Finite Group Databasebeta

← C61×#13070 #29516503

Subgroups — C61×#13070 #29516503

Order 15616.

456 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3407C211yesmaximal, characteristic, complemented
2C61×#3067C211yesmaximal, characteristic
3C2×C61×#360C211yesmaximal, characteristic, complemented
4C61×#2143C211yesmaximal, characteristic, complemented
5C61×#1815C211yesmaximal, characteristic, complemented
6C61×#1388C211yesmaximal, characteristic, complemented
7C61×#1383C211yesmaximal, characteristic, complemented
8C61×#575—21no—
9C2×#135×C61C2211yescharacteristic
10C2×#131×C61C2211yescharacteristic
11C61×#504—22no—
12C61×#504—22no—
13C2×M32×C61—22no—
14C2×M32×C61C2211yescharacteristic
15C2×M32×C61C2211yescharacteristic
16C61×#473C412yescomplemented
17C61×#472C412yescomplemented
18C61×#471—22no—
19C2×#108×C61C2211yescharacteristic
20C2×#108×C61C2211yescharacteristic
21C2×#106×C61C2211yescharacteristic
22C61×#417—21no—
23C61×#413—21no—
24C61×#360—22no—
25C61×#359—22no—
26C61×#343—21no—
27C2×#41×C61—21no—
28C2×#41×C61D411yescharacteristic
29#137×C61—22no—
30#137×C61—41no—
31AGL(1,ℤ/8)×C61—22no—
32AGL(1,ℤ/8)×C61—41no—
33#135×C61—21no—
34#135×C61—21no—
35#135×C61—21no—
36#135×C61—21no—
37#135×C61—42no—
38C2×Q16×C61C2×C411yescharacteristic
39C2×SD16×C61—21no—
40C2×D8×C61C2×C411yescharacteristic
41#131×C61—21no—
42#131×C61—21no—
43#131×C61C2×C412yes—
44#131×C61D412yes—
45C2×M16×C61—21no—
46C2×M16×C61—21no—
47C2×M16×C61—21no—
48C2×M16×C61D411yescharacteristic
49C22×C8×C61—21no—
50C22×C8×C61C2311yescharacteristic
51C2×C4⋊C4×C61—21no—
52M32×C61—24no—
53M32×C61—21no—
54M32×C61—21no—
55M32×C61—21no—
56M32×C61D412yes—
57C2×C16×C61—24no—
58C2×C16×C61—21no—
59C2×C16×C61D412yes—
60#108×C61—21no—
61#108×C61—21no—
62#108×C61—21no—
63#108×C61C2×C412yes—
64#106×C61—21no—
65#106×C61—21no—
66#103×C61—41no—
67#102×C61—41no—
68#101×C61—22no—
69#100×C61—22no—
70#41×C61—21no—
71#41×C61—21no—
72#41×C61—41no—
73#41×C61—41no—
74#41×C61—41no—
75#41×C61—41no—
76#41×C61C22⋊C412yes—
77#41×C61SD1612yes—
78C2×Q8×C61—21no—
79C2×Q8×C61D811yescharacteristic
80C2×D4×C61—21no—
81C2×D4×C61—21no—
82C2×D4×C61—41no—
83C2×D4×C61D811yescharacteristic
84C22×C4×C61—21no—
85C22×C4×C61—41no—
86C22×C4×C61—41no—
87C22×C4×C61C2×D411yescharacteristic
88Q16×C61—21no—
89Q16×C61—21no—
90Q16×C61—42no—
91SD16×C61—42no—
92SD16×C61—42no—
93SD16×C61—41no—
94SD16×C61—41no—
95D8×C61—21no—
96D8×C61—21no—
97D8×C61—42no—
98M16×C61—21no—
99M16×C61—22no—
100M16×C61—22no—
101M16×C61—22no—
102M16×C61—41no—
103M16×C61—41no—
104M16×C61—41no—
105M16×C61C22⋊C412yes—
106C2×C8×C61—21no—
107C2×C8×C61—22no—
108C2×C8×C61—22no—
109C2×C8×C61—41no—
110C2×C8×C61—41no—
111C2×C8×C61C22×C411yescharacteristic
112C2×C8×C61C2×D411yescharacteristic
113C2×C8×C61C2×D411yescharacteristic
114C2×C8×C61C2×D411yescharacteristic
115C2×C8×C61#4111yescharacteristic
116C2×C8×C61#4111yescharacteristic
117C4⋊C4×C61—41no—
118C4⋊C4×C61—41no—
119C16×C61—22no—
120C16×C61—22no—
121C23×C61—21no—
122C23×C61—41no—
