Finite Group Databasebeta

← C61×#9326 #29512759

Subgroups — C61×#9326 #29512759

Order 15616.

574 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3112C211yesmaximal, characteristic
2C61×#2276C211yesmaximal, characteristic, complemented
3C61×#1980C211yesmaximal, characteristic
4C61×#1505C211yesmaximal, characteristic
5C61×#1491C211yesmaximal, characteristic, complemented
6C61×#1300C211yesmaximal, characteristic, complemented
7C61×#1285C211yesmaximal, characteristic, complemented
8C61×#532C2211yescharacteristic
9C2×C4×Q8×C61—21no—
10C2×C4×Q8×C61C2211yescharacteristic
11C61×#480—21no—
12C61×#477C412yescomplemented
13C61×#460C412yescomplemented
14C61×#448—21no—
15C61×#440—22no—
16C61×#432C2211yescharacteristic
17C61×#432C2211yescharacteristic
18C2×#104×C61—22no—
19C4×M16×C61C2211yescharacteristic
20C4×C4⋊C4×C61—21no—
21C4×C4⋊C4×C61—22no—
22C4×C4⋊C4×C61—21no—
23C4×C4⋊C4×C61C2211yescharacteristic
24C61×#376—21no—
25C61×#376C2211yescharacteristic
26C61×#327—21no—
27C61×#327—21no—
28C61×Q8⋊C8—22no—
29C2×#41×C61—21no—
30C22×Q8×C61D411yescharacteristic
31C2×SD16×C61—22no—
32C2×M16×C61—21no—
33C4⋊Q8×C61C2×C411yescharacteristic
34#127×C61C2×C411yescharacteristic
35#124×C61—21no—
36#121×C61—21no—
37#121×C61—21no—
38C4×Q8×C61—28no—
39C4×Q8×C61—21no—
40C4×Q8×C61—21no—
41C4×Q8×C61C2×C412yes—
42C4×Q8×C61D412yes—
43C4×D4×C61—21no—
44C4×D4×C61—21no—
45C2×C4⋊C4×C61—22no—
46C2×C4⋊C4×C61—21no—
47C2×C4⋊C4×C61—21no—
48C2×C4⋊C4×C61D411yescharacteristic
49C2×C42×C61—22no—
50C2×C42×C61—21no—
51C2×C42×C61—21no—
52C2×C42×C61—22no—
53C2×C42×C61D412yes—
54C2×C42×C61C2311yescharacteristic
55#107×C61—22no—
56C4⋊C8×C61—21no—
57C4⋊C8×C61C2×C412yes—
58#104×C61—44no—
59#103×C61—22no—
60#102×C61—22no—
61C22⋊C8×C61—21no—
62C22⋊C8×C61—21no—
63#97×C61—21no—
64#97×C61—21no—
65#97×C61—21no—
66C4×C8×C61—21no—
67#95×C61—22no—
68#95×C61—21no—
69#95×C61—21no—
70#95×C61D411yescharacteristic
71#95×C61D411yescharacteristic
72#41×C61—42no—
73#41×C61—42no—
74C2×Q8×C61—24no—
75C2×Q8×C61—21no—
76C2×Q8×C61—21no—
77C2×Q8×C61C22⋊C412yes—
78C2×D4×C61—21no—
79C2×D4×C61—21no—
80C2×D4×C61—21no—
81C2×D4×C61—41no—
82C22×C4×C61—21no—
83C22×C4×C61—21no—
84C22×C4×C61—21no—
85C22×C4×C61—22no—
86C22×C4×C61—21no—
87C22×C4×C61—41no—
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61C2×D411yescharacteristic
90C22×C4×C61C2×D411yescharacteristic
91SD16×C61—44no—
92M16×C61—22no—
93M16×C61—41no—
94C2×C8×C61—22no—
95C2×C8×C61—41no—
96C2×C8×C61—41no—
97C4⋊C4×C61—28no—
98C4⋊C4×C61—24no—
99C4⋊C4×C61—22no—
100C4⋊C4×C61—22no—
101C4⋊C4×C61—21no—
102C4⋊C4×C61—21no—
103C4⋊C4×C61—21no—
104C4⋊C4×C61C22⋊C412yes—
105C22⋊C4×C61—41no—
106C22⋊C4×C61—41no—
107C42×C61—28no—
108C42×C61—24no—
109C42×C61—22no—
110C42×C61—22no—
111C42×C61—42no—
112C42×C61—82no—
113C42×C61C22×C411yescharacteristic
114C42×C61C2×D411yescharacteristic
115C42×C61#4111yescharacteristic
