Finite Group Databasebeta

← #29654325

Subgroups — #29654325

Order 15616.

876 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459224C211yesmaximal, characteristic
2#21457025C212yesmaximal, complemented
3#21444860C212yesmaximal, complemented
4#21444843C212yesmaximal
5#21444826C212yesmaximal, complemented
6#21444809C212yesmaximal
7#21444330C212yesmaximal, complemented
8#21444153C211yesmaximal, characteristic
9C61×#2611C211yesmaximal, 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#16840172—22no—
21#16840132—22no—
22#16840097C2214yes—
23#16840092C2214yes—
24#16840066—24no—
25#16839819C2212yes—
26#16839498C2214yes—
27#16839498C2214yes—
28#16839488C2212yes—
29#16839486C2212yes—
30C2×#125×C61C2211yescharacteristic
31C2×#117×C61C2211yescharacteristic
32C61×#400C2211yescharacteristic
33C61×#399C2211yescharacteristic
34C61×#398C2211yescharacteristic
35C61×#397C2211yescharacteristic
36C61×#389—21no—
37C61×#388—21no—
38C61×#387—21no—
39C61×#385—21no—
40C61×#376C2211yescharacteristic
41#14519777—21no—
42#14519777—21no—
43#14519777D412yes—
44#14519777D412yes—
45#14519776—24no—
46#14519776—24no—
47#14519769—22no—
48#14519769—22no—
49#14519768—24no—
50#14519768—24no—
51#14519756—22no—
52#14519756—22no—
53#14519756—22no—
54#14519756C2314yes—
55#14519754—24no—
56#14519754—24no—
57#14519754—24no—
58#14519754—24no—
59C4×Dic122—22no—
60C4×Dic122—22no—
61C4×Dic122—22no—
62C4×Dic122D414yes—
63#14519736—22no—
64#14519736—22no—
65#14519736—22no—
66#14519736—22no—
67C2×C4⋊Dic61—21no—
68C2×C4⋊Dic61—21no—
69C2×C22⋊Dic61—22no—
70C2×C4×Dic61—22no—
71#14519710—24no—
72#14519708—24no—
73C4⋊#92418—22no—
74#14519700—24no—
75#14519700—24no—
76C22⋊#92418C2314yes—
77#14519688—22no—
78C23×C4×C61D411yescharacteristic
79#125×C61—22no—
80#125×C61—22no—
81#117×C61—22no—
82#117×C61—22no—
83C2×C4⋊C4×C61—21no—
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×C4⋊C4×C61C2311yescharacteristic
91C2×C22⋊C4×C61—21no—
92C2×C22⋊C4×C61—21no—
93C2×C22⋊C4×C61D411yescharacteristic
94C2×C22⋊C4×C61C2311yescharacteristic
95C2×C42×C61—21no—
96C2×C42×C61D411yescharacteristic
97C2×C42×C61C2311yescharacteristic
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
106C22×C4×C61—22no—
107C22×C4×C61—21no—
108C22×C4×C61—21no—
109C22×C4×C61—22no—
110C22×C4×C61—21no—
111C22×C4×C61—21no—
112C22×C4×C61—21no—
113C22×C4×C61—21no—
114C22×C4×C61C2×D411yescharacteristic
115C22×C4×C61C2×D411yescharacteristic
116C22×C4×C61C2×D411yescharacteristic
117C22×C4×C61C2×D411yescharacteristic
118C22×C4×C61C2×D411yescharacteristic
119C22×C4×C61C2411yescharacteristic
120C22×Dic61—22no—
121C22×Dic61—22no—
122C2×Dic122—22no—
123C2×Dic122—22no—
124C2×Dic122—22no—
125C2×Dic122C2×D414yes—
126C4⋊C4×C61—22no—
127C4⋊C4×C61—22no—
128C4⋊C4×C61—22no—
129C4⋊C4×C61—22no—
130C4⋊C4×C61—42no—
131C4⋊C4×C61—41no—
132C4⋊C4×C61—42no—
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—
146C4⋊Dic61—22no—
147C4⋊Dic61—22no—
148C4⋊Dic61—22no—
149C4⋊Dic61—22no—
150C4⋊Dic61—22no—
151C4⋊Dic61—22no—
152C4⋊Dic61—22no—
153C4⋊Dic61C2×D414yes—
154#11758196—24no—
155#11758196—24no—
156#11758196—24no—
157#11758196—24no—
158C4×Dic61—24no—
