Finite Group Databasebeta

← #29837592

Subgroups — #29837592

Order 15616.

464 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458188C211yesmaximal, characteristic
2#21448095C211yesmaximal, characteristic, complemented
3#21448027C211yesmaximal, characteristic, complemented
4#21448024C211yesmaximal, characteristic, complemented
5#21448021C211yesmaximal, characteristic, complemented
6#21448019C211yesmaximal, characteristic, complemented
7#21447983C211yesmaximal, characteristic, complemented
8#21447980C211yesmaximal, characteristic, complemented
9#21447925C211yesmaximal, characteristic, complemented
10#21447925C211yesmaximal, characteristic, complemented
11C4×#14519723C211yesmaximal, characteristic, complemented
12#21447651C211yesmaximal, characteristic
13#21447608C211yesmaximal, characteristic, complemented
14#21447605C211yesmaximal, characteristic, complemented
15C61×#3336C211yesmaximal, characteristic
16#16840452—21no—
17C2×#14519723C2211yescharacteristic
18C2×#14519717C2211yescharacteristic
19C2×#14519717C2211yescharacteristic
20#16840164C2211yescharacteristic
21#16840104—21no—
22#16840093—21no—
23#16840070—21no—
24#16840003C2211yescharacteristic
25#16840003C2211yescharacteristic
26C4×Dic244C2211yescharacteristic
27#16839800C2211yescharacteristic
28C2×#14519711C2211yescharacteristic
29#16839589C2211yescharacteristic
30#16839589C2211yescharacteristic
31#16839589C2211yescharacteristic
32#16839589C2211yescharacteristic
33#16839587C2211yescharacteristic
34#16839587C2211yescharacteristic
35#16839587C2211yescharacteristic
36#16839587C2211yescharacteristic
37#16839587C2211yescharacteristic
38C4⋊#11758185C2211yescharacteristic
39#16839566C2211yescharacteristic
40#16839566C2211yescharacteristic
41#16839566C2211yescharacteristic
42#16839565C2211yescharacteristic
43#16839565C2211yescharacteristic
44#16839565C2211yescharacteristic
45C22⋊#11758185C2211yescharacteristic
46C22⋊#11758185C2211yescharacteristic
47C4×#11758185C2211yescharacteristic
48C61×#552—21no—
49C61×#499C2211yescharacteristic
50C61×#485—21no—
51C61×#483—21no—
52C61×#479—21no—
53C61×#467C2211yescharacteristic
54C61×#467C2211yescharacteristic
55C4×Q16×C61C2211yescharacteristic
56C8×D4×C61C2211yescharacteristic
57C61×#427C2211yescharacteristic
58C2×#107×C61C2211yescharacteristic
59C2×Dic244C2311yescharacteristic
60#14519770—41no—
61#14519769—21no—
62#14519767—41no—
63#14519758—41no—
64#14519756—21no—
65#14519756—21no—
66C4×Dic122—21no—
67#14519736—21no—
68#14519733—41no—
69C2×C4⋊Dic61—21no—
70#14519723—22no—
71#14519717—22no—
72#14519717—22no—
73C2×#11758185C2311yescharacteristic
74C2×#11758185C2311yescharacteristic
75C2×#11758185C2311yescharacteristic
76C2×#11758185C2311yescharacteristic
77#14519711—21no—
78#14519711C2311yescharacteristic
79#14519711C2311yescharacteristic
80#14519711C2311yescharacteristic
