Finite Group Databasebeta

← C2×C61×#1346 #29515129

Subgroups — C2×C61×#1346 #29515129

Order 15616.

544 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#398C211yesmaximal, characteristic
2C2×C61×#343C211yesmaximal, characteristic
3C2×C61×#324C211yesmaximal, characteristic
4C61×#1346C214yesmaximal, direct product factor
5C22×M16×C61—21no—
6C22×C4⋊C4×C61—21no—
7C22×C4⋊C4×C61C411yescharacteristic
8C22×C4⋊C4×C61C2211yescharacteristic
9C2×C22⋊C8×C61—21no—
10C61×#398—21no—
11C61×#398—21no—
12C61×#398C412yes—
13C61×#398C2212yes—
14C2×#95×C61—21no—
15C2×#95×C61C411yescharacteristic
16C61×#343—21no—
17C61×#343C2212yes—
18C61×#324—21no—
19C61×#324C2212yes—
20C23×C4×C61—21no—
21C23×C4×C61—21no—
22C23×C4×C61C2×C411yescharacteristic
23C23×C4×C61D411yescharacteristic
24C23×C4×C61D411yescharacteristic
25C2×M16×C61—24no—
26C2×M16×C61—22no—
27C2×M16×C61—41no—
28C2×M16×C61—42no—
29C22×C8×C61—41no—
30C22×C8×C61—41no—
31C2×C4⋊C4×C61—21no—
32C2×C4⋊C4×C61—22no—
33C2×C4⋊C4×C61—22no—
34C2×C4⋊C4×C61—41no—
35C2×C4⋊C4×C61—41no—
36C2×C4⋊C4×C61—41no—
37C2×C4⋊C4×C61—41no—
38C2×C4⋊C4×C61—42no—
39C2×C4⋊C4×C61—42no—
40C2×C4⋊C4×C61C2×C412yes—
41C2×C4⋊C4×C61C2×C411yescharacteristic
42C2×C4⋊C4×C61D411yescharacteristic
43C2×C4⋊C4×C61D411yescharacteristic
44C2×C4⋊C4×C61C2311yescharacteristic
45C22⋊C8×C61—22no—
46C22⋊C8×C61—41no—
47#95×C61—22no—
48#95×C61—21no—
49#95×C61—22no—
50#95×C61C2×C412yes—
51C24×C61C22⋊C411yescharacteristic
52C22×C4×C61—21no—
53C22×C4×C61—21no—
54C22×C4×C61—22no—
55C22×C4×C61—24no—
56C22×C4×C61—21no—
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61—22no—
60C22×C4×C61—21no—
61C22×C4×C61—22no—
62C22×C4×C61—42no—
63C22×C4×C61—42no—
64C22×C4×C61—42no—
65C22×C4×C61—42no—
66C22×C4×C61—41no—
67C22×C4×C61—41no—
68C22×C4×C61—42no—
69C22×C4×C61—42no—
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61D812yes—
74C22×C4×C61SD1612yes—
75C22×C4×C61C22×C411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78M16×C61—24no—
79M16×C61—44no—
80M16×C61—42no—
81C2×C8×C61—44no—
82C2×C8×C61—42no—
83C2×C8×C61—42no—
84C2×C8×C61—82no—
85C4⋊C4×C61—41no—
86C4⋊C4×C61—41no—
87C4⋊C4×C61—41no—
88C4⋊C4×C61—41no—
89C4⋊C4×C61—42no—
90C4⋊C4×C61—42no—
91C4⋊C4×C61—44no—
92C4⋊C4×C61—42no—
93C4⋊C4×C61—42no—
94C23×C61—22no—
95C23×C61—22no—
96C23×C61#9911yescharacteristic
97C23×C61#9911yescharacteristic
98C23×C61#10212yes—
99C23×C61#10412yes—
100C23×C61C2×C22⋊C411yescharacteristic
101C2×C4×C61—22no—
102C2×C4×C61—22no—
103C2×C4×C61—22no—
104C2×C4×C61—22no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—24no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—48no—
115C2×C4×C61—42no—
116C2×C4×C61—42no—
117C2×C4×C61—42no—
118C2×C4×C61—42no—
119C2×C4×C61—42no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—42no—
125C2×C4×C61—42no—
126C2×C4×C61—42no—
127C2×C4×C61—81no—
128C2×C4×C61—82no—
129C2×C4×C61—82no—
130C2×C4×C61#10212yes—
131C2×C4×C61C2×D811yescharacteristic
132C2×C4×C61C2×SD1611yescharacteristic
133C8×C61—44no—
134C8×C61—82no—
135C2×#1346C6111yesmaximal, characteristic, direct product factor, Sylow
136C22×C61—24no—
137C22×C61—24no—
138C22×C61—21no—
139C22×C61—21no—
140C22×C61—21no—
141C22×C61—21no—
142C22×C61#32712yes—
143C22×C61#32712yes—
144C22×C61#35212yes—
145C22×C61#35612yes—
146C22×C61C2×#9911yescharacteristic
147C22×C61C2×#10211yescharacteristic
148C22×C61C2×#10411yescharacteristic
149C4×C61—21no—
150C4×C61—22no—
151C4×C61—21no—
152C4×C61—44no—
153C4×C61—41no—
154C4×C61—41no—
155C4×C61—41no—
156C4×C61—41no—
157C4×C61—82no—
158C2×#398C2×C6111yescharacteristic
159C2×#343C2×C6111yescharacteristic
160C2×#324C2×C6111yescharacteristic
161#1346C2×C6114yesdirect product factor
