Finite Group Databasebeta

← C61×#61828 #29565261

Subgroups — C61×#61828 #29565261

Order 15616.

1914 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×#3497C211yesmaximal, characteristic
2C2×C61×#557C211yesmaximal, characteristic, complemented
3C61×#3386C218yesmaximal, complemented
4C61×#3368C218yesmaximal, complemented
5C61×#3234C214yesmaximal, complemented
6C61×#3226C212yesmaximal, complemented
7C61×#3112C214yesmaximal, complemented
8C61×#3103C212yesmaximal, complemented
9C61×#2983C211yesmaximal, characteristic, complemented
10C2×2−1+4×C61—21no—
11C61×#557—24no—
12C61×#557C2218yes—
13C61×#550C2214yes—
14D4×Q8×C61C2214yes—
15C61×#548—24no—
16C61×#537—21no—
17C61×#537—22no—
18C61×#532C2212yes—
19C61×#532C2214yes—
20C2×C4⋊Q8×C61—21no—
21C2×C4⋊Q8×C61C2211yescharacteristic
22C2×#125×C61—22no—
23C2×#125×C61C2212yes—
24C2×C4×Q8×C61—21no—
25C2×C4×Q8×C61C2211yescharacteristic
26C2×C4×Q8×C61C2212yes—
27C2×C4×Q8×C61C2211yescharacteristic
28C61×#501C2218yes—
29C61×#500C2214yes—
30C61×#490C2218yes—
31C61×#486C2214yes—
32C61×#481C2214yes—
33C61×#480C2218yes—
34C61×#478C22116yes—
35C61×#477C2218yes—
36C61×#475C2214yes—
37C61×#474C2218yes—
38C61×#460C2214yes—
39C61×#460C2218yes—
40C61×#448C2214yes—
41C61×#446C2218yes—
42C61×#440C22116yes—
43C4×SD16×C61C2218yes—
44C61×#432C2214yes—
45C61×#431C2212yes—
462−1+4×C61—48no—
47C2×#41×C61—24no—
48C2×#41×C61—24no—
49C2×#41×C61—22no—
50C22×Q8×C61—24no—
51C22×Q8×C61—21no—
52C22×Q8×C61D411yescharacteristic
53C22×Q8×C61C2311yescharacteristic
54C2×SD16×C61C2318yes—
55C4⋊Q8×C61—28no—
56C4⋊Q8×C61—22no—
57C4⋊Q8×C61C2314yes—
58C4⋊Q8×C61C2312yes—
59C4⋊Q8×C61C2314yes—
60#127×C61C2312yes—
61#127×C61C2314yes—
62#125×C61—216no—
63#125×C61—24no—
64#125×C61C2318yes—
65#124×C61—24no—
66#124×C61—22no—
67C22⋊Q8×C61—24no—
68C22⋊Q8×C61—28no—
69#121×C61—24no—
70#121×C61—22no—
71#121×C61—24no—
72#121×C61—28no—
73#121×C61C2314yes—
74C4×Q8×C61—28no—
75C4×Q8×C61—24no—
76C4×Q8×C61—22no—
77C4×Q8×C61D414yes—
78C4×Q8×C61C2314yes—
79C4×Q8×C61C2318yes—
80C4×Q8×C61C2314yes—
81C4×D4×C61—24no—
82C4×D4×C61—22no—
83C4×D4×C61C2314yes—
84C4×D4×C61C2318yes—
85C2×C4⋊C4×C61—22no—
86C2×C4⋊C4×C61—22no—
87C2×C4⋊C4×C61—21no—
88C2×C4⋊C4×C61—22no—
89C2×C4⋊C4×C61—21no—
90C2×C4⋊C4×C61D411yescharacteristic
91C2×C4⋊C4×C61D412yes—
92C2×C4⋊C4×C61C2312yes—
93C2×C4⋊C4×C61C2311yescharacteristic
94C2×C42×C61—21no—
95C2×C42×C61—22no—
96C2×C42×C61C2311yescharacteristic
97C2×C42×C61C2312yes—
98#107×C61C23116yes—
99#106×C61C2318yes—
100C4⋊C8×C61C2314yes—
101C4⋊C8×C61C2318yes—
102#103×C61C2318yes—
103#102×C61C2318yes—
104#102×C61C23116yes—
105C22⋊C8×C61C2314yes—
