Finite Group Databasebeta

← C61×#12986 #29516419

Subgroups — C61×#12986 #29516419

Order 15616.

456 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3407C211yesmaximal, characteristic, complemented
2C2×C61×#444C211yesmaximal, characteristic
3C61×#2117C211yesmaximal, characteristic, complemented
4C61×#2117C211yesmaximal, characteristic, complemented
5C61×#2115C211yesmaximal, characteristic, complemented
6C61×#1377C211yesmaximal, characteristic, complemented
7C61×#1375C211yesmaximal, characteristic, complemented
8C2×#135×C61C411yescharacteristic
9C2×#131×C61C2211yescharacteristic
10C2×#131×C61C2211yescharacteristic
11C61×#504—22no—
12C61×#504—22no—
13C2×M32×C61—22no—
14C2×M32×C61C2211yescharacteristic
15C2×M32×C61C2211yescharacteristic
16C2×M32×C61C2211yescharacteristic
17C2×M32×C61C2211yescharacteristic
18C61×#444—22no—
19C61×#444—22no—
20C2×#108×C61C411yescharacteristic
21C2×#104×C61C411yescharacteristic
22C2×#104×C61C411yescharacteristic
23C2×#97×C61C2211yescharacteristic
24C61×#350—22no—
25C61×#350—22no—
26C61×#349—22no—
27C2×#41×C61C2×C411yescharacteristic
28C2×#41×C61C2×C411yescharacteristic
29#135×C61—22no—
30#135×C61—22no—
31C2×Q16×C61C811yescharacteristic
32C2×SD16×C61C811yescharacteristic
33C2×SD16×C61C811yescharacteristic
34C2×D8×C61C811yescharacteristic
35#131×C61—21no—
36#131×C61—21no—
37#131×C61—21no—
38#131×C61—21no—
39#131×C61—21no—
40#131×C61—21no—
41#131×C61D412yes—
42#131×C61D412yes—
43C2×M16×C61—21no—
44C2×M16×C61—21no—
45C2×M16×C61C2×C411yescharacteristic
46C2×M16×C61C2×C411yescharacteristic
47C22×C8×C61—21no—
48C22×C8×C61—21no—
49C22×C8×C61C2×C411yescharacteristic
50C22×C8×C61C2311yescharacteristic
51C2×C42×C61C2×C411yescharacteristic
52M32×C61—24no—
53M32×C61—21no—
54M32×C61—21no—
55M32×C61—21no—
56M32×C61—21no—
57M32×C61—21no—
58M32×C61—21no—
59M32×C61—21no—
60M32×C61D412yes—
61C2×C16×C61—24no—
62C2×C16×C61—21no—
63C2×C16×C61—21no—
64C2×C16×C61—21no—
65C2×C16×C61D412yes—
66#108×C61—22no—
67#104×C61—22no—
68#104×C61—22no—
69#97×C61—21no—
70#97×C61—21no—
71#41×C61—21no—
72#41×C61—21no—
73#41×C61—21no—
74#41×C61—21no—
75#41×C61—21no—
76#41×C61—21no—
77#41×C61C22⋊C412yes—
78#41×C61M1612yes—
79C2×Q8×C61C2×C811yescharacteristic
80C2×Q8×C61C2×C811yescharacteristic
81C2×D4×C61—21no—
82C2×D4×C61—21no—
83C2×D4×C61C2×C811yescharacteristic
84C2×D4×C61C2×C811yescharacteristic
85C22×C4×C61—21no—
86C22×C4×C61—21no—
87C22×C4×C61—21no—
88C22×C4×C61C22×C411yescharacteristic
89Q16×C61—22no—
90SD16×C61—22no—
91SD16×C61—22no—
92D8×C61—22no—
93M16×C61—21no—
94M16×C61—22no—
95M16×C61—22no—
96M16×C61—21no—
97M16×C61—21no—
98M16×C61—41no—
99M16×C61—41no—
100M16×C61C22⋊C412yes—
101C2×C8×C61—21no—
102C2×C8×C61—21no—
103C2×C8×C61—21no—
104C2×C8×C61—22no—
105C2×C8×C61—22no—
106C2×C8×C61—21no—
107C2×C8×C61—41no—
108C2×C8×C61—41no—
109C2×C8×C61C2×C811yescharacteristic
110C2×C8×C61C2×C811yescharacteristic
111C2×C8×C61C2×D411yescharacteristic
112C2×C8×C61C2×D411yescharacteristic
113C2×C8×C61C2×D411yescharacteristic
114C2×C8×C61C2×D411yescharacteristic
115C2×C8×C61#4111yescharacteristic
116C2×C8×C61#4111yescharacteristic
117C42×C61—21no—
