Finite Group Databasebeta

← C61×#33798 #29537231

Subgroups — C61×#33798 #29537231

Order 15616.

468 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×#3168C211yesmaximal, characteristic
2C2×C61×#499C211yesmaximal, characteristic, complemented
3C61×#2253C212yesmaximal, complemented
4C61×#2242C212yesmaximal, complemented
5C61×#2236C211yesmaximal, characteristic, complemented
6C61×#2235C211yesmaximal, characteristic, complemented
7C61×#2233C211yesmaximal, characteristic
8C61×#2232C211yesmaximal, characteristic
9C61×#2229C212yesmaximal, complemented
10C61×#2228C212yesmaximal, complemented
11C61×#2162C211yesmaximal, characteristic, complemented
12C61×#529—21no—
13C2×#125×C61—21no—
14C61×#499—21no—
15C61×#499—21no—
16C61×#499C2212yes—
17C61×#499C2212yes—
18C61×#499C2211yescharacteristic
19C61×#495C2211yescharacteristic
20C61×#488—21no—
21C61×#467C2211yescharacteristic
22C61×#466C2211yescharacteristic
23C61×#465—21no—
24C4×Q16×C61C2211yescharacteristic
25C4×SD16×C61—21no—
26C4×D8×C61C2211yescharacteristic
27C2×#107×C61C2211yescharacteristic
28C2×#107×C61C2211yescharacteristic
29C2×#106×C61—21no—
30C2×C4×C8×C61C2211yescharacteristic
31C61×#367C2212yes—
32C61×#367C2212yes—
33C61×#366C2212yes—
34C61×#366C2212yes—
35C61×C4⋊C16C2212yes—
36C61×#358C2212yes—
37C61×#358C2212yes—
38C61×#357C2212yes—
39C61×#357C2212yes—
40C61×C22⋊C16C2211yescharacteristic
41C61×C22⋊C16C2211yescharacteristic
42C4×C16×C61C2212yes—
43C2×Q16×C61C2311yescharacteristic
44C2×SD16×C61—21no—
45C2×D8×C61C2311yescharacteristic
46C22×C8×C61D411yescharacteristic
47C22×C8×C61C2311yescharacteristic
48#126×C61—41no—
49#125×C61—21no—
50#125×C61—22no—
51#125×C61—22no—
52#125×C61—41no—
53#125×C61—41no—
54#124×C61—21no—
55#123×C61—41no—
56C22⋊Q8×C61—21no—
57#121×C61—21no—
58C4×Q8×C61—21no—
59C4×D4×C61—21no—
60C4×D4×C61—41no—
61#117×C61—41no—
62C2×C4⋊C4×C61—21no—
63C2×C4⋊C4×C61—21no—
64C2×C4⋊C4×C61—41no—
65C2×C4⋊C4×C61—41no—
66C2×C42×C61D411yescharacteristic
67C2×C16×C61C2312yes—
68C2×C16×C61C2312yes—
69#107×C61—21no—
70#107×C61—21no—
71#107×C61C2312yes—
72#107×C61C2312yes—
73#107×C61C2311yescharacteristic
74#107×C61C2311yescharacteristic
75#106×C61—22no—
76#106×C61—22no—
77#106×C61—21no—
78#103×C61—21no—
79#103×C61—21no—
80#102×C61—21no—
81#102×C61—21no—
82C4×C8×C61D411yescharacteristic
83C4×C8×C61D411yescharacteristic
84C4×C8×C61C2311yescharacteristic
85C4×C8×C61C2311yescharacteristic
86C2×Q8×C61—21no—
87C2×D4×C61—21no—
88C2×D4×C61—41no—
89C22×C4×C61—41no—
90C22×C4×C61—41no—
91C22×C4×C61—41no—
92C22×C4×C61D811yescharacteristic
93C22×C4×C61D811yescharacteristic
94C22×C4×C61C2×D411yescharacteristic
95Q16×C61—22no—
96SD16×C61—42no—
97D8×C61—22no—
98C2×C8×C61—22no—
99C2×C8×C61—22no—
100C2×C8×C61C2×D411yescharacteristic
101C2×C8×C61C2×D411yescharacteristic
102C2×C8×C61C2×D411yescharacteristic
103C2×C8×C61C2411yescharacteristic
104C4⋊C4×C61—21no—
105C4⋊C4×C61—21no—
106C4⋊C4×C61—22no—
107C4⋊C4×C61—22no—
108C4⋊C4×C61—41no—
109C4⋊C4×C61—41no—
110C4⋊C4×C61—42no—
111C4⋊C4×C61—42no—
112C4⋊C4×C61—42no—
113C4⋊C4×C61—42no—
114C4⋊C4×C61—41no—
115C4⋊C4×C61—41no—
116C4⋊C4×C61—41no—
