Finite Group Databasebeta

← C61×#10245 #29513678

Subgroups — C61×#10245 #29513678

Order 15616.

558 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3227C211yesmaximal, characteristic
2C61×#3037C211yesmaximal, characteristic
3C61×#2567C211yesmaximal, characteristic, complemented
4C61×#1549C211yesmaximal, characteristic, complemented
5C61×#1502C211yesmaximal, characteristic
6C61×#1479C211yesmaximal, characteristic, complemented
7C61×#1303C211yesmaximal, characteristic, complemented
8C2×#137×C61—21no—
9C61×#532C2211yescharacteristic
10C2×C4⋊Q8×C61C2211yescharacteristic
11C2×C4×Q8×C61C2211yescharacteristic
12C61×#498—21no—
13C61×#486—21no—
14C61×#481—22no—
15C61×#476—22no—
16C61×#464—22no—
17C61×#462—21no—
18C61×#460—21no—
19C61×#431C2211yescharacteristic
20C61×#431C2211yescharacteristic
21C61×#423C2211yescharacteristic
22C61×#417—21no—
23C61×#395—22no—
24C61×#391—21no—
25C61×#389—22no—
26C61×#384—21no—
27C4×C4⋊C4×C61C2211yescharacteristic
28C61×#332—22no—
29C61×#327—22no—
30C61×Q8⋊C8—22no—
31C2×#41×C61—21no—
32C22×Q8×C61—21no—
33C22×Q8×C61D411yescharacteristic
34#137×C61—42no—
35#137×C61—42no—
36C2×Q16×C61—22no—
37C2×SD16×C61—22no—
38C2×M16×C61—21no—
39C4⋊Q8×C61—21no—
40C4⋊Q8×C61—21no—
41C4⋊Q8×C61—21no—
42C4⋊Q8×C61—21no—
43C4⋊Q8×C61D411yescharacteristic
44#127×C61D411yescharacteristic
45#124×C61—21no—
46#121×C61—21no—
47#121×C61—21no—
48C4×Q8×C61—21no—
49C4×Q8×C61—21no—
50C4×Q8×C61—21no—
51C4×Q8×C61—21no—
52C4×D4×C61—21no—
53C4×D4×C61—21no—
54C2×C4⋊C4×C61—21no—
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61—21no—
57C2×C4⋊C4×C61—24no—
58C2×C4⋊C4×C61D412yes—
59C2×C4⋊C4×C61D411yescharacteristic
60C2×C42×C61—21no—
61C2×C42×C61—21no—
62C2×C42×C61C2311yescharacteristic
63#106×C61—24no—
64C4⋊C8×C61—21no—
65C4⋊C8×C61—21no—
66C4⋊C8×C61D412yes—
67C4⋊C8×C61D412yes—
68#103×C61—22no—
69#102×C61—22no—
70#102×C61—24no—
71C22⋊C8×C61—21no—
72C22⋊C8×C61—21no—
73C4×C8×C61—21no—
74C4×C8×C61—21no—
75#95×C61—24no—
76#95×C61D412yes—
77#41×C61—41no—
78#41×C61—41no—
79#41×C61—41no—
80#41×C61—41no—
81C2×Q8×C61—21no—
82C2×Q8×C61—21no—
83C2×Q8×C61—21no—
84C2×Q8×C61—21no—
85C2×Q8×C61—21no—
86C2×Q8×C61—21no—
87C2×Q8×C61—41no—
88C2×Q8×C61—41no—
89C2×Q8×C61—82no—
90C2×Q8×C61SD1612yes—
91C2×D4×C61—21no—
92C2×D4×C61—21no—
93C2×D4×C61—21no—
94C2×D4×C61—41no—
95C22×C4×C61—21no—
96C22×C4×C61—22no—
97C22×C4×C61—22no—
98C22×C4×C61—21no—
99C22×C4×C61—41no—
100C22×C4×C61C2×D411yescharacteristic
101C22×C4×C61C2×D411yescharacteristic
102C22×C4×C61C2×D411yescharacteristic
103Q16×C61—44no—
104SD16×C61—44no—
105M16×C61—41no—
106M16×C61—41no—
107C2×C8×C61—22no—
108C2×C8×C61—22no—
109C2×C8×C61—41no—
110C4⋊C4×C61—24no—
111C4⋊C4×C61—21no—
112C4⋊C4×C61—22no—
113C4⋊C4×C61—21no—
114C4⋊C4×C61—21no—
115C4⋊C4×C61—22no—
116C4⋊C4×C61—21no—
117C4⋊C4×C61—41no—
118C4⋊C4×C61—41no—
119C4⋊C4×C61—41no—
120C4⋊C4×C61—41no—
121C4⋊C4×C61—84no—
122C22⋊C4×C61—41no—
123C22⋊C4×C61—41no—
124C42×C61—41no—
125C42×C61—41no—
126C42×C61—41no—
127C42×C61—41no—
128C42×C61C2×D411yescharacteristic
129C42×C61C2×D411yescharacteristic
130C42×C61C2×D411yescharacteristic
131C42×C61#4111yescharacteristic
