Finite Group Databasebeta

← C61×#18735 #29522168

Subgroups — C61×#18735 #29522168

Order 15616.

876 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3550C211yesmaximal, characteristic
2C61×#3229C211yesmaximal, characteristic, complemented
3C61×#3206C211yesmaximal, characteristic
4C61×#3165C211yesmaximal, characteristic, complemented
5C61×#1651C214yesmaximal, complemented
6C61×#1650C214yesmaximal, complemented
7C61×#1544C211yesmaximal, characteristic, complemented
8C61×#1485C211yesmaximal, characteristic, complemented
9C61×#1484C211yesmaximal, characteristic
10C61×#563—22no—
11C61×#559—21no—
12Q82×C61—21no—
13C61×#556—21no—
14C61×#556C2212yes—
15D4×Q8×C61—21no—
16D4×Q8×C61C2212yes—
17C61×#542—22no—
18C61×#542—22no—
19C61×#536—22no—
20C61×#533C2211yescharacteristic
21C61×#533C2211yescharacteristic
22C61×#532C2211yescharacteristic
23C2×C4⋊Q8×C61C2211yescharacteristic
24C61×#501—22no—
25C61×#500C2212yes—
26C61×#498—21no—
27C61×#498C2212yes—
28C61×#492—21no—
29C61×#487—21no—
30C61×#487—21no—
31C61×#483—22no—
32C61×#475C2214yes—
33C61×#461C2214yes—
34C61×#448—22no—
35C61×#431C2211yescharacteristic
36C61×#431C2211yescharacteristic
37C61×#428—22no—
38C4×M16×C61C2211yescharacteristic
39C61×#332C2212yes—
40C61×#332C2212yes—
41C61×Q8⋊C8C2214yes—
42C61×D4⋊C8C2214yes—
43C2×#41×C61—21no—
44C22×Q8×C61—22no—
45C22×Q8×C61—21no—
46C2×SD16×C61—24no—
47C2×M16×C61—21no—
48C4⋊Q8×C61—24no—
49C4⋊Q8×C61—22no—
50C4⋊Q8×C61—22no—
51C4⋊Q8×C61—21no—
52C4⋊Q8×C61—21no—
53C4⋊Q8×C61—21no—
54C4⋊Q8×C61D411yescharacteristic
55C4⋊Q8×C61D411yescharacteristic
56C4⋊Q8×C61D411yescharacteristic
57C4⋊Q8×C61C2312yes—
58C4⋊Q8×C61C2311yescharacteristic
59C4⋊Q8×C61C2311yescharacteristic
60#127×C61D411yescharacteristic
61#126×C61—24no—
62#126×C61—24no—
63#125×C61—21no—
64#125×C61D412yes—
65#124×C61—24no—
66#124×C61—22no—
67#124×C61—22no—
68#124×C61—21no—
69#123×C61—24no—
70#123×C61—24no—
71C22⋊Q8×C61—24no—
72C22⋊Q8×C61—22no—
73C22⋊Q8×C61—21no—
74C22⋊Q8×C61—21no—
75C22⋊Q8×C61—21no—
76C22⋊Q8×C61—22no—
77C22⋊Q8×C61—24no—
78C22⋊Q8×C61D412yes—
79#121×C61—21no—
80#121×C61D412yes—
81C4×Q8×C61—22no—
82C4×Q8×C61—22no—
83C4×Q8×C61—21no—
84C4×Q8×C61—21no—
85C4×Q8×C61—21no—
86C4×Q8×C61C2312yes—
87C4×D4×C61—22no—
88C4×D4×C61—22no—
89C4×D4×C61—21no—
90C4×D4×C61C2312yes—
91#117×C61—21no—
92#117×C61—22no—
93#117×C61D412yes—
94C2×C4⋊C4×C61—21no—
95C2×C4⋊C4×C61—21no—
96C2×C42×C61C2311yescharacteristic
97#107×C61—24no—
98#106×C61—24no—
99#106×C61—24no—
100C4⋊C8×C61C2312yes—
101C4⋊C8×C61C2312yes—
102#103×C61—24no—
103#103×C61—24no—
