Finite Group Databasebeta

← #29663597

Subgroups — #29663597

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#21457136C211yesmaximal, characteristic
2#21456965C211yesmaximal, characteristic, complemented
3#21456278C211yesmaximal, characteristic
4#21454766C211yesmaximal, characteristic, complemented
5#21445314C212yesmaximal, complemented
6#21445292C212yesmaximal, complemented
7#21445190C212yesmaximal, complemented
8#21445168C212yesmaximal, complemented
9#21444466C211yesmaximal, characteristic
10C2×#16839507C211yesmaximal, characteristic, complemented
11C61×#1565C211yesmaximal, characteristic, complemented
12C2×#14519810—21no—
13C2×#14519810—21no—
14#16840319C2211yescharacteristic
15#16840312C2211yescharacteristic
16C2×#14519777C2211yescharacteristic
17#16840160—21no—
18#16840156—22no—
19#16840142C2212yes—
20#16840135C2212yes—
21#16840113—21no—
22#16840093—22no—
23#16840053—21no—
24#16840048C2212yes—
25#16840048C2212yes—
26#16840048C2212yes—
27#16839991—22no—
28#16839968—21no—
29#16839963C2212yes—
30#16839892C2212yes—
31#16839890—22no—
32C8×Dic122C2212yes—
33#16839790—21no—
34C2×C4⋊#92418C2211yescharacteristic
35#16839720—21no—
36#16839507C2212yes—
37#16839507C2211yescharacteristic
38#16839507C2212yes—
39#16839507C2211yescharacteristic
40#16839505C2211yescharacteristic
41#16839505C2211yescharacteristic
42C61×#431C2211yescharacteristic
43C2×C4⋊C8×C61C2211yescharacteristic
44C4×M16×C61C2211yescharacteristic
45C61×#335C2212yes—
46C61×#334C2212yes—
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×#11758190—22no—
56C22×#92418—21no—
57#14519777—21no—
58#14519777—21no—
59#14519777—21no—
60#14519777D411yescharacteristic
61#14519777D411yescharacteristic
62#14519777C2312yes—
63#14519777C2311yescharacteristic
64#14519774C2311yescharacteristic
65#14519769—21no—
66#14519765—21no—
67#14519756—21no—
68#14519756D412yes—
69#14519751—21no—
70#14519751—21no—
71C4×Dic122—21no—
72C4×Dic122C2312yes—
73C4×D244—21no—
74C4×D244—21no—
75#14519736—21no—
76C2×C4⋊Dic61—21no—
77C2×C4⋊Dic61—21no—
78#14519709—22no—
79#14519709—22no—
80#14519709—22no—
81C4⋊#92418—21no—
82C4⋊#92418C2311yescharacteristic
83C4⋊#92418C2311yescharacteristic
84#14519706—22no—
85#14519706—22no—
86#14519702—22no—
87#14519702—22no—
88#14519702—22no—
89#14519699—22no—
90#14519687—22no—
91C8×Dic61—22no—
92C2×M16×C61D411yescharacteristic
93C2×M16×C61D411yescharacteristic
94C22×C8×C61—21no—
95C2×C42×C61C2311yescharacteristic
96C4⋊C8×C61—21no—
97C4⋊C8×C61C2312yes—
98C4⋊C8×C61C2311yescharacteristic
99C4⋊C8×C61C2311yescharacteristic
100C22⋊C8×C61—21no—
101#97×C61D412yes—
102C4×C8×C61—21no—
103C4×C8×C61C2312yes—
104C22×C4×C61C2×D411yescharacteristic
105C22×C4×C61C2×D411yescharacteristic
106C22×C4×C61#4111yescharacteristic
107C2×C22⋊D61—41no—
108C22×Dic61—41no—
109#11758222—42no—
110#11758222—42no—
111C2×D244—21no—
112C2×D244—21no—
113C2×D244—21no—
114C2×C4×D61—41no—
115C2×Dic122—22no—
116C2×Dic122—21no—
117C2×Dic122—21no—
118C2×Dic122—42no—
119C2×Dic122—42no—
120C2×Dic122—41no—
121C2×Dic122C2×D412yes—
122M16×C61—22no—
123M16×C61SD1614yescomplemented
124C2×C8×C61—21no—
125C2×C8×C61—21no—
126C2×C8×C61—22no—
127C2×C8×C61—81no—
