Finite Group Databasebeta

← C61×#19171 #29522604

Subgroups — C61×#19171 #29522604

Order 15616.

682 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3152C211yesmaximal, characteristic
2C61×#3103C211yesmaximal, characteristic
3C2×C61×#475C211yesmaximal, characteristic, complemented
4Q8×M16×C61C211yesmaximal, characteristic, complemented
5C61×#1690C212yesmaximal, complemented
6C61×#1686C212yesmaximal, complemented
7C61×#1670C212yesmaximal, complemented
8C61×#1666C212yesmaximal, complemented
9C61×#1565C211yesmaximal, characteristic, complemented
10C61×#1547C211yesmaximal, characteristic
11C61×#1546C211yesmaximal, characteristic, complemented
12C2×#137×C61—21no—
13C2×#137×C61—21no—
14C61×#532C2211yescharacteristic
15C2×C4⋊Q8×C61C2211yescharacteristic
16C2×C4×Q8×C61C2211yescharacteristic
17C61×#497—22no—
18C61×#494C2212yes—
19C61×#492C2212yes—
20C61×#481—21no—
21C61×#475—21no—
22C61×#475—21no—
23C61×#475C2212yes—
24C61×#475C2212yes—
25C61×#475C2211yescharacteristic
26C61×#475C2211yescharacteristic
27C61×#460C2211yescharacteristic
28C61×#460C2211yescharacteristic
29C61×#448—21no—
30C61×#446—22no—
31C61×#446C2212yes—
32C8×Q8×C61C2212yes—
33C4×SD16×C61—21no—
34C4×SD16×C61—21no—
35C61×#431C2211yescharacteristic
36C2×#106×C61—21no—
37C61×#423—21no—
38C61×#423C2211yescharacteristic
39C2×C4⋊C8×C61C2211yescharacteristic
40C2×#103×C61—21no—
41C4×M16×C61—21no—
42C4×M16×C61C2211yescharacteristic
43C61×#335C2212yes—
44C61×#334C2212yes—
45C61×#332C2212yes—
46C61×#332C2212yes—
47C61×#332C2212yes—
48C61×#331C2212yes—
49C2×#41×C61—21no—
50C22×Q8×C61—21no—
51C22×Q8×C61D411yescharacteristic
52#137×C61—44no—
53#137×C61—44no—
54C2×Q16×C61—22no—
55C2×Q16×C61—22no—
56C2×SD16×C61—21no—
57C2×SD16×C61—21no—
58C2×SD16×C61—22no—
59C2×SD16×C61—22no—
60C2×M16×C61—21no—
61C2×M16×C61D411yescharacteristic
62C2×M16×C61D411yescharacteristic
63C22×C8×C61—21no—
64C4⋊Q8×C61—21no—
65C4⋊Q8×C61—21no—
66C4⋊Q8×C61—21no—
67C4⋊Q8×C61C2312yes—
68C4⋊Q8×C61C2311yescharacteristic
69#127×C61C2311yescharacteristic
70#124×C61—21no—
71#121×C61—21no—
72#121×C61—21no—
73C4×Q8×C61—21no—
74C4×Q8×C61—21no—
75C4×Q8×C61D411yescharacteristic
76C4×Q8×C61D411yescharacteristic
77C4×Q8×C61C2311yescharacteristic
78C4×Q8×C61C2311yescharacteristic
79C4×D4×C61—21no—
80C4×D4×C61—21no—
81C2×C4⋊C4×C61—21no—
82C2×C4⋊C4×C61—21no—
83C2×C4⋊C4×C61—21no—
84C2×C4⋊C4×C61D411yescharacteristic
85C2×C42×C61—21no—
86C2×C42×C61C2311yescharacteristic
87#106×C61—22no—
88#106×C61—22no—
89#106×C61—21no—
90#106×C61—21no—
91C4⋊C8×C61—22no—
92C4⋊C8×C61—22no—
93C4⋊C8×C61—21no—
94C4⋊C8×C61—21no—
95C4⋊C8×C61C2312yes—
96C4⋊C8×C61C2312yes—
97C4⋊C8×C61C2311yescharacteristic
98C4⋊C8×C61C2311yescharacteristic
99#103×C61—22no—
100#103×C61—22no—
101#103×C61—21no—
102#103×C61—21no—
103#102×C61—21no—
104#102×C61—21no—
105C22⋊C8×C61—21no—
106#97×C61—22no—
107#97×C61D412yes—
108C4×C8×C61—22no—
109C4×C8×C61—21no—
110C4×C8×C61C2312yes—
111#41×C61—42no—
112#41×C61—42no—
