Finite Group Databasebeta

← C61×#13030 #29516463

Subgroups — C61×#13030 #29516463

Order 15616.

476 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3414C211yesmaximal, characteristic
2C61×#2952C211yesmaximal, characteristic, complemented
3C61×#2145C211yesmaximal, characteristic, complemented
4C2×C61×#360C211yesmaximal, characteristic, complemented
5C61×#1976C211yesmaximal, characteristic, complemented
6C61×#1386C211yesmaximal, characteristic, complemented
7C61×#1378C211yesmaximal, characteristic, complemented
8C2×#135×C61C2211yescharacteristic
9C2×#135×C61C2211yescharacteristic
10C61×#520—21no—
11C61×#510—21no—
12C61×#510C412yescomplemented
13C61×#509—21no—
14C61×#509C412yescomplemented
15C61×#508—22no—
16C2×M32×C61C2211yescharacteristic
17C2×M32×C61C2211yescharacteristic
18C61×#442—21no—
19C61×#441—21no—
20C4×SD16×C61—22no—
21C61×#427C2211yescharacteristic
22C2×#106×C61C2211yescharacteristic
23C61×#421—21no—
24C61×#417—21no—
25C61×#410—21no—
26C61×#405C2211yescharacteristic
27C61×#360—22no—
28C61×#360—22no—
29C2×#41×C61—21no—
30C2×#41×C61—21no—
31#135×C61—21no—
32#135×C61—21no—
33#135×C61—21no—
34#135×C61—21no—
35#135×C61—21no—
36#135×C61—21no—
37#135×C61C2×C412yes—
38#135×C61D412yes—
39C2×Q16×C61C2×C411yescharacteristic, complemented
40C2×Q16×C61D411yescharacteristic
41C2×SD16×C61—21no—
42C2×SD16×C61—21no—
43C2×D8×C61C2×C411yescharacteristic, complemented
44C2×D8×C61D411yescharacteristic
45C2×M16×C61D411yescharacteristic
46C22×C8×C61C2311yescharacteristic
47C4×Q8×C61—22no—
48C4×D4×C61—22no—
49C4×D4×C61—42no—
50#117×C61—21no—
51#117×C61—41no—
52#117×C61D411yescharacteristic
53C2×C4⋊C4×C61—21no—
54C2×C4⋊C4×C61—41no—
55Q32×C61—22no—
56SD32×C61—22no—
57SD32×C61—22no—
58D16×C61—22no—
59M32×C61—21no—
60M32×C61—21no—
61M32×C61—21no—
62M32×C61C2×C412yescomplemented
63C2×C16×C61—21no—
64C2×C16×C61—21no—
65#107×C61—21no—
66#106×C61—21no—
67#106×C61—21no—
68#106×C61D412yes—
69#104×C61—42no—
70#103×C61—22no—
71#102×C61—22no—
72#99×C61—42no—
73#97×C61—21no—
74C4×C8×C61—21no—
75#41×C61—22no—
76#41×C61—22no—
77#41×C61—41no—
78#41×C61—41no—
79#41×C61—41no—
80#41×C61—41no—
81#41×C61—41no—
82#41×C61—41no—
83C2×Q8×C61—21no—
84C2×Q8×C61—21no—
85C2×D4×C61—21no—
86C2×D4×C61—21no—
87C2×D4×C61—41no—
88C2×D4×C61—41no—
89C22×C4×C61—42no—
90C22×C4×C61—41no—
91C22×C4×C61—41no—
92C22×C4×C61—41no—
93C22×C4×C61C2×D411yescharacteristic
94Q16×C61—21no—
95Q16×C61—21no—
96Q16×C61—21no—
97Q16×C61C22⋊C412yes—
98SD16×C61—22no—
99SD16×C61—22no—
100SD16×C61—41no—
101SD16×C61—41no—
102D8×C61—21no—
103D8×C61—21no—
104D8×C61—21no—
105D8×C61C22⋊C412yes—
106M16×C61—21no—
107M16×C61—21no—
108C2×C8×C61—21no—
109C2×C8×C61C22×C411yescharacteristic
110C2×C8×C61C2×D411yescharacteristic
111C2×C8×C61C2×D411yescharacteristic
112C2×C8×C61C2×D411yescharacteristic
113C2×C8×C61#4111yescharacteristic
114C2×C8×C61#4111yescharacteristic
115C4⋊C4×C61—21no—
116C4⋊C4×C61—22no—
117C4⋊C4×C61—42no—
118C4⋊C4×C61—41no—
119C4⋊C4×C61—41no—
120C22⋊C4×C61—42no—
121C22⋊C4×C61—41no—
122C22⋊C4×C61D812yes—
123C42×C61—21no—
124C42×C61—42no—
125C42×C61—41no—
126C16×C61—22no—
127C16×C61—41no—
128C23×C61—41no—
129C23×C61—41no—
