Finite Group Databasebeta

← C61×#13386 #29516819

Subgroups — C61×#13386 #29516819

Order 15616.

432 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3054C211yesmaximal, characteristic
2C61×#2159C211yesmaximal, characteristic, complemented
3C2×C61×#360C211yesmaximal, characteristic, complemented
4C61×#2139C211yesmaximal, characteristic, complemented
5C2×C61×#349C211yesmaximal, characteristic, complemented
6C61×#1809C211yesmaximal, characteristic, complemented
7C61×#1386C211yesmaximal, characteristic, complemented
8C2×#135×C61C2211yescharacteristic
9C22×M16×C61C2211yescharacteristic
10C61×#525—21no—
11C2×M32×C61C2211yescharacteristic
12C2×M32×C61C2211yescharacteristic
13C61×#470—21no—
14C61×#469—21no—
15C61×#468—21no—
16C61×#468—21no—
17C61×#427C2211yescharacteristic
18C2×#107×C61C2211yescharacteristic
19C2×#106×C61C2211yescharacteristic
20C61×#416—21no—
21C61×#380—21no—
22C61×#367—21no—
23C61×#366—21no—
24C61×#360—22no—
25C61×#358—21no—
26C61×#357—21no—
27C61×#349—22no—
28C61×#340—21no—
29C2×#41×C61—21no—
30C23×C4×C61D411yescharacteristic
31#135×C61—21no—
32#135×C61—21no—
33#135×C61—21no—
34#135×C61—21no—
35C2×Q16×C61D411yescharacteristic
36C2×SD16×C61—21no—
37C2×D8×C61D411yescharacteristic
38C2×M16×C61—21no—
39C2×M16×C61—21no—
40C2×M16×C61—21no—
41C2×M16×C61—21no—
42C2×M16×C61—21no—
43C2×M16×C61—21no—
44C22×C8×C61D411yescharacteristic
45C22×C8×C61C2311yescharacteristic
46#123×C61—41no—
47C22⋊Q8×C61—21no—
48C22⋊Q8×C61—21no—
49#121×C61—21no—
50#121×C61—21no—
51#120×C61—41no—
52C4×D4×C61—41no—
53C4×D4×C61—41no—
54#117×C61—21no—
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61—21no—
57C2×C22⋊C4×C61—41no—
58M32×C61—21no—
59M32×C61—21no—
60M32×C61—21no—
61M32×C61D412yescomplemented
62C2×C16×C61—21no—
63C2×C16×C61—21no—
64#107×C61—21no—
65#107×C61—21no—
66#107×C61D411yescharacteristic
67#107×C61D411yescharacteristic
68#106×C61—21no—
69#106×C61—21no—
70#106×C61—21no—
71#103×C61—21no—
72#103×C61—21no—
73#102×C61—21no—
74#102×C61—21no—
75#95×C61—41no—
76C24×C61D811yescharacteristic
77#41×C61—41no—
78#41×C61—41no—
79#41×C61—41no—
80#41×C61—41no—
81C2×Q8×C61—21no—
82C2×D4×C61—21no—
83C2×D4×C61—41no—
84C2×D4×C61—41no—
85C2×D4×C61—41no—
86C22×C4×C61—21no—
87C22×C4×C61—21no—
88C22×C4×C61—21no—
89C22×C4×C61—21no—
90C22×C4×C61—21no—
91C22×C4×C61—21no—
92C22×C4×C61—41no—
93C22×C4×C61—41no—
94C22×C4×C61—41no—
95C22×C4×C61D811yescharacteristic
96C22×C4×C61C2×D411yescharacteristic
97Q16×C61—21no—
98Q16×C61—21no—
99SD16×C61—41no—
100SD16×C61—41no—
101D8×C61—21no—
102D8×C61—21no—
103M16×C61—41no—
104M16×C61—41no—
105M16×C61—41no—
106M16×C61—41no—
107C2×C8×C61—21no—
108C2×C8×C61—21no—
109C2×C8×C61—21no—
110C2×C8×C61C2×D411yescharacteristic
111C2×C8×C61C2×D411yescharacteristic
112C2×C8×C61C2×D411yescharacteristic
113C2×C8×C61#4111yescharacteristic
114C2×C8×C61#4111yescharacteristic
115C2×C8×C61#4111yescharacteristic
116C4⋊C4×C61—21no—
117C4⋊C4×C61—21no—
118C4⋊C4×C61—41no—
119C4⋊C4×C61—41no—
120C4⋊C4×C61—41no—
121C4⋊C4×C61—41no—
122C4⋊C4×C61—41no—
123C4⋊C4×C61—41no—
124C22⋊C4×C61—41no—
125C22⋊C4×C61—41no—
