Finite Group Databasebeta

← #29571008

Subgroups — #29571008

Order 15616.

522 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454509C211yesmaximal, characteristic
2#21445597C211yesmaximal, characteristic, complemented
3C22⋊C4×#92418C211yesmaximal, characteristic, complemented
4#21444308C211yesmaximal, characteristic
5#21444308C211yesmaximal, characteristic
6#21443706C211yesmaximal, characteristic, complemented
7C61×#1297C211yesmaximal, characteristic, complemented
8C2×#14519785C411yescharacteristic, complemented
9C23×#92418C2211yescharacteristic
10#16840273C2211yescharacteristic
11#16839830—21no—
12#16839830—21no—
13#16839825—21no—
14#16839825—21no—
15#16839790C411yescharacteristic, complemented
16#16839730C411yescharacteristic, complemented
17C2×C22⋊#92418C2211yescharacteristic
18C2×C22⋊#92418C2211yescharacteristic
19#16839720C411yescharacteristic, complemented
20C2×#14519688—21no—
21C2×C4×#92418—21no—
22#16839517—21no—
23#16839517—21no—
24#16839498C412yescomplemented
25#16839498C412yescomplemented
26#16839495C412yescomplemented
27#16839495C412yescomplemented
28C61×#407C2211yescharacteristic
29C4×C22⋊C4×C61C2211yescharacteristic
30C4×C22⋊C4×C61C2211yescharacteristic
31C2×#11758222C2×C411yescharacteristic
32#14519785—42no—
33C2×#11758189—21no—
34C22×#92418—21no—
35C22×#92418—21no—
36C22×#92418—42no—
37C22×#92418C2×C411yescharacteristic
38C22×#92418C2×C411yescharacteristic
39C22×#92418D411yescharacteristic
40C22×#92418D411yescharacteristic
41C22×#92418D411yescharacteristic
42C22×#92418D411yescharacteristic
43C2×C8×D61—21no—
44#14519760—21no—
45#14519756C2×C411yescharacteristic
46#14519756C2×C411yescharacteristic
47#14519751C2×C411yescharacteristic
48#14519751C2×C411yescharacteristic
49#14519746—21no—
50C4×C22⋊D61—21no—
51C4×C22⋊D61—21no—
52#14519736C2×C411yescharacteristic
53#14519706—21no—
54#14519706—21no—
55C22⋊#92418—21no—
56C22⋊#92418—21no—
57C22⋊#92418C2×C412yes—
58C22⋊#92418C2×C412yes—
59#14519689—21no—
60#14519689—21no—
61#14519688—42no—
62#14519687—21no—
63C4×#92418—42no—
64C8×Dic61—21no—
65C23×C4×C61C2311yescharacteristic
66C2×M16×C61C2×C411yescharacteristic
67C2×M16×C61C2×C411yescharacteristic
68C2×C22⋊C4×C61—21no—
69C2×C22⋊C4×C61—21no—
70C2×C42×C61—21no—
71C2×C42×C61—21no—
72C22⋊C8×C61—21no—
73C22⋊C8×C61—21no—
74#95×C61C2×C412yes—
75#95×C61C2×C412yes—
76C24×C61#4111yescharacteristic
77C22×C4×C61—22no—
78C22×C4×C61—22no—
79C22×C4×C61—41no—
80C22×C4×C61—41no—
81C22×C4×C61C22×C411yescharacteristic
82C22×C4×C61C22×C411yescharacteristic
83C22×C4×C61C22×C411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61#4111yescharacteristic
87C2×C22⋊D61—21no—
88C2×C22⋊D61—21no—
89C2×C22⋊D61—21no—
90#11758222—41no—
91#11758222—41no—
92C2×D244C4211yescharacteristic
93C2×C4×D61—21no—
94C2×Dic122C4211yescharacteristic
95M16×C61—41no—
96M16×C61—41no—
97C2×C8×C61—21no—
98C2×C8×C61—21no—
99C22⋊C4×C61—24no—
100C22⋊C4×C61—42no—
101C42×C61—41no—
102C42×C61—41no—
103C42×C61—41no—
104C42×C61—41no—
105C22⋊Dic61—21no—
106C22⋊Dic61—21no—
107C22⋊Dic61—21no—
108#11758198—21no—
109#11758198—21no—
110C4⋊Dic61C4211yescharacteristic
111C4⋊Dic61C4211yescharacteristic
112#11758196—21no—
113#11758196—21no—
114C4×Dic61—21no—
115C2×#92418—22no—
116C2×#92418—22no—