132C23×C61—41no—
133C23×C61#12011yescharacteristic
134Q8×C61—22no—
135Q8×C61—22no—
136Q8×C61—41no—
137Q8×C61—41no—
138Q8×C61—41no—
139Q8×C61—41no—
140Q8×C61—82no—
141Q8×C61—82no—
142D4×C61—41no—
143D4×C61—41no—
144D4×C61—42no—
145D4×C61—81no—
146D4×C61—81no—
147D4×C61—81no—
148C2×C4×C61—22no—
149C2×C4×C61—24no—
150C2×C4×C61—22no—
151C2×C4×C61—41no—
152C2×C4×C61—42no—
153C2×C4×C61—41no—
154C2×C4×C61—42no—
155C2×C4×C61—41no—
156C2×C4×C61—42no—
157C2×C4×C61—44no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—42no—
161C2×C4×C61—81no—
162C2×C4×C61—81no—
163C2×C4×C61#12011yescharacteristic
164C2×C4×C61#12011yescharacteristic
165C2×C4×C61#12111yescharacteristic
166C2×C4×C61#12111yescharacteristic
167C2×C4×C61#12111yescharacteristic
168C2×C4×C61#12711yescharacteristic
169C2×C4×C61C2×SD1611yescharacteristic
170C2×C4×C61#13511yescharacteristic
171C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C61#13711yescharacteristic
173C8×C61—42no—
174C8×C61—42no—
175C8×C61—81no—
176#10245C6111yesmaximal, characteristic, direct product factor, Sylow
177C22×C61—21no—
178C22×C61—21no—
179C22×C61—81no—
180C22×C61—81no—
181C22×C61—81no—
182C22×C61#39211yescharacteristic
183C22×C61#44811yescharacteristic
184C22×C61#44911yescharacteristic
185C4×C61—21no—
186C4×C61—21no—
187C4×C61—21no—
188C4×C61—44no—
189C4×C61—42no—
190C4×C61—81no—
191C4×C61—81no—
192C4×C61—82no—
193C4×C61#45011yescharacteristic
194C4×C61#45211yescharacteristic
195C4×C61#45612yes—
196C4×C61#46511yescharacteristic
197C4×C61#46811yescharacteristic
198#3227C2×C6111yescharacteristic
199#3037C2×C6111yescharacteristic
200#2567C2×C6111yescharacteristic, complemented
201#1549C2×C6111yescharacteristic, complemented
202#1502C2×C6111yescharacteristic
203#1479C2×C6111yescharacteristic, complemented
204#1303C2×C6111yescharacteristic, complemented
205C2×C61—21no—
206C2×C61—21no—
207C2×C61—161no—
208C2×C61#200011yescharacteristic
209C2×C61#200511yescharacteristic
210C2×C61#200811yescharacteristic
211C2×#137—21no—
212#532C22×C6111yescharacteristic
213C2×C4⋊Q8C22×C6111yescharacteristic
214C2×C4×Q8C22×C6111yescharacteristic
215#498—21no—
216#486—21no—
217#481—22no—
218#476—22no—
219#464—22no—
220#462—21no—
221#460—21no—
222#431C22×C6111yescharacteristic
223#431C22×C6111yescharacteristic
224#423C22×C6111yescharacteristic
225#417—21no—
226#395—22no—
227#391—21no—
228#389—22no—
229#384—21no—
230C4×C4⋊C4C22×C6111yescharacteristic
231#332—22no—
232#327—22no—
233Q8⋊C8—22no—
234C61#1024511yescharacteristic, direct product factor, Sylow
235C2×#41—21no—
236C22×Q8—21no—
237C22×Q8D4×C6111yescharacteristic
238#137—42no—
239#137—42no—
240C2×Q16—22no—
241C2×SD16—22no—
242C2×M16—21no—
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8—21no—
246C4⋊Q8—21no—
247C4⋊Q8D4×C6111yescharacteristic
248#127D4×C6111yescharacteristic
249#124—21no—
250#121—21no—
251#121—21no—
252C4×Q8—21no—
253C4×Q8—21no—
254C4×Q8—21no—
255C4×Q8—21no—
256C4×D4—21no—
257C4×D4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4D4×C6111yescharacteristic
263C2×C4⋊C4D4×C6112yes—
264C2×C42—21no—
265C2×C42—21no—
