Finite Group Databasebeta

← D61×#2229 #29834644

Subgroups — D61×#2229 #29834644

Order 15616.

542 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#499×D61C211yesmaximal, characteristic
2C4×Q16×D61C211yesmaximal, characteristic
3#21447986C211yesmaximal, characteristic, complemented
4#21447985C211yesmaximal, characteristic, complemented
5#21447984C211yesmaximal, characteristic, complemented
6#21447983C211yesmaximal, characteristic, complemented
7#21447982C211yesmaximal, characteristic, complemented
8#21447981C211yesmaximal, characteristic, complemented
9#21447980C211yesmaximal, characteristic, complemented
10#367×D61C211yesmaximal, characteristic
11#366×D61C211yesmaximal, characteristic
12C4⋊C16×D61C211yesmaximal, characteristic
13#358×D61C211yesmaximal, characteristic
14#358×D61C211yesmaximal, characteristic
15C61×#2229C211yesmaximal, characteristic, complemented
16C2×Q16×D61C2211yescharacteristic
17#125×D61—21no—
18C4×Q8×D61—21no—
19C2×C16×D61C2211yescharacteristic
20C2×C16×D61C2211yescharacteristic
21#16840164C2211yescharacteristic
22#16840163C2211yescharacteristic
23#16840163C2211yescharacteristic
24#16840162—21no—
25#16840161—21no—
26C4×Dic244C2211yescharacteristic
27Q16×Dic61C2211yescharacteristic
28#16839856C2211yescharacteristic
29C4×#11758202—21no—
30#16839854—21no—
31#107×D61C2211yescharacteristic
32#107×D61C2211yescharacteristic
33#107×D61C2211yescharacteristic
34#106×D61—21no—
35#103×D61—21no—
36C4×C8×D61C2211yescharacteristic
37#16839590C2211yescharacteristic
38#16839589C2211yescharacteristic
39#16839589C2211yescharacteristic
40#16839588C2211yescharacteristic
41#16839587C2211yescharacteristic
42#16839587C2211yescharacteristic
43C4⋊#11758185C2211yescharacteristic
44#16839580C2211yescharacteristic
45#16839580C2211yescharacteristic
46#16839567C2211yescharacteristic
47#16839567C2211yescharacteristic
48#16839566C2211yescharacteristic
49#16839566C2211yescharacteristic
50#16839565C2211yescharacteristic
51#16839565C2211yescharacteristic
52C61×#499C2211yescharacteristic
53C4×Q16×C61C2211yescharacteristic
54C61×#367C2211yescharacteristic
55C61×#366C2211yescharacteristic
56C61×C4⋊C16C2211yescharacteristic
57C61×#358C2211yescharacteristic
58C61×#358C2211yescharacteristic
59C2×Q8×D61—21no—
60C2×Dic244C2311yescharacteristic
61C2×#11758202—21no—
62Q16×D61—22no—
63Q16×D61Q814yes—
64C2×C8×D61D411yescharacteristic
65C2×C8×D61C2311yescharacteristic
66#14519769—21no—
67#14519768—21no—
68#14519768—21no—
69#14519767—41no—
70#14519767—41no—
71Q8×Dic61—21no—
72C4×Dic122—21no—
73C4×Dic122—41no—
74#14519742—21no—
75#14519742—41no—
76C4⋊C4×D61—21no—
77C4⋊C4×D61—21no—
78C4⋊C4×D61—21no—
79C4⋊C4×D61—41no—
80C4⋊C4×D61—41no—
81C4⋊C4×D61—41no—
82C42×D61—41no—
83C42×D61D411yescharacteristic
84C2×#11758185C2311yescharacteristic
