Finite Group Databasebeta

← C61×#19287 #29522720

Subgroups — C61×#19287 #29522720

Order 15616.

582 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×#3170C211yesmaximal, characteristic
2C61×#3078C212yesmaximal
3C2×C61×#446C211yesmaximal, characteristic
4C61×#1704C214yesmaximal, complemented
5C61×#1696C212yesmaximal, complemented
6C61×#1690C212yesmaximal, complemented
7C61×#1566C211yesmaximal, characteristic
8C61×#1550C212yesmaximal
9C61×#533C2212yes—
10C2×C4×Q8×C61C2211yescharacteristic
11C61×#500C2211yescharacteristic
12C61×#494C2211yescharacteristic
13C61×#487C2212yes—
14C61×#479—24no—
15C61×#477C2214yes—
16C61×#475C2214yes—
17C61×#467—21no—
18C61×#467—21no—
19C61×#446—21no—
20C61×#446—21no—
21C61×#446C2212yes—
22C61×#446C2212yes—
23C4×Q16×C61—21no—
24C4×Q16×C61—21no—
25C61×#428—22no—
26C61×#423C2212yes—
27C2×C4⋊C8×C61—21no—
28C2×C4⋊C8×C61C2211yescharacteristic
29C61×#419—22no—
30C2×#97×C61—21no—
31C2×C4×C8×C61C2211yescharacteristic
32C61×#334C2212yes—
33C61×#334C2212yes—
34C61×#333C2214yes—
35C61×#332C2214yes—
36C22×Q8×C61D411yescharacteristic
37C2×Q16×C61—21no—
38C2×Q16×C61—21no—
39C2×M16×C61—22no—
40C22×C8×C61—21no—
41C22×C8×C61D411yescharacteristic
42C22×C8×C61D411yescharacteristic
43C4⋊Q8×C61C2312yes—
44C4⋊Q8×C61C2312yes—
45#125×C61—22no—
46C22⋊Q8×C61—22no—
47C22⋊Q8×C61—22no—
48C4×Q8×C61—21no—
49C4×Q8×C61—21no—
50C4×Q8×C61—22no—
51C4×Q8×C61—22no—
52C4×Q8×C61D412yes—
53C4×Q8×C61C2312yes—
54#117×C61—22no—
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61D411yescharacteristic
57C2×C42×C61—21no—
58C2×C42×C61C2311yescharacteristic
59#107×C61—21no—
60#107×C61—21no—
61#107×C61—24no—
62#106×C61—24no—
63C4⋊C8×C61—22no—
64C4⋊C8×C61—22no—
65C4⋊C8×C61—21no—
66C4⋊C8×C61—22no—
67C4⋊C8×C61C2312yes—
68C4⋊C8×C61C2314yes—
69#103×C61—24no—
70#103×C61—24no—
71#103×C61—22no—
72#103×C61—22no—
73#97×C61—22no—
74#97×C61—22no—
75C4×C8×C61D411yescharacteristic
76C4×C8×C61D411yescharacteristic
77C4×C8×C61C2311yescharacteristic
78C4×C8×C61C2311yescharacteristic
79C2×Q8×C61—21no—
80C2×Q8×C61—24no—
81C2×Q8×C61—22no—
82C2×Q8×C61—22no—
83C2×Q8×C61C2×D412yes—
84C22×C4×C61—21no—
85C22×C4×C61—21no—
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61C2×D411yescharacteristic
88C22×C4×C61#4111yescharacteristic
89Q16×C61—42no—
90Q16×C61—42no—
91M16×C61—44no—
92C2×C8×C61—22no—
93C2×C8×C61—22no—
94C2×C8×C61—24no—
95C2×C8×C61—41no—
96C2×C8×C61—42no—
97C2×C8×C61C2×D411yescharacteristic
98C2×C8×C61C2×D411yescharacteristic
99C2×C8×C61C2×D411yescharacteristic
100C2×C8×C61C2×D411yescharacteristic
101C4⋊C4×C61—22no—
102C4⋊C4×C61—21no—
103C4⋊C4×C61—22no—
104C4⋊C4×C61—22no—
105C4⋊C4×C61—22no—
106C4⋊C4×C61—22no—
107C4⋊C4×C61—22no—
108C4⋊C4×C61—42no—
