Finite Group Databasebeta

← C61×#9682 #29513115

Subgroups — C61×#9682 #29513115

Order 15616.

700 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#2850C211yesmaximal, characteristic
2C61×#1749C211yesmaximal, characteristic, complemented
3C2×C61×#328C212yesmaximal, complemented
4C2×C61×#327C212yesmaximal
5C61×C4⋊#95C211yesmaximal, characteristic, complemented
6C2×#124×C61C411yescharacteristic, complemented
7C2×C22⋊Q8×C61C2211yescharacteristic
8C2×#121×C61C2211yescharacteristic
9C22×C4⋊C4×C61—21no—
10C22×C42×C61C2211yescharacteristic
11C2×C22⋊C8×C61C2212yes—
12C2×#97×C61—21no—
13C61×#391C411yescharacteristic, complemented
14C61×#390C411yescharacteristic, complemented
15C61×#388—21no—
16C61×#388—21no—
17C61×#386—21no—
18C61×#386—21no—
19C61×#382C411yescharacteristic, complemented
20C2×#95×C61—21no—
21C2×#95×C61C2212yes—
22C61×#336—21no—
23C61×#328—24no—
24C61×#327—24no—
25C22×Q8×C61C2×C411yescharacteristic
26C22×D4×C61—21no—
27C22×D4×C61C2×C411yescharacteristic
28C23×C4×C61—22no—
29C23×C4×C61D411yescharacteristic
30C23×C4×C61D411yescharacteristic
31C23×C4×C61C2311yescharacteristic
32C22×C8×C61—22no—
33#124×C61—42no—
34C22⋊Q8×C61—22no—
35C22⋊Q8×C61—22no—
36#121×C61—22no—
37#121×C61—22no—
38C2×C4⋊C4×C61—24no—
39C2×C4⋊C4×C61—21no—
40C2×C4⋊C4×C61—42no—
41C2×C4⋊C4×C61—42no—
42C2×C4⋊C4×C61C2×C411yescharacteristic
43C2×C4⋊C4×C61C2×C411yescharacteristic
44C2×C22⋊C4×C61—21no—
45C2×C22⋊C4×C61—21no—
46C2×C22⋊C4×C61—21no—
47C2×C22⋊C4×C61—21no—
48C2×C22⋊C4×C61—21no—
49C2×C22⋊C4×C61—21no—
50C2×C42×C61—42no—
51C2×C42×C61C2×C411yescharacteristic
52C2×C42×C61C2×C411yescharacteristic
53C2×C42×C61D411yescharacteristic
54C2×C42×C61D411yescharacteristic
55C22⋊C8×C61—22no—
56C22⋊C8×C61D414yes—
57#97×C61—42no—
58#95×C61—21no—
59#95×C61—21no—
60#95×C61—21no—
61#95×C61—21no—
62#95×C61—22no—
63#95×C61—22no—
64#95×C61—42no—
65C24×C61—21no—
66C24×C61C2×D411yescharacteristic
67C2×Q8×C61—22no—
68C2×Q8×C61—41no—
69C2×Q8×C61—41no—
70C2×D4×C61—22no—
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—
79C22×C4×C61—21no—
80C22×C4×C61—21no—
81C22×C4×C61—22no—
82C22×C4×C61—22no—
83C22×C4×C61—21no—
84C22×C4×C61—21no—
85C22×C4×C61—24no—
86C22×C4×C61—21no—
87C22×C4×C61—21no—
88C22×C4×C61—21no—
89C22×C4×C61—41no—
90C22×C4×C61—41no—
91C22×C4×C61—41no—
92C22×C4×C61—41no—
93C22×C4×C61—42no—
94C22×C4×C61—42no—
95C22×C4×C61—42no—
96C22×C4×C61—42no—
97C22×C4×C61—42no—
98C22×C4×C61—42no—
99C22×C4×C61C22⋊C411yescharacteristic
100C22×C4×C61C22⋊C411yescharacteristic
101C22×C4×C61C22⋊C411yescharacteristic
102C22×C4×C61C22⋊C411yescharacteristic
103C22×C4×C61C22×C411yescharacteristic
104C22×C4×C61C2×D411yescharacteristic
105C22×C4×C61C2×D412yes—
106C22×C4×C61#4112yes—
107C2×C8×C61—24no—
108C2×C8×C61—42no—
109C2×C8×C61—42no—
110C4⋊C4×C61—22no—
111C4⋊C4×C61—22no—
112C4⋊C4×C61—48no—
113C4⋊C4×C61—42no—
114C22⋊C4×C61—42no—
115C22⋊C4×C61—42no—
116C22⋊C4×C61—41no—
117C22⋊C4×C61—41no—
118C22⋊C4×C61—42no—
119C22⋊C4×C61—42no—
120C22⋊C4×C61—42no—
121C42×C61—22no—
122C42×C61—22no—
123C42×C61—41no—
124C42×C61—41no—
125C23×C61—21no—
126C23×C61—21no—
127C23×C61—21no—
128C23×C61—21no—
129C23×C61—41no—
130C23×C61—41no—
131C23×C61—41no—
132C23×C61—41no—
133C23×C61—41no—
134C23×C61—41no—
135C23×C61—41no—
136C23×C61C2×C22⋊C411yescharacteristic
137C23×C61#12411yescharacteristic
138C23×C61#12711yescharacteristic
139C23×C61AGL(1,ℤ/8)11yescharacteristic
140C23×C61AGL(1,ℤ/8)11yescharacteristic
141C23×C61#13711yescharacteristic
142C23×C61#13711yescharacteristic
143Q8×C61—82no—
144D4×C61—82no—
145D4×C61—81no—
