Finite Group Databasebeta

← C61×#10412 #29513845

Subgroups — C61×#10412 #29513845

Order 15616.

516 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#2563C211yesmaximal, characteristic
2C61×#1956C211yesmaximal, characteristic, complemented
3C61×#1948C211yesmaximal, characteristic, complemented
4C61×#1802C211yesmaximal, characteristic
5C2×C61×#333C211yesmaximal, characteristic, complemented
6C2×C61×D4⋊C8C211yesmaximal, characteristic
7C61×#1279C211yesmaximal, characteristic, complemented
8C2×C4⋊Q8×C61C2211yescharacteristic
9C2×C4×D4×C61C2211yescharacteristic
10C2×#106×C61—21no—
11C2×C4⋊C8×C61C2211yescharacteristic
12C2×C4⋊C8×C61C2211yescharacteristic
13C2×#103×C61—22no—
14C2×#102×C61—21no—
15C2×C4×C8×C61C2211yescharacteristic
16C61×#393—22no—
17C61×#390—21no—
18C61×#384C2211yescharacteristic
19C61×#382—21no—
20C61×#380—21no—
21C61×#380—21no—
22C4×C4⋊C4×C61C2211yescharacteristic
23C61×#340—21no—
24C61×#340—21no—
25C61×#333—22no—
26C61×D4⋊C8—22no—
27C22×Q8×C61D412yes—
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—
37C4×D4×C61—21no—
38C4×D4×C61—21no—
39C4×D4×C61—21no—
40C4×D4×C61—21no—
41C2×C4⋊C4×C61—21no—
42C2×C4⋊C4×C61—21no—
43C2×C4⋊C4×C61—21no—
44C2×C4⋊C4×C61—21no—
45C2×C4⋊C4×C61—21no—
46C2×C4⋊C4×C61D411yescharacteristic
47C2×C4⋊C4×C61D411yescharacteristic
48C2×C4⋊C4×C61D411yescharacteristic
49C2×C22⋊C4×C61—21no—
50C2×C22⋊C4×C61—22no—
51C2×C22⋊C4×C61—22no—
52C2×C42×C61—21no—
53C2×C42×C61C2311yescharacteristic
54#106×C61—42no—
55C4⋊C8×C61—21no—
56C4⋊C8×C61—21no—
57C4⋊C8×C61—21no—
58C4⋊C8×C61D412yes—
59#103×C61—44no—
60#102×C61—42no—
61C4×C8×C61—21no—
62C4×C8×C61—21no—
63#95×C61—22no—
64#95×C61—22no—
65#95×C61—21no—
66C24×C61—21no—
67C2×Q8×C61—22no—
68C2×Q8×C61—22no—
69C2×Q8×C61—42no—
70C2×Q8×C61—42no—
71C2×D4×C61—21no—
72C2×D4×C61—21no—
73C2×D4×C61—21no—
74C2×D4×C61—21no—
75C2×D4×C61—21no—
76C2×D4×C61SD1612yes—
77C22×C4×C61—21no—
78C22×C4×C61—21no—
79C22×C4×C61—21no—
80C22×C4×C61—22no—
81C22×C4×C61—41no—
82C22×C4×C61—41no—
83C22×C4×C61—41no—
84C22×C4×C61—41no—
85C22×C4×C61—41no—
86C22×C4×C61—41no—
87C22×C4×C61—41no—
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61C2×D411yescharacteristic
90C22×C4×C61C2×D411yescharacteristic
91C2×C8×C61—22no—
92C2×C8×C61—22no—
93C2×C8×C61—41no—
94C2×C8×C61—41no—
95C2×C8×C61—41no—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C2×C8×C61—41no—
99C2×C8×C61—41no—
100C4⋊C4×C61—21no—
101C4⋊C4×C61—21no—
102C4⋊C4×C61—21no—
103C4⋊C4×C61—21no—
104C4⋊C4×C61—21no—
105C4⋊C4×C61—21no—
106C4⋊C4×C61—42no—
107C4⋊C4×C61—41no—
108C4⋊C4×C61—41no—
109C4⋊C4×C61—41no—
110C4⋊C4×C61—41no—
111C4⋊C4×C61—41no—
112C4⋊C4×C61—41no—
113C4⋊C4×C61—41no—
114C4⋊C4×C61—41no—
115C22⋊C4×C61—41no—
116C22⋊C4×C61—41no—
117C22⋊C4×C61—82no—
118C22⋊C4×C61—82no—
119C42×C61—41no—
120C42×C61—41no—
121C42×C61C2×D411yescharacteristic
122C42×C61#4111yescharacteristic
123C42×C61#4111yescharacteristic
124C42×C61#4111yescharacteristic
125C23×C61—22no—
126C23×C61—41no—
127C23×C61—41no—
128C23×C61—41no—
129C23×C61—41no—
130C23×C61—41no—
131C23×C61—41no—
132C23×C61#12011yescharacteristic
133Q8×C61—44no—
134Q8×C61—82no—
135D4×C61—22no—
136D4×C61—22no—
137D4×C61—41no—
