Finite Group Databasebeta

← C61×#9159 #29512592

Subgroups — C61×#9159 #29512592

Order 15616.

452 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3116C211yesmaximal, characteristic
2C61×#2970C211yesmaximal, characteristic
3C61×#1759C211yesmaximal, characteristic
4C61×#1526C211yesmaximal, characteristic, complemented
5C61×#1506C211yesmaximal, characteristic, complemented
6C61×#1300C211yesmaximal, characteristic, complemented
7C61×#1291C211yesmaximal, characteristic, complemented
8C61×#533C2211yescharacteristic
9C4×#41×C61C2211yescharacteristic
10C61×#485—21no—
11C61×#477C411yescharacteristic, complemented
12C61×#476C411yescharacteristic, complemented
13C61×#462C411yescharacteristic, complemented
14C61×#461C411yescharacteristic, complemented
15C61×#452—21no—
16C61×#446—21no—
17C61×#441—21no—
18C61×#440—21no—
19C61×#435—22no—
20C8×D4×C61—21no—
21C61×#432—21no—
22C61×#432C2211yescharacteristic
23C61×#432C2211yescharacteristic
24C2×#104×C61—21no—
25C4×M16×C61C2211yescharacteristic
26C4×M16×C61C2211yescharacteristic
27C2×#97×C61—21no—
28C61×#376C2211yescharacteristic
29C61×#339—21no—
30C61×#330—21no—
31C61×#330—21no—
32C61×#328—22no—
33C2×#41×C61D411yescharacteristic
34C2×Q16×C61—21no—
35C2×SD16×C61—21no—
36C2×M16×C61—21no—
37C2×M16×C61—21no—
38C22×C8×C61—22no—
39C4⋊Q8×C61C2×C411yescharacteristic
40C4⋊Q8×C61C2×C411yescharacteristic
41#125×C61—21no—
42C22⋊Q8×C61—21no—
43C22⋊Q8×C61—21no—
44C4×Q8×C61—21no—
45C4×Q8×C61—21no—
46C4×Q8×C61C2×C411yescharacteristic
47C4×Q8×C61D411yescharacteristic
48C4×D4×C61—21no—
49C4×D4×C61—21no—
50C4×D4×C61C2×C411yescharacteristic
51C4×D4×C61D411yescharacteristic
52#117×C61—21no—
53#117×C61—21no—
54#117×C61D411yescharacteristic
55C2×C42×C61—21no—
56C2×C42×C61—21no—
57C2×C42×C61C2311yescharacteristic
58#107×C61—21no—
59#106×C61—21no—
60C4⋊C8×C61—22no—
61C4⋊C8×C61—21no—
62C4⋊C8×C61C2×C411yescharacteristic
63C4⋊C8×C61C2×C411yescharacteristic
64#104×C61—24no—
65#103×C61—21no—
66#103×C61—21no—
67#103×C61—21no—
68#102×C61—21no—
69C22⋊C8×C61—22no—
70C22⋊C8×C61—21no—
71C22⋊C8×C61D412yes—
72#97×C61—22no—
73#97×C61—21no—
74#97×C61—21no—
75#97×C61—21no—
76#97×C61D411yescharacteristic
77#97×C61D411yescharacteristic
78C4×C8×C61—21no—
79C4×C8×C61—21no—
80#95×C61—21no—
81#95×C61—21no—
82#41×C61—22no—
83#41×C61—41no—
84C2×Q8×C61—21no—
85C2×Q8×C61—21no—
86C2×Q8×C61C22⋊C411yescharacteristic
87C2×D4×C61—21no—
88C2×D4×C61C22⋊C411yescharacteristic
89C22×C4×C61—21no—
90C22×C4×C61—21no—
91C22×C4×C61—21no—
92C22×C4×C61—41no—
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61C2×D411yescharacteristic
95C22×C4×C61#4111yescharacteristic
96Q16×C61—42no—
97SD16×C61—42no—
98M16×C61—22no—
99M16×C61—42no—
100M16×C61—41no—
101C2×C8×C61—21no—
102C2×C8×C61—21no—
103C2×C8×C61—21no—
104C2×C8×C61—21no—
105C2×C8×C61—22no—
106C2×C8×C61—44no—
107C2×C8×C61—41no—
108C4⋊C4×C61—21no—
109C4⋊C4×C61—21no—
110C4⋊C4×C61—21no—
111C4⋊C4×C61—21no—
112C4⋊C4×C61—21no—
113C4⋊C4×C61—21no—
114C4⋊C4×C61—41no—
115C4⋊C4×C61—41no—
116C4⋊C4×C61C22⋊C411yescharacteristic
117C4⋊C4×C61C22⋊C411yescharacteristic
