Finite Group Databasebeta

← C61×#13326 #29516759

Subgroups — C61×#13326 #29516759

Order 15616.

614 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×SD32×C61C211yesmaximal, characteristic, complemented
2C22×D16×C61C211yesmaximal, characteristic
3C2×C61×#495C211yesmaximal, characteristic, complemented
4C2×C61×#358C211yesmaximal, characteristic, complemented
5C2×C61×#357C211yesmaximal, characteristic, complemented
6C61×#1970C211yesmaximal, characteristic, complemented
7C61×#1374C211yesmaximal, characteristic, complemented
8C22×Q16×C61C2211yescharacteristic
9C22×SD16×C61—21no—
10C22×D8×C61C2211yescharacteristic
11C22×D8×C61C2211yescharacteristic
12C2×#124×C61—21no—
13C2×SD32×C61—22no—
14C2×SD32×C61—22no—
15C2×SD32×C61—22no—
16C2×D16×C61—22no—
17C2×D16×C61—22no—
18C2×D16×C61—22no—
19C22×C16×C61C2211yescharacteristic
20C22×C16×C61C2211yescharacteristic
21C61×#495—22no—
22C61×#495—22no—
23C2×#107×C61C2211yescharacteristic
24C2×#102×C61—21no—
25C2×C4×C8×C61C2211yescharacteristic
26C61×#390—21no—
27C61×#358—22no—
28C61×#357—22no—
29C22×Q8×C61—21no—
30C22×D4×C61—21no—
31C22×D4×C61—21no—
32C2×Q16×C61—21no—
33C2×Q16×C61—21no—
34C2×Q16×C61—21no—
35C2×Q16×C61—21no—
36C2×Q16×C61—21no—
37C2×Q16×C61D412yes—
38C2×SD16×C61—24no—
39C2×SD16×C61—42no—
40C2×SD16×C61—42no—
41C2×D8×C61—21no—
42C2×D8×C61—21no—
43C2×D8×C61—21no—
44C2×D8×C61—21no—
45C2×D8×C61—21no—
46C2×D8×C61—21no—
47C2×D8×C61—21no—
48C2×D8×C61—21no—
49C2×D8×C61—21no—
50C2×D8×C61—21no—
51C2×D8×C61D412yes—
52C2×D8×C61D412yes—
53C22×C8×C61D411yescharacteristic
54C22×C8×C61C2311yescharacteristic
55#124×C61—24no—
56#124×C61—42no—
57C2×C4⋊C4×C61—21no—
58C2×C22⋊C4×C61—42no—
59C2×C22⋊C4×C61—42no—
60C2×C42×C61D411yescharacteristic
61SD32×C61—28no—
62D16×C61—28no—
63C2×C16×C61—21no—
64C2×C16×C61—21no—
65C2×C16×C61—21no—
66C2×C16×C61—21no—
67C2×C16×C61D412yes—
68C2×C16×C61D412yes—
69#107×C61—21no—
70#107×C61—21no—
71#102×C61—42no—
72C4×C8×C61—21no—
73C4×C8×C61—21no—
74C24×C61—41no—
75C24×C61—41no—
76C2×Q8×C61—22no—
77C2×Q8×C61—41no—
78C2×Q8×C61—41no—
79C2×Q8×C61—41no—
80C2×Q8×C61—41no—
81C2×Q8×C61—41no—
82C2×D4×C61—22no—
83C2×D4×C61—22no—
84C2×D4×C61—41no—
85C2×D4×C61—41no—
86C2×D4×C61—41no—
87C2×D4×C61—41no—
88C2×D4×C61—41no—
89C2×D4×C61—41no—
90C2×D4×C61—41no—
91C2×D4×C61—41no—
92C2×D4×C61—41no—
93C2×D4×C61—41no—
94C22×C4×C61—41no—
95C22×C4×C61—41no—
96C22×C4×C61D812yes—
97C22×C4×C61C2×D411yescharacteristic
98Q16×C61—22no—
99Q16×C61—22no—
100Q16×C61—41no—
101Q16×C61—41no—
102SD16×C61—48no—
103D8×C61—22no—
104D8×C61—22no—
105D8×C61—22no—
106D8×C61—22no—
107D8×C61—41no—
108D8×C61—41no—
109D8×C61—41no—
110D8×C61—41no—
111C2×C8×C61—21no—
112C2×C8×C61—21no—
113C2×C8×C61D812yes—
114C2×C8×C61C2×D411yescharacteristic
115C2×C8×C61C2×D411yescharacteristic
116C2×C8×C61C2×D411yescharacteristic
117C2×C8×C61C2×D411yescharacteristic
118C2×C8×C61C2×D411yescharacteristic
119C2×C8×C61#4111yescharacteristic
120C4⋊C4×C61—41no—
121C4⋊C4×C61—41no—
122C22⋊C4×C61—48no—
123C22⋊C4×C61—84no—
124C42×C61—21no—
125C42×C61—21no—
126C16×C61—22no—
127C16×C61—22no—
128C23×C61—42no—
129C23×C61—42no—
130C23×C61—81no—
131C23×C61—81no—
132C23×C61—81no—
133C23×C61—81no—
