Finite Group Databasebeta

← #29665495

Subgroups — #29665495

Order 15616.

640 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456963C211yesmaximal, characteristic, complemented
2#21455609C211yesmaximal, characteristic
3#21455302C211yesmaximal, characteristic
4#21454928C211yesmaximal, characteristic
5#21445252C212yesmaximal, complemented
6#21445245C212yesmaximal, complemented
7#21445200C212yesmaximal, complemented
8#21445193C212yesmaximal, complemented
9#21444589C211yesmaximal, characteristic, complemented
10#21444507C211yesmaximal, characteristic, complemented
11C2×C61×#332C211yesmaximal, characteristic, complemented
12C2×#14519808—21no—
13#16840319C2211yescharacteristic
14C4×#11758222C2211yescharacteristic
15#16840158C2212yes—
16#16840114C2212yes—
17#16840092—22no—
18#16840070—21no—
19#16840063—21no—
20#16840058C2211yescharacteristic
21#16840053C2211yescharacteristic
22#16840048C2211yescharacteristic
23#16840044—21no—
24#16840044—21no—
25#16840043C2211yescharacteristic
26#16839969—21no—
27#16839969C2212yes—
28#16839964—21no—
29#16839964C2212yes—
30#16839886C2212yes—
31#16839827C2212yes—
32C8×C22⋊D61—22no—
33#16839815C2211yescharacteristic
34#16839814—21no—
35#16839800—21no—
36#16839786C2211yescharacteristic
37C4⋊C8×D61—21no—
38#16839771—21no—
39#16839759—21no—
40#16839512C2212yes—
41#16839512C2212yes—
42#16839510C2212yes—
43#16839509C2212yes—
44C2×C4⋊Q8×C61C2211yescharacteristic
45C2×C4⋊C8×C61C2211yescharacteristic
46C2×C4⋊C8×C61C2211yescharacteristic
47C61×#332C2212yes—
48C61×#332C2212yes—
49C2×#11758222D411yescharacteristic
50#14519808—44no—
51C2×#11758202—22no—
52C2×#11758201—22no—
53C2×#11758194—21no—
54C2×C8×D61—22no—
55#14519777C2311yescharacteristic
56#14519777C2311yescharacteristic
57#14519769—21no—
58#14519756—21no—
59#14519756—21no—
60C4×Dic122—21no—
61C4×Dic122—21no—
62C4×Dic122D411yescharacteristic
63C4×Dic122C2311yescharacteristic
64C4×D244D411yescharacteristic
65C4×D244C2311yescharacteristic
66C4×C22⋊D61—21no—
67C4×C22⋊D61—21no—
68#14519736—21no—
69#14519736D411yescharacteristic
70#14519734—21no—
71C42×D61—21no—
72#14519711—21no—
73#14519711—21no—
74#14519709—21no—
75#14519709—21no—
76#14519708—22no—
77#14519708—22no—
78C4⋊#92418—21no—
79C4⋊#92418D411yescharacteristic
80C4⋊#92418D411yescharacteristic
81C4⋊#92418C2312yes—
82#14519706—22no—
83#14519702—21no—
84#14519702—21no—
85#14519701—22no—
86#14519701—22no—
87#14519700—22no—
88#14519700—22no—
89#14519699—21no—
90#14519699—21no—
91C22⋊#92418D412yes—
92#14519689—22no—
93C4×#92418C2312yes—
94C8×Dic61—22no—
95C22×Q8×C61—21no—
96C22×C8×C61—21no—
97C22×C8×C61—21no—
98C4⋊Q8×C61—21no—
99C4⋊Q8×C61—21no—
100C4⋊Q8×C61—21no—
101C4⋊Q8×C61C2312yes—