85C2×#11758185C2311yescharacteristic
86C16×D61—22no—
87C16×D61—22no—
88#14519711C2311yescharacteristic
89#14519711C2311yescharacteristic
90#14519711C2311yescharacteristic
91#14519710—21no—
92#14519710—21no—
93#14519710—21no—
94#14519709—21no—
95#14519708—21no—
96#14519708—21no—
97#14519702—21no—
98#14519701—21no—
99#14519700—21no—
100C4×#92418D411yescharacteristic
101C8×Dic61D411yescharacteristic
102C8×Dic61C2311yescharacteristic
103C2×Q16×C61C2311yescharacteristic
104#125×C61—21no—
105C4×Q8×C61—21no—
106C2×C16×C61C2311yescharacteristic
107C2×C16×C61C2311yescharacteristic
108#107×C61C2311yescharacteristic
109#107×C61C2311yescharacteristic
110#107×C61C2311yescharacteristic
111#106×C61—21no—
112#103×C61—21no—
113C4×C8×C61C2311yescharacteristic
114C2×Q8×C61—21no—
115Q8×D61—24no—
116Q8×D61—42no—
117C2×C4×D61—41no—
118C2×C4×D61—41no—
119C2×C4×D61—41no—
120C2×C4×D61—41no—
121C2×C4×D61D811yescharacteristic
122C2×C4×D61D811yescharacteristic
123C2×C4×D61C2×D411yescharacteristic
124C2×Dic122—21no—
125C2×Dic122—41no—
126Q16×C61—21no—
127Q16×C61C2×Q812yes—
128C2×C8×C61C2×D411yescharacteristic
129C2×C8×C61C2411yescharacteristic
130C4⋊C4×C61—21no—
131C4⋊C4×C61—21no—
132C4⋊C4×C61—21no—
133C4⋊C4×C61—41no—
134C4⋊C4×C61—41no—
135C4⋊C4×C61—41no—
136C42×C61—41no—
137C42×C61C2×D411yescharacteristic
138#11758202—24no—
139C4⋊Dic61—21no—
140C4⋊Dic61—21no—
141C4⋊Dic61—21no—
142C4⋊Dic61—41no—
143C4⋊Dic61—41no—
144C4⋊Dic61—41no—
145#11758196—41no—
146#11758196—41no—
147#11758196—41no—
148#11758196—41no—
149#11758196—41no—
150#11758196—41no—
151#11758196—41no—
152#11758196—41no—
153#11758196—41no—
154C4×Dic61—41no—
155C4×Dic61—41no—
156C4×Dic61—41no—
157C4×Dic61D811yescharacteristic
158C4×Dic61D811yescharacteristic
159C4×Dic61C2×D411yescharacteristic
160C2×#92418C2×D411yescharacteristic
161C2×#92418C2×D411yescharacteristic
162Dic244—21no—
163Dic244C2×Q812yes—
164C8×D61—22no—
165C8×D61C2×Q812yes—
166C8×D61#4112yes—
167C16×C61—21no—
168C16×C61—21no—
169#11758185—21no—
170#11758185—21no—
171C22×D61C2×D811yescharacteristic
172Q8×C61—22no—
173Q8×C61—41no—
174C2×C4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61—41no—
177C2×C4×C61—41no—
178C2×C4×C61C2×D811yescharacteristic
179C2×C4×C61C2×D811yescharacteristic
180C2×C4×C61C22×D411yescharacteristic
181C2×Dic61—41no—
182C2×Dic61—41no—
183C2×Dic61—41no—
184C2×Dic61—41no—
185C2×Dic61C2×D811yescharacteristic
186C2×Dic61C2×D811yescharacteristic
187C2×Dic61C2×D811yescharacteristic
188C4×D61—22no—
189C4×D61—22no—
190C4×D61—44no—
191C4×D61—82no—
192C4×D61—82no—
193C4×D61—82no—
194C4×D61C22⋊Q812yes—
195C4×D61#13712yes—
196Dic122—22no—
197Dic122—41no—
198Dic122—44no—
199C8×C61—21no—
200C8×C61C22×Q811yescharacteristic
201C8×C61C2×#4111yescharacteristic
202#92418—21no—
203#92418C22⋊Q812yes—
