Finite Group Databasebeta

← C61×#8916 #29512349

Subgroups — C61×#8916 #29512349

Order 15616.

354 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#2995C211yesmaximal, characteristic
2C61×#1849C211yesmaximal, characteristic, complemented
3C61×#1569C211yesmaximal, characteristic, complemented
4C61×#1524C211yesmaximal, characteristic
5C61×#1495C211yesmaximal, characteristic
6C61×#1302C211yesmaximal, characteristic, complemented
7C61×#1299C211yesmaximal, characteristic, complemented
8C61×#529C2211yescharacteristic
9C61×#446—21no—
10C61×#436—21no—
11C61×#435—21no—
12C61×#435—21no—
13C61×#433—21no—
14C61×#432C2211yescharacteristic
15C61×#431C2211yescharacteristic
16C2×#108×C61—21no—
17C2×#108×C61—21no—
18C61×#424—21no—
19C61×#423C2211yescharacteristic
20C61×#423C2211yescharacteristic
21C4×M16×C61C2211yescharacteristic
22C2×#97×C61C2211yescharacteristic
23C61×#335—21no—
24C61×#334—21no—
25C61×#330C411yescharacteristic
26C61×#330C411yescharacteristic
27C61×#329C411yescharacteristic
28C61×#329C411yescharacteristic
29C61×Q8⋊C8—21no—
30C61×D4⋊C8—21no—
31C2×M16×C61—21no—
32C2×M16×C61—21no—
33C2×M16×C61—21no—
34C2×M16×C61D411yescharacteristic
35C2×M16×C61D411yescharacteristic
36C22×C8×C61—21no—
37C22×C8×C61—21no—
38#126×C61—21no—
39#125×C61C2×C411yescharacteristic
40#124×C61C2×C411yescharacteristic
41#123×C61—21no—
42C22⋊Q8×C61Q811yescharacteristic
43#121×C61Q811yescharacteristic
44C4×Q8×C61D411yescharacteristic
45C4×D4×C61—21no—
46C4×D4×C61D411yescharacteristic
47#117×C61—21no—
48C2×C42×C61C2311yescharacteristic
49#108×C61—42no—
50#108×C61—42no—
51C4⋊C8×C61—21no—
52C4⋊C8×C61—21no—
53C4⋊C8×C61—21no—
54C4⋊C8×C61—21no—
55C4⋊C8×C61—21no—
56C4⋊C8×C61—21no—
57C4⋊C8×C61—21no—
58C4⋊C8×C61D411yescharacteristic
59C4⋊C8×C61D411yescharacteristic
60C22⋊C8×C61—21no—
61C22⋊C8×C61—21no—
62C22⋊C8×C61—21no—
63C22⋊C8×C61—21no—
64#97×C61—21no—
65#97×C61—21no—
66#97×C61—21no—
67#97×C61C2×C411yescharacteristic
68#97×C61C2×C411yescharacteristic
69#97×C61C2×C411yescharacteristic
70#97×C61C2×C411yescharacteristic
71C4×C8×C61—21no—
72C4×C8×C61—21no—
73C4×C8×C61—21no—
74C2×Q8×C61C4⋊C411yescharacteristic
75C2×D4×C61—21no—
76C2×D4×C61C4⋊C411yescharacteristic
77C22×C4×C61—21no—
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61C2×Q811yescharacteristic
80C22×C4×C61#4111yescharacteristic
81M16×C61—42no—
82M16×C61—41no—
83M16×C61—41no—
84M16×C61—41no—
85M16×C61—41no—
86M16×C61—81no—
87C2×C8×C61—22no—
88C2×C8×C61—22no—
89C2×C8×C61—21no—
90C2×C8×C61—21no—
91C2×C8×C61—21no—
92C2×C8×C61—21no—
93C2×C8×C61—21no—
94C2×C8×C61—21no—
95C2×C8×C61—21no—
96C2×C8×C61—21no—
97C2×C8×C61—41no—
98C2×C8×C61—41no—
99C2×C8×C61—81no—
100C4⋊C4×C61—21no—
101C4⋊C4×C61—21no—
102C4⋊C4×C61—21no—
103C4⋊C4×C61—21no—
104C4⋊C4×C61C4⋊C411yescharacteristic
105C4⋊C4×C61C4⋊C411yescharacteristic
106C22⋊C4×C61—21no—
107C22⋊C4×C61—21no—
108C22⋊C4×C61—21no—
109C22⋊C4×C61—21no—
110C22⋊C4×C61—21no—
111C42×C61—21no—
112C42×C61C22×C411yescharacteristic
113C42×C61C2×D411yescharacteristic
114C42×C61C2×D411yescharacteristic
115C42×C61#4111yescharacteristic
116C23×C61—21no—
117C23×C61C22⋊Q811yescharacteristic
118Q8×C61—41no—
119D4×C61—41no—
120D4×C61—81no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61C2×C4⋊C411yescharacteristic
131C2×C4×C61C4×D411yescharacteristic
132C2×C4×C61C4×D411yescharacteristic
133C2×C4×C61#12011yescharacteristic
134C2×C4×C61C22⋊Q811yescharacteristic
135C2×C4×C61#12311yescharacteristic
136C8×C61—22no—
137C8×C61—22no—
138C8×C61—22no—
139C8×C61—41no—
140C8×C61—41no—
141C8×C61—41no—
142C8×C61—41no—
143C8×C61—41no—
144C8×C61—81no—
145C8×C61—81no—
146#8916C6111yesmaximal, characteristic, direct product factor, Sylow
147C22×C61—21no—
148C22×C61—21no—
149C22×C61—21no—
150C22×C61—41no—
151C22×C61—41no—
152C22×C61—41no—
153C22×C61#38511yescharacteristic
154C4×C61—21no—
155C4×C61—21no—
156C4×C61—21no—
157C4×C61—21no—
158C4×C61—21no—
159C4×C61—41no—
160C4×C61—41no—
161C4×C61—41no—
162C4×C61#45311yescharacteristic
163C4×C61#45611yescharacteristic
164#2995C2×C6111yescharacteristic
