Finite Group Databasebeta

← #29663596

Subgroups — #29663596

Order 15616.

658 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457131C211yesmaximal, characteristic
2#21456960C211yesmaximal, characteristic, complemented
3#21456278C211yesmaximal, characteristic
4#21445313C212yesmaximal, complemented
5#21445291C212yesmaximal, complemented
6#21445189C212yesmaximal, complemented
7#21445167C212yesmaximal, complemented
8#21444571C211yesmaximal, characteristic, complemented
9#21444469C211yesmaximal, characteristic
10C2×#16839509C211yesmaximal, characteristic, complemented
11C61×#2962C211yesmaximal, characteristic, complemented
12C2×#14519810—21no—
13C2×#14519810—21no—
14#16840312C2211yescharacteristic
15C2×#14519777C2211yescharacteristic
16#16840158—21no—
17#16840156—22no—
18#16840142C2212yes—
19#16840135C2212yes—
20#16840112—21no—
21#16840090—22no—
22#16840049—21no—
23#16840047C2212yes—
24#16840047C2212yes—
25#16840047C2212yes—
26#16839993—22no—
27#16839964—21no—
28#16839962C2212yes—
29#16839815C2211yescharacteristic
30C2×C4⋊#92418C2211yescharacteristic
31#16839515C2212yes—
32#16839513C2212yes—
33#16839509C2212yes—
34#16839509C2211yescharacteristic
35#16839509C2212yes—
36#16839509C2211yescharacteristic
37#16839505C2211yescharacteristic
38#16839505C2211yescharacteristic
39C61×#533C2211yescharacteristic
40C61×#446—22no—
41C61×#446C2212yes—
42C8×Q8×C61C2212yes—
43C61×#424—21no—
44C2×C4⋊C8×C61C2211yescharacteristic
45C61×#405—21no—
46C4×M16×C61C2211yescharacteristic
47C2×#11758222—21no—
48C22×Dic122—21no—
49#14519810—44no—
50#14519810—44no—
51C2×Dic244—22no—
52C2×Dic244—22no—
53C2×#11758190—22no—
54C2×#11758190—22no—
55C2×#11758201—22no—
56C22×#92418—21no—
57#14519777—21no—
58#14519777—21no—
59#14519777—21no—
60#14519777C2312yes—
61#14519777C2311yescharacteristic
62#14519774C2311yescharacteristic
63#14519765—21no—
64#14519751—21no—
65#14519751—21no—
66C4×D244—21no—
67C4×D244—21no—
68C2×C4⋊Dic61—21no—
69C2×C4⋊Dic61—21no—
70#14519708—22no—
71#14519708—22no—
72#14519708—22no—
73C4⋊#92418—21no—
74C4⋊#92418C2312yes—
75C4⋊#92418C2311yescharacteristic
76C4⋊#92418C2311yescharacteristic
77#14519701—22no—
78#14519701—22no—
79#14519701—22no—
80#14519697—22no—
81C22⋊#92418—21no—
82C4×#92418—21no—
83C2×M16×C61D411yescharacteristic
84C2×M16×C61D411yescharacteristic
85C22×C8×C61—21no—
86C4⋊Q8×C61D411yescharacteristic
87C4⋊Q8×C61D411yescharacteristic
88#125×C61—21no—
89C22⋊Q8×C61—21no—
90C22⋊Q8×C61D412yes—
91C4×Q8×C61—21no—
92C4×Q8×C61C2312yes—
93#117×C61—21no—
94C2×C42×C61C2311yescharacteristic
95C4⋊C8×C61—22no—
96C4⋊C8×C61—22no—
97C4⋊C8×C61—21no—
98C4⋊C8×C61C2311yescharacteristic