146D4×C61—81no—
147D4×C61—81no—
148D4×C61—81no—
149C2×C4×C61—24no—
150C2×C4×C61—24no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61—21no—
155C2×C4×C61—21no—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61—21no—
160C2×C4×C61—21no—
161C2×C4×C61—21no—
162C2×C4×C61—21no—
163C2×C4×C61—21no—
164C2×C4×C61—21no—
165C2×C4×C61—42no—
166C2×C4×C61—42no—
167C2×C4×C61—42no—
168C2×C4×C61—42no—
169C2×C4×C61—44no—
170C2×C4×C61—44no—
171C2×C4×C61—44no—
172C2×C4×C61—41no—
173C2×C4×C61—41no—
174C2×C4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61—41no—
177C2×C4×C61—41no—
178C2×C4×C61—41no—
179C2×C4×C61—41no—
180C2×C4×C61—41no—
181C2×C4×C61—82no—
182C2×C4×C61—82no—
183C2×C4×C61—82no—
184C2×C4×C61—82no—
185C2×C4×C61#9912yes—
186C2×C4×C61#10412yes—
187C2×C4×C61C4×D412yes—
188C2×C4×C61#12112yes—
189C8×C61—44no—
190#9682C6111yesmaximal, characteristic, direct product factor, Sylow
191C22×C61—21no—
192C22×C61—21no—
193C22×C61—21no—
194C22×C61—21no—
195C22×C61—21no—
196C22×C61—21no—
197C22×C61—21no—
198C22×C61—21no—
199C22×C61—21no—
200C22×C61—21no—
201C22×C61—21no—
202C22×C61—21no—
203C22×C61—81no—
204C22×C61—81no—
205C22×C61—81no—
206C22×C61—81no—
207C22×C61—81no—
208C22×C61—81no—
209C22×C61—81no—
210C22×C61#39011yescharacteristic
211C22×C61C2×#9911yescharacteristic
212C22×C61#41011yescharacteristic
213C22×C61#41711yescharacteristic
214C22×C61#41711yescharacteristic
215C22×C61C2×#10411yescharacteristic
216C22×C61#42111yescharacteristic
217C22×C61#48911yescharacteristic
218C22×C61#48911yescharacteristic
219C22×C61#49611yescharacteristic
220C22×C61#49711yescharacteristic
221C4×C61—22no—
222C4×C61—22no—
223C4×C61—22no—
224C4×C61—22no—
225C4×C61—41no—
226C4×C61—41no—
227C4×C61—84no—
228C4×C61—81no—
229C4×C61—81no—
230C4×C61—81no—
231#2850C2×C6111yescharacteristic
232#1749C2×C6111yescharacteristic, complemented
233C2×#328C2×C6112yescomplemented
234C2×#327C2×C6112yes—
235C4⋊#95C2×C6111yescharacteristic, complemented
236C2×C61—21no—
237C2×C61—21no—
238C2×C61—21no—
239C2×C61—21no—
240C2×C61—161no—
241C2×C61#150411yescharacteristic
242C2×C61#150911yescharacteristic
243C2×C61#151211yescharacteristic
244C2×C61#151311yescharacteristic
245C2×C61#195911yescharacteristic
246C2×C61#196411yescharacteristic
247C2×C61#198011yescharacteristic
248C2×#124C4×C6111yescharacteristic, complemented
249C2×C22⋊Q8C22×C6111yescharacteristic
250C2×#121C22×C6111yescharacteristic
251C22×C4⋊C4—21no—
252C22×C42C22×C6111yescharacteristic
253C2×C22⋊C8C22×C6112yes—
254C2×#97—21no—
255#391C4×C6111yescharacteristic, complemented
256#390C4×C6111yescharacteristic, complemented
257#388—21no—
258#388—21no—
259#386—21no—
260#386—21no—
261#382C4×C6111yescharacteristic, complemented
262C2×#95—21no—
263C2×#95C22×C6112yes—
264#336—21no—
265#328—24no—
266#327—24no—
267C61#968211yescharacteristic, direct product factor, Sylow
268C22×Q8C2×C4×C6111yescharacteristic
269C22×D4—21no—
270C22×D4C2×C4×C6111yescharacteristic
271C23×C4—22no—
272C23×C4D4×C6111yescharacteristic
273C23×C4D4×C6111yescharacteristic
274C23×C4C23×C6111yescharacteristic
275C22×C8—22no—
276#124—42no—
277C22⋊Q8—22no—
278C22⋊Q8—22no—
279#121—22no—
280#121—22no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—42no—
285C2×C4⋊C4C2×C4×C6111yescharacteristic
286C2×C4⋊C4C2×C4×C6111yescharacteristic
287C2×C22⋊C4—21no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—21no—
293C2×C42—42no—
294C2×C42C2×C4×C6111yescharacteristic
295C2×C42C2×C4×C6111yescharacteristic
296C2×C42D4×C6111yescharacteristic
297C2×C42D4×C6111yescharacteristic
