Finite Group Databasebeta

← C61×#33737 #29537170

Subgroups — C61×#33737 #29537170

Order 15616.

554 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3169C211yesmaximal, characteristic, complemented
2C61×#3168C211yesmaximal, characteristic, complemented
3C61×#2255C211yesmaximal, characteristic, complemented
4C61×#2250C211yesmaximal, characteristic, complemented
5C61×#2244C211yesmaximal, characteristic, complemented
6C61×#2243C211yesmaximal, characteristic, complemented
7C61×#2220C212yesmaximal, complemented
8C61×#2218C212yesmaximal, complemented
9C4×SD32×C61C212yesmaximal, complemented
10C4×D16×C61C212yesmaximal, complemented
11C4×M32×C61C211yesmaximal, characteristic, complemented
12C61×#532—21no—
13C61×#529—21no—
14C2×SD32×C61C2212yes—
15C2×D16×C61C2212yes—
16C2×M32×C61C2212yes—
17C61×#500C2211yescharacteristic
18C61×#499C2211yescharacteristic
19C61×#495C2211yescharacteristic
20C61×#493C2211yescharacteristic
21C61×#488—21no—
22C61×#486—21no—
23C61×#467C2211yescharacteristic
24C61×#466—21no—
25C61×#466C2211yescharacteristic
26C61×#466C2212yes—
27C61×#465—21no—
28C4×Q16×C61C2211yescharacteristic
29C4×SD16×C61—21no—
30C4×D8×C61—21no—
31C4×D8×C61C2211yescharacteristic
32C4×D8×C61C2212yes—
33C2×C4×C8×C61C2211yescharacteristic
34C61×#367C2212yes—
35C61×#366C2212yes—
36C61×#358C2212yes—
37C61×#357C2212yes—
38C61×#357C2212yes—
39C61×#357C2212yes—
40C61×#346C2211yescharacteristic
41C61×#346C2211yescharacteristic
42C4×C16×C61C2212yes—
43C2×#41×C61—41no—
44C2×Q16×C61C2311yescharacteristic
45C2×SD16×C61—21no—
46C2×D8×C61—21no—
47C2×D8×C61C2312yes—
48C2×D8×C61C2311yescharacteristic
49C22×C8×C61D411yescharacteristic
50C22×C8×C61C2311yescharacteristic
51C4⋊Q8×C61—21no—
52#127×C61—21no—
53#126×C61—41no—
54#125×C61—21no—
55#124×C61—21no—
56#124×C61—41no—
57#123×C61—41no—
58C22⋊Q8×C61—21no—
59#121×C61—22no—
60#121×C61—21no—
61#121×C61—41no—
62C4×Q8×C61—21no—
63C4×D4×C61—22no—
64C4×D4×C61—21no—
65C4×D4×C61—41no—
66C4×D4×C61—41no—
67#117×C61—41no—
68C2×C42×C61D411yescharacteristic
69SD32×C61—24no—
70D16×C61—24no—
71M32×C61—24no—
72C2×C16×C61C2312yes—
73C2×C16×C61C2312yes—
74#107×C61—21no—
75#107×C61C2311yescharacteristic
76#107×C61C2311yescharacteristic
77#107×C61C2312yes—
78#106×C61—21no—
79#103×C61—21no—
80#103×C61—21no—
81#102×C61—22no—
82#102×C61—21no—
83#102×C61—22no—
84#102×C61—21no—
85C4×C8×C61D411yescharacteristic
86C4×C8×C61D411yescharacteristic
87C4×C8×C61C2311yescharacteristic
88C4×C8×C61C2311yescharacteristic
89#41×C61—84no—
90C2×Q8×C61—21no—
91C2×Q8×C61—41no—
92C2×D4×C61—21no—
93C2×D4×C61—22no—
94C2×D4×C61—41no—
95C2×D4×C61—42no—
96C2×D4×C61—41no—
97C2×D4×C61—41no—
98C22×C4×C61—41no—
99C22×C4×C61—42no—
100C22×C4×C61D811yescharacteristic
101C22×C4×C61D811yescharacteristic
102C22×C4×C61C2×D411yescharacteristic
103Q16×C61—22no—
104SD16×C61—42no—
105D8×C61—22no—
106D8×C61—22no—
107D8×C61—22no—
108D8×C61—42no—
109C2×C8×C61—22no—
110C2×C8×C61—22no—
111C2×C8×C61C2×D411yescharacteristic
112C2×C8×C61C2×D411yescharacteristic
113C2×C8×C61C2×D411yescharacteristic
114C2×C8×C61C2411yescharacteristic
115C4⋊C4×C61—22no—
116C4⋊C4×C61—21no—
117C4⋊C4×C61—21no—
118C4⋊C4×C61—41no—
119C4⋊C4×C61—41no—
120C4⋊C4×C61—41no—
121C4⋊C4×C61—41no—
122C4⋊C4×C61—41no—
123C22⋊C4×C61—41no—
124C22⋊C4×C61—41no—
125C22⋊C4×C61—41no—
126C22⋊C4×C61—42no—
127C22⋊C4×C61—41no—
128C22⋊C4×C61—42no—
129C22⋊C4×C61—41no—
130C42×C61—41no—
131C42×C61D811yescharacteristic
