Finite Group Databasebeta

← C61×#13071 #29516504

Subgroups — C61×#13071 #29516504

Order 15616.

456 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#504C211yesmaximal, characteristic, complemented
2C61×#3067C211yesmaximal, characteristic
3C61×#2145C211yesmaximal, characteristic, complemented
4C2×C61×#359C211yesmaximal, characteristic, complemented
5C61×#1814C211yesmaximal, characteristic, complemented
6C61×#1388C211yesmaximal, characteristic, complemented
7C61×#1382C211yesmaximal, characteristic, complemented
8C61×#575—21no—
9C2×#135×C61C2211yescharacteristic
10C2×#131×C61C2211yescharacteristic
11C61×#504—22no—
12C61×#504—22no—
13C2×M32×C61—21no—
14C2×M32×C61C2211yescharacteristic
15C22×C16×C61—21no—
16C22×C16×C61C2211yescharacteristic
17C61×#473C412yescomplemented
18C61×#472C412yescomplemented
19C61×#471—22no—
20C2×#108×C61C2211yescharacteristic
21C2×#108×C61C2211yescharacteristic
22C61×#427C2211yescharacteristic
23C61×#421—21no—
24C61×#413—21no—
25C61×#360—22no—
26C61×#359—21no—
27C61×#359—21no—
28C61×#344—21no—
29C2×#41×C61—21no—
30C2×#41×C61D411yescharacteristic
31#137×C61—22no—
32#137×C61—41no—
33AGL(1,ℤ/8)×C61—22no—
34AGL(1,ℤ/8)×C61—41no—
35#135×C61—21no—
36#135×C61—21no—
37#135×C61—21no—
38#135×C61—21no—
39#135×C61—42no—
40C2×Q16×C61C2×C411yescharacteristic
41C2×SD16×C61—21no—
42C2×D8×C61C2×C411yescharacteristic
43#131×C61—21no—
44#131×C61—21no—
45#131×C61C2×C412yes—
46#131×C61D412yes—
47C2×M16×C61—21no—
48C2×M16×C61—21no—
49C2×M16×C61—21no—
50C2×M16×C61D411yescharacteristic
51C22×C8×C61—21no—
52C22×C8×C61C2311yescharacteristic
53#117×C61—21no—
54M32×C61—24no—
55M32×C61—21no—
56M32×C61D412yes—
57C2×C16×C61—24no—
58C2×C16×C61—21no—
59C2×C16×C61—21no—
60C2×C16×C61—21no—
61C2×C16×C61D411yescharacteristic
62C2×C16×C61D411yescharacteristic
63#108×C61—21no—
64#108×C61—21no—
65#108×C61—21no—
66#108×C61C2×C412yes—
67#107×C61—21no—
68#106×C61—21no—
69#104×C61—42no—
70#101×C61—22no—
71#100×C61—22no—
72#41×C61—21no—
73#41×C61—21no—
74#41×C61—41no—
75#41×C61—41no—
76#41×C61—41no—
77#41×C61—41no—
78#41×C61C22⋊C412yes—
79#41×C61D812yes—
80C2×Q8×C61—21no—
81C2×Q8×C61SD1611yescharacteristic
82C2×D4×C61—21no—
83C2×D4×C61—21no—
84C2×D4×C61—41no—
85C2×D4×C61SD1611yescharacteristic
86C22×C4×C61—21no—
87C22×C4×C61—41no—
88C22×C4×C61C2×D411yescharacteristic
89Q16×C61—21no—
90Q16×C61—21no—
91Q16×C61—42no—
92SD16×C61—42no—
93SD16×C61—42no—
94SD16×C61—41no—
95SD16×C61—41no—
96D8×C61—21no—
97D8×C61—21no—
98D8×C61—42no—
99M16×C61—21no—
100M16×C61—22no—
101M16×C61—22no—
102M16×C61—22no—
103M16×C61—41no—
104M16×C61—41no—
105M16×C61—41no—
106M16×C61C22⋊C412yes—
107C2×C8×C61—21no—
108C2×C8×C61—22no—
109C2×C8×C61—22no—
110C2×C8×C61—41no—
111C2×C8×C61—41no—
112C2×C8×C61C22×C411yescharacteristic
113C2×C8×C61C2×D411yescharacteristic
114C2×C8×C61C2×D411yescharacteristic
115C2×C8×C61C2×D411yescharacteristic
116C2×C8×C61#4111yescharacteristic
117C2×C8×C61#4111yescharacteristic
118C4⋊C4×C61—41no—
119C22⋊C4×C61—41no—
120C42×C61—41no—
121C16×C61—21no—
122C16×C61—22no—
123C16×C61—21no—
