Finite Group Databasebeta

← C61×#9370 #29512803

Subgroups — C61×#9370 #29512803

Order 15616.

424 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3219C211yesmaximal, characteristic
2C61×#2967C211yesmaximal, characteristic, complemented
3C61×#1521C211yesmaximal, characteristic, complemented
4C61×#1514C211yesmaximal, characteristic, complemented
5C61×#1484C211yesmaximal, characteristic, complemented
6C61×#1288C211yesmaximal, characteristic, complemented
7C61×#1287C211yesmaximal, characteristic, complemented
8C61×#532C2211yescharacteristic
9C61×#529C2211yescharacteristic
10C61×#497C411yescharacteristic, complemented
11C61×#496C411yescharacteristic, complemented
12C61×#491C411yescharacteristic, complemented
13C61×#490C411yescharacteristic, complemented
14C61×#464—21no—
15C61×#463—21no—
16C61×#452—21no—
17C61×#449—21no—
18C61×#446—21no—
19C61×#436—21no—
20C61×#435—21no—
21C61×#435—21no—
22C61×#433—21no—
23C61×#432C2211yescharacteristic
24C61×#432C2211yescharacteristic
25C61×#431C2211yescharacteristic
26C61×#405—21no—
27C4×M16×C61C2211yescharacteristic
28C61×#383C2211yescharacteristic
29C61×#328—21no—
30C61×#327—21no—
31C61×#327—21no—
32C61×#327—21no—
33C61×D4⋊C8—21no—
34C61×D4⋊C8—21no—
35C2×#41×C61—21no—
36C2×Q16×C61—21no—
37C2×SD16×C61—21no—
38C2×SD16×C61—21no—
39C2×D8×C61—21no—
40C2×M16×C61—21no—
41C2×M16×C61—21no—
42C22×C8×C61—21no—
43C4⋊Q8×C61C2×C411yescharacteristic
44#127×C61C2×C411yescharacteristic
45#126×C61—21no—
46#125×C61C2×C411yescharacteristic
47#124×C61—21no—
48#124×C61C2×C411yescharacteristic
49#123×C61—21no—
50C22⋊Q8×C61D411yescharacteristic
51#121×C61—21no—
52#121×C61—21no—
53#121×C61D411yescharacteristic
54C4×Q8×C61D411yescharacteristic
55C4×D4×C61—21no—
56C4×D4×C61—21no—
57C4×D4×C61—21no—
58C4×D4×C61D411yescharacteristic
59#117×C61—21no—
60C2×C42×C61C2311yescharacteristic
61C4⋊C8×C61—21no—
62C4⋊C8×C61—21no—
63C4⋊C8×C61—21no—
64C4⋊C8×C61—21no—
65C4⋊C8×C61—21no—
66#103×C61—21no—
67#103×C61—21no—
68#102×C61—21no—
69#102×C61—21no—
70C22⋊C8×C61—21no—
71C22⋊C8×C61—21no—
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×C61C2×C411yescharacteristic
80#97×C61C2×C411yescharacteristic
81C4×C8×C61—21no—
82C4×C8×C61—21no—
83C4×C8×C61D411yescharacteristic
84C4×C8×C61D411yescharacteristic
85#95×C61—21no—
86#95×C61—21no—
87#95×C61—21no—
88#41×C61—81no—
89#41×C61—81no—
90C2×Q8×C61—21no—
91C2×Q8×C61C22⋊C411yescharacteristic
92C2×D4×C61—21no—
93C2×D4×C61—21no—
94C2×D4×C61—21no—
95C2×D4×C61—21no—
96C2×D4×C61—41no—
97C2×D4×C61C22⋊C411yescharacteristic
98C22×C4×C61—21no—
99C22×C4×C61—41no—
100C22×C4×C61—41no—
101C22×C4×C61C2×D411yescharacteristic
102C22×C4×C61C2×D411yescharacteristic
103C22×C4×C61#4111yescharacteristic
104Q16×C61—81no—
105SD16×C61—81no—
106SD16×C61—81no—
107D8×C61—81no—
108M16×C61—42no—
109M16×C61—42no—
110C2×C8×C61—21no—
111C2×C8×C61—21no—
112C2×C8×C61—21no—
113C2×C8×C61—21no—
114C2×C8×C61—21no—
115C2×C8×C61—21no—
116C2×C8×C61—42no—
117C2×C8×C61—41no—
118C4⋊C4×C61—21no—
119C4⋊C4×C61—21no—
120C4⋊C4×C61—21no—
121C4⋊C4×C61—21no—
122C4⋊C4×C61—21no—
123C4⋊C4×C61—21no—
124C4⋊C4×C61C22⋊C411yescharacteristic
125C4⋊C4×C61C22⋊C411yescharacteristic
126C22⋊C4×C61—21no—
127C22⋊C4×C61—21no—
128C22⋊C4×C61—21no—
