Finite Group Databasebeta

← C61×#10194 #29513627

Subgroups — C61×#10194 #29513627

Order 15616.

640 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3246C211yesmaximal, characteristic, complemented
2C61×#3208C211yesmaximal, characteristic, complemented
3C61×#3151C211yesmaximal, characteristic
4C61×#1986C211yesmaximal, characteristic, complemented
5C61×#1982C211yesmaximal, characteristic, complemented
6C61×#1502C211yesmaximal, characteristic, complemented
7C61×#1283C211yesmaximal, characteristic, complemented
8C2×AGL(1,ℤ/8)×C61—22no—
9C61×#533C2211yescharacteristic
10C61×#532C2211yescharacteristic
11C2×#127×C61C2211yescharacteristic
12C61×#496—22no—
13C61×#493—21no—
14C61×#492—21no—
15C61×#492—21no—
16C61×#486—21no—
17C61×#476—21no—
18C61×#475—21no—
19C61×#465—22no—
20C61×#461—21no—
21C61×#460—22no—
22C61×#460—21no—
23C61×#450—22no—
24C61×#431C2211yescharacteristic
25C2×C4⋊C8×C61C2211yescharacteristic
26C2×#102×C61—22no—
27C4×M16×C61C2211yescharacteristic
28C4×C4⋊C4×C61C2211yescharacteristic
29C61×#339—22no—
30C61×#327—22no—
31C2×#41×C61—21no—
32C22×D4×C61—21no—
33C22×D4×C61—21no—
34C22×D4×C61—21no—
35AGL(1,ℤ/8)×C61—44no—
36AGL(1,ℤ/8)×C61—44no—
37C2×SD16×C61—24no—
38C2×SD16×C61—24no—
39C2×SD16×C61—22no—
40C2×D8×C61—24no—
41C2×M16×C61D412yes—
42C22×C8×C61D412yes—
43C4⋊Q8×C61D411yescharacteristic
44C4⋊Q8×C61D411yescharacteristic
45C4⋊Q8×C61D411yescharacteristic
46#127×C61—21no—
47#127×C61—21no—
48#127×C61—21no—
49#127×C61D412yes—
50#127×C61D411yescharacteristic
51#125×C61—21no—
52#124×C61—21no—
53C22⋊Q8×C61—21no—
54C22⋊Q8×C61—21no—
55#121×C61—21no—
56#121×C61—21no—
57C4×Q8×C61—21no—
58C4×Q8×C61—21no—
59C4×D4×C61—21no—
60C4×D4×C61—21no—
61#117×C61—21no—
62C2×C4⋊C4×C61—21no—
63C2×C42×C61—21no—
64C2×C42×C61C2311yescharacteristic
65#106×C61—22no—
66C4⋊C8×C61—21no—
67C4⋊C8×C61—21no—
68C4⋊C8×C61—21no—
69#103×C61—22no—
70#102×C61—24no—
71#102×C61—22no—
72#102×C61—44no—
73C22⋊C8×C61D412yes—
74#97×C61—21no—
75C4×C8×C61—21no—
76C4×C8×C61—21no—
77#95×C61—21no—
78C24×C61—41no—
79#41×C61—42no—
80#41×C61—42no—
81C2×Q8×C61—21no—
82C2×Q8×C61—21no—
83C2×Q8×C61—21no—
84C2×D4×C61—21no—
85C2×D4×C61—22no—
86C2×D4×C61—21no—
87C2×D4×C61—22no—
88C2×D4×C61—22no—
89C2×D4×C61—21no—
90C2×D4×C61—42no—
91C2×D4×C61—42no—
92C2×D4×C61—41no—
93C2×D4×C61—41no—
94C2×D4×C61—41no—
95C2×D4×C61—41no—
96C2×D4×C61—42no—
97C2×D4×C61—42no—
98C2×D4×C61—82no—
99C22×C4×C61—41no—
100C22×C4×C61—41no—
101C22×C4×C61C2×D411yescharacteristic
102C22×C4×C61C2×D411yescharacteristic
103C22×C4×C61C2×D411yescharacteristic
104SD16×C61—48no—
105SD16×C61—84no—
106SD16×C61—82no—
107D8×C61—48no—
108M16×C61—22no—
109M16×C61SD1614yescomplemented
110C2×C8×C61—22no—
111C2×C8×C61—22no—
112C2×C8×C61—22no—
113C2×C8×C61—42no—
114C4⋊C4×C61—22no—
115C4⋊C4×C61—21no—
116C4⋊C4×C61—21no—
117C4⋊C4×C61—21no—
118C4⋊C4×C61—21no—
119C4⋊C4×C61—21no—
120C4⋊C4×C61—21no—
121C4⋊C4×C61—41no—
122C4⋊C4×C61—41no—
123C4⋊C4×C61—41no—
124C22⋊C4×C61—41no—
125C22⋊C4×C61—41no—
126C22⋊C4×C61—41no—
127C42×C61—41no—
128C42×C61—42no—
129C42×C61C2×D411yescharacteristic
130C42×C61C2×D411yescharacteristic
131C42×C61C2×D411yescharacteristic