104C22⋊C8×C61—21no—
105C22⋊C8×C61—21no—
106#97×C61—21no—
107C4×C8×C61—21no—
108C4×C8×C61—21no—
109C4×C8×C61C2312yes—
110#41×C61—82no—
111C2×Q8×C61—24no—
112C2×Q8×C61—21no—
113C2×Q8×C61—21no—
114C2×Q8×C61—21no—
115C2×Q8×C61—21no—
116C2×Q8×C61—22no—
117C2×Q8×C61—41no—
118C2×Q8×C61—82no—
119C2×Q8×C61—84no—
120C2×Q8×C61C2×D412yes—
121C2×D4×C61—22no—
122C2×D4×C61—21no—
123C2×D4×C61—21no—
124C2×D4×C61C2×D412yes—
125C22×C4×C61—24no—
126C22×C4×C61—22no—
127C22×C4×C61—41no—
128C22×C4×C61C2×D411yescharacteristic
129C22×C4×C61C2×D411yescharacteristic
130C22×C4×C61C2×D411yescharacteristic
131SD16×C61—84no—
132M16×C61—24no—
133C2×C8×C61—22no—
134C2×C8×C61—22no—
135C2×C8×C61—22no—
136C4⋊C4×C61—24no—
137C4⋊C4×C61—24no—
138C4⋊C4×C61—21no—
139C4⋊C4×C61—21no—
140C4⋊C4×C61—21no—
141C4⋊C4×C61—21no—
142C4⋊C4×C61—22no—
143C4⋊C4×C61—22no—
144C4⋊C4×C61—22no—
145C4⋊C4×C61—21no—
146C4⋊C4×C61—21no—
147C4⋊C4×C61—22no—
148C4⋊C4×C61—22no—
149C4⋊C4×C61—22no—
150C4⋊C4×C61—41no—
151C4⋊C4×C61—41no—
152C4⋊C4×C61C2×D412yes—
153C4⋊C4×C61C2×D412yes—
154C4⋊C4×C61C2×D412yes—
155C4⋊C4×C61C2×D412yes—
156C22⋊C4×C61—24no—
157C22⋊C4×C61—24no—
158C22⋊C4×C61—24no—
159C22⋊C4×C61—22no—
160C22⋊C4×C61—22no—
161C22⋊C4×C61—22no—
162C22⋊C4×C61—22no—
163C42×C61—24no—
164C42×C61—22no—
165C42×C61—22no—
166C42×C61C2×D411yescharacteristic
167C42×C61C2×D411yescharacteristic
168C42×C61C2×D411yescharacteristic
169C42×C61C2411yescharacteristic
170C23×C61—22no—
171C23×C61#12011yescharacteristic
172Q8×C61—24no—
173Q8×C61—42no—
174Q8×C61—42no—
175Q8×C61—42no—
176Q8×C61—44no—
177Q8×C61—81no—
178Q8×C61—82no—
179Q8×C61—84no—
180D4×C61—24no—
181D4×C61—42no—
182D4×C61—81no—
183D4×C61—82no—
184C2×C4×C61—22no—
185C2×C4×C61—22no—
186C2×C4×C61—22no—
187C2×C4×C61—22no—
188C2×C4×C61—22no—
189C2×C4×C61—22no—
190C2×C4×C61—22no—
191C2×C4×C61—22no—
192C2×C4×C61—44no—
193C2×C4×C61—42no—
194C2×C4×C61—84no—
195C2×C4×C61—82no—
196C2×C4×C61#12011yescharacteristic
197C2×C4×C61#12011yescharacteristic
198C2×C4×C61#12011yescharacteristic
199C2×C4×C61C22×D411yescharacteristic
200C2×C4×C61C22×D411yescharacteristic
201C2×C4×C61C22×D411yescharacteristic
202C8×C61—24no—
203C8×C61—42no—
204C8×C61—42no—
205#18735C6111yesmaximal, characteristic, direct product factor, Sylow
206C22×C61—21no—
207C22×C61—21no—
208C22×C61—21no—
209C22×C61—42no—
210C22×C61—42no—
211C22×C61—42no—
212C22×C61C2×#12011yescharacteristic
213C4×C61—21no—
214C4×C61—21no—
215C4×C61—21no—
216C4×C61—42no—
217C4×C61—42no—
218C4×C61—42no—
219C4×C61—42no—
220C4×C61—42no—
221C4×C61—82no—
222C4×C61#45612yes—
