Finite Group Databasebeta

← C61×#18749 #29522182

Subgroups — C61×#18749 #29522182

Order 15616.

966 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#554C211yesmaximal, characteristic
2C61×#3209C211yesmaximal, characteristic, complemented
3C61×#3104C211yesmaximal, characteristic, complemented
4C61×#3077C211yesmaximal, characteristic
5C61×#1644C214yesmaximal, complemented
6C61×#1632C214yesmaximal, complemented
7C61×#1548C211yesmaximal, characteristic, complemented
8C61×#1487C211yesmaximal, characteristic, complemented
9C61×#1478C211yesmaximal, characteristic
10C61×#554—22no—
11C61×#554—22no—
12C61×#554—22no—
13C61×#554C2214yes—
14C61×#533C2211yescharacteristic
15C2×C4⋊Q8×C61C2211yescharacteristic
16C2×#125×C61—21no—
17C2×C22⋊Q8×C61—21no—
18C2×C22⋊Q8×C61—22no—
19C2×C4×Q8×C61C2211yescharacteristic
20C2×C4×D4×C61—21no—
21C2×C4×D4×C61C2211yescharacteristic
22C22×C4⋊C4×C61—21no—
23C61×#494C2212yescomplemented
24C61×#487C2212yescomplemented
25C61×#484—21no—
26C61×#478—22no—
27C61×#477C2212yescomplemented
28C61×#476C2212yes—
29C61×#474C2212yes—
30C61×#462—22no—
31C61×#462C2212yescomplemented
32C61×#451—21no—
33C61×#451—22no—
34C4×Q16×C61—22no—
35C61×#431C2211yescharacteristic
36C61×#431C2211yescharacteristic
37C61×#428—21no—
38C61×#423C2211yescharacteristic
39C61×#418—21no—
40C61×#333C2214yescomplemented
41C61×Q8⋊C8C2214yescomplemented
42C61×D4⋊C8C2214yes—
43C22×Q8×C61D411yescharacteristic
44C22×Q8×C61D412yes—
45C22×D4×C61D411yescharacteristic
46C23×C4×C61—22no—
47C23×C4×C61—21no—
48C2×Q16×C61—22no—
49C2×Q16×C61—24no—
50C2×M16×C61—21no—
51C4⋊Q8×C61—21no—
52C4⋊Q8×C61—21no—
53C4⋊Q8×C61D412yes—
54C4⋊Q8×C61C2311yescharacteristic
55C4⋊Q8×C61C2311yescharacteristic
56C4⋊Q8×C61C2312yes—
57#125×C61—24no—
58#125×C61—24no—
59#125×C61—21no—
60C22⋊Q8×C61—24no—
61C22⋊Q8×C61—28no—
62C22⋊Q8×C61—24no—
63C22⋊Q8×C61—28no—
64C22⋊Q8×C61—21no—
65C22⋊Q8×C61—21no—
66C4×Q8×C61—21no—
67C4×Q8×C61—21no—
68C4×Q8×C61—21no—
69C4×Q8×C61—21no—
70C4×Q8×C61D412yes—
71C4×Q8×C61C2312yes—
72C4×D4×C61—24no—
73C4×D4×C61—24no—
74C4×D4×C61—21no—
75C4×D4×C61—21no—
76C4×D4×C61D412yes—
77C4×D4×C61C2312yes—
78#117×C61—21no—
79C2×C4⋊C4×C61—24no—
80C2×C4⋊C4×C61—22no—
81C2×C4⋊C4×C61—22no—
82C2×C4⋊C4×C61—21no—
83C2×C4⋊C4×C61—21no—
84C2×C4⋊C4×C61—21no—
85C2×C4⋊C4×C61—24no—
86C2×C4⋊C4×C61D411yescharacteristic
87C2×C4⋊C4×C61D411yescharacteristic
88C2×C22⋊C4×C61—22no—
89C2×C22⋊C4×C61—21no—
90C2×C42×C61—21no—
91C2×C42×C61C2311yescharacteristic
92#107×C61—22no—
93#107×C61—22no—
94#106×C61—22no—
95C4⋊C8×C61—21no—
96C4⋊C8×C61—21no—
97C4⋊C8×C61C2312yes—
98C4⋊C8×C61C2312yes—
99#103×C61—22no—
100#103×C61—24no—
101#103×C61—22no—
102#102×C61—22no—
103#102×C61—22no—
104C22⋊C8×C61—21no—
105C22⋊C8×C61—21no—
106C4×C8×C61—21no—
107C4×C8×C61C2312yes—
108C24×C61—21no—
109C2×Q8×C61—21no—
110C2×Q8×C61—22no—
111C2×Q8×C61—21no—
