Finite Group Databasebeta

← C61×#9048 #29512481

Subgroups — C61×#9048 #29512481

Order 15616.

424 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3104C211yesmaximal, characteristic
2C61×#2961C211yesmaximal, characteristic
3C61×#1985C211yesmaximal, characteristic
4C61×#1542C211yesmaximal, characteristic
5C61×#1487C211yesmaximal, characteristic
6C61×#1301C211yesmaximal, characteristic
7C61×#1281C211yesmaximal, characteristic
8C61×#533C2211yescharacteristic
9C2×C4×Q8×C61C2211yescharacteristic
10C61×#484C412yes—
11C61×#477—21no—
12C61×#462—21no—
13C61×#451C412yes—
14C61×#446—22no—
15C61×#446—22no—
16C4×Q16×C61—22no—
17C61×#431C2211yescharacteristic
18C61×#431C2211yescharacteristic
19C61×#424—21no—
20C61×#423C2211yescharacteristic
21C2×C4⋊C8×C61C2211yescharacteristic
22C61×#405—21no—
23C2×#97×C61C2211yescharacteristic
24C61×#336—21no—
25C61×#336—21no—
26C61×#333—21no—
27C61×#332—21no—
28C61×Q8⋊C8—22no—
29C22×Q8×C61C2×C411yescharacteristic
30C2×Q16×C61—22no—
31C2×M16×C61—21no—
32C22×C8×C61—21no—
33C22×C8×C61D411yescharacteristic
34C22×C8×C61D411yescharacteristic
35C4⋊Q8×C61D411yescharacteristic
36C4⋊Q8×C61D411yescharacteristic
37#125×C61—21no—
38C22⋊Q8×C61—21no—
39C22⋊Q8×C61C2×C412yes—
40C4×Q8×C61—21no—
41C4×Q8×C61—21no—
42C4×Q8×C61—21no—
43C4×Q8×C61—21no—
44C4×Q8×C61—21no—
45C4×Q8×C61D412yes—
46#117×C61—21no—
47C2×C4⋊C4×C61—21no—
48C2×C4⋊C4×C61C2×C411yescharacteristic
49C2×C42×C61—21no—
50C2×C42×C61C2311yescharacteristic
51#107×C61—22no—
52C4⋊C8×C61—24no—
53C4⋊C8×C61—21no—
54C4⋊C8×C61—21no—
55C4⋊C8×C61—21no—
56C4⋊C8×C61—21no—
57C4⋊C8×C61—21no—
58C4⋊C8×C61D412yes—
59#103×C61—22no—
60#103×C61—22no—
61C22⋊C8×C61—21no—
62C22⋊C8×C61C2×C412yes—
63#97×C61—22no—
64#97×C61—21no—
65#97×C61—21no—
66C4×C8×C61—22no—
67C4×C8×C61—21no—
68C4×C8×C61—21no—
69C2×Q8×C61—21no—
70C2×Q8×C61—21no—
71C2×Q8×C61—21no—
72C2×Q8×C61—42no—
73C2×Q8×C61C22⋊C412yes—
74C22×C4×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61C22×C411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61#4111yescharacteristic
79Q16×C61—44no—
80M16×C61—41no—
81M16×C61—41no—
82C2×C8×C61—21no—
83C2×C8×C61—21no—
84C2×C8×C61—22no—
85C2×C8×C61—22no—
86C2×C8×C61—21no—
87C2×C8×C61—21no—
88C2×C8×C61—21no—
89C2×C8×C61—41no—
90C2×C8×C61—41no—
91C2×C8×C61—41no—
92C2×C8×C61—41no—
93C2×C8×C61Q1612yescomplemented
94C4⋊C4×C61—22no—
95C4⋊C4×C61—21no—
96C4⋊C4×C61—21no—
97C4⋊C4×C61—21no—
98C4⋊C4×C61—22no—
99C4⋊C4×C61—21no—
100C4⋊C4×C61—21no—
101C4⋊C4×C61—41no—
102C4⋊C4×C61—41no—
103C4⋊C4×C61C22⋊C412yes—
104C22⋊C4×C61—22no—
105C42×C61—22no—
106C42×C61—41no—
107C42×C61—41no—
108C42×C61C2×D411yescharacteristic
109C42×C61C2×D411yescharacteristic
110C42×C61C2×D411yescharacteristic
111C42×C61#4111yescharacteristic
112C23×C61C4×D411yescharacteristic
113Q8×C61—22no—
114Q8×C61—22no—
115Q8×C61—41no—
116Q8×C61—41no—
117Q8×C61—42no—
118Q8×C61—81no—
119C2×C4×C61—22no—
120C2×C4×C61—22no—
121C2×C4×C61—22no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—42no—
127C2×C4×C61—41no—
128C2×C4×C61C2×C22⋊C411yescharacteristic
129C2×C4×C61C4×D411yescharacteristic
130C2×C4×C61#12011yescharacteristic
131C2×C4×C61#12111yescharacteristic
132C2×C4×C61#12111yescharacteristic
133C2×C4×C61#12311yescharacteristic
134C2×C4×C61C2×Q1611yescharacteristic
135C2×C4×C61#13511yescharacteristic
136C2×C4×C61#13711yescharacteristic
137C2×C4×C61#13711yescharacteristic
138C8×C61—22no—
139C8×C61—42no—
140C8×C61—41no—
141C8×C61—42no—
142C8×C61—81no—
143C8×C61—81no—
144#9048C6111yesmaximal, characteristic, direct product factor, Sylow
145C22×C61—21no—
146C22×C61—21no—
147C22×C61#38611yescharacteristic
148C22×C61C4×Q1611yescharacteristic
149C22×C61#44111yescharacteristic
150C4×C61—21no—
151C4×C61—21no—
152C4×C61—21no—
153C4×C61—21no—
154C4×C61—42no—
155C4×C61—42no—
156C4×C61—42no—
157C4×C61—81no—
158C4×C61#45111yescharacteristic
159C4×C61#45211yescharacteristic
160C4×C61#46211yescharacteristic
161C4×C61#46411yescharacteristic
