Finite Group Databasebeta

← C61×#19176 #29522609

Subgroups — C61×#19176 #29522609

Order 15616.

618 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3141C211yesmaximal, characteristic
2C61×#3103C211yesmaximal, characteristic
3C2×C61×#477C211yesmaximal, characteristic, complemented
4Q8×M16×C61C211yesmaximal, characteristic, complemented
5C61×#1704C212yesmaximal, complemented
6C61×#1698C212yesmaximal, complemented
7C61×#1684C212yesmaximal, complemented
8C61×#1678C212yesmaximal, complemented
9C61×#1565C211yesmaximal, characteristic, complemented
10C61×#1548C211yesmaximal, characteristic, complemented
11C61×#1547C211yesmaximal, characteristic
12C61×#532C2211yescharacteristic
13C2×C4⋊Q8×C61C2211yescharacteristic
14C2×C4×Q8×C61C2211yescharacteristic
15C61×#489—22no—
16C61×#487C2212yes—
17C61×#486C2212yes—
18C61×#481—21no—
19C61×#477—21no—
20C61×#477—21no—
21C61×#477C2212yes—
22C61×#477C2212yes—
23C61×#475C2211yescharacteristic
24C61×#475C2211yescharacteristic
25C61×#460C2211yescharacteristic
26C61×#460C2211yescharacteristic
27C61×#448—21no—
28C61×#446—22no—
29C61×#446C2212yes—
30C8×Q8×C61C2212yes—
31C4×SD16×C61—21no—
32C4×SD16×C61—21no—
33C61×#431C2211yescharacteristic
34C2×#107×C61—21no—
35C61×#423—21no—
36C61×#423C2211yescharacteristic
37C2×C4⋊C8×C61C2211yescharacteristic
38C61×#417—21no—
39C61×#417—21no—
40C2×#103×C61—21no—
41C4×M16×C61—21no—
42C4×M16×C61C2211yescharacteristic
43C61×#335C2212yes—
44C61×#334C2212yes—
45C61×#333C2212yes—
46C61×#333C2212yes—
47C61×#332C2212yes—
48C61×#331C2212yes—
49C2×#41×C61—21no—
50C22×Q8×C61—21no—
51C22×Q8×C61D411yescharacteristic
52C2×SD16×C61—21no—
53C2×SD16×C61—21no—
54C2×M16×C61—21no—
55C2×M16×C61D411yescharacteristic
56C2×M16×C61D411yescharacteristic
57C22×C8×C61—21no—
58C4⋊Q8×C61—21no—
59C4⋊Q8×C61—21no—
60C4⋊Q8×C61—21no—
61C4⋊Q8×C61C2312yes—
62C4⋊Q8×C61C2311yescharacteristic
63#127×C61C2311yescharacteristic
64#124×C61—21no—
65#121×C61—21no—
66#121×C61—21no—
67C4×Q8×C61—21no—
68C4×Q8×C61—21no—
69C4×Q8×C61D411yescharacteristic
70C4×Q8×C61D411yescharacteristic
71C4×Q8×C61C2311yescharacteristic
72C4×Q8×C61C2311yescharacteristic
73C4×D4×C61—21no—
74C4×D4×C61—21no—
75C2×C4⋊C4×C61—21no—
76C2×C4⋊C4×C61—21no—
77C2×C4⋊C4×C61—21no—
78C2×C4⋊C4×C61D411yescharacteristic
79C2×C42×C61—21no—
80C2×C42×C61C2311yescharacteristic
81#107×C61—22no—
82#107×C61—22no—
83#106×C61—21no—
84#106×C61—21no—
85C4⋊C8×C61—22no—
86C4⋊C8×C61—22no—
87C4⋊C8×C61—21no—
88C4⋊C8×C61—21no—
89C4⋊C8×C61C2312yes—
90C4⋊C8×C61C2312yes—
91C4⋊C8×C61C2311yescharacteristic
92C4⋊C8×C61C2311yescharacteristic
93#103×C61—22no—
94#103×C61—22no—
95#103×C61—21no—
96#103×C61—21no—
97#103×C61—22no—
98#103×C61—22no—
99#102×C61—22no—
100#102×C61—22no—
101#102×C61—21no—
102#102×C61—21no—
103C22⋊C8×C61—21no—
104#97×C61—22no—
105#97×C61D412yes—
106C4×C8×C61—22no—
107C4×C8×C61—21no—
