Finite Group Databasebeta

← C61×#19416 #29522849

Subgroups — C61×#19416 #29522849

Order 15616.

694 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3226C211yesmaximal, characteristic, complemented
2C61×#3039C211yesmaximal, characteristic, complemented
3C61×#3035C211yesmaximal, characteristic
4C61×#2988C211yesmaximal, characteristic, complemented
5C61×#1682C212yesmaximal, complemented
6C61×#1681C212yesmaximal, complemented
7C61×#1674C212yesmaximal, complemented
8C61×#1673C212yesmaximal, complemented
9C61×#1571C211yesmaximal, characteristic, complemented
10C61×#1547C211yesmaximal, characteristic, complemented
11C2×C61×#332C211yesmaximal, characteristic, complemented
12C2×#137×C61—21no—
13C2×#135×C61—21no—
14C61×#532C2211yescharacteristic
15C2×C4⋊Q8×C61C2211yescharacteristic
16C4×#41×C61C2211yescharacteristic
17C61×#500C2212yes—
18C61×#486C2212yes—
19C61×#480—22no—
20C61×#474—21no—
21C61×#474—21no—
22C61×#464—21no—
23C61×#463—21no—
24C61×#462—21no—
25C61×#462C2211yescharacteristic
26C61×#462C2212yes—
27C61×#461—21no—
28C61×#461C2211yescharacteristic
29C61×#461C2212yes—
30C61×#460C2211yescharacteristic
31C61×#459C2211yescharacteristic
32C8×Q8×C61C2212yes—
33C8×D4×C61—22no—
34C8×D4×C61C2212yes—
35C61×#431—21no—
36C61×#431C2211yescharacteristic
37C61×#423C2211yescharacteristic
38C2×C4⋊C8×C61—21no—
39C2×C4⋊C8×C61C2211yescharacteristic
40C2×C4⋊C8×C61C2211yescharacteristic
41C61×#419—21no—
42C61×#416—21no—
43C61×#335C2212yes—
44C61×#335C2212yes—
45C61×#332C2212yes—
46C61×#332C2212yes—
47C61×#332C2212yes—
48C61×#331C2212yes—
49C2×#41×C61—21no—
50C2×#41×C61D411yescharacteristic
51C22×Q8×C61—21no—
52#137×C61—44no—
53#135×C61—44no—
54C2×Q16×C61—21no—
55C2×Q16×C61—22no—
56C2×SD16×C61—21no—
57C2×SD16×C61—21no—
58C2×SD16×C61—22no—
59C2×D8×C61—21no—
60C2×M16×C61—21no—
61C22×C8×C61—21no—
62C22×C8×C61—21no—
63C22×C8×C61—22no—
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×C61D411yescharacteristic
74C4×Q8×C61C2311yescharacteristic
75C4×D4×C61—21no—
76C4×D4×C61—21no—
77C4×D4×C61—21no—
78C4×D4×C61—21no—
79C4×D4×C61D411yescharacteristic
80C4×D4×C61C2311yescharacteristic
81#117×C61—21no—
82#117×C61D411yescharacteristic
83C2×C4⋊C4×C61—21no—
84C2×C4⋊C4×C61—21no—
85C2×C42×C61—21no—
86C2×C42×C61C2311yescharacteristic
87#107×C61—22no—
88#107×C61—22no—
89C4⋊C8×C61—22no—
90C4⋊C8×C61—21no—
91C4⋊C8×C61—21no—
92C4⋊C8×C61—21no—
93C4⋊C8×C61D411yescharacteristic
94C4⋊C8×C61D411yescharacteristic
95C4⋊C8×C61C2312yes—
96C4⋊C8×C61C2312yes—
97C4⋊C8×C61C2311yescharacteristic
98C4⋊C8×C61C2311yescharacteristic
99#103×C61—21no—
100#103×C61—21no—
101#103×C61—22no—
102#103×C61—22no—
103#102×C61—22no—
104#102×C61—22no—
105#102×C61—21no—
106#102×C61—21no—
107C22⋊C8×C61—22no—
108C22⋊C8×C61D412yes—
109C4×C8×C61—22no—
110C4×C8×C61C2312yes—
111#41×C61—22no—
112#41×C61—42no—
113#41×C61—42no—
114#41×C61D814yes—
115C2×Q8×C61—21no—
116C2×Q8×C61—22no—
117C2×Q8×C61—41no—
118C2×Q8×C61—42no—
119C2×Q8×C61—42no—
