Finite Group Databasebeta

← C61×#13380 #29516813

Subgroups — C61×#13380 #29516813

Order 15616.

498 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#466C211yesmaximal, characteristic
2C2×C61×#366C211yesmaximal, characteristic, complemented
3C2×C61×#357C211yesmaximal, characteristic, complemented
4C2×C61×#357C211yesmaximal, characteristic, complemented
5C2×C61×C22⋊C16C211yesmaximal, characteristic, complemented
6C61×#1808C211yesmaximal, characteristic, complemented
7C61×#1380C211yesmaximal, characteristic, complemented
8C22×D8×C61C2211yescharacteristic
9C23×C8×C61C2211yescharacteristic
10C2×#121×C61—21no—
11C22×C16×C61C2211yescharacteristic
12C22×C16×C61C2211yescharacteristic
13C61×#466—22no—
14C61×#466—22no—
15C2×#107×C61C2211yescharacteristic
16C2×#107×C61C2211yescharacteristic
17C2×#107×C61C2211yescharacteristic
18C2×#102×C61—21no—
19C61×#380—21no—
20C61×#366—22no—
21C61×#357—22no—
22C61×#357—22no—
23C61×C22⋊C16—22no—
24C61×#340—21no—
25C22×D4×C61—21no—
26C22×D4×C61—41no—
27C23×C4×C61D411yescharacteristic
28C2×D8×C61—21no—
29C2×D8×C61—21no—
30C2×D8×C61—21no—
31C2×D8×C61—21no—
32C2×D8×C61—21no—
33C2×D8×C61D412yes—
34C22×C8×C61—21no—
35C22×C8×C61—21no—
36C22×C8×C61—21no—
37C22×C8×C61—21no—
38C22×C8×C61—21no—
39C22×C8×C61—21no—
40C22×C8×C61D411yescharacteristic
41C22×C8×C61C2311yescharacteristic
42#121×C61—24no—
43#121×C61—42no—
44C2×C4⋊C4×C61—21no—
45C2×C4⋊C4×C61—21no—
46C2×C4⋊C4×C61—21no—
47C2×C22⋊C4×C61—41no—
48C2×C22⋊C4×C61—41no—
49C2×C16×C61—21no—
50C2×C16×C61—21no—
51C2×C16×C61—21no—
52C2×C16×C61—21no—
53C2×C16×C61—21no—
54C2×C16×C61D412yescomplemented
55#107×C61—21no—
56#107×C61—21no—
57#107×C61—21no—
58#107×C61—21no—
59#107×C61—21no—
60#107×C61D412yes—
61#102×C61—24no—
62#95×C61—41no—
63C24×C61—41no—
64C24×C61D811yescharacteristic
65C2×D4×C61—22no—
66C2×D4×C61—44no—
67C2×D4×C61—41no—
68C2×D4×C61—41no—
69C2×D4×C61—41no—
70C2×D4×C61—41no—
71C2×D4×C61—41no—
72C2×D4×C61—82no—
73C2×D4×C61—82no—
74C22×C4×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61—21no—
78C22×C4×C61—21no—
79C22×C4×C61—21no—
80C22×C4×C61—41no—
81C22×C4×C61—41no—
82C22×C4×C61—41no—
83C22×C4×C61D811yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85D8×C61—22no—
86D8×C61—22no—
87D8×C61—41no—
88D8×C61—41no—
89C2×C8×C61—21no—
90C2×C8×C61—21no—
91C2×C8×C61—21no—
92C2×C8×C61—41no—
93C2×C8×C61—41no—
94C2×C8×C61—41no—
95C2×C8×C61—41no—
96C2×C8×C61C2×D411yescharacteristic
97C2×C8×C61C2×D411yescharacteristic
98C2×C8×C61C2×D411yescharacteristic
99C2×C8×C61#4111yescharacteristic
100C2×C8×C61#4111yescharacteristic
101C2×C8×C61#4111yescharacteristic
102C4⋊C4×C61—22no—
103C4⋊C4×C61—41no—
104C4⋊C4×C61—41no—
105C4⋊C4×C61—41no—
106C4⋊C4×C61—41no—
107C4⋊C4×C61—41no—
108C22⋊C4×C61—44no—
109C22⋊C4×C61—82no—
110C16×C61—22no—
111C16×C61—41no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61—21no—
115C23×C61—21no—
116C23×C61—21no—
117C23×C61—21no—
118C23×C61—42no—
119C23×C61—81no—
120C23×C61—81no—
121C23×C61—81no—
122C23×C61—81no—
123C23×C61—81no—
124C23×C61—81no—
125C23×C61D1612yes—
126C23×C61C2×D811yescharacteristic
127D4×C61—42no—
128D4×C61—42no—
