Finite Group Databasebeta

← #29652566

Subgroups — #29652566

Order 15616.

904 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459224C211yesmaximal, characteristic
2#21455949C212yesmaximal, complemented
3#21444826C212yesmaximal, complemented
4#21444809C212yesmaximal
5#21444792C212yesmaximal, complemented
6#21444775C212yesmaximal
7#21444369C212yesmaximal, complemented
8#21444153C211yesmaximal, characteristic
9C61×#2599C211yesmaximal, characteristic
10#16840393—21no—
11#16840393C2212yes—
12#16840390—22no—
13#16840390—22no—
14#16840388—21no—
15#16840388C2212yes—
16#16840319—21no—
17#16840319C2212yes—
18#16840315—24no—
19C2×#14519736—21no—
20#16840092C2214yes—
21#16840047—22no—
22#16839972—22no—
23#16839918C2214yes—
24#16839867—24no—
25#16839819C2212yes—
26#16839498C2214yes—
27#16839498C2214yes—
28#16839488C2212yes—
29#16839486C2212yes—
30C2×C4×Q8×C61C2211yescharacteristic
31C2×#117×C61C2211yescharacteristic
32C61×#398C2211yescharacteristic
33C61×#397C2211yescharacteristic
34C61×#395C2211yescharacteristic
35C61×#393C2211yescharacteristic
36C61×#388—21no—
37C61×#387—21no—
38C61×#387—21no—
39C61×#385—21no—
40C61×#383C2211yescharacteristic
41C2×#11758202—24no—
42#14519777—21no—
43#14519777—21no—
44#14519777D412yes—
45#14519777D412yes—
46#14519776—24no—
47#14519776—24no—
48#14519769—22no—
49#14519769—22no—
50#14519768—24no—
51#14519768—24no—
52#14519756—22no—
53#14519756—22no—
54#14519756—22no—
55#14519756C2314yes—
56#14519754—24no—
57#14519754—24no—
58#14519754—24no—
59#14519754—24no—
60C4×Dic122—22no—
61C4×Dic122—22no—
62C4×Dic122—22no—
63C4×Dic122D414yes—
64#14519736—22no—
65#14519736—22no—
66#14519736—22no—
67#14519736—22no—
68C2×C4⋊Dic61—21no—
69C2×C4⋊Dic61—21no—
70C2×C22⋊Dic61—22no—
71C2×C4×Dic61—22no—
72#14519708—24no—
73C4⋊#92418—22no—
74#14519701—24no—
75#14519700—24no—
76C22⋊#92418C2314yes—
77#14519688—22no—
78C22×Q8×C61C2311yescharacteristic
79C23×C4×C61D411yescharacteristic
80C4×Q8×C61—22no—
81C4×Q8×C61—22no—
82#117×C61—22no—
83#117×C61—22no—
84C2×C4⋊C4×C61—21no—
85C2×C4⋊C4×C61—21no—
86C2×C4⋊C4×C61—21no—
87C2×C4⋊C4×C61D411yescharacteristic
88C2×C4⋊C4×C61C2311yescharacteristic
89C2×C4⋊C4×C61C2311yescharacteristic
90C2×C22⋊C4×C61—21no—
91C2×C22⋊C4×C61—21no—
92C2×C22⋊C4×C61D411yescharacteristic
93C2×C22⋊C4×C61C2311yescharacteristic
94C2×C42×C61—21no—
95C2×C42×C61D411yescharacteristic
96C2×C42×C61C2311yescharacteristic
97#95×C61—21no—
98#95×C61—21no—
99#95×C61—21no—
100#95×C61—21no—
101#95×C61—21no—
102#95×C61—21no—
103#95×C61C2311yescharacteristic
104#95×C61C2311yescharacteristic
105C24×C61C2×D411yescharacteristic
106C2×Q8×C61—22no—
107C2×Q8×C61—42no—
108C22×C4×C61—22no—
109C22×C4×C61—21no—
110C22×C4×C61—21no—
111C22×C4×C61—22no—
112C22×C4×C61—21no—
113C22×C4×C61—21no—
114C22×C4×C61—21no—
115C22×C4×C61—21no—
116C22×C4×C61C2×D411yescharacteristic
117C22×C4×C61C2×D411yescharacteristic
118C22×C4×C61C2×D411yescharacteristic
119C22×C4×C61C2×D411yescharacteristic
120C22×C4×C61C2×D411yescharacteristic
121C22×C4×C61C2411yescharacteristic
122C22×Dic61—22no—
123C22×Dic61—22no—
124C2×Dic122—22no—
125C2×Dic122—22no—
126C2×Dic122—22no—
127C2×Dic122C2×D414yes—
128C4⋊C4×C61—22no—
129C4⋊C4×C61—22no—
130C4⋊C4×C61—22no—
131C4⋊C4×C61—42no—
132C4⋊C4×C61—41no—
133C4⋊C4×C61—41no—
134C4⋊C4×C61—42no—
135C22⋊C4×C61—22no—
136C22⋊C4×C61—22no—
137C22⋊C4×C61—42no—
138C22⋊C4×C61—42no—
139C42×C61—21no—
140C42×C61—21no—
141C42×C61—42no—