266C2×C42C23×C6111yescharacteristic
267#106—24no—
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8D4×C6112yes—
271C4⋊C8D4×C6112yes—
272#103—22no—
273#102—22no—
274#102—24no—
275C22⋊C8—21no—
276C22⋊C8—21no—
277C4×C8—21no—
278C4×C8—21no—
279#95—24no—
280#95D4×C6112yes—
281#41—41no—
282#41—41no—
283#41—41no—
284#41—41no—
285C2×Q8—21no—
286C2×Q8—21no—
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8—21no—
291C2×Q8—41no—
292C2×Q8—41no—
293C2×Q8—82no—
294C2×Q8SD16×C6112yes—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—41no—
299C22×C4—21no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—21no—
303C22×C4—41no—
304C22×C4C2×D4×C6111yescharacteristic
305C22×C4C2×D4×C6111yescharacteristic
306C22×C4C2×D4×C6111yescharacteristic
307Q16—44no—
308SD16—44no—
309M16—41no—
310M16—41no—
311C2×C8—22no—
312C2×C8—22no—
313C2×C8—41no—
314C4⋊C4—24no—
315C4⋊C4—21no—
316C4⋊C4—22no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—22no—
320C4⋊C4—21no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—84no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C42—41no—
329C42—41no—
330C42—41no—
331C42—41no—
332C42C2×D4×C6111yescharacteristic
333C42C2×D4×C6111yescharacteristic
334C42C2×D4×C6111yescharacteristic
335C42#41×C6111yescharacteristic
336C23—41no—
337C23#120×C6111yescharacteristic
338Q8—22no—
339Q8—22no—
340Q8—41no—
341Q8—41no—
342Q8—41no—
343Q8—41no—
344Q8—82no—
345Q8—82no—
346D4—41no—
347D4—41no—
348D4—42no—
349D4—81no—
350D4—81no—
351D4—81no—
352C2×C4—22no—
353C2×C4—24no—
354C2×C4—22no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—42no—
361C2×C4—44no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—42no—
365C2×C4—81no—
366C2×C4—81no—
367C2×C4#120×C6111yescharacteristic
368C2×C4#120×C6111yescharacteristic
369C2×C4#121×C6111yescharacteristic
370C2×C4#121×C6111yescharacteristic
371C2×C4#121×C6111yescharacteristic
372C2×C4#127×C6111yescharacteristic
373C2×C4C2×SD16×C6111yescharacteristic
374C2×C4#135×C6111yescharacteristic
375C2×C4AGL(1,ℤ/8)×C6111yescharacteristic
376C2×C4#137×C6111yescharacteristic
377C8—42no—
378C8—42no—
379C8—81no—
380C22—21no—
381C22—21no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22C61×#39211yescharacteristic
386C22C61×#44811yescharacteristic
387C22C61×#44911yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—44no—
392C4—42no—
393C4—81no—
394C4—82no—
395C4—81no—
396C4C61×#45011yescharacteristic
397C4C61×#45211yescharacteristic
398C4C61×#45612yes—
399C4C61×#46511yescharacteristic
400C4C61×#46811yescharacteristic
401C2—21no—
402C2—21no—
403C2—161no—
404C2C61×#200011yescharacteristic
405C2C61×#200511yescharacteristic
406C2C61×#200811yescharacteristic
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×#2567C2semidirect
4. C61×#1549C2semidirect
6. C61×#1479C2semidirect
7. C61×#1303C2semidirect
176. #10245C61direct (N × H)
200. #2567C2×C61semidirect
201. #1549C2×C61semidirect
203. #1479C2×C61semidirect
204. #1303C2×C61semidirect
234. C61#10245direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#32272
C61×#30372
C61×#25672
C61×#15492
C61×#15022
C61×#14792
C61×#13032
#1024561