Finite Group Databasebeta

← C61×#25695 #29529128

Subgroups — C61×#25695 #29529128

Order 15616.

974 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3507C211yesmaximal, characteristic
2C61×#3165C211yesmaximal, characteristic, complemented
3C61×#3141C211yesmaximal, characteristic
4C61×#2567C211yesmaximal, characteristic, complemented
5C61×#2038C214yesmaximal, complemented
6C61×#1986C211yesmaximal, characteristic, complemented
7C61×#1980C211yesmaximal, characteristic
8C61×#1859C214yesmaximal, complemented
9C4×#101×C61C211yesmaximal, characteristic, complemented
10C61×#559—21no—
11C61×#557—21no—
12C61×#556—21no—
13C61×#556—22no—
14C61×#554—21no—
15C61×#552—22no—
16C61×#539—22no—
17C61×#536C2212yes—
18C61×#533C2211yescharacteristic
19C61×#532C2211yescharacteristic
20C2×C4⋊Q8×C61C2211yescharacteristic
21C61×#529—22no—
22C61×#520C2212yes—
23C2×C4×Q8×C61C2211yescharacteristic
24C61×#501—22no—
25C61×#500—21no—
26C61×#498—21no—
27C61×#489—22no—
28C61×#487—21no—
29C61×#486—21no—
30C61×#428C2214yes—
31C2×#104×C61C2214yes—
32C61×#417C2214yes—
33C2×#101×C61C2212yes—
34C4×M16×C61C2211yescharacteristic
35C4×M16×C61C2211yescharacteristic
36C61×#395—22no—
37C61×#391C2212yes—
38C61×#389—22no—
39C61×#384C2212yes—
40C4×C4⋊C4×C61C2211yescharacteristic
41C61×#343C2212yes—
42C61×#339C2214yes—
43C2×#41×C61C2312yes—
44C22×Q8×C61—21no—
45C22×Q8×C61C2311yescharacteristic
46C2×M16×C61C2312yes—
47C2×M16×C61C2312yes—
48C4⋊Q8×C61—22no—
49C4⋊Q8×C61—21no—
50C4⋊Q8×C61—21no—
51C4⋊Q8×C61—21no—
52C4⋊Q8×C61—21no—
53C4⋊Q8×C61D411yescharacteristic
54C4⋊Q8×C61D411yescharacteristic
55C4⋊Q8×C61D411yescharacteristic
56#127×C61D411yescharacteristic
57#126×C61—24no—
58#126×C61—24no—
59#125×C61—24no—
60#125×C61—22no—
61#125×C61D412yes—
62#124×C61—22no—
63#124×C61—22no—
64#124×C61D412yes—
65#123×C61—24no—
66#123×C61—24no—
67C22⋊Q8×C61—24no—
68C22⋊Q8×C61—21no—
69C22⋊Q8×C61—21no—
70C22⋊Q8×C61—22no—
71C22⋊Q8×C61—22no—
72#121×C61—21no—
73#121×C61—21no—
74C4×Q8×C61—22no—
75C4×Q8×C61—22no—
76C4×Q8×C61—21no—
77C4×Q8×C61—21no—
78C4×Q8×C61—21no—
79C4×Q8×C61—21no—
80C4×Q8×C61—21no—
81C4×Q8×C61—21no—
82C4×D4×C61—22no—
83C4×D4×C61—22no—
84C4×D4×C61—24no—
85C4×D4×C61—21no—
86C4×D4×C61—21no—
87#117×C61—24no—
88#117×C61—22no—
89#117×C61C2312yes—
90C2×C4⋊C4×C61—21no—
91C2×C4⋊C4×C61—22no—
92C2×C4⋊C4×C61—21no—
93C2×C4⋊C4×C61—24no—
94C2×C4⋊C4×C61D412yes—
95C2×C4⋊C4×C61C2312yes—
96C2×C4⋊C4×C61C2311yescharacteristic
97C2×C42×C61D412yes—
98C2×C42×C61C2312yes—
99C2×C42×C61C2311yescharacteristic
100#107×C61—24no—
101#106×C61—24no—
102#104×C61—28no—
103#103×C61—24no—
104#102×C61—24no—
105#101×C61—24no—
106#97×C61—21no—
107#97×C61—21no—
108C4×C8×C61—21no—
109C4×C8×C61—21no—
110#95×C61—21no—
111#95×C61—24no—
112#41×C61—24no—
113#41×C61—24no—
114C2×Q8×C61—21no—