134C23×C61—82no—
135C23×C61—82no—
136C23×C61—82no—
137C23×C61—82no—
138C23×C61C2×D811yescharacteristic
139Q8×C61—42no—
140Q8×C61—42no—
141Q8×C61—81no—
142Q8×C61—81no—
143D4×C61—42no—
144D4×C61—42no—
145D4×C61—42no—
146D4×C61—42no—
147D4×C61—81no—
148D4×C61—81no—
149D4×C61—81no—
150D4×C61—81no—
151C2×C4×C61—22no—
152C2×C4×C61—22no—
153C2×C4×C61—22no—
154C2×C4×C61—42no—
155C2×C4×C61—81no—
156C2×C4×C61—81no—
157C2×C4×C61—81no—
158C2×C4×C61—82no—
159C2×C4×C61#12011yescharacteristic
160C2×C4×C61#12111yescharacteristic
161C2×C4×C61#12711yescharacteristic
162C2×C4×C61C2×D811yescharacteristic
163C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
165C8×C61—22no—
166C8×C61#12011yescharacteristic
167C8×C61#12011yescharacteristic
168C8×C61#12111yescharacteristic
169C8×C61#12111yescharacteristic
170#13326C6111yesmaximal, characteristic, direct product factor, Sylow
171C22×C61—84no—
172C22×C61—84no—
173C22×C61—82no—
174C22×C61—82no—
175C22×C61—162no—
176C22×C61—162no—
177C22×C61—161no—
178C22×C61—161no—
179C22×C61—161no—
180C22×C61—161no—
181C22×C61#44711yescharacteristic
182C22×C61#45911yescharacteristic
183C22×C61#49311yescharacteristic
184C22×C61#50812yes—
185C22×C61#50912yes—
186C4×C61—42no—
187C4×C61—82no—
188C4×C61—161no—
189C4×C61#39211yescharacteristic
190C4×C61#44711yescharacteristic
191C4×C61#45911yescharacteristic
192C4×C61#49611yescharacteristic
193C22×SD32C2×C6111yescharacteristic, complemented
194C22×D16C2×C6111yescharacteristic
195C2×#495C2×C6111yescharacteristic, complemented
196C2×#358C2×C6111yescharacteristic, complemented
197C2×#357C2×C6111yescharacteristic, complemented
198#1970C2×C6111yescharacteristic, complemented
199#1374C2×C6111yescharacteristic, complemented
200C2×C61—162no—
201C2×C61—162no—
202C2×C61#201111yescharacteristic
203C2×C61#218612yes—
204C2×C61#221012yes—
205C2×C61#224911yescharacteristic
206C2×C61#225011yescharacteristic
207C22×Q16C22×C6111yescharacteristic
208C22×SD16—21no—
209C22×D8C22×C6111yescharacteristic
210C22×D8C22×C6111yescharacteristic
211C2×#124—21no—
212C2×SD32—22no—
213C2×SD32—22no—
214C2×SD32—22no—
215C2×D16—22no—
216C2×D16—22no—
217C2×D16—22no—
218C22×C16C22×C6111yescharacteristic
219C22×C16C22×C6111yescharacteristic
220#495—22no—
221#495—22no—
222C2×#107C22×C6111yescharacteristic
223C2×#102—21no—
224C2×C4×C8C22×C6111yescharacteristic
225#390—21no—
226#358—22no—
227#357—22no—
228C61#1332611yescharacteristic, direct product factor, Sylow
229C22×Q8—21no—
230C22×D4—21no—
231C22×D4—21no—
232C2×Q16—21no—
233C2×Q16—21no—
234C2×Q16—21no—
235C2×Q16—21no—
236C2×Q16—21no—
237C2×Q16D4×C6112yes—
238C2×SD16—24no—
239C2×SD16—42no—
240C2×SD16—42no—
241C2×D8—21no—
242C2×D8—21no—
243C2×D8—21no—
244C2×D8—21no—
245C2×D8—21no—
246C2×D8—21no—
247C2×D8—21no—
248C2×D8—21no—
249C2×D8—21no—
250C2×D8—21no—
251C2×D8D4×C6112yes—
252C2×D8D4×C6112yes—
253C22×C8D4×C6111yescharacteristic
254C22×C8C23×C6111yescharacteristic
255#124—24no—
256#124—42no—
257C2×C4⋊C4—21no—
258C2×C22⋊C4—42no—
259C2×C22⋊C4—42no—
260C2×C42D4×C6111yescharacteristic
261SD32—28no—
262D16—28no—
263C2×C16—21no—
264C2×C16—21no—
265C2×C16—21no—
266C2×C16—21no—
267C2×C16D4×C6112yes—
