Finite Group Databasebeta

← C61×#10354 #29513787

Subgroups — C61×#10354 #29513787

Order 15616.

536 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#2552C211yesmaximal, characteristic, complemented
2C61×#1982C211yesmaximal, characteristic
3C61×#1982C211yesmaximal, characteristic
4C61×#1957C211yesmaximal, characteristic
5C61×#1296C211yesmaximal, characteristic, complemented
6C61×#1279C211yesmaximal, characteristic, complemented
7C61×#1279C211yesmaximal, characteristic, complemented
8C2×#127×C61C2211yescharacteristic
9C2×#125×C61—21no—
10C2×C4⋊C8×C61C2211yescharacteristic
11C2×C4⋊C8×C61C2211yescharacteristic
12C2×#102×C61—22no—
13C2×#102×C61—21no—
14C2×#102×C61—21no—
15C2×#102×C61—21no—
16C2×#102×C61—21no—
17C2×C4×C8×C61C2211yescharacteristic
18C61×#398—22no—
19C61×#389—21no—
20C61×#389—21no—
21C61×#384—21no—
22C61×#384C2211yescharacteristic
23C4×C4⋊C4×C61C2211yescharacteristic
24C4×C4⋊C4×C61C2211yescharacteristic
25C22×D4×C61—21no—
26C22×D4×C61—21no—
27C22×D4×C61—21no—
28C22×C8×C61—21no—
29C22×C8×C61—21no—
30C22×C8×C61—21no—
31#127×C61—21no—
32#127×C61—21no—
33#127×C61—21no—
34#127×C61Q812yes—
35#125×C61—42no—
36#125×C61—42no—
37C2×C4⋊C4×C61—22no—
38C2×C4⋊C4×C61—22no—
39C2×C4⋊C4×C61—21no—
40C2×C4⋊C4×C61—21no—
41C2×C4⋊C4×C61—22no—
42C2×C4⋊C4×C61D411yescharacteristic
43C2×C4⋊C4×C61D411yescharacteristic
44C2×C4⋊C4×C61D411yescharacteristic
45C2×C4⋊C4×C61D411yescharacteristic
46C2×C4⋊C4×C61D412yes—
47C2×C42×C61—21no—
48C2×C42×C61—21no—
49C2×C42×C61C2311yescharacteristic
50C4⋊C8×C61—21no—
51C4⋊C8×C61—21no—
52C4⋊C8×C61—21no—
53C4⋊C8×C61—21no—
54#102×C61—42no—
55#102×C61—42no—
56#102×C61—44no—
57#102×C61—42no—
58#102×C61—42no—
59C4×C8×C61—21no—
60C4×C8×C61—21no—
61#95×C61—22no—
62#95×C61—21no—
63#95×C61—21no—
64C24×C61—41no—
65C2×D4×C61—22no—
66C2×D4×C61—22no—
67C2×D4×C61—22no—
68C2×D4×C61—42no—
69C2×D4×C61—42no—
70C2×D4×C61—41no—
71C2×D4×C61—41no—
72C2×D4×C61—41no—
73C2×D4×C61—41no—
74C2×D4×C61—41no—
75C2×D4×C61—41no—
76C2×D4×C61—41no—
77C2×D4×C61—41no—
78C2×D4×C61—41no—
79C2×D4×C61—41no—
80C2×D4×C61—41no—
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61—21no—
84C22×C4×C61—21no—
85C22×C4×C61—22no—
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61C2×D411yescharacteristic
88C22×C4×C61C2×D411yescharacteristic
89C2×C8×C61—22no—
90C2×C8×C61—41no—
91C2×C8×C61—41no—
92C2×C8×C61—41no—
93C2×C8×C61—41no—
94C2×C8×C61—41no—
95C2×C8×C61—41no—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C4⋊C4×C61—21no—
99C4⋊C4×C61—21no—
100C4⋊C4×C61—21no—
101C4⋊C4×C61—21no—
102C4⋊C4×C61—21no—
103C4⋊C4×C61—21no—
104C4⋊C4×C61—44no—
105C4⋊C4×C61—44no—
106C4⋊C4×C61—42no—
107C4⋊C4×C61—41no—
108C4⋊C4×C61—41no—
109C4⋊C4×C61—41no—
110C4⋊C4×C61—41no—
111C4⋊C4×C61—82no—
112C4⋊C4×C61D812yes—
113C4⋊C4×C61SD1612yes—
114C42×C61—41no—
115C42×C61—41no—
116C42×C61—41no—
117C42×C61—41no—
118C42×C61C2×Q811yescharacteristic
119C42×C61#4111yescharacteristic
120C42×C61#4111yescharacteristic
121C42×C61#4111yescharacteristic
122C23×C61—42no—
123C23×C61—81no—
124C23×C61—81no—
125C23×C61—81no—
126C23×C61—81no—
127C23×C61—81no—
128C23×C61—81no—
129C23×C61#12011yescharacteristic
130D4×C61—44no—
131D4×C61—42no—
132D4×C61—42no—
133D4×C61—42no—
134D4×C61—42no—
135D4×C61—82no—