115C2×Q8×C61—21no—
116C2×Q8×C61—21no—
117C2×Q8×C61—21no—
118C2×Q8×C61—22no—
119C2×Q8×C61—22no—
120C2×Q8×C61—41no—
121C2×Q8×C61—41no—
122C2×Q8×C61—82no—
123C2×Q8×C61C2×D412yes—
124C2×D4×C61—22no—
125C2×D4×C61—21no—
126C2×D4×C61—21no—
127C2×D4×C61C2×D412yes—
128C22×C4×C61—22no—
129C22×C4×C61—24no—
130C22×C4×C61—22no—
131C22×C4×C61—22no—
132C22×C4×C61C2×D412yes—
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2×D412yes—
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2411yescharacteristic
137M16×C61—22no—
138M16×C61—22no—
139M16×C61—22no—
140M16×C61#4114yes—
141C2×C8×C61—22no—
142C2×C8×C61—22no—
143C4⋊C4×C61—24no—
144C4⋊C4×C61—24no—
145C4⋊C4×C61—24no—
146C4⋊C4×C61—24no—
147C4⋊C4×C61—22no—
148C4⋊C4×C61—22no—
149C4⋊C4×C61—22no—
150C4⋊C4×C61—21no—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—21no—
153C4⋊C4×C61—22no—
154C4⋊C4×C61—21no—
155C4⋊C4×C61—21no—
156C4⋊C4×C61—21no—
157C4⋊C4×C61—22no—
158C4⋊C4×C61—22no—
159C4⋊C4×C61—41no—
160C4⋊C4×C61—41no—
161C4⋊C4×C61—84no—
162C4⋊C4×C61C2×D412yes—
163C4⋊C4×C61C2×D412yes—
164C22⋊C4×C61—24no—
165C22⋊C4×C61—24no—
166C22⋊C4×C61—24no—
167C22⋊C4×C61—22no—
168C22⋊C4×C61—22no—
169C22⋊C4×C61—22no—
170C42×C61—24no—
171C42×C61—22no—
172C42×C61—22no—
173C42×C61—22no—
174C42×C61—24no—
175C42×C61C2×D411yescharacteristic
176C42×C61C2×D411yescharacteristic
177C42×C61C2×D411yescharacteristic
178C42×C61C2×D411yescharacteristic
179C23×C61—22no—
180C23×C61C22×D411yescharacteristic
181Q8×C61—24no—
182Q8×C61—42no—
183Q8×C61—42no—
184Q8×C61—42no—
185Q8×C61—81no—
186Q8×C61—82no—
187Q8×C61—82no—
188D4×C61—24no—
189D4×C61—42no—
190D4×C61—42no—
191D4×C61—42no—
192D4×C61—81no—
193C2×C4×C61—22no—
194C2×C4×C61—24no—
195C2×C4×C61—22no—
196C2×C4×C61—22no—
197C2×C4×C61—22no—
198C2×C4×C61—22no—
199C2×C4×C61—22no—
200C2×C4×C61—22no—
201C2×C4×C61—22no—
202C2×C4×C61—41no—
203C2×C4×C61—42no—
204C2×C4×C61—42no—
205C2×C4×C61—44no—
206C2×C4×C61—42no—
207C2×C4×C61—44no—
208C2×C4×C61—42no—
209C2×C4×C61—84no—
210C2×C4×C61#12011yescharacteristic
211C2×C4×C61#12011yescharacteristic
212C2×C4×C61#12011yescharacteristic
213C2×C4×C61#12011yescharacteristic
214C2×C4×C61C22×D411yescharacteristic
215C2×C4×C61C22×D411yescharacteristic
216C2×C4×C61C2×#4112yes—
217C2×C4×C612−1+412yes—
218C8×C61—24no—
219C8×C61—42no—
220#25695C6111yesmaximal, characteristic, direct product factor, Sylow
221C22×C61—21no—
222C22×C61—21no—
223C22×C61—42no—
224C22×C61—42no—
225C22×C61—42no—
226C22×C61C2×#12011yescharacteristic
227C22×C61#53211yescharacteristic
228C22×C61#53611yescharacteristic
229C4×C61—21no—
230C4×C61—21no—
231C4×C61—21no—
232C4×C61—44no—
233C4×C61—42no—
234C4×C61—42no—
235C4×C61—42no—
236C4×C61—42no—
237C4×C61—42no—
238C4×C61—82no—
239C4×C61#45612yes—
240C4×C61#54712yes—
241C4×C61#54812yes—