138D4×C61—41no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—41no—
142C2×C4×C61—42no—
143C2×C4×C61—41no—
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—42no—
153C2×C4×C61—81no—
154C2×C4×C61—81no—
155C2×C4×C61—81no—
156C2×C4×C61—81no—
157C2×C4×C61—81no—
158C2×C4×C61—81no—
159C2×C4×C61—81no—
160C2×C4×C61#12111yescharacteristic
161C2×C4×C61#12111yescharacteristic
162C2×C4×C61#12111yescharacteristic
163C2×C4×C61#12311yescharacteristic
164C2×C4×C61#12311yescharacteristic
165C2×C4×C61#12411yescharacteristic
166C2×C4×C61C2×SD1611yescharacteristic
167C2×C4×C61#13511yescharacteristic
168C2×C4×C61#13511yescharacteristic
169C2×C4×C61#13511yescharacteristic
170C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C61#13711yescharacteristic
172C2×C4×C61#13711yescharacteristic
173C2×C4×C61#13711yescharacteristic
174C8×C61—42no—
175C8×C61—42no—
176C8×C61—81no—
177#10412C6111yesmaximal, characteristic, direct product factor, Sylow
178C22×C61—42no—
179C22×C61—42no—
180C22×C61—42no—
181C22×C61—81no—
182C22×C61—81no—
183C22×C61—81no—
184C22×C61—81no—
185C22×C61#39411yescharacteristic
186C22×C61#44811yescharacteristic
187C22×C61#44911yescharacteristic
188C22×C61#45211yescharacteristic
189C22×C61#45211yescharacteristic
190C22×C61#45311yescharacteristic
191C22×C61#45511yescharacteristic
192C4×C61—21no—
193C4×C61—21no—
194C4×C61—81no—
195C4×C61—81no—
196C4×C61—82no—
197C4×C61—81no—
198C4×C61—161no—
199C4×C61#46311yescharacteristic
200C4×C61#46411yescharacteristic
201C4×C61#46511yescharacteristic
202C4×C61#47011yescharacteristic
203C4×C61#48311yescharacteristic
204C4×C61#48511yescharacteristic
205C4×C61#48811yescharacteristic
206C4×C61#48911yescharacteristic
207#2563C2×C6111yescharacteristic
208#1956C2×C6111yescharacteristic, complemented
209#1948C2×C6111yescharacteristic, complemented
210#1802C2×C6111yescharacteristic
211C2×#333C2×C6111yescharacteristic, complemented
212C2×D4⋊C8C2×C6111yescharacteristic
213#1279C2×C6111yescharacteristic, complemented
214C2×C61—82no—
215C2×C61#162211yescharacteristic
216C2×C61#163411yescharacteristic
217C2×C61#164311yescharacteristic
218C2×C61#164611yescharacteristic
219C2×C61#203511yescharacteristic
220C2×C61#203711yescharacteristic
221C2×C61#204211yescharacteristic
222C2×C4⋊Q8C22×C6111yescharacteristic
223C2×C4×D4C22×C6111yescharacteristic
224C2×#106—21no—
225C2×C4⋊C8C22×C6111yescharacteristic
226C2×C4⋊C8C22×C6111yescharacteristic
227C2×#103—22no—
228C2×#102—21no—
229C2×C4×C8C22×C6111yescharacteristic
230#393—22no—
231#390—21no—
232#384C22×C6111yescharacteristic
233#382—21no—
234#380—21no—
235#380—21no—
236C4×C4⋊C4C22×C6111yescharacteristic
237#340—21no—
238#340—21no—
239#333—22no—
240D4⋊C8—22no—
241C61#1041211yescharacteristic, direct product factor, Sylow
242C22×Q8D4×C6112yes—
243C22×D4D4×C6111yescharacteristic
244C23×C4—21no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—21no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8—21no—
251C4⋊Q8—21no—
252C4×D4—21no—
253C4×D4—21no—
254C4×D4—21no—
255C4×D4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4D4×C6111yescharacteristic
262C2×C4⋊C4D4×C6111yescharacteristic
263C2×C4⋊C4D4×C6111yescharacteristic
