Finite Group Databasebeta

← C61×#9163 #29512596

Subgroups — C61×#9163 #29512596

Order 15616.

508 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3109C211yesmaximal, characteristic
2C61×#2974C211yesmaximal, characteristic, complemented
3C61×#1762C211yesmaximal, characteristic, complemented
4C61×#1530C211yesmaximal, characteristic, complemented
5C61×#1502C211yesmaximal, characteristic, complemented
6C61×#1302C211yesmaximal, characteristic, complemented
7C61×#1285C211yesmaximal, characteristic, complemented
8C61×#532C2211yescharacteristic
9C2×C4×D4×C61C2211yescharacteristic
10C61×#481—21no—
11C61×#476C411yescharacteristic, complemented
12C61×#476C411yescharacteristic, complemented
13C61×#459C411yescharacteristic, complemented
14C61×#459C411yescharacteristic, complemented
15C61×#447—21no—
16C61×#442—21no—
17C61×#442—21no—
18C61×#436—21no—
19C61×#435—22no—
20C8×D4×C61—21no—
21C61×#432C2211yescharacteristic
22C61×#432C2211yescharacteristic
23C61×#431C2211yescharacteristic
24C2×#102×C61—21no—
25C61×#407—21no—
26C2×C22⋊C8×C61—21no—
27C2×#97×C61C2211yescharacteristic
28C4×C4⋊C4×C61C2211yescharacteristic
29C61×#340—21no—
30C61×#329—22no—
31C61×#327—21no—
32C61×#327—21no—
33C2×#41×C61—21no—
34C22×D4×C61D411yescharacteristic
35C23×C4×C61—21no—
36C2×D8×C61—21no—
37C2×D8×C61—21no—
38C2×M16×C61—22no—
39C22×C8×C61—21no—
40C22×C8×C61—22no—
41C4⋊Q8×C61C2×C411yescharacteristic
42#127×C61C2×C411yescharacteristic
43#124×C61—21no—
44#121×C61—21no—
45#121×C61—21no—
46C4×D4×C61—21no—
47C4×D4×C61—21no—
48C4×D4×C61—21no—
49C4×D4×C61—21no—
50C4×D4×C61C2×C411yescharacteristic
51C4×D4×C61C2×C411yescharacteristic
52C4×D4×C61D411yescharacteristic
53C4×D4×C61D411yescharacteristic
54C2×C4⋊C4×C61—21no—
55C2×C4⋊C4×C61D411yescharacteristic
56C2×C22⋊C4×C61—21no—
57C2×C42×C61—21no—
58C2×C42×C61C2311yescharacteristic
59#106×C61—21no—
60#106×C61—21no—
61C4⋊C8×C61—21no—
62C4⋊C8×C61—21no—
63C4⋊C8×C61C2×C411yescharacteristic
64C4⋊C8×C61C2×C411yescharacteristic
65#102×C61—24no—
66#102×C61—21no—
67#102×C61—21no—
68#102×C61—21no—
69#102×C61—21no—
70C22⋊C8×C61—22no—
71C22⋊C8×C61—22no—
72C22⋊C8×C61—21no—
73C22⋊C8×C61—21no—
74C22⋊C8×C61D411yescharacteristic
75C22⋊C8×C61D411yescharacteristic
76#97×C61—21no—
77#97×C61—21no—
78#97×C61—21no—
79#97×C61D412yes—
80C4×C8×C61—21no—
81#95×C61—21no—
82C24×C61—21no—
83#41×C61—81no—
84#41×C61—81no—
85C2×Q8×C61—21no—
86C2×D4×C61—22no—
87C2×D4×C61—21no—
88C2×D4×C61—21no—
89C2×D4×C61—21no—
90C2×D4×C61—21no—
91C2×D4×C61—41no—
92C2×D4×C61—41no—
93C2×D4×C61C22⋊C411yescharacteristic
94C2×D4×C61C22⋊C411yescharacteristic
95C22×C4×C61—21no—
96C22×C4×C61—21no—
97C22×C4×C61—21no—
98C22×C4×C61—21no—
99C22×C4×C61—21no—
100C22×C4×C61—41no—
101C22×C4×C61—41no—
102C22×C4×C61—82no—
103C22×C4×C61C2×D411yescharacteristic
104C22×C4×C61C2×D411yescharacteristic
105C22×C4×C61#4111yescharacteristic
106D8×C61—42no—
107D8×C61—42no—
108M16×C61—82no—
109C2×C8×C61—22no—
110C2×C8×C61—21no—
111C2×C8×C61—21no—
112C2×C8×C61—21no—
113C2×C8×C61—21no—
114C2×C8×C61—22no—
115C2×C8×C61—41no—
116C2×C8×C61—41no—
117C2×C8×C61—82no—
118C4⋊C4×C61—21no—
119C4⋊C4×C61—22no—
120C4⋊C4×C61—21no—
121C4⋊C4×C61—21no—
122C4⋊C4×C61—41no—
123C4⋊C4×C61C22⋊C411yescharacteristic
124C4⋊C4×C61C22⋊C411yescharacteristic
125C22⋊C4×C61—21no—
126C22⋊C4×C61—21no—
127C22⋊C4×C61—21no—
128C22⋊C4×C61—21no—
129C22⋊C4×C61—41no—
130C22⋊C4×C61—41no—
131C42×C61—81no—
132C42×C61C22×C411yescharacteristic
133C42×C61C2×D411yescharacteristic
134C42×C61C2×D411yescharacteristic
135C42×C61#4111yescharacteristic