136D4×C61—81no—
137D4×C61—81no—
138D4×C61—81no—
139D4×C61—81no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—22no—
143C2×C4×C61—22no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
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—42no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61C22⋊Q811yescharacteristic
158C2×C4×C61C22⋊Q811yescharacteristic
159C2×C4×C61C22⋊Q811yescharacteristic
160C2×C4×C61#12411yescharacteristic
161C2×C4×C61#12411yescharacteristic
162C2×C4×C61#12411yescharacteristic
163C2×C4×C61C2×D811yescharacteristic
164C2×C4×C61C2×SD1611yescharacteristic
165C2×C4×C61#13511yescharacteristic
166C2×C4×C61#13511yescharacteristic
167C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C61#13711yescharacteristic
171C8×C61—42no—
172C8×C61—81no—
173C8×C61—81no—
174#10354C6111yesmaximal, characteristic, direct product factor, Sylow
175C22×C61—82no—
176C22×C61—82no—
177C22×C61—82no—
178C22×C61—161no—
179C22×C61—161no—
180C22×C61—161no—
181C22×C61—161no—
182C22×C61#39311yescharacteristic
183C22×C61#44711yescharacteristic
184C22×C61#44811yescharacteristic
185C22×C61#44911yescharacteristic
186C22×C61#44911yescharacteristic
187C22×C61#45311yescharacteristic
188C22×C61#45411yescharacteristic
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—42no—
192C4×C61—42no—
193C4×C61—81no—
194C4×C61—82no—
195C4×C61—81no—
196C4×C61#47411yescharacteristic
197C4×C61#47611yescharacteristic
198C4×C61#47811yescharacteristic
199C4×C61#47811yescharacteristic
200C4×C61#48611yescharacteristic
201C4×C61#48811yescharacteristic
202C4×C61#48911yescharacteristic
203C4×C61#49011yescharacteristic
204#2552C2×C6111yescharacteristic, complemented
205#1982C2×C6111yescharacteristic
206#1982C2×C6111yescharacteristic
207#1957C2×C6111yescharacteristic
208#1296C2×C6111yescharacteristic, complemented
209#1279C2×C6111yescharacteristic, complemented
210#1279C2×C6111yescharacteristic, complemented
211C2×C61—162no—
212C2×C61#162111yescharacteristic
213C2×C61#162211yescharacteristic
214C2×C61#162511yescharacteristic
215C2×C61#162611yescharacteristic
216C2×C61#202311yescharacteristic
217C2×C61#202511yescharacteristic
218C2×C61#202711yescharacteristic
219C2×#127C22×C6111yescharacteristic
220C2×#125—21no—
221C2×C4⋊C8C22×C6111yescharacteristic
222C2×C4⋊C8C22×C6111yescharacteristic
223C2×#102—22no—
224C2×#102—21no—
225C2×#102—21no—
226C2×#102—21no—
227C2×#102—21no—
228C2×C4×C8C22×C6111yescharacteristic
229#398—22no—
230#389—21no—
231#389—21no—
232#384—21no—
233#384C22×C6111yescharacteristic
234C4×C4⋊C4C22×C6111yescharacteristic
235C4×C4⋊C4C22×C6111yescharacteristic
236C61#1035411yescharacteristic, direct product factor, Sylow
237C22×D4—21no—
238C22×D4—21no—
239C22×D4—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—21no—
243#127—21no—
244#127—21no—
245#127—21no—
246#127Q8×C6112yes—
247#125—42no—
248#125—42no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4D4×C6111yescharacteristic
255C2×C4⋊C4D4×C6111yescharacteristic
256C2×C4⋊C4D4×C6111yescharacteristic
257C2×C4⋊C4D4×C6111yescharacteristic
258C2×C4⋊C4D4×C6112yes—
259C2×C42—21no—
260C2×C42—21no—
261C2×C42C23×C6111yescharacteristic
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266#102—42no—
267#102—42no—