130C23×C61C2×D811yescharacteristic
131Q8×C61—22no—
132Q8×C61—41no—
133Q8×C61—41no—
134Q8×C61—41no—
135D4×C61—22no—
136D4×C61—42no—
137D4×C61—42no—
138D4×C61—41no—
139D4×C61—41no—
140D4×C61—41no—
141D4×C61—81no—
142D4×C61—81no—
143C2×C4×C61—22no—
144C2×C4×C61—41no—
145C2×C4×C61—42no—
146C2×C4×C61—42no—
147C2×C4×C61—41no—
148C2×C4×C61—42no—
149C2×C4×C61—81no—
150C2×C4×C61—81no—
151C2×C4×C61—81no—
152C2×C4×C61—162no—
153C2×C4×C61—161no—
154C2×C4×C61C4×D411yescharacteristic
155C2×C4×C61#12011yescharacteristic
156C2×C4×C61#12111yescharacteristic
157C2×C4×C61#13511yescharacteristic
158C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
160C8×C61—41no—
161C8×C61C2×C22⋊C411yescharacteristic
162C8×C61C4×D411yescharacteristic
163C8×C61#12111yescharacteristic
164C8×C61#12311yescharacteristic
165#13030C6111yesmaximal, characteristic, direct product factor, Sylow
166C22×C61—41no—
167C22×C61—42no—
168C22×C61—81no—
169C22×C61—81no—
170C22×C61—81no—
171C22×C61—161no—
172C22×C61C4×D811yescharacteristic
173C22×C61#44711yescharacteristic
174C22×C61#45911yescharacteristic
175C4×C61—42no—
176C4×C61—42no—
177C4×C61—82no—
178C4×C61—81no—
179C4×C61—161no—
180C4×C61#38611yescharacteristic
181C4×C61#44211yescharacteristic
182C4×C61#44911yescharacteristic
183C4×C61#46311yescharacteristic
184#3414C2×C6111yescharacteristic
185#2952C2×C6111yescharacteristic, complemented
186#2145C2×C6111yescharacteristic, complemented
187C2×#360C2×C6111yescharacteristic, complemented
188#1976C2×C6111yescharacteristic, complemented
189#1386C2×C6111yescharacteristic, complemented
190#1378C2×C6111yescharacteristic, complemented
191C2×C61—21no—
192C2×C61—21no—
193C2×C61—21no—
194C2×C61—82no—
195C2×C61—161no—
196C2×C61#187911yescharacteristic
197C2×#135C22×C6111yescharacteristic
198C2×#135C22×C6111yescharacteristic
199#520—21no—
200#510—21no—
201#510C4×C6112yescomplemented
202#509—21no—
203#509C4×C6112yescomplemented
204#508—22no—
205C2×M32C22×C6111yescharacteristic
206C2×M32C22×C6111yescharacteristic
207#442—21no—
208#441—21no—
209C4×SD16—22no—
210#427C22×C6111yescharacteristic
211C2×#106C22×C6111yescharacteristic
212#421—21no—
213#417—21no—
214#410—21no—
215#405C22×C6111yescharacteristic
216#360—22no—
217#360—22no—
218C61#1303011yescharacteristic, direct product factor, Sylow
219C2×#41—21no—
220C2×#41—21no—
221#135—21no—
222#135—21no—
223#135—21no—
224#135—21no—
225#135—21no—
226#135—21no—
227#135C2×C4×C6112yes—
228#135D4×C6112yes—
229C2×Q16C2×C4×C6111yescharacteristic, complemented
230C2×Q16D4×C6111yescharacteristic
231C2×SD16—21no—
232C2×SD16—21no—
233C2×D8C2×C4×C6111yescharacteristic, complemented
234C2×D8D4×C6111yescharacteristic
235C2×M16D4×C6111yescharacteristic
236C22×C8C23×C6111yescharacteristic
237C4×Q8—22no—
238C4×D4—22no—
239C4×D4—42no—
240#117—21no—
241#117—41no—
242#117D4×C6111yescharacteristic
243C2×C4⋊C4—21no—
244C2×C4⋊C4—41no—
245Q32—22no—
246SD32—22no—
247SD32—22no—
248D16—22no—
249M32—21no—
250M32—21no—
251M32—21no—
252M32C2×C4×C6112yescomplemented
253C2×C16—21no—
254C2×C16—21no—
255#107—21no—
256#106—21no—
257#106—21no—
258#106D4×C6112yes—
259#104—42no—
260#103—22no—
261#102—22no—
262#99—42no—