117C2×#92418—22no—
118C2×#92418—22no—
119C2×#92418—22no—
120C2×#92418—41no—
121C2×#92418—41no—
122C2×#92418—41no—
123C2×#92418—41no—
124C2×#92418—41no—
125C2×#92418—41no—
126C2×#92418—41no—
127C2×#92418C22⋊C411yescharacteristic
128C2×#92418C22⋊C411yescharacteristic
129C2×#92418C22⋊C411yescharacteristic
130C2×#92418C22⋊C411yescharacteristic
131#11758189—42no—
132C8×D61—42no—
133C23×C61—22no—
134C23×C61—22no—
135C23×C61—41no—
136C23×C61#11711yescharacteristic
137C23×C61C4×D411yescharacteristic
138C23×C61C4×D411yescharacteristic
139C22×D61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—24no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—42no—
151C2×C4×C61—42no—
152C2×C4×C61—42no—
153C2×C4×C61—42no—
154C2×C4×C61—42no—
155C2×C4×C61C2×C4211yescharacteristic
156C2×C4×C61C2×C22⋊C411yescharacteristic
157C2×C4×C61C4×D411yescharacteristic
158C2×C4×C61C4×D411yescharacteristic
159C22⋊D61—42no—
160C22⋊D61—42no—
161C22⋊D61—42no—
162C2×Dic61—21no—
163C2×Dic61—21no—
164C2×Dic61—21no—
165D244—41no—
166C4×D61—41no—
167C4×D61—41no—
168Dic122—41no—
169C8×C61—41no—
170C8×C61—41no—
171#92418—21no—
172#92418—21no—
173#92418—21no—
174#92418—42no—
175#92418—42no—
176#92418#9912yes—
177#8240—611nomaximal, Sylow
178C22×C61—21no—
179C22×C61—21no—
180C22×C61—21no—
181C22×C61—21no—
182C22×C61—21no—
183C22×C61—21no—
184C22×C61—21no—
185C22×C61—44no—
186C22×C61C4×C22⋊C411yescharacteristic
187C22×C61#44312yes—
188C22×C61#44412yes—
189C2×D61—41no—
190C2×D61—41no—
191C2×D61—41no—
192C4×C61—21no—
193C4×C61—21no—
194C4×C61—21no—
195C4×C61—44no—
196C4×C61—82no—
197C4×C61C2×#9911yescharacteristic
198C4×C61#41011yescharacteristic
199Dic61—41no—
200Dic61—41no—
201Dic61—41no—
202#2929—611no—
203#1752—611no—
204C8×C22⋊C4—611no—
205#1501—611no—
206#1501—611no—
207#1298—611no—
208#1297D6111yescharacteristic, complemented
209C2×C61—22no—
210C2×C61—22no—
211C2×C61—41no—
212C2×C61C4×#9911yescharacteristic
213C2×C61#176411yescharacteristic
214C2×C61#176511yescharacteristic
215D61—81no—
216C2×#131—611no—
217C23×C8—611no—
218#525—611no—
219#435—1221no—
220#435—1221no—
221C8×D4—1221no—
222C8×D4—1221no—
223#424—611no—
224#408—611no—
225#407C2×D6111yescharacteristic
226C2×C22⋊C8—611no—
227C2×C22⋊C8—611no—
228#405—611no—
229C2×#97—1221no—
230C2×C4×C8—1221no—
231C4×C22⋊C4C2×D6111yescharacteristic
232C4×C22⋊C4C2×D6111yescharacteristic
233#336—1221no—
234#336—1221no—
235#328—612no—
236#328—612no—
237#327—612no—
238#327—612no—
239C61#824011yescharacteristic, complemented, Sylow
240C2×#41—611no—
241C23×C4C22×D6111yescharacteristic
242#131—2442no—
243C2×M16—1221no—
244C2×M16C4×D6111yescharacteristic
245C2×M16C4×D6111yescharacteristic
246C22×C8—611no—
247C22×C8—611no—
248C22×C8—611no—
249C22×C8—611no—
250C22×C8—611no—
251C22×C8—611no—
252C22×C8—1221no—
253C22×C8—1221no—
254C22×C8—1221no—
255C22×C8—2442no—
256#123—1221no—
257C22⋊Q8—611no—
258C22⋊Q8—611no—
259#121—611no—
260#121—611no—
261#120—1221no—
262C4×D4—1221no—
263C4×D4—1221no—
264#117—611no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C42—21no—
268C2×C42—21no—
269C4⋊C8—1221no—
270C4⋊C8—1221no—
271C22⋊C8—21no—
272C22⋊C8—21no—
273C22⋊C8—612no—
274C22⋊C8—612no—
275C22⋊C8—1221no—
276C22⋊C8—1221no—
277C22⋊C8—1221no—
278C22⋊C8—1221no—
