Finite Group Databasebeta

← #29665486

Subgroups — #29665486

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#21455601C211yesmaximal, characteristic
2#21455302C211yesmaximal, characteristic
3#21454927C211yesmaximal, characteristic
4#21445246C212yesmaximal, complemented
5#21445239C212yesmaximal, complemented
6#21445198C212yesmaximal, complemented
7#21445191C212yesmaximal, complemented
8#21444590C211yesmaximal, characteristic, complemented
9#21444509C211yesmaximal, characteristic, complemented
10C2×#16839508C211yesmaximal, characteristic, complemented
11C61×#3229C211yesmaximal, characteristic, complemented
12C2×#14519808—21no—
13C4×#11758222C2211yescharacteristic
14#16840066—21no—
15#16840059—21no—
16#16840054C2211yescharacteristic
17#16840049C2211yescharacteristic
18#16840044C2211yescharacteristic
19#16840039C2211yescharacteristic
20#16839969—21no—
21#16839969C2212yes—
22#16839964—21no—
23#16839964C2212yes—
24C8×Dic122C2212yes—
25C8×D244C2212yes—
26#16839825—22no—
27#16839814—21no—
28#16839798—21no—
29#16839786C2211yescharacteristic
30C2×C4⋊#92418C2211yescharacteristic
31C2×C4⋊#92418C2211yescharacteristic
32C4⋊C8×D61—21no—
33#16839771—21no—
34#16839756—21no—
35#16839513C2212yes—
36#16839513C2212yes—
37#16839511C2212yes—
38#16839508C2212yes—
39#16839508C2212yes—
40#16839508C2212yes—
41C61×#533C2211yescharacteristic
42C2×C4⋊Q8×C61C2211yescharacteristic
43C61×#498C2212yes—
44C61×#487C2212yes—
45C61×#483—22no—
46C61×#475—21no—
47C61×#475—21no—
48C61×#431C2211yescharacteristic
49C2×#11758222D411yescharacteristic
50#14519808—44no—
51C2×#11758202—22no—
52C2×#11758201—22no—
53C2×#11758194—21no—
54C22×#92418—21no—
55C22×#92418—21no—
56C2×C8×D61—22no—
57C4×Dic122D411yescharacteristic
58C4×Dic122C2311yescharacteristic
59C4×D244D411yescharacteristic
60C4×D244C2311yescharacteristic
61C4×C22⋊D61—21no—
62C4×C22⋊D61—21no—
63#14519736D411yescharacteristic
64#14519734—21no—
65C42×D61—21no—
66#14519710—21no—
67#14519710—21no—
68#14519708—21no—
69#14519708—21no—
70C4⋊#92418—21no—
71C4⋊#92418—21no—
72C4⋊#92418—21no—
73C4⋊#92418C2312yes—
74C4⋊#92418C2312yes—
75C4⋊#92418C2311yescharacteristic
76C4⋊#92418C2311yescharacteristic
77#14519706—22no—
78#14519701—22no—
79#14519701—22no—
80#14519700—21no—
81#14519700—21no—
82#14519697—21no—
83#14519697—21no—
84#14519689—22no—
85C8×Dic61—22no—
86C22×Q8×C61—21no—
87C4⋊Q8×C61—21no—
88C4⋊Q8×C61—21no—
89C4⋊Q8×C61—21no—
90C4⋊Q8×C61C2312yes—
91C4⋊Q8×C61C2311yescharacteristic
92C4⋊Q8×C61C2311yescharacteristic
93#125×C61—21no—
94C22⋊Q8×C61—21no—
95C22⋊Q8×C61—21no—
96C4×Q8×C61—21no—
97C4×Q8×C61—21no—
98#117×C61—21no—
99C2×C4⋊C4×C61—21no—
100C2×C4⋊C4×C61—21no—
101C2×C42×C61C2311yescharacteristic
102#106×C61—22no—
103#106×C61—22no—
104C4⋊C8×C61D411yescharacteristic
105C4⋊C8×C61D411yescharacteristic
106#103×C61—22no—
107#103×C61—22no—
108C22⋊C8×C61D412yes—
109C4×C8×C61C2312yes—
110C2×Q8×C61—21no—
111C2×Q8×C61—22no—
112C2×Q8×C61—21no—
113C2×Q8×C61—41no—
114C2×Q8×C61—42no—
115C2×Q8×C61—42no—
116C22×C4×C61—41no—
117C22×C4×C61C2×D411yescharacteristic
118C22×C4×C61C2×D411yescharacteristic
119C22×C4×C61#4111yescharacteristic
120C2×C22⋊D61—21no—
121#11758222—22no—
122#11758222SD1614yes—
123C2×D244C2×D411yescharacteristic
124C2×C4×D61—21no—
125C2×C4×D61—21no—
126C2×C4×D61—21no—
127C2×Dic122C2×D411yescharacteristic
128C2×C8×C61C2×D412yes—
129C2×C8×C61C2×D412yes—
130C4⋊C4×C61—22no—
131C4⋊C4×C61—21no—
132C4⋊C4×C61—21no—
133C4⋊C4×C61—21no—