204C2×#2229—611nomaximal, Sylow
205C22×C61C22×D811yescharacteristic
206C2×D61#47412yes—
207C2×D61#50812yes—
208C2×D61#51012yes—
209C4×C61—21no—
210C4×C61—21no—
211C4×C61—42no—
212C4×C61—81no—
213C4×C61—81no—
214C4×C61—81no—
215C4×C61C2×C22⋊Q811yescharacteristic
216C4×C61C2×#13711yescharacteristic
217Dic61—21no—
218Dic61—21no—
219Dic61—42no—
220Dic61—81no—
221Dic61—81no—
222Dic61—81no—
223Dic61#47412yes—
224C2×#499—611no—
225C2×C4×Q16—611no—
226#2229—611no—
227#2229—611no—
228#2229—611no—
229#2229—611no—
230#2229—611no—
231#2229—611no—
232#2229—611no—
233#2229D6111yescharacteristic, direct product factor
234C2×#367—611no—
235C2×#366—611no—
236C2×C4⋊C16—611no—
237C2×#358—611no—
238C2×#358—611no—
239C2×C61C2×#47411yescharacteristic
240C2×C61C2×#50811yescharacteristic
241C2×C61C2×#51011yescharacteristic
242D61#222914yesdirect product factor
243C22×Q16—611no—
244C2×#125—1221no—
245C2×C4×Q8—1221no—
246C22×C16—611no—
247C22×C16—611no—
248#499—611no—
249#499—611no—
250#499—611no—
251#499—1221no—
252#499—1221no—
253#499C2×D6111yescharacteristic
254C4×Q16—611no—
255C4×Q16—611no—
256C4×Q16—611no—
257C4×Q16—1221no—
258C4×Q16—1221no—
259C4×Q16C2×D6111yescharacteristic
260C2×#107—611no—
261C2×#107—611no—
262C2×#107—611no—
263C2×#106—1221no—
264C2×#103—1221no—
265C2×C4×C8—611no—
266#367—611no—
267#367—611no—
268#367—611no—
269#367C2×D6111yescharacteristic
270#366—611no—
271#366—611no—
272#366—611no—
273#366C2×D6111yescharacteristic
274C4⋊C16—611no—
275C4⋊C16—611no—
276C4⋊C16—611no—
277C4⋊C16C2×D6111yescharacteristic
278#358—611no—
279#358—611no—
280#358—611no—
281#358—611no—
282#358—611no—
283#358—611no—
284#358C2×D6111yescharacteristic
285#358C2×D6111yescharacteristic
286C61C2×#222911yescharacteristic, complemented, Sylow
287C22×Q8—1221no—
288C2×Q16—614no—
289C2×Q16—611no—
290C2×Q16—1222no—
291C2×Q16—1221no—
292C2×Q16C22×D6111yescharacteristic
293C22×C8—611no—
294C22×C8—611no—
295#125—21no—
296#125—1221no—
297#125—1221no—
298#125—1221no—
299#125—2441no—
300#125—2441no—
301C4×Q8—21no—
302C4×Q8—1221no—
303C4×Q8—1221no—
304C4×Q8—1221no—
305C4×Q8—2441no—
306C4×Q8—2441no—
307C2×C4⋊C4—1221no—
308C2×C4⋊C4—1221no—
309C2×C4⋊C4—1221no—
310C2×C4⋊C4—2441no—
311C2×C4⋊C4—2441no—
312C2×C4⋊C4—2441no—
313C2×C42—611no—
314C2×C42—2441no—
315C2×C16—611no—
316C2×C16—611no—
317C2×C16—1222no—
318C2×C16—1222no—
319C2×C16C22×D6111yescharacteristic
320C2×C16C22×D6111yescharacteristic
321#107—611no—
322#107—611no—
323#107—611no—
324#107—1221no—
325#107—1221no—
326#107—1221no—
327#107C22×D6111yescharacteristic
328#107C22×D6111yescharacteristic
329#107C22×D6111yescharacteristic
330#106—21no—
331#106—1221no—
332#106—1221no—
333#106—1221no—
334#103—21no—
335#103—1221no—
336#103—1221no—
337#103—1221no—
338C4×C8—611no—
339C4×C8—611no—
340C4×C8—611no—