120C2×Q8×C61C2×D411yescharacteristic
121C2×D4×C61—21no—
122C2×D4×C61—21no—
123C2×D4×C61—21no—
124C2×D4×C61—21no—
125C2×D4×C61—41no—
126C2×D4×C61C2×D411yescharacteristic
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—41no—
131C22×C4×C61—41no—
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61#4111yescharacteristic
135Q16×C61—42no—
136Q16×C61—44no—
137SD16×C61—42no—
138SD16×C61—42no—
139SD16×C61—44no—
140D8×C61—42no—
141M16×C61—42no—
142C2×C8×C61—22no—
143C2×C8×C61—21no—
144C2×C8×C61—21no—
145C2×C8×C61—22no—
146C2×C8×C61—42no—
147C2×C8×C61—82no—
148C2×C8×C61—81no—
149C2×C8×C61C2×D412yes—
150C2×C8×C61C2×D412yes—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—21no—
153C4⋊C4×C61—22no—
154C4⋊C4×C61—21no—
155C4⋊C4×C61—22no—
156C4⋊C4×C61—21no—
157C4⋊C4×C61—41no—
158C4⋊C4×C61—41no—
159C4⋊C4×C61C2×D411yescharacteristic
160C4⋊C4×C61C2×D411yescharacteristic
161C22⋊C4×C61—21no—
162C22⋊C4×C61—21no—
163C22⋊C4×C61—21no—
164C22⋊C4×C61—41no—
165C22⋊C4×C61—41no—
166C42×C61—21no—
167C42×C61—21no—
168C42×C61—21no—
169C42×C61C2×D411yescharacteristic
170C42×C61C2×D411yescharacteristic
171C42×C61#4111yescharacteristic
172C42×C61C2411yescharacteristic
173C23×C61—21no—
174C23×C61—41no—
175C23×C61#12111yescharacteristic
176Q8×C61—21no—
177Q8×C61—42no—
178Q8×C61—41no—
179Q8×C61—42no—
180Q8×C61—41no—
181Q8×C61—82no—
182Q8×C61C2×D812yes—
183D4×C61—24no—
184D4×C61—21no—
185D4×C61—41no—
186D4×C61—41no—
187D4×C61—41no—
188D4×C61—41no—
189D4×C61—81no—
190D4×C61—82no—
191D4×C61C2×D812yes—
192C2×C4×C61—21no—
193C2×C4×C61—21no—
194C2×C4×C61—21no—
195C2×C4×C61—24no—
196C2×C4×C61—21no—
197C2×C4×C61—21no—
198C2×C4×C61—41no—
199C2×C4×C61—41no—
200C2×C4×C61—41no—
201C2×C4×C61—41no—
202C2×C4×C61—42no—
203C2×C4×C61—81no—
204C2×C4×C61—82no—
205C2×C4×C61—82no—
206C2×C4×C61#12111yescharacteristic
207C2×C4×C61#12111yescharacteristic
208C2×C4×C61#12111yescharacteristic
209C2×C4×C61C2×D812yes—
210C2×C4×C61#13512yes—
211C2×C4×C61C22×D411yescharacteristic
212C2×C4×C61C22×D411yescharacteristic
213C2×C4×C61C2×#4111yescharacteristic
214C8×C61—22no—
215C8×C61—22no—
216C8×C61—41no—
217C8×C61—41no—
218C8×C61—42no—
219C8×C61—42no—
220#19416C6111yesmaximal, characteristic, direct product factor, Sylow
221C22×C61—21no—
222C22×C61—21no—
223C22×C61—22no—
224C22×C61—41no—
225C22×C61—41no—
226C22×C61—81no—
227C22×C61—81no—
228C22×C61—81no—
229C22×C61#46612yes—
230C22×C61C2×#12111yescharacteristic
231C4×C61—21no—
232C4×C61—22no—
233C4×C61—21no—
234C4×C61—21no—
235C4×C61—41no—
236C4×C61—41no—
237C4×C61—81no—
238C4×C61—82no—
239C4×C61#46612yes—
240C4×C61C22×D811yescharacteristic
241C4×C61C2×#13511yescharacteristic
242C4×C61#57711yescharacteristic
243C4×C61#57811yescharacteristic
244#3226C2×C6111yescharacteristic, complemented
245#3039C2×C6111yescharacteristic, complemented
246#3035C2×C6111yescharacteristic
247#2988C2×C6111yescharacteristic, complemented
248#1682C2×C6112yescomplemented
249#1681C2×C6112yescomplemented
250#1674C2×C6112yescomplemented
