Finite Group Databasebeta

← C61×#10417 #29513850

Subgroups — C61×#10417 #29513850

Order 15616.

520 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#2547C211yesmaximal, characteristic
2C61×#1990C211yesmaximal, characteristic, complemented
3C61×#1948C211yesmaximal, characteristic, complemented
4C61×#1802C211yesmaximal, characteristic
5C2×C61×#332C211yesmaximal, characteristic, complemented
6C2×C61×D4⋊C8C211yesmaximal, characteristic
7C61×#1279C211yesmaximal, characteristic, complemented
8C2×C4⋊Q8×C61C2211yescharacteristic
9C2×#124×C61—21no—
10C2×C4×D4×C61C2211yescharacteristic
11C2×#106×C61—21no—
12C2×C4⋊C8×C61C2211yescharacteristic
13C2×C4⋊C8×C61C2211yescharacteristic
14C2×#102×C61—21no—
15C2×C4×C8×C61C2211yescharacteristic
16C61×#397—22no—
17C61×#391—21no—
18C61×#384C2211yescharacteristic
19C61×#380—21no—
20C61×#380—21no—
21C4×C4⋊C4×C61C2211yescharacteristic
22C61×#340—21no—
23C61×#340—21no—
24C61×#340—22no—
25C61×#332—22no—
26C61×D4⋊C8—22no—
27C22×Q8×C61—21no—
28C22×D4×C61D411yescharacteristic
29C23×C4×C61—21no—
30C22×C8×C61—21no—
31C22×C8×C61—21no—
32C22×C8×C61—21no—
33C4⋊Q8×C61—21no—
34C4⋊Q8×C61—21no—
35C4⋊Q8×C61—21no—
36C4⋊Q8×C61—21no—
37#124×C61—42no—
38#124×C61—42no—
39C4×D4×C61—21no—
40C4×D4×C61—21no—
41C4×D4×C61—21no—
42C4×D4×C61—21no—
43C2×C4⋊C4×C61—21no—
44C2×C4⋊C4×C61—21no—
45C2×C4⋊C4×C61—21no—
46C2×C4⋊C4×C61—21no—
47C2×C4⋊C4×C61D412yes—
48C2×C4⋊C4×C61D411yescharacteristic
49C2×C4⋊C4×C61D411yescharacteristic
50C2×C4⋊C4×C61D411yescharacteristic
51C2×C22⋊C4×C61—22no—
52C2×C22⋊C4×C61—22no—
53C2×C22⋊C4×C61—21no—
54C2×C42×C61—21no—
55C2×C42×C61C2311yescharacteristic
56#106×C61—42no—
57C4⋊C8×C61—21no—
58C4⋊C8×C61—21no—
59C4⋊C8×C61—21no—
60C4⋊C8×C61D412yes—
61#102×C61—42no—
62C4×C8×C61—21no—
63C4×C8×C61—21no—
64#95×C61—22no—
65#95×C61—22no—
66#95×C61—21no—
67C24×C61—21no—
68C2×Q8×C61—41no—
69C2×Q8×C61—41no—
70C2×Q8×C61—41no—
71C2×Q8×C61—41no—
72C2×Q8×C61—41no—
73C2×Q8×C61—41no—
74C2×D4×C61—21no—
75C2×D4×C61—21no—
76C2×D4×C61—21no—
77C2×D4×C61—21no—
78C2×D4×C61—21no—
79C2×D4×C61SD1612yes—
80C22×C4×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61—22no—
84C22×C4×C61—41no—
85C22×C4×C61—41no—
86C22×C4×C61—41no—
87C22×C4×C61—41no—
88C22×C4×C61—41no—
89C22×C4×C61—41no—
90C22×C4×C61—41no—
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61C2×D411yescharacteristic
93C22×C4×C61C2×D411yescharacteristic
94C2×C8×C61—22no—
95C2×C8×C61—22no—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C2×C8×C61—41no—
99C2×C8×C61—41no—
100C2×C8×C61—41no—
101C2×C8×C61—41no—
102C2×C8×C61—41no—
103C4⋊C4×C61—21no—
104C4⋊C4×C61—22no—
105C4⋊C4×C61—21no—
106C4⋊C4×C61—22no—
107C4⋊C4×C61—21no—
108C4⋊C4×C61—21no—
109C4⋊C4×C61—21no—
110C4⋊C4×C61—21no—
111C4⋊C4×C61—42no—
112C4⋊C4×C61—41no—
113C4⋊C4×C61—41no—
114C4⋊C4×C61—41no—
115C4⋊C4×C61—41no—
116C4⋊C4×C61—41no—
117C4⋊C4×C61—41no—
118C22⋊C4×C61—44no—
119C22⋊C4×C61—44no—
120C22⋊C4×C61—41no—
121C22⋊C4×C61—41no—
122C42×C61—41no—
123C42×C61—41no—
124C42×C61C2×D411yescharacteristic
125C42×C61#4111yescharacteristic
126C42×C61#4111yescharacteristic
127C42×C61#4111yescharacteristic
128C23×C61—22no—
129C23×C61—41no—
130C23×C61—41no—
131C23×C61—41no—
132C23×C61—41no—
133C23×C61—41no—
134C23×C61—41no—
135C23×C61#12011yescharacteristic
136Q8×C61—81no—
137Q8×C61—81no—
138Q8×C61—81no—
139Q8×C61—81no—
140D4×C61—22no—
141D4×C61—22no—
142D4×C61—41no—