113C2×Q8×C61—21no—
114C2×Q8×C61—22no—
115C2×Q8×C61—21no—
116C2×Q8×C61—22no—
117C2×Q8×C61—41no—
118C2×Q8×C61—41no—
119C2×Q8×C61—42no—
120C2×Q8×C61—42no—
121C2×Q8×C61C2×D411yescharacteristic
122C2×Q8×C61C2×D411yescharacteristic
123C2×D4×C61—21no—
124C2×D4×C61—21no—
125C2×D4×C61—21no—
126C2×D4×C61—41no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—41no—
130C22×C4×C61—41no—
131C22×C4×C61C2×D411yescharacteristic
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61#4111yescharacteristic
134Q16×C61—44no—
135Q16×C61—44no—
136SD16×C61—44no—
137SD16×C61—42no—
138SD16×C61—42no—
139SD16×C61—44no—
140M16×C61—22no—
141M16×C61—42no—
142M16×C61SD1614yescomplemented
143C2×C8×C61—22no—
144C2×C8×C61—21no—
145C2×C8×C61—21no—
146C2×C8×C61—22no—
147C2×C8×C61—42no—
148C2×C8×C61C2×D412yes—
149C2×C8×C61C2×D412yes—
150C4⋊C4×C61—21no—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—21no—
153C4⋊C4×C61—21no—
154C4⋊C4×C61—21no—
155C4⋊C4×C61—22no—
156C4⋊C4×C61—21no—
157C4⋊C4×C61—22no—
158C4⋊C4×C61—21no—
159C4⋊C4×C61—41no—
160C4⋊C4×C61—41no—
161C4⋊C4×C61C2×D411yescharacteristic
162C4⋊C4×C61C2×D411yescharacteristic
163C22⋊C4×C61—41no—
164C22⋊C4×C61—41no—
165C42×C61—21no—
166C42×C61—21no—
167C42×C61—21no—
168C42×C61—21no—
169C42×C61C2×D411yescharacteristic
170C42×C61C2×D411yescharacteristic
171C42×C61#4111yescharacteristic
172C42×C61C2411yescharacteristic
173C23×C61—41no—
174C23×C61#12111yescharacteristic
175Q8×C61—21no—
176Q8×C61—21no—
177Q8×C61—21no—
178Q8×C61—42no—
179Q8×C61—42no—
180Q8×C61—41no—
181Q8×C61—42no—
182Q8×C61—41no—
183Q8×C61—82no—
184Q8×C61#13712yescomplemented
185D4×C61—41no—
186D4×C61—41no—
187D4×C61—41no—
188D4×C61—41no—
189D4×C61—81no—
190D4×C61—82no—
191C2×C4×C61—21no—
192C2×C4×C61—21no—
193C2×C4×C61—21no—
194C2×C4×C61—21no—
195C2×C4×C61—21no—
196C2×C4×C61—21no—
197C2×C4×C61—41no—
198C2×C4×C61—42no—
199C2×C4×C61—41no—
200C2×C4×C61—42no—
201C2×C4×C61—81no—
202C2×C4×C61—82no—
203C2×C4×C61—82no—
204C2×C4×C61#12111yescharacteristic
205C2×C4×C61#12111yescharacteristic
206C2×C4×C61#12111yescharacteristic
207C2×C4×C61C2×SD1612yes—
208C2×C4×C61AGL(1,ℤ/8)12yes—
209C2×C4×C61C22×D411yescharacteristic
210C2×C4×C61C22×D411yescharacteristic
211C2×C4×C61C2×#4111yescharacteristic
212C8×C61—22no—
213C8×C61—42no—
214C8×C61—41no—
215C8×C61—42no—
216C8×C61—41no—
217C8×C61C2×SD1614yes—
218#19171C6111yesmaximal, characteristic, direct product factor, Sylow
219C22×C61—21no—
220C22×C61—21no—
221C22×C61—81no—
222C22×C61—81no—
223C22×C61—81no—
224C22×C61#46012yes—
225C22×C61C2×#12111yescharacteristic
226C4×C61—21no—
227C4×C61—22no—
228C4×C61—21no—
229C4×C61—21no—
230C4×C61—41no—
231C4×C61—41no—
232C4×C61—41no—
233C4×C61—81no—
234C4×C61—82no—
235C4×C61#46012yes—
236C4×C61C22×SD1611yescharacteristic
237C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
238C4×C61C2×#13711yescharacteristic
239C4×C61#57511yescharacteristic
240#3152C2×C6111yescharacteristic
241#3103C2×C6111yescharacteristic