264C2×C22⋊C4—21no—
265C2×C22⋊C4—22no—
266C2×C22⋊C4—22no—
267C2×C42—21no—
268C2×C42C23×C6111yescharacteristic
269#106—42no—
270C4⋊C8—21no—
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8D4×C6112yes—
274#103—44no—
275#102—42no—
276C4×C8—21no—
277C4×C8—21no—
278#95—22no—
279#95—22no—
280#95—21no—
281C24—21no—
282C2×Q8—22no—
283C2×Q8—22no—
284C2×Q8—42no—
285C2×Q8—42no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4SD16×C6112yes—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—22no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4C2×D4×C6111yescharacteristic
304C22×C4C2×D4×C6111yescharacteristic
305C22×C4C2×D4×C6111yescharacteristic
306C2×C8—22no—
307C2×C8—22no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—41no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—42no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—82no—
333C22⋊C4—82no—
334C42—41no—
335C42—41no—
336C42C2×D4×C6111yescharacteristic
337C42#41×C6111yescharacteristic
338C42#41×C6111yescharacteristic
339C42#41×C6111yescharacteristic
340C23—22no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23#120×C6111yescharacteristic
348Q8—44no—
349Q8—82no—
350D4—22no—
351D4—22no—
352D4—41no—
353D4—41no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4#121×C6111yescharacteristic
376C2×C4#121×C6111yescharacteristic
377C2×C4#121×C6111yescharacteristic
378C2×C4#123×C6111yescharacteristic
379C2×C4#123×C6111yescharacteristic
380C2×C4#124×C6111yescharacteristic
381C2×C4C2×SD16×C6111yescharacteristic
382C2×C4#135×C6111yescharacteristic
383C2×C4#135×C6111yescharacteristic
384C2×C4#135×C6111yescharacteristic
385C2×C4AGL(1,ℤ/8)×C6111yescharacteristic
386C2×C4#137×C6111yescharacteristic
387C2×C4#137×C6111yescharacteristic
388C2×C4#137×C6111yescharacteristic
389C8—42no—
390C8—42no—
391C8—81no—
392C22—42no—
393C22—42no—
394C22—42no—
395C22—81no—
396C22—81no—
397C22—81no—
398C22—81no—
399C22C61×#39411yescharacteristic
400C22C61×#44811yescharacteristic
401C22C61×#44911yescharacteristic
402C22C61×#45211yescharacteristic
403C22C61×#45211yescharacteristic
404C22C61×#45311yescharacteristic
405C22C61×#45511yescharacteristic
406C4—21no—
407C4—21no—
408C4—82no—
409C4—81no—
410C4—81no—
411C4—81no—
412C4—161no—
413C4C61×#46311yescharacteristic
414C4C61×#46411yescharacteristic
415C4C61×#46511yescharacteristic
416C4C61×#47011yescharacteristic
417C4C61×#48311yescharacteristic
418C4C61×#48511yescharacteristic
419C4C61×#48811yescharacteristic
420C4C61×#48911yescharacteristic
421C2—82no—
422C2C61×#162211yescharacteristic
423C2C61×#163411yescharacteristic
424C2C61×#164311yescharacteristic
425C2C61×#164611yescharacteristic
426C2C61×#203511yescharacteristic
427C2C61×#203711yescharacteristic
428C2C61×#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×#1956C2semidirect
3. C61×#1948C2semidirect
5. C2×C61×#333C2semidirect
7. C61×#1279C2semidirect
177. #10412C61direct (N × H)
208. #1956C2×C61semidirect
209. #1948C2×C61semidirect
211. C2×#333C2×C61semidirect
213. #1279C2×C61semidirect
241. C61#10412direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#25632
C61×#19562
C61×#19482
C61×#18022
C2×C61×#3332
C2×C61×D4⋊C82
C61×#12792
#1041261