Finite Group Databasebeta

← C61×#9329 #29512762

Subgroups — C61×#9329 #29512762

Order 15616.

530 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3109C211yesmaximal, characteristic
2C61×#2319C211yesmaximal, characteristic, complemented
3C61×#1980C211yesmaximal, characteristic, complemented
4C61×#1505C211yesmaximal, characteristic, complemented
5C61×#1490C211yesmaximal, characteristic, complemented
6C61×#1300C211yesmaximal, characteristic, complemented
7C61×#1285C211yesmaximal, characteristic, complemented
8C61×#532C2211yescharacteristic
9C2×C4×D4×C61C2211yescharacteristic
10C61×#481—21no—
11C61×#476C412yescomplemented
12C61×#459C412yescomplemented
13C61×#447—21no—
14C61×#442—22no—
15C61×#432C2211yescharacteristic
16C61×#432C2211yescharacteristic
17C2×#104×C61—22no—
18C4×M16×C61C2211yescharacteristic
19C61×#390—21no—
20C61×#389—21no—
21C61×#388—22no—
22C61×#381—21no—
23C61×#380—21no—
24C4×C4⋊C4×C61C2211yescharacteristic
25C61×#376C2211yescharacteristic
26C61×#327—21no—
27C61×#327—21no—
28C61×D4⋊C8—22no—
29C2×#41×C61—21no—
30C22×D4×C61D411yescharacteristic
31C23×C4×C61—21no—
32C2×D8×C61—22no—
33C2×M16×C61—21no—
34C4⋊Q8×C61C2×C411yescharacteristic
35#127×C61C2×C411yescharacteristic
36#124×C61—21no—
37#121×C61—21no—
38#121×C61—21no—
39C4×D4×C61—21no—
40C4×D4×C61—21no—
41C4×D4×C61—21no—
42C4×D4×C61—21no—
43C4×D4×C61C2×C412yes—
44C4×D4×C61D412yes—
45C2×C4⋊C4×C61—21no—
46C2×C4⋊C4×C61—22no—
47C2×C4⋊C4×C61D411yescharacteristic
48C2×C22⋊C4×C61—21no—
49C2×C22⋊C4×C61—22no—
50C2×C22⋊C4×C61—22no—
51C2×C42×C61—21no—
52C2×C42×C61D412yes—
53C2×C42×C61C2311yescharacteristic
54#106×C61—22no—
55C4⋊C8×C61—21no—
56C4⋊C8×C61C2×C412yes—
57#104×C61—44no—
58#102×C61—22no—
59#102×C61—22no—
60C22⋊C8×C61—21no—
61C22⋊C8×C61—21no—
62#97×C61—21no—
63#97×C61—21no—
64#97×C61—21no—
65C4×C8×C61—21no—
66#95×C61—22no—
67#95×C61—21no—
68#95×C61—21no—
69#95×C61D411yescharacteristic
70#95×C61D411yescharacteristic
71C24×C61—21no—
72#41×C61—42no—
73#41×C61—42no—
74C2×Q8×C61—21no—
75C2×D4×C61—21no—
76C2×D4×C61—21no—
77C2×D4×C61—21no—
78C2×D4×C61—21no—
79C2×D4×C61—42no—
80C2×D4×C61—41no—
81C2×D4×C61C22⋊C412yes—
82C22×C4×C61—21no—
83C22×C4×C61—22no—
84C22×C4×C61—22no—
85C22×C4×C61—21no—
86C22×C4×C61—22no—
87C22×C4×C61—21no—
88C22×C4×C61—41no—
89C22×C4×C61—82no—
90C22×C4×C61C2×D411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61C2×D411yescharacteristic
93D8×C61—44no—
94M16×C61—22no—
95M16×C61—41no—
96C2×C8×C61—22no—
97C2×C8×C61—41no—
98C2×C8×C61—41no—
99C4⋊C4×C61—21no—
100C4⋊C4×C61—21no—
101C4⋊C4×C61—21no—
102C4⋊C4×C61—42no—
103C4⋊C4×C61—82no—
104C4⋊C4×C61C22⋊C412yes—
105C22⋊C4×C61—22no—
106C22⋊C4×C61—22no—
107C22⋊C4×C61—41no—
108C22⋊C4×C61—41no—
109C22⋊C4×C61—82no—
110C22⋊C4×C61—82no—
111C42×C61—42no—
112C42×C61—42no—
113C42×C61C22×C411yescharacteristic
114C42×C61C2×D411yescharacteristic
115C42×C61#4111yescharacteristic
116C42×C61#4111yescharacteristic
117C23×C61—22no—
118C23×C61—42no—