132C42×C61D811yescharacteristic
133C42×C61C2×D411yescharacteristic
134C42×C61C2×D411yescharacteristic
135C16×C61—22no—
136C16×C61#4114yescomplemented
137C23×C61—41no—
138C23×C61—42no—
139C23×C61C2×D811yescharacteristic
140Q8×C61—41no—
141Q8×C61—41no—
142Q8×C61—82no—
143D4×C61—41no—
144D4×C61—42no—
145D4×C61—42no—
146D4×C61—41no—
147D4×C61—82no—
148D4×C61—82no—
149D4×C61—82no—
150D4×C61—84no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61—22no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—42no—
159C2×C4×C61—82no—
160C2×C4×C61—84no—
161C2×C4×C61C2×D811yescharacteristic
162C2×C4×C61C2×D811yescharacteristic
163C2×C4×C61C2×D811yescharacteristic
164C2×C4×C61C2×D811yescharacteristic
165C2×C4×C61C2×D811yescharacteristic
166C2×C4×C61C22×D411yescharacteristic
167C8×C61—21no—
168C8×C61—21no—
169C8×C61#13512yes—
170C8×C61C2×#4112yes—
171#33737C6111yesmaximal, characteristic, direct product factor, Sylow
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—82no—
176C22×C61—81no—
177C22×C61—82no—
178C22×C61—81no—
179C22×C61—82no—
180C22×C61—81no—
181C22×C61C22×D811yescharacteristic
182C4×C61—21no—
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—21no—
186C4×C61—81no—
187C4×C61—82no—
188C4×C61—81no—
189C4×C61—81no—
190C4×C61#50912yes—
191C4×C61#53211yescharacteristic
192C4×C61C2×#13511yescharacteristic
193#3169C2×C6111yescharacteristic, complemented
194#3168C2×C6111yescharacteristic, complemented
195#2255C2×C6111yescharacteristic, complemented
196#2250C2×C6111yescharacteristic, complemented
197#2244C2×C6111yescharacteristic, complemented
198#2243C2×C6111yescharacteristic, complemented
199#2220C2×C6112yescomplemented
200#2218C2×C6112yescomplemented
201C4×SD32C2×C6112yescomplemented
202C4×D16C2×C6112yescomplemented
203C4×M32C2×C6111yescharacteristic, complemented
204C2×C61—41no—
205C2×C61—162no—
206C2×C61—161no—
207C2×C61#316911yescharacteristic
208C2×C61C2×#50911yescharacteristic
209C2×C61#341411yescharacteristic
210#532—21no—
211#529—21no—
212C2×SD32C22×C6112yes—
213C2×D16C22×C6112yes—
214C2×M32C22×C6112yes—
215#500C22×C6111yescharacteristic
216#499C22×C6111yescharacteristic
217#495C22×C6111yescharacteristic
218#493C22×C6111yescharacteristic
219#488—21no—
220#486—21no—
221#467C22×C6111yescharacteristic
222#466—21no—
223#466C22×C6111yescharacteristic
224#466C22×C6112yes—
225#465—21no—
226C4×Q16C22×C6111yescharacteristic
227C4×SD16—21no—
228C4×D8—21no—
229C4×D8C22×C6111yescharacteristic
230C4×D8C22×C6112yes—
231C2×C4×C8C22×C6111yescharacteristic
232#367C22×C6112yes—
233#366C22×C6112yes—
234#358C22×C6112yes—
235#357C22×C6112yes—
236#357C22×C6112yes—
237#357C22×C6112yes—
238#346C22×C6111yescharacteristic
239#346C22×C6111yescharacteristic
240C4×C16C22×C6112yes—
241C61#3373711yescharacteristic, direct product factor, Sylow
242C2×#41—41no—
243C2×Q16C23×C6111yescharacteristic
244C2×SD16—21no—
245C2×D8—21no—
246C2×D8C23×C6112yes—
247C2×D8C23×C6111yescharacteristic
248C22×C8D4×C6111yescharacteristic
249C22×C8C23×C6111yescharacteristic
250C4⋊Q8—21no—
251#127—21no—
252#126—41no—
253#125—21no—
254#124—21no—
255#124—41no—
256#123—41no—
257C22⋊Q8—21no—
258#121—21no—
259#121—22no—
260#121—41no—
261C4×Q8—21no—
262C4×D4—21no—
263C4×D4—22no—
264C4×D4—41no—
265C4×D4—41no—
266#117—41no—
267C2×C42D4×C6111yescharacteristic
268SD32—24no—
269D16—24no—
270M32—24no—
271C2×C16C23×C6112yes—
272C2×C16C23×C6112yes—