136C23×C61—21no—
137C23×C61—21no—
138C23×C61—42no—
139C23×C61—41no—
140C23×C61—41no—
141C23×C61—41no—
142C23×C61—81no—
143C23×C61#12111yescharacteristic
144Q8×C61—81no—
145D4×C61—21no—
146D4×C61—21no—
147D4×C61—21no—
148D4×C61—42no—
149D4×C61—41no—
150D4×C61—41no—
151D4×C61—81no—
152D4×C61—81no—
153D4×C61—81no—
154D4×C61—81no—
155D4×C61#10412yes—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61—21no—
160C2×C4×C61—21no—
161C2×C4×C61—21no—
162C2×C4×C61—41no—
163C2×C4×C61—42no—
164C2×C4×C61—42no—
165C2×C4×C61—42no—
166C2×C4×C61—41no—
167C2×C4×C61—81no—
168C2×C4×C61—81no—
169C2×C4×C61—82no—
170C2×C4×C61—81no—
171C2×C4×C61—81no—
172C2×C4×C61—81no—
173C2×C4×C61C2×C22⋊C411yescharacteristic
174C2×C4×C61C4×D411yescharacteristic
175C2×C4×C61C4×D411yescharacteristic
176C2×C4×C61#12011yescharacteristic
177C2×C4×C61#12111yescharacteristic
178C2×C4×C61#12311yescharacteristic
179C8×C61—42no—
180C8×C61—41no—
181C8×C61—42no—
182C8×C61—41no—
183C8×C61—41no—
184C8×C61—41no—
185#9163C6111yesmaximal, characteristic, direct product factor, Sylow
186C22×C61—21no—
187C22×C61—21no—
188C22×C61—22no—
189C22×C61—41no—
190C22×C61—41no—
191C22×C61—41no—
192C22×C61—41no—
193C22×C61—41no—
194C22×C61—82no—
195C22×C61—82no—
196C22×C61—81no—
197C22×C61—81no—
198C22×C61—81no—
199C22×C61#38611yescharacteristic
200C22×C61#47111yescharacteristic
201C22×C61#47211yescharacteristic
202C4×C61—21no—
203C4×C61—21no—
204C4×C61—21no—
205C4×C61—21no—
206C4×C61—21no—
207C4×C61—41no—
208C4×C61—41no—
209C4×C61—82no—
210C4×C61—81no—
211C4×C61C2×#10411yescharacteristic
212C4×C61#42111yescharacteristic
213#3109C2×C6111yescharacteristic
214#2974C2×C6111yescharacteristic, complemented
215#1762C2×C6111yescharacteristic, complemented
216#1530C2×C6111yescharacteristic, complemented
217#1502C2×C6111yescharacteristic, complemented
218#1302C2×C6111yescharacteristic, complemented
219#1285C2×C6111yescharacteristic, complemented
220C2×C61—21no—
221C2×C61—21no—
222C2×C61—42no—
223C2×C61—81no—
224C2×C61—161no—
225C2×C61#187111yescharacteristic
226C2×C61#190411yescharacteristic
227C2×C61#190711yescharacteristic
228#532C22×C6111yescharacteristic
229C2×C4×D4C22×C6111yescharacteristic
230#481—21no—
231#476C4×C6111yescharacteristic, complemented
232#476C4×C6111yescharacteristic, complemented
233#459C4×C6111yescharacteristic, complemented
234#459C4×C6111yescharacteristic, complemented
235#447—21no—
236#442—21no—
237#442—21no—
238#436—21no—
239#435—22no—
240C8×D4—21no—
241#432C22×C6111yescharacteristic
242#432C22×C6111yescharacteristic
243#431C22×C6111yescharacteristic
244C2×#102—21no—
245#407—21no—
246C2×C22⋊C8—21no—
247C2×#97C22×C6111yescharacteristic
248C4×C4⋊C4C22×C6111yescharacteristic
249#340—21no—
250#329—22no—
251#327—21no—
252#327—21no—
253C61#916311yescharacteristic, direct product factor, Sylow
254C2×#41—21no—
255C22×D4D4×C6111yescharacteristic
256C23×C4—21no—
257C2×D8—21no—
258C2×D8—21no—
259C2×M16—22no—
260C22×C8—21no—
261C22×C8—22no—
262C4⋊Q8C2×C4×C6111yescharacteristic
263#127C2×C4×C6111yescharacteristic
264#124—21no—
265#121—21no—
266#121—21no—
267C4×D4—21no—
268C4×D4—21no—
269C4×D4—21no—
270C4×D4—21no—
271C4×D4C2×C4×C6111yescharacteristic
272C4×D4C2×C4×C6111yescharacteristic
273C4×D4D4×C6111yescharacteristic
274C4×D4D4×C6111yescharacteristic
275C2×C4⋊C4—21no—
276C2×C4⋊C4D4×C6111yescharacteristic
277C2×C22⋊C4—21no—
278C2×C42—21no—
279C2×C42C23×C6111yescharacteristic
280#106—21no—
281#106—21no—
282C4⋊C8—21no—
283C4⋊C8—21no—
284C4⋊C8C2×C4×C6111yescharacteristic
