Finite Group Databasebeta

← C61×#13022 #29516455

Subgroups — C61×#13022 #29516455

Order 15616.

494 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#509C211yesmaximal, characteristic
2C61×#2951C211yesmaximal, characteristic, complemented
3C2×C61×#359C211yesmaximal, characteristic, complemented
4C2×C61×#357C211yesmaximal, characteristic, complemented
5C61×#1978C211yesmaximal, characteristic, complemented
6C61×#1387C211yesmaximal, characteristic, complemented
7C61×#1379C211yesmaximal, characteristic, complemented
8C2×#135×C61C2211yescharacteristic
9C22×D8×C61C2211yescharacteristic
10C61×#520—21no—
11C61×#509—22no—
12C61×#509C414yescomplemented
13C2×SD32×C61—21no—
14C2×D16×C61—21no—
15C2×M32×C61C2211yescharacteristic
16C22×C16×C61C2211yescharacteristic
17C61×#440—22no—
18C4×Q16×C61—21no—
19C4×D8×C61—21no—
20C2×#108×C61C2211yescharacteristic
21C2×#107×C61C2211yescharacteristic
22C61×#418—21no—
23C61×#417—21no—
24C2×#100×C61—21no—
25C61×#405C2211yescharacteristic
26C61×#359—22no—
27C61×#357—22no—
28C2×#41×C61—21no—
29C22×D4×C61—21no—
30#135×C61—21no—
31#135×C61—21no—
32#135×C61C2×C412yes—
33#135×C61D412yes—
34C2×Q16×C61D411yescharacteristic
35C2×SD16×C61—21no—
36C2×D8×C61—21no—
37C2×D8×C61—21no—
38C2×D8×C61—21no—
39C2×D8×C61—21no—
40C2×D8×C61—21no—
41C2×D8×C61C2×C412yescomplemented
42C2×D8×C61D411yescharacteristic
43C2×M16×C61—21no—
44C2×M16×C61D411yescharacteristic
45C22×C8×C61C2311yescharacteristic
46C4×Q8×C61—22no—
47C4×D4×C61—22no—
48C4×D4×C61—42no—
49#117×C61—41no—
50#117×C61D411yescharacteristic
51C2×C4⋊C4×C61—21no—
52C2×C4⋊C4×C61—41no—
53SD32×C61—24no—
54D16×C61—24no—
55M32×C61—21no—
56M32×C61C2×C412yescomplemented
57C2×C16×C61—21no—
58C2×C16×C61—21no—
59C2×C16×C61—21no—
60C2×C16×C61—21no—
61#108×C61—21no—
62#108×C61—21no—
63#107×C61—21no—
64#107×C61D412yes—
65#103×C61—22no—
66#102×C61—22no—
67#102×C61—41no—
68#102×C61—41no—
69#100×C61—42no—
70#97×C61—21no—
71C4×C8×C61—21no—
72C24×C61—41no—
73#41×C61—22no—
74#41×C61—22no—
75#41×C61—41no—
76#41×C61—41no—
77C2×Q8×C61—21no—
78C2×D4×C61—22no—
79C2×D4×C61—21no—
80C2×D4×C61—41no—
81C2×D4×C61—41no—
82C2×D4×C61—41no—
83C2×D4×C61—41no—
84C2×D4×C61—41no—
85C2×D4×C61—41no—
86C22×C4×C61—42no—
87C22×C4×C61—41no—
88C22×C4×C61—41no—
89C22×C4×C61C2×D411yescharacteristic
90Q16×C61—21no—
91Q16×C61C22⋊C412yes—
92SD16×C61—22no—
93SD16×C61—22no—
94D8×C61—22no—
95D8×C61—22no—
96D8×C61—21no—
97D8×C61—41no—
98D8×C61—41no—
99D8×C61C22⋊C412yes—
100M16×C61—21no—
101M16×C61—21no—
102M16×C61—41no—
103M16×C61—41no—
104C2×C8×C61—21no—
105C2×C8×C61—41no—
106C2×C8×C61C22×C411yescharacteristic
107C2×C8×C61C2×D411yescharacteristic
108C2×C8×C61C2×D411yescharacteristic
109C2×C8×C61C2×D411yescharacteristic
110C2×C8×C61#4111yescharacteristic
111C2×C8×C61#4111yescharacteristic
112C4⋊C4×C61—22no—
113C4⋊C4×C61—42no—
114C4⋊C4×C61—41no—
115C4⋊C4×C61D811yescharacteristic
116C4⋊C4×C61D811yescharacteristic
117C22⋊C4×C61—21no—
118C22⋊C4×C61—42no—
119C42×C61—21no—
120C42×C61—42no—
121C16×C61—22no—
122C16×C61—41no—
123C23×C61—41no—
124C23×C61—42no—
125C23×C61—81no—
126C23×C61—81no—
127C23×C61—161no—
128C23×C61—161no—
