Finite Group Databasebeta

← C61×#19642 #29523075

Subgroups — C61×#19642 #29523075

Order 15616.

698 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3231C211yesmaximal, characteristic, complemented
2C61×#3210C211yesmaximal, characteristic
3C61×#3185C211yesmaximal, characteristic, complemented
4C61×#3182C211yesmaximal, characteristic
5C61×#3167C211yesmaximal, characteristic
6C61×#3160C211yesmaximal, characteristic, complemented
7C61×#1723C211yesmaximal, characteristic, complemented
8C61×#1722C211yesmaximal, characteristic, complemented
9C61×#1719C211yesmaximal, characteristic, complemented
10C61×#1718C211yesmaximal, characteristic, complemented
11C61×#1708C211yesmaximal, characteristic, complemented
12C61×#1707C211yesmaximal, characteristic, complemented
13C61×#1707C211yesmaximal, characteristic, complemented
14C61×#1705C211yesmaximal, characteristic, complemented
15C8×M16×C61C211yesmaximal, characteristic, complemented
16C61×#533C2211yescharacteristic
17C61×#533C2211yescharacteristic
18C61×#533C2211yescharacteristic
19C61×#532C2211yescharacteristic
20C61×#500C2211yescharacteristic
21C61×#500C2211yescharacteristic
22C61×#500C2211yescharacteristic
23C61×#500C2211yescharacteristic
24C61×#499—22no—
25C61×#498C2211yescharacteristic
26C61×#498C2211yescharacteristic
27C61×#498C2211yescharacteristic
28C61×#498C2211yescharacteristic
29C61×#498C2211yescharacteristic
30C61×#494C2211yescharacteristic
31C61×#494C2211yescharacteristic
32C61×#492C2211yescharacteristic
33C61×#492C2211yescharacteristic
34C61×#492C2211yescharacteristic
35C61×#487C2211yescharacteristic
36C61×#487C2211yescharacteristic
37C61×#487C2211yescharacteristic
38C61×#487C2211yescharacteristic
39C61×#487C2211yescharacteristic
40C61×#487C2211yescharacteristic
41C61×#487C2211yescharacteristic
42C61×#486C2211yescharacteristic
43C61×#486C2211yescharacteristic
44C61×#486C2211yescharacteristic
45C61×#485—22no—
46C61×#479—22no—
47C61×#470—22no—
48C61×#468—22no—
49C61×#465—22no—
50C61×#464—22no—
51C61×#452—22no—
52C61×#441—22no—
53C61×#440—22no—
54C4×SD16×C61—22no—
55C61×#431C2211yescharacteristic
56C61×#427—22no—
57C4×M16×C61C2211yescharacteristic
58C2×C4×C8×C61C2211yescharacteristic
59C61×#322C2211yescharacteristic
60C61×#322C2211yescharacteristic
61C82×C61C2211yescharacteristic
62C82×C61C2211yescharacteristic
63C2×#41×C61—21no—
64C2×Q16×C61—22no—
65C2×Q16×C61—22no—
66C2×SD16×C61—22no—
67C2×SD16×C61—22no—
68C2×SD16×C61—22no—
69C2×M16×C61D412yes—
70C22×C8×C61D412yes—
71C4⋊Q8×C61C2311yescharacteristic
72C4⋊Q8×C61C2311yescharacteristic
73C4⋊Q8×C61C2311yescharacteristic
74C4⋊Q8×C61C2311yescharacteristic
75C4⋊Q8×C61C2311yescharacteristic
76C4⋊Q8×C61C2311yescharacteristic
77C4⋊Q8×C61C2311yescharacteristic
78#127×C61C2311yescharacteristic
79#125×C61—21no—
80#125×C61—21no—
81#125×C61—21no—
82#124×C61—21no—
83C22⋊Q8×C61—21no—
84C22⋊Q8×C61—21no—
85C22⋊Q8×C61—21no—
86C22⋊Q8×C61—21no—
87C22⋊Q8×C61—21no—
88C22⋊Q8×C61—21no—
89#121×C61—21no—
90#121×C61—21no—
91C4×Q8×C61—21no—
92C4×Q8×C61—21no—
93C4×Q8×C61—21no—
94C4×Q8×C61—21no—
95C4×Q8×C61—21no—
96C4×Q8×C61—21no—
97C4×D4×C61—21no—
98C4×D4×C61—21no—
99#117×C61—21no—
100#117×C61—21no—
