Finite Group Databasebeta

← #29579414

Subgroups — #29579414

Order 15616.

440 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456378C211yesmaximal, characteristic
2#21444582C211yesmaximal, characteristic, complemented
3#21444433C211yesmaximal, characteristic, complemented
4#21444429C211yesmaximal, characteristic
5#21444330C211yesmaximal, characteristic, complemented
6#21444326C211yesmaximal, characteristic
7C61×#1726C211yesmaximal, characteristic, complemented
8#16840319C2211yescharacteristic
9#16840312C2211yescharacteristic
10#16840160C411yescharacteristic, complemented
11#16840135C411yescharacteristic, complemented
12#16840113C411yescharacteristic, complemented
13#16840109C411yescharacteristic, complemented
14#16839991—21no—
15#16839991—21no—
16C4×#11758190—21no—
17C4×#11758190—21no—
18#16839819C2211yescharacteristic
19#16839819C2211yescharacteristic
20#16839515—21no—
21#16839513—21no—
22#16839503—22no—
23#16839501—22no—
24#16839498—22no—
25#16839495—22no—
26C2×#97×C61—21no—
27C2×#97×C61C2211yescharacteristic
28C2×C4×C8×C61—21no—
29C2×C4×C8×C61C2211yescharacteristic
30C61×#376C2211yescharacteristic
31C2×#11758222—21no—
32C2×#11758190—21no—
33C2×#11758190—21no—
34#14519777C2×C411yescharacteristic
35#14519777C2×C411yescharacteristic
36#14519777C2×C411yescharacteristic
37#14519774C2×C411yescharacteristic
38#14519769—21no—
39#14519765—21no—
40#14519756—21no—
41#14519756—21no—
42#14519751—21no—
43#14519751—21no—
44C4×Dic122—21no—
45C4×Dic122—21no—
46C4×D244—21no—
47C4×D244—21no—
48#14519736—21no—
49#14519709—21no—
50#14519709—21no—
51C4⋊#92418—21no—
52C4⋊#92418—21no—
53#14519702—21no—
54#14519702—21no—
55#14519699—21no—
56#14519699—21no—
57C22⋊#92418—21no—
58C22⋊#92418—21no—
59#14519688—21no—
60#14519688—21no—
61C22×C8×C61—21no—
62C22×C8×C61D411yescharacteristic
63C22×C8×C61D411yescharacteristic
64C2×C42×C61—21no—
65C2×C42×C61C2311yescharacteristic
66#97×C61—24no—
67#97×C61—21no—
68#97×C61D412yes—
69C4×C8×C61—24no—
70C4×C8×C61C2×C411yescharacteristic
71C4×C8×C61C2×C411yescharacteristic
72C4×C8×C61D411yescharacteristic
73C4×C8×C61D411yescharacteristic
74#95×C61—21no—
75#95×C61D412yes—
76C22×C4×C61—22no—
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61#4111yescharacteristic
80C2×C22⋊D61—41no—
81#11758222—82no—
82C2×D244—21no—
83C2×D244—21no—
84C2×D244—21no—
85C2×C4×D61—41no—
86C2×Dic122—21no—
87C2×Dic122—21no—
88C2×Dic122—21no—
89C2×C8×C61—22no—
90C2×C8×C61—22no—
91C2×C8×C61—22no—
92C2×C8×C61—22no—
93C2×C8×C61—22no—
94C2×C8×C61C22⋊C411yescharacteristic
95C2×C8×C61C22⋊C411yescharacteristic
96C2×C8×C61C22⋊C411yescharacteristic
97C2×C8×C61C22⋊C411yescharacteristic
98C42×C61—22no—
99C42×C61—22no—
100C42×C61C22×C411yescharacteristic
101C42×C61C2×D411yescharacteristic
102C42×C61C2×D411yescharacteristic
103C42×C61#4111yescharacteristic
104C22⋊Dic61—41no—
105#11758198—41no—
106#11758198—41no—
107C4⋊Dic61—21no—
108C4⋊Dic61—21no—