123C23×C61#13511yescharacteristic
124Q8×C61—21no—
125Q8×C61—41no—
126Q8×C61—41no—
127Q8×C61#10212yes—
128D4×C61—22no—
129D4×C61—22no—
130D4×C61—21no—
131D4×C61—41no—
132D4×C61—41no—
133D4×C61—81no—
134D4×C61—81no—
135D4×C61#10212yes—
136C2×C4×C61—21no—
137C2×C4×C61—22no—
138C2×C4×C61—22no—
139C2×C4×C61—41no—
140C2×C4×C61—81no—
141C2×C4×C61—81no—
142C2×C4×C61—81no—
143C2×C4×C61—161no—
144C2×C4×C61C2×C22⋊C411yescharacteristic
145C2×C4×C61#12111yescharacteristic
146C2×C4×C61#12111yescharacteristic
147C2×C4×C61C2×D811yescharacteristic
148C2×C4×C61C2×SD1611yescharacteristic
149C2×C4×C61#13511yescharacteristic
150C8×C61—22no—
151C8×C61—42no—
152C8×C61—81no—
153C8×C61C4×D411yescharacteristic
154C8×C61C4×D411yescharacteristic
155C8×C61#12011yescharacteristic
156C8×C61#12311yescharacteristic
157#13070C6111yesmaximal, characteristic, direct product factor, Sylow
158C22×C61—22no—
159C22×C61—41no—
160C22×C61—81no—
161C22×C61—81no—
162C22×C61—161no—
163C22×C61#41611yescharacteristic
164C22×C61#46511yescharacteristic
165C22×C61#46611yescharacteristic
166C4×C61—22no—
167C4×C61—81no—
168C4×C61—161no—
169C4×C61#38611yescharacteristic
170C4×C61C2×#10211yescharacteristic
171C4×C61#46511yescharacteristic
172C4×C61#46611yescharacteristic
173#3407C2×C6111yescharacteristic, complemented
174#3067C2×C6111yescharacteristic
175C2×#360C2×C6111yescharacteristic, complemented
176#2143C2×C6111yescharacteristic, complemented
177#1815C2×C6111yescharacteristic, complemented
178#1388C2×C6111yescharacteristic, complemented
179#1383C2×C6111yescharacteristic, complemented
180C2×C61—21no—
181C2×C61—21no—
182C2×C61—21no—
183C2×C61—42no—
184C2×C61—161no—
185C2×C61#189311yescharacteristic
186#575—21no—
187C2×#135C22×C6111yescharacteristic
188C2×#131C22×C6111yescharacteristic
189#504—22no—
190#504—22no—
191C2×M32—22no—
192C2×M32C22×C6111yescharacteristic
193C2×M32C22×C6111yescharacteristic
194#473C4×C6112yescomplemented
195#472C4×C6112yescomplemented
196#471—22no—
197C2×#108C22×C6111yescharacteristic
198C2×#108C22×C6111yescharacteristic
199C2×#106C22×C6111yescharacteristic
200#417—21no—
201#413—21no—
202#360—22no—
203#359—22no—
204#343—21no—
205C61#1307011yescharacteristic, direct product factor, Sylow
206C2×#41—21no—
207C2×#41D4×C6111yescharacteristic
208#137—22no—
209#137—41no—
210AGL(1,ℤ/8)—22no—
211AGL(1,ℤ/8)—41no—
212#135—21no—
213#135—21no—
214#135—21no—
215#135—21no—
216#135—42no—
217C2×Q16C2×C4×C6111yescharacteristic
218C2×SD16—21no—
219C2×D8C2×C4×C6111yescharacteristic
220#131—21no—
221#131—21no—
222#131C2×C4×C6112yes—
223#131D4×C6112yes—
224C2×M16—21no—
225C2×M16—21no—
226C2×M16—21no—
227C2×M16D4×C6111yescharacteristic
228C22×C8—21no—
229C22×C8C23×C6111yescharacteristic
230C2×C4⋊C4—21no—
231M32—24no—
232M32—21no—
233M32—21no—
234M32—21no—
235M32D4×C6112yes—
236C2×C16—24no—
237C2×C16—21no—
238C2×C16D4×C6112yes—
239#108—21no—
240#108—21no—
241#108—21no—
242#108C2×C4×C6112yes—
243#106—21no—
244#106—21no—
245#103—41no—
246#102—41no—
247#101—22no—