126C22⋊C4×C61—41no—
127C22⋊C4×C61—41no—
128C22⋊C4×C61—41no—
129C22⋊C4×C61—82no—
130C42×C61—41no—
131C16×C61—22no—
132C16×C61—41no—
133C23×C61—21no—
134C23×C61—21no—
135C23×C61—21no—
136C23×C61—41no—
137C23×C61—41no—
138C23×C61—41no—
139C23×C61C2×D811yescharacteristic
140Q8×C61—41no—
141Q8×C61—41no—
142D4×C61—41no—
143D4×C61—41no—
144D4×C61—82no—
145D4×C61—82no—
146D4×C61—81no—
147D4×C61—81no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—81no—
159C2×C4×C61—81no—
160C2×C4×C61—81no—
161C2×C4×C61—81no—
162C2×C4×C61—81no—
163C2×C4×C61—81no—
164C2×C4×C61—81no—
165C2×C4×C61—81no—
166C2×C4×C61#12011yescharacteristic
167C2×C4×C61#12111yescharacteristic
168C2×C4×C61#12311yescharacteristic
169C2×C4×C61#13511yescharacteristic
170C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C61#13711yescharacteristic
172C8×C61—41no—
173C8×C61#12111yescharacteristic
174C8×C61#12111yescharacteristic
175C8×C61#12311yescharacteristic
176C8×C61#12411yescharacteristic
177#13386C6111yesmaximal, characteristic, direct product factor, Sylow
178C22×C61—21no—
179C22×C61—21no—
180C22×C61—42no—
181C22×C61—41no—
182C22×C61—41no—
183C22×C61—41no—
184C22×C61—81no—
185C22×C61—81no—
186C22×C61—81no—
187C22×C61—81no—
188C22×C61#44711yescharacteristic
189C22×C61#46611yescharacteristic
190C22×C61#48011yescharacteristic
191C4×C61—41no—
192C4×C61—81no—
193C4×C61—81no—
194C4×C61—81no—
195C4×C61—161no—
196C4×C61—161no—
197C4×C61#39411yescharacteristic
198C4×C61#45211yescharacteristic
199C4×C61#46811yescharacteristic
200C4×C61#48211yescharacteristic
201#3054C2×C6111yescharacteristic
202#2159C2×C6111yescharacteristic, complemented
203C2×#360C2×C6111yescharacteristic, complemented
204#2139C2×C6111yescharacteristic, complemented
205C2×#349C2×C6111yescharacteristic, complemented
206#1809C2×C6111yescharacteristic, complemented
207#1386C2×C6111yescharacteristic, complemented
208C2×C61—21no—
209C2×C61—21no—
210C2×C61—81no—
211C2×C61—161no—
212C2×C61#203311yescharacteristic
213C2×C61#219011yescharacteristic
214C2×C61#219111yescharacteristic
215C2×#135C22×C6111yescharacteristic
216C22×M16C22×C6111yescharacteristic
217#525—21no—
218C2×M32C22×C6111yescharacteristic
219C2×M32C22×C6111yescharacteristic
220#470—21no—
221#469—21no—
222#468—21no—
223#468—21no—
224#427C22×C6111yescharacteristic
225C2×#107C22×C6111yescharacteristic
226C2×#106C22×C6111yescharacteristic
227#416—21no—
228#380—21no—
229#367—21no—
230#366—21no—
231#360—22no—
232#358—21no—
233#357—21no—
234#349—22no—
235#340—21no—
236C61#1338611yescharacteristic, direct product factor, Sylow
237C2×#41—21no—
238C23×C4D4×C6111yescharacteristic
239#135—21no—
240#135—21no—
241#135—21no—
242#135—21no—
243C2×Q16D4×C6111yescharacteristic
244C2×SD16—21no—
245C2×D8D4×C6111yescharacteristic
246C2×M16—21no—
247C2×M16—21no—
248C2×M16—21no—
249C2×M16—21no—
250C2×M16—21no—
251C2×M16—21no—
252C22×C8D4×C6111yescharacteristic
253C22×C8C23×C6111yescharacteristic
254#123—41no—
255C22⋊Q8—21no—
256C22⋊Q8—21no—
257#121—21no—
258#121—21no—
259#120—41no—
260C4×D4—41no—
261C4×D4—41no—