117C4⋊C4×C61—41no—
118C22⋊C4×C61—41no—
119C22⋊C4×C61—41no—
120C22⋊C4×C61—41no—
121C22⋊C4×C61—41no—
122C22⋊C4×C61—41no—
123C42×C61—41no—
124C42×C61D811yescharacteristic
125C42×C61D811yescharacteristic
126C42×C61C2×D411yescharacteristic
127C42×C61C2×D411yescharacteristic
128C16×C61—22no—
129C16×C61—22no—
130C23×C61—41no—
131C23×C61C2×D811yescharacteristic
132Q8×C61—41no—
133Q8×C61—41no—
134D4×C61—41no—
135D4×C61—41no—
136D4×C61—82no—
137C2×C4×C61—22no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—42no—
145C2×C4×C61—42no—
146C2×C4×C61—82no—
147C2×C4×C61—82no—
148C2×C4×C61—82no—
149C2×C4×C61C2×D811yescharacteristic
150C2×C4×C61C2×D811yescharacteristic
151C2×C4×C61C2×D811yescharacteristic
152C2×C4×C61C2×D811yescharacteristic
153C2×C4×C61C2×D811yescharacteristic
154C2×C4×C61C22×D411yescharacteristic
155C8×C61—21no—
156C8×C61—21no—
157C8×C61#13712yes—
158C8×C612−1+412yes—
159#33798C6111yesmaximal, characteristic, direct product factor, Sylow
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—81no—
163C22×C61—81no—
164C22×C61—81no—
165C22×C61#50812yes—
166C22×C61C22×D811yescharacteristic
167C4×C61—21no—
168C4×C61—21no—
169C4×C61—21no—
170C4×C61—21no—
171C4×C61—21no—
172C4×C61—82no—
173C4×C61—81no—
174C4×C61—81no—
175C4×C61—82no—
176C4×C61—81no—
177C4×C61#53611yescharacteristic
178C4×C61C2×#13711yescharacteristic
179#3168C2×C6111yescharacteristic
180C2×#499C2×C6111yescharacteristic, complemented
181#2253C2×C6112yescomplemented
182#2242C2×C6112yescomplemented
183#2236C2×C6111yescharacteristic, complemented
184#2235C2×C6111yescharacteristic, complemented
185#2233C2×C6111yescharacteristic
186#2232C2×C6111yescharacteristic
187#2229C2×C6112yescomplemented
188#2228C2×C6112yescomplemented
189#2162C2×C6111yescharacteristic, complemented
190C2×C61—22no—
191C2×C61—161no—
192C2×C61#322611yescharacteristic
193C2×C61C2×#50811yescharacteristic
194C2×C61#341411yescharacteristic
195#529—21no—
196C2×#125—21no—
197#499—21no—
198#499—21no—
199#499C22×C6112yes—
200#499C22×C6112yes—
201#499C22×C6111yescharacteristic
202#495C22×C6111yescharacteristic
203#488—21no—
204#467C22×C6111yescharacteristic
205#466C22×C6111yescharacteristic
206#465—21no—
207C4×Q16C22×C6111yescharacteristic
208C4×SD16—21no—
209C4×D8C22×C6111yescharacteristic
210C2×#107C22×C6111yescharacteristic
211C2×#107C22×C6111yescharacteristic
212C2×#106—21no—
213C2×C4×C8C22×C6111yescharacteristic
214#367C22×C6112yes—
215#367C22×C6112yes—
216#366C22×C6112yes—
217#366C22×C6112yes—
218C4⋊C16C22×C6112yes—
219#358C22×C6112yes—
220#358C22×C6112yes—
221#357C22×C6112yes—
222#357C22×C6112yes—
223C22⋊C16C22×C6111yescharacteristic
224C22⋊C16C22×C6111yescharacteristic
225C4×C16C22×C6112yes—
226C61#3379811yescharacteristic, direct product factor, Sylow
227C2×Q16C23×C6111yescharacteristic
228C2×SD16—21no—
229C2×D8C23×C6111yescharacteristic
230C22×C8D4×C6111yescharacteristic
231C22×C8C23×C6111yescharacteristic
232#126—41no—
233#125—22no—
234#125—22no—
235#125—21no—
236#125—41no—
237#125—41no—
238#124—21no—
239#123—41no—
240C22⋊Q8—21no—
241#121—21no—
242C4×Q8—21no—
243C4×D4—21no—
244C4×D4—41no—