119C23×C61—42no—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61—41no—
123C23×C61#12011yescharacteristic
124Q8×C61—42no—
125D4×C61—22no—
126D4×C61—22no—
127D4×C61—42no—
128D4×C61—42no—
129D4×C61—42no—
130D4×C61—81no—
131D4×C61—81no—
132D4×C61—81no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—22no—
136C2×C4×C61—22no—
137C2×C4×C61—41no—
138C2×C4×C61—42no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—42no—
143C2×C4×C61—42no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—42no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—82no—
150C2×C4×C61—82no—
151C2×C4×C61—82no—
152C2×C4×C61C2×C22⋊C411yescharacteristic
153C2×C4×C61C4×D411yescharacteristic
154C2×C4×C61C4×D411yescharacteristic
155C2×C4×C61#12111yescharacteristic
156C2×C4×C61#12111yescharacteristic
157C2×C4×C61#12311yescharacteristic
158C8×C61—42no—
159C8×C61—42no—
160C8×C61—81no—
161#9329C6111yesmaximal, characteristic, direct product factor, Sylow
162C22×C61—21no—
163C22×C61—21no—
164C22×C61—42no—
165C22×C61—42no—
166C22×C61—42no—
167C22×C61—82no—
168C22×C61—82no—
169C22×C61—81no—
170C22×C61—81no—
171C22×C61—81no—
172C22×C61#38611yescharacteristic
173C22×C61#45311yescharacteristic
174C22×C61#45411yescharacteristic
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—42no—
181C4×C61—81no—
182C4×C61—82no—
183C4×C61—81no—
184C4×C61—81no—
185C4×C61#42112yes—
186#3109C2×C6111yescharacteristic
187#2319C2×C6111yescharacteristic, complemented
188#1980C2×C6111yescharacteristic, complemented
189#1505C2×C6111yescharacteristic, complemented
190#1490C2×C6111yescharacteristic, complemented
191#1300C2×C6111yescharacteristic, complemented
192#1285C2×C6111yescharacteristic, complemented
193C2×C61—21no—
194C2×C61—21no—
195C2×C61—82no—
196C2×C61—161no—
197C2×C61#188311yescharacteristic
198C2×C61#189711yescharacteristic
199C2×C61#190411yescharacteristic
200#532C22×C6111yescharacteristic
201C2×C4×D4C22×C6111yescharacteristic
202#481—21no—
203#476C4×C6112yescomplemented
204#459C4×C6112yescomplemented
205#447—21no—
206#442—22no—
207#432C22×C6111yescharacteristic
208#432C22×C6111yescharacteristic
209C2×#104—22no—
210C4×M16C22×C6111yescharacteristic
211#390—21no—
212#389—21no—
213#388—22no—
214#381—21no—
215#380—21no—
216C4×C4⋊C4C22×C6111yescharacteristic
217#376C22×C6111yescharacteristic
218#327—21no—
219#327—21no—
220D4⋊C8—22no—
221C61#932911yescharacteristic, direct product factor, Sylow
222C2×#41—21no—
223C22×D4D4×C6111yescharacteristic
224C23×C4—21no—
225C2×D8—22no—
226C2×M16—21no—
227C4⋊Q8C2×C4×C6111yescharacteristic
228#127C2×C4×C6111yescharacteristic
229#124—21no—
230#121—21no—
231#121—21no—
232C4×D4—21no—
233C4×D4—21no—
234C4×D4—21no—
235C4×D4—21no—
236C4×D4C2×C4×C6112yes—
237C4×D4D4×C6112yes—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—22no—
240C2×C4⋊C4D4×C6111yescharacteristic
241C2×C22⋊C4—21no—
242C2×C22⋊C4—22no—
243C2×C22⋊C4—22no—
244C2×C42—21no—
245C2×C42D4×C6112yes—
246C2×C42C23×C6111yescharacteristic
247#106—22no—
248C4⋊C8—21no—