109C4⋊C4×C61—42no—
110C4⋊C4×C61C2×D412yes—
111C22⋊C4×C61—42no—
112C42×C61—22no—
113C42×C61—22no—
114C42×C61—42no—
115C42×C61C2×D411yescharacteristic
116C42×C61C2×D411yescharacteristic
117C42×C61#4111yescharacteristic
118C42×C61C2411yescharacteristic
119C23×C61#12111yescharacteristic
120Q8×C61—24no—
121Q8×C61—42no—
122Q8×C61—42no—
123Q8×C61—42no—
124Q8×C61—82no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—22no—
128C2×C4×C61—22no—
129C2×C4×C61—41no—
130C2×C4×C61—42no—
131C2×C4×C61—42no—
132C2×C4×C61—42no—
133C2×C4×C61—42no—
134C2×C4×C61#12111yescharacteristic
135C2×C4×C61#12111yescharacteristic
136C2×C4×C61#12111yescharacteristic
137C2×C4×C61#13714yes—
138C2×C4×C61C22×D411yescharacteristic
139C2×C4×C61C22×D411yescharacteristic
140C2×C4×C61C2×#4111yescharacteristic
141C8×C61—21no—
142C8×C61—21no—
143C8×C61—21no—
144C8×C61—44no—
145C8×C61—42no—
146C8×C61#13712yes—
147#19287C6111yesmaximal, characteristic, direct product factor, Sylow
148C22×C61—21no—
149C22×C61—21no—
150C22×C61#47012yes—
151C22×C61C2×#12111yescharacteristic
152C4×C61—21no—
153C4×C61—21no—
154C4×C61—21no—
155C4×C61—42no—
156C4×C61—42no—
157C4×C61—82no—
158C4×C61—82no—
159C4×C61#47012yes—
160C4×C61C2×#13711yescharacteristic
161C4×C61C2×#13712yes—
162C4×C61#57511yescharacteristic
163#3170C2×C6111yescharacteristic
164#3078C2×C6112yes—
165C2×#446C2×C6111yescharacteristic
166#1704C2×C6114yescomplemented
167#1696C2×C6112yescomplemented
168#1690C2×C6112yescomplemented
169#1566C2×C6111yescharacteristic
170#1550C2×C6112yes—
171C2×C61—22no—
172C2×C61#303711yescharacteristic
173C2×C61C2×#47011yescharacteristic
174C2×C61#306711yescharacteristic
175#533C22×C6112yes—
176C2×C4×Q8C22×C6111yescharacteristic
177#500C22×C6111yescharacteristic
178#494C22×C6111yescharacteristic
179#487C22×C6112yes—
180#479—24no—
181#477C22×C6114yes—
182#475C22×C6114yes—
183#467—21no—
184#467—21no—
185#446—21no—
186#446—21no—
187#446C22×C6112yes—
188#446C22×C6112yes—
189C4×Q16—21no—
190C4×Q16—21no—
191#428—22no—
192#423C22×C6112yes—
193C2×C4⋊C8—21no—
194C2×C4⋊C8C22×C6111yescharacteristic
195#419—22no—
196C2×#97—21no—
197C2×C4×C8C22×C6111yescharacteristic
198#334C22×C6112yes—
199#334C22×C6112yes—
200#333C22×C6114yes—
201#332C22×C6114yes—
202C61#1928711yescharacteristic, direct product factor, Sylow
203C22×Q8D4×C6111yescharacteristic
204C2×Q16—21no—
205C2×Q16—21no—
206C2×M16—22no—
207C22×C8—21no—
208C22×C8D4×C6111yescharacteristic
209C22×C8D4×C6111yescharacteristic
210C4⋊Q8C23×C6112yes—
211C4⋊Q8C23×C6112yes—
212#125—22no—
213C22⋊Q8—22no—
214C22⋊Q8—22no—
215C4×Q8—21no—
216C4×Q8—21no—
217C4×Q8—22no—
218C4×Q8—22no—
219C4×Q8D4×C6112yes—
220C4×Q8C23×C6112yes—