116C42×C61#4111yescharacteristic
117C23×C61—41no—
118C23×C61#12011yescharacteristic
119Q8×C61—24no—
120Q8×C61—22no—
121Q8×C61—42no—
122Q8×C61#10414yescomplemented
123D4×C61—42no—
124D4×C61—42no—
125D4×C61—81no—
126D4×C61—81no—
127D4×C61—81no—
128C2×C4×C61—24no—
129C2×C4×C61—22no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—22no—
133C2×C4×C61—22no—
134C2×C4×C61—24no—
135C2×C4×C61—22no—
136C2×C4×C61—22no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—42no—
140C2×C4×C61—41no—
141C2×C4×C61—42no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—82no—
148C2×C4×C61C2×C22⋊C411yescharacteristic
149C2×C4×C61C4×D411yescharacteristic
150C2×C4×C61C4×D411yescharacteristic
151C2×C4×C61#12111yescharacteristic
152C2×C4×C61#12111yescharacteristic
153C2×C4×C61#12311yescharacteristic
154C8×C61—42no—
155C8×C61—42no—
156C8×C61—81no—
157#9326C6111yesmaximal, characteristic, direct product factor, Sylow
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—81no—
161C22×C61—81no—
162C22×C61—81no—
163C22×C61#38611yescharacteristic
164C22×C61#45311yescharacteristic
165C22×C61#45411yescharacteristic
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—24no—
169C4×C61—21no—
170C4×C61—21no—
171C4×C61—21no—
172C4×C61—44no—
173C4×C61—42no—
174C4×C61—42no—
175C4×C61—42no—
176C4×C61—81no—
177C4×C61C2×#10412yes—
178#3112C2×C6111yescharacteristic
179#2276C2×C6111yescharacteristic, complemented
180#1980C2×C6111yescharacteristic
181#1505C2×C6111yescharacteristic
182#1491C2×C6111yescharacteristic, complemented
183#1300C2×C6111yescharacteristic, complemented
184#1285C2×C6111yescharacteristic, complemented
185C2×C61—21no—
186C2×C61—21no—
187C2×C61—161no—
188C2×C61#188311yescharacteristic
189C2×C61#189611yescharacteristic
190C2×C61#190511yescharacteristic
191#532C22×C6111yescharacteristic
192C2×C4×Q8—21no—
193C2×C4×Q8C22×C6111yescharacteristic
194#480—21no—
195#477C4×C6112yescomplemented
196#460C4×C6112yescomplemented
197#448—21no—
198#440—22no—
199#432C22×C6111yescharacteristic
200#432C22×C6111yescharacteristic
201C2×#104—22no—
202C4×M16C22×C6111yescharacteristic
203C4×C4⋊C4—21no—
204C4×C4⋊C4—22no—
205C4×C4⋊C4—21no—
206C4×C4⋊C4C22×C6111yescharacteristic
207#376—21no—
208#376C22×C6111yescharacteristic
209#327—21no—
210#327—21no—
211Q8⋊C8—22no—
212C61#932611yescharacteristic, direct product factor, Sylow
213C2×#41—21no—
214C22×Q8D4×C6111yescharacteristic
215C2×SD16—22no—
216C2×M16—21no—
217C4⋊Q8C2×C4×C6111yescharacteristic
218#127C2×C4×C6111yescharacteristic
219#124—21no—
220#121—21no—
221#121—21no—
222C4×Q8—28no—
223C4×Q8—21no—
224C4×Q8—21no—
225C4×Q8C2×C4×C6112yes—
226C4×Q8D4×C6112yes—
227C4×D4—21no—
228C4×D4—21no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4D4×C6111yescharacteristic
233C2×C42—22no—
234C2×C42—21no—
235C2×C42—21no—
236C2×C42—22no—
237C2×C42D4×C6112yes—
238C2×C42C23×C6111yescharacteristic
239#107—22no—