102C2×C4⋊C4×C61—21no—
103C2×C4⋊C4×C61—21no—
104C2×C42×C61C2311yescharacteristic
105C4⋊C8×C61—21no—
106C4⋊C8×C61—21no—
107C4⋊C8×C61C2312yes—
108C4⋊C8×C61C2311yescharacteristic
109C4⋊C8×C61C2311yescharacteristic
110C2×Q8×C61—22no—
111C2×Q8×C61—41no—
112C2×Q8×C61—42no—
113C2×Q8×C61—42no—
114C22×C4×C61—41no—
115C22×C4×C61C2×D411yescharacteristic
116C22×C4×C61C2×D411yescharacteristic
117C22×C4×C61#4111yescharacteristic
118C2×C22⋊D61—21no—
119#11758222—22no—
120#11758222SD1614yes—
121C2×D244C2×D411yescharacteristic
122C2×C4×D61—21no—
123C2×C4×D61—21no—
124C2×C4×D61—21no—
125C2×Dic122—21no—
126C2×Dic122—21no—
127C2×Dic122C2×D411yescharacteristic
128C2×C8×C61—22no—
129C2×C8×C61—21no—
130C2×C8×C61—21no—
131C2×C8×C61—42no—
132C2×C8×C61—81no—
133C4⋊C4×C61—22no—
134C4⋊C4×C61—22no—
135C4⋊C4×C61—41no—
136C4⋊C4×C61—41no—
137C42×C61C2×D411yescharacteristic
138C42×C61C2×D411yescharacteristic
139C42×C61#4111yescharacteristic
140C42×C61C2411yescharacteristic
141C22⋊Dic61—21no—
142C22⋊Dic61—41no—
143#11758202—44no—
144#11758201—44no—
145#11758198—21no—
146#11758198—21no—
147C4⋊Dic61—21no—
148C4⋊Dic61—21no—
149C4⋊Dic61—21no—
150C4⋊Dic61—21no—
151C4⋊Dic61C2×D411yescharacteristic
152C4⋊Dic61C2×D411yescharacteristic
153#11758196—21no—
154#11758196—21no—
155#11758196—41no—
156#11758196—41no—
157C4×Dic61—21no—
158C4×Dic61—21no—
159C4×Dic61—21no—
160C4×Dic61—41no—
161#11758194—42no—
162C2×#92418—22no—
163C2×#92418C2×D412yes—
164C2×#92418C2×D412yes—
165C8×D61—82no—
166C23×C61#12111yescharacteristic
167C22×D61—21no—
168Q8×C61—42no—
169Q8×C61—42no—
170Q8×C61—82no—
171C2×C4×C61—21no—
172C2×C4×C61—21no—
173C2×C4×C61—41no—
174C2×C4×C61—42no—
175C2×C4×C61—82no—
176C2×C4×C61#12111yescharacteristic
177C2×C4×C61#12111yescharacteristic
178C2×C4×C61#12111yescharacteristic
179C2×C4×C61C2×SD1612yes—
180C2×C4×C61#13512yes—
181C2×C4×C61C22×D411yescharacteristic
182C2×C4×C61C22×D411yescharacteristic
183C2×C4×C61C2×#4111yescharacteristic
184C22⋊D61—24no—
185C2×Dic61—21no—
186C2×Dic61—21no—
187C2×Dic61—21no—
188C2×Dic61—41no—
189C2×Dic61—41no—
190D244—21no—
191D244C2×SD1612yes—
192C4×D61—24no—
193C4×D61—41no—
194C4×D61—41no—
195C4×D61—81no—
196Dic122—21no—
197Dic122—41no—
198Dic122—41no—
199Dic122—81no—
200Dic122C2×SD1612yes—
201C8×C61—41no—
202C8×C61—41no—
203C8×C61—42no—
204#92418—22no—
205#92418—22no—
206#92418—42no—
207#19415—611nomaximal, Sylow
208C22×C61—21no—
209C22×C61—21no—
210C22×C61#46512yes—
211C22×C61C2×#12111yescharacteristic
212C2×D61—22no—
213C2×D61—41no—
214C2×D61—41no—
215C4×C61—21no—
216C4×C61—21no—
217C4×C61—21no—
218C4×C61—82no—
219C4×C61#46512yes—
220C4×C61C22×SD1611yescharacteristic
221C4×C61C2×#13511yescharacteristic