268C2×C16D4×C6112yes—
269#107—21no—
270#107—21no—
271#102—42no—
272C4×C8—21no—
273C4×C8—21no—
274C24—41no—
275C24—41no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×D4—22no—
283C2×D4—22no—
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—
293C2×D4—41no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4D8×C6112yes—
297C22×C4C2×D4×C6111yescharacteristic
298Q16—22no—
299Q16—22no—
300Q16—41no—
301Q16—41no—
302SD16—48no—
303D8—22no—
304D8—22no—
305D8—22no—
306D8—22no—
307D8—41no—
308D8—41no—
309D8—41no—
310D8—41no—
311C2×C8—21no—
312C2×C8—21no—
313C2×C8D8×C6112yes—
314C2×C8C2×D4×C6111yescharacteristic
315C2×C8C2×D4×C6111yescharacteristic
316C2×C8C2×D4×C6111yescharacteristic
317C2×C8C2×D4×C6111yescharacteristic
318C2×C8C2×D4×C6111yescharacteristic
319C2×C8#41×C6111yescharacteristic
320C4⋊C4—41no—
321C4⋊C4—41no—
322C22⋊C4—48no—
323C22⋊C4—84no—
324C42—21no—
325C42—21no—
326C16—22no—
327C16—22no—
328C23—42no—
329C23—42no—
330C23—81no—
331C23—81no—
332C23—81no—
333C23—81no—
334C23—82no—
335C23—82no—
336C23—82no—
337C23—82no—
338C23C2×D8×C6111yescharacteristic
339Q8—42no—
340Q8—42no—
341Q8—81no—
342Q8—81no—
343D4—42no—
344D4—42no—
345D4—42no—
346D4—42no—
347D4—81no—
348D4—81no—
349D4—81no—
350D4—81no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—42no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—82no—
359C2×C4#120×C6111yescharacteristic
360C2×C4#121×C6111yescharacteristic
361C2×C4#127×C6111yescharacteristic
362C2×C4C2×D8×C6111yescharacteristic
363C2×C4AGL(1,ℤ/8)×C6111yescharacteristic
364C2×C4AGL(1,ℤ/8)×C6111yescharacteristic
365C8—22no—
366C8#120×C6111yescharacteristic
367C8#120×C6111yescharacteristic
368C8#121×C6111yescharacteristic
369C8#121×C6111yescharacteristic
370C22—82no—
371C22—82no—
372C22—84no—
373C22—84no—
374C22—162no—
375C22—162no—
376C22—161no—
377C22—161no—
378C22—161no—
379C22—161no—
380C22C61×#44711yescharacteristic
381C22C61×#45911yescharacteristic
382C22C61×#49311yescharacteristic
383C22C61×#50812yes—
384C22C61×#50912yes—
385C4—42no—
386C4—82no—
387C4—161no—
388C4C61×#39211yescharacteristic
389C4C61×#44711yescharacteristic
390C4C61×#45911yescharacteristic
391C4C61×#49611yescharacteristic
392C2—162no—
393C2—162no—
394C2C61×#201111yescharacteristic
395C2C61×#218612yes—
396C2C61×#221012yes—
397C2C61×#224911yescharacteristic
398C2C61×#225011yescharacteristic
subgroupG/H
center, socleC23×C61C2×D8
commutator, Frattini, cosocleC22×C8C23×C61
prime radicalC22×D16×C61C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C2×C42×C61 ◁ C2×C4×C8×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×SD32×C61C2semidirect
3. C2×C61×#495C2semidirect
4. C2×C61×#358C2semidirect
5. C2×C61×#357C2semidirect
6. C61×#1970C2semidirect
7. C61×#1374C2semidirect
170. #13326C61direct (N × H)
193. C22×SD32C2×C61semidirect
195. C2×#495C2×C61semidirect
196. C2×#358C2×C61semidirect
197. C2×#357C2×C61semidirect
198. #1970C2×C61semidirect
199. #1374C2×C61semidirect
228. C61#13326direct (N × H)

Maximal subgroups

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

subgroupindex
C22×SD32×C612
C22×D16×C612
C2×C61×#4952
C2×C61×#3582
C2×C61×#3572
C61×#19702
C61×#13742
#1332661