101#117×C61—21no—
102C2×C42×C61C2311yescharacteristic
103#107×C61—22no—
104#107×C61—22no—
105#107×C61—22no—
106#107×C61—22no—
107#106×C61—22no—
108#106×C61—22no—
109#106×C61—22no—
110#106×C61—22no—
111#106×C61—22no—
112C4⋊C8×C61D412yes—
113#103×C61—22no—
114#103×C61—22no—
115#103×C61—22no—
116#103×C61—22no—
117#103×C61—22no—
118#103×C61—22no—
119#103×C61—22no—
120#102×C61—22no—
121#102×C61—22no—
122#102×C61—22no—
123C22⋊C8×C61D412yes—
124#97×C61D412yes—
125C4×C8×C61D412yes—
126C4×C8×C61C2311yescharacteristic
127C4×C8×C61C2311yescharacteristic
128C4×C8×C61C2311yescharacteristic
129C4×C8×C61C2311yescharacteristic
130C4×C8×C61C2311yescharacteristic
131C4×C8×C61C2311yescharacteristic
132#41×C61—82no—
133C2×Q8×C61—21no—
134C2×Q8×C61—21no—
135C2×Q8×C61—21no—
136C2×Q8×C61—21no—
137C2×Q8×C61—21no—
138C2×Q8×C61—21no—
139C2×Q8×C61—21no—
140C2×D4×C61—21no—
141C2×D4×C61—21no—
142C2×D4×C61—21no—
143C2×D4×C61—41no—
144C22×C4×C61—41no—
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61C2×D411yescharacteristic
148Q16×C61—44no—
149Q16×C61—82no—
150SD16×C61—44no—
151SD16×C61—44no—
152SD16×C61—82no—
153M16×C61—24no—
154C2×C8×C61—24no—
155C2×C8×C61C2×D412yes—
156C2×C8×C61C2×D412yes—
157C2×C8×C61C2×D412yes—
158C2×C8×C61C2×D412yes—
159C2×C8×C61C2×D412yes—
160C2×C8×C61C2×D412yes—
161C4⋊C4×C61—21no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—41no—
176C4⋊C4×C61—41no—
177C4⋊C4×C61—41no—
178C4⋊C4×C61—41no—
179C4⋊C4×C61—41no—
180C4⋊C4×C61—41no—
181C22⋊C4×C61—41no—
182C22⋊C4×C61—41no—
183C22⋊C4×C61—41no—
184C22⋊C4×C61—41no—
185C22⋊C4×C61—41no—
186C42×C61—41no—
187C42×C61—41no—
188C42×C61—41no—
189C42×C61C2×D411yescharacteristic
190C42×C61C2×D411yescharacteristic
191C42×C61C2×D411yescharacteristic
192C42×C61C2411yescharacteristic
193C23×C61—41no—
194C23×C61#12711yescharacteristic
195Q8×C61—42no—
196Q8×C61—42no—
197Q8×C61—42no—
198Q8×C61—42no—
199Q8×C61—42no—
200Q8×C61—42no—
201Q8×C61—42no—
202D4×C61—42no—
203D4×C61—42no—
204D4×C61—42no—
205D4×C61—82no—
206C2×C4×C61—22no—
207C2×C4×C61—22no—
208C2×C4×C61—22no—
209C2×C4×C61—41no—
210C2×C4×C61—41no—
211C2×C4×C61—41no—
212C2×C4×C61—41no—
213C2×C4×C61—41no—
214C2×C4×C61—41no—
215C2×C4×C61—41no—
216C2×C4×C61—82no—
217C2×C4×C61#12711yescharacteristic
218C2×C4×C61#12711yescharacteristic
219C2×C4×C61#12711yescharacteristic
220C2×C4×C61C22×D411yescharacteristic
221C2×C4×C61C22×D411yescharacteristic
222C2×C4×C61C22×D411yescharacteristic
223C8×C61—22no—
224C8×C61—22no—
225C8×C61—22no—
226C8×C61—22no—
227C8×C61#13514yes—
228C8×C61#13714yes—
229#19642C6111yesmaximal, characteristic, direct product factor, Sylow
230C22×C61—21no—
231C22×C61—21no—
232C22×C61—21no—
233C22×C61—81no—
234C22×C61—81no—
235C22×C61—81no—
236C22×C61C2×#12711yescharacteristic
237C4×C61—21no—
238C4×C61—21no—
239C4×C61—21no—
240C4×C61—81no—
241C4×C61—81no—
242C4×C61—81no—
243C4×C61—81no—
244C4×C61—81no—
245C4×C61—81no—
246C4×C61—81no—
247C4×C61C2×#13512yes—
248C4×C61C2×#13712yes—
249C4×C61#57712yes—
250#3231C2×C6111yescharacteristic, complemented
251#3210C2×C6111yescharacteristic
252#3185C2×C6111yescharacteristic, complemented
253#3182C2×C6111yescharacteristic
254#3167C2×C6111yescharacteristic
