Finite Group Databasebeta

← C61×#10240 #29513673

Subgroups — C61×#10240 #29513673

Order 15616.

658 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3206C211yesmaximal, characteristic, complemented
2C61×#3036C211yesmaximal, characteristic
3C61×#2542C211yesmaximal, characteristic, complemented
4C61×#1548C211yesmaximal, characteristic, complemented
5C61×#1502C211yesmaximal, characteristic, complemented
6C61×#1478C211yesmaximal, characteristic, complemented
7C61×#1303C211yesmaximal, characteristic, complemented
8C2×AGL(1,ℤ/8)×C61—21no—
9C61×#532C2211yescharacteristic
10C2×C4⋊Q8×C61C2211yescharacteristic
11C2×C22⋊Q8×C61—22no—
12C2×C4×D4×C61C2211yescharacteristic
13C61×#492—21no—
14C61×#487—21no—
15C61×#463—22no—
16C61×#461—21no—
17C61×#461—22no—
18C61×#459—21no—
19C61×#448—22no—
20C61×#431C2211yescharacteristic
21C61×#431C2211yescharacteristic
22C61×#423C2211yescharacteristic
23C61×#417—21no—
24C61×#399—22no—
25C61×#390—21no—
26C61×#384—21no—
27C4×C4⋊C4×C61C2211yescharacteristic
28C61×#333—22no—
29C61×#327—22no—
30C61×D4⋊C8—22no—
31C2×#41×C61—21no—
32C22×Q8×C61D412yes—
33C22×D4×C61D411yescharacteristic
34C23×C4×C61—21no—
35AGL(1,ℤ/8)×C61—42no—
36AGL(1,ℤ/8)×C61—42no—
37C2×SD16×C61—22no—
38C2×SD16×C61—24no—
39C2×D8×C61—22no—
40C2×M16×C61—21no—
41C4⋊Q8×C61—21no—
42C4⋊Q8×C61—21no—
43C4⋊Q8×C61—21no—
44C4⋊Q8×C61—21no—
45C4⋊Q8×C61D411yescharacteristic
46#127×C61D411yescharacteristic
47#124×C61—21no—
48C22⋊Q8×C61—48no—
49#121×C61—21no—
50#121×C61—21no—
51C4×D4×C61—21no—
52C4×D4×C61—21no—
53C4×D4×C61—21no—
54C4×D4×C61—21no—
55C4×D4×C61—21no—
56C4×D4×C61—21no—
57C2×C4⋊C4×C61—21no—
58C2×C4⋊C4×C61—24no—
59C2×C4⋊C4×C61—21no—
60C2×C4⋊C4×C61—21no—
61C2×C4⋊C4×C61D411yescharacteristic
62C2×C22⋊C4×C61—24no—
63C2×C22⋊C4×C61—21no—
64C2×C42×C61—21no—
65C2×C42×C61C2311yescharacteristic
66C4⋊C8×C61—21no—
67C4⋊C8×C61—21no—
68C4⋊C8×C61D412yes—
69C4⋊C8×C61D412yes—
70#103×C61—22no—
71#103×C61—24no—
72#102×C61—22no—
73C22⋊C8×C61—21no—
74C22⋊C8×C61—21no—
75C4×C8×C61—21no—
76C4×C8×C61—21no—
77#95×C61D412yes—
78C24×C61—21no—
79#41×C61—41no—
80#41×C61—41no—
81#41×C61—41no—
82#41×C61—41no—
83C2×Q8×C61—21no—
84C2×Q8×C61—22no—
85C2×Q8×C61—22no—
86C2×Q8×C61—44no—
87C2×D4×C61—21no—
88C2×D4×C61—21no—
89C2×D4×C61—21no—
90C2×D4×C61—21no—
91C2×D4×C61—21no—
92C2×D4×C61—21no—
93C2×D4×C61—21no—
94C2×D4×C61—21no—
95C2×D4×C61—41no—
96C2×D4×C61SD1612yescomplemented
97C22×C4×C61—22no—
98C22×C4×C61—22no—
99C22×C4×C61—21no—
100C22×C4×C61—44no—
101C22×C4×C61—41no—
102C22×C4×C61—41no—
103C22×C4×C61—41no—
104C22×C4×C61C2×D411yescharacteristic
105C22×C4×C61C2×D411yescharacteristic
106C22×C4×C61C2×D411yescharacteristic
107SD16×C61—44no—
108SD16×C61—84no—
109D8×C61—44no—
110M16×C61—41no—
111M16×C61—41no—
112C2×C8×C61—22no—
113C2×C8×C61—22no—
114C2×C8×C61—41no—
115C4⋊C4×C61—24no—
116C4⋊C4×C61—21no—
117C4⋊C4×C61—21no—
118C4⋊C4×C61—21no—
119C4⋊C4×C61—21no—
120C4⋊C4×C61—48no—
121C4⋊C4×C61—41no—
122C4⋊C4×C61—41no—
123C4⋊C4×C61—41no—
124C4⋊C4×C61—41no—
125C22⋊C4×C61—48no—
126C22⋊C4×C61—41no—
127C22⋊C4×C61—41no—
128C22⋊C4×C61—41no—
129C22⋊C4×C61—41no—
130C42×C61—41no—
131C42×C61—41no—
132C42×C61C2×D411yescharacteristic
133C42×C61C2×D411yescharacteristic
134C42×C61C2×D411yescharacteristic
135C42×C61#4111yescharacteristic
136C23×C61—22no—
137C23×C61—42no—
138C23×C61—42no—
139C23×C61—41no—
140C23×C61—41no—