159C4×Dic61—24no—
160C2×#92418—24no—
161C23×C61—21no—
162C23×C61—21no—
163C23×C61—41no—
164C23×C61—41no—
165C23×C61#13712yes—
166C23×C61C22×D411yescharacteristic
167C2×C4×C61—24no—
168C2×C4×C61—24no—
169C2×C4×C61—21no—
170C2×C4×C61—21no—
171C2×C4×C61—21no—
172C2×C4×C61—21no—
173C2×C4×C61—22no—
174C2×C4×C61—21no—
175C2×C4×C61—21no—
176C2×C4×C61—41no—
177C2×C4×C61—41no—
178C2×C4×C61—41no—
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#12011yescharacteristic
192C2×C4×C61#12012yes—
193C2×C4×C61#12011yescharacteristic
194C2×C4×C61#13712yes—
195C2×C4×C61C22×D412yes—
196C2×Dic61—24no—
197C2×Dic61—24no—
198C2×Dic61—82no—
199C2×Dic61—82no—
200Dic122—44no—
201Dic122—82no—
202Dic122—82no—
203Dic122—82no—
204#92418—44no—
205#18340—611nomaximal, Sylow
206C22×C61—21no—
207C22×C61—21no—
208C22×C61—22no—
209C22×C61—42no—
210C22×C61—41no—
211C22×C61—41no—
212C22×C61—81no—
213C22×C61C2×#12011yescharacteristic
214C22×C61C2×#13711yescharacteristic
215C22×C61C2×#13711yescharacteristic
216C4×C61—21no—
217C4×C61—21no—
218C4×C61—22no—
219C4×C61—22no—
220C4×C61—22no—
221C4×C61—42no—
222C4×C61—41no—
223C4×C61—41no—
224C4×C61—81no—
225C4×C61—81no—
226C4×C61—81no—
227Dic61—44no—
228Dic61—44no—
229#3458—611no—
230#3236—612no—
231#2611D6111yescharacteristic
232#1617—612no—
233#1614—612no—
234#1611—612no—
235#1608—612no—
236#1506—612no—
237#1464—611no—
238C2×C61—21no—
239C2×C61—21no—
240C2×C61—42no—
241C2×C61#300411yescharacteristic
242C2×C61#301811yescharacteristic
243C2×C61#302811yescharacteristic
244#544—612no—
245#544—1222no—
246#544—1222no—
247#544—1221no—
248#543—612no—
249#543—1221no—
250#533—612no—
251#533—1224no—
252#533—1221no—
253C2×#125C2×D6111yescharacteristic
254C2×#117—1221no—
255C2×#117C2×D6111yescharacteristic
256#501—1222no—
257#491—1222no—
258#484—614no—
259#483—614no—
260#479—1224no—
261#432—612no—
262#400C2×D6111yescharacteristic
263#399C2×D6111yescharacteristic
264#398C2×D6111yescharacteristic
265#397C2×D6111yescharacteristic
266#389—21no—
267#388—21no—
268#387—21no—
269#385—21no—
270#376C2×D6111yescharacteristic
271#328—614no—
272#328—614no—
273#324—612no—
274#323—612no—
275C61#1834011yescharacteristic, complemented, Sylow
276C23×C4C22⋊D6111yescharacteristic
277C4⋊Q8—612no—
278C4⋊Q8—612no—
279C4⋊Q8—1221no—
280C4⋊Q8—1221no—
281C4⋊Q8—1224no—
282C4⋊Q8—1224no—
283#125—22no—
284#125—22no—
285#125—1222no—
286#125—1224no—
287#125—1224no—
288#125—1222no—
289C22⋊Q8—614no—
290C22⋊Q8—1224no—
291C22⋊Q8—1224no—
292C22⋊Q8—1224no—
293C22⋊Q8—1224no—
294C22⋊Q8—1222no—
295C22⋊Q8—1222no—
296C22⋊Q8—1222no—
297C4×Q8—614no—
298C4×Q8—1222no—
299C4×Q8—1222no—
300C4×Q8—1222no—
301#117—22no—
302#117—22no—
303#117—1222no—
304#117—1222no—
305#117—1222no—
306#117—1222no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—1221no—
312C2×C4⋊C4—1221no—
313C2×C4⋊C4C22⋊D6111yescharacteristic
314C2×C4⋊C4C22×D6111yescharacteristic
315C2×C4⋊C4C22×D6111yescharacteristic
316C2×C4⋊C4C22×D6111yescharacteristic
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—1222no—
320C2×C22⋊C4C22⋊D6111yescharacteristic
321C2×C22⋊C4C22×D6111yescharacteristic
322C2×C42—21no—
323C2×C42—1222no—