255#3160C2×C6111yescharacteristic, complemented
256#1723C2×C6111yescharacteristic, complemented
257#1722C2×C6111yescharacteristic, complemented
258#1719C2×C6111yescharacteristic, complemented
259#1718C2×C6111yescharacteristic, complemented
260#1708C2×C6111yescharacteristic, complemented
261#1707C2×C6111yescharacteristic, complemented
262#1707C2×C6111yescharacteristic, complemented
263#1705C2×C6111yescharacteristic, complemented
264C8×M16C2×C6111yescharacteristic, complemented
265C2×C61—41no—
266C2×C61—161no—
267C2×C61#314711yescharacteristic
268C2×C61#315211yescharacteristic
269C2×C61#315411yescharacteristic
270#533C22×C6111yescharacteristic
271#533C22×C6111yescharacteristic
272#533C22×C6111yescharacteristic
273#532C22×C6111yescharacteristic
274#500C22×C6111yescharacteristic
275#500C22×C6111yescharacteristic
276#500C22×C6111yescharacteristic
277#500C22×C6111yescharacteristic
278#499—22no—
279#498C22×C6111yescharacteristic
280#498C22×C6111yescharacteristic
281#498C22×C6111yescharacteristic
282#498C22×C6111yescharacteristic
283#498C22×C6111yescharacteristic
284#494C22×C6111yescharacteristic
285#494C22×C6111yescharacteristic
286#492C22×C6111yescharacteristic
287#492C22×C6111yescharacteristic
288#492C22×C6111yescharacteristic
289#487C22×C6111yescharacteristic
290#487C22×C6111yescharacteristic
291#487C22×C6111yescharacteristic
292#487C22×C6111yescharacteristic
293#487C22×C6111yescharacteristic
294#487C22×C6111yescharacteristic
295#487C22×C6111yescharacteristic
296#486C22×C6111yescharacteristic
297#486C22×C6111yescharacteristic
298#486C22×C6111yescharacteristic
299#485—22no—
300#479—22no—
301#470—22no—
302#468—22no—
303#465—22no—
304#464—22no—
305#452—22no—
306#441—22no—
307#440—22no—
308C4×SD16—22no—
309#431C22×C6111yescharacteristic
310#427—22no—
311C4×M16C22×C6111yescharacteristic
312C2×C4×C8C22×C6111yescharacteristic
313#322C22×C6111yescharacteristic
314#322C22×C6111yescharacteristic
315C82C22×C6111yescharacteristic
316C82C22×C6111yescharacteristic
317C61#1964211yescharacteristic, direct product factor, Sylow
318C2×#41—21no—
319C2×Q16—22no—
320C2×Q16—22no—
321C2×SD16—22no—
322C2×SD16—22no—
323C2×SD16—22no—
324C2×M16D4×C6112yes—
325C22×C8D4×C6112yes—
326C4⋊Q8C23×C6111yescharacteristic
327C4⋊Q8C23×C6111yescharacteristic
328C4⋊Q8C23×C6111yescharacteristic
329C4⋊Q8C23×C6111yescharacteristic
330C4⋊Q8C23×C6111yescharacteristic
331C4⋊Q8C23×C6111yescharacteristic
332C4⋊Q8C23×C6111yescharacteristic
333#127C23×C6111yescharacteristic
334#125—21no—
335#125—21no—
336#125—21no—
337#124—21no—
338C22⋊Q8—21no—
339C22⋊Q8—21no—
340C22⋊Q8—21no—
341C22⋊Q8—21no—
342C22⋊Q8—21no—
343C22⋊Q8—21no—
344#121—21no—
345#121—21no—
346C4×Q8—21no—
347C4×Q8—21no—
348C4×Q8—21no—
349C4×Q8—21no—
350C4×Q8—21no—
351C4×Q8—21no—
352C4×D4—21no—
353C4×D4—21no—
354#117—21no—
355#117—21no—
356#117—21no—
357C2×C42C23×C6111yescharacteristic
358#107—22no—
359#107—22no—
360#107—22no—
361#107—22no—
362#106—22no—
363#106—22no—
364#106—22no—
365#106—22no—
366#106—22no—
367C4⋊C8D4×C6112yes—
368#103—22no—
369#103—22no—
370#103—22no—
371#103—22no—
372#103—22no—
373#103—22no—
374#103—22no—
375#102—22no—
376#102—22no—
377#102—22no—
378C22⋊C8D4×C6112yes—