128C2×C8×C61C2×D412yes—
129C2×C8×C61C2×D412yes—
130C42×C61C2×D411yescharacteristic
131C42×C61C2×D411yescharacteristic
132C42×C61#4111yescharacteristic
133C42×C61C2411yescharacteristic
134C22⋊Dic61—22no—
135#11758198—41no—
136#11758198—41no—
137C4⋊Dic61—21no—
138C4⋊Dic61—21no—
139C4⋊Dic61—21no—
140C4⋊Dic61—22no—
141C4⋊Dic61—21no—
142C4⋊Dic61—22no—
143C4⋊Dic61—21no—
144C4⋊Dic61—41no—
145C4⋊Dic61—41no—
146C4⋊Dic61C2×D412yes—
147#11758196—22no—
148#11758196—22no—
149C4×Dic61—22no—
150C2×#92418—21no—
151C2×#92418—21no—
152C2×#92418—42no—
153Dic244—44no—
154Dic244—44no—
155#11758190—44no—
156#11758190—44no—
157#11758190—82no—
158C23×C61#12111yescharacteristic
159C22×D61—41no—
160C2×C4×C61—21no—
161C2×C4×C61—21no—
162C2×C4×C61—41no—
163C2×C4×C61#12111yescharacteristic
164C2×C4×C61#12111yescharacteristic
165C2×C4×C61#12111yescharacteristic
166C2×C4×C61C2×SD1612yes—
167C2×C4×C61AGL(1,ℤ/8)12yes—
168C2×C4×C61C22×D411yescharacteristic
169C2×C4×C61C22×D411yescharacteristic
170C2×C4×C61C2×#4111yescharacteristic
171C22⋊D61—82no—
172C2×Dic61—22no—
173C2×Dic61—22no—
174C2×Dic61—42no—
175C2×Dic61—41no—
176C2×Dic61—82no—
177D244—41no—
178D244—41no—
179D244—41no—
180D244—41no—
181D244—81no—
182C4×D61—82no—
183Dic122—22no—
184Dic122—22no—
185Dic122—42no—
186Dic122—41no—
187Dic122—42no—
188Dic122—41no—
189Dic122—81no—
190Dic122—82no—
191C8×C61—22no—
192C8×C61—42no—
193C8×C61—41no—
194C8×C61—41no—
195C8×C61C2×SD1614yes—
196#92418—41no—
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#46012yes—
210C4×C61C22×SD1611yescharacteristic
211C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
212C4×C61#57711yescharacteristic
213C4×C61#57811yescharacteristic
214Dic61—42no—
215Dic61—42no—
216Dic61—82no—
217Dic61—81no—
218#3246—611no—
219#3229—611no—
220#3152—611no—
221#2962—611no—
222#1690—612no—
223#1686—612no—
224#1670—612no—
225#1666—612no—
226#1565D6111yescharacteristic, complemented
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#533—611no—
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—612no—
253#446—1222no—
254C8×Q8—612no—
255#431C2×D6111yescharacteristic
256#424—1221no—
257C2×C4⋊C8—611no—
258C2×C4⋊C8C2×D6111yescharacteristic
259#405—1221no—
260C4×M16C2×D6111yescharacteristic
261#335C2×D6112yes—
262#334C2×D6112yes—
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×M16D24411yescharacteristic
280C2×M16D24411yescharacteristic
281C22×C8—21no—
282C22×C8—1221no—
283C4⋊Q8—611no—
284C4⋊Q8—611no—
285C4⋊Q8—612no—
286C4⋊Q8—611no—
287C4⋊Q8—1221no—
288C4⋊Q8—1221no—
289C4⋊Q8—1221no—
290#127—611no—
291#125—1221no—
292#124—1221no—
293C22⋊Q8—612no—
294C22⋊Q8—1221no—
295#121—1221no—
296#121—1221no—
297C4×Q8—612no—
298C4×Q8—1221no—
299C4×D4—1221no—
300C4×D4—1221no—
301#117—1221no—
302C2×C4⋊C4—1221no—
303C2×C4⋊C4—1221no—
304C2×C42C22×D6111yescharacteristic
305#106—1222no—
306#106—1222no—
307#106—1222no—
308C4⋊C8—21no—
309C4⋊C8—611no—
310C4⋊C8—611no—
311C4⋊C8—1222no—
312C4⋊C8—1222no—
313C4⋊C8—1221no—
314C4⋊C8C22×D6111yescharacteristic
315C4⋊C8C22×D6111yescharacteristic
316C4⋊C8C22×D6112yes—
317#103—1222no—
318#103—1222no—
319#103—1222no—
320#102—1222no—
321C22⋊C8—21no—
322#97—1222no—
