Finite Group Databasebeta

← C61×#13388 #29516821

Subgroups — C61×#13388 #29516821

Order 15616.

396 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3059C211yesmaximal, characteristic
2C61×#2159C211yesmaximal, characteristic, complemented
3C2×C61×#362C211yesmaximal, characteristic, complemented
4C2×C61×#358C211yesmaximal, characteristic, complemented
5C2×C61×#350C211yesmaximal, characteristic
6C61×#1816C211yesmaximal, characteristic
7C61×#1382C211yesmaximal, characteristic, complemented
8C22×Q16×C61C2211yescharacteristic
9C2×#131×C61C2211yescharacteristic
10C61×#536—21no—
11C2×M32×C61C2211yescharacteristic
12C22×C16×C61C2211yescharacteristic
13C61×#470—22no—
14C61×#467—21no—
15C61×#467—21no—
16C2×#108×C61C2211yescharacteristic
17C61×#427C2211yescharacteristic
18C2×#107×C61C2211yescharacteristic
19C61×#419—21no—
20C61×#417—21no—
21C61×#367—21no—
22C61×#366—21no—
23C61×#362—22no—
24C61×#358—22no—
25C61×#350—22no—
26C61×#343—21no—
27C2×#41×C61D411yescharacteristic
28C22×Q8×C61—21no—
29C2×Q16×C61—21no—
30C2×Q16×C61—21no—
31C2×Q16×C61—21no—
32C2×Q16×C61—21no—
33C2×Q16×C61—21no—
34C2×Q16×C61D412yes—
35#131×C61—21no—
36#131×C61—21no—
37#131×C61—21no—
38#131×C61—21no—
39C2×M16×C61—21no—
40C2×M16×C61—21no—
41C2×M16×C61D411yescharacteristic
42C22×C8×C61—21no—
43C22×C8×C61C2311yescharacteristic
44C4⋊Q8×C61—41no—
45#124×C61—41no—
46#123×C61—42no—
47C22⋊Q8×C61—22no—
48C22⋊Q8×C61—22no—
49#117×C61—21no—
50C2×C4⋊C4×C61—21no—
51M32×C61—21no—
52M32×C61D412yes—
53C2×C16×C61—21no—
54C2×C16×C61—21no—
55C2×C16×C61—21no—
56C2×C16×C61—21no—
57#108×C61—21no—
58#108×C61—21no—
59#107×C61—21no—
60#107×C61—21no—
61#107×C61D411yescharacteristic
62#107×C61D411yescharacteristic
63#106×C61—21no—
64#103×C61—22no—
65#103×C61—22no—
66#103×C61—41no—
67#102×C61—41no—
68#41×C61—21no—
69#41×C61—21no—
70#41×C61—21no—
71#41×C61—21no—
72C2×Q8×C61—22no—
73C2×Q8×C61—41no—
74C2×Q8×C61—41no—
75C2×Q8×C61—41no—
76C2×Q8×C61—41no—
77C2×Q8×C61—41no—
78C2×Q8×C61D811yescharacteristic
79C2×D4×C61—21no—
80C2×D4×C61D811yescharacteristic
81C22×C4×C61—21no—
82C22×C4×C61—41no—
83C22×C4×C61—41no—
84C22×C4×C61C2×D411yescharacteristic
85Q16×C61—22no—
86Q16×C61—22no—
87Q16×C61—41no—
88Q16×C61—41no—
89M16×C61—21no—
90M16×C61—21no—
91M16×C61—41no—
92M16×C61—41no—
93M16×C61—41no—
94M16×C61—41no—
95C2×C8×C61—21no—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C2×C8×C61—41no—
99C2×C8×C61C2×D411yescharacteristic
100C2×C8×C61C2×D411yescharacteristic
101C2×C8×C61C2×D411yescharacteristic
102C2×C8×C61#4111yescharacteristic
103C2×C8×C61#4111yescharacteristic
104C2×C8×C61#4111yescharacteristic
105C4⋊C4×C61—21no—
106C4⋊C4×C61—21no—
107C4⋊C4×C61—42no—
108C4⋊C4×C61—42no—
109C4⋊C4×C61—41no—
110C4⋊C4×C61—41no—
111C22⋊C4×C61—42no—
112C22⋊C4×C61—42no—
113C22⋊C4×C61—41no—
114C42×C61—41no—
115C16×C61—22no—
116C16×C61—41no—