99C4⋊C8×C61C2311yescharacteristic
100#97×C61—22no—
101#97×C61D412yes—
102C4×C8×C61—22no—
103C4×C8×C61C2312yes—
104C2×Q8×C61—21no—
105C2×Q8×C61C2×D412yes—
106C22×C4×C61C2×D411yescharacteristic
107C22×C4×C61C2×D411yescharacteristic
108C22×C4×C61#4111yescharacteristic
109C2×C22⋊D61—41no—
110C22×Dic61—41no—
111#11758222—42no—
112#11758222—42no—
113C2×D244—21no—
114C2×D244—21no—
115C2×D244—21no—
116C2×C4×D61—41no—
117C2×Dic122—22no—
118C2×Dic122—21no—
119C2×Dic122—42no—
120C2×Dic122—42no—
121C2×Dic122—41no—
122M16×C61—22no—
123M16×C61SD1614yescomplemented
124C2×C8×C61—21no—
125C2×C8×C61—21no—
126C2×C8×C61—42no—
127C2×C8×C61C2×D412yes—
128C2×C8×C61C2×D412yes—
129C4⋊C4×C61—21no—
130C4⋊C4×C61—21no—
131C4⋊C4×C61—21no—
132C4⋊C4×C61—22no—
133C4⋊C4×C61—22no—
134C4⋊C4×C61C2×D412yes—
135C22⋊C4×C61—22no—
136C42×C61—22no—
137C42×C61C2×D411yescharacteristic
138C42×C61C2×D411yescharacteristic
139C42×C61#4111yescharacteristic
140C42×C61C2411yescharacteristic
141#11758201—82no—
142#11758198—41no—
143#11758198—41no—
144C4⋊Dic61—22no—
145C4⋊Dic61—21no—
146C4⋊Dic61—22no—
147C4⋊Dic61—21no—
148C4⋊Dic61—41no—
149C4⋊Dic61—41no—
150C2×#92418—21no—
151C2×#92418—21no—
152C2×#92418—22no—
153C2×#92418—81no—
154Dic244—44no—
155Dic244—44no—
156#11758190—44no—
157#11758190—44no—
158C23×C61#12111yescharacteristic
159C22×D61—41no—
160Q8×C61—22no—
161Q8×C61—22no—
162Q8×C61—81no—
163C2×C4×C61—21no—
164C2×C4×C61—21no—
165C2×C4×C61—22no—
166C2×C4×C61—22no—
167C2×C4×C61—41no—
168C2×C4×C61#12111yescharacteristic
169C2×C4×C61#12111yescharacteristic
170C2×C4×C61#12111yescharacteristic
171C2×C4×C61C2×SD1612yes—
172C2×C4×C61AGL(1,ℤ/8)12yes—
173C2×C4×C61C22×D411yescharacteristic
174C2×C4×C61C22×D411yescharacteristic
175C2×C4×C61C2×#4111yescharacteristic
176C22⋊D61—82no—
177C2×Dic61—42no—
178C2×Dic61—41no—
179C2×Dic61—82no—
180D244—41no—
181D244—41no—
182D244—41no—
183D244—41no—
184D244—81no—
185C4×D61—82no—
186Dic122—42no—
187Dic122—41no—
188Dic122—42no—
189Dic122—41no—
190Dic122—82no—
191C8×C61—22no—
192C8×C61—41no—
193C8×C61—41no—
194C8×C61C2×SD1614yes—
195#92418—41no—
196#92418—42no—
197#92418—41no—
198#19239—611nomaximal, Sylow
199C22×C61—21no—
200C22×C61—21no—
201C22×C61#46012yes—
202C22×C61C2×#12111yescharacteristic
203C2×D61—81no—
204C2×D61—81no—
205C2×D61—81no—
206C4×C61—21no—
207C4×C61—21no—
208C4×C61—21no—
209C4×C61—42no—
210C4×C61—42no—
211C4×C61#46012yes—
212C4×C61C22×SD1611yescharacteristic
213C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
214C4×C61#57711yescharacteristic
215C4×C61#57811yescharacteristic
216Dic61—82no—
217Dic61—81no—
218#3246—611no—
219#3229—611no—
220#3152—611no—