106#97×C61C2318yes—
107C4×C8×C61C2314yes—
108#41×C61—416no—
109#41×C61—416no—
110#41×C61—48no—
111C2×Q8×C61—24no—
112C2×Q8×C61—24no—
113C2×Q8×C61—21no—
114C2×Q8×C61—24no—
115C2×Q8×C61—24no—
116C2×Q8×C61—22no—
117C2×Q8×C61—416no—
118C2×Q8×C61—44no—
119C2×Q8×C61C2×D414yes—
120C2×Q8×C61C2412yes—
121C2×D4×C61—24no—
122C2×D4×C61—24no—
123C2×D4×C61—22no—
124C2×D4×C61—24no—
125C2×D4×C61—22no—
126C2×D4×C61C2414yes—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—22no—
130C22×C4×C61—28no—
131C22×C4×C61—24no—
132C22×C4×C61C2×D412yes—
133C22×C4×C61C2×D412yes—
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2411yescharacteristic
137SD16×C61—216no—
138C2×C8×C61C2418yes—
139C4⋊C4×C61—28no—
140C4⋊C4×C61—24no—
141C4⋊C4×C61—28no—
142C4⋊C4×C61—24no—
143C4⋊C4×C61—28no—
144C4⋊C4×C61—21no—
145C4⋊C4×C61—22no—
146C4⋊C4×C61—24no—
147C4⋊C4×C61—22no—
148C4⋊C4×C61C2×D414yes—
149C4⋊C4×C61C2×D418yes—
150C4⋊C4×C61C2412yes—
151C4⋊C4×C61C2414yes—
152C4⋊C4×C61C2414yes—
153C22⋊C4×C61—24no—
154C22⋊C4×C61—28no—
155C22⋊C4×C61—24no—
156C42×C61—28no—
157C42×C61—24no—
158C42×C61C2×D414yes—
159C42×C61C2×D412yes—
160C42×C61C2412yes—
161C42×C61C2414yes—
162C23×C61—24no—
163C23×C61C22×D411yescharacteristic
164Q8×C61—24no—
165Q8×C61—28no—
166Q8×C61—22no—
167Q8×C61—48no—
168Q8×C61—48no—
169Q8×C61—44no—
170Q8×C612−1+414yescomplemented
171D4×C61—28no—
172D4×C61—48no—
173D4×C61—48no—
174D4×C61—44no—
175D4×C61—84no—
176D4×C61—82no—
177C2×C4×C61—24no—
178C2×C4×C61—24no—
179C2×C4×C61—22no—
180C2×C4×C61—22no—
181C2×C4×C61—22no—
182C2×C4×C61—24no—
183C2×C4×C61—24no—
184C2×C4×C61—42no—
185C2×C4×C61—41no—
186C2×C4×C61—416no—
187C2×C4×C61—42no—
188C2×C4×C61—44no—
189C2×C4×C61—48no—
190C2×C4×C61AGL(1,ℤ/8)14yes—
191C2×C4×C61C22×D414yes—
192C2×C4×C61C22×D411yescharacteristic
193C2×C4×C61C22×D412yes—
194C2×C4×C61C22×D414yes—
195C2×C4×C61C22×D412yes—
196C2×C4×C61C2511yescharacteristic
197C8×C61—28no—
198#61828C6111yesmaximal, characteristic, direct product factor, Sylow
199C22×C61—21no—
200C22×C61—21no—
201C22×C61—44no—
202C22×C61—44no—
203C22×C61—44no—
204C22×C61C2×AGL(1,ℤ/8)12yes—
205C22×C61C23×D411yescharacteristic
206C4×C61—24no—
207C4×C61—22no—
208C4×C61—24no—
209C4×C61—21no—
210C4×C61—24no—
211C4×C61—42no—
212C4×C61—44no—
213C4×C61—44no—
214C4×C61C2×AGL(1,ℤ/8)14yes—
215C4×C61C2×2−1+412yes—
216#3497C2×C6111yescharacteristic
217C2×#557C2×C6111yescharacteristic, complemented
218#3386C2×C6118yescomplemented
219#3368C2×C6118yescomplemented
220#3234C2×C6114yescomplemented
221#3226C2×C6112yescomplemented
222#3112C2×C6114yescomplemented
223#3103C2×C6112yescomplemented