242C2×#475C2×C6111yescharacteristic, complemented
243Q8×M16C2×C6111yescharacteristic, complemented
244#1690C2×C6112yescomplemented
245#1686C2×C6112yescomplemented
246#1670C2×C6112yescomplemented
247#1666C2×C6112yescomplemented
248#1565C2×C6111yescharacteristic, complemented
249#1547C2×C6111yescharacteristic
250#1546C2×C6111yescharacteristic, complemented
251C2×C61—22no—
252C2×C61—161no—
253C2×C61C2×#46011yescharacteristic
254C2×C61#305611yescharacteristic
255C2×C61#306911yescharacteristic
256C2×#137—21no—
257C2×#137—21no—
258#532C22×C6111yescharacteristic
259C2×C4⋊Q8C22×C6111yescharacteristic
260C2×C4×Q8C22×C6111yescharacteristic
261#497—22no—
262#494C22×C6112yes—
263#492C22×C6112yes—
264#481—21no—
265#475—21no—
266#475—21no—
267#475C22×C6112yes—
268#475C22×C6112yes—
269#475C22×C6111yescharacteristic
270#475C22×C6111yescharacteristic
271#460C22×C6111yescharacteristic
272#460C22×C6111yescharacteristic
273#448—21no—
274#446—22no—
275#446C22×C6112yes—
276C8×Q8C22×C6112yes—
277C4×SD16—21no—
278C4×SD16—21no—
279#431C22×C6111yescharacteristic
280C2×#106—21no—
281#423—21no—
282#423C22×C6111yescharacteristic
283C2×C4⋊C8C22×C6111yescharacteristic
284C2×#103—21no—
285C4×M16—21no—
286C4×M16C22×C6111yescharacteristic
287#335C22×C6112yes—
288#334C22×C6112yes—
289#332C22×C6112yes—
290#332C22×C6112yes—
291#332C22×C6112yes—
292#331C22×C6112yes—
293C61#1917111yescharacteristic, direct product factor, Sylow
294C2×#41—21no—
295C22×Q8—21no—
296C22×Q8D4×C6111yescharacteristic
297#137—44no—
298#137—44no—
299C2×Q16—22no—
300C2×Q16—22no—
301C2×SD16—21no—
302C2×SD16—21no—
303C2×SD16—22no—
304C2×SD16—22no—
305C2×M16—21no—
306C2×M16D4×C6111yescharacteristic
307C2×M16D4×C6111yescharacteristic
308C22×C8—21no—
309C4⋊Q8—21no—
310C4⋊Q8—21no—
311C4⋊Q8—21no—
312C4⋊Q8C23×C6112yes—
313C4⋊Q8C23×C6111yescharacteristic
314#127C23×C6111yescharacteristic
315#124—21no—
316#121—21no—
317#121—21no—
318C4×Q8—21no—
319C4×Q8—21no—
320C4×Q8D4×C6111yescharacteristic
321C4×Q8D4×C6111yescharacteristic
322C4×Q8C23×C6111yescharacteristic
323C4×Q8C23×C6111yescharacteristic
324C4×D4—21no—
325C4×D4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4D4×C6111yescharacteristic
330C2×C42—21no—
331C2×C42C23×C6111yescharacteristic
332#106—22no—
333#106—22no—
334#106—21no—
335#106—21no—
336C4⋊C8—22no—
337C4⋊C8—22no—
338C4⋊C8—21no—
339C4⋊C8—21no—
340C4⋊C8C23×C6112yes—
341C4⋊C8C23×C6112yes—
342C4⋊C8C23×C6111yescharacteristic
343C4⋊C8C23×C6111yescharacteristic
344#103—22no—
345#103—22no—
346#103—21no—
347#103—21no—
348#102—21no—
349#102—21no—
350C22⋊C8—21no—
351#97—22no—
352#97D4×C6112yes—
353C4×C8—22no—
354C4×C8—21no—
355C4×C8C23×C6112yes—
356#41—42no—
357#41—42no—
358C2×Q8—21no—
359C2×Q8—22no—
360C2×Q8—21no—
361C2×Q8—22no—
362C2×Q8—41no—
363C2×Q8—41no—
364C2×Q8—42no—
365C2×Q8—42no—
366C2×Q8C2×D4×C6111yescharacteristic
367C2×Q8C2×D4×C6111yescharacteristic
368C2×D4—21no—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—41no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4C2×D4×C6111yescharacteristic