242#3507C2×C6111yescharacteristic
243#3165C2×C6111yescharacteristic, complemented
244#3141C2×C6111yescharacteristic
245#2567C2×C6111yescharacteristic, complemented
246#2038C2×C6114yescomplemented
247#1986C2×C6111yescharacteristic, complemented
248#1980C2×C6111yescharacteristic
249#1859C2×C6114yescomplemented
250C4×#101C2×C6111yescharacteristic, complemented
251C2×C61—21no—
252C2×C61—21no—
253C2×C61—82no—
254C2×C61#243211yescharacteristic
255C2×C61C2×#45611yescharacteristic
256C2×C61#302111yescharacteristic
257#559—21no—
258#557—21no—
259#556—21no—
260#556—22no—
261#554—21no—
262#552—22no—
263#539—22no—
264#536C22×C6112yes—
265#533C22×C6111yescharacteristic
266#532C22×C6111yescharacteristic
267C2×C4⋊Q8C22×C6111yescharacteristic
268#529—22no—
269#520C22×C6112yes—
270C2×C4×Q8C22×C6111yescharacteristic
271#501—22no—
272#500—21no—
273#498—21no—
274#489—22no—
275#487—21no—
276#486—21no—
277#428C22×C6114yes—
278C2×#104C22×C6114yes—
279#417C22×C6114yes—
280C2×#101C22×C6112yes—
281C4×M16C22×C6111yescharacteristic
282C4×M16C22×C6111yescharacteristic
283#395—22no—
284#391C22×C6112yes—
285#389—22no—
286#384C22×C6112yes—
287C4×C4⋊C4C22×C6111yescharacteristic
288#343C22×C6112yes—
289#339C22×C6114yes—
290C61#2569511yescharacteristic, direct product factor, Sylow
291C2×#41C23×C6112yes—
292C22×Q8—21no—
293C22×Q8C23×C6111yescharacteristic
294C2×M16C23×C6112yes—
295C2×M16C23×C6112yes—
296C4⋊Q8—22no—
297C4⋊Q8—21no—
298C4⋊Q8—21no—
299C4⋊Q8—21no—
300C4⋊Q8—21no—
301C4⋊Q8D4×C6111yescharacteristic
302C4⋊Q8D4×C6111yescharacteristic
303C4⋊Q8D4×C6111yescharacteristic
304#127D4×C6111yescharacteristic
305#126—24no—
306#126—24no—
307#125—22no—
308#125—24no—
309#125D4×C6112yes—
310#124—22no—
311#124—22no—
312#124D4×C6112yes—
313#123—24no—
314#123—24no—
315C22⋊Q8—24no—
316C22⋊Q8—21no—
317C22⋊Q8—21no—
318C22⋊Q8—22no—
319C22⋊Q8—22no—
320#121—21no—
321#121—21no—
322C4×Q8—22no—
323C4×Q8—22no—
324C4×Q8—21no—
325C4×Q8—21no—
326C4×Q8—21no—
327C4×Q8—21no—
328C4×Q8—21no—
329C4×Q8—21no—
330C4×D4—22no—
331C4×D4—22no—
332C4×D4—24no—
333C4×D4—21no—
334C4×D4—21no—
335#117—24no—
336#117—22no—
337#117C23×C6112yes—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4D4×C6112yes—
343C2×C4⋊C4C23×C6112yes—
344C2×C4⋊C4C23×C6111yescharacteristic
345C2×C42D4×C6112yes—
346C2×C42C23×C6112yes—
347C2×C42C23×C6111yescharacteristic
348#107—24no—
349#106—24no—
350#104—28no—
351#103—24no—
352#102—24no—
353#101—24no—
354#97—21no—
355#97—21no—
356C4×C8—21no—
357C4×C8—21no—
358#95—21no—
359#95—24no—
360#41—24no—
361#41—24no—
362C2×Q8—21no—
363C2×Q8—21no—
364C2×Q8—21no—
365C2×Q8—21no—
366C2×Q8—22no—
367C2×Q8—22no—
368C2×Q8—41no—
369C2×Q8—41no—
370C2×Q8—82no—
371C2×Q8C2×D4×C6112yes—
372C2×D4—22no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4C2×D4×C6112yes—