263#97—21no—
264C4×C8—21no—
265#41—22no—
266#41—22no—
267#41—41no—
268#41—41no—
269#41—41no—
270#41—41no—
271#41—41no—
272#41—41no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—41no—
278C2×D4—41no—
279C22×C4—42no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4C2×D4×C6111yescharacteristic
284Q16—21no—
285Q16—21no—
286Q16—21no—
287Q16C22⋊C4×C6112yes—
288SD16—22no—
289SD16—22no—
290SD16—41no—
291SD16—41no—
292D8—21no—
293D8—21no—
294D8—21no—
295D8C22⋊C4×C6112yes—
296M16—21no—
297M16—21no—
298C2×C8—21no—
299C2×C8C22×C4×C6111yescharacteristic
300C2×C8C2×D4×C6111yescharacteristic
301C2×C8C2×D4×C6111yescharacteristic
302C2×C8C2×D4×C6111yescharacteristic
303C2×C8#41×C6111yescharacteristic
304C2×C8#41×C6111yescharacteristic
305C4⋊C4—21no—
306C4⋊C4—22no—
307C4⋊C4—42no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C22⋊C4—42no—
311C22⋊C4—41no—
312C22⋊C4D8×C6112yes—
313C42—21no—
314C42—42no—
315C42—41no—
316C16—22no—
317C16—41no—
318C23—41no—
319C23—41no—
320C23C2×D8×C6111yescharacteristic
321Q8—22no—
322Q8—41no—
323Q8—41no—
324Q8—41no—
325D4—22no—
326D4—42no—
327D4—42no—
328D4—41no—
329D4—41no—
330D4—41no—
331D4—81no—
332D4—81no—
333C2×C4—22no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—162no—
343C2×C4—161no—
344C2×C4C4×D4×C6111yescharacteristic
345C2×C4#120×C6111yescharacteristic
346C2×C4#121×C6111yescharacteristic
347C2×C4#135×C6111yescharacteristic
348C2×C4AGL(1,ℤ/8)×C6111yescharacteristic
349C2×C4AGL(1,ℤ/8)×C6111yescharacteristic
350C8—41no—
351C8C2×C22⋊C4×C6111yescharacteristic
352C8C4×D4×C6111yescharacteristic
353C8#121×C6111yescharacteristic
354C8#123×C6111yescharacteristic
355C22—41no—
356C22—42no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22—161no—
361C22C4×D8×C6111yescharacteristic
362C22C61×#44711yescharacteristic
363C22C61×#45911yescharacteristic
364C4—42no—
365C4—42no—
366C4—82no—
367C4—81no—
368C4—161no—
369C4C61×#38611yescharacteristic
370C4C61×#44211yescharacteristic
371C4C61×#44911yescharacteristic
372C4C61×#46311yescharacteristic
373C2—21no—
374C2—21no—
375C2—21no—
376C2—82no—
377C2—161no—
378C2C61×#187911yescharacteristic
subgroupG/H
center, socleC2×C61#1879
commutatorC2×C8C22×C4×C61
Frattini, cosocleC22×C8C23×C61
prime radicalC61×#3414C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C61 ◁ C22×C4×C61 ◁ C61×#405 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#2952C2semidirect
3. C61×#2145C2semidirect
4. C2×C61×#360C2semidirect
5. C61×#1976C2semidirect
6. C61×#1386C2semidirect
7. C61×#1378C2semidirect
12. C61×#510C4semidirect
14. C61×#509C4semidirect
39. C2×Q16×C61C2×C4semidirect
43. C2×D8×C61C2×C4semidirect
62. M32×C61C2×C4semidirect
165. #13030C61direct (N × H)
185. #2952C2×C61semidirect
186. #2145C2×C61semidirect
187. C2×#360C2×C61semidirect
188. #1976C2×C61semidirect
189. #1386C2×C61semidirect
190. #1378C2×C61semidirect
201. #510C4×C61semidirect
203. #509C4×C61semidirect
218. C61#13030direct (N × H)
229. C2×Q16C2×C4×C61semidirect
233. C2×D8C2×C4×C61semidirect
252. M32C2×C4×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#34142
C61×#29522
C61×#21452
C2×C61×#3602
C61×#19762
C61×#13862
C61×#13782
#1303061