143D4×C61—41no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—41no—
147C2×C4×C61—42no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—42no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—42no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—81no—
159C2×C4×C61—81no—
160C2×C4×C61—81no—
161C2×C4×C61—81no—
162C2×C4×C61—81no—
163C2×C4×C61—81no—
164C2×C4×C61—81no—
165C2×C4×C61#12111yescharacteristic
166C2×C4×C61#12111yescharacteristic
167C2×C4×C61#12111yescharacteristic
168C2×C4×C61#12311yescharacteristic
169C2×C4×C61#12311yescharacteristic
170C2×C4×C61#12411yescharacteristic
171C2×C4×C61C2×SD1611yescharacteristic
172C2×C4×C61#13511yescharacteristic
173C2×C4×C61#13511yescharacteristic
174C2×C4×C61#13511yescharacteristic
175C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
176C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
177C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
178C2×C4×C61#13711yescharacteristic
179C8×C61—42no—
180C8×C61—42no—
181C8×C61—81no—
182#10417C6111yesmaximal, characteristic, direct product factor, Sylow
183C22×C61—42no—
184C22×C61—42no—
185C22×C61—42no—
186C22×C61—81no—
187C22×C61—81no—
188C22×C61—81no—
189C22×C61—81no—
190C22×C61#39411yescharacteristic
191C22×C61#44911yescharacteristic
192C22×C61#44911yescharacteristic
193C22×C61#45011yescharacteristic
194C22×C61#45211yescharacteristic
195C22×C61#45411yescharacteristic
196C22×C61#45611yescharacteristic
197C4×C61—21no—
198C4×C61—21no—
199C4×C61—81no—
200C4×C61—81no—
201C4×C61—82no—
202C4×C61—81no—
203C4×C61—161no—
204C4×C61#46311yescharacteristic
205C4×C61#46411yescharacteristic
206C4×C61#46511yescharacteristic
207C4×C61#46911yescharacteristic
208C4×C61#48111yescharacteristic
209C4×C61#48211yescharacteristic
210C4×C61#48811yescharacteristic
211C4×C61#48911yescharacteristic
212#2547C2×C6111yescharacteristic
213#1990C2×C6111yescharacteristic, complemented
214#1948C2×C6111yescharacteristic, complemented
215#1802C2×C6111yescharacteristic
216C2×#332C2×C6111yescharacteristic, complemented
217C2×D4⋊C8C2×C6111yescharacteristic
218#1279C2×C6111yescharacteristic, complemented
219C2×C61—82no—
220C2×C61#162811yescharacteristic
221C2×C61#163511yescharacteristic
222C2×C61#165011yescharacteristic
223C2×C61#165411yescharacteristic
224C2×C61#203411yescharacteristic
225C2×C61#203811yescharacteristic
226C2×C61#204211yescharacteristic
227C2×C4⋊Q8C22×C6111yescharacteristic
228C2×#124—21no—
229C2×C4×D4C22×C6111yescharacteristic
230C2×#106—21no—
231C2×C4⋊C8C22×C6111yescharacteristic
232C2×C4⋊C8C22×C6111yescharacteristic
233C2×#102—21no—
234C2×C4×C8C22×C6111yescharacteristic
235#397—22no—
236#391—21no—
237#384C22×C6111yescharacteristic
238#380—21no—
239#380—21no—
240C4×C4⋊C4C22×C6111yescharacteristic
241#340—21no—
242#340—21no—
243#340—22no—
244#332—22no—
245D4⋊C8—22no—
246C61#1041711yescharacteristic, direct product factor, Sylow
247C22×Q8—21no—
248C22×D4D4×C6111yescharacteristic
249C23×C4—21no—
250C22×C8—21no—
251C22×C8—21no—
252C22×C8—21no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4⋊Q8—21no—
257#124—42no—
258#124—42no—
259C4×D4—21no—
260C4×D4—21no—
261C4×D4—21no—
262C4×D4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4D4×C6111yescharacteristic
268C2×C4⋊C4D4×C6112yes—
269C2×C4⋊C4D4×C6111yescharacteristic
270C2×C4⋊C4D4×C6111yescharacteristic
271C2×C22⋊C4—22no—
272C2×C22⋊C4—22no—
273C2×C22⋊C4—21no—