117C23×C61—21no—
118C23×C61AGL(1,ℤ/8)11yescharacteristic
119Q8×C61—21no—
120Q8×C61—21no—
121Q8×C61—42no—
122Q8×C61—42no—
123Q8×C61—81no—
124Q8×C61—81no—
125D4×C61—21no—
126D4×C61—21no—
127D4×C61—41no—
128D4×C61—41no—
129C2×C4×C61—21no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—42no—
135C2×C4×C61—81no—
136C2×C4×C61—81no—
137C2×C4×C61—81no—
138C2×C4×C61—161no—
139C2×C4×C61#12011yescharacteristic
140C2×C4×C61#12111yescharacteristic
141C2×C4×C61#12311yescharacteristic
142C2×C4×C61C2×D811yescharacteristic
143C2×C4×C61#13511yescharacteristic
144C2×C4×C61#13711yescharacteristic
145C8×C61—41no—
146C8×C61—81no—
147C8×C61#12111yescharacteristic
148C8×C61#12111yescharacteristic
149C8×C61#12311yescharacteristic
150C8×C61#12411yescharacteristic
151#13388C6111yesmaximal, characteristic, direct product factor, Sylow
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—41no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61#44711yescharacteristic
158C22×C61#46811yescharacteristic
159C22×C61#48211yescharacteristic
160C4×C61—41no—
161C4×C61—81no—
162C4×C61—81no—
163C4×C61—82no—
164C4×C61—161no—
165C4×C61#39411yescharacteristic
166C4×C61#45211yescharacteristic
167C4×C61#46611yescharacteristic
168C4×C61#48011yescharacteristic
169#3059C2×C6111yescharacteristic
170#2159C2×C6111yescharacteristic, complemented
171C2×#362C2×C6111yescharacteristic, complemented
172C2×#358C2×C6111yescharacteristic, complemented
173C2×#350C2×C6111yescharacteristic
174#1816C2×C6111yescharacteristic
175#1382C2×C6111yescharacteristic, complemented
176C2×C61—21no—
177C2×C61—21no—
178C2×C61—81no—
179C2×C61#203311yescharacteristic
180C2×C61#219311yescharacteristic
181C2×C61#219511yescharacteristic
182C22×Q16C22×C6111yescharacteristic
183C2×#131C22×C6111yescharacteristic
184#536—21no—
185C2×M32C22×C6111yescharacteristic
186C22×C16C22×C6111yescharacteristic
187#470—22no—
188#467—21no—
189#467—21no—
190C2×#108C22×C6111yescharacteristic
191#427C22×C6111yescharacteristic
192C2×#107C22×C6111yescharacteristic
193#419—21no—
194#417—21no—
195#367—21no—
196#366—21no—
197#362—22no—
198#358—22no—
199#350—22no—
200#343—21no—
201C61#1338811yescharacteristic, direct product factor, Sylow
202C2×#41D4×C6111yescharacteristic
203C22×Q8—21no—
204C2×Q16—21no—
205C2×Q16—21no—
206C2×Q16—21no—
207C2×Q16—21no—
208C2×Q16—21no—
209C2×Q16D4×C6112yes—
210#131—21no—
211#131—21no—
212#131—21no—
213#131—21no—
214C2×M16—21no—
215C2×M16—21no—
216C2×M16D4×C6111yescharacteristic
217C22×C8—21no—
218C22×C8C23×C6111yescharacteristic
219C4⋊Q8—41no—
220#124—41no—
221#123—42no—
222C22⋊Q8—22no—
223C22⋊Q8—22no—
224#117—21no—
225C2×C4⋊C4—21no—
226M32—21no—
227M32D4×C6112yes—
228C2×C16—21no—
229C2×C16—21no—
230C2×C16—21no—
231C2×C16—21no—
232#108—21no—
233#108—21no—
234#107—21no—
235#107—21no—
236#107D4×C6111yescharacteristic
237#107D4×C6111yescharacteristic