129D4×C61—88no—
130D4×C61—81no—
131D4×C61—81no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—42no—
140C2×C4×C61—81no—
141C2×C4×C61—81no—
142C2×C4×C61—81no—
143C2×C4×C61—81no—
144C2×C4×C61—81no—
145C2×C4×C61—81no—
146C2×C4×C61—81no—
147C2×C4×C61—81no—
148C2×C4×C61#12011yescharacteristic
149C2×C4×C61#12111yescharacteristic
150C2×C4×C61#12311yescharacteristic
151C2×C4×C61#13511yescharacteristic
152C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C61#13711yescharacteristic
154C8×C61—41no—
155C8×C61#12111yescharacteristic
156C8×C61#12111yescharacteristic
157C8×C61#12311yescharacteristic
158C8×C61#12411yescharacteristic
159#13380C6111yesmaximal, characteristic, direct product factor, Sylow
160C22×C61—22no—
161C22×C61—22no—
162C22×C61—22no—
163C22×C61—41no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61—82no—
168C22×C61—82no—
169C22×C61—82no—
170C22×C61—161no—
171C22×C61—161no—
172C22×C61—161no—
173C22×C61—161no—
174C22×C61#44711yescharacteristic
175C22×C61#46611yescharacteristic
176C22×C61#48011yescharacteristic
177C22×C61C2×D1611yescharacteristic
178C22×C61#50811yescharacteristic
179C22×C61#50911yescharacteristic
180C22×C61#51011yescharacteristic
181C4×C61—41no—
182C4×C61—82no—
183C4×C61—161no—
184C4×C61—161no—
185C4×C61#39411yescharacteristic
186C4×C61#45211yescharacteristic
187C4×C61#46811yescharacteristic
188C4×C61#48211yescharacteristic
189C2×#466C2×C6111yescharacteristic
190C2×#366C2×C6111yescharacteristic, complemented
191C2×#357C2×C6111yescharacteristic, complemented
192C2×#357C2×C6111yescharacteristic, complemented
193C2×C22⋊C16C2×C6111yescharacteristic, complemented
194#1808C2×C6111yescharacteristic, complemented
195#1380C2×C6111yescharacteristic, complemented
196C2×C61—42no—
197C2×C61—162no—
198C2×C61#203311yescharacteristic
199C2×C61#218411yescharacteristic
200C2×C61#218911yescharacteristic
201C2×C61#221511yescharacteristic
202C2×C61#222011yescharacteristic
203C2×C61#223211yescharacteristic
204C2×C61#223411yescharacteristic
205C22×D8C22×C6111yescharacteristic
206C23×C8C22×C6111yescharacteristic
207C2×#121—21no—
208C22×C16C22×C6111yescharacteristic
209C22×C16C22×C6111yescharacteristic
210#466—22no—
211#466—22no—
212C2×#107C22×C6111yescharacteristic
213C2×#107C22×C6111yescharacteristic
214C2×#107C22×C6111yescharacteristic
215C2×#102—21no—
216#380—21no—
217#366—22no—
218#357—22no—
219#357—22no—
220C22⋊C16—22no—
221#340—21no—
222C61#1338011yescharacteristic, direct product factor, Sylow
223C22×D4—21no—
224C22×D4—41no—
225C23×C4D4×C6111yescharacteristic
226C2×D8—21no—
227C2×D8—21no—
228C2×D8—21no—
229C2×D8—21no—
230C2×D8—21no—
231C2×D8D4×C6112yes—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8D4×C6111yescharacteristic
239C22×C8C23×C6111yescharacteristic
240#121—24no—
241#121—42no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C22⋊C4—41no—
246C2×C22⋊C4—41no—
247C2×C16—21no—
248C2×C16—21no—
249C2×C16—21no—
250C2×C16—21no—
251C2×C16—21no—
252C2×C16D4×C6112yescomplemented
253#107—21no—
254#107—21no—
255#107—21no—
256#107—21no—
257#107—21no—
258#107D4×C6112yes—
259#102—24no—
260#95—41no—