129C23×C61AGL(1,ℤ/8)11yescharacteristic
130Q8×C61—22no—
131Q8×C61—41no—
132D4×C61—22no—
133D4×C61—42no—
134D4×C61—42no—
135D4×C61—42no—
136D4×C61—42no—
137D4×C61—41no—
138D4×C61—81no—
139D4×C61—81no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—41no—
143C2×C4×C61—42no—
144C2×C4×C61—42no—
145C2×C4×C61—42no—
146C2×C4×C61—162no—
147C2×C4×C61—161no—
148C2×C4×C61C4×D411yescharacteristic
149C2×C4×C61#12011yescharacteristic
150C2×C4×C61#12111yescharacteristic
151C2×C4×C61C2×D811yescharacteristic
152C2×C4×C61#13511yescharacteristic
153C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
154C8×C61—41no—
155C8×C61—81no—
156C8×C61C2×C22⋊C411yescharacteristic
157C8×C61C4×D411yescharacteristic
158C8×C61#12111yescharacteristic
159C8×C61#12311yescharacteristic
160#13022C6111yesmaximal, characteristic, direct product factor, Sylow
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—42no—
164C22×C61—81no—
165C22×C61—81no—
166C22×C61—82no—
167C22×C61—162no—
168C22×C61—162no—
169C22×C61—161no—
170C22×C61—161no—
171C22×C61#44211yescharacteristic
172C22×C61#44711yescharacteristic
173C22×C61#46311yescharacteristic
174C4×C61—42no—
175C4×C61—41no—
176C4×C61—41no—
177C4×C61—82no—
178C4×C61#38611yescharacteristic
179C4×C61C4×D811yescharacteristic
180C4×C61#44911yescharacteristic
181C4×C61#45911yescharacteristic
182C2×#509C2×C6111yescharacteristic
183#2951C2×C6111yescharacteristic, complemented
184C2×#359C2×C6111yescharacteristic, complemented
185C2×#357C2×C6111yescharacteristic, complemented
186#1978C2×C6111yescharacteristic, complemented
187#1387C2×C6111yescharacteristic, complemented
188#1379C2×C6111yescharacteristic, complemented
189C2×C61—21no—
190C2×C61—21no—
191C2×C61—82no—
192C2×C61—162no—
193C2×C61#187911yescharacteristic
194C2×C61#219211yescharacteristic
195C2×C61#219311yescharacteristic
196C2×#135C22×C6111yescharacteristic
197C22×D8C22×C6111yescharacteristic
198#520—21no—
199#509—22no—
200#509C4×C6114yescomplemented
201C2×SD32—21no—
202C2×D16—21no—
203C2×M32C22×C6111yescharacteristic
204C22×C16C22×C6111yescharacteristic
205#440—22no—
206C4×Q16—21no—
207C4×D8—21no—
208C2×#108C22×C6111yescharacteristic
209C2×#107C22×C6111yescharacteristic
210#418—21no—
211#417—21no—
212C2×#100—21no—
213#405C22×C6111yescharacteristic
214#359—22no—
215#357—22no—
216C61#1302211yescharacteristic, direct product factor, Sylow
217C2×#41—21no—
218C22×D4—21no—
219#135—21no—
220#135—21no—
221#135C2×C4×C6112yes—
222#135D4×C6112yes—
223C2×Q16D4×C6111yescharacteristic
224C2×SD16—21no—
225C2×D8—21no—
226C2×D8—21no—
227C2×D8—21no—
228C2×D8—21no—
229C2×D8—21no—
230C2×D8C2×C4×C6112yescomplemented
231C2×D8D4×C6111yescharacteristic
232C2×M16—21no—
233C2×M16D4×C6111yescharacteristic
234C22×C8C23×C6111yescharacteristic
235C4×Q8—22no—
236C4×D4—22no—
237C4×D4—42no—
238#117—41no—
239#117D4×C6111yescharacteristic
240C2×C4⋊C4—21no—
241C2×C4⋊C4—41no—
242SD32—24no—
243D16—24no—
244M32—21no—
245M32C2×C4×C6112yescomplemented
246C2×C16—21no—
247C2×C16—21no—
248C2×C16—21no—
249C2×C16—21no—
250#108—21no—
251#108—21no—
252#107—21no—
253#107D4×C6112yes—
254#103—22no—
255#102—22no—
256#102—41no—
257#102—41no—
258#100—42no—