221#2962D6111yescharacteristic, complemented
222#1690—612no—
223#1686—612no—
224#1670—612no—
225#1666—612no—
226#1565—611no—
227#1540—611no—
228C2×#332—611no—
229C2×C61—22no—
230C2×C61C2×#46011yescharacteristic
231C2×C61#306311yescharacteristic
232C2×C61#306911yescharacteristic
233D61—161no—
234C2×#137—1221no—
235C2×#137—1221no—
236#533C2×D6111yescharacteristic
237#532—611no—
238C2×C4⋊Q8—611no—
239#498—1221no—
240#497—1222no—
241#494—612no—
242#492—612no—
243#487—1221no—
244#483—1222no—
245#476—1221no—
246#475—612no—
247#475—612no—
248#475—612no—
249#465—1222no—
250#461—1221no—
251#460—612no—
252#446—22no—
253#446C2×D6112yes—
254C8×Q8C2×D6112yes—
255#431—611no—
256#424—21no—
257C2×C4⋊C8—611no—
258C2×C4⋊C8C2×D6111yescharacteristic
259#405—21no—
260C4×M16C2×D6111yescharacteristic
261#335—612no—
262#334—612no—
263#332—612no—
264#332—612no—
265#332—611no—
266#332—611no—
267#331—611no—
268#331—611no—
269C61#1923911yescharacteristic, complemented, Sylow
270C2×#41—1221no—
271C22×Q8—1221no—
272#137—2444no—
273#137—2444no—
274C2×Q16—1222no—
275C2×Q16—1222no—
276C2×SD16—1222no—
277C2×SD16—1222no—
278C2×SD16—1222no—
279C2×M16C22⋊D6111yescharacteristic
280C2×M16C22⋊D6111yescharacteristic
281C22×C8—21no—
282C22×C8—1221no—
283C4⋊Q8—612no—
284C4⋊Q8—611no—
285C4⋊Q8—1221no—
286C4⋊Q8—1221no—
287C4⋊Q8—1221no—
288C4⋊Q8D24411yescharacteristic
289C4⋊Q8D24411yescharacteristic
290#127—611no—
291#125—21no—
292#124—1221no—
293C22⋊Q8—21no—
294C22⋊Q8D24412yes—
295#121—1221no—
296#121—1221no—
297C4×Q8—21no—
298C4×Q8C22×D6112yes—
299C4×D4—1221no—
300C4×D4—1221no—
301#117—21no—
302C2×C4⋊C4—1221no—
303C2×C4⋊C4—1221no—
304C2×C42C22×D6111yescharacteristic
305#106—1222no—
306#106—1222no—
307#106—1222no—
308C4⋊C8—22no—
309C4⋊C8—22no—
310C4⋊C8—21no—
311C4⋊C8—611no—
312C4⋊C8—611no—
313C4⋊C8—612no—
314C4⋊C8—1221no—
315C4⋊C8C22×D6111yescharacteristic
316C4⋊C8C22×D6111yescharacteristic
317#103—1222no—
318#103—1222no—
319#103—1222no—
320#102—1222no—
321C22⋊C8—1221no—
322#97—22no—
323#97C22⋊D6112yes—
324C4×C8—22no—
325C4×C8—1221no—
326C4×C8C22×D6112yes—
327#41—2442no—
328#41—2442no—
329C2×Q8—21no—
330C2×Q8—1221no—
331C2×Q8—1222no—
332C2×Q8—2442no—
333C2×Q8—2442no—
334C2×Q8—2441no—
335C2×Q8C2×D24412yes—
336C2×D4—1221no—
337C2×D4—1221no—
338C2×D4—1221no—
339C2×D4—2441no—
340C22×C4—2441no—
341C22×C4—2441no—
342C22×C4C2×D24411yescharacteristic
343C22×C4#1175822211yescharacteristic
344C22×C4C2×C22⋊D6111yescharacteristic
345Q16—2444no—
346Q16—2444no—
347SD16—4882no—
348SD16—2444no—
349SD16—2444no—
350M16—22no—
351M16#1175820114yescomplemented
352C2×C8—21no—
353C2×C8—21no—
354C2×C8—42no—
355C2×C8—1221no—