165#1849C2×C6111yescharacteristic, complemented
166#1569C2×C6111yescharacteristic, complemented
167#1524C2×C6111yescharacteristic
168#1495C2×C6111yescharacteristic
169#1302C2×C6111yescharacteristic, complemented
170#1299C2×C6111yescharacteristic, complemented
171C2×C61—41no—
172C2×C61—81no—
173C2×C61#185811yescharacteristic
174C2×C61#185911yescharacteristic
175C2×C61#186111yescharacteristic
176#529C22×C6111yescharacteristic
177#446—21no—
178#436—21no—
179#435—21no—
180#435—21no—
181#433—21no—
182#432C22×C6111yescharacteristic
183#431C22×C6111yescharacteristic
184C2×#108—21no—
185C2×#108—21no—
186#424—21no—
187#423C22×C6111yescharacteristic
188#423C22×C6111yescharacteristic
189C4×M16C22×C6111yescharacteristic
190C2×#97C22×C6111yescharacteristic
191#335—21no—
192#334—21no—
193#330C4×C6111yescharacteristic
194#330C4×C6111yescharacteristic
195#329C4×C6111yescharacteristic
196#329C4×C6111yescharacteristic
197Q8⋊C8—21no—
198D4⋊C8—21no—
199C61#891611yescharacteristic, direct product factor, Sylow
200C2×M16—21no—
201C2×M16—21no—
202C2×M16—21no—
203C2×M16D4×C6111yescharacteristic
204C2×M16D4×C6111yescharacteristic
205C22×C8—21no—
206C22×C8—21no—
207#126—21no—
208#125C2×C4×C6111yescharacteristic
209#124C2×C4×C6111yescharacteristic
210#123—21no—
211C22⋊Q8Q8×C6111yescharacteristic
212#121Q8×C6111yescharacteristic
213C4×Q8D4×C6111yescharacteristic
214C4×D4—21no—
215C4×D4D4×C6111yescharacteristic
216#117—21no—
217C2×C42C23×C6111yescharacteristic
218#108—42no—
219#108—42no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8D4×C6111yescharacteristic
228C4⋊C8D4×C6111yescharacteristic
229C22⋊C8—21no—
230C22⋊C8—21no—
231C22⋊C8—21no—
232C22⋊C8—21no—
233#97—21no—
234#97—21no—
235#97—21no—
236#97C2×C4×C6111yescharacteristic
237#97C2×C4×C6111yescharacteristic
238#97C2×C4×C6111yescharacteristic
239#97C2×C4×C6111yescharacteristic
240C4×C8—21no—
241C4×C8—21no—
242C4×C8—21no—
243C2×Q8C4⋊C4×C6111yescharacteristic
244C2×D4—21no—
245C2×D4C4⋊C4×C6111yescharacteristic
246C22×C4—21no—
247C22×C4C2×D4×C6111yescharacteristic
248C22×C4C2×Q8×C6111yescharacteristic
249C22×C4#41×C6111yescharacteristic
250M16—42no—
251M16—41no—
252M16—41no—
253M16—41no—
254M16—41no—
255M16—81no—
256C2×C8—22no—
257C2×C8—22no—
258C2×C8—21no—
259C2×C8—21no—
260C2×C8—21no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—21no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—81no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4C4⋊C4×C6111yescharacteristic
274C4⋊C4C4⋊C4×C6111yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—21no—
280C42—21no—
281C42C22×C4×C6111yescharacteristic
282C42C2×D4×C6111yescharacteristic
283C42C2×D4×C6111yescharacteristic
284C42#41×C6111yescharacteristic
285C23—21no—
286C23C22⋊Q8×C6111yescharacteristic
287Q8—41no—
288D4—41no—
289D4—81no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4C2×C4⋊C4×C6111yescharacteristic
300C2×C4C4×D4×C6111yescharacteristic
301C2×C4C4×D4×C6111yescharacteristic
302C2×C4#120×C6111yescharacteristic
303C2×C4C22⋊Q8×C6111yescharacteristic
304C2×C4#123×C6111yescharacteristic
305C8—22no—
306C8—22no—
307C8—22no—
308C8—41no—
309C8—41no—
310C8—41no—
311C8—41no—
312C8—41no—
313C8—81no—
314C8—81no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22C61×#38511yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4C61×#45311yescharacteristic
331C4C61×#45611yescharacteristic
332C2—41no—
333C2—81no—
334C2C61×#185811yescharacteristic
335C2C61×#185911yescharacteristic
336C2C61×#186111yescharacteristic
subgroupG/H
centerC2×C4×C61#120
commutatorC42C22×C4×C61
Frattini, cosocleC2×C42C23×C61
socleC22×C61#385
prime radical#121×C61Q8
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#1849C2semidirect
3. C61×#1569C2semidirect
6. C61×#1302C2semidirect
7. C61×#1299C2semidirect
146. #8916C61direct (N × H)
165. #1849C2×C61semidirect
166. #1569C2×C61semidirect
169. #1302C2×C61semidirect
170. #1299C2×C61semidirect
199. C61#8916direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#29952
C61×#18492
C61×#15692
C61×#15242
C61×#14952
C61×#13022
C61×#12992
#891661