248#100—22no—
249#41—21no—
250#41—21no—
251#41—41no—
252#41—41no—
253#41—41no—
254#41—41no—
255#41C22⋊C4×C6112yes—
256#41SD16×C6112yes—
257C2×Q8—21no—
258C2×Q8D8×C6111yescharacteristic
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—41no—
262C2×D4D8×C6111yescharacteristic
263C22×C4—21no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4C2×D4×C6111yescharacteristic
267Q16—21no—
268Q16—21no—
269Q16—42no—
270SD16—42no—
271SD16—42no—
272SD16—41no—
273SD16—41no—
274D8—21no—
275D8—21no—
276D8—42no—
277M16—21no—
278M16—22no—
279M16—22no—
280M16—22no—
281M16—41no—
282M16—41no—
283M16—41no—
284M16C22⋊C4×C6112yes—
285C2×C8—21no—
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8C22×C4×C6111yescharacteristic
291C2×C8C2×D4×C6111yescharacteristic
292C2×C8C2×D4×C6111yescharacteristic
293C2×C8C2×D4×C6111yescharacteristic
294C2×C8#41×C6111yescharacteristic
295C2×C8#41×C6111yescharacteristic
296C4⋊C4—41no—
297C4⋊C4—41no—
298C16—22no—
299C16—22no—
300C23—21no—
301C23—41no—
302C23#135×C6111yescharacteristic
303Q8—21no—
304Q8—41no—
305Q8—41no—
306Q8#102×C6112yes—
307D4—22no—
308D4—22no—
309D4—21no—
310D4—41no—
311D4—41no—
312D4—81no—
313D4—81no—
314D4#102×C6112yes—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—41no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—161no—
323C2×C4C2×C22⋊C4×C6111yescharacteristic
324C2×C4#121×C6111yescharacteristic
325C2×C4#121×C6111yescharacteristic
326C2×C4C2×D8×C6111yescharacteristic
327C2×C4C2×SD16×C6111yescharacteristic
328C2×C4#135×C6111yescharacteristic
329C8—22no—
330C8—42no—
331C8—81no—
332C8C4×D4×C6111yescharacteristic
333C8C4×D4×C6111yescharacteristic
334C8#120×C6111yescharacteristic
335C8#123×C6111yescharacteristic
336C22—22no—
337C22—41no—
338C22—81no—
339C22—81no—
340C22—161no—
341C22C61×#41611yescharacteristic
342C22C61×#46511yescharacteristic
343C22C61×#46611yescharacteristic
344C4—22no—
345C4—81no—
346C4—161no—
347C4C61×#38611yescharacteristic
348C4C2×#102×C6111yescharacteristic
349C4C61×#46511yescharacteristic
350C4C61×#46611yescharacteristic
351C2—21no—
352C2—21no—
353C2—21no—
354C2—42no—
355C2—161no—
356C2C61×#189311yescharacteristic
subgroupG/H
center, socleC2×C61#1893
commutatorC2×C8C22×C4×C61
Frattini, cosocleC22×C8C23×C61
prime radicalC61×#3067C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C61 ◁ C22×C4×C61 ◁ C2×#131×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3407C2semidirect
3. C2×C61×#360C2semidirect
4. C61×#2143C2semidirect
5. C61×#1815C2semidirect
6. C61×#1388C2semidirect
7. C61×#1383C2semidirect
16. C61×#473C4semidirect
17. C61×#472C4semidirect
157. #13070C61direct (N × H)
173. #3407C2×C61semidirect
175. C2×#360C2×C61semidirect
176. #2143C2×C61semidirect
177. #1815C2×C61semidirect
178. #1388C2×C61semidirect
179. #1383C2×C61semidirect
194. #473C4×C61semidirect
195. #472C4×C61semidirect
205. C61#13070direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#34072
C61×#30672
C2×C61×#3602
C61×#21432
C61×#18152
C61×#13882
C61×#13832
#1307061