118C42×C61—21no—
119C16×C61—22no—
120C16×C61—22no—
121C16×C61—41no—
122C16×C61—41no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61#13111yescharacteristic
126Q8×C61—21no—
127Q8×C61—21no—
128Q8×C61—21no—
129Q8×C61C22⋊C812yes—
130D4×C61—22no—
131D4×C61—22no—
132D4×C61—21no—
133D4×C61—21no—
134D4×C61—21no—
135D4×C61—41no—
136D4×C61—41no—
137D4×C61C22⋊C812yes—
138C2×C4×C61—21no—
139C2×C4×C61—22no—
140C2×C4×C61—22no—
141C2×C4×C61—21no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—81no—
146C2×C4×C61C2×C22⋊C411yescharacteristic
147C2×C4×C61C4×D411yescharacteristic
148C2×C4×C61C4×D411yescharacteristic
149C2×C4×C61C22×C811yescharacteristic
150C2×C4×C61C2×M1611yescharacteristic
151C2×C4×C61#13111yescharacteristic
152C8×C61—22no—
153C8×C61—21no—
154C8×C61—21no—
155C8×C61—41no—
156C8×C61#12011yescharacteristic
157C8×C61#12111yescharacteristic
158C8×C61#12111yescharacteristic
159C8×C61#12311yescharacteristic
160#12986C6111yesmaximal, characteristic, direct product factor, Sylow
161C22×C61—22no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61—81no—
165C22×C61—81no—
166C22×C61#40811yescharacteristic
167C22×C61C8×D411yescharacteristic
168C22×C61#43511yescharacteristic
169C4×C61—22no—
170C4×C61—41no—
171C4×C61—81no—
172C4×C61#38611yescharacteristic
173C4×C61C2×C22⋊C811yescharacteristic
174C4×C61C8×D411yescharacteristic
175C4×C61#43511yescharacteristic
176#3407C2×C6111yescharacteristic, complemented
177C2×#444C2×C6111yescharacteristic
178#2117C2×C6111yescharacteristic, complemented
179#2117C2×C6111yescharacteristic, complemented
180#2115C2×C6111yescharacteristic, complemented
181#1377C2×C6111yescharacteristic, complemented
182#1375C2×C6111yescharacteristic, complemented
183C2×C61—21no—
184C2×C61—21no—
185C2×C61—21no—
186C2×C61—42no—
187C2×C61—81no—
188C2×C61#186911yescharacteristic
189C2×#135C4×C6111yescharacteristic
190C2×#131C22×C6111yescharacteristic
191C2×#131C22×C6111yescharacteristic
192#504—22no—
193#504—22no—
194C2×M32—22no—
195C2×M32C22×C6111yescharacteristic
196C2×M32C22×C6111yescharacteristic
197C2×M32C22×C6111yescharacteristic
198C2×M32C22×C6111yescharacteristic
199#444—22no—
200#444—22no—
201C2×#108C4×C6111yescharacteristic
202C2×#104C4×C6111yescharacteristic
203C2×#104C4×C6111yescharacteristic
204C2×#97C22×C6111yescharacteristic
205#350—22no—
206#350—22no—
207#349—22no—
208C61#1298611yescharacteristic, direct product factor, Sylow
209C2×#41C2×C4×C6111yescharacteristic
210C2×#41C2×C4×C6111yescharacteristic
211#135—22no—
212#135—22no—
213C2×Q16C8×C6111yescharacteristic
214C2×SD16C8×C6111yescharacteristic
215C2×SD16C8×C6111yescharacteristic
216C2×D8C8×C6111yescharacteristic
217#131—21no—
218#131—21no—
219#131—21no—
220#131—21no—
221#131—21no—
222#131—21no—
223#131D4×C6112yes—
224#131D4×C6112yes—
225C2×M16—21no—
226C2×M16—21no—
227C2×M16C2×C4×C6111yescharacteristic
228C2×M16C2×C4×C6111yescharacteristic
229C22×C8—21no—
230C22×C8—21no—
231C22×C8C2×C4×C6111yescharacteristic
232C22×C8C23×C6111yescharacteristic
233C2×C42C2×C4×C6111yescharacteristic
234M32—24no—
235M32—21no—
236M32—21no—
237M32—21no—
238M32—21no—