238#106—21no—
239#103—22no—
240#103—22no—
241#103—41no—
242#102—41no—
243#41—21no—
244#41—21no—
245#41—21no—
246#41—21no—
247C2×Q8—22no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×Q8—41no—
253C2×Q8D8×C6111yescharacteristic
254C2×D4—21no—
255C2×D4D8×C6111yescharacteristic
256C22×C4—21no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4C2×D4×C6111yescharacteristic
260Q16—22no—
261Q16—22no—
262Q16—41no—
263Q16—41no—
264M16—21no—
265M16—21no—
266M16—41no—
267M16—41no—
268M16—41no—
269M16—41no—
270C2×C8—21no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8—41no—
274C2×C8C2×D4×C6111yescharacteristic
275C2×C8C2×D4×C6111yescharacteristic
276C2×C8C2×D4×C6111yescharacteristic
277C2×C8#41×C6111yescharacteristic
278C2×C8#41×C6111yescharacteristic
279C2×C8#41×C6111yescharacteristic
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—42no—
283C4⋊C4—42no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C22⋊C4—42no—
287C22⋊C4—42no—
288C22⋊C4—41no—
289C42—41no—
290C16—22no—
291C16—41no—
292C23—21no—
293C23AGL(1,ℤ/8)×C6111yescharacteristic
294Q8—21no—
295Q8—21no—
296Q8—42no—
297Q8—42no—
298Q8—81no—
299Q8—81no—
300D4—21no—
301D4—21no—
302D4—41no—
303D4—41no—
304C2×C4—21no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—42no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—161no—
314C2×C4#120×C6111yescharacteristic
315C2×C4#121×C6111yescharacteristic
316C2×C4#123×C6111yescharacteristic
317C2×C4C2×D8×C6111yescharacteristic
318C2×C4#135×C6111yescharacteristic
319C2×C4#137×C6111yescharacteristic
320C8—41no—
321C8—81no—
322C8#121×C6111yescharacteristic
323C8#121×C6111yescharacteristic
324C8#123×C6111yescharacteristic
325C8#124×C6111yescharacteristic
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22C61×#44711yescharacteristic
332C22C61×#46811yescharacteristic
333C22C61×#48211yescharacteristic
334C4—41no—
335C4—82no—
336C4—81no—
337C4—81no—
338C4—161no—
339C4C61×#39411yescharacteristic
340C4C61×#45211yescharacteristic
341C4C61×#46611yescharacteristic
342C4C61×#48011yescharacteristic
343C2—21no—
344C2—21no—
345C2—81no—
346C2C61×#203311yescharacteristic
347C2C61×#219311yescharacteristic
348C2C61×#219511yescharacteristic
subgroupG/H
center, socleC22×C61#447
commutator, Frattini, cosocleC22×C8C23×C61
prime radicalC2×#41×C61D4
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C22×C4×C61 ◁ C2×#131×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#2159C2semidirect
3. C2×C61×#362C2semidirect
4. C2×C61×#358C2semidirect
7. C61×#1382C2semidirect
151. #13388C61direct (N × H)
170. #2159C2×C61semidirect
171. C2×#362C2×C61semidirect
172. C2×#358C2×C61semidirect
175. #1382C2×C61semidirect
201. C61#13388direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#30592
C61×#21592
C2×C61×#3622
C2×C61×#3582
C2×C61×#3502
C61×#18162
C61×#13822
#1338861