222C4×C61#57711yescharacteristic
223C4×C61#57811yescharacteristic
224Dic61—22no—
225Dic61—41no—
226Dic61—41no—
227Dic61—81no—
228Dic61—81no—
229#3229—611no—
230#3076—611no—
231#3039—611no—
232#2988—611no—
233#1680—612no—
234#1679—612no—
235#1672—612no—
236#1671—612no—
237#1570—611no—
238#1550—611no—
239C2×#332D6111yescharacteristic, complemented
240C2×C61—22no—
241C2×C61#304611yescharacteristic
242C2×C61C2×#46511yescharacteristic
243C2×C61#306911yescharacteristic
244D61—42no—
245C2×#137—1221no—
246#533—611no—
247C2×C4⋊Q8C2×D6111yescharacteristic
248C4×#41—611no—
249#498—612no—
250#487—612no—
251#483—1222no—
252#479—1221no—
253#478—1221no—
254#477—611no—
255#476—611no—
256#475—611no—
257#475—1221no—
258#475—1221no—
259#474—611no—
260#462—612no—
261#462—1221no—
262#461—612no—
263#461—1221no—
264C8×Q8—612no—
265C8×D4—612no—
266C8×D4—1222no—
267#431—611no—
268#431—1221no—
269#427—1221no—
270#423—611no—
271C2×C4⋊C8—1221no—
272C2×C4⋊C8C2×D6111yescharacteristic
273C2×C4⋊C8C2×D6111yescharacteristic
274#419—1221no—
275#416—1221no—
276#334—612no—
277#334—612no—
278#333—612no—
279#332—612no—
280#332C2×D6112yes—
281#332C2×D6112yes—
282C61#1941511yescharacteristic, complemented, Sylow
283C2×#41—611no—
284C22×Q8—21no—
285#137—2444no—
286C2×Q16—1222no—
287C2×SD16—1222no—
288C2×M16—1221no—
289C22×C8—21no—
290C22×C8—21no—
291C22×C8—1222no—
292C4⋊Q8—21no—
293C4⋊Q8—21no—
294C4⋊Q8—21no—
295C4⋊Q8—611no—
296C4⋊Q8—611no—
297C4⋊Q8C22×D6112yes—
298#125—1221no—
299C22⋊Q8—1221no—
300C22⋊Q8—1221no—
301C4×Q8—611no—
302C4×Q8—611no—
303C4×Q8—1221no—
304C4×Q8—1221no—
305C4×D4—611no—
306C4×D4—611no—
307C4×D4—1221no—
308C4×D4—1221no—
309#117—611no—
310#117—1221no—
311#117—1221no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C42—1221no—
315C2×C42C22×D6111yescharacteristic
316#107—1221no—
317#107—1221no—
318#106—1222no—
319#106—1222no—
320#106—1221no—
321#106—1221no—
322C4⋊C8—21no—
323C4⋊C8—21no—
324C4⋊C8—611no—
325C4⋊C8—611no—
326C4⋊C8—612no—
327C4⋊C8—1222no—
328C4⋊C8—1221no—
329C4⋊C8C22×D6112yes—
330C4⋊C8C22×D6111yescharacteristic
331C4⋊C8C22×D6111yescharacteristic
332#103—1222no—
333#103—1222no—
334#103—1222no—
335#103—1222no—
336#103—1221no—
337#103—1221no—
338#102—1221no—
339#102—1221no—
340C22⋊C8—612no—
341C22⋊C8—1222no—
342C4×C8—612no—
343C4×C8—1222no—
344#41—614no—
345#41—1222no—
346C2×Q8—22no—
347C2×Q8—41no—
348C2×Q8—42no—
349C2×Q8—42no—
350C2×Q8—611no—
351C2×Q8—1221no—
352C2×Q8—1221no—
353C2×D4—611no—
354C2×D4—1221no—
355C22×C4—41no—
356C22×C4—1221no—
357C22×C4—1221no—
358C22×C4—1221no—
359C22×C4#1175822211yescharacteristic
360C22×C4D4×D6111yescharacteristic
361C22×C4D4×D6111yescharacteristic
362Q16—2444no—
363SD16—2444no—