223C4×C61#57712yes—
224C4×C61#57712yes—
225#3550C2×C6111yescharacteristic
226#3229C2×C6111yescharacteristic, complemented
227#3206C2×C6111yescharacteristic
228#3165C2×C6111yescharacteristic, complemented
229#1651C2×C6114yescomplemented
230#1650C2×C6114yescomplemented
231#1544C2×C6111yescharacteristic, complemented
232#1485C2×C6111yescharacteristic, complemented
233#1484C2×C6111yescharacteristic
234C2×C61—41no—
235C2×C61—82no—
236C2×C61#300911yescharacteristic
237C2×C61#301011yescharacteristic
238C2×C61C2×#45611yescharacteristic
239#563—22no—
240#559—21no—
241Q82—21no—
242#556—21no—
243#556C22×C6112yes—
244D4×Q8—21no—
245D4×Q8C22×C6112yes—
246#542—22no—
247#542—22no—
248#536—22no—
249#533C22×C6111yescharacteristic
250#533C22×C6111yescharacteristic
251#532C22×C6111yescharacteristic
252C2×C4⋊Q8C22×C6111yescharacteristic
253#501—22no—
254#500C22×C6112yes—
255#498—21no—
256#498C22×C6112yes—
257#492—21no—
258#487—21no—
259#487—21no—
260#483—22no—
261#475C22×C6114yes—
262#461C22×C6114yes—
263#448—22no—
264#431C22×C6111yescharacteristic
265#431C22×C6111yescharacteristic
266#428—22no—
267C4×M16C22×C6111yescharacteristic
268#332C22×C6112yes—
269#332C22×C6112yes—
270Q8⋊C8C22×C6114yes—
271D4⋊C8C22×C6114yes—
272C61#1873511yescharacteristic, direct product factor, Sylow
273C2×#41—21no—
274C22×Q8—22no—
275C22×Q8—21no—
276C2×SD16—24no—
277C2×M16—21no—
278C4⋊Q8—24no—
279C4⋊Q8—22no—
280C4⋊Q8—22no—
281C4⋊Q8—21no—
282C4⋊Q8—21no—
283C4⋊Q8—21no—
284C4⋊Q8D4×C6111yescharacteristic
285C4⋊Q8D4×C6111yescharacteristic
286C4⋊Q8D4×C6111yescharacteristic
287C4⋊Q8C23×C6112yes—
288C4⋊Q8C23×C6111yescharacteristic
289C4⋊Q8C23×C6111yescharacteristic
290#127D4×C6111yescharacteristic
291#126—24no—
292#126—24no—
293#125—21no—
294#125D4×C6112yes—
295#124—24no—
296#124—22no—
297#124—22no—
298#124—21no—
299#123—24no—
300#123—24no—
301C22⋊Q8—24no—
302C22⋊Q8—22no—
303C22⋊Q8—21no—
304C22⋊Q8—21no—
305C22⋊Q8—21no—
306C22⋊Q8—22no—
307C22⋊Q8—24no—
308C22⋊Q8D4×C6112yes—
309#121—21no—
310#121D4×C6112yes—
311C4×Q8—22no—
312C4×Q8—22no—
313C4×Q8—21no—
314C4×Q8—21no—
315C4×Q8—21no—
316C4×Q8C23×C6112yes—
317C4×D4—22no—
318C4×D4—22no—
319C4×D4—21no—
320C4×D4C23×C6112yes—
321#117—21no—
322#117—22no—
323#117D4×C6112yes—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C42C23×C6111yescharacteristic
327#107—24no—
328#106—24no—
329#106—24no—
330C4⋊C8C23×C6112yes—
331C4⋊C8C23×C6112yes—
332#103—24no—
333#103—24no—
334C22⋊C8—21no—
335C22⋊C8—21no—
336#97—21no—
337C4×C8—21no—
338C4×C8—21no—
339C4×C8C23×C6112yes—
340#41—82no—