129C22⋊C4×C61—21no—
130C22⋊C4×C61—21no—
131C22⋊C4×C61—41no—
132C22⋊C4×C61—41no—
133C42×C61—21no—
134C42×C61C22×C411yescharacteristic
135C42×C61C2×D411yescharacteristic
136C42×C61C2×D411yescharacteristic
137C42×C61#4111yescharacteristic
138C23×C61—21no—
139C23×C61—41no—
140C23×C61#12111yescharacteristic
141Q8×C61—41no—
142Q8×C61—41no—
143Q8×C61—41no—
144D4×C61—41no—
145D4×C61—41no—
146D4×C61—41no—
147D4×C61—42no—
148D4×C61—81no—
149D4×C61—81no—
150D4×C61—82no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—82no—
161C2×C4×C61—81no—
162C2×C4×C61—81no—
163C2×C4×C61—81no—
164C2×C4×C61C2×C22⋊C411yescharacteristic
165C2×C4×C61C4×D411yescharacteristic
166C2×C4×C61C4×D411yescharacteristic
167C2×C4×C61#12011yescharacteristic
168C2×C4×C61#12111yescharacteristic
169C2×C4×C61#12311yescharacteristic
170C8×C61—22no—
171C8×C61—41no—
172C8×C61—41no—
173C8×C61—41no—
174C8×C61—41no—
175C8×C61—41no—
176C8×C61—81no—
177#9370C6111yesmaximal, characteristic, direct product factor, Sylow
178C22×C61—21no—
179C22×C61—21no—
180C22×C61—21no—
181C22×C61—41no—
182C22×C61—41no—
183C22×C61—41no—
184C22×C61—81no—
185C22×C61—81no—
186C22×C61—81no—
187C22×C61#38611yescharacteristic
188C4×C61—21no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—21no—
192C4×C61—21no—
193C4×C61—21no—
194C4×C61—41no—
195C4×C61—41no—
196C4×C61—41no—
197C4×C61—81no—
198C4×C61—161no—
199#3219C2×C6111yescharacteristic
200#2967C2×C6111yescharacteristic, complemented
201#1521C2×C6111yescharacteristic, complemented
202#1514C2×C6111yescharacteristic, complemented
203#1484C2×C6111yescharacteristic, complemented
204#1288C2×C6111yescharacteristic, complemented
205#1287C2×C6111yescharacteristic, complemented
206C2×C61—41no—
207C2×C61—81no—
208C2×C61—161no—
209C2×C61#188111yescharacteristic
210C2×C61#190611yescharacteristic
211C2×C61#191011yescharacteristic
212#532C22×C6111yescharacteristic
213#529C22×C6111yescharacteristic
214#497C4×C6111yescharacteristic, complemented
215#496C4×C6111yescharacteristic, complemented
216#491C4×C6111yescharacteristic, complemented
217#490C4×C6111yescharacteristic, complemented
218#464—21no—
219#463—21no—
220#452—21no—
221#449—21no—
222#446—21no—
223#436—21no—
224#435—21no—
225#435—21no—
226#433—21no—
227#432C22×C6111yescharacteristic
228#432C22×C6111yescharacteristic
229#431C22×C6111yescharacteristic
230#405—21no—
231C4×M16C22×C6111yescharacteristic
232#383C22×C6111yescharacteristic
233#328—21no—
234#327—21no—
235#327—21no—
236#327—21no—
237D4⋊C8—21no—
238D4⋊C8—21no—
239C61#937011yescharacteristic, direct product factor, Sylow
240C2×#41—21no—
241C2×Q16—21no—
242C2×SD16—21no—
243C2×SD16—21no—
244C2×D8—21no—
245C2×M16—21no—
246C2×M16—21no—
247C22×C8—21no—
248C4⋊Q8C2×C4×C6111yescharacteristic
249#127C2×C4×C6111yescharacteristic
250#126—21no—
251#125C2×C4×C6111yescharacteristic
252#124—21no—
253#124C2×C4×C6111yescharacteristic
254#123—21no—
255C22⋊Q8D4×C6111yescharacteristic
256#121—21no—
257#121—21no—
258#121D4×C6111yescharacteristic
259C4×Q8D4×C6111yescharacteristic
260C4×D4—21no—
261C4×D4—21no—
262C4×D4—21no—
263C4×D4D4×C6111yescharacteristic
264#117—21no—
265C2×C42C23×C6111yescharacteristic
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271#103—21no—