377C22×C4C2×D4×C6111yescharacteristic
378C22×C4#41×C6111yescharacteristic
379Q16—44no—
380Q16—44no—
381SD16—44no—
382SD16—42no—
383SD16—42no—
384SD16—44no—
385M16—22no—
386M16—42no—
387M16SD16×C6114yescomplemented
388C2×C8—22no—
389C2×C8—21no—
390C2×C8—21no—
391C2×C8—22no—
392C2×C8—42no—
393C2×C8C2×D4×C6112yes—
394C2×C8C2×D4×C6112yes—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—22no—
401C4⋊C4—21no—
402C4⋊C4—22no—
403C4⋊C4—21no—
404C4⋊C4—41no—
405C4⋊C4—41no—
406C4⋊C4C2×D4×C6111yescharacteristic
407C4⋊C4C2×D4×C6111yescharacteristic
408C22⋊C4—41no—
409C22⋊C4—41no—
410C42—21no—
411C42—21no—
412C42—21no—
413C42—21no—
414C42C2×D4×C6111yescharacteristic
415C42C2×D4×C6111yescharacteristic
416C42#41×C6111yescharacteristic
417C42C24×C6111yescharacteristic
418C23—41no—
419C23#121×C6111yescharacteristic
420Q8—21no—
421Q8—21no—
422Q8—21no—
423Q8—42no—
424Q8—42no—
425Q8—41no—
426Q8—42no—
427Q8—41no—
428Q8—82no—
429Q8#137×C6112yescomplemented
430D4—41no—
431D4—41no—
432D4—41no—
433D4—41no—
434D4—81no—
435D4—82no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—41no—
443C2×C4—42no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—81no—
447C2×C4—82no—
448C2×C4—82no—
449C2×C4#121×C6111yescharacteristic
450C2×C4#121×C6111yescharacteristic
451C2×C4#121×C6111yescharacteristic
452C2×C4C2×SD16×C6112yes—
453C2×C4AGL(1,ℤ/8)×C6112yes—
454C2×C4C22×D4×C6111yescharacteristic
455C2×C4C22×D4×C6111yescharacteristic
456C2×C4C2×#41×C6111yescharacteristic
457C8—22no—
458C8—42no—
459C8—41no—
460C8—42no—
461C8—41no—
462C8C2×SD16×C6114yes—
463C22—21no—
464C22—21no—
465C22—81no—
466C22—81no—
467C22—81no—
468C22C61×#46012yes—
469C22C2×#121×C6111yescharacteristic
470C4—21no—
471C4—22no—
472C4—21no—
473C4—21no—
474C4—41no—
475C4—41no—
476C4—41no—
477C4—81no—
478C4—82no—
479C4C61×#46012yes—
480C4C22×SD16×C6111yescharacteristic
481C4C2×AGL(1,ℤ/8)×C6111yescharacteristic
482C4C2×#137×C6111yescharacteristic
483C4C61×#57511yescharacteristic
484C2—22no—
485C2—161no—
486C2C2×C61×#46011yescharacteristic
487C2C61×#305611yescharacteristic
488C2C61×#306911yescharacteristic
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×#475C2semidirect
4. Q8×M16×C61C2semidirect
5. C61×#1690C2semidirect
6. C61×#1686C2semidirect
7. C61×#1670C2semidirect
8. C61×#1666C2semidirect
9. C61×#1565C2semidirect
11. C61×#1546C2semidirect
142. M16×C61SD16semidirect
184. Q8×C61#137semidirect
218. #19171C61direct (N × H)
242. C2×#475C2×C61semidirect
243. Q8×M16C2×C61semidirect
244. #1690C2×C61semidirect
245. #1686C2×C61semidirect
246. #1670C2×C61semidirect
247. #1666C2×C61semidirect
248. #1565C2×C61semidirect
250. #1546C2×C61semidirect
293. C61#19171direct (N × H)
387. M16SD16×C61semidirect
429. Q8#137×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#31522
C61×#31032
C2×C61×#4752
Q8×M16×C612
C61×#16902
C61×#16862
C61×#16702
C61×#16662
C61×#15652
C61×#15472
C61×#15462
#1917161