240C4⋊C8—21no—
241C4⋊C8C2×C4×C6112yes—
242#104—44no—
243#103—22no—
244#102—22no—
245C22⋊C8—21no—
246C22⋊C8—21no—
247#97—21no—
248#97—21no—
249#97—21no—
250C4×C8—21no—
251#95—22no—
252#95—21no—
253#95—21no—
254#95D4×C6111yescharacteristic
255#95D4×C6111yescharacteristic
256#41—42no—
257#41—42no—
258C2×Q8—24no—
259C2×Q8—21no—
260C2×Q8—21no—
261C2×Q8C22⋊C4×C6112yes—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—41no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—22no—
270C22×C4—21no—
271C22×C4—41no—
272C22×C4C2×D4×C6111yescharacteristic
273C22×C4C2×D4×C6111yescharacteristic
274C22×C4C2×D4×C6111yescharacteristic
275SD16—44no—
276M16—22no—
277M16—41no—
278C2×C8—22no—
279C2×C8—41no—
280C2×C8—41no—
281C4⋊C4—28no—
282C4⋊C4—24no—
283C4⋊C4—22no—
284C4⋊C4—22no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4C22⋊C4×C6112yes—
289C22⋊C4—41no—
290C22⋊C4—41no—
291C42—28no—
292C42—24no—
293C42—22no—
294C42—22no—
295C42—42no—
296C42—82no—
297C42C22×C4×C6111yescharacteristic
298C42C2×D4×C6111yescharacteristic
299C42#41×C6111yescharacteristic
300C42#41×C6111yescharacteristic
301C23—41no—
302C23#120×C6111yescharacteristic
303Q8—24no—
304Q8—22no—
305Q8—42no—
306Q8#104×C6114yescomplemented
307D4—42no—
308D4—42no—
309D4—81no—
310D4—81no—
311D4—81no—
312C2×C4—24no—
313C2×C4—22no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—24no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—82no—
332C2×C4C2×C22⋊C4×C6111yescharacteristic
333C2×C4C4×D4×C6111yescharacteristic
334C2×C4C4×D4×C6111yescharacteristic
335C2×C4#121×C6111yescharacteristic
336C2×C4#121×C6111yescharacteristic
337C2×C4#123×C6111yescharacteristic
338C8—42no—
339C8—42no—
340C8—81no—
341C22—21no—
342C22—21no—
343C22—81no—
344C22—81no—
345C22—81no—
346C22C61×#38611yescharacteristic
347C22C61×#45311yescharacteristic
348C22C61×#45411yescharacteristic
349C4—21no—
350C4—21no—
351C4—24no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—44no—
356C4—42no—
357C4—42no—
358C4—42no—
359C4—81no—
360C4C2×#104×C6112yes—
361C2—21no—
362C2—21no—
363C2—161no—
364C2C61×#188311yescharacteristic
365C2C61×#189611yescharacteristic
366C2C61×#190511yescharacteristic
subgroupG/H
center, socleC22×C61#386
commutatorC42C22×C4×C61
Frattini, cosocleC2×C42C23×C61
prime radicalC61×#532C22
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
2. C61×#2276C2semidirect
5. C61×#1491C2semidirect
6. C61×#1300C2semidirect
7. C61×#1285C2semidirect
12. C61×#477C4semidirect
13. C61×#460C4semidirect
122. Q8×C61#104semidirect
157. #9326C61direct (N × H)
179. #2276C2×C61semidirect
182. #1491C2×C61semidirect
183. #1300C2×C61semidirect
184. #1285C2×C61semidirect
195. #477C4×C61semidirect
196. #460C4×C61semidirect
212. C61#9326direct (N × H)
306. Q8#104×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#31122
C61×#22762
C61×#19802
C61×#15052
C61×#14912
C61×#13002
C61×#12852
#932661