239M32—21no—
240M32—21no—
241M32—21no—
242M32D4×C6112yes—
243C2×C16—24no—
244C2×C16—21no—
245C2×C16—21no—
246C2×C16—21no—
247C2×C16D4×C6112yes—
248#108—22no—
249#104—22no—
250#104—22no—
251#97—21no—
252#97—21no—
253#41—21no—
254#41—21no—
255#41—21no—
256#41—21no—
257#41—21no—
258#41—21no—
259#41C22⋊C4×C6112yes—
260#41M16×C6112yes—
261C2×Q8C2×C8×C6111yescharacteristic
262C2×Q8C2×C8×C6111yescharacteristic
263C2×D4—21no—
264C2×D4—21no—
265C2×D4C2×C8×C6111yescharacteristic
266C2×D4C2×C8×C6111yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4C22×C4×C6111yescharacteristic
271Q16—22no—
272SD16—22no—
273SD16—22no—
274D8—22no—
275M16—21no—
276M16—22no—
277M16—22no—
278M16—21no—
279M16—21no—
280M16—41no—
281M16—41no—
282M16C22⋊C4×C6112yes—
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—21no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8C2×C8×C6111yescharacteristic
292C2×C8C2×C8×C6111yescharacteristic
293C2×C8C2×D4×C6111yescharacteristic
294C2×C8C2×D4×C6111yescharacteristic
295C2×C8C2×D4×C6111yescharacteristic
296C2×C8C2×D4×C6111yescharacteristic
297C2×C8#41×C6111yescharacteristic
298C2×C8#41×C6111yescharacteristic
299C42—21no—
300C42—21no—
301C16—22no—
302C16—22no—
303C16—41no—
304C16—41no—
305C23—21no—
306C23—21no—
307C23#131×C6111yescharacteristic
308Q8—21no—
309Q8—21no—
310Q8—21no—
311Q8C22⋊C8×C6112yes—
312D4—22no—
313D4—22no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—41no—
318D4—41no—
319D4C22⋊C8×C6112yes—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—81no—
328C2×C4C2×C22⋊C4×C6111yescharacteristic
329C2×C4C4×D4×C6111yescharacteristic
330C2×C4C4×D4×C6111yescharacteristic
331C2×C4C22×C8×C6111yescharacteristic
332C2×C4C2×M16×C6111yescharacteristic
333C2×C4#131×C6111yescharacteristic
334C8—22no—
335C8—21no—
336C8—21no—
337C8—41no—
338C8#120×C6111yescharacteristic
339C8#121×C6111yescharacteristic
340C8#121×C6111yescharacteristic
341C8#123×C6111yescharacteristic
342C22—22no—
343C22—41no—
344C22—41no—
345C22—81no—
346C22—81no—
347C22C61×#40811yescharacteristic
348C22C8×D4×C6111yescharacteristic
349C22C61×#43511yescharacteristic
350C4—22no—
351C4—41no—
352C4—81no—
353C4C61×#38611yescharacteristic
354C4C2×C22⋊C8×C6111yescharacteristic
355C4C8×D4×C6111yescharacteristic
356C4C61×#43511yescharacteristic
357C2—21no—
358C2—21no—
359C2—21no—
360C2—42no—
361C2—81no—
362C2C61×#186911yescharacteristic
subgroupG/H
centerC4×C61#386
commutatorC2×C4C22×C8×C61
Frattini, cosocleC22×C8C23×C61
socleC2×C61#1869
prime radicalC2×#135×C61C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C61 ◁ C22×C8×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3407C2semidirect
3. C61×#2117C2semidirect
4. C61×#2117C2semidirect
5. C61×#2115C2semidirect
6. C61×#1377C2semidirect
7. C61×#1375C2semidirect
160. #12986C61direct (N × H)
176. #3407C2×C61semidirect
178. #2117C2×C61semidirect
179. #2117C2×C61semidirect
180. #2115C2×C61semidirect
181. #1377C2×C61semidirect
182. #1375C2×C61semidirect
208. C61#12986direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#34072
C2×C61×#4442
C61×#21172
C61×#21152
C61×#13772
C61×#13752
#1298661