108C4×C8×C61C2312yes—
109#41×C61—42no—
110#41×C61—42no—
111C2×Q8×C61—21no—
112C2×Q8×C61—22no—
113C2×Q8×C61—21no—
114C2×Q8×C61—22no—
115C2×Q8×C61—41no—
116C2×Q8×C61—41no—
117C2×Q8×C61—82no—
118C2×Q8×C61C2×D411yescharacteristic
119C2×Q8×C61C2×D411yescharacteristic
120C2×D4×C61—21no—
121C2×D4×C61—21no—
122C2×D4×C61—21no—
123C2×D4×C61—41no—
124C22×C4×C61—21no—
125C22×C4×C61—21no—
126C22×C4×C61—41no—
127C22×C4×C61—41no—
128C22×C4×C61C2×D411yescharacteristic
129C22×C4×C61C2×D411yescharacteristic
130C22×C4×C61#4111yescharacteristic
131SD16×C61—42no—
132SD16×C61—42no—
133M16×C61—22no—
134M16×C61—22no—
135M16×C61—42no—
136C2×C8×C61—22no—
137C2×C8×C61—21no—
138C2×C8×C61—21no—
139C2×C8×C61—22no—
140C2×C8×C61—42no—
141C2×C8×C61C2×D412yes—
142C2×C8×C61C2×D412yes—
143C4⋊C4×C61—21no—
144C4⋊C4×C61—21no—
145C4⋊C4×C61—21no—
146C4⋊C4×C61—21no—
147C4⋊C4×C61—21no—
148C4⋊C4×C61—22no—
149C4⋊C4×C61—21no—
150C4⋊C4×C61—22no—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—41no—
153C4⋊C4×C61—41no—
154C4⋊C4×C61C2×D411yescharacteristic
155C4⋊C4×C61C2×D411yescharacteristic
156C22⋊C4×C61—41no—
157C22⋊C4×C61—41no—
158C42×C61—21no—
159C42×C61—21no—
160C42×C61—21no—
161C42×C61—21no—
162C42×C61C2×D411yescharacteristic
163C42×C61C2×D411yescharacteristic
164C42×C61#4111yescharacteristic
165C42×C61C2411yescharacteristic
166C23×C61—41no—
167C23×C61#12111yescharacteristic
168Q8×C61—21no—
169Q8×C61—21no—
170Q8×C61—21no—
171Q8×C61—42no—
172Q8×C61—41no—
173Q8×C61—41no—
174Q8×C61—82no—
175Q8×C61—82no—
176Q8×C61#13712yes—
177D4×C61—41no—
178D4×C61—41no—
179D4×C61—41no—
180D4×C61—41no—
181D4×C61—81no—
182D4×C61—82no—
183C2×C4×C61—21no—
184C2×C4×C61—21no—
185C2×C4×C61—21no—
186C2×C4×C61—21no—
187C2×C4×C61—21no—
188C2×C4×C61—21no—
189C2×C4×C61—41no—
190C2×C4×C61—42no—
191C2×C4×C61—41no—
192C2×C4×C61—42no—
193C2×C4×C61—81no—
194C2×C4×C61—82no—
195C2×C4×C61—82no—
196C2×C4×C61#12111yescharacteristic
197C2×C4×C61#12111yescharacteristic
198C2×C4×C61#12111yescharacteristic
199C2×C4×C61#13512yes—
200C2×C4×C61#13712yes—
201C2×C4×C61C22×D411yescharacteristic
202C2×C4×C61C22×D411yescharacteristic
203C2×C4×C61C2×#4111yescharacteristic
204C8×C61—22no—
205C8×C61—22no—
206C8×C61—42no—
207C8×C61—41no—
208C8×C61—42no—
209C8×C61—41no—
210#19176C6111yesmaximal, characteristic, direct product factor, Sylow
211C22×C61—21no—
212C22×C61—21no—
213C22×C61—81no—
214C22×C61—81no—
215C22×C61—81no—
216C22×C61#46412yes—
217C22×C61C2×#12111yescharacteristic
218C4×C61—21no—
219C4×C61—22no—
220C4×C61—21no—
221C4×C61—21no—
222C4×C61—41no—
223C4×C61—41no—
224C4×C61—41no—
225C4×C61—81no—
226C4×C61—82no—
227C4×C61#46412yes—
228C4×C61C2×#13511yescharacteristic
229C4×C61C2×#13711yescharacteristic
230C4×C61C2×#13711yescharacteristic
231C4×C61#57511yescharacteristic
232#3141C2×C6111yescharacteristic
233#3103C2×C6111yescharacteristic