112C2×Q8×C61—21no—
113C2×Q8×C61—42no—
114C2×Q8×C61—82no—
115C2×Q8×C61C2×D412yes—
116C2×Q8×C61C2×D414yes—
117C2×D4×C61—21no—
118C2×D4×C61—22no—
119C2×D4×C61Q1614yescomplemented
120C2×D4×C61C2×D412yes—
121C22×C4×C61—21no—
122C22×C4×C61—21no—
123C22×C4×C61—21no—
124C22×C4×C61—22no—
125C22×C4×C61—28no—
126C22×C4×C61—22no—
127C22×C4×C61—22no—
128C22×C4×C61—44no—
129C22×C4×C61—84no—
130C22×C4×C61C2×D411yescharacteristic
131C22×C4×C61C2×D411yescharacteristic
132C22×C4×C61C2×D411yescharacteristic
133Q16×C61—44no—
134Q16×C61—84no—
135M16×C61—42no—
136C2×C8×C61—22no—
137C2×C8×C61—22no—
138C2×C8×C61—22no—
139C4⋊C4×C61—28no—
140C4⋊C4×C61—28no—
141C4⋊C4×C61—21no—
142C4⋊C4×C61—22no—
143C4⋊C4×C61—22no—
144C4⋊C4×C61—22no—
145C4⋊C4×C61—21no—
146C4⋊C4×C61—22no—
147C4⋊C4×C61—22no—
148C4⋊C4×C61—22no—
149C4⋊C4×C61—21no—
150C4⋊C4×C61—21no—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—21no—
153C4⋊C4×C61—41no—
154C4⋊C4×C61—41no—
155C4⋊C4×C61C2×D412yes—
156C4⋊C4×C61C2×D412yes—
157C22⋊C4×C61—28no—
158C22⋊C4×C61—22no—
159C22⋊C4×C61—22no—
160C22⋊C4×C61—41no—
161C42×C61—22no—
162C42×C61—22no—
163C42×C61—41no—
164C42×C61C2×D411yescharacteristic
165C42×C61C2×D411yescharacteristic
166C42×C61C2×D411yescharacteristic
167C42×C61C2411yescharacteristic
168C23×C61—22no—
169C23×C61—24no—
170C23×C61—42no—
171C23×C61—42no—
172C23×C61#12011yescharacteristic
173Q8×C61—22no—
174Q8×C61—22no—
175Q8×C61—42no—
176Q8×C61—44no—
177Q8×C61—42no—
178Q8×C61—42no—
179Q8×C61—82no—
180D4×C61—22no—
181D4×C61—24no—
182D4×C61C2×Q1614yes—
183C2×C4×C61—22no—
184C2×C4×C61—22no—
185C2×C4×C61—22no—
186C2×C4×C61—22no—
187C2×C4×C61—24no—
188C2×C4×C61—41no—
189C2×C4×C61—44no—
190C2×C4×C61—42no—
191C2×C4×C61—42no—
192C2×C4×C61—44no—
193C2×C4×C61—42no—
194C2×C4×C61—44no—
195C2×C4×C61—41no—
196C2×C4×C61—41no—
197C2×C4×C61—88no—
198C2×C4×C61#12011yescharacteristic
199C2×C4×C61#12011yescharacteristic
200C2×C4×C61#12011yescharacteristic
201C2×C4×C61C2×Q1612yes—
202C2×C4×C61#13712yes—
203C2×C4×C61C22×D411yescharacteristic
204C2×C4×C61C22×D411yescharacteristic
205C2×C4×C61C22×D411yescharacteristic
206C8×C61—42no—
207C8×C61—42no—
208C8×C61—42no—
209#18749C6111yesmaximal, characteristic, direct product factor, Sylow
210C22×C61—21no—
211C22×C61—21no—
212C22×C61—24no—
213C22×C61—48no—
214C22×C61—42no—
215C22×C61—42no—
216C22×C61#45112yes—
217C22×C61C2×#12011yescharacteristic
218C4×C61—21no—
219C4×C61—21no—
220C4×C61—21no—
221C4×C61—42no—
222C4×C61—42no—
223C4×C61—42no—
224C4×C61—44no—
225C4×C61—81no—
226C4×C61—81no—
227C4×C61#45112yes—
228C4×C61C22×Q1611yescharacteristic
229C4×C61C2×#13711yescharacteristic
230C4×C61#57512yes—
231C2×#554C2×C6111yescharacteristic
232#3209C2×C6111yescharacteristic, complemented
233#3104C2×C6111yescharacteristic, complemented
234#3077C2×C6111yescharacteristic
235#1644C2×C6114yescomplemented