376C22×C4—22no—
377C22×C4—24no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4C2×D4×C6112yes—
381C22×C4C2×D4×C6111yescharacteristic
382C22×C4C2×D4×C6112yes—
383C22×C4C2×D4×C6111yescharacteristic
384C22×C4C24×C6111yescharacteristic
385M16—22no—
386M16—22no—
387M16—22no—
388M16#41×C6114yes—
389C2×C8—22no—
390C2×C8—22no—
391C4⋊C4—24no—
392C4⋊C4—24no—
393C4⋊C4—24no—
394C4⋊C4—24no—
395C4⋊C4—22no—
396C4⋊C4—22no—
397C4⋊C4—22no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—22no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—41no—
408C4⋊C4—41no—
409C4⋊C4—84no—
410C4⋊C4C2×D4×C6112yes—
411C4⋊C4C2×D4×C6112yes—
412C22⋊C4—24no—
413C22⋊C4—24no—
414C22⋊C4—24no—
415C22⋊C4—22no—
416C22⋊C4—22no—
417C22⋊C4—22no—
418C42—24no—
419C42—22no—
420C42—22no—
421C42—22no—
422C42—24no—
423C42C2×D4×C6111yescharacteristic
424C42C2×D4×C6111yescharacteristic
425C42C2×D4×C6111yescharacteristic
426C42C2×D4×C6111yescharacteristic
427C23—22no—
428C23C22×D4×C6111yescharacteristic
429Q8—24no—
430Q8—42no—
431Q8—42no—
432Q8—42no—
433Q8—81no—
434Q8—82no—
435Q8—82no—
436D4—24no—
437D4—42no—
438D4—42no—
439D4—42no—
440D4—81no—
441C2×C4—22no—
442C2×C4—24no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—41no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—44no—
454C2×C4—42no—
455C2×C4—44no—
456C2×C4—42no—
457C2×C4—84no—
458C2×C4#120×C6111yescharacteristic
459C2×C4#120×C6111yescharacteristic
460C2×C4#120×C6111yescharacteristic
461C2×C4#120×C6111yescharacteristic
462C2×C4C22×D4×C6111yescharacteristic
463C2×C4C22×D4×C6111yescharacteristic
464C2×C4C2×#41×C6112yes—
465C2×C42−1+4×C6112yes—
466C8—24no—
467C8—42no—
468C22—21no—
469C22—21no—
470C22—42no—
471C22—42no—
472C22—42no—
473C22C2×#120×C6111yescharacteristic
474C22C61×#53211yescharacteristic
475C22C61×#53611yescharacteristic
476C4—21no—
477C4—21no—
478C4—21no—
479C4—44no—
480C4—42no—
481C4—42no—
482C4—42no—
483C4—42no—
484C4—42no—
485C4—82no—
486C4C61×#45612yes—
487C4C61×#54712yes—
488C4C61×#54812yes—
489C2—21no—
490C2—21no—
491C2—82no—
492C2C61×#243211yescharacteristic
493C2C2×C61×#45611yescharacteristic
494C2C61×#302111yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC61×#532C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C61×#3165C2semidirect
4. C61×#2567C2semidirect
5. C61×#2038C2semidirect
6. C61×#1986C2semidirect
8. C61×#1859C2semidirect
9. C4×#101×C61C2semidirect
220. #25695C61direct (N × H)
243. #3165C2×C61semidirect
245. #2567C2×C61semidirect
246. #2038C2×C61semidirect
247. #1986C2×C61semidirect
249. #1859C2×C61semidirect
250. C4×#101C2×C61semidirect
290. C61#25695direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#35072
C61×#31652
C61×#31412
C61×#25672
C61×#20382
C61×#19862
C61×#19802
C61×#18592
C4×#101×C612
#2569561