249C4⋊C8C2×C4×C6112yes—
250#104—44no—
251#102—22no—
252#102—22no—
253C22⋊C8—21no—
254C22⋊C8—21no—
255#97—21no—
256#97—21no—
257#97—21no—
258C4×C8—21no—
259#95—22no—
260#95—21no—
261#95—21no—
262#95D4×C6111yescharacteristic
263#95D4×C6111yescharacteristic
264C24—21no—
265#41—42no—
266#41—42no—
267C2×Q8—21no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—42no—
273C2×D4—41no—
274C2×D4C22⋊C4×C6112yes—
275C22×C4—21no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—21no—
279C22×C4—22no—
280C22×C4—21no—
281C22×C4—41no—
282C22×C4—82no—
283C22×C4C2×D4×C6111yescharacteristic
284C22×C4C2×D4×C6111yescharacteristic
285C22×C4C2×D4×C6111yescharacteristic
286D8—44no—
287M16—22no—
288M16—41no—
289C2×C8—22no—
290C2×C8—41no—
291C2×C8—41no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—42no—
296C4⋊C4—82no—
297C4⋊C4C22⋊C4×C6112yes—
298C22⋊C4—22no—
299C22⋊C4—22no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—82no—
303C22⋊C4—82no—
304C42—42no—
305C42—42no—
306C42C22×C4×C6111yescharacteristic
307C42C2×D4×C6111yescharacteristic
308C42#41×C6111yescharacteristic
309C42#41×C6111yescharacteristic
310C23—22no—
311C23—42no—
312C23—42no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23#120×C6111yescharacteristic
317Q8—42no—
318D4—22no—
319D4—22no—
320D4—42no—
321D4—42no—
322D4—42no—
323D4—81no—
324D4—81no—
325D4—81no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—82no—
343C2×C4—82no—
344C2×C4—82no—
345C2×C4C2×C22⋊C4×C6111yescharacteristic
346C2×C4C4×D4×C6111yescharacteristic
347C2×C4C4×D4×C6111yescharacteristic
348C2×C4#121×C6111yescharacteristic
349C2×C4#121×C6111yescharacteristic
350C2×C4#123×C6111yescharacteristic
351C8—42no—
352C8—42no—
353C8—81no—
354C22—21no—
355C22—21no—
356C22—42no—
357C22—42no—
358C22—42no—
359C22—82no—
360C22—82no—
361C22—81no—
362C22—81no—
363C22—81no—
364C22C61×#38611yescharacteristic
365C22C61×#45311yescharacteristic
366C22C61×#45411yescharacteristic
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—42no—
373C4—81no—
374C4—82no—
375C4—81no—
376C4—81no—
377C4C61×#42112yes—
378C2—21no—
379C2—21no—
380C2—82no—
381C2—161no—
382C2C61×#188311yescharacteristic
383C2C61×#189711yescharacteristic
384C2C61×#190411yescharacteristic
subgroupG/H
center, socleC22×C61#386
commutatorC42C22×C4×C61
Frattini, cosocleC2×C42C23×C61
prime radicalC61×#3109C2
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×#2319C2semidirect
3. C61×#1980C2semidirect
4. C61×#1505C2semidirect
5. C61×#1490C2semidirect
6. C61×#1300C2semidirect
7. C61×#1285C2semidirect
11. C61×#476C4semidirect
12. C61×#459C4semidirect
161. #9329C61direct (N × H)
187. #2319C2×C61semidirect
188. #1980C2×C61semidirect
189. #1505C2×C61semidirect
190. #1490C2×C61semidirect
191. #1300C2×C61semidirect
192. #1285C2×C61semidirect
203. #476C4×C61semidirect
204. #459C4×C61semidirect
221. C61#9329direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#31092
C61×#23192
C61×#19802
C61×#15052
C61×#14902
C61×#13002
C61×#12852
#932961