61×#18122
C61×#13952
#1280661