Finite Group Databasebeta

← #29665434

Subgroups — #29665434

Order 15616.

620 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455628C211yesmaximal, characteristic
2#21455601C211yesmaximal, characteristic
3#21454927C211yesmaximal, characteristic
4#21445274C212yesmaximal, complemented
5#21445267C212yesmaximal, complemented
6#21445186C212yesmaximal, complemented
7#21445181C212yesmaximal, complemented
8#21444594C211yesmaximal, characteristic, complemented
9#21444509C211yesmaximal, characteristic, complemented
10C2×#16839508C211yesmaximal, characteristic, complemented
11C61×#3209C211yesmaximal, characteristic, complemented
12C4×#11758222C2211yescharacteristic
13#16840066—21no—
14#16840059—21no—
15#16840054—21no—
16#16840054C2211yescharacteristic
17#16840049—21no—
18#16840049C2211yescharacteristic
19#16840044C2212yes—
20#16840044C2211yescharacteristic
21#16840039C2212yes—
22#16840039C2211yescharacteristic
23C8×Dic122C2212yes—
24C8×D244C2212yes—
25#16839825—22no—
26#16839814—21no—
27#16839802—21no—
28#16839798—21no—
29#16839786C2211yescharacteristic
30C2×C4⋊#92418C2211yescharacteristic
31C2×C4⋊#92418C2211yescharacteristic
32C4⋊C8×D61—21no—
33#16839761—21no—
34#16839756—21no—
35#16839515C2212yes—
36#16839515C2212yes—
37#16839511C2212yes—
38#16839508C2212yes—
39#16839508C2212yes—
40#16839508C2212yes—
41C61×#533C2211yescharacteristic
42C2×C4⋊Q8×C61C2211yescharacteristic
43C61×#494C2212yes—
44C61×#487C2212yes—
45C61×#462—21no—
46C61×#462—21no—
47C61×#451—22no—
48C61×#431C2211yescharacteristic
49C2×#11758222D411yescharacteristic
50C2×#11758194—21no—
51C22×#92418—21no—
52C22×#92418—21no—
53C2×C8×D61—22no—
54C4×Dic122D411yescharacteristic
55C4×Dic122C2311yescharacteristic
56C4×D244D411yescharacteristic
57C4×D244C2311yescharacteristic
58C4×C22⋊D61—21no—
59C4×C22⋊D61—21no—
60#14519736D411yescharacteristic
61#14519734—21no—
62C42×D61—21no—
63#14519710—21no—
64#14519710—22no—
65#14519710—21no—
66#14519708—22no—
67#14519708—21no—
68#14519708—21no—
69C4⋊#92418—21no—
70C4⋊#92418—21no—
71C4⋊#92418—21no—
72C4⋊#92418C2312yes—
73C4⋊#92418C2311yescharacteristic
74C4⋊#92418C2311yescharacteristic
75C4⋊#92418C2312yes—
76#14519706—22no—
77#14519700—21no—
78#14519700—21no—
79#14519700—22no—
80#14519697—21no—
81#14519697—21no—
82#14519697—22no—
83#14519689—22no—
84C8×Dic61—22no—
85C22×Q8×C61—21no—
86C2×Q16×C61—22no—
87C2×Q16×C61—22no—
88C4⋊Q8×C61—21no—
89C4⋊Q8×C61—21no—
90C4⋊Q8×C61—21no—
91C4⋊Q8×C61C2312yes—
92C4⋊Q8×C61C2311yescharacteristic
93C4⋊Q8×C61C2311yescharacteristic
94#125×C61—21no—
95C22⋊Q8×C61—21no—
96C22⋊Q8×C61—21no—
97C4×Q8×C61—21no—
98C4×Q8×C61—21no—
99#117×C61—21no—
100C2×C4⋊C4×C61—21no—
101C2×C4⋊C4×C61—21no—