81#14519709—21no—
82#14519709—21no—
83#14519702—21no—
84#14519702—21no—
85#14519702—21no—
86C2×Q16×C61C2311yescharacteristic
87C22×C8×C61C2311yescharacteristic
88C22×C8×C61C2311yescharacteristic
89#126×C61—41no—
90#125×C61—21no—
91#125×C61—41no—
92#123×C61—41no—
93C22⋊Q8×C61—21no—
94C22⋊Q8×C61—21no—
95C4×Q8×C61—21no—
96C4×D4×C61D411yescharacteristic
97#117×C61—21no—
98#117×C61—41no—
99C2×C4⋊C4×C61—21no—
100#107×C61—21no—
101#107×C61C2311yescharacteristic
102#107×C61C2311yescharacteristic
103#107×C61C2311yescharacteristic
104#106×C61—21no—
105#106×C61—21no—
106C4⋊C8×C61D411yescharacteristic
107#103×C61—21no—
108#103×C61—21no—
109#103×C61—21no—
110C22⋊C8×C61D411yescharacteristic
111C22⋊C8×C61D411yescharacteristic
112C4×C8×C61C2311yescharacteristic
113C2×Q8×C61—21no—
114C2×D4×C61D811yescharacteristic
115C22×C4×C61—41no—
116C22×C4×C61C2×D411yescharacteristic
117C22×C4×C61C2×D411yescharacteristic
118C22×Dic61—41no—
119C2×Dic122—21no—
120Q16×C61—21no—
121Q16×C61—21no—
122C2×C8×C61—21no—
123C2×C8×C61—21no—
124C2×C8×C61—21no—
125C2×C8×C61—21no—
126C2×C8×C61C2×D411yescharacteristic
127C2×C8×C61C2×D411yescharacteristic
128C2×C8×C61C2×D411yescharacteristic
129C2×C8×C61C2411yescharacteristic
130C4⋊C4×C61—21no—
131C4⋊C4×C61—21no—
132C4⋊C4×C61—21no—
133C4⋊C4×C61—41no—
134C4⋊C4×C61—41no—
135C4⋊C4×C61—41no—
136C4⋊C4×C61—41no—
137C4⋊C4×C61—41no—
138C4⋊C4×C61—41no—
139C4⋊C4×C61D811yescharacteristic
140C22⋊C4×C61—41no—
141C22⋊C4×C61—41no—
142C22⋊C4×C61—41no—
143C22⋊C4×C61D811yescharacteristic
144C22⋊C4×C61D811yescharacteristic
145C42×C61—41no—
146C42×C61—41no—
147C42×C61C2×D411yescharacteristic
148C22⋊Dic61—41no—
149C22⋊Dic61—41no—
150C22⋊Dic61—41no—
151C4⋊Dic61—21no—
152C4⋊Dic61—21no—
153C4⋊Dic61—21no—
154C4⋊Dic61—41no—
155#11758196—41no—
156#11758196—41no—
157#11758196—41no—
158#11758196—41no—
159#11758196—41no—
160C4×Dic61—41no—
161C4×Dic61—41no—
162Dic244—21no—
163Dic244—21no—
164#11758185—21no—
165#11758185—21no—
166#11758185—21no—
167#11758185#4112yes—
168C23×C61C2×D811yescharacteristic
169C23×C61C2×D811yescharacteristic
170Q8×C61—41no—
171Q8×C61—41no—
172D4×C61—41no—
173C2×C4×C61—21no—
174C2×C4×C61—21no—
175C2×C4×C61—21no—
176C2×C4×C61—21no—
177C2×C4×C61—41no—
178C2×C4×C61—41no—
179C2×C4×C61—41no—
180C2×C4×C61—41no—
181C2×C4×C61—82no—
182C2×C4×C61C2×D811yescharacteristic
183C2×C4×C61C2×D811yescharacteristic
184C2×C4×C61C2×D811yescharacteristic
185C2×C4×C61C2×D811yescharacteristic
186C2×C4×C61C22×D411yescharacteristic
187C2×Dic61—41no—
188C2×Dic61—41no—
189C2×Dic61—41no—
190C2×Dic61—41no—
191C2×Dic61—82no—
192Dic122—41no—
193Dic122—41no—
194C8×C61—21no—
195C8×C61—21no—
196C8×C61—21no—
197C8×C61C2×#4111yescharacteristic
198C8×C612−1+411yescharacteristic
199#33919—611nomaximal, Sylow
200C22×C61—21no—
201C22×C61—21no—
202C22×C61—21no—
203C22×C61—21no—
204C22×C61—21no—
205C22×C61—21no—