134C4⋊C4×C61—22no—
135C4⋊C4×C61—21no—
136C4⋊C4×C61—41no—
137C4⋊C4×C61—41no—
138C4⋊C4×C61—41no—
139C4⋊C4×C61—41no—
140C22⋊C4×C61—41no—
141C42×C61—41no—
142C42×C61C2×D411yescharacteristic
143C42×C61C2×D411yescharacteristic
144C42×C61#4111yescharacteristic
145C42×C61C2411yescharacteristic
146C22⋊Dic61—21no—
147#11758202—44no—
148#11758201—44no—
149#11758198—21no—
150#11758198—21no—
151C4⋊Dic61C2×D411yescharacteristic
152C4⋊Dic61C2×D411yescharacteristic
153#11758196—21no—
154#11758196—21no—
155C4×Dic61—21no—
156C4×Dic61—21no—
157C4×Dic61—21no—
158#11758194—42no—
159C2×#92418—22no—
160C2×#92418—21no—
161C2×#92418—21no—
162C2×#92418—22no—
163C2×#92418—42no—
164C2×#92418—81no—
165C8×D61—82no—
166C23×C61#12111yescharacteristic
167C22×D61—21no—
168Q8×C61—42no—
169Q8×C61—42no—
170Q8×C61—41no—
171Q8×C61—41no—
172Q8×C61—81no—
173Q8×C61—82no—
174C2×C4×C61—21no—
175C2×C4×C61—21no—
176C2×C4×C61—41no—
177C2×C4×C61—41no—
178C2×C4×C61—41no—
179C2×C4×C61—42no—
180C2×C4×C61—82no—
181C2×C4×C61#12111yescharacteristic
182C2×C4×C61#12111yescharacteristic
183C2×C4×C61#12111yescharacteristic
184C2×C4×C61C2×SD1612yes—
185C2×C4×C61#13512yes—
186C2×C4×C61C22×D411yescharacteristic
187C2×C4×C61C22×D411yescharacteristic
188C2×C4×C61C2×#4111yescharacteristic
189C22⋊D61—24no—
190C2×Dic61—21no—
191C2×Dic61—21no—
192C2×Dic61—21no—
193D244—21no—
194D244C2×SD1612yes—
195C4×D61—24no—
196C4×D61—41no—
197C4×D61—41no—
198C4×D61—81no—
199Dic122—21no—
200Dic122C2×SD1612yes—
201C8×C61—22no—
202C8×C61—22no—
203#92418—42no—
204#92418—41no—
205#92418—41no—
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—81no—
219C4×C61—82no—
220C4×C61—81no—
221C4×C61#46512yes—
222C4×C61C22×SD1611yescharacteristic
223C4×C61C2×#13511yescharacteristic
224C4×C61#57711yescharacteristic
225C4×C61#57811yescharacteristic
226Dic61—22no—
227Dic61—41no—
228Dic61—41no—
229#3229D6111yescharacteristic, complemented
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×#332—611no—
240C2×C61—22no—
241C2×C61#304611yescharacteristic
242C2×C61C2×#46511yescharacteristic
243C2×C61#306911yescharacteristic
244D61—42no—
245C2×#137—1221no—
246#533C2×D6111yescharacteristic
247C2×C4⋊Q8C2×D6111yescharacteristic
248C4×#41—611no—
249#498C2×D6112yes—
250#487C2×D6112yes—
251#483—22no—
252#479—1221no—
253#478—1221no—
254#477—611no—
255#476—611no—
256#475—21no—
257#475—21no—
258#475—611no—
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—1221no—
268#431C2×D6111yescharacteristic
269#427—1221no—
270#423—611no—
271C2×C4⋊C8—611no—
272C2×C4⋊C8—611no—
273C2×C4⋊C8—1221no—
274#419—1221no—
275#416—1221no—
276#334—612no—
277#334—612no—
278#333—612no—
279#332—612no—
280#332—612no—
281#332—612no—
282C61#1941511yescharacteristic, complemented, Sylow
283C2×#41—611no—
284C22×Q8—21no—
285#137—2444no—
286C2×Q16—1222no—
287C2×SD16—1222no—
288C2×M16—1221no—
289C22×C8—1221no—
290C22×C8—1221no—
291C22×C8—1222no—
292C4⋊Q8—21no—
293C4⋊Q8—21no—
294C4⋊Q8—21no—
295C4⋊Q8C22×D6112yes—
296C4⋊Q8C22×D6111yescharacteristic
297C4⋊Q8C22×D6111yescharacteristic
298#125—21no—
299C22⋊Q8—21no—
300C22⋊Q8—21no—
301C4×Q8—21no—
302C4×Q8—21no—
303C4×Q8—611no—
304C4×Q8—611no—
305C4×D4—611no—
306C4×D4—611no—
307C4×D4—1221no—
308C4×D4—1221no—
309#117—21no—
310#117—611no—
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—22no—
319#106—22no—
320#106—1221no—
321#106—1221no—
322C4⋊C8—612no—
323C4⋊C8—611no—
324C4⋊C8—611no—
325C4⋊C8—612no—
326C4⋊C8—1222no—
327C4⋊C8—1221no—
328C4⋊C8—1221no—