272#103—21no—
273#102—21no—
274#102—21no—
275C22⋊C8—21no—
276C22⋊C8—21no—
277C22⋊C8—21no—
278C22⋊C8—21no—
279C22⋊C8D4×C6111yescharacteristic
280C22⋊C8D4×C6111yescharacteristic
281#97—21no—
282#97—21no—
283#97—21no—
284#97C2×C4×C6111yescharacteristic
285#97C2×C4×C6111yescharacteristic
286C4×C8—21no—
287C4×C8—21no—
288C4×C8D4×C6111yescharacteristic
289C4×C8D4×C6111yescharacteristic
290#95—21no—
291#95—21no—
292#95—21no—
293#41—81no—
294#41—81no—
295C2×Q8—21no—
296C2×Q8C22⋊C4×C6111yescharacteristic
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—41no—
302C2×D4C22⋊C4×C6111yescharacteristic
303C22×C4—21no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4C2×D4×C6111yescharacteristic
307C22×C4C2×D4×C6111yescharacteristic
308C22×C4#41×C6111yescharacteristic
309Q16—81no—
310SD16—81no—
311SD16—81no—
312D8—81no—
313M16—42no—
314M16—42no—
315C2×C8—21no—
316C2×C8—21no—
317C2×C8—21no—
318C2×C8—21no—
319C2×C8—21no—
320C2×C8—21no—
321C2×C8—42no—
322C2×C8—41no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4C22⋊C4×C6111yescharacteristic
330C4⋊C4C22⋊C4×C6111yescharacteristic
331C22⋊C4—21no—
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—21no—
335C22⋊C4—21no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C42—21no—
339C42C22×C4×C6111yescharacteristic
340C42C2×D4×C6111yescharacteristic
341C42C2×D4×C6111yescharacteristic
342C42#41×C6111yescharacteristic
343C23—21no—
344C23—41no—
345C23#121×C6111yescharacteristic
346Q8—41no—
347Q8—41no—
348Q8—41no—
349D4—41no—
350D4—41no—
351D4—41no—
352D4—42no—
353D4—81no—
354D4—81no—
355D4—82no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—82no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4C2×C22⋊C4×C6111yescharacteristic
370C2×C4C4×D4×C6111yescharacteristic
371C2×C4C4×D4×C6111yescharacteristic
372C2×C4#120×C6111yescharacteristic
373C2×C4#121×C6111yescharacteristic
374C2×C4#123×C6111yescharacteristic
375C8—22no—
376C8—41no—
377C8—41no—
378C8—41no—
379C8—41no—
380C8—41no—
381C8—81no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22C61×#38611yescharacteristic
392C4—21no—
393C4—21no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—41no—
399C4—41no—
400C4—41no—
401C4—81no—
402C4—161no—
403C2—41no—
404C2—81no—
405C2—161no—
406C2C61×#188111yescharacteristic
407C2C61×#190611yescharacteristic
408C2C61×#191011yescharacteristic
subgroupG/H
center, socleC22×C61#386
commutatorC42C22×C4×C61
Frattini, cosocleC2×C42C23×C61
prime radicalC61×#3219C2
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×#2967C2semidirect
3. C61×#1521C2semidirect
4. C61×#1514C2semidirect
5. C61×#1484C2semidirect
6. C61×#1288C2semidirect
7. C61×#1287C2semidirect
10. C61×#497C4semidirect
11. C61×#496C4semidirect
12. C61×#491C4semidirect
13. C61×#490C4semidirect
177. #9370C61direct (N × H)
200. #2967C2×C61semidirect
201. #1521C2×C61semidirect
202. #1514C2×C61semidirect
203. #1484C2×C61semidirect
204. #1288C2×C61semidirect
205. #1287C2×C61semidirect
214. #497C4×C61semidirect
215. #496C4×C61semidirect
216. #491C4×C61semidirect
217. #490C4×C61semidirect
239. C61#9370direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#32192
C61×#29672
C61×#15212
C61×#15142
C61×#14842
C61×#12882
C61×#12872
#937061