261C24—41no—
262C24D8×C6111yescharacteristic
263C2×D4—22no—
264C2×D4—44no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—82no—
271C2×D4—82no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4D8×C6111yescharacteristic
282C22×C4C2×D4×C6111yescharacteristic
283D8—22no—
284D8—22no—
285D8—41no—
286D8—41no—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—21no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8C2×D4×C6111yescharacteristic
295C2×C8C2×D4×C6111yescharacteristic
296C2×C8C2×D4×C6111yescharacteristic
297C2×C8#41×C6111yescharacteristic
298C2×C8#41×C6111yescharacteristic
299C2×C8#41×C6111yescharacteristic
300C4⋊C4—22no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C22⋊C4—44no—
307C22⋊C4—82no—
308C16—22no—
309C16—41no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—42no—
317C23—81no—
318C23—81no—
319C23—81no—
320C23—81no—
321C23—81no—
322C23—81no—
323C23D16×C6112yes—
324C23C2×D8×C6111yescharacteristic
325D4—42no—
326D4—42no—
327D4—88no—
328D4—81no—
329D4—81no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4#120×C6111yescharacteristic
347C2×C4#121×C6111yescharacteristic
348C2×C4#123×C6111yescharacteristic
349C2×C4#135×C6111yescharacteristic
350C2×C4AGL(1,ℤ/8)×C6111yescharacteristic
351C2×C4#137×C6111yescharacteristic
352C8—41no—
353C8#121×C6111yescharacteristic
354C8#121×C6111yescharacteristic
355C8#123×C6111yescharacteristic
356C8#124×C6111yescharacteristic
357C22—22no—
358C22—22no—
359C22—22no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—82no—
365C22—82no—
366C22—82no—
367C22—161no—
368C22—161no—
369C22—161no—
370C22—161no—
371C22C61×#44711yescharacteristic
372C22C61×#46611yescharacteristic
373C22C61×#48011yescharacteristic
374C22C2×D16×C6111yescharacteristic
375C22C61×#50811yescharacteristic
376C22C61×#50911yescharacteristic
377C22C61×#51011yescharacteristic
378C4—41no—
379C4—82no—
380C4—161no—
381C4—161no—
382C4C61×#39411yescharacteristic
383C4C61×#45211yescharacteristic
384C4C61×#46811yescharacteristic
385C4C61×#48211yescharacteristic
386C2—42no—
387C2—162no—
388C2C61×#203311yescharacteristic
389C2C61×#218411yescharacteristic
390C2C61×#218911yescharacteristic
391C2C61×#221511yescharacteristic
392C2C61×#222011yescharacteristic
393C2C61×#223211yescharacteristic
394C2C61×#223411yescharacteristic
subgroupG/H
center, socleC23×C61C2×D8
commutator, Frattini, cosocleC22×C8C23×C61
prime radicalC2×C61×#466C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C23×C4×C61 ◁ C23×C8×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C61×#366C2semidirect
3. C2×C61×#357C2semidirect
4. C2×C61×#357C2semidirect
5. C2×C61×C22⋊C16C2semidirect
6. C61×#1808C2semidirect
7. C61×#1380C2semidirect
54. C2×C16×C61D4semidirect
159. #13380C61direct (N × H)
190. C2×#366C2×C61semidirect
191. C2×#357C2×C61semidirect
192. C2×#357C2×C61semidirect
193. C2×C22⋊C16C2×C61semidirect
194. #1808C2×C61semidirect
195. #1380C2×C61semidirect
222. C61#13380direct (N × H)
252. C2×C16D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#4662
C2×C61×#3662
C2×C61×#3572
C2×C61×C22⋊C162
C61×#18082
C61×#13802
#1338061