273#107—21no—
274#107C23×C6111yescharacteristic
275#107C23×C6111yescharacteristic
276#107C23×C6112yes—
277#106—21no—
278#103—21no—
279#103—21no—
280#102—22no—
281#102—21no—
282#102—22no—
283#102—21no—
284C4×C8D4×C6111yescharacteristic
285C4×C8D4×C6111yescharacteristic
286C4×C8C23×C6111yescharacteristic
287C4×C8C23×C6111yescharacteristic
288#41—84no—
289C2×Q8—21no—
290C2×Q8—41no—
291C2×D4—21no—
292C2×D4—22no—
293C2×D4—41no—
294C2×D4—42no—
295C2×D4—41no—
296C2×D4—41no—
297C22×C4—41no—
298C22×C4—42no—
299C22×C4D8×C6111yescharacteristic
300C22×C4D8×C6111yescharacteristic
301C22×C4C2×D4×C6111yescharacteristic
302Q16—22no—
303SD16—42no—
304D8—22no—
305D8—22no—
306D8—22no—
307D8—42no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8C2×D4×C6111yescharacteristic
311C2×C8C2×D4×C6111yescharacteristic
312C2×C8C2×D4×C6111yescharacteristic
313C2×C8C24×C6111yescharacteristic
314C4⋊C4—22no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—42no—
326C22⋊C4—41no—
327C22⋊C4—42no—
328C22⋊C4—41no—
329C42—41no—
330C42D8×C6111yescharacteristic
331C42D8×C6111yescharacteristic
332C42C2×D4×C6111yescharacteristic
333C42C2×D4×C6111yescharacteristic
334C16—22no—
335C16#41×C6114yescomplemented
336C23—41no—
337C23—42no—
338C23C2×D8×C6111yescharacteristic
339Q8—41no—
340Q8—41no—
341Q8—82no—
342D4—41no—
343D4—42no—
344D4—42no—
345D4—41no—
346D4—82no—
347D4—82no—
348D4—82no—
349D4—84no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—22no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—82no—
359C2×C4—84no—
360C2×C4C2×D8×C6111yescharacteristic
361C2×C4C2×D8×C6111yescharacteristic
362C2×C4C2×D8×C6111yescharacteristic
363C2×C4C2×D8×C6111yescharacteristic
364C2×C4C2×D8×C6111yescharacteristic
365C2×C4C22×D4×C6111yescharacteristic
366C8—21no—
367C8—21no—
368C8#135×C6112yes—
369C8C2×#41×C6112yes—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—82no—
374C22—81no—
375C22—82no—
376C22—81no—
377C22—82no—
378C22—81no—
379C22C22×D8×C6111yescharacteristic
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—81no—
385C4—82no—
386C4—81no—
387C4—81no—
388C4C61×#50912yes—
389C4C61×#53211yescharacteristic
390C4C2×#135×C6111yescharacteristic
391C2—41no—
392C2—162no—
393C2—161no—
394C2C61×#316911yescharacteristic
395C2C2×C61×#50911yescharacteristic
396C2C61×#341411yescharacteristic
subgroupG/H
centerC2×C4×C61C2×D8
commutator, Frattini, cosocleC2×C8C24×C61
socleC22×C61C22×D8
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C61 ◁ C2×C42×C61 ◁ C2×C4×C8×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3169C2semidirect
2. C61×#3168C2semidirect
3. C61×#2255C2semidirect
4. C61×#2250C2semidirect
5. C61×#2244C2semidirect
6. C61×#2243C2semidirect
7. C61×#2220C2semidirect
8. C61×#2218C2semidirect
9. C4×SD32×C61C2semidirect
10. C4×D16×C61C2semidirect
11. C4×M32×C61C2semidirect
136. C16×C61#41semidirect
171. #33737C61direct (N × H)
193. #3169C2×C61semidirect
194. #3168C2×C61semidirect
195. #2255C2×C61semidirect
196. #2250C2×C61semidirect
197. #2244C2×C61semidirect
198. #2243C2×C61semidirect
199. #2220C2×C61semidirect
200. #2218C2×C61semidirect
201. C4×SD32C2×C61semidirect
202. C4×D16C2×C61semidirect
203. C4×M32C2×C61semidirect
241. C61#33737direct (N × H)
335. C16#41×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#31692
C61×#31682
C61×#22552
C61×#22502
C61×#22442
C61×#22432
C61×#22202
C61×#22182
C4×SD32×C612
C4×D16×C612
C4×M32×C612
#3373761