141C23×C61—41no—
142C23×C61#12011yescharacteristic
143Q8×C61—41no—
144Q8×C61—41no—
145Q8×C61—44no—
146Q8×C61—82no—
147D4×C61—22no—
148D4×C61—22no—
149D4×C61—41no—
150D4×C61—41no—
151D4×C61—41no—
152D4×C61—42no—
153D4×C61—41no—
154D4×C61—81no—
155D4×C61—81no—
156D4×C61—81no—
157C2×C4×C61—22no—
158C2×C4×C61—24no—
159C2×C4×C61—41no—
160C2×C4×C61—42no—
161C2×C4×C61—42no—
162C2×C4×C61—44no—
163C2×C4×C61—42no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—42no—
167C2×C4×C61—82no—
168C2×C4×C61—82no—
169C2×C4×C61—81no—
170C2×C4×C61—81no—
171C2×C4×C61#12011yescharacteristic
172C2×C4×C61#12011yescharacteristic
173C2×C4×C61#12111yescharacteristic
174C2×C4×C61#12111yescharacteristic
175C2×C4×C61#12111yescharacteristic
176C2×C4×C61#12711yescharacteristic
177C2×C4×C61C2×SD1611yescharacteristic
178C2×C4×C61#13511yescharacteristic
179C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
180C2×C4×C61#13711yescharacteristic
181C8×C61—42no—
182C8×C61—42no—
183C8×C61—81no—
184#10240C6111yesmaximal, characteristic, direct product factor, Sylow
185C22×C61—21no—
186C22×C61—21no—
187C22×C61—44no—
188C22×C61—42no—
189C22×C61—82no—
190C22×C61—81no—
191C22×C61—81no—
192C22×C61—81no—
193C22×C61—81no—
194C22×C61—81no—
195C22×C61#39211yescharacteristic
196C22×C61#44811yescharacteristic
197C22×C61#44911yescharacteristic
198C4×C61—21no—
199C4×C61—21no—
200C4×C61—21no—
201C4×C61—44no—
202C4×C61—81no—
203C4×C61—81no—
204C4×C61—82no—
205C4×C61#45011yescharacteristic
206C4×C61#45211yescharacteristic
207C4×C61#45312yes—
208C4×C61#46511yescharacteristic
209C4×C61#46811yescharacteristic
210#3206C2×C6111yescharacteristic, complemented
211#3036C2×C6111yescharacteristic
212#2542C2×C6111yescharacteristic, complemented
213#1548C2×C6111yescharacteristic, complemented
214#1502C2×C6111yescharacteristic, complemented
215#1478C2×C6111yescharacteristic, complemented
216#1303C2×C6111yescharacteristic, complemented
217C2×C61—21no—
218C2×C61—21no—
219C2×C61—82no—
220C2×C61—161no—
221C2×C61#200011yescharacteristic
222C2×C61#200211yescharacteristic
223C2×C61#200911yescharacteristic
224C2×AGL(1,ℤ/8)—21no—
225#532C22×C6111yescharacteristic
226C2×C4⋊Q8C22×C6111yescharacteristic
227C2×C22⋊Q8—22no—
228C2×C4×D4C22×C6111yescharacteristic
229#492—21no—
230#487—21no—
231#463—22no—
232#461—21no—
233#461—22no—
234#459—21no—
235#448—22no—
236#431C22×C6111yescharacteristic
237#431C22×C6111yescharacteristic
238#423C22×C6111yescharacteristic
239#417—21no—
240#399—22no—
241#390—21no—
242#384—21no—
243C4×C4⋊C4C22×C6111yescharacteristic
244#333—22no—
245#327—22no—
246D4⋊C8—22no—
247C61#1024011yescharacteristic, direct product factor, Sylow
248C2×#41—21no—
249C22×Q8D4×C6112yes—
250C22×D4D4×C6111yescharacteristic
251C23×C4—21no—
252AGL(1,ℤ/8)—42no—
253AGL(1,ℤ/8)—42no—
254C2×SD16—22no—
255C2×SD16—24no—
256C2×D8—22no—
257C2×M16—21no—
258C4⋊Q8—21no—
259C4⋊Q8—21no—
260C4⋊Q8—21no—
261C4⋊Q8—21no—
262C4⋊Q8D4×C6111yescharacteristic
263#127D4×C6111yescharacteristic
264#124—21no—
265C22⋊Q8—48no—
266#121—21no—
267#121—21no—
268C4×D4—21no—
269C4×D4—21no—
270C4×D4—21no—
271C4×D4—21no—
272C4×D4—21no—
273C4×D4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4D4×C6111yescharacteristic
279C2×C22⋊C4—24no—
280C2×C22⋊C4—21no—
281C2×C42—21no—
282C2×C42C23×C6111yescharacteristic
283C4⋊C8—21no—
284C4⋊C8—21no—
285C4⋊C8D4×C6112yes—