118C22⋊C4×C61—21no—
119C22⋊C4×C61—21no—
120C22⋊C4×C61—21no—
121C22⋊C4×C61—41no—
122C42×C61—21no—
123C42×C61—21no—
124C42×C61—21no—
125C42×C61—22no—
126C42×C61—41no—
127C42×C61—41no—
128C42×C61C22×C411yescharacteristic
129C42×C61C2×D411yescharacteristic
130C42×C61C2×D411yescharacteristic
131C42×C61#4111yescharacteristic
132C23×C61—21no—
133C23×C61#12111yescharacteristic
134Q8×C61—21no—
135Q8×C61—21no—
136Q8×C61—41no—
137Q8×C61—41no—
138Q8×C61—81no—
139D4×C61—21no—
140D4×C61—42no—
141D4×C61#10412yes—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—42no—
150C2×C4×C61—42no—
151C2×C4×C61—42no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—81no—
155C2×C4×C61—81no—
156C2×C4×C61—81no—
157C2×C4×C61C2×C22⋊C411yescharacteristic
158C2×C4×C61C4×D411yescharacteristic
159C2×C4×C61C4×D411yescharacteristic
160C2×C4×C61#12011yescharacteristic
161C2×C4×C61#12111yescharacteristic
162C2×C4×C61#12311yescharacteristic
163C8×C61—22no—
164C8×C61—42no—
165C8×C61—41no—
166C8×C61—42no—
167C8×C61—41no—
168C8×C61—41no—
169#9159C6111yesmaximal, characteristic, direct product factor, Sylow
170C22×C61—21no—
171C22×C61—22no—
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—41no—
175C22×C61—41no—
176C22×C61#38611yescharacteristic
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—41no—
183C4×C61—41no—
184C4×C61—41no—
185C4×C61—82no—
186C4×C61—81no—
187C4×C61—81no—
188C4×C61C2×#10411yescharacteristic
189C4×C61#42111yescharacteristic
190#3116C2×C6111yescharacteristic
191#2970C2×C6111yescharacteristic
192#1759C2×C6111yescharacteristic
193#1526C2×C6111yescharacteristic, complemented
194#1506C2×C6111yescharacteristic, complemented
195#1300C2×C6111yescharacteristic, complemented
196#1291C2×C6111yescharacteristic, complemented
197C2×C61—41no—
198C2×C61—42no—
199C2×C61#187111yescharacteristic
200C2×C61#190211yescharacteristic
201C2×C61#190611yescharacteristic
202#533C22×C6111yescharacteristic
203C4×#41C22×C6111yescharacteristic
204#485—21no—
205#477C4×C6111yescharacteristic, complemented
206#476C4×C6111yescharacteristic, complemented
207#462C4×C6111yescharacteristic, complemented
208#461C4×C6111yescharacteristic, complemented
209#452—21no—
210#446—21no—
211#441—21no—
212#440—21no—
213#435—22no—
214C8×D4—21no—
215#432—21no—
216#432C22×C6111yescharacteristic
217#432C22×C6111yescharacteristic
218C2×#104—21no—
219C4×M16C22×C6111yescharacteristic
220C4×M16C22×C6111yescharacteristic
221C2×#97—21no—
222#376C22×C6111yescharacteristic
223#339—21no—
224#330—21no—
225#330—21no—
226#328—22no—
227C61#915911yescharacteristic, direct product factor, Sylow
228C2×#41D4×C6111yescharacteristic
229C2×Q16—21no—
230C2×SD16—21no—
231C2×M16—21no—
232C2×M16—21no—
233C22×C8—22no—
234C4⋊Q8C2×C4×C6111yescharacteristic
235C4⋊Q8C2×C4×C6111yescharacteristic
236#125—21no—
237C22⋊Q8—21no—
238C22⋊Q8—21no—
239C4×Q8—21no—
240C4×Q8—21no—
241C4×Q8C2×C4×C6111yescharacteristic
242C4×Q8D4×C6111yescharacteristic
243C4×D4—21no—
244C4×D4—21no—
245C4×D4C2×C4×C6111yescharacteristic
246C4×D4D4×C6111yescharacteristic
247#117—21no—
248#117—21no—
