Finite Group Databasebeta

← C61×#10288 #29513721

Subgroups — C61×#10288 #29513721

Order 15616.

554 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3226C211yesmaximal, characteristic
2C61×#3206C211yesmaximal, characteristic
3C61×#2862C211yesmaximal, characteristic, complemented
4C61×#1962C211yesmaximal, characteristic
5C61×#1548C211yesmaximal, characteristic, complemented
6C61×#1546C211yesmaximal, characteristic, complemented
7C61×#1276C211yesmaximal, characteristic, complemented
8C61×#532C2211yescharacteristic
9C2×C4⋊Q8×C61C2211yescharacteristic
10C2×C4⋊Q8×C61C2211yescharacteristic
11C61×#500—21no—
12C61×#492—21no—
13C61×#487—21no—
14C61×#486—21no—
15C61×#480—22no—
16C61×#474—22no—
17C61×#461—22no—
18C61×#448—22no—
19C61×#431C2211yescharacteristic
20C61×#431C2211yescharacteristic
21C61×#423C2211yescharacteristic
22C2×#104×C61—22no—
23C61×#391—22no—
24C61×#391—22no—
25C61×#382—22no—
26C43×C61C2211yescharacteristic
27C61×#333—22no—
28C61×#332—22no—
29C2×#41×C61—21no—
30C22×Q8×C61—21no—
31C22×Q8×C61D412yes—
32C2×SD16×C61—24no—
33C2×M16×C61—21no—
34C4⋊Q8×C61—21no—
35C4⋊Q8×C61—21no—
36C4⋊Q8×C61—21no—
37C4⋊Q8×C61—21no—
38C4⋊Q8×C61—21no—
39C4⋊Q8×C61—21no—
40C4⋊Q8×C61—21no—
41C4⋊Q8×C61—21no—
42C4⋊Q8×C61D411yescharacteristic
43#127×C61D411yescharacteristic
44#124×C61—21no—
45#121×C61—21no—
46#121×C61—21no—
47C4×D4×C61—21no—
48C4×D4×C61—21no—
49C2×C4⋊C4×C61—21no—
50C2×C4⋊C4×C61—21no—
51C2×C4⋊C4×C61—21no—
52C2×C4⋊C4×C61D412yes—
53C2×C42×C61—21no—
54C2×C42×C61—21no—
55C2×C42×C61D412yes—
56C2×C42×C61C2311yescharacteristic
57#107×C61—24no—
58C4⋊C8×C61—21no—
59C4⋊C8×C61—21no—
60C4⋊C8×C61D412yes—
61C4⋊C8×C61D412yes—
62#104×C61—44no—
63#103×C61—24no—
64#102×C61—24no—
65C22⋊C8×C61—21no—
66C22⋊C8×C61—21no—
67C4×C8×C61—21no—
68C4×C8×C61—21no—
69#95×C61—28no—
70#41×C61—42no—
71#41×C61—42no—
72C2×Q8×C61—22no—
73C2×Q8×C61—21no—
74C2×Q8×C61—22no—
75C2×Q8×C61—44no—
76C2×Q8×C61—41no—
77C2×Q8×C61—41no—
78C2×Q8×C61—42no—
79C2×Q8×C61—42no—
80C2×D4×C61—21no—
81C2×D4×C61—21no—
82C2×D4×C61—21no—
83C2×D4×C61—41no—
84C22×C4×C61—22no—
85C22×C4×C61—22no—
86C22×C4×C61—22no—
87C22×C4×C61—41no—
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61C2×D411yescharacteristic
90C22×C4×C61C2×D411yescharacteristic
91SD16×C61—84no—
92M16×C61—42no—
93C2×C8×C61—22no—
94C2×C8×C61—22no—
95C2×C8×C61—41no—
96C4⋊C4×C61—22no—
97C4⋊C4×C61—21no—
98C4⋊C4×C61—21no—
99C4⋊C4×C61—22no—
100C4⋊C4×C61—41no—
101C4⋊C4×C61—41no—
102C4⋊C4×C61—41no—
103C4⋊C4×C61—41no—
104C4⋊C4×C61—41no—
105C4⋊C4×C61—41no—
106C22⋊C4×C61—41no—
107C22⋊C4×C61—41no—
108C42×C61—24no—
109C42×C61—22no—
110C42×C61—22no—
111C42×C61—42no—
112C42×C61C2×D411yescharacteristic
113C42×C61C2×D411yescharacteristic
114C42×C61C2×D411yescharacteristic
115C42×C61#4111yescharacteristic
116C23×C61—41no—
117C23×C61#12011yescharacteristic
118Q8×C61—44no—
119Q8×C61—42no—
120Q8×C61—82no—
121Q8×C61—82no—
122Q8×C61—81no—
123Q8×C61—81no—
124D4×C61—42no—
125D4×C61—42no—
126D4×C61—42no—
127D4×C61—82no—
128C2×C4×C61—22no—
129C2×C4×C61—22no—
130C2×C4×C61—24no—
131C2×C4×C61—42no—
132C2×C4×C61—42no—
133C2×C4×C61—44no—
134C2×C4×C61—41no—
135C2×C4×C61—42no—
136C2×C4×C61—42no—
137C2×C4×C61—44no—
138C2×C4×C61—81no—
139C2×C4×C61—81no—
140C2×C4×C61#12011yescharacteristic
141C2×C4×C61#12011yescharacteristic
142C2×C4×C61#12111yescharacteristic
143C2×C4×C61#12111yescharacteristic
144C2×C4×C61#12111yescharacteristic
145C2×C4×C61#12711yescharacteristic
146C2×C4×C61#13512yes—
147C2×C4×C61AGL(1,ℤ/8)12yes—
148C8×C61—42no—
149C8×C61—42no—
150C8×C61—81no—
151#10288C6111yesmaximal, characteristic, direct product factor, Sylow
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—81no—
155C22×C61—81no—
156C22×C61—81no—
157C22×C61#39211yescharacteristic
158C22×C61#44912yes—
159C4×C61—21no—
160C4×C61—21no—
161C4×C61—44no—
162C4×C61—82no—
163C4×C61—82no—
164C4×C61—81no—
165C4×C61#45512yes—
166C4×C61#45612yes—
167C4×C61#46312yes—
168C4×C61#49511yescharacteristic
169C4×C61#49611yescharacteristic
170#3226C2×C6111yescharacteristic
171#3206C2×C6111yescharacteristic
172#2862C2×C6111yescharacteristic, complemented