162#3104C2×C6111yescharacteristic
163#2961C2×C6111yescharacteristic
164#1985C2×C6111yescharacteristic
165#1542C2×C6111yescharacteristic
166#1487C2×C6111yescharacteristic
167#1301C2×C6111yescharacteristic
168#1281C2×C6111yescharacteristic
169C2×C61—21no—
170C2×C61—21no—
171C2×C61#187811yescharacteristic
172C2×C61#188111yescharacteristic
173C2×C61#189111yescharacteristic
174#533C22×C6111yescharacteristic
175C2×C4×Q8C22×C6111yescharacteristic
176#484C4×C6112yes—
177#477—21no—
178#462—21no—
179#451C4×C6112yes—
180#446—22no—
181#446—22no—
182C4×Q16—22no—
183#431C22×C6111yescharacteristic
184#431C22×C6111yescharacteristic
185#424—21no—
186#423C22×C6111yescharacteristic
187C2×C4⋊C8C22×C6111yescharacteristic
188#405—21no—
189C2×#97C22×C6111yescharacteristic
190#336—21no—
191#336—21no—
192#333—21no—
193#332—21no—
194Q8⋊C8—22no—
195C61#904811yescharacteristic, direct product factor, Sylow
196C22×Q8C2×C4×C6111yescharacteristic
197C2×Q16—22no—
198C2×M16—21no—
199C22×C8—21no—
200C22×C8D4×C6111yescharacteristic
201C22×C8D4×C6111yescharacteristic
202C4⋊Q8D4×C6111yescharacteristic
203C4⋊Q8D4×C6111yescharacteristic
204#125—21no—
205C22⋊Q8—21no—
206C22⋊Q8C2×C4×C6112yes—
207C4×Q8—21no—
208C4×Q8—21no—
209C4×Q8—21no—
210C4×Q8—21no—
211C4×Q8—21no—
212C4×Q8D4×C6112yes—
213#117—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4C2×C4×C6111yescharacteristic
216C2×C42—21no—
217C2×C42C23×C6111yescharacteristic
218#107—22no—
219C4⋊C8—24no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8D4×C6112yes—
226#103—22no—
227#103—22no—
228C22⋊C8—21no—
229C22⋊C8C2×C4×C6112yes—
230#97—22no—
231#97—21no—
232#97—21no—
233C4×C8—22no—
234C4×C8—21no—
235C4×C8—21no—
236C2×Q8—21no—
237C2×Q8—21no—
238C2×Q8—21no—
239C2×Q8—42no—
240C2×Q8C22⋊C4×C6112yes—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4C22×C4×C6111yescharacteristic
244C22×C4C2×D4×C6111yescharacteristic
245C22×C4#41×C6111yescharacteristic
246Q16—44no—
247M16—41no—
248M16—41no—
249C2×C8—21no—
250C2×C8—21no—
251C2×C8—22no—
252C2×C8—22no—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8Q16×C6112yescomplemented
261C4⋊C4—22no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—22no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4C22⋊C4×C6112yes—
271C22⋊C4—22no—
272C42—22no—
273C42—41no—
274C42—41no—
275C42C2×D4×C6111yescharacteristic
276C42C2×D4×C6111yescharacteristic
277C42C2×D4×C6111yescharacteristic
278C42#41×C6111yescharacteristic
279C23C4×D4×C6111yescharacteristic
280Q8—22no—
281Q8—22no—
282Q8—42no—
283Q8—41no—
284Q8—41no—
285Q8—81no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—41no—
295C2×C4C2×C22⋊C4×C6111yescharacteristic
296C2×C4C4×D4×C6111yescharacteristic
297C2×C4#120×C6111yescharacteristic
298C2×C4#121×C6111yescharacteristic
299C2×C4#121×C6111yescharacteristic
300C2×C4#123×C6111yescharacteristic
301C2×C4C2×Q16×C6111yescharacteristic
302C2×C4#135×C6111yescharacteristic
303C2×C4#137×C6111yescharacteristic
304C2×C4#137×C6111yescharacteristic
305C8—22no—
306C8—42no—
307C8—41no—
308C8—42no—
309C8—81no—
310C8—81no—
311C22—21no—
312C22—21no—
313C22C61×#38611yescharacteristic
314C22C4×Q16×C6111yescharacteristic
315C22C61×#44111yescharacteristic
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—42no—
321C4—42no—
322C4—42no—
323C4—81no—
324C4C61×#45111yescharacteristic
325C4C61×#45211yescharacteristic
326C4C61×#46211yescharacteristic
327C4C61×#46411yescharacteristic
328C2—21no—
329C2—21no—
330C2C61×#187811yescharacteristic
331C2C61×#188111yescharacteristic
332C2C61×#189111yescharacteristic
subgroupG/H
centerC2×C4×C61#120
commutatorC22×C4C22×C4×C61
Frattini, cosocleC2×C42C23×C61
socleC22×C61#386
prime radicalC23×C61C4×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
93. C2×C8×C61Q16semidirect
144. #9048C61direct (N × H)
195. C61#9048direct (N × H)
260. C2×C8Q16×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#31042
C61×#29612
C61×#19852
C61×#15422
C61×#14872
C61×#13012
C61×#12812
#904861