274C2×C42—21no—
275C2×C42C23×C6111yescharacteristic
276#106—42no—
277C4⋊C8—21no—
278C4⋊C8—21no—
279C4⋊C8—21no—
280C4⋊C8D4×C6112yes—
281#102—42no—
282C4×C8—21no—
283C4×C8—21no—
284#95—22no—
285#95—22no—
286#95—21no—
287C24—21no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×Q8—41no—
293C2×Q8—41no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4SD16×C6112yes—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—22no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4C2×D4×C6111yescharacteristic
312C22×C4C2×D4×C6111yescharacteristic
313C22×C4C2×D4×C6111yescharacteristic
314C2×C8—22no—
315C2×C8—22no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C4⋊C4—21no—
324C4⋊C4—22no—
325C4⋊C4—21no—
326C4⋊C4—22no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—42no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C22⋊C4—44no—
339C22⋊C4—44no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C42—41no—
343C42—41no—
344C42C2×D4×C6111yescharacteristic
345C42#41×C6111yescharacteristic
346C42#41×C6111yescharacteristic
347C42#41×C6111yescharacteristic
348C23—22no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23#120×C6111yescharacteristic
356Q8—81no—
357Q8—81no—
358Q8—81no—
359Q8—81no—
360D4—22no—
361D4—22no—
362D4—41no—
363D4—41no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4#121×C6111yescharacteristic
386C2×C4#121×C6111yescharacteristic
387C2×C4#121×C6111yescharacteristic
388C2×C4#123×C6111yescharacteristic
389C2×C4#123×C6111yescharacteristic
390C2×C4#124×C6111yescharacteristic
391C2×C4C2×SD16×C6111yescharacteristic
392C2×C4#135×C6111yescharacteristic
393C2×C4#135×C6111yescharacteristic
394C2×C4#135×C6111yescharacteristic
395C2×C4AGL(1,ℤ/8)×C6111yescharacteristic
396C2×C4AGL(1,ℤ/8)×C6111yescharacteristic
397C2×C4AGL(1,ℤ/8)×C6111yescharacteristic
398C2×C4#137×C6111yescharacteristic
399C8—42no—
400C8—42no—
401C8—81no—
402C22—42no—
403C22—42no—
404C22—42no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22—81no—
409C22C61×#39411yescharacteristic
410C22C61×#44911yescharacteristic
411C22C61×#44911yescharacteristic
412C22C61×#45011yescharacteristic
413C22C61×#45211yescharacteristic
414C22C61×#45411yescharacteristic
415C22C61×#45611yescharacteristic
416C4—21no—
417C4—21no—
418C4—82no—
419C4—81no—
420C4—81no—
421C4—81no—
422C4—161no—
423C4C61×#46311yescharacteristic
424C4C61×#46411yescharacteristic
425C4C61×#46511yescharacteristic
426C4C61×#46911yescharacteristic
427C4C61×#48111yescharacteristic
428C4C61×#48211yescharacteristic
429C4C61×#48811yescharacteristic
430C4C61×#48911yescharacteristic
431C2—82no—
432C2C61×#162811yescharacteristic
433C2C61×#163511yescharacteristic
434C2C61×#165011yescharacteristic
435C2C61×#165411yescharacteristic
436C2C61×#203411yescharacteristic
437C2C61×#203811yescharacteristic
438C2C61×#204211yescharacteristic
subgroupG/H
center, socleC23×C61#120
commutator, Frattini, cosocleC2×C42C23×C61
prime radicalC22×D4×C61D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#1990C2semidirect
3. C61×#1948C2semidirect
5. C2×C61×#332C2semidirect
7. C61×#1279C2semidirect
182. #10417C61direct (N × H)
213. #1990C2×C61semidirect
214. #1948C2×C61semidirect
216. C2×#332C2×C61semidirect
218. #1279C2×C61semidirect
246. C61#10417direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#25472
C61×#19902
C61×#19482
C61×#18022
C2×C61×#3322
C2×C61×D4⋊C82
C61×#12792
#1041761