142C42×C61C2×D412yes—
143C42×C61C2×D412yes—
144C22⋊Dic61—24no—
145C22⋊Dic61—24no—
146#11758202—48no—
147C4⋊Dic61—22no—
148C4⋊Dic61—22no—
149C4⋊Dic61—22no—
150C4⋊Dic61—22no—
151C4⋊Dic61—22no—
152C4⋊Dic61—22no—
153C4⋊Dic61—22no—
154C4⋊Dic61C2×D414yes—
155#11758196—24no—
156#11758196—24no—
157#11758196—24no—
158#11758196—24no—
159C4×Dic61—24no—
160C4×Dic61—24no—
161C2×#92418—24no—
162C23×C61—21no—
163C23×C61—21no—
164C23×C61—41no—
165C23×C61—41no—
166C23×C61#13712yes—
167C23×C61C22×D411yescharacteristic
168Q8×C61—24no—
169Q8×C61—42no—
170C2×C4×C61—24no—
171C2×C4×C61—24no—
172C2×C4×C61—21no—
173C2×C4×C61—21no—
174C2×C4×C61—21no—
175C2×C4×C61—21no—
176C2×C4×C61—22no—
177C2×C4×C61—21no—
178C2×C4×C61—21no—
179C2×C4×C61—41no—
180C2×C4×C61—41no—
181C2×C4×C61—41no—
182C2×C4×C61—41no—
183C2×C4×C61—41no—
184C2×C4×C61—41no—
185C2×C4×C61—41no—
186C2×C4×C61—41no—
187C2×C4×C61—41no—
188C2×C4×C61—41no—
189C2×C4×C61—41no—
190C2×C4×C61—41no—
191C2×C4×C61—41no—
192C2×C4×C61—41no—
193C2×C4×C61—41no—
194C2×C4×C61#12011yescharacteristic
195C2×C4×C61#12012yes—
196C2×C4×C61#12011yescharacteristic
197C2×C4×C61#13712yes—
198C2×C4×C61C22×D412yes—
199C2×Dic61—24no—
200C2×Dic61—24no—
201C2×Dic61—82no—
202C2×Dic61—82no—
203Dic122—44no—
204Dic122—82no—
205Dic122—82no—
206Dic122—82no—
207#92418—44no—
208#18155—611nomaximal, Sylow
209C22×C61—21no—
210C22×C61—21no—
211C22×C61—22no—
212C22×C61—42no—
213C22×C61—41no—
214C22×C61—41no—
215C22×C61—81no—
216C22×C61C2×#12011yescharacteristic
217C22×C61C2×#13711yescharacteristic
218C22×C61C2×#13711yescharacteristic
219C4×C61—21no—
220C4×C61—21no—
221C4×C61—22no—
222C4×C61—22no—
223C4×C61—22no—
224C4×C61—41no—
225C4×C61—41no—
226C4×C61—42no—
227C4×C61—81no—
228C4×C61—81no—
229C4×C61—81no—
230Dic61—44no—
231Dic61—44no—
232#3458—611no—
233#3113—612no—
234#2599D6111yescharacteristic
235#1611—612no—
236#1608—612no—
237#1605—612no—
238#1602—612no—
239#1515—612no—
240#1464—611no—
241C2×C61—21no—
242C2×C61—21no—
243C2×C61—42no—
244C2×C61#300411yescharacteristic
245C2×C61#302211yescharacteristic
246C2×C61#302511yescharacteristic
247#544—612no—
248#544—1222no—
249#544—1222no—
250#544—1221no—
251#543—612no—
252#543—1221no—
253#533—612no—
254#533—1224no—
255#533—1221no—
256C2×C4×Q8C2×D6111yescharacteristic
257C2×#117—1221no—
258C2×#117C2×D6111yescharacteristic
259#483—614no—
260#475—1222no—
261#462—1222no—
262#451—614no—
263#441—1224no—
264#432—612no—
265#398C2×D6111yescharacteristic
266#397C2×D6111yescharacteristic
267#395C2×D6111yescharacteristic
268#393C2×D6111yescharacteristic
269#388—21no—
270#387—21no—
271#387—21no—
272#385—21no—
273#383C2×D6111yescharacteristic
274#328—614no—
275#328—614no—
276#324—612no—
277#323—612no—
278C61#1815511yescharacteristic, complemented, Sylow
279C22×Q8C22×D6111yescharacteristic
280C23×C4C22⋊D6111yescharacteristic
281C2×Q16—1224no—
282C4⋊Q8—612no—
283C4⋊Q8—612no—
284C4⋊Q8—1221no—
285C4⋊Q8—1221no—
286C4⋊Q8—1224no—
287C4⋊Q8—1224no—
288#125—1222no—
289#125—1224no—
290#125—1224no—
291#125—1222no—
292C22⋊Q8—614no—
293C22⋊Q8—1224no—
294C22⋊Q8—1224no—
295C22⋊Q8—1224no—
296C22⋊Q8—1224no—
297C22⋊Q8—1222no—
298C22⋊Q8—1222no—
299C22⋊Q8—1222no—
300C4×Q8—22no—
301C4×Q8—22no—
302C4×Q8—614no—
303C4×Q8—1222no—
304C4×Q8—1222no—
305C4×Q8—1222no—
306#117—22no—
307#117—22no—
308#117—1222no—
309#117—1222no—
310#117—1222no—
311#117—1222no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—1221no—