245#117—41no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—41no—
249C2×C4⋊C4—41no—
250C2×C42D4×C6111yescharacteristic
251C2×C16C23×C6112yes—
252C2×C16C23×C6112yes—
253#107—21no—
254#107—21no—
255#107C23×C6112yes—
256#107C23×C6112yes—
257#107C23×C6111yescharacteristic
258#107C23×C6111yescharacteristic
259#106—22no—
260#106—22no—
261#106—21no—
262#103—21no—
263#103—21no—
264#102—21no—
265#102—21no—
266C4×C8D4×C6111yescharacteristic
267C4×C8D4×C6111yescharacteristic
268C4×C8C23×C6111yescharacteristic
269C4×C8C23×C6111yescharacteristic
270C2×Q8—21no—
271C2×D4—21no—
272C2×D4—41no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4D8×C6111yescharacteristic
277C22×C4D8×C6111yescharacteristic
278C22×C4C2×D4×C6111yescharacteristic
279Q16—22no—
280SD16—42no—
281D8—22no—
282C2×C8—22no—
283C2×C8—22no—
284C2×C8C2×D4×C6111yescharacteristic
285C2×C8C2×D4×C6111yescharacteristic
286C2×C8C2×D4×C6111yescharacteristic
287C2×C8C24×C6111yescharacteristic
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—42no—
295C4⋊C4—42no—
296C4⋊C4—42no—
297C4⋊C4—42no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C42—41no—
308C42D8×C6111yescharacteristic
309C42D8×C6111yescharacteristic
310C42C2×D4×C6111yescharacteristic
311C42C2×D4×C6111yescharacteristic
312C16—22no—
313C16—22no—
314C23—41no—
315C23C2×D8×C6111yescharacteristic
316Q8—41no—
317Q8—41no—
318D4—41no—
319D4—41no—
320D4—82no—
321C2×C4—22no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—82no—
331C2×C4—82no—
332C2×C4—82no—
333C2×C4C2×D8×C6111yescharacteristic
334C2×C4C2×D8×C6111yescharacteristic
335C2×C4C2×D8×C6111yescharacteristic
336C2×C4C2×D8×C6111yescharacteristic
337C2×C4C2×D8×C6111yescharacteristic
338C2×C4C22×D4×C6111yescharacteristic
339C8—21no—
340C8—21no—
341C8#137×C6112yes—
342C82−1+4×C6112yes—
343C22—21no—
344C22—21no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22C61×#50812yes—
349C22C22×D8×C6111yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—82no—
356C4—81no—
357C4—81no—
358C4—82no—
359C4—81no—
360C4C61×#53611yescharacteristic
361C4C2×#137×C6111yescharacteristic
362C2—22no—
363C2—161no—
364C2C61×#322611yescharacteristic
365C2C2×C61×#50811yescharacteristic
366C2C61×#341411yescharacteristic
subgroupG/H
center, socleC22×C61C22×D8
commutator, Frattini, cosocleC2×C8C24×C61
prime radicalC61×#466C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C42×C61 ◁ C2×C4×C8×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C61×#499C2semidirect
3. C61×#2253C2semidirect
4. C61×#2242C2semidirect
5. C61×#2236C2semidirect
6. C61×#2235C2semidirect
9. C61×#2229C2semidirect
10. C61×#2228C2semidirect
11. C61×#2162C2semidirect
159. #33798C61direct (N × H)
180. C2×#499C2×C61semidirect
181. #2253C2×C61semidirect
182. #2242C2×C61semidirect
183. #2236C2×C61semidirect
184. #2235C2×C61semidirect
187. #2229C2×C61semidirect
188. #2228C2×C61semidirect
189. #2162C2×C61semidirect
226. C61#33798direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#31682
C2×C61×#4992
C61×#22532
C61×#22422
C61×#22362
C61×#22352
C61×#22332
C61×#22322
C61×#22292
C61×#22282
C61×#21622
#3379861