341C2×Q8—24no—
342C2×Q8—21no—
343C2×Q8—21no—
344C2×Q8—21no—
345C2×Q8—21no—
346C2×Q8—22no—
347C2×Q8—41no—
348C2×Q8—82no—
349C2×Q8—84no—
350C2×Q8C2×D4×C6112yes—
351C2×D4—22no—
352C2×D4—21no—
353C2×D4—21no—
354C2×D4C2×D4×C6112yes—
355C22×C4—24no—
356C22×C4—22no—
357C22×C4—41no—
358C22×C4C2×D4×C6111yescharacteristic
359C22×C4C2×D4×C6111yescharacteristic
360C22×C4C2×D4×C6111yescharacteristic
361SD16—84no—
362M16—24no—
363C2×C8—22no—
364C2×C8—22no—
365C2×C8—22no—
366C4⋊C4—24no—
367C4⋊C4—24no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4C2×D4×C6112yes—
383C4⋊C4C2×D4×C6112yes—
384C4⋊C4C2×D4×C6112yes—
385C4⋊C4C2×D4×C6112yes—
386C22⋊C4—24no—
387C22⋊C4—24no—
388C22⋊C4—24no—
389C22⋊C4—22no—
390C22⋊C4—22no—
391C22⋊C4—22no—
392C22⋊C4—22no—
393C42—24no—
394C42—22no—
395C42—22no—
396C42C2×D4×C6111yescharacteristic
397C42C2×D4×C6111yescharacteristic
398C42C2×D4×C6111yescharacteristic
399C42C24×C6111yescharacteristic
400C23—22no—
401C23#120×C6111yescharacteristic
402Q8—24no—
403Q8—42no—
404Q8—42no—
405Q8—42no—
406Q8—44no—
407Q8—81no—
408Q8—82no—
409Q8—84no—
410D4—24no—
411D4—42no—
412D4—81no—
413D4—82no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—44no—
423C2×C4—42no—
424C2×C4—84no—
425C2×C4—82no—
426C2×C4#120×C6111yescharacteristic
427C2×C4#120×C6111yescharacteristic
428C2×C4#120×C6111yescharacteristic
429C2×C4C22×D4×C6111yescharacteristic
430C2×C4C22×D4×C6111yescharacteristic
431C2×C4C22×D4×C6111yescharacteristic
432C8—24no—
433C8—42no—
434C8—42no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—42no—
439C22—42no—
440C22—42no—
441C22C2×#120×C6111yescharacteristic
442C4—21no—
443C4—21no—
444C4—21no—
445C4—42no—
446C4—42no—
447C4—42no—
448C4—42no—
449C4—42no—
450C4—82no—
451C4C61×#45612yes—
452C4C61×#57712yes—
453C4C61×#57712yes—
454C2—41no—
455C2—82no—
456C2C61×#300911yescharacteristic
457C2C61×#301011yescharacteristic
458C2C2×C61×#45611yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC42C24×C61
prime radicalC61×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#3229C2semidirect
4. C61×#3165C2semidirect
5. C61×#1651C2semidirect
6. C61×#1650C2semidirect
7. C61×#1544C2semidirect
8. C61×#1485C2semidirect
205. #18735C61direct (N × H)
226. #3229C2×C61semidirect
228. #3165C2×C61semidirect
229. #1651C2×C61semidirect
230. #1650C2×C61semidirect
231. #1544C2×C61semidirect
232. #1485C2×C61semidirect
272. C61#18735direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#35502
C61×#32292
C61×#32062
C61×#31652
C61×#16512
C61×#16502
C61×#15442
C61×#14852
C61×#14842
#1873561