236#1632C2×C6114yescomplemented
237#1548C2×C6111yescharacteristic, complemented
238#1487C2×C6111yescharacteristic, complemented
239#1478C2×C6111yescharacteristic
240C2×C61—22no—
241C2×C61—44no—
242C2×C61C2×#45111yescharacteristic
243C2×C61#300511yescharacteristic
244C2×C61#301911yescharacteristic
245#554—22no—
246#554—22no—
247#554—22no—
248#554C22×C6114yes—
249#533C22×C6111yescharacteristic
250C2×C4⋊Q8C22×C6111yescharacteristic
251C2×#125—21no—
252C2×C22⋊Q8—21no—
253C2×C22⋊Q8—22no—
254C2×C4×Q8C22×C6111yescharacteristic
255C2×C4×D4—21no—
256C2×C4×D4C22×C6111yescharacteristic
257C22×C4⋊C4—21no—
258#494C22×C6112yescomplemented
259#487C22×C6112yescomplemented
260#484—21no—
261#478—22no—
262#477C22×C6112yescomplemented
263#476C22×C6112yes—
264#474C22×C6112yes—
265#462—22no—
266#462C22×C6112yescomplemented
267#451—21no—
268#451—22no—
269C4×Q16—22no—
270#431C22×C6111yescharacteristic
271#431C22×C6111yescharacteristic
272#428—21no—
273#423C22×C6111yescharacteristic
274#418—21no—
275#333C22×C6114yescomplemented
276Q8⋊C8C22×C6114yescomplemented
277D4⋊C8C22×C6114yes—
278C61#1874911yescharacteristic, direct product factor, Sylow
279C22×Q8D4×C6111yescharacteristic
280C22×Q8D4×C6112yes—
281C22×D4D4×C6111yescharacteristic
282C23×C4—22no—
283C23×C4—21no—
284C2×Q16—22no—
285C2×Q16—24no—
286C2×M16—21no—
287C4⋊Q8—21no—
288C4⋊Q8—21no—
289C4⋊Q8D4×C6112yes—
290C4⋊Q8C23×C6111yescharacteristic
291C4⋊Q8C23×C6111yescharacteristic
292C4⋊Q8C23×C6112yes—
293#125—24no—
294#125—24no—
295#125—21no—
296C22⋊Q8—24no—
297C22⋊Q8—28no—
298C22⋊Q8—24no—
299C22⋊Q8—28no—
300C22⋊Q8—21no—
301C22⋊Q8—21no—
302C4×Q8—21no—
303C4×Q8—21no—
304C4×Q8—21no—
305C4×Q8—21no—
306C4×Q8D4×C6112yes—
307C4×Q8C23×C6112yes—
308C4×D4—24no—
309C4×D4—24no—
310C4×D4—21no—
311C4×D4—21no—
312C4×D4D4×C6112yes—
313C4×D4C23×C6112yes—
314#117—21no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4D4×C6111yescharacteristic
323C2×C4⋊C4D4×C6111yescharacteristic
324C2×C22⋊C4—22no—
325C2×C22⋊C4—21no—
326C2×C42—21no—
327C2×C42C23×C6111yescharacteristic
328#107—22no—
329#107—22no—
330#106—22no—
331C4⋊C8—21no—
332C4⋊C8—21no—
333C4⋊C8C23×C6112yes—
334C4⋊C8C23×C6112yes—
335#103—22no—
336#103—24no—
337#103—22no—
338#102—22no—
339#102—22no—
340C22⋊C8—21no—
341C22⋊C8—21no—
342C4×C8—21no—
343C4×C8C23×C6112yes—
344C24—21no—
345C2×Q8—21no—
346C2×Q8—22no—
347C2×Q8—21no—
348C2×Q8—21no—
349C2×Q8—42no—
350C2×Q8—82no—
351C2×Q8C2×D4×C6112yes—
352C2×Q8C2×D4×C6114yes—
353C2×D4—21no—
354C2×D4—22no—
355C2×D4Q16×C6114yescomplemented
356C2×D4C2×D4×C6112yes—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—22no—
361C22×C4—28no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—44no—
365C22×C4—84no—
366C22×C4C2×D4×C6111yescharacteristic
367C22×C4C2×D4×C6111yescharacteristic
368C22×C4C2×D4×C6111yescharacteristic
369Q16—44no—