234C2×#477C2×C6111yescharacteristic, complemented
235Q8×M16C2×C6111yescharacteristic, complemented
236#1704C2×C6112yescomplemented
237#1698C2×C6112yescomplemented
238#1684C2×C6112yescomplemented
239#1678C2×C6112yescomplemented
240#1565C2×C6111yescharacteristic, complemented
241#1548C2×C6111yescharacteristic, complemented
242#1547C2×C6111yescharacteristic
243C2×C61—22no—
244C2×C61—161no—
245C2×C61C2×#46411yescharacteristic
246C2×C61#305611yescharacteristic
247C2×C61#306811yescharacteristic
248#532C22×C6111yescharacteristic
249C2×C4⋊Q8C22×C6111yescharacteristic
250C2×C4×Q8C22×C6111yescharacteristic
251#489—22no—
252#487C22×C6112yes—
253#486C22×C6112yes—
254#481—21no—
255#477—21no—
256#477—21no—
257#477C22×C6112yes—
258#477C22×C6112yes—
259#475C22×C6111yescharacteristic
260#475C22×C6111yescharacteristic
261#460C22×C6111yescharacteristic
262#460C22×C6111yescharacteristic
263#448—21no—
264#446—22no—
265#446C22×C6112yes—
266C8×Q8C22×C6112yes—
267C4×SD16—21no—
268C4×SD16—21no—
269#431C22×C6111yescharacteristic
270C2×#107—21no—
271#423—21no—
272#423C22×C6111yescharacteristic
273C2×C4⋊C8C22×C6111yescharacteristic
274#417—21no—
275#417—21no—
276C2×#103—21no—
277C4×M16—21no—
278C4×M16C22×C6111yescharacteristic
279#335C22×C6112yes—
280#334C22×C6112yes—
281#333C22×C6112yes—
282#333C22×C6112yes—
283#332C22×C6112yes—
284#331C22×C6112yes—
285C61#1917611yescharacteristic, direct product factor, Sylow
286C2×#41—21no—
287C22×Q8—21no—
288C22×Q8D4×C6111yescharacteristic
289C2×SD16—21no—
290C2×SD16—21no—
291C2×M16—21no—
292C2×M16D4×C6111yescharacteristic
293C2×M16D4×C6111yescharacteristic
294C22×C8—21no—
295C4⋊Q8—21no—
296C4⋊Q8—21no—
297C4⋊Q8—21no—
298C4⋊Q8C23×C6112yes—
299C4⋊Q8C23×C6111yescharacteristic
300#127C23×C6111yescharacteristic
301#124—21no—
302#121—21no—
303#121—21no—
304C4×Q8—21no—
305C4×Q8—21no—
306C4×Q8D4×C6111yescharacteristic
307C4×Q8D4×C6111yescharacteristic
308C4×Q8C23×C6111yescharacteristic
309C4×Q8C23×C6111yescharacteristic
310C4×D4—21no—
311C4×D4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4D4×C6111yescharacteristic
316C2×C42—21no—
317C2×C42C23×C6111yescharacteristic
318#107—22no—
319#107—22no—
320#106—21no—
321#106—21no—
322C4⋊C8—22no—
323C4⋊C8—22no—
324C4⋊C8—21no—
325C4⋊C8—21no—
326C4⋊C8C23×C6112yes—
327C4⋊C8C23×C6112yes—
328C4⋊C8C23×C6111yescharacteristic
329C4⋊C8C23×C6111yescharacteristic
330#103—22no—
331#103—22no—
332#103—21no—
333#103—21no—
334#103—22no—
335#103—22no—
336#102—22no—
337#102—22no—
338#102—21no—
339#102—21no—
340C22⋊C8—21no—
341#97—22no—
342#97D4×C6112yes—
343C4×C8—22no—
344C4×C8—21no—
345C4×C8C23×C6112yes—
346#41—42no—
347#41—42no—
348C2×Q8—21no—
349C2×Q8—22no—
350C2×Q8—21no—
351C2×Q8—22no—
352C2×Q8—41no—
353C2×Q8—41no—
354C2×Q8—82no—
355C2×Q8C2×D4×C6111yescharacteristic
356C2×Q8C2×D4×C6111yescharacteristic