206C22×C61C22×D811yescharacteristic
207C4×C61—21no—
208C4×C61—21no—
209C4×C61—21no—
210C4×C61—21no—
211C4×C61—81no—
212C4×C61—81no—
213C4×C61—81no—
214C4×C61—81no—
215C4×C61#54711yescharacteristic
216C4×C61#57811yescharacteristic
217Dic61—81no—
218Dic61—81no—
219Dic61—81no—
220Dic61—81no—
221#3336—611no—
222#3336D6111yescharacteristic
223#2253—611no—
224#2237—611no—
225#2237—611no—
226#2236—611no—
227#2236—611no—
228#2229—611no—
229#2229—611no—
230#2219—611no—
231#2219—611no—
232C4×Q32—611no—
233#2169—611no—
234#2159—611no—
235#2159—611no—
236C2×C61—41no—
237C2×C61—41no—
238C2×C61#333411yescharacteristic
239C2×C61#341411yescharacteristic
240C2×C61#341711yescharacteristic
241#552—21no—
242#552—1221no—
243C2×Q32—611no—
244C2×M32—611no—
245C2×M32—611no—
246#499—611no—
247#499C2×D6111yescharacteristic
248#485—21no—
249#485—1221no—
250#483—21no—
251#483—1221no—
252#479—21no—
253#479—1221no—
254#467—611no—
255#467—611no—
256#467C2×D6111yescharacteristic
257#467C2×D6111yescharacteristic
258C4×Q16—611no—
259C4×Q16C2×D6111yescharacteristic
260C8×D4C2×D6111yescharacteristic
261#427—611no—
262#427C2×D6111yescharacteristic
263C2×#107—611no—
264C2×#107C2×D6111yescharacteristic
265#367—611no—
266#367—611no—
267#367—611no—
268#367—611no—
269#366—611no—
270#366—611no—
271#366—611no—
272#366—611no—
273#366—611no—
274C4⋊C16—611no—
275#358—611no—
276#358—611no—
277#358—611no—
278#358—611no—
279#358—611no—
280#358—611no—
281C22⋊C16—611no—
282C22⋊C16—611no—
283C4×C16—611no—
284C61#3391911yescharacteristic, complemented, Sylow
285C2×Q16—611no—
286C2×Q16C22×D6111yescharacteristic
287C22×C8C22×D6111yescharacteristic
288C22×C8C22×D6111yescharacteristic
289#126—41no—
290#126—2441no—
291#125—21no—
292#125—41no—
293#125—1221no—
294#125—2441no—
295#123—41no—
296#123—2441no—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C22⋊Q8—1221no—
300C22⋊Q8—1221no—
301C4×Q8—21no—
302C4×Q8—1221no—
303C4×D4C22⋊D6111yescharacteristic
304#117—21no—
305#117—41no—
306#117—1221no—
307#117—2441no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—1221no—
310Q32—1222no—
311M32—1222no—
312M32—1222no—
313C2×C16—611no—
314C2×C16—611no—
315C2×C16—611no—
316C2×C16—611no—
317#107—21no—
318#107—611no—
319#107—611no—
320#107—611no—
321#107—1221no—
322#107C22×D6111yescharacteristic
323#107C22×D6111yescharacteristic
324#107C22×D6111yescharacteristic
325#106—21no—
326#106—21no—
327#106—1221no—
328#106—1221no—
329C4⋊C8C22⋊D6111yescharacteristic
330#103—21no—
331#103—21no—
332#103—21no—
333#103—1221no—
334#103—1221no—
335#103—1221no—
336C22⋊C8C22⋊D6111yescharacteristic
337C22⋊C8C22⋊D6111yescharacteristic
338C4×C8C22×D6111yescharacteristic
339C2×Q8—21no—
340C2×Q8—1221no—
341C2×D4#1175819911yescharacteristic
342C22×C4—41no—
343C22×C4—2441no—
344C22×C4C2×C22⋊D6111yescharacteristic
345C22×C4C2×C22⋊D6111yescharacteristic
346Q16—21no—