251#1673C2×C6112yescomplemented
252#1571C2×C6111yescharacteristic, complemented
253#1547C2×C6111yescharacteristic, complemented
254C2×#332C2×C6111yescharacteristic, complemented
255C2×C61—22no—
256C2×C61—42no—
257C2×C61—161no—
258C2×C61#304611yescharacteristic
259C2×C61C2×#46611yescharacteristic
260C2×C61#306911yescharacteristic
261C2×#137—21no—
262C2×#135—21no—
263#532C22×C6111yescharacteristic
264C2×C4⋊Q8C22×C6111yescharacteristic
265C4×#41C22×C6111yescharacteristic
266#500C22×C6112yes—
267#486C22×C6112yes—
268#480—22no—
269#474—21no—
270#474—21no—
271#464—21no—
272#463—21no—
273#462—21no—
274#462C22×C6111yescharacteristic
275#462C22×C6112yes—
276#461—21no—
277#461C22×C6111yescharacteristic
278#461C22×C6112yes—
279#460C22×C6111yescharacteristic
280#459C22×C6111yescharacteristic
281C8×Q8C22×C6112yes—
282C8×D4—22no—
283C8×D4C22×C6112yes—
284#431—21no—
285#431C22×C6111yescharacteristic
286#423C22×C6111yescharacteristic
287C2×C4⋊C8—21no—
288C2×C4⋊C8C22×C6111yescharacteristic
289C2×C4⋊C8C22×C6111yescharacteristic
290#419—21no—
291#416—21no—
292#335C22×C6112yes—
293#335C22×C6112yes—
294#332C22×C6112yes—
295#332C22×C6112yes—
296#332C22×C6112yes—
297#331C22×C6112yes—
298C61#1941611yescharacteristic, direct product factor, Sylow
299C2×#41—21no—
300C2×#41D4×C6111yescharacteristic
301C22×Q8—21no—
302#137—44no—
303#135—44no—
304C2×Q16—21no—
305C2×Q16—22no—
306C2×SD16—21no—
307C2×SD16—21no—
308C2×SD16—22no—
309C2×D8—21no—
310C2×M16—21no—
311C22×C8—21no—
312C22×C8—21no—
313C22×C8—22no—
314C4⋊Q8—21no—
315C4⋊Q8—21no—
316C4⋊Q8—21no—
317C4⋊Q8C23×C6112yes—
318C4⋊Q8C23×C6111yescharacteristic
319#127C23×C6111yescharacteristic
320#124—21no—
321#121—21no—
322#121—21no—
323C4×Q8D4×C6111yescharacteristic
324C4×Q8C23×C6111yescharacteristic
325C4×D4—21no—
326C4×D4—21no—
327C4×D4—21no—
328C4×D4—21no—
329C4×D4D4×C6111yescharacteristic
330C4×D4C23×C6111yescharacteristic
331#117—21no—
332#117D4×C6111yescharacteristic
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C42—21no—
336C2×C42C23×C6111yescharacteristic
337#107—22no—
338#107—22no—
339C4⋊C8—22no—
340C4⋊C8—21no—
341C4⋊C8—21no—
342C4⋊C8—21no—
343C4⋊C8D4×C6111yescharacteristic
344C4⋊C8D4×C6111yescharacteristic
345C4⋊C8C23×C6112yes—
346C4⋊C8C23×C6112yes—
347C4⋊C8C23×C6111yescharacteristic
348C4⋊C8C23×C6111yescharacteristic
349#103—21no—
350#103—21no—
351#103—22no—
352#103—22no—
353#102—22no—
354#102—22no—
355#102—21no—
356#102—21no—
357C22⋊C8—22no—
358C22⋊C8D4×C6112yes—
359C4×C8—22no—
360C4×C8C23×C6112yes—
361#41—22no—
362#41—42no—
363#41—42no—
364#41D8×C6114yes—
365C2×Q8—21no—
366C2×Q8—22no—
367C2×Q8—41no—
368C2×Q8—42no—
369C2×Q8—42no—
370C2×Q8C2×D4×C6111yescharacteristic
371C2×D4—21no—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—41no—
376C2×D4C2×D4×C6111yescharacteristic
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4C2×D4×C6111yescharacteristic
383C22×C4C2×D4×C6111yescharacteristic
384C22×C4#41×C6111yescharacteristic
385Q16—42no—