224#2983C2×C6111yescharacteristic, complemented
225C2×C61—22no—
226C2×C61—84no—
227C2×C61#348611yescharacteristic
228C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
229C2×C61#358611yescharacteristic
230C2×2−1+4—21no—
231#557—24no—
232#557C22×C6118yes—
233#550C22×C6114yes—
234D4×Q8C22×C6114yes—
235#548—24no—
236#537—21no—
237#537—22no—
238#532C22×C6112yes—
239#532C22×C6114yes—
240C2×C4⋊Q8—21no—
241C2×C4⋊Q8C22×C6111yescharacteristic
242C2×#125—22no—
243C2×#125C22×C6112yes—
244C2×C4×Q8—21no—
245C2×C4×Q8C22×C6111yescharacteristic
246C2×C4×Q8C22×C6112yes—
247C2×C4×Q8C22×C6111yescharacteristic
248#501C22×C6118yes—
249#500C22×C6114yes—
250#490C22×C6118yes—
251#486C22×C6114yes—
252#481C22×C6114yes—
253#480C22×C6118yes—
254#478C22×C61116yes—
255#477C22×C6118yes—
256#475C22×C6114yes—
257#474C22×C6118yes—
258#460C22×C6114yes—
259#460C22×C6118yes—
260#448C22×C6114yes—
261#446C22×C6118yes—
262#440C22×C61116yes—
263C4×SD16C22×C6118yes—
264#432C22×C6114yes—
265#431C22×C6112yes—
266C61#6182811yescharacteristic, direct product factor, Sylow
2672−1+4—48no—
268C2×#41—24no—
269C2×#41—24no—
270C2×#41—22no—
271C22×Q8—24no—
272C22×Q8—21no—
273C22×Q8D4×C6111yescharacteristic
274C22×Q8C23×C6111yescharacteristic
275C2×SD16C23×C6118yes—
276C4⋊Q8—28no—
277C4⋊Q8—22no—
278C4⋊Q8C23×C6114yes—
279C4⋊Q8C23×C6112yes—
280C4⋊Q8C23×C6114yes—
281#127C23×C6112yes—
282#127C23×C6114yes—
283#125—216no—
284#125—24no—
285#125C23×C6118yes—
286#124—24no—
287#124—22no—
288C22⋊Q8—24no—
289C22⋊Q8—28no—
290#121—24no—
291#121—22no—
292#121—24no—
293#121—28no—
294#121C23×C6114yes—
295C4×Q8—28no—
296C4×Q8—24no—
297C4×Q8—22no—
298C4×Q8D4×C6114yes—
299C4×Q8C23×C6114yes—
300C4×Q8C23×C6118yes—
301C4×Q8C23×C6114yes—
302C4×D4—24no—
303C4×D4—22no—
304C4×D4C23×C6114yes—
305C4×D4C23×C6118yes—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4D4×C6111yescharacteristic
312C2×C4⋊C4D4×C6112yes—
313C2×C4⋊C4C23×C6111yescharacteristic
314C2×C4⋊C4C23×C6112yes—
315C2×C42—22no—
316C2×C42—21no—
317C2×C42C23×C6112yes—
318C2×C42C23×C6111yescharacteristic
319#107C23×C61116yes—
320#106C23×C6118yes—
321C4⋊C8C23×C6114yes—
322C4⋊C8C23×C6118yes—
323#103C23×C6118yes—
324#102C23×C6118yes—
325#102C23×C61116yes—
326C22⋊C8C23×C6114yes—
327#97C23×C6118yes—
328C4×C8C23×C6114yes—
329#41—416no—
330#41—416no—
331#41—48no—
332C2×Q8—24no—
333C2×Q8—24no—
334C2×Q8—21no—
335C2×Q8—24no—
336C2×Q8—24no—
337C2×Q8—22no—
338C2×Q8—416no—
339C2×Q8—44no—
340C2×Q8C2×D4×C6114yes—
341C2×Q8C24×C6112yes—
342C2×D4—24no—
343C2×D4—24no—
344C2×D4—22no—
345C2×D4—24no—
346C2×D4—22no—
347C2×D4C24×C6114yes—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—22no—