347Q16—21no—
348Q16—1221no—
349Q16—1221no—
350C2×C8—21no—
351C2×C8—21no—
352C2×C8—21no—
353C2×C8—21no—
354C2×C8C2×C22⋊D6111yescharacteristic
355C2×C8C2×C22⋊D6111yescharacteristic
356C2×C8C2×C22⋊D6111yescharacteristic
357C2×C8C23×D6111yescharacteristic
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—41no—
362C4⋊C4—41no—
363C4⋊C4—41no—
364C4⋊C4—41no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—1221no—
368C4⋊C4—1221no—
369C4⋊C4—1221no—
370C4⋊C4—2441no—
371C4⋊C4—2441no—
372C4⋊C4—2441no—
373C4⋊C4—2441no—
374C4⋊C4—2441no—
375C4⋊C4—2441no—
376C4⋊C4#1175819911yescharacteristic
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—2441no—
381C22⋊C4—2441no—
382C22⋊C4—2441no—
383C22⋊C4#1175819911yescharacteristic
384C22⋊C4#1175819911yescharacteristic
385C42—41no—
386C42—41no—
387C42—2441no—
388C42—2441no—
389C42C2×C22⋊D6111yescharacteristic
390C16—612no—
391C16—1221no—
392C16—1221no—
393C16—1221no—
394C23C2×#1175819911yescharacteristic
395C23C2×#1175819911yescharacteristic
396Q8—41no—
397Q8—41no—
398Q8—2441no—
399Q8—2441no—
400D4—41no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—82no—
410C2×C4—4882no—
411C2×C4—2441no—
412C2×C4—2441no—
413C2×C4—2441no—
414C2×C4—2441no—
415C2×C4C2×#1175819911yescharacteristic
416C2×C4C2×#1175819911yescharacteristic
417C2×C4C2×#1175819911yescharacteristic
418C2×C4C2×#1175819911yescharacteristic
419C2×C4C22×C22⋊D6111yescharacteristic
420C8—21no—
421C8—21no—
422C8—21no—
423C8#41×D6111yescharacteristic
424C8#1451982411yescharacteristic
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22C22×#1175819911yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—81no—
437C4—81no—
438C4—81no—
439C4—81no—
440C4—4881no—
441C4—4881no—
442C4—4881no—
443C4—4881no—
444C4#1684041111yescharacteristic
445C4#1684057711yescharacteristic
446C2—41no—
447C2—41no—
448C2#2145816211yescharacteristic
449C2#2145895311yescharacteristic
450C2#2145897011yescharacteristic
subgroupG/H
centerC22C22×#11758199
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#3336C2
socleC22×C61C22×D8
prime radicalC2×D4×C61D8
hypercenter#3336D61
hypocenterC61#33919
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3336

Complements

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

NH ≅ G/Ntype
2. #21448095C2semidirect
3. #21448027C2semidirect
4. #21448024C2semidirect
5. #21448021C2semidirect
6. #21448019C2semidirect
7. #21447983C2semidirect
8. #21447980C2semidirect
9. #21447925C2semidirect
10. #21447925C2semidirect
11. C4×#14519723C2semidirect
13. #21447608C2semidirect
14. #21447605C2semidirect
284. C61#33919semidirect

Maximal subgroups

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

subgroupindex
#214581882
#214480952
#214480272
#214480242
#214480212
#214480192
#214479832
#214479802
#214479252
C4×#145197232
#214476512
#214476082
#214476052
C61×#33362
#3391961