298C22⋊C8—22no—
299C22⋊C8D4×C6114yes—
300#97—42no—
301#95—21no—
302#95—21no—
303#95—21no—
304#95—21no—
305#95—22no—
306#95—22no—
307#95—42no—
308C24—21no—
309C24C2×D4×C6111yescharacteristic
310C2×Q8—22no—
311C2×Q8—41no—
312C2×Q8—41no—
313C2×D4—22no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—24no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4—41no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4—42no—
339C22×C4—42no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4C22⋊C4×C6111yescharacteristic
343C22×C4C22⋊C4×C6111yescharacteristic
344C22×C4C22⋊C4×C6111yescharacteristic
345C22×C4C22⋊C4×C6111yescharacteristic
346C22×C4C22×C4×C6111yescharacteristic
347C22×C4C2×D4×C6111yescharacteristic
348C22×C4C2×D4×C6112yes—
349C22×C4#41×C6112yes—
350C2×C8—24no—
351C2×C8—42no—
352C2×C8—42no—
353C4⋊C4—22no—
354C4⋊C4—22no—
355C4⋊C4—48no—
356C4⋊C4—42no—
357C22⋊C4—42no—
358C22⋊C4—42no—
359C22⋊C4—41no—
360C22⋊C4—41no—
361C22⋊C4—42no—
362C22⋊C4—42no—
363C22⋊C4—42no—
364C42—22no—
365C42—22no—
366C42—41no—
367C42—41no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—41no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23C2×C22⋊C4×C6111yescharacteristic
380C23#124×C6111yescharacteristic
381C23#127×C6111yescharacteristic
382C23AGL(1,ℤ/8)×C6111yescharacteristic
383C23AGL(1,ℤ/8)×C6111yescharacteristic
384C23#137×C6111yescharacteristic
385C23#137×C6111yescharacteristic
386Q8—82no—
387D4—82no—
388D4—81no—
389D4—81no—
390D4—81no—
391D4—81no—
392C2×C4—24no—
393C2×C4—24no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—44no—
413C2×C4—44no—
414C2×C4—44no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—82no—
425C2×C4—82no—
426C2×C4—82no—
427C2×C4—82no—
428C2×C4#99×C6112yes—
429C2×C4#104×C6112yes—
430C2×C4C4×D4×C6112yes—
431C2×C4#121×C6112yes—
432C8—44no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—81no—
446C22—81no—
447C22—81no—
448C22—81no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22C61×#39011yescharacteristic
453C22C2×#99×C6111yescharacteristic
454C22C61×#41011yescharacteristic
455C22C61×#41711yescharacteristic
456C22C61×#41711yescharacteristic
457C22C2×#104×C6111yescharacteristic
458C22C61×#42111yescharacteristic
459C22C61×#48911yescharacteristic
460C22C61×#48911yescharacteristic
461C22C61×#49611yescharacteristic
462C22C61×#49711yescharacteristic
463C4—22no—
464C4—22no—
465C4—22no—
466C4—22no—
467C4—41no—
468C4—41no—
469C4—84no—
470C4—81no—
471C4—81no—
472C4—81no—
473C2—21no—
474C2—21no—
475C2—21no—
476C2—21no—
477C2—161no—
478C2C61×#150411yescharacteristic
479C2C61×#150911yescharacteristic
480C2C61×#151211yescharacteristic
481C2C61×#151311yescharacteristic
482C2C61×#195911yescharacteristic
483C2C61×#196411yescharacteristic
484C2C61×#198011yescharacteristic
subgroupG/H
center, socleC23×C61C2×C22⋊C4
commutatorC22×C4C22×C4×C61
Frattini, cosocleC23×C4C23×C61
prime radicalC2×#121×C61C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C61 ◁ C22×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#1749C2semidirect
3. C2×C61×#328C2semidirect
5. C61×C4⋊#95C2semidirect
6. C2×#124×C61C4semidirect
13. C61×#391C4semidirect
14. C61×#390C4semidirect
19. C61×#382C4semidirect
190. #9682C61direct (N × H)
232. #1749C2×C61semidirect
233. C2×#328C2×C61semidirect
235. C4⋊#95C2×C61semidirect
248. C2×#124C4×C61semidirect
255. #391C4×C61semidirect
256. #390C4×C61semidirect
261. #382C4×C61semidirect
267. C61#9682direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#28502
C61×#17492
C2×C61×#3282
C2×C61×#3272
C61×C4⋊#952
#968261