386Q16—44no—
387SD16—42no—
388SD16—42no—
389SD16—44no—
390D8—42no—
391M16—42no—
392C2×C8—22no—
393C2×C8—21no—
394C2×C8—21no—
395C2×C8—22no—
396C2×C8—42no—
397C2×C8—82no—
398C2×C8—81no—
399C2×C8C2×D4×C6112yes—
400C2×C8C2×D4×C6112yes—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—22no—
404C4⋊C4—21no—
405C4⋊C4—22no—
406C4⋊C4—21no—
407C4⋊C4—41no—
408C4⋊C4—41no—
409C4⋊C4C2×D4×C6111yescharacteristic
410C4⋊C4C2×D4×C6111yescharacteristic
411C22⋊C4—21no—
412C22⋊C4—21no—
413C22⋊C4—21no—
414C22⋊C4—41no—
415C22⋊C4—41no—
416C42—21no—
417C42—21no—
418C42—21no—
419C42C2×D4×C6111yescharacteristic
420C42C2×D4×C6111yescharacteristic
421C42#41×C6111yescharacteristic
422C42C24×C6111yescharacteristic
423C23—21no—
424C23—41no—
425C23#121×C6111yescharacteristic
426Q8—21no—
427Q8—42no—
428Q8—41no—
429Q8—42no—
430Q8—41no—
431Q8—82no—
432Q8C2×D8×C6112yes—
433D4—24no—
434D4—21no—
435D4—41no—
436D4—41no—
437D4—41no—
438D4—41no—
439D4—81no—
440D4—82no—
441D4C2×D8×C6112yes—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—24no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—42no—
453C2×C4—81no—
454C2×C4—82no—
455C2×C4—82no—
456C2×C4#121×C6111yescharacteristic
457C2×C4#121×C6111yescharacteristic
458C2×C4#121×C6111yescharacteristic
459C2×C4C2×D8×C6112yes—
460C2×C4#135×C6112yes—
461C2×C4C22×D4×C6111yescharacteristic
462C2×C4C22×D4×C6111yescharacteristic
463C2×C4C2×#41×C6111yescharacteristic
464C8—22no—
465C8—22no—
466C8—41no—
467C8—41no—
468C8—42no—
469C8—42no—
470C22—21no—
471C22—21no—
472C22—22no—
473C22—41no—
474C22—41no—
475C22—81no—
476C22—81no—
477C22—81no—
478C22C61×#46612yes—
479C22C2×#121×C6111yescharacteristic
480C4—21no—
481C4—22no—
482C4—21no—
483C4—21no—
484C4—41no—
485C4—41no—
486C4—81no—
487C4—82no—
488C4C61×#46612yes—
489C4C22×D8×C6111yescharacteristic
490C4C2×#135×C6111yescharacteristic
491C4C61×#57711yescharacteristic
492C4C61×#57811yescharacteristic
493C2—22no—
494C2—42no—
495C2—161no—
496C2C61×#304611yescharacteristic
497C2C2×C61×#46611yescharacteristic
498C2C61×#306911yescharacteristic
subgroupG/H
center, socleC22×C61C2×#121
commutator, Frattini, cosocleC42C24×C61
prime radicalC61×#3035C2
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×#3226C2semidirect
2. C61×#3039C2semidirect
4. C61×#2988C2semidirect
5. C61×#1682C2semidirect
6. C61×#1681C2semidirect
7. C61×#1674C2semidirect
8. C61×#1673C2semidirect
9. C61×#1571C2semidirect
10. C61×#1547C2semidirect
11. C2×C61×#332C2semidirect
220. #19416C61direct (N × H)
244. #3226C2×C61semidirect
245. #3039C2×C61semidirect
247. #2988C2×C61semidirect
248. #1682C2×C61semidirect
249. #1681C2×C61semidirect
250. #1674C2×C61semidirect
251. #1673C2×C61semidirect
252. #1571C2×C61semidirect
253. #1547C2×C61semidirect
254. C2×#332C2×C61semidirect
298. C61#19416direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#32262
C61×#30392
C61×#30352
C61×#29882
C61×#16822
C61×#16812
C61×#16742
C61×#16732
C61×#15712
C61×#15472
C2×C61×#3322
#1941661