124C23×C61—21no—
125C23×C61—41no—
126C23×C61#13511yescharacteristic
127Q8×C61—21no—
128Q8×C61—41no—
129Q8×C61—41no—
130Q8×C61#10212yes—
131D4×C61—22no—
132D4×C61—22no—
133D4×C61—21no—
134D4×C61—41no—
135D4×C61—41no—
136D4×C61—81no—
137D4×C61—81no—
138D4×C61#10212yes—
139C2×C4×C61—21no—
140C2×C4×C61—22no—
141C2×C4×C61—22no—
142C2×C4×C61—41no—
143C2×C4×C61—81no—
144C2×C4×C61—81no—
145C2×C4×C61—81no—
146C2×C4×C61C2×C22⋊C411yescharacteristic
147C2×C4×C61#12111yescharacteristic
148C2×C4×C61#12111yescharacteristic
149C2×C4×C61C2×D811yescharacteristic
150C2×C4×C61C2×SD1611yescharacteristic
151C2×C4×C61#13511yescharacteristic
152C8×C61—22no—
153C8×C61—42no—
154C8×C61—81no—
155C8×C61C4×D411yescharacteristic
156C8×C61C4×D411yescharacteristic
157C8×C61#12011yescharacteristic
158C8×C61#12311yescharacteristic
159#13071C6111yesmaximal, characteristic, direct product factor, Sylow
160C22×C61—22no—
161C22×C61—41no—
162C22×C61—42no—
163C22×C61—81no—
164C22×C61—161no—
165C22×C61#41611yescharacteristic
166C22×C61#46511yescharacteristic
167C22×C61#46611yescharacteristic
168C4×C61—22no—
169C4×C61—81no—
170C4×C61—161no—
171C4×C61#38611yescharacteristic
172C4×C61C2×#10211yescharacteristic
173C4×C61#46511yescharacteristic
174C4×C61#46611yescharacteristic
175C2×#504C2×C6111yescharacteristic, complemented
176#3067C2×C6111yescharacteristic
177#2145C2×C6111yescharacteristic, complemented
178C2×#359C2×C6111yescharacteristic, complemented
179#1814C2×C6111yescharacteristic, complemented
180#1388C2×C6111yescharacteristic, complemented
181#1382C2×C6111yescharacteristic, complemented
182C2×C61—21no—
183C2×C61—21no—
184C2×C61—21no—
185C2×C61—42no—
186C2×C61—161no—
187C2×C61#189311yescharacteristic
188#575—21no—
189C2×#135C22×C6111yescharacteristic
190C2×#131C22×C6111yescharacteristic
191#504—22no—
192#504—22no—
193C2×M32—21no—
194C2×M32C22×C6111yescharacteristic
195C22×C16—21no—
196C22×C16C22×C6111yescharacteristic
197#473C4×C6112yescomplemented
198#472C4×C6112yescomplemented
199#471—22no—
200C2×#108C22×C6111yescharacteristic
201C2×#108C22×C6111yescharacteristic
202#427C22×C6111yescharacteristic
203#421—21no—
204#413—21no—
205#360—22no—
206#359—21no—
207#359—21no—
208#344—21no—
209C61#1307111yescharacteristic, direct product factor, Sylow
210C2×#41—21no—
211C2×#41D4×C6111yescharacteristic
212#137—22no—
213#137—41no—
214AGL(1,ℤ/8)—22no—
215AGL(1,ℤ/8)—41no—
216#135—21no—
217#135—21no—
218#135—21no—
219#135—21no—
220#135—42no—
221C2×Q16C2×C4×C6111yescharacteristic
222C2×SD16—21no—
223C2×D8C2×C4×C6111yescharacteristic
224#131—21no—
225#131—21no—
226#131C2×C4×C6112yes—
227#131D4×C6112yes—
228C2×M16—21no—
229C2×M16—21no—
230C2×M16—21no—
231C2×M16D4×C6111yescharacteristic
232C22×C8—21no—
233C22×C8C23×C6111yescharacteristic
234#117—21no—
235M32—24no—
236M32—21no—
237M32D4×C6112yes—
238C2×C16—24no—
239C2×C16—21no—
240C2×C16—21no—
241C2×C16—21no—
242C2×C16D4×C6111yescharacteristic
243C2×C16D4×C6111yescharacteristic
244#108—21no—
245#108—21no—
246#108—21no—
247#108C2×C4×C6112yes—
248#107—21no—
249#106—21no—