286C4⋊C8D4×C6112yes—
287#103—22no—
288#103—24no—
289#102—22no—
290C22⋊C8—21no—
291C22⋊C8—21no—
292C4×C8—21no—
293C4×C8—21no—
294#95D4×C6112yes—
295C24—21no—
296#41—41no—
297#41—41no—
298#41—41no—
299#41—41no—
300C2×Q8—21no—
301C2×Q8—22no—
302C2×Q8—22no—
303C2×Q8—44no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—41no—
313C2×D4SD16×C6112yescomplemented
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—21no—
317C22×C4—44no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4C2×D4×C6111yescharacteristic
322C22×C4C2×D4×C6111yescharacteristic
323C22×C4C2×D4×C6111yescharacteristic
324SD16—44no—
325SD16—84no—
326D8—44no—
327M16—41no—
328M16—41no—
329C2×C8—22no—
330C2×C8—22no—
331C2×C8—41no—
332C4⋊C4—24no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—48no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C22⋊C4—48no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C42—41no—
348C42—41no—
349C42C2×D4×C6111yescharacteristic
350C42C2×D4×C6111yescharacteristic
351C42C2×D4×C6111yescharacteristic
352C42#41×C6111yescharacteristic
353C23—22no—
354C23—42no—
355C23—42no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23#120×C6111yescharacteristic
360Q8—41no—
361Q8—41no—
362Q8—44no—
363Q8—82no—
364D4—22no—
365D4—22no—
366D4—41no—
367D4—41no—
368D4—41no—
369D4—42no—
370D4—41no—
371D4—81no—
372D4—81no—
373D4—81no—
374C2×C4—22no—
375C2×C4—24no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—44no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—42no—
384C2×C4—82no—
385C2×C4—82no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4#120×C6111yescharacteristic
389C2×C4#120×C6111yescharacteristic
390C2×C4#121×C6111yescharacteristic
391C2×C4#121×C6111yescharacteristic
392C2×C4#121×C6111yescharacteristic
393C2×C4#127×C6111yescharacteristic
394C2×C4C2×SD16×C6111yescharacteristic
395C2×C4#135×C6111yescharacteristic
396C2×C4AGL(1,ℤ/8)×C6111yescharacteristic
397C2×C4#137×C6111yescharacteristic
398C8—42no—
399C8—42no—
400C8—81no—
401C22—21no—
402C22—21no—
403C22—44no—
404C22—42no—
405C22—82no—
406C22—81no—
407C22—81no—
408C22—81no—
409C22—81no—
410C22—81no—
411C22C61×#39211yescharacteristic
412C22C61×#44811yescharacteristic
413C22C61×#44911yescharacteristic
414C4—21no—
415C4—21no—
416C4—21no—
417C4—44no—
418C4—81no—
419C4—81no—
420C4—82no—
421C4C61×#45011yescharacteristic
422C4C61×#45211yescharacteristic
423C4C61×#45312yes—
424C4C61×#46511yescharacteristic
425C4C61×#46811yescharacteristic
426C2—21no—
427C2—21no—
428C2—82no—
429C2—161no—
430C2C61×#200011yescharacteristic
431C2C61×#200211yescharacteristic
432C2C61×#200911yescharacteristic
subgroupG/H
center, socleC22×C61#392
commutator, Frattini, cosocleC2×C42C23×C61
prime radicalC61×#3036C2
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
1. C61×#3206C2semidirect
3. C61×#2542C2semidirect
4. C61×#1548C2semidirect
5. C61×#1502C2semidirect
6. C61×#1478C2semidirect
7. C61×#1303C2semidirect
96. C2×D4×C61SD16semidirect
184. #10240C61direct (N × H)
210. #3206C2×C61semidirect
212. #2542C2×C61semidirect
213. #1548C2×C61semidirect
214. #1502C2×C61semidirect
215. #1478C2×C61semidirect
216. #1303C2×C61semidirect
247. C61#10240direct (N × H)
313. C2×D4SD16×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#32062
C61×#30362
C61×#25422
C61×#15482
C61×#15022
C61×#14782
C61×#13032
#1024061