221#117—22no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4D4×C6111yescharacteristic
224C2×C42—21no—
225C2×C42C23×C6111yescharacteristic
226#107—21no—
227#107—21no—
228#107—24no—
229#106—24no—
230C4⋊C8—22no—
231C4⋊C8—22no—
232C4⋊C8—21no—
233C4⋊C8—22no—
234C4⋊C8C23×C6112yes—
235C4⋊C8C23×C6114yes—
236#103—24no—
237#103—24no—
238#103—22no—
239#103—22no—
240#97—22no—
241#97—22no—
242C4×C8D4×C6111yescharacteristic
243C4×C8D4×C6111yescharacteristic
244C4×C8C23×C6111yescharacteristic
245C4×C8C23×C6111yescharacteristic
246C2×Q8—21no—
247C2×Q8—24no—
248C2×Q8—22no—
249C2×Q8—22no—
250C2×Q8C2×D4×C6112yes—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4C2×D4×C6111yescharacteristic
254C22×C4C2×D4×C6111yescharacteristic
255C22×C4#41×C6111yescharacteristic
256Q16—42no—
257Q16—42no—
258M16—44no—
259C2×C8—22no—
260C2×C8—22no—
261C2×C8—24no—
262C2×C8—41no—
263C2×C8—42no—
264C2×C8C2×D4×C6111yescharacteristic
265C2×C8C2×D4×C6111yescharacteristic
266C2×C8C2×D4×C6111yescharacteristic
267C2×C8C2×D4×C6111yescharacteristic
268C4⋊C4—22no—
269C4⋊C4—21no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—42no—
276C4⋊C4—42no—
277C4⋊C4C2×D4×C6112yes—
278C22⋊C4—42no—
279C42—22no—
280C42—22no—
281C42—42no—
282C42C2×D4×C6111yescharacteristic
283C42C2×D4×C6111yescharacteristic
284C42#41×C6111yescharacteristic
285C42C24×C6111yescharacteristic
286C23#121×C6111yescharacteristic
287Q8—24no—
288Q8—42no—
289Q8—42no—
290Q8—42no—
291Q8—82no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4#121×C6111yescharacteristic
302C2×C4#121×C6111yescharacteristic
303C2×C4#121×C6111yescharacteristic
304C2×C4#137×C6114yes—
305C2×C4C22×D4×C6111yescharacteristic
306C2×C4C22×D4×C6111yescharacteristic
307C2×C4C2×#41×C6111yescharacteristic
308C8—21no—
309C8—21no—
310C8—21no—
311C8—44no—
312C8—42no—
313C8#137×C6112yes—
314C22—21no—
315C22—21no—
316C22C61×#47012yes—
317C22C2×#121×C6111yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—42no—
322C4—42no—
323C4—82no—
324C4—82no—
325C4C61×#47012yes—
326C4C2×#137×C6111yescharacteristic
327C4C2×#137×C6112yes—
328C4C61×#57511yescharacteristic
329C2—22no—
330C2C61×#303711yescharacteristic
331C2C2×C61×#47011yescharacteristic
332C2C61×#306711yescharacteristic
subgroupG/H
center, socleC22×C61C2×#121
commutator, Frattini, cosocleC42C24×C61
prime radicalC23×C61#121
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
4. C61×#1704C2semidirect
5. C61×#1696C2semidirect
6. C61×#1690C2semidirect
147. #19287C61direct (N × H)
166. #1704C2×C61semidirect
167. #1696C2×C61semidirect
168. #1690C2×C61semidirect
202. C61#19287direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#31702
C61×#30782
C2×C61×#4462
C61×#17042
C61×#16962
C61×#16902
C61×#15662
C61×#15502
#1928761