379#97D4×C6112yes—
380C4×C8D4×C6112yes—
381C4×C8C23×C6111yescharacteristic
382C4×C8C23×C6111yescharacteristic
383C4×C8C23×C6111yescharacteristic
384C4×C8C23×C6111yescharacteristic
385C4×C8C23×C6111yescharacteristic
386C4×C8C23×C6111yescharacteristic
387#41—82no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—21no—
393C2×Q8—21no—
394C2×Q8—21no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—21no—
398C2×D4—41no—
399C22×C4—41no—
400C22×C4C2×D4×C6111yescharacteristic
401C22×C4C2×D4×C6111yescharacteristic
402C22×C4C2×D4×C6111yescharacteristic
403Q16—44no—
404Q16—82no—
405SD16—44no—
406SD16—44no—
407SD16—82no—
408M16—24no—
409C2×C8—24no—
410C2×C8C2×D4×C6112yes—
411C2×C8C2×D4×C6112yes—
412C2×C8C2×D4×C6112yes—
413C2×C8C2×D4×C6112yes—
414C2×C8C2×D4×C6112yes—
415C2×C8C2×D4×C6112yes—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—41no—
431C4⋊C4—41no—
432C4⋊C4—41no—
433C4⋊C4—41no—
434C4⋊C4—41no—
435C4⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—41no—
440C22⋊C4—41no—
441C42—41no—
442C42—41no—
443C42—41no—
444C42C2×D4×C6111yescharacteristic
445C42C2×D4×C6111yescharacteristic
446C42C2×D4×C6111yescharacteristic
447C42C24×C6111yescharacteristic
448C23—41no—
449C23#127×C6111yescharacteristic
450Q8—42no—
451Q8—42no—
452Q8—42no—
453Q8—42no—
454Q8—42no—
455Q8—42no—
456Q8—42no—
457D4—42no—
458D4—42no—
459D4—42no—
460D4—82no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—82no—
472C2×C4#127×C6111yescharacteristic
473C2×C4#127×C6111yescharacteristic
474C2×C4#127×C6111yescharacteristic
475C2×C4C22×D4×C6111yescharacteristic
476C2×C4C22×D4×C6111yescharacteristic
477C2×C4C22×D4×C6111yescharacteristic
478C8—22no—
479C8—22no—
480C8—22no—
481C8—22no—
482C8#135×C6114yes—
483C8#137×C6114yes—
484C22—21no—
485C22—21no—
486C22—21no—
487C22—81no—
488C22—81no—
489C22—81no—
490C22C2×#127×C6111yescharacteristic
491C4—21no—
492C4—21no—
493C4—21no—
494C4—81no—
495C4—81no—
496C4—81no—
497C4—81no—
498C4—81no—
499C4—81no—
500C4—81no—
501C4C2×#135×C6112yes—
502C4C2×#137×C6112yes—
503C4C61×#57712yes—
504C2—41no—
505C2—161no—
506C2C61×#314711yescharacteristic
507C2C61×#315211yescharacteristic
508C2C61×#315411yescharacteristic
subgroupG/H
center, socleC22×C61C2×#127
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
1. C61×#3231C2semidirect
3. C61×#3185C2semidirect
6. C61×#3160C2semidirect
7. C61×#1723C2semidirect
8. C61×#1722C2semidirect
9. C61×#1719C2semidirect
10. C61×#1718C2semidirect
11. C61×#1708C2semidirect
12. C61×#1707C2semidirect
13. C61×#1707C2semidirect
14. C61×#1705C2semidirect
15. C8×M16×C61C2semidirect
229. #19642C61direct (N × H)
250. #3231C2×C61semidirect
252. #3185C2×C61semidirect
255. #3160C2×C61semidirect
256. #1723C2×C61semidirect
257. #1722C2×C61semidirect
258. #1719C2×C61semidirect
259. #1718C2×C61semidirect
260. #1708C2×C61semidirect
261. #1707C2×C61semidirect
262. #1707C2×C61semidirect
263. #1705C2×C61semidirect
264. C8×M16C2×C61semidirect
317. C61#19642direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#32312
C61×#32102
C61×#31852
C61×#31822
C61×#31672
C61×#31602
C61×#17232
C61×#17222
C61×#17192
C61×#17182
C61×#17082
C61×#17072
C61×#17052
C8×M16×C612
#1964261