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—41no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4C2×D4×C6111yescharacteristic
366C22×C4C2×D4×C6111yescharacteristic
367C22×C4#41×C6111yescharacteristic
368SD16—42no—
369SD16—42no—
370M16—22no—
371M16—22no—
372M16—42no—
373C2×C8—22no—
374C2×C8—21no—
375C2×C8—21no—
376C2×C8—22no—
377C2×C8—42no—
378C2×C8C2×D4×C6112yes—
379C2×C8C2×D4×C6112yes—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—22no—
386C4⋊C4—21no—
387C4⋊C4—22no—
388C4⋊C4—21no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4C2×D4×C6111yescharacteristic
392C4⋊C4C2×D4×C6111yescharacteristic
393C22⋊C4—41no—
394C22⋊C4—41no—
395C42—21no—
396C42—21no—
397C42—21no—
398C42—21no—
399C42C2×D4×C6111yescharacteristic
400C42C2×D4×C6111yescharacteristic
401C42#41×C6111yescharacteristic
402C42C24×C6111yescharacteristic
403C23—41no—
404C23#121×C6111yescharacteristic
405Q8—21no—
406Q8—21no—
407Q8—21no—
408Q8—42no—
409Q8—41no—
410Q8—41no—
411Q8—82no—
412Q8—82no—
413Q8#137×C6112yes—
414D4—41no—
415D4—41no—
416D4—41no—
417D4—41no—
418D4—81no—
419D4—82no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—42no—
430C2×C4—81no—
431C2×C4—82no—
432C2×C4—82no—
433C2×C4#121×C6111yescharacteristic
434C2×C4#121×C6111yescharacteristic
435C2×C4#121×C6111yescharacteristic
436C2×C4#135×C6112yes—
437C2×C4#137×C6112yes—
438C2×C4C22×D4×C6111yescharacteristic
439C2×C4C22×D4×C6111yescharacteristic
440C2×C4C2×#41×C6111yescharacteristic
441C8—22no—
442C8—22no—
443C8—42no—
444C8—41no—
445C8—42no—
446C8—41no—
447C22—21no—
448C22—21no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22C61×#46412yes—
453C22C2×#121×C6111yescharacteristic
454C4—21no—
455C4—22no—
456C4—21no—
457C4—21no—
458C4—41no—
459C4—41no—
460C4—41no—
461C4—81no—
462C4—82no—
463C4C61×#46412yes—
464C4C2×#135×C6111yescharacteristic
465C4C2×#137×C6111yescharacteristic
466C4C2×#137×C6111yescharacteristic
467C4C61×#57511yescharacteristic
468C2—22no—
469C2—161no—
470C2C2×C61×#46411yescharacteristic
471C2C61×#305611yescharacteristic
472C2C61×#306811yescharacteristic
subgroupG/H
center, socleC22×C61C2×#121
commutator, Frattini, cosocleC42C24×C61
prime radicalC61×#532C22
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
3. C2×C61×#477C2semidirect
4. Q8×M16×C61C2semidirect
5. C61×#1704C2semidirect
6. C61×#1698C2semidirect
7. C61×#1684C2semidirect
8. C61×#1678C2semidirect
9. C61×#1565C2semidirect
10. C61×#1548C2semidirect
210. #19176C61direct (N × H)
234. C2×#477C2×C61semidirect
235. Q8×M16C2×C61semidirect
236. #1704C2×C61semidirect
237. #1698C2×C61semidirect
238. #1684C2×C61semidirect
239. #1678C2×C61semidirect
240. #1565C2×C61semidirect
241. #1548C2×C61semidirect
285. C61#19176direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#31412
C61×#31032
C2×C61×#4772
Q8×M16×C612
C61×#17042
C61×#16982
C61×#16842
C61×#16782
C61×#15652
C61×#15482
C61×#15472
#1917661