324C2×C42C22⋊D6111yescharacteristic
325C2×C42C22×D6111yescharacteristic
326#107—1224no—
327#106—1224no—
328C4⋊C8—1222no—
329#103—1224no—
330#103—1224no—
331C22⋊C8—614no—
332#97—1222no—
333#95—21no—
334#95—21no—
335#95—21no—
336#95—21no—
337#95—21no—
338#95C22×D6111yescharacteristic
339#95C22×D6111yescharacteristic
340C24C2×C22⋊D6111yescharacteristic
341C2×Q8—614no—
342C2×Q8—1222no—
343C2×Q8—1222no—
344C2×Q8—1222no—
345C22×C4—22no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—22no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—1222no—
354C22×C4—1222no—
355C22×C4C2×C22⋊D6111yescharacteristic
356C22×C4C2×C22⋊D6111yescharacteristic
357C22×C4C2×C22⋊D6111yescharacteristic
358C22×C4C2×C22⋊D6111yescharacteristic
359C22×C4C2×C22⋊D6111yescharacteristic
360C22×C4C23×D6111yescharacteristic
361C2×C8—1224no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—42no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—42no—
370C4⋊C4—42no—
371C4⋊C4—614no—
372C4⋊C4—1222no—
373C4⋊C4—1222no—
374C4⋊C4—1224no—
375C4⋊C4—1224no—
376C4⋊C4—1222no—
377C4⋊C4—1222no—
378C4⋊C4—1224no—
379C4⋊C4—1222no—
380C4⋊C4—1222no—
381C4⋊C4—1224no—
382C4⋊C4—1222no—
383C22⋊C4—22no—
384C22⋊C4—22no—
385C22⋊C4—42no—
386C22⋊C4—42no—
387C22⋊C4—1224no—
388C22⋊C4—1224no—
389C42—21no—
390C42—21no—
391C42—42no—
392C42—1224no—
393C42—1224no—
394C42D4×D6112yes—
395C42D4×D6112yes—
396C23—21no—
397C23—21no—
398C23—41no—
399C23—41no—
400C23#1451980712yes—
401C23C22×C22⋊D6111yescharacteristic
402Q8—4882no—
403Q8—4882no—
404Q8—4882no—
405Q8—2444no—
406C2×C4—24no—
407C2×C4—24no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—22no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
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—1224no—
431C2×C4—1224no—
432C2×C4—4882no—
433C2×C4—4882no—
434C2×C4#1451974511yescharacteristic
435C2×C4#1451974511yescharacteristic
436C2×C4#1451974512yes—
437C2×C4#1451980712yes—
438C2×C4C2×D4×D6112yes—
439C8—2444no—
440C22—21no—
441C22—21no—
442C22—22no—
443C22—42no—
444C22—41no—
445C22—41no—
446C22—81no—
447C22C2×#1451974511yescharacteristic
448C22C2×#1451980711yescharacteristic
449C22C2×#1451980711yescharacteristic
450C4—22no—
451C4—22no—
452C4—21no—
453C4—21no—
454C4—22no—
455C4—42no—
456C4—41no—
457C4—41no—
458C4—81no—
459C4—81no—
460C4—81no—
461C4—2444no—
462C4—2444no—
463C2—21no—
464C2—21no—
465C2—42no—
466C2#2145505211yescharacteristic
467C2#2145516711yescharacteristic
468C2#2145522411yescharacteristic
subgroupG/H
centerC22C2×#14519745
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2611C2
socleC22×C61C2×#120
prime radicalC24×C61C2×D4
hypercenter#2611D61
hypocenterC61#18340
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2611

Complements

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

NH ≅ G/Ntype
2. #21457025C2semidirect
3. #21444860C2semidirect
5. #21444826C2semidirect
7. #21444330C2semidirect
275. C61#18340semidirect

Maximal subgroups

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

subgroupindex
#214592242
#214570252
#214448602
#214448432
#214448262
#214448092
#214443302
#214441532
C61×#26112
#1834061