329C4⋊C8—1221no—
330C4⋊C8C22⋊D6111yescharacteristic
331C4⋊C8C22⋊D6111yescharacteristic
332#103—22no—
333#103—22no—
334#103—1221no—
335#103—1221no—
336#103—1222no—
337#103—1222no—
338#102—1221no—
339#102—1221no—
340C22⋊C8—1222no—
341C22⋊C8C22⋊D6112yes—
342C4×C8—1222no—
343C4×C8C22×D6112yes—
344#41—614no—
345#41—1222no—
346C2×Q8—22no—
347C2×Q8—21no—
348C2×Q8—21no—
349C2×Q8—41no—
350C2×Q8—42no—
351C2×Q8—42no—
352C2×Q8—611no—
353C2×D4—611no—
354C2×D4—1221no—
355C22×C4—41no—
356C22×C4—1221no—
357C22×C4—1221no—
358C22×C4—1221no—
359C22×C4D4×D6111yescharacteristic
360C22×C4#1175822411yescharacteristic
361C22×C4C2×C22⋊D6111yescharacteristic
362Q16—2444no—
363SD16—2444no—
364M16—2442no—
365C2×C8—1221no—
366C2×C8—1221no—
367C2×C8—1222no—
368C2×C8—1222no—
369C2×C8—4882no—
370C2×C8—4881no—
371C2×C8—2442no—
372C2×C8C2×C22⋊D6112yes—
373C2×C8C2×C22⋊D6112yes—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—22no—
377C4⋊C4—21no—
378C4⋊C4—22no—
379C4⋊C4—21no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—611no—
385C4⋊C4—611no—
386C4⋊C4—1221no—
387C4⋊C4—1221no—
388C22⋊C4—41no—
389C22⋊C4—1221no—
390C22⋊C4—1221no—
391C22⋊C4—1221no—
392C42—41no—
393C42—1221no—
394C42—1221no—
395C42—1221no—
396C42D4×D6111yescharacteristic
397C42#1175822411yescharacteristic
398C42C2×C22⋊D6111yescharacteristic
399C42C23×D6111yescharacteristic
400C23—1221no—
401C23#1451974811yescharacteristic
402Q8—42no—
403Q8—42no—
404Q8—41no—
405Q8—41no—
406Q8—81no—
407Q8—82no—
408Q8—612no—
409Q8—1221no—
410D4—612no—
411D4—1224no—
412D4—1221no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—42no—
419C2×C4—82no—
420C2×C4—1221no—
421C2×C4—1224no—
422C2×C4—1221no—
423C2×C4—1221no—
424C2×C4—4881no—
425C2×C4—2441no—
426C2×C4—2441no—
427C2×C4#1451974811yescharacteristic
428C2×C4#1451974811yescharacteristic
429C2×C4#1451974811yescharacteristic
430C2×C4SD16×D6112yes—
431C2×C4#1451979812yes—
432C2×C4C2×D4×D6111yescharacteristic
433C2×C4C22×C22⋊D6111yescharacteristic
434C2×C4C2×#1175822411yescharacteristic
435C8—22no—
436C8—22no—
437C8—2442no—
438C8—2441no—
439C8—2441no—
440C8—2442no—
441C22—21no—
442C22—21no—
443C22—1222no—
444C22—2441no—
445C22—2441no—
446C22#1683998812yes—
447C22C2×#1451974811yescharacteristic
448C4—21no—
449C4—21no—
450C4—21no—
451C4—81no—
452C4—82no—
453C4—81no—
454C4—1222no—
455C4—2441no—
456C4—2441no—
457C4#1683998812yes—
458C4C2×SD16×D6111yescharacteristic
459C4C2×#1451979811yescharacteristic
460C4#1684057011yescharacteristic
461C4#1684057711yescharacteristic
462C2—22no—
463C2—2442no—
464C2#2145536511yescharacteristic
465C2C2×#1683998811yescharacteristic
466C2#2145555211yescharacteristic
subgroupG/H
centerC22C2×#14519748
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3229C2
socleC22×C61C2×#121
prime radicalC2×#11758222D4
hypercenter#3229D61
hypocenterC61#19415
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3229

Complements

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

NH ≅ G/Ntype
4. #21445246C2semidirect
5. #21445239C2semidirect
6. #21445198C2semidirect
7. #21445191C2semidirect
8. #21444590C2semidirect
9. #21444509C2semidirect
10. C2×#16839508C2semidirect
11. C61×#3229C2semidirect
229. #3229D61semidirect
282. C61#19415semidirect

Maximal subgroups

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

subgroupindex
#214556012
#214553022
#214549272
#214452462
#214452392
#214451982
#214451912
#214445902
#214445092
C2×#168395082
C61×#32292
#1941561