268#102—44no—
269#102—42no—
270#102—42no—
271C4×C8—21no—
272C4×C8—21no—
273#95—22no—
274#95—21no—
275#95—21no—
276C24—41no—
277C2×D4—22no—
278C2×D4—22no—
279C2×D4—22no—
280C2×D4—42no—
281C2×D4—42no—
282C2×D4—41no—
283C2×D4—41no—
284C2×D4—41no—
285C2×D4—41no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4—41no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—22no—
298C22×C4C2×D4×C6111yescharacteristic
299C22×C4C2×D4×C6111yescharacteristic
300C22×C4C2×D4×C6111yescharacteristic
301C2×C8—22no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—42no—
317C4⋊C4—44no—
318C4⋊C4—44no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—82no—
324C4⋊C4D8×C6112yes—
325C4⋊C4SD16×C6112yes—
326C42—41no—
327C42—41no—
328C42—41no—
329C42—41no—
330C42C2×Q8×C6111yescharacteristic
331C42#41×C6111yescharacteristic
332C42#41×C6111yescharacteristic
333C42#41×C6111yescharacteristic
334C23—42no—
335C23—81no—
336C23—81no—
337C23—81no—
338C23—81no—
339C23—81no—
340C23—81no—
341C23#120×C6111yescharacteristic
342D4—44no—
343D4—42no—
344D4—42no—
345D4—42no—
346D4—42no—
347D4—82no—
348D4—81no—
349D4—81no—
350D4—81no—
351D4—81no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4C22⋊Q8×C6111yescharacteristic
370C2×C4C22⋊Q8×C6111yescharacteristic
371C2×C4C22⋊Q8×C6111yescharacteristic
372C2×C4#124×C6111yescharacteristic
373C2×C4#124×C6111yescharacteristic
374C2×C4#124×C6111yescharacteristic
375C2×C4C2×D8×C6111yescharacteristic
376C2×C4C2×SD16×C6111yescharacteristic
377C2×C4#135×C6111yescharacteristic
378C2×C4#135×C6111yescharacteristic
379C2×C4AGL(1,ℤ/8)×C6111yescharacteristic
380C2×C4AGL(1,ℤ/8)×C6111yescharacteristic
381C2×C4AGL(1,ℤ/8)×C6111yescharacteristic
382C2×C4#137×C6111yescharacteristic
383C8—42no—
384C8—81no—
385C8—81no—
386C22—82no—
387C22—82no—
388C22—82no—
389C22—161no—
390C22—161no—
391C22—161no—
392C22—161no—
393C22C61×#39311yescharacteristic
394C22C61×#44711yescharacteristic
395C22C61×#44811yescharacteristic
396C22C61×#44911yescharacteristic
397C22C61×#44911yescharacteristic
398C22C61×#45311yescharacteristic
399C22C61×#45411yescharacteristic
400C4—21no—
401C4—21no—
402C4—42no—
403C4—42no—
404C4—81no—
405C4—82no—
406C4—81no—
407C4C61×#47411yescharacteristic
408C4C61×#47611yescharacteristic
409C4C61×#47811yescharacteristic
410C4C61×#47811yescharacteristic
411C4C61×#48611yescharacteristic
412C4C61×#48811yescharacteristic
413C4C61×#48911yescharacteristic
414C4C61×#49011yescharacteristic
415C2—162no—
416C2C61×#162111yescharacteristic
417C2C61×#162211yescharacteristic
418C2C61×#162511yescharacteristic
419C2C61×#162611yescharacteristic
420C2C61×#202311yescharacteristic
421C2C61×#202511yescharacteristic
422C2C61×#202711yescharacteristic
subgroupG/H
center, socleC23×C61#120
commutator, Frattini, cosocleC2×C42C23×C61
prime radicalC2×#127×C61C22
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
1. C61×#2552C2semidirect
5. C61×#1296C2semidirect
6. C61×#1279C2semidirect
7. C61×#1279C2semidirect
174. #10354C61direct (N × H)
204. #2552C2×C61semidirect
208. #1296C2×C61semidirect
209. #1279C2×C61semidirect
210. #1279C2×C61semidirect
236. C61#10354direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#25522
C61×#19822
C61×#19572
C61×#12962
C61×#12792
#1035461