259#97—21no—
260C4×C8—21no—
261C24—41no—
262#41—22no—
263#41—22no—
264#41—41no—
265#41—41no—
266C2×Q8—21no—
267C2×D4—22no—
268C2×D4—21no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C22×C4—42no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4C2×D4×C6111yescharacteristic
279Q16—21no—
280Q16C22⋊C4×C6112yes—
281SD16—22no—
282SD16—22no—
283D8—22no—
284D8—22no—
285D8—21no—
286D8—41no—
287D8—41no—
288D8C22⋊C4×C6112yes—
289M16—21no—
290M16—21no—
291M16—41no—
292M16—41no—
293C2×C8—21no—
294C2×C8—41no—
295C2×C8C22×C4×C6111yescharacteristic
296C2×C8C2×D4×C6111yescharacteristic
297C2×C8C2×D4×C6111yescharacteristic
298C2×C8C2×D4×C6111yescharacteristic
299C2×C8#41×C6111yescharacteristic
300C2×C8#41×C6111yescharacteristic
301C4⋊C4—22no—
302C4⋊C4—42no—
303C4⋊C4—41no—
304C4⋊C4D8×C6111yescharacteristic
305C4⋊C4D8×C6111yescharacteristic
306C22⋊C4—21no—
307C22⋊C4—42no—
308C42—21no—
309C42—42no—
310C16—22no—
311C16—41no—
312C23—41no—
313C23—42no—
314C23—81no—
315C23—81no—
316C23—161no—
317C23—161no—
318C23AGL(1,ℤ/8)×C6111yescharacteristic
319Q8—22no—
320Q8—41no—
321D4—22no—
322D4—42no—
323D4—42no—
324D4—42no—
325D4—42no—
326D4—41no—
327D4—81no—
328D4—81no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—162no—
336C2×C4—161no—
337C2×C4C4×D4×C6111yescharacteristic
338C2×C4#120×C6111yescharacteristic
339C2×C4#121×C6111yescharacteristic
340C2×C4C2×D8×C6111yescharacteristic
341C2×C4#135×C6111yescharacteristic
342C2×C4AGL(1,ℤ/8)×C6111yescharacteristic
343C8—41no—
344C8—81no—
345C8C2×C22⋊C4×C6111yescharacteristic
346C8C4×D4×C6111yescharacteristic
347C8#121×C6111yescharacteristic
348C8#123×C6111yescharacteristic
349C22—21no—
350C22—21no—
351C22—42no—
352C22—81no—
353C22—81no—
354C22—82no—
355C22—162no—
356C22—162no—
357C22—161no—
358C22—161no—
359C22C61×#44211yescharacteristic
360C22C61×#44711yescharacteristic
361C22C61×#46311yescharacteristic
362C4—42no—
363C4—41no—
364C4—41no—
365C4—82no—
366C4C61×#38611yescharacteristic
367C4C4×D8×C6111yescharacteristic
368C4C61×#44911yescharacteristic
369C4C61×#45911yescharacteristic
370C2—21no—
371C2—21no—
372C2—82no—
373C2—162no—
374C2C61×#187911yescharacteristic
375C2C61×#219211yescharacteristic
376C2C61×#219311yescharacteristic
subgroupG/H
center, socleC22×C61#447
commutatorC2×C8C22×C4×C61
Frattini, cosocleC22×C8C23×C61
prime radicalC2×C61×#509C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C22×C4×C61 ◁ C61×#405 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#2951C2semidirect
3. C2×C61×#359C2semidirect
4. C2×C61×#357C2semidirect
5. C61×#1978C2semidirect
6. C61×#1387C2semidirect
7. C61×#1379C2semidirect
12. C61×#509C4semidirect
41. C2×D8×C61C2×C4semidirect
56. M32×C61C2×C4semidirect
160. #13022C61direct (N × H)
183. #2951C2×C61semidirect
184. C2×#359C2×C61semidirect
185. C2×#357C2×C61semidirect
186. #1978C2×C61semidirect
187. #1387C2×C61semidirect
188. #1379C2×C61semidirect
200. #509C4×C61semidirect
216. C61#13022direct (N × H)
230. C2×D8C2×C4×C61semidirect
245. M32C2×C4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#5092
C61×#29512
C2×C61×#3592
C2×C61×#3572
C61×#19782
C61×#13872
C61×#13792
#1302261