351C22×C4—28no—
352C22×C4—24no—
353C22×C4C2×D4×C6112yes—
354C22×C4C2×D4×C6112yes—
355C22×C4C2×D4×C6111yescharacteristic
356C22×C4C2×D4×C6111yescharacteristic
357C22×C4C24×C6111yescharacteristic
358SD16—216no—
359C2×C8C24×C6118yes—
360C4⋊C4—28no—
361C4⋊C4—24no—
362C4⋊C4—28no—
363C4⋊C4—24no—
364C4⋊C4—28no—
365C4⋊C4—21no—
366C4⋊C4—22no—
367C4⋊C4—24no—
368C4⋊C4—22no—
369C4⋊C4C2×D4×C6114yes—
370C4⋊C4C2×D4×C6118yes—
371C4⋊C4C24×C6112yes—
372C4⋊C4C24×C6114yes—
373C4⋊C4C24×C6114yes—
374C22⋊C4—24no—
375C22⋊C4—28no—
376C22⋊C4—24no—
377C42—28no—
378C42—24no—
379C42C2×D4×C6114yes—
380C42C2×D4×C6112yes—
381C42C24×C6112yes—
382C42C24×C6114yes—
383C23—24no—
384C23C22×D4×C6111yescharacteristic
385Q8—24no—
386Q8—28no—
387Q8—22no—
388Q8—48no—
389Q8—48no—
390Q8—44no—
391Q82−1+4×C6114yescomplemented
392D4—28no—
393D4—48no—
394D4—48no—
395D4—44no—
396D4—84no—
397D4—82no—
398C2×C4—24no—
399C2×C4—24no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—24no—
404C2×C4—24no—
405C2×C4—42no—
406C2×C4—41no—
407C2×C4—416no—
408C2×C4—42no—
409C2×C4—44no—
410C2×C4—48no—
411C2×C4AGL(1,ℤ/8)×C6114yes—
412C2×C4C22×D4×C6114yes—
413C2×C4C22×D4×C6111yescharacteristic
414C2×C4C22×D4×C6112yes—
415C2×C4C22×D4×C6114yes—
416C2×C4C22×D4×C6112yes—
417C2×C4C25×C6111yescharacteristic
418C8—28no—
419C22—21no—
420C22—21no—
421C22—44no—
422C22—44no—
423C22—44no—
424C22C2×AGL(1,ℤ/8)×C6112yes—
425C22C23×D4×C6111yescharacteristic
426C4—24no—
427C4—24no—
428C4—22no—
429C4—24no—
430C4—21no—
431C4—44no—
432C4—44no—
433C4—42no—
434C4C2×AGL(1,ℤ/8)×C6114yes—
435C4C2×2−1+4×C6112yes—
436C2—22no—
437C2—84no—
438C2C61×#348611yescharacteristic
439C2C22×AGL(1,ℤ/8)×C6111yescharacteristic
440C2C61×#358611yescharacteristic
subgroupG/H
center, socleC22×C61C23×D4
commutator, Frattini, cosocleC2×C4C25×C61
prime radicalC61×#3497C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C4×Q8×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C61×#557C2semidirect
3. C61×#3386C2semidirect
4. C61×#3368C2semidirect
5. C61×#3234C2semidirect
6. C61×#3226C2semidirect
7. C61×#3112C2semidirect
8. C61×#3103C2semidirect
9. C61×#2983C2semidirect
170. Q8×C612−1+4semidirect
198. #61828C61direct (N × H)
217. C2×#557C2×C61semidirect
218. #3386C2×C61semidirect
219. #3368C2×C61semidirect
220. #3234C2×C61semidirect
221. #3226C2×C61semidirect
222. #3112C2×C61semidirect
223. #3103C2×C61semidirect
224. #2983C2×C61semidirect
266. C61#61828direct (N × H)
391. Q82−1+4×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#34972
C2×C61×#5572
C61×#33862
C61×#33682
C61×#32342
C61×#32262
C61×#31122
C61×#31032
C61×#29832
#6182861