102C2×C42×C61C2311yescharacteristic
103C4⋊C8×C61D411yescharacteristic
104C4⋊C8×C61D411yescharacteristic
105#103×C61—22no—
106#103×C61—22no—
107C22⋊C8×C61D412yes—
108C4×C8×C61C2312yes—
109C2×Q8×C61—22no—
110C2×Q8×C61—21no—
111C2×Q8×C61—21no—
112C2×Q8×C61—41no—
113C2×Q8×C61—81no—
114C2×Q8×C61—81no—
115C22×C4×C61—41no—
116C22×C4×C61C2×D411yescharacteristic
117C22×C4×C61C2×D411yescharacteristic
118C22×C4×C61#4111yescharacteristic
119C2×C22⋊D61—21no—
120#11758222—22no—
121#11758222Q1614yescomplemented
122C2×D244C2×D411yescharacteristic
123C2×C4×D61—21no—
124C2×C4×D61—21no—
125C2×C4×D61—21no—
126C2×Dic122C2×D411yescharacteristic
127Q16×C61—82no—
128Q16×C61—82no—
129C2×C8×C61C2×D412yes—
130C2×C8×C61C2×D412yes—
131C4⋊C4×C61—21no—
132C4⋊C4×C61—22no—
133C4⋊C4×C61—21no—
134C4⋊C4×C61—21no—
135C4⋊C4×C61—22no—
136C4⋊C4×C61—21no—
137C4⋊C4×C61—41no—
138C4⋊C4×C61—41no—
139C4⋊C4×C61—41no—
140C4⋊C4×C61—41no—
141C22⋊C4×C61—41no—
142C42×C61—41no—
143C42×C61C2×D411yescharacteristic
144C42×C61C2×D411yescharacteristic
145C42×C61#4111yescharacteristic
146C42×C61C2411yescharacteristic
147C22⋊Dic61—21no—
148#11758198—21no—
149#11758198—21no—
150C4⋊Dic61C2×D411yescharacteristic
151C4⋊Dic61C2×D411yescharacteristic
152#11758196—21no—
153#11758196—21no—
154C4×Dic61—21no—
155C4×Dic61—21no—
156C4×Dic61—21no—
157#11758194—42no—
158C2×#92418—22no—
159C2×#92418—21no—
160C2×#92418—22no—
161C2×#92418—21no—
162C2×#92418—42no—
163C2×#92418—81no—
164C8×D61—82no—
165C23×C61#12111yescharacteristic
166C22×D61—21no—
167Q8×C61—41no—
168Q8×C61—42no—
169Q8×C61—41no—
170Q8×C61—42no—
171Q8×C61—82no—
172Q8×C61—81no—
173C2×C4×C61—21no—
174C2×C4×C61—21no—
175C2×C4×C61—41no—
176C2×C4×C61—41no—
177C2×C4×C61—41no—
178C2×C4×C61—42no—
179C2×C4×C61—82no—
180C2×C4×C61#12111yescharacteristic
181C2×C4×C61#12111yescharacteristic
182C2×C4×C61#12111yescharacteristic
183C2×C4×C61C2×Q1612yes—
184C2×C4×C61#13512yes—
185C2×C4×C61C22×D411yescharacteristic
186C2×C4×C61C22×D411yescharacteristic
187C2×C4×C61C2×#4111yescharacteristic
188C22⋊D61—24no—
189C2×Dic61—21no—
190C2×Dic61—21no—
191C2×Dic61—21no—
192D244—21no—
193D244C2×Q1612yes—
194C4×D61—24no—
195C4×D61—41no—
196C4×D61—41no—
197C4×D61—81no—
198Dic122—21no—
199Dic122C2×Q1612yes—
200C8×C61—22no—
201C8×C61—22no—
202#92418—41no—
203#92418—41no—
204#92418—42no—
205#92418—42no—
206#19411—611nomaximal, Sylow
207C22×C61—21no—
208C22×C61—21no—
209C22×C61#46712yes—
210C22×C61C2×#12111yescharacteristic
211C2×D61—22no—
212C2×D61—41no—
213C2×D61—41no—
214C4×C61—21no—
215C4×C61—21no—
216C4×C61—21no—
217C4×C61—82no—
218C4×C61—81no—
219C4×C61—81no—
220C4×C61#46712yes—
221C4×C61C22×Q1611yescharacteristic
222C4×C61C2×#13511yescharacteristic