370Q16—84no—
371M16—42no—
372C2×C8—22no—
373C2×C8—22no—
374C2×C8—22no—
375C4⋊C4—28no—
376C4⋊C4—28no—
377C4⋊C4—21no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—21no—
382C4⋊C4—22no—
383C4⋊C4—22no—
384C4⋊C4—22no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4C2×D4×C6112yes—
392C4⋊C4C2×D4×C6112yes—
393C22⋊C4—28no—
394C22⋊C4—22no—
395C22⋊C4—22no—
396C22⋊C4—41no—
397C42—22no—
398C42—22no—
399C42—41no—
400C42C2×D4×C6111yescharacteristic
401C42C2×D4×C6111yescharacteristic
402C42C2×D4×C6111yescharacteristic
403C42C24×C6111yescharacteristic
404C23—24no—
405C23—22no—
406C23—42no—
407C23—42no—
408C23#120×C6111yescharacteristic
409Q8—22no—
410Q8—22no—
411Q8—44no—
412Q8—42no—
413Q8—42no—
414Q8—42no—
415Q8—82no—
416D4—22no—
417D4—24no—
418D4C2×Q16×C6114yes—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—24no—
424C2×C4—41no—
425C2×C4—44no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—44no—
429C2×C4—42no—
430C2×C4—44no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—88no—
434C2×C4#120×C6111yescharacteristic
435C2×C4#120×C6111yescharacteristic
436C2×C4#120×C6111yescharacteristic
437C2×C4C2×Q16×C6112yes—
438C2×C4#137×C6112yes—
439C2×C4C22×D4×C6111yescharacteristic
440C2×C4C22×D4×C6111yescharacteristic
441C2×C4C22×D4×C6111yescharacteristic
442C8—42no—
443C8—42no—
444C8—42no—
445C22—21no—
446C22—21no—
447C22—24no—
448C22—48no—
449C22—42no—
450C22—42no—
451C22C61×#45112yes—
452C22C2×#120×C6111yescharacteristic
453C4—21no—
454C4—21no—
455C4—21no—
456C4—42no—
457C4—42no—
458C4—42no—
459C4—44no—
460C4—81no—
461C4—81no—
462C4C61×#45112yes—
463C4C22×Q16×C6111yescharacteristic
464C4C2×#137×C6111yescharacteristic
465C4C61×#57512yes—
466C2—22no—
467C2—44no—
468C2C2×C61×#45111yescharacteristic
469C2C61×#300511yescharacteristic
470C2C61×#301911yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC42C24×C61
prime radicalC22×D4×C61D4
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×#3209C2semidirect
3. C61×#3104C2semidirect
5. C61×#1644C2semidirect
6. C61×#1632C2semidirect
7. C61×#1548C2semidirect
8. C61×#1487C2semidirect
23. C61×#494C22semidirect
24. C61×#487C22semidirect
27. C61×#477C22semidirect
31. C61×#462C22semidirect
40. C61×#333C22semidirect
41. C61×Q8⋊C8C22semidirect
119. C2×D4×C61Q16semidirect
209. #18749C61direct (N × H)
232. #3209C2×C61semidirect
233. #3104C2×C61semidirect
235. #1644C2×C61semidirect
236. #1632C2×C61semidirect
237. #1548C2×C61semidirect
238. #1487C2×C61semidirect
258. #494C22×C61semidirect
259. #487C22×C61semidirect
262. #477C22×C61semidirect
266. #462C22×C61semidirect
275. #333C22×C61semidirect
276. Q8⋊C8C22×C61semidirect
278. C61#18749direct (N × H)
355. C2×D4Q16×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#5542
C61×#32092
C61×#31042
C61×#30772
C61×#16442
C61×#16322
C61×#15482
C61×#14872
C61×#14782
#1874961