356C2×C8—1221no—
357C2×C8—1222no—
358C2×C8—4881no—
359C2×C8C2×C22⋊D6112yes—
360C2×C8C2×C22⋊D6112yes—
361C4⋊C4—22no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—22no—
366C4⋊C4—1222no—
367C4⋊C4—1221no—
368C4⋊C4—1222no—
369C4⋊C4—1221no—
370C4⋊C4—2441no—
371C4⋊C4—2441no—
372C4⋊C4C2×D24412yes—
373C22⋊C4—22no—
374C22⋊C4—2441no—
375C22⋊C4—2441no—
376C42—22no—
377C42C2×D24411yescharacteristic
378C42#1175822211yescharacteristic
379C42C2×C22⋊D6111yescharacteristic
380C42C23×D6111yescharacteristic
381C23—2441no—
382C23#1451975111yescharacteristic
383Q8—22no—
384Q8—22no—
385Q8—81no—
386Q8—4882no—
387Q8—2442no—
388Q8—2441no—
389Q8—2442no—
390Q8—2441no—
391D4—4881no—
392D4—4882no—
393D4—2441no—
394D4—2441no—
395D4—2441no—
396D4—2441no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—41no—
402C2×C4—4882no—
403C2×C4—4882no—
404C2×C4—2441no—
405C2×C4—2442no—
406C2×C4#1451975111yescharacteristic
407C2×C4#1451975111yescharacteristic
408C2×C4#1451975111yescharacteristic
409C2×C4C2×#1175820112yes—
410C2×C4#1451980212yes—
411C2×C4C22×C22⋊D6111yescharacteristic
412C2×C4C22×D24411yescharacteristic
413C2×C4C2×#1175822211yescharacteristic
414C8—22no—
415C8—41no—
416C8—41no—
417C8—2441no—
418C8—2442no—
419C8—2441no—
420C8C2×#1175820114yes—
421C22—21no—
422C22—21no—
423C22—4881no—
424C22—4881no—
425C22—4881no—
426C22#1683996212yes—
427C22C2×#1451975111yescharacteristic
428C4—21no—
429C4—21no—
430C4—21no—
431C4—42no—
432C4—42no—
433C4—4881no—
434C4—4882no—
435C4#1683996212yes—
436C4C22×#1175820111yescharacteristic
437C4C2×#1451980211yescharacteristic
438C4#1684057411yescharacteristic
439C4#1684057911yescharacteristic
440C2—22no—
441C2—9761no—
442C2C2×#1683996211yescharacteristic
443C2#2145551011yescharacteristic
444C2#2145555611yescharacteristic
subgroupG/H
centerC22C2×#14519751
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#2962C2
socleC22×C61C2×#121
prime radical#16840312C22
hypercenter#2962D61
hypocenterC61#19239
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2962

Complements

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

NH ≅ G/Ntype
2. #21456960C2semidirect
4. #21445313C2semidirect
5. #21445291C2semidirect
6. #21445189C2semidirect
7. #21445167C2semidirect
8. #21444571C2semidirect
10. C2×#16839509C2semidirect
11. C61×#2962C2semidirect
123. M16×C61SD16semidirect
221. #2962D61semidirect
269. C61#19239semidirect
351. M16#11758201semidirect

Maximal subgroups

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

subgroupindex
#214571312
#214569602
#214562782
#214453132
#214452912
#214451892
#214451672
#214445712
#214444692
C2×#168395092
C61×#29622
#1923961