249#117D4×C6111yescharacteristic
250C2×C42—21no—
251C2×C42—21no—
252C2×C42C23×C6111yescharacteristic
253#107—21no—
254#106—21no—
255C4⋊C8—22no—
256C4⋊C8—21no—
257C4⋊C8C2×C4×C6111yescharacteristic
258C4⋊C8C2×C4×C6111yescharacteristic
259#104—24no—
260#103—21no—
261#103—21no—
262#103—21no—
263#102—21no—
264C22⋊C8—22no—
265C22⋊C8—21no—
266C22⋊C8D4×C6112yes—
267#97—22no—
268#97—21no—
269#97—21no—
270#97—21no—
271#97D4×C6111yescharacteristic
272#97D4×C6111yescharacteristic
273C4×C8—21no—
274C4×C8—21no—
275#95—21no—
276#95—21no—
277#41—22no—
278#41—41no—
279C2×Q8—21no—
280C2×Q8—21no—
281C2×Q8C22⋊C4×C6111yescharacteristic
282C2×D4—21no—
283C2×D4C22⋊C4×C6111yescharacteristic
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—41no—
288C22×C4C2×D4×C6111yescharacteristic
289C22×C4C2×D4×C6111yescharacteristic
290C22×C4#41×C6111yescharacteristic
291Q16—42no—
292SD16—42no—
293M16—22no—
294M16—42no—
295M16—41no—
296C2×C8—21no—
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—21no—
300C2×C8—22no—
301C2×C8—44no—
302C2×C8—41no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4C22⋊C4×C6111yescharacteristic
312C4⋊C4C22⋊C4×C6111yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—41no—
317C42—21no—
318C42—21no—
319C42—21no—
320C42—22no—
321C42—41no—
322C42—41no—
323C42C22×C4×C6111yescharacteristic
324C42C2×D4×C6111yescharacteristic
325C42C2×D4×C6111yescharacteristic
326C42#41×C6111yescharacteristic
327C23—21no—
328C23#121×C6111yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—41no—
332Q8—41no—
333Q8—81no—
334D4—21no—
335D4—42no—
336D4#104×C6112yes—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4C2×C22⋊C4×C6111yescharacteristic
353C2×C4C4×D4×C6111yescharacteristic
354C2×C4C4×D4×C6111yescharacteristic
355C2×C4#120×C6111yescharacteristic
356C2×C4#121×C6111yescharacteristic
357C2×C4#123×C6111yescharacteristic
358C8—22no—
359C8—42no—
360C8—41no—
361C8—42no—
362C8—41no—
363C8—41no—
364C22—21no—
365C22—22no—
366C22—21no—
367C22—21no—
368C22—41no—
369C22—41no—
370C22C61×#38611yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—82no—
380C4—81no—
381C4—81no—
382C4C2×#104×C6111yescharacteristic
383C4C61×#42111yescharacteristic
384C2—41no—
385C2—42no—
386C2C61×#187111yescharacteristic
387C2C61×#190211yescharacteristic
388C2C61×#190611yescharacteristic
subgroupG/H
center, socleC22×C61#386
commutatorC42C22×C4×C61
Frattini, cosocleC2×C42C23×C61
prime radicalC2×#41×C61D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
4. C61×#1526C2semidirect
5. C61×#1506C2semidirect
6. C61×#1300C2semidirect
7. C61×#1291C2semidirect
11. C61×#477C4semidirect
12. C61×#476C4semidirect
13. C61×#462C4semidirect
14. C61×#461C4semidirect
169. #9159C61direct (N × H)
193. #1526C2×C61semidirect
194. #1506C2×C61semidirect
195. #1300C2×C61semidirect
196. #1291C2×C61semidirect
205. #477C4×C61semidirect
206. #476C4×C61semidirect
207. #462C4×C61semidirect
208. #461C4×C61semidirect
227. C61#9159direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#31162
C61×#29702
C61×#17592
C61×#15262
C61×#15062
C61×#13002
C61×#12912
#915961