173#1962C2×C6111yescharacteristic
174#1548C2×C6111yescharacteristic, complemented
175#1546C2×C6111yescharacteristic, complemented
176#1276C2×C6111yescharacteristic, complemented
177C2×C61—22no—
178C2×C61—161no—
179C2×C61#200411yescharacteristic
180C2×C61#200511yescharacteristic
181C2×C61#201211yescharacteristic
182#532C22×C6111yescharacteristic
183C2×C4⋊Q8C22×C6111yescharacteristic
184C2×C4⋊Q8C22×C6111yescharacteristic
185#500—21no—
186#492—21no—
187#487—21no—
188#486—21no—
189#480—22no—
190#474—22no—
191#461—22no—
192#448—22no—
193#431C22×C6111yescharacteristic
194#431C22×C6111yescharacteristic
195#423C22×C6111yescharacteristic
196C2×#104—22no—
197#391—22no—
198#391—22no—
199#382—22no—
200C43C22×C6111yescharacteristic
201#333—22no—
202#332—22no—
203C61#1028811yescharacteristic, direct product factor, Sylow
204C2×#41—21no—
205C22×Q8—21no—
206C22×Q8D4×C6112yes—
207C2×SD16—24no—
208C2×M16—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—21no—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8—21no—
215C4⋊Q8—21no—
216C4⋊Q8—21no—
217C4⋊Q8D4×C6111yescharacteristic
218#127D4×C6111yescharacteristic
219#124—21no—
220#121—21no—
221#121—21no—
222C4×D4—21no—
223C4×D4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4D4×C6112yes—
228C2×C42—21no—
229C2×C42—21no—
230C2×C42D4×C6112yes—
231C2×C42C23×C6111yescharacteristic
232#107—24no—
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8D4×C6112yes—
236C4⋊C8D4×C6112yes—
237#104—44no—
238#103—24no—
239#102—24no—
240C22⋊C8—21no—
241C22⋊C8—21no—
242C4×C8—21no—
243C4×C8—21no—
244#95—28no—
245#41—42no—
246#41—42no—
247C2×Q8—22no—
248C2×Q8—21no—
249C2×Q8—22no—
250C2×Q8—44no—
251C2×Q8—41no—
252C2×Q8—41no—
253C2×Q8—42no—
254C2×Q8—42no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—41no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—41no—
263C22×C4C2×D4×C6111yescharacteristic
264C22×C4C2×D4×C6111yescharacteristic
265C22×C4C2×D4×C6111yescharacteristic
266SD16—84no—
267M16—42no—
268C2×C8—22no—
269C2×C8—22no—
270C2×C8—41no—
271C4⋊C4—22no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—22no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C42—24no—
284C42—22no—
285C42—22no—
286C42—42no—
287C42C2×D4×C6111yescharacteristic
288C42C2×D4×C6111yescharacteristic
289C42C2×D4×C6111yescharacteristic
290C42#41×C6111yescharacteristic
291C23—41no—
292C23#120×C6111yescharacteristic
293Q8—44no—
294Q8—42no—
295Q8—82no—
296Q8—82no—
297Q8—81no—
298Q8—81no—
299D4—42no—
300D4—42no—
301D4—42no—
302D4—82no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—24no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—44no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—44no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4#120×C6111yescharacteristic
316C2×C4#120×C6111yescharacteristic
317C2×C4#121×C6111yescharacteristic
318C2×C4#121×C6111yescharacteristic
319C2×C4#121×C6111yescharacteristic
320C2×C4#127×C6111yescharacteristic
321C2×C4#135×C6112yes—
322C2×C4AGL(1,ℤ/8)×C6112yes—
323C8—42no—
324C8—42no—
325C8—81no—
326C22—21no—
327C22—21no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22C61×#39211yescharacteristic
332C22C61×#44912yes—
333C4—21no—
334C4—21no—
335C4—44no—
336C4—82no—
337C4—81no—
338C4—82no—
339C4C61×#45512yes—
340C4C61×#45612yes—
341C4C61×#46312yes—
342C4C61×#49511yescharacteristic
343C4C61×#49611yescharacteristic
344C2—22no—
345C2—161no—
346C2C61×#200411yescharacteristic
347C2C61×#200511yescharacteristic
348C2C61×#201211yescharacteristic
subgroupG/H
center, socleC22×C61#392
commutator, Frattini, cosocleC2×C42C23×C61
prime radicalC61×#532C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
3. C61×#2862C2semidirect
5. C61×#1548C2semidirect
6. C61×#1546C2semidirect
7. C61×#1276C2semidirect
151. #10288C61direct (N × H)
172. #2862C2×C61semidirect
174. #1548C2×C61semidirect
175. #1546C2×C61semidirect
176. #1276C2×C61semidirect
203. C61#10288direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#32262
C61×#32062
C61×#28622
C61×#19622
C61×#15482
C61×#15462
C61×#12762
#1028861