323#97D24412yes—
324C4×C8—21no—
325C4×C8—1222no—
326C4×C8C22×D6112yes—
327#41—2442no—
328#41—2442no—
329C2×Q8—612no—
330C2×Q8—1221no—
331C2×Q8—1221no—
332C2×Q8—1222no—
333C2×Q8—2442no—
334C2×Q8—2442no—
335C2×Q8—2441no—
336C2×D4—1221no—
337C2×D4—1221no—
338C2×D4—1221no—
339C2×D4—2441no—
340C22×C4—2441no—
341C22×C4—2441no—
342C22×C4C2×D24411yescharacteristic
343C22×C4D4×D6111yescharacteristic
344C22×C4#1175822611yescharacteristic
345Q16—2444no—
346Q16—2444no—
347SD16—4882no—
348SD16—2444no—
349SD16—2444no—
350M16—22no—
351M16#1175819014yescomplemented
352C2×C8—21no—
353C2×C8—21no—
354C2×C8—22no—
355C2×C8—81no—
356C2×C8—1221no—
357C2×C8—1221no—
358C2×C8—2442no—
359C2×C8C2×D24412yes—
360C2×C8C2×D24412yes—
361C4⋊C4—612no—
362C4⋊C4—1222no—
363C4⋊C4—1222no—
364C4⋊C4—1221no—
365C4⋊C4—1221no—
366C4⋊C4—1221no—
367C4⋊C4—1222no—
368C4⋊C4—1221no—
369C4⋊C4—1222no—
370C4⋊C4—1221no—
371C4⋊C4—2441no—
372C4⋊C4—2441no—
373C22⋊C4—1222no—
374C22⋊C4—2441no—
375C22⋊C4—2441no—
376C42—1222no—
377C42C2×D24411yescharacteristic
378C42D4×D6111yescharacteristic
379C42#1175822611yescharacteristic
380C42C23×D6111yescharacteristic
381C23—2441no—
382C23#1451975211yescharacteristic
383Q8—1222no—
384Q8—1222no—
385Q8—4881no—
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—41no—
400C2×C4—1222no—
401C2×C4—1222no—
402C2×C4—4882no—
403C2×C4—4882no—
404C2×C4—2441no—
405C2×C4—2442no—
406C2×C4#1451975211yescharacteristic
407C2×C4#1451975211yescharacteristic
408C2×C4#1451975211yescharacteristic
409C2×C4C2×#1175819012yes—
410C2×C4#1451980512yes—
411C2×C4C2×D4×D6111yescharacteristic
412C2×C4C22×D24411yescharacteristic
413C2×C4C2×#1175822611yescharacteristic
414C8—22no—
415C8—41no—
416C8—42no—
417C8—41no—
418C8—2441no—
419C8—2441no—
420C8C2×#1175819014yes—
421C22—21no—
422C22—21no—
423C22—4881no—
424C22—4881no—
425C22—4881no—
426C22#1683996312yes—
427C22C2×#1451975211yescharacteristic
428C4—21no—
429C4—21no—
430C4—21no—
431C4—4881no—
432C4—4882no—
433C4—2442no—
434C4—2442no—
435C4#1683996312yes—
436C4C22×#1175819011yescharacteristic
437C4C2×#1451980511yescharacteristic
438C4#1684057211yescharacteristic
439C4#1684057811yescharacteristic
440C2—22no—
441C2—9761no—
442C2C2×#1683996311yescharacteristic
443C2#2145551111yescharacteristic
444C2#2145555711yescharacteristic
subgroupG/H
centerC22C2×#14519752
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1565C2
socleC22×C61C2×#121
prime radical#16840312C22
hypercenter#1565D61
hypocenterC61#19239
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1565

Complements

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

NH ≅ G/Ntype
2. #21456965C2semidirect
4. #21454766C2semidirect
5. #21445314C2semidirect
6. #21445292C2semidirect
7. #21445190C2semidirect
8. #21445168C2semidirect
10. C2×#16839507C2semidirect
11. C61×#1565C2semidirect
123. M16×C61SD16semidirect
226. #1565D61semidirect
269. C61#19239semidirect
351. M16#11758190semidirect

Maximal subgroups

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

subgroupindex
#214571362
#214569652
#214562782
#214547662
#214453142
#214452922
#214451902
#214451682
#214444662
C2×#168395072
C61×#15652
#1923961