285C4⋊C8C2×C4×C6111yescharacteristic
286#102—24no—
287#102—21no—
288#102—21no—
289#102—21no—
290#102—21no—
291C22⋊C8—22no—
292C22⋊C8—22no—
293C22⋊C8—21no—
294C22⋊C8—21no—
295C22⋊C8D4×C6111yescharacteristic
296C22⋊C8D4×C6111yescharacteristic
297#97—21no—
298#97—21no—
299#97—21no—
300#97D4×C6112yes—
301C4×C8—21no—
302#95—21no—
303C24—21no—
304#41—81no—
305#41—81no—
306C2×Q8—21no—
307C2×D4—22no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4C22⋊C4×C6111yescharacteristic
315C2×D4C22⋊C4×C6111yescharacteristic
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—82no—
324C22×C4C2×D4×C6111yescharacteristic
325C22×C4C2×D4×C6111yescharacteristic
326C22×C4#41×C6111yescharacteristic
327D8—42no—
328D8—42no—
329M16—82no—
330C2×C8—22no—
331C2×C8—21no—
332C2×C8—21no—
333C2×C8—21no—
334C2×C8—21no—
335C2×C8—22no—
336C2×C8—41no—
337C2×C8—41no—
338C2×C8—82no—
339C4⋊C4—21no—
340C4⋊C4—22no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—41no—
344C4⋊C4C22⋊C4×C6111yescharacteristic
345C4⋊C4C22⋊C4×C6111yescharacteristic
346C22⋊C4—21no—
347C22⋊C4—21no—
348C22⋊C4—21no—
349C22⋊C4—21no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C42—81no—
353C42C22×C4×C6111yescharacteristic
354C42C2×D4×C6111yescharacteristic
355C42C2×D4×C6111yescharacteristic
356C42#41×C6111yescharacteristic
357C23—21no—
358C23—21no—
359C23—42no—
360C23—41no—
361C23—41no—
362C23—41no—
363C23—81no—
364C23#121×C6111yescharacteristic
365Q8—81no—
366D4—21no—
367D4—21no—
368D4—21no—
369D4—42no—
370D4—41no—
371D4—41no—
372D4—81no—
373D4—81no—
374D4—81no—
375D4—81no—
376D4#104×C6112yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—41no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4—82no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4C2×C22⋊C4×C6111yescharacteristic
395C2×C4C4×D4×C6111yescharacteristic
396C2×C4C4×D4×C6111yescharacteristic
397C2×C4#120×C6111yescharacteristic
398C2×C4#121×C6111yescharacteristic
399C2×C4#123×C6111yescharacteristic
400C8—42no—
401C8—41no—
402C8—42no—
403C8—41no—
404C8—41no—
405C8—41no—
406C22—21no—
407C22—21no—
408C22—22no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—82no—
415C22—82no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22C61×#38611yescharacteristic
420C22C61×#47111yescharacteristic
421C22C61×#47211yescharacteristic
422C4—21no—
423C4—21no—
424C4—21no—
425C4—21no—
426C4—21no—
427C4—41no—
428C4—41no—
429C4—82no—
430C4—81no—
431C4C2×#104×C6111yescharacteristic
432C4C61×#42111yescharacteristic
433C2—21no—
434C2—21no—
435C2—42no—
436C2—81no—
437C2—161no—
438C2C61×#187111yescharacteristic
439C2C61×#190411yescharacteristic
440C2C61×#190711yescharacteristic
subgroupG/H
center, socleC22×C61#386
commutatorC42C22×C4×C61
Frattini, cosocleC2×C42C23×C61
prime radicalC61×#3109C2
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
2. C61×#2974C2semidirect
3. C61×#1762C2semidirect
4. C61×#1530C2semidirect
5. C61×#1502C2semidirect
6. C61×#1302C2semidirect
7. C61×#1285C2semidirect
11. C61×#476C4semidirect
12. C61×#476C4semidirect
13. C61×#459C4semidirect
14. C61×#459C4semidirect
185. #9163C61direct (N × H)
214. #2974C2×C61semidirect
215. #1762C2×C61semidirect
216. #1530C2×C61semidirect
217. #1502C2×C61semidirect
218. #1302C2×C61semidirect
219. #1285C2×C61semidirect
231. #476C4×C61semidirect
232. #476C4×C61semidirect
233. #459C4×C61semidirect
234. #459C4×C61semidirect
253. C61#9163direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#31092
C61×#29742
C61×#17622
C61×#15302
C61×#15022
C61×#13022
C61×#12852
#916361