279#97—1221no—
280#97—2442no—
281C4×C8—1221no—
282C4×C8—2442no—
283#95C4×D6112yes—
284#95C4×D6112yes—
285C24#1175822411yescharacteristic
286#41—2441no—
287#41—2441no—
288C2×Q8—611no—
289C2×D4—611no—
290C2×D4—1221no—
291C2×D4—1221no—
292C2×D4—1221no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—1221no—
298C22×C4C2×C4×D6111yescharacteristic
299C22×C4C2×C4×D6111yescharacteristic
300C22×C4C2×C4×D6111yescharacteristic
301C22×C4D4×D6111yescharacteristic
302C22×C4D4×D6111yescharacteristic
303C22×C4#1175822611yescharacteristic
304M16—41no—
305M16—41no—
306M16—2442no—
307C2×C8—21no—
308C2×C8—21no—
309C2×C8—611no—
310C2×C8—611no—
311C2×C8—611no—
312C2×C8—611no—
313C2×C8—1222no—
314C2×C8—1222no—
315C2×C8—1222no—
316C2×C8—1222no—
317C2×C8—1222no—
318C2×C8—2442no—
319C2×C8—2441no—
320C2×C8—2441no—
321C2×C8—2441no—
322C2×C8—2441no—
323C2×C8—2441no—
324C2×C8—2441no—
325C2×C8—2441no—
326C4⋊C4—611no—
327C4⋊C4—611no—
328C4⋊C4—1221no—
329C4⋊C4—1221no—
330C22⋊C4—24no—
331C22⋊C4—42no—
332C22⋊C4—1221no—
333C22⋊C4—1221no—
334C22⋊C4—1221no—
335C22⋊C4—1221no—
336C22⋊C4—1221no—
337C42—41no—
338C42—41no—
339C42—41no—
340C42—41no—
341C42—1221no—
342C23—22no—
343C23—22no—
344C23—41no—
345C23—1221no—
346C23#1451973511yescharacteristic
347C23#1451973711yescharacteristic
348C23#1451973711yescharacteristic
349Q8—2441no—
350D4—2441no—
351D4—2442no—
352D4—2442no—
353D4—2442no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—24no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—1221no—
370C2×C4—1221no—
371C2×C4—1221no—
372C2×C4—2441no—
373C2×C4—2441no—
374C2×C4C42×D6111yescharacteristic
375C2×C4C22⋊C4×D6111yescharacteristic
376C2×C4#1451973911yescharacteristic
377C2×C4#1451973911yescharacteristic
378C8—41no—
379C8—41no—
380C8—612no—
381C8—1221no—
382C8—1221no—
383C8—1221no—
384C8—2442no—
385C8—2442no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—44no—
394C22—2441no—
395C22—2441no—
396C22—2441no—
397C22#1683960911yescharacteristic
398C22#1683987612yes—
399C22#1683988112yes—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—44no—
404C4—82no—
405C4—2441no—
406C4—2441no—
407C4—2441no—
408C4#99×D6111yescharacteristic
409C4#1683973411yescharacteristic
410C2—22no—
411C2—22no—
412C2—41no—
413C2—4881no—
414C2#2144560611yescharacteristic
415C2#2144565311yescharacteristic
416C2#2144566011yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC2×C4×C61C2×C42
FrattiniC23×C4C22×D61
FittingC61×#1297C2
socleC22×C61C4×C22⋊C4
prime radical#16840273C22
cosocleC23×C4×C61C23
hypercenter#1297D61
hypocenterC61#8240
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1297

Complements

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

NH ≅ G/Ntype
2. #21445597C2semidirect
3. C22⋊C4×#92418C2semidirect
6. #21443706C2semidirect
7. C61×#1297C2semidirect
8. C2×#14519785C4semidirect
15. #16839790C4semidirect
16. #16839730C4semidirect
19. #16839720C4semidirect
24. #16839498C4semidirect
25. #16839498C4semidirect
26. #16839495C4semidirect
27. #16839495C4semidirect
208. #1297D61semidirect
239. C61#8240semidirect

Maximal subgroups

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

subgroupindex
#214545092
#214455972
C22⋊C4×#924182
#214443082
#214437062
C61×#12972
#824061