132C42×C61#4111yescharacteristic
133C23×C61—41no—
134C23×C61—42no—
135C23×C61—82no—
136C23×C61—82no—
137C23×C61—81no—
138C23×C61—81no—
139C23×C61#12711yescharacteristic
140Q8×C61—42no—
141Q8×C61—42no—
142Q8×C61—41no—
143Q8×C61—41no—
144D4×C61—44no—
145D4×C61—44no—
146D4×C61—42no—
147D4×C61—44no—
148D4×C61—41no—
149D4×C61—41no—
150D4×C61—81no—
151D4×C61—82no—
152D4×C61—81no—
153D4×C61—81no—
154D4×C61—81no—
155D4×C61—81no—
156D4×C61—82no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61—41no—
160C2×C4×C61—42no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—81no—
165C2×C4×C61—81no—
166C2×C4×C61—82no—
167C2×C4×C61#12011yescharacteristic
168C2×C4×C61#12011yescharacteristic
169C2×C4×C61#12011yescharacteristic
170C2×C4×C61#12111yescharacteristic
171C2×C4×C61#12111yescharacteristic
172C2×C4×C61#12111yescharacteristic
173C2×C4×C61C2×SD1612yes—
174C2×C4×C61AGL(1,ℤ/8)12yes—
175C8×C61—24no—
176C8×C61—42no—
177C8×C61—42no—
178#10194C6111yesmaximal, characteristic, direct product factor, Sylow
179C22×C61—21no—
180C22×C61—21no—
181C22×C61—82no—
182C22×C61—81no—
183C22×C61—82no—
184C22×C61—81no—
185C22×C61—81no—
186C22×C61—82no—
187C22×C61—162no—
188C22×C61—162no—
189C22×C61#39211yescharacteristic
190C22×C61#49211yescharacteristic
191C22×C61#49611yescharacteristic
192C4×C61—21no—
193C4×C61—21no—
194C4×C61—21no—
195C4×C61—82no—
196C4×C61—81no—
197C4×C61—81no—
198C4×C61—81no—
199C4×C61#45012yes—
200C4×C61#45311yescharacteristic
201C4×C61#45411yescharacteristic
202C4×C61#46012yes—
203#3246C2×C6111yescharacteristic, complemented
204#3208C2×C6111yescharacteristic, complemented
205#3151C2×C6111yescharacteristic
206#1986C2×C6111yescharacteristic, complemented
207#1982C2×C6111yescharacteristic, complemented
208#1502C2×C6111yescharacteristic, complemented
209#1283C2×C6111yescharacteristic, complemented
210C2×C61—21no—
211C2×C61—21no—
212C2×C61—161no—
213C2×C61—162no—
214C2×C61#200611yescharacteristic
215C2×C61#200811yescharacteristic
216C2×C61#201411yescharacteristic
217C2×AGL(1,ℤ/8)—22no—
218#533C22×C6111yescharacteristic
219#532C22×C6111yescharacteristic
220C2×#127C22×C6111yescharacteristic
221#496—22no—
222#493—21no—
223#492—21no—
224#492—21no—
225#486—21no—
226#476—21no—
227#475—21no—
228#465—22no—
229#461—21no—
230#460—22no—
231#460—21no—
232#450—22no—
233#431C22×C6111yescharacteristic
234C2×C4⋊C8C22×C6111yescharacteristic
235C2×#102—22no—
236C4×M16C22×C6111yescharacteristic
237C4×C4⋊C4C22×C6111yescharacteristic
238#339—22no—
239#327—22no—
240C61#1019411yescharacteristic, direct product factor, Sylow
241C2×#41—21no—
242C22×D4—21no—
243C22×D4—21no—
244C22×D4—21no—
245AGL(1,ℤ/8)—44no—
246AGL(1,ℤ/8)—44no—
247C2×SD16—24no—
248C2×SD16—24no—
249C2×SD16—22no—
250C2×D8—24no—
251C2×M16D4×C6112yes—
252C22×C8D4×C6112yes—
253C4⋊Q8D4×C6111yescharacteristic
254C4⋊Q8D4×C6111yescharacteristic
255C4⋊Q8D4×C6111yescharacteristic
256#127—21no—
257#127—21no—
258#127—21no—
259#127D4×C6112yes—
260#127D4×C6111yescharacteristic
261#125—21no—
262#124—21no—
263C22⋊Q8—21no—
264C22⋊Q8—21no—
265#121—21no—
266#121—21no—
267C4×Q8—21no—
268C4×Q8—21no—
269C4×D4—21no—
270C4×D4—21no—