341C4×C8C22×D6111yescharacteristic
342C2×Q8—21no—
343C2×Q8—1224no—
344C2×Q8—1221no—
345C2×Q8—2441no—
346C2×Q8—2442no—
347C22×C4—611no—
348C22×C4—611no—
349C22×C4—611no—
350C22×C4—2441no—
351C22×C4—2441no—
352C22×C4—2441no—
353C22×C4—2441no—
354Q16—21no—
355Q16—612no—
356Q16—1224no—
357Q16—1221no—
358Q16Q8×D6112yes—
359C2×C8—611no—
360C2×C8—612no—
361C2×C8—612no—
362C2×C8—611no—
363C2×C8—1222no—
364C2×C8D4×D6111yescharacteristic
365C2×C8C23×D6111yescharacteristic
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—1221no—
373C4⋊C4—1221no—
374C4⋊C4—1221no—
375C4⋊C4—2441no—
376C4⋊C4—2441no—
377C4⋊C4—2441no—
378C4⋊C4—2441no—
379C4⋊C4—2441no—
380C4⋊C4—2441no—
381C4⋊C4—2441no—
382C4⋊C4—2441no—
383C4⋊C4—2441no—
384C4⋊C4—2441no—
385C4⋊C4—2441no—
386C4⋊C4—2441no—
387C42—41no—
388C42—611no—
389C42—611no—
390C42—611no—
391C42—2441no—
392C42—2441no—
393C42—2441no—
394C42D4×D6111yescharacteristic
395C16—21no—
396C16—21no—
397C16—1221no—
398C16—1221no—
399C23—611no—
400Q8—22no—
401Q8—41no—
402Q8—1222no—
403Q8—2444no—
404Q8—2441no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—611no—
410C2×C4—612no—
411C2×C4—612no—
412C2×C4—611no—
413C2×C4—611no—
414C2×C4—1222no—
415C2×C4—1222no—
416C2×C4—4882no—
417C2×C4—4882no—
418C2×C4—4882no—
419C2×C4—2444no—
420C2×C4—2441no—
421C2×C4—2441no—
422C2×C4—2441no—
423C2×C4—2441no—
424C2×C4D8×D6111yescharacteristic
425C2×C4D8×D6111yescharacteristic
426C2×C4C2×D4×D6111yescharacteristic
427C8—21no—
428C8—612no—
429C8—1221no—
430C8C2×Q8×D6111yescharacteristic
431C8#41×D6111yescharacteristic
432C22—612no—
433C22—612no—
434C22—612no—
435C22C2×D8×D6111yescharacteristic
436C4—21no—
437C4—21no—
438C4—42no—
439C4—81no—
440C4—81no—
441C4—81no—
442C4—612no—
443C4—1221no—
444C4—1221no—
445C4—4881no—
446C4—4881no—
447C4—4881no—
448C4—2442no—
449C4C22⋊Q8×D6111yescharacteristic
450C4#137×D6111yescharacteristic
451C2—614no—
452C2#474×D6111yescharacteristic
453C2#508×D6111yescharacteristic
454C2#510×D6111yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2229C2
socleC22×C61C22×D8
prime radicalC22×D61C2×D8
hypercenter#2229D61
hypocenterC61C2×#2229
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2229

Complements

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

NH ≅ G/Ntype
3. #21447986C2semidirect
4. #21447985C2semidirect
5. #21447984C2semidirect
6. #21447983C2semidirect
7. #21447982C2semidirect
8. #21447981C2semidirect
9. #21447980C2semidirect
15. C61×#2229C2semidirect
233. #2229D61direct (N × H)
242. D61#2229direct (N × H)
286. C61C2×#2229semidirect

Maximal subgroups

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

subgroupindex
#499×D612
C4×Q16×D612
#214479862
#214479852
#214479842
#214479832
#214479822
#214479812
#214479802
#367×D612
#366×D612
C4⋊C16×D612
#358×D612
C61×#22292
C2×#222961