364M16—2442no—
365C2×C8—22no—
366C2×C8—21no—
367C2×C8—21no—
368C2×C8—42no—
369C2×C8—81no—
370C2×C8—612no—
371C2×C8—612no—
372C2×C8—1222no—
373C2×C8—4882no—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—611no—
379C4⋊C4—611no—
380C4⋊C4—1221no—
381C4⋊C4—1221no—
382C4⋊C4—1221no—
383C4⋊C4—1221no—
384C4⋊C4—1221no—
385C4⋊C4—1221no—
386C4⋊C4—2441no—
387C4⋊C4—2441no—
388C22⋊C4—1221no—
389C22⋊C4—1221no—
390C22⋊C4—1221no—
391C22⋊C4—2441no—
392C42—1221no—
393C42—1221no—
394C42—1221no—
395C42—2441no—
396C42#1175822211yescharacteristic
397C42D4×D6111yescharacteristic
398C42D4×D6111yescharacteristic
399C42C23×D6111yescharacteristic
400C23—1221no—
401C23#1451975011yescharacteristic
402Q8—42no—
403Q8—42no—
404Q8—82no—
405Q8—612no—
406Q8—1221no—
407Q8—4881no—
408Q8—2441no—
409Q8—2441no—
410D4—612no—
411D4—1224no—
412D4—1221no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—82no—
418C2×C4—1221no—
419C2×C4—1224no—
420C2×C4—1221no—
421C2×C4—1221no—
422C2×C4—4881no—
423C2×C4—2441no—
424C2×C4—2441no—
425C2×C4—2441no—
426C2×C4—2441no—
427C2×C4#1451975011yescharacteristic
428C2×C4#1451975011yescharacteristic
429C2×C4#1451975011yescharacteristic
430C2×C4SD16×D6112yes—
431C2×C4#1451979612yes—
432C2×C4C2×D4×D6111yescharacteristic
433C2×C4C2×D4×D6111yescharacteristic
434C2×C4C2×#1175822211yescharacteristic
435C8—41no—
436C8—41no—
437C8—42no—
438C8—1222no—
439C8—1222no—
440C8—2442no—
441C22—21no—
442C22—21no—
443C22—1222no—
444C22—2441no—
445C22—2441no—
446C22#1683999012yes—
447C22C2×#1451975011yescharacteristic
448C4—21no—
449C4—21no—
450C4—21no—
451C4—82no—
452C4—1222no—
453C4—4881no—
454C4—4881no—
455C4—2441no—
456C4—2441no—
457C4#1683999012yes—
458C4C2×SD16×D6111yescharacteristic
459C4C2×#1451979611yescharacteristic
460C4#1684056811yescharacteristic
461C4#1684057511yescharacteristic
462C2—22no—
463C2—2442no—
464C2#2145537411yescharacteristic
465C2C2×#1683999011yescharacteristic
466C2#2145555511yescharacteristic
subgroupG/H
centerC22C2×#14519750
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#332C2
socleC22×C61C2×#121
prime radicalC2×#11758222D4
hypercenterC2×#332D61
hypocenterC61#19415
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
1. #21456963C2semidirect
5. #21445252C2semidirect
6. #21445245C2semidirect
7. #21445200C2semidirect
8. #21445193C2semidirect
9. #21444589C2semidirect
10. #21444507C2semidirect
11. C2×C61×#332C2semidirect
239. C2×#332D61semidirect
282. C61#19415semidirect

Maximal subgroups

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

subgroupindex
#214569632
#214556092
#214553022
#214549282
#214452522
#214452452
#214452002
#214451932
#214445892
#214445072
C2×C61×#3322
#1941561