262#117—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C22⋊C4—41no—
266M32—21no—
267M32—21no—
268M32—21no—
269M32D4×C6112yescomplemented
270C2×C16—21no—
271C2×C16—21no—
272#107—21no—
273#107—21no—
274#107D4×C6111yescharacteristic
275#107D4×C6111yescharacteristic
276#106—21no—
277#106—21no—
278#106—21no—
279#103—21no—
280#103—21no—
281#102—21no—
282#102—21no—
283#95—41no—
284C24D8×C6111yescharacteristic
285#41—41no—
286#41—41no—
287#41—41no—
288#41—41no—
289C2×Q8—21no—
290C2×D4—21no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4D8×C6111yescharacteristic
304C22×C4C2×D4×C6111yescharacteristic
305Q16—21no—
306Q16—21no—
307SD16—41no—
308SD16—41no—
309D8—21no—
310D8—21no—
311M16—41no—
312M16—41no—
313M16—41no—
314M16—41no—
315C2×C8—21no—
316C2×C8—21no—
317C2×C8—21no—
318C2×C8C2×D4×C6111yescharacteristic
319C2×C8C2×D4×C6111yescharacteristic
320C2×C8C2×D4×C6111yescharacteristic
321C2×C8#41×C6111yescharacteristic
322C2×C8#41×C6111yescharacteristic
323C2×C8#41×C6111yescharacteristic
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—82no—
338C42—41no—
339C16—22no—
340C16—41no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23C2×D8×C6111yescharacteristic
348Q8—41no—
349Q8—41no—
350D4—41no—
351D4—41no—
352D4—82no—
353D4—82no—
354D4—81no—
355D4—81no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4#120×C6111yescharacteristic
375C2×C4#121×C6111yescharacteristic
376C2×C4#123×C6111yescharacteristic
377C2×C4#135×C6111yescharacteristic
378C2×C4AGL(1,ℤ/8)×C6111yescharacteristic
379C2×C4#137×C6111yescharacteristic
380C8—41no—
381C8#121×C6111yescharacteristic
382C8#121×C6111yescharacteristic
383C8#123×C6111yescharacteristic
384C8#124×C6111yescharacteristic
385C22—21no—
386C22—21no—
387C22—42no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—81no—
392C22—81no—
393C22—81no—
394C22—81no—
395C22C61×#44711yescharacteristic
396C22C61×#46611yescharacteristic
397C22C61×#48011yescharacteristic
398C4—41no—
399C4—81no—
400C4—81no—
401C4—81no—
402C4—161no—
403C4—161no—
404C4C61×#39411yescharacteristic
405C4C61×#45211yescharacteristic
406C4C61×#46811yescharacteristic
407C4C61×#48211yescharacteristic
408C2—21no—
409C2—21no—
410C2—81no—
411C2—161no—
412C2C61×#203311yescharacteristic
413C2C61×#219011yescharacteristic
414C2C61×#219111yescharacteristic
subgroupG/H
center, socleC22×C61#447
commutator, Frattini, cosocleC22×C8C23×C61
prime radicalC61×#3054C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C22×C4×C61 ◁ C22×M16×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#2159C2semidirect
3. C2×C61×#360C2semidirect
4. C61×#2139C2semidirect
5. C2×C61×#349C2semidirect
6. C61×#1809C2semidirect
7. C61×#1386C2semidirect
61. M32×C61D4semidirect
177. #13386C61direct (N × H)
202. #2159C2×C61semidirect
203. C2×#360C2×C61semidirect
204. #2139C2×C61semidirect
205. C2×#349C2×C61semidirect
206. #1809C2×C61semidirect
207. #1386C2×C61semidirect
236. C61#13386direct (N × H)
269. M32D4×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#30542
C61×#21592
C2×C61×#3602
C61×#21392
C2×C61×#3492
C61×#18092
C61×#13862
#1338661