316C2×C4⋊C4—1221no—
317C2×C4⋊C4C22⋊D6111yescharacteristic
318C2×C4⋊C4C22×D6111yescharacteristic
319C2×C4⋊C4C22×D6111yescharacteristic
320C2×C22⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—1222no—
323C2×C22⋊C4C22⋊D6111yescharacteristic
324C2×C22⋊C4C22×D6111yescharacteristic
325C2×C42—21no—
326C2×C42—1222no—
327C2×C42C22⋊D6111yescharacteristic
328C2×C42C22×D6111yescharacteristic
329#106—1224no—
330C4⋊C8—1222no—
331#103—1224no—
332#103—1224no—
333C22⋊C8—614no—
334#97—1222no—
335#95—21no—
336#95—21no—
337#95—21no—
338#95—21no—
339#95—21no—
340#95—21no—
341#95C22×D6111yescharacteristic
342#95C22×D6111yescharacteristic
343C24C2×C22⋊D6111yescharacteristic
344C2×Q8—22no—
345C2×Q8—42no—
346C2×Q8—614no—
347C2×Q8—1222no—
348C2×Q8—1222no—
349C2×Q8—1222no—
350C22×C4—22no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—22no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—1222no—
359C22×C4—1222no—
360C22×C4C2×C22⋊D6111yescharacteristic
361C22×C4C2×C22⋊D6111yescharacteristic
362C22×C4C2×C22⋊D6111yescharacteristic
363C22×C4C2×C22⋊D6111yescharacteristic
364C22×C4C2×C22⋊D6111yescharacteristic
365C22×C4C23×D6111yescharacteristic
366Q16—2448no—
367C2×C8—1224no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—42no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—42no—
375C4⋊C4—614no—
376C4⋊C4—1222no—
377C4⋊C4—1222no—
378C4⋊C4—1224no—
379C4⋊C4—1224no—
380C4⋊C4—1222no—
381C4⋊C4—1222no—
382C4⋊C4—1224no—
383C4⋊C4—1222no—
384C4⋊C4—1222no—
385C4⋊C4—1224no—
386C4⋊C4—1222no—
387C22⋊C4—22no—
388C22⋊C4—22no—
389C22⋊C4—42no—
390C22⋊C4—42no—
391C22⋊C4—1224no—
392C22⋊C4—1224no—
393C42—21no—
394C42—21no—
395C42—42no—
396C42—1224no—
397C42—1224no—
398C42D4×D6112yes—
399C42D4×D6112yes—
400C23—21no—
401C23—21no—
402C23—41no—
403C23—41no—
404C23#1451980712yes—
405C23C22×C22⋊D6111yescharacteristic
406Q8—24no—
407Q8—42no—
408Q8—4882no—
409Q8—4882no—
410Q8—4882no—
411Q8—2444no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—22no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—1224no—
437C2×C4—1224no—
438C2×C4—4882no—
439C2×C4—4882no—
440C2×C4#1451974511yescharacteristic
441C2×C4#1451974511yescharacteristic
442C2×C4#1451974512yes—
443C2×C4#1451980712yes—
444C2×C4C2×D4×D6112yes—
445C8—2444no—
446C22—21no—
447C22—21no—
448C22—22no—
449C22—42no—
450C22—41no—
451C22—41no—
452C22—81no—
453C22C2×#1451974511yescharacteristic
454C22C2×#1451980711yescharacteristic
455C22C2×#1451980711yescharacteristic
456C4—22no—
457C4—22no—
458C4—21no—
459C4—21no—
460C4—22no—
461C4—41no—
462C4—42no—
463C4—41no—
464C4—81no—
465C4—81no—
466C4—81no—
467C4—2444no—
468C4—2444no—
469C2—21no—
470C2—21no—
471C2—42no—
472C2#2145505211yescharacteristic
473C2#2145519711yescharacteristic
474C2#2145521011yescharacteristic
subgroupG/H
centerC22C2×#14519745
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2599C2
socleC22×C61C2×#120
prime radicalC24×C61C2×D4
hypercenter#2599D61
hypocenterC61#18155
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2599

Complements

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

NH ≅ G/Ntype
2. #21455949C2semidirect
3. #21444826C2semidirect
5. #21444792C2semidirect
7. #21444369C2semidirect
278. C61#18155semidirect

Maximal subgroups

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

subgroupindex
#214592242
#214559492
#214448262
#214448092
#214447922
#214447752
#214443692
#214441532
C61×#25992
#1815561