223C4×C61#57611yescharacteristic
224C4×C61#57711yescharacteristic
225Dic61—22no—
226Dic61—41no—
227Dic61—41no—
228#3209D6111yescharacteristic, complemented
229#3079—611no—
230#3076—611no—
231#2988—611no—
232#1684—612no—
233#1683—612no—
234#1670—612no—
235#1669—612no—
236#1571—611no—
237#1550—611no—
238C2×#332—611no—
239C2×C61—22no—
240C2×C61#304511yescharacteristic
241C2×C61C2×#46711yescharacteristic
242C2×C61#306911yescharacteristic
243D61—42no—
244#533C2×D6111yescharacteristic
245C2×C4⋊Q8C2×D6111yescharacteristic
246C4×#41—611no—
247#494C2×D6112yes—
248#487C2×D6112yes—
249#479—1221no—
250#478—1221no—
251#477—611no—
252#477—1221no—
253#476—611no—
254#476—1221no—
255#475—611no—
256#475—612no—
257#474—611no—
258#474—612no—
259#462—21no—
260#462—21no—
261#451—22no—
262C8×Q8—612no—
263C8×D4—612no—
264C8×D4—1222no—
265#431—1221no—
266#431C2×D6111yescharacteristic
267#428—1221no—
268#427—1221no—
269#423—611no—
270C2×C4⋊C8—611no—
271C2×C4⋊C8—611no—
272C2×C4⋊C8—1221no—
273#417—1221no—
274#416—1221no—
275#335—612no—
276#335—612no—
277#333—612no—
278#332—612no—
279#332—612no—
280#332—612no—
281C61#1941111yescharacteristic, complemented, Sylow
282C2×#41—611no—
283C22×Q8—21no—
284C2×Q16—22no—
285C2×Q16—22no—
286C2×M16—1221no—
287C22×C8—1221no—
288C22×C8—1221no—
289C22×C8—1222no—
290C4⋊Q8—21no—
291C4⋊Q8—21no—
292C4⋊Q8—21no—
293C4⋊Q8C22×D6112yes—
294C4⋊Q8C22×D6111yescharacteristic
295C4⋊Q8C22×D6111yescharacteristic
296#125—21no—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C4×Q8—21no—
300C4×Q8—21no—
301C4×Q8—611no—
302C4×Q8—611no—
303C4×D4—611no—
304C4×D4—611no—
305C4×D4—1221no—
306C4×D4—1221no—
307#117—21no—
308#117—611no—
309#117—1221no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C42—1221no—
313C2×C42C22×D6111yescharacteristic
314#107—1221no—
315#107—1221no—
316#107—1222no—
317#106—1221no—
318#106—1221no—
319#106—1222no—
320C4⋊C8—612no—
321C4⋊C8—611no—
322C4⋊C8—611no—
323C4⋊C8—612no—
324C4⋊C8—1222no—
325C4⋊C8—1221no—
326C4⋊C8—1221no—
327C4⋊C8—1221no—
328C4⋊C8C22⋊D6111yescharacteristic
329C4⋊C8C22⋊D6111yescharacteristic
330#103—22no—
331#103—22no—
332#103—1221no—
333#103—1221no—
334#103—1222no—
335#102—1221no—
336#102—1221no—
337#102—1222no—
338C22⋊C8—1222no—
339C22⋊C8C22⋊D6112yes—
340C4×C8—1222no—
341C4×C8C22×D6112yes—
342#41—614no—
343#41—1222no—
344C2×Q8—22no—
345C2×Q8—21no—
346C2×Q8—21no—
347C2×Q8—41no—
348C2×Q8—81no—
349C2×Q8—81no—
350C2×Q8—611no—
351C2×D4—611no—
352C2×D4—1221no—
353C22×C4—41no—
354C22×C4—1221no—
355C22×C4—1221no—
356C22×C4—1221no—
357C22×C4D4×D6111yescharacteristic
358C22×C4#1175822411yescharacteristic
359C22×C4C2×C22⋊D6111yescharacteristic
360Q16—82no—
361Q16—82no—
362M16—2442no—