271#117—21no—
272C2×C4⋊C4—21no—
273C2×C42—21no—
274C2×C42C23×C6111yescharacteristic
275#106—22no—
276C4⋊C8—21no—
277C4⋊C8—21no—
278C4⋊C8—21no—
279#103—22no—
280#102—24no—
281#102—22no—
282#102—44no—
283C22⋊C8D4×C6112yes—
284#97—21no—
285C4×C8—21no—
286C4×C8—21no—
287#95—21no—
288C24—41no—
289#41—42no—
290#41—42no—
291C2×Q8—21no—
292C2×Q8—21no—
293C2×Q8—21no—
294C2×D4—21no—
295C2×D4—22no—
296C2×D4—21no—
297C2×D4—22no—
298C2×D4—22no—
299C2×D4—21no—
300C2×D4—42no—
301C2×D4—42no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—42no—
307C2×D4—42no—
308C2×D4—82no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4C2×D4×C6111yescharacteristic
312C22×C4C2×D4×C6111yescharacteristic
313C22×C4C2×D4×C6111yescharacteristic
314SD16—48no—
315SD16—84no—
316SD16—82no—
317D8—48no—
318M16—22no—
319M16SD16×C6114yescomplemented
320C2×C8—22no—
321C2×C8—22no—
322C2×C8—22no—
323C2×C8—42no—
324C4⋊C4—22no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C42—41no—
338C42—42no—
339C42C2×D4×C6111yescharacteristic
340C42C2×D4×C6111yescharacteristic
341C42C2×D4×C6111yescharacteristic
342C42#41×C6111yescharacteristic
343C23—41no—
344C23—42no—
345C23—82no—
346C23—82no—
347C23—81no—
348C23—81no—
349C23#127×C6111yescharacteristic
350Q8—42no—
351Q8—42no—
352Q8—41no—
353Q8—41no—
354D4—44no—
355D4—44no—
356D4—42no—
357D4—44no—
358D4—41no—
359D4—41no—
360D4—81no—
361D4—82no—
362D4—81no—
363D4—81no—
364D4—81no—
365D4—81no—
366D4—82no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—81no—
375C2×C4—81no—
376C2×C4—82no—
377C2×C4#120×C6111yescharacteristic
378C2×C4#120×C6111yescharacteristic
379C2×C4#120×C6111yescharacteristic
380C2×C4#121×C6111yescharacteristic
381C2×C4#121×C6111yescharacteristic
382C2×C4#121×C6111yescharacteristic
383C2×C4C2×SD16×C6112yes—
384C2×C4AGL(1,ℤ/8)×C6112yes—
385C8—24no—
386C8—42no—
387C8—42no—
388C22—21no—
389C22—21no—
390C22—82no—
391C22—81no—
392C22—81no—
393C22—82no—
394C22—82no—
395C22—81no—
396C22—162no—
397C22—162no—
398C22C61×#39211yescharacteristic
399C22C61×#49211yescharacteristic
400C22C61×#49611yescharacteristic
401C4—21no—
402C4—21no—
403C4—21no—
404C4—82no—
405C4—81no—
406C4—81no—
407C4—81no—
408C4C61×#45012yes—
409C4C61×#45311yescharacteristic
410C4C61×#45411yescharacteristic
411C4C61×#46012yes—
412C2—21no—
413C2—21no—
414C2—162no—
415C2—161no—
416C2C61×#200611yescharacteristic
417C2C61×#200811yescharacteristic
418C2C61×#201411yescharacteristic
subgroupG/H
center, socleC22×C61#392
commutator, Frattini, cosocleC2×C42C23×C61
prime radicalC61×#3151C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3246C2semidirect
2. C61×#3208C2semidirect
4. C61×#1986C2semidirect
5. C61×#1982C2semidirect
6. C61×#1502C2semidirect
7. C61×#1283C2semidirect
109. M16×C61SD16semidirect
178. #10194C61direct (N × H)
203. #3246C2×C61semidirect
204. #3208C2×C61semidirect
206. #1986C2×C61semidirect
207. #1982C2×C61semidirect
208. #1502C2×C61semidirect
209. #1283C2×C61semidirect
240. C61#10194direct (N × H)
319. M16SD16×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#32462
C61×#32082
C61×#31512
C61×#19862
C61×#19822
C61×#15022
C61×#12832
#1019461