162C2×C61—21no—
163C2×C61—22no—
164C2×C61—21no—
165C2×C61#134614yesdirect product factor
166C2×C61C2×#32711yescharacteristic
167C2×C61C2×#35211yescharacteristic
168C2×C61C2×#35611yescharacteristic
169C22×M16—21no—
170C22×C4⋊C4—21no—
171C22×C4⋊C4C4×C6111yescharacteristic
172C22×C4⋊C4C22×C6111yescharacteristic
173C2×C22⋊C8—21no—
174#398—21no—
175#398—21no—
176#398C4×C6112yes—
177#398C22×C6112yes—
178C2×#95—21no—
179C2×#95C4×C6111yescharacteristic
180#343—21no—
181#343C22×C6112yes—
182#324—21no—
183#324C22×C6112yes—
184C61C2×#134611yescharacteristic, direct product factor, Sylow
185C23×C4—21no—
186C23×C4—21no—
187C23×C4C2×C4×C6111yescharacteristic
188C23×C4D4×C6111yescharacteristic
189C23×C4D4×C6111yescharacteristic
190C2×M16—24no—
191C2×M16—22no—
192C2×M16—41no—
193C2×M16—42no—
194C22×C8—41no—
195C22×C8—41no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—22no—
199C2×C4⋊C4—41no—
200C2×C4⋊C4—41no—
201C2×C4⋊C4—41no—
202C2×C4⋊C4—41no—
203C2×C4⋊C4—42no—
204C2×C4⋊C4—42no—
205C2×C4⋊C4C2×C4×C6112yes—
206C2×C4⋊C4C2×C4×C6111yescharacteristic
207C2×C4⋊C4D4×C6111yescharacteristic
208C2×C4⋊C4D4×C6111yescharacteristic
209C2×C4⋊C4C23×C6111yescharacteristic
210C22⋊C8—22no—
211C22⋊C8—41no—
212#95—22no—
213#95—21no—
214#95—22no—
215#95C2×C4×C6112yes—
216C24C22⋊C4×C6111yescharacteristic
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—22no—
220C22×C4—24no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—22no—
225C22×C4—21no—
226C22×C4—22no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4C22⋊C4×C6111yescharacteristic
236C22×C4C22⋊C4×C6111yescharacteristic
237C22×C4C22⋊C4×C6111yescharacteristic
238C22×C4D8×C6112yes—
239C22×C4SD16×C6112yes—
240C22×C4C22×C4×C6111yescharacteristic
241C22×C4C2×D4×C6111yescharacteristic
242C22×C4C2×D4×C6111yescharacteristic
243M16—24no—
244M16—44no—
245M16—42no—
246C2×C8—44no—
247C2×C8—42no—
248C2×C8—42no—
249C2×C8—82no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—42no—
255C4⋊C4—42no—
256C4⋊C4—44no—
257C4⋊C4—42no—
258C4⋊C4—42no—
259C23—22no—
260C23—22no—
261C23#99×C6111yescharacteristic
262C23#99×C6111yescharacteristic
263C23#102×C6112yes—
264C23#104×C6112yes—
265C23C2×C22⋊C4×C6111yescharacteristic
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—24no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—48no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—81no—
293C2×C4—82no—
294C2×C4—82no—
295C2×C4#102×C6112yes—
296C2×C4C2×D8×C6111yescharacteristic
297C2×C4C2×SD16×C6111yescharacteristic
298C8—44no—
299C8—82no—
300C22—24no—
301C22—24no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22C61×#32712yes—
307C22C61×#32712yes—
308C22C61×#35212yes—
309C22C61×#35612yes—
310C22C2×#99×C6111yescharacteristic
311C22C2×#102×C6111yescharacteristic
312C22C2×#104×C6111yescharacteristic
313C4—21no—
314C4—22no—
315C4—21no—
316C4—44no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—82no—
322C2—21no—
323C2—22no—
324C2—21no—
325C2C61×#134614yesdirect product factor
326C2C2×C61×#32711yescharacteristic
327C2C2×C61×#35211yescharacteristic
328C2C2×C61×#35611yescharacteristic
subgroupG/H
center, socleC23×C61#99
commutatorC22×C4C22×C4×C61
Frattini, cosocleC2×C4⋊C4C23×C61
prime radicalC24×C61C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C24×C61 ◁ C22×C4⋊C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
4. C61×#1346C2direct (N × H)
135. C2×#1346C61direct (N × H)
161. #1346C2×C61direct (N × H)
165. C2×C61#1346direct (N × H)
184. C61C2×#1346direct (N × H)
325. C2C61×#1346direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C61×#3982
C2×C61×#3432
C2×C61×#3242
C61×#13462
C2×#134661