363C2×C8—1221no—
364C2×C8—1222no—
365C2×C8—1221no—
366C2×C8—1222no—
367C2×C8—4882no—
368C2×C8—4881no—
369C2×C8—2442no—
370C2×C8C2×C22⋊D6112yes—
371C2×C8C2×C22⋊D6112yes—
372C4⋊C4—22no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—22no—
377C4⋊C4—21no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—611no—
383C4⋊C4—611no—
384C4⋊C4—1221no—
385C4⋊C4—1221no—
386C22⋊C4—41no—
387C22⋊C4—1221no—
388C22⋊C4—1221no—
389C22⋊C4—1221no—
390C42—41no—
391C42—1221no—
392C42—1221no—
393C42—1221no—
394C42D4×D6111yescharacteristic
395C42#1175822411yescharacteristic
396C42C2×C22⋊D6111yescharacteristic
397C42C23×D6111yescharacteristic
398C23—1221no—
399C23#1451974811yescharacteristic
400Q8—41no—
401Q8—42no—
402Q8—41no—
403Q8—42no—
404Q8—81no—
405Q8—82no—
406Q8—612no—
407Q8—1221no—
408D4—612no—
409D4—1224no—
410D4—1221no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—41no—
414C2×C4—41no—
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#1451974811yescharacteristic
426C2×C4#1451974811yescharacteristic
427C2×C4#1451974811yescharacteristic
428C2×C4Q16×D6112yes—
429C2×C4#1451980012yes—
430C2×C4C2×D4×D6111yescharacteristic
431C2×C4C22×C22⋊D6111yescharacteristic
432C2×C4C2×#1175822411yescharacteristic
433C8—22no—
434C8—22no—
435C8—2441no—
436C8—2441no—
437C8—2442no—
438C8—2442no—
439C22—21no—
440C22—21no—
441C22—1222no—
442C22—2441no—
443C22—2441no—
444C22#1684000012yes—
445C22C2×#1451974811yescharacteristic
446C4—21no—
447C4—21no—
448C4—21no—
449C4—81no—
450C4—82no—
451C4—81no—
452C4—1222no—
453C4—2441no—
454C4—2441no—
455C4#1684000012yes—
456C4C2×Q16×D6111yescharacteristic
457C4C2×#1451980011yescharacteristic
458C4#1684056511yescharacteristic
459C4#1684057311yescharacteristic
460C2—22no—
461C2—2442no—
462C2#2145535411yescharacteristic
463C2C2×#1684000011yescharacteristic
464C2#2145555211yescharacteristic
subgroupG/H
centerC22C2×#14519748
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3209C2
socleC22×C61C2×#121
prime radicalC2×#11758222D4
hypercenter#3209D61
hypocenterC61#19411
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3209

Complements

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

NH ≅ G/Ntype
4. #21445274C2semidirect
5. #21445267C2semidirect
6. #21445186C2semidirect
7. #21445181C2semidirect
8. #21444594C2semidirect
9. #21444509C2semidirect
10. C2×#16839508C2semidirect
11. C61×#3209C2semidirect
121. #11758222Q16semidirect
228. #3209D61semidirect
281. C61#19411semidirect

Maximal subgroups

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

subgroupindex
#214556282
#214556012
#214549272
#214452742
#214452672
#214451862
#214451812
#214445942
#214445092
C2×#168395082
C61×#32092
#1941161