250#104—42no—
251#101—22no—
252#100—22no—
253#41—21no—
254#41—21no—
255#41—41no—
256#41—41no—
257#41—41no—
258#41—41no—
259#41C22⋊C4×C6112yes—
260#41D8×C6112yes—
261C2×Q8—21no—
262C2×Q8SD16×C6111yescharacteristic
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—41no—
266C2×D4SD16×C6111yescharacteristic
267C22×C4—21no—
268C22×C4—41no—
269C22×C4C2×D4×C6111yescharacteristic
270Q16—21no—
271Q16—21no—
272Q16—42no—
273SD16—42no—
274SD16—42no—
275SD16—41no—
276SD16—41no—
277D8—21no—
278D8—21no—
279D8—42no—
280M16—21no—
281M16—22no—
282M16—22no—
283M16—22no—
284M16—41no—
285M16—41no—
286M16—41no—
287M16C22⋊C4×C6112yes—
288C2×C8—21no—
289C2×C8—22no—
290C2×C8—22no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8C22×C4×C6111yescharacteristic
294C2×C8C2×D4×C6111yescharacteristic
295C2×C8C2×D4×C6111yescharacteristic
296C2×C8C2×D4×C6111yescharacteristic
297C2×C8#41×C6111yescharacteristic
298C2×C8#41×C6111yescharacteristic
299C4⋊C4—41no—
300C22⋊C4—41no—
301C42—41no—
302C16—21no—
303C16—22no—
304C16—21no—
305C23—21no—
306C23—41no—
307C23#135×C6111yescharacteristic
308Q8—21no—
309Q8—41no—
310Q8—41no—
311Q8#102×C6112yes—
312D4—22no—
313D4—22no—
314D4—21no—
315D4—41no—
316D4—41no—
317D4—81no—
318D4—81no—
319D4#102×C6112yes—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—41no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4C2×C22⋊C4×C6111yescharacteristic
328C2×C4#121×C6111yescharacteristic
329C2×C4#121×C6111yescharacteristic
330C2×C4C2×D8×C6111yescharacteristic
331C2×C4C2×SD16×C6111yescharacteristic
332C2×C4#135×C6111yescharacteristic
333C8—22no—
334C8—42no—
335C8—81no—
336C8C4×D4×C6111yescharacteristic
337C8C4×D4×C6111yescharacteristic
338C8#120×C6111yescharacteristic
339C8#123×C6111yescharacteristic
340C22—22no—
341C22—41no—
342C22—42no—
343C22—81no—
344C22—161no—
345C22C61×#41611yescharacteristic
346C22C61×#46511yescharacteristic
347C22C61×#46611yescharacteristic
348C4—22no—
349C4—81no—
350C4—161no—
351C4C61×#38611yescharacteristic
352C4C2×#102×C6111yescharacteristic
353C4C61×#46511yescharacteristic
354C4C61×#46611yescharacteristic
355C2—21no—
356C2—21no—
357C2—21no—
358C2—42no—
359C2—161no—
360C2C61×#189311yescharacteristic
subgroupG/H
centerC4×C61#466
commutatorC2×C8C22×C4×C61
Frattini, cosocleC22×C8C23×C61
socleC2×C61#1893
prime radicalC61×#3067C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C61 ◁ C22×C4×C61 ◁ C2×#131×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#504C2semidirect
3. C61×#2145C2semidirect
4. C2×C61×#359C2semidirect
5. C61×#1814C2semidirect
6. C61×#1388C2semidirect
7. C61×#1382C2semidirect
17. C61×#473C4semidirect
18. C61×#472C4semidirect
159. #13071C61direct (N × H)
175. C2×#504C2×C61semidirect
177. #2145C2×C61semidirect
178. C2×#359C2×C61semidirect
179. #1814C2×C61semidirect
180. #1388C2×C61semidirect
181. #1382C2×C61semidirect
197. #473C4×C61semidirect
198. #472C4×C61semidirect
209. C61#13071direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C61×#5042
C61×#30672
C61×#21452
C2×C61×#3592
C61×#18142
C61×#13882
C61×#13822
#1307161