109C4⋊Dic61—21no—
110C4⋊Dic61—21no—
111C4⋊Dic61—21no—
112C4⋊Dic61—21no—
113#11758196—41no—
114#11758196—41no—
115C4×Dic61—41no—
116C2×#92418—41no—
117C2×#92418—41no—
118#11758190—42no—
119#11758190—42no—
120C23×C61#12111yescharacteristic
121C22×D61—41no—
122C2×C4×C61—22no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—24no—
126C2×C4×C61—41no—
127C2×C4×C61—42no—
128C2×C4×C61—42no—
129C2×C4×C61C2×C22⋊C411yescharacteristic
130C2×C4×C61C4×D411yescharacteristic
131C2×C4×C61C4×D411yescharacteristic
132C2×C4×C61#12111yescharacteristic
133C2×C4×C61#12411yescharacteristic
134C2×C4×C61#12711yescharacteristic
135C22⋊D61—82no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139D244—41no—
140D244—41no—
141D244—81no—
142D244—81no—
143C4×D61—82no—
144Dic122—41no—
145Dic122—41no—
146Dic122—81no—
147Dic122—81no—
148C8×C61—24no—
149C8×C61—21no—
150C8×C61—21no—
151C8×C61#10412yes—
152C8×C61#10412yes—
153#92418—81no—
154#92418—81no—
155#9761—611nomaximal, Sylow
156C22×C61—21no—
157C22×C61—21no—
158C22×C61#39011yescharacteristic
159C22×C61#47112yes—
160C2×D61—81no—
161C2×D61—81no—
162C2×D61—81no—
163C4×C61—21no—
164C4×C61—21no—
165C4×C61—21no—
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—44no—
169C4×C61C2×#10411yescharacteristic
170C4×C61C2×#10411yescharacteristic
171Dic61—81no—
172Dic61—81no—
173Dic61—81no—
174#3167—611no—
175#1726D6111yescharacteristic, complemented
176#1568—611no—
177#1531—611no—
178#1530—611no—
179#1506—611no—
180#1505—611no—
181C2×C61—22no—
182C2×C61#196211yescharacteristic
183C2×C61#197611yescharacteristic
184C2×C61#197711yescharacteristic
185D61—161no—
186#533—611no—
187#532—611no—
188#498—611no—
189#492—611no—
190#487—611no—
191#486—611no—
192#465—1221no—
193#465—1221no—
194C4×SD16—1221no—
195C4×SD16—1221no—
196#432—611no—
197#432—611no—
198C2×#97—21no—
199C2×#97C2×D6111yescharacteristic
200C2×C4×C8—21no—
201C2×C4×C8C2×D6111yescharacteristic
202#376C2×D6111yescharacteristic
203#335—1221no—
204#334—1221no—
205#330—1222no—
206#329—1222no—
207#328—1222no—
208#327—1222no—
209C61#976111yescharacteristic, complemented, Sylow
210C2×#41—1221no—
211C2×SD16—1221no—
212C2×SD16—1221no—
213C22×C8—21no—
214C22×C8C22⋊D6111yescharacteristic
215C22×C8C22⋊D6111yescharacteristic
216C4⋊Q8—611no—
217C4⋊Q8—611no—
218C4⋊Q8—611no—
219#127—611no—
220#125—1221no—
221#124—1221no—
222C22⋊Q8—1221no—
223C22⋊Q8—1221no—
224#121—1221no—
225#121—1221no—
226C4×Q8—1221no—
227C4×Q8—1221no—
228C4×D4—1221no—
229C4×D4—1221no—
230#117—1221no—
231C2×C42—21no—
232C2×C42C22×D6111yescharacteristic
233#106—1221no—
234#106—1221no—
235C4⋊C8—1221no—
236C4⋊C8—1221no—
237#103—1221no—
238#103—1221no—
239#102—1221no—
240#102—1221no—
241C22⋊C8—1221no—
242C22⋊C8—1221no—
243#97—24no—
244#97—21no—
245#97—1221no—
246#97—1221no—
247#97D24412yes—
248C4×C8—24no—
249C4×C8C4×D6111yescharacteristic
250C4×C8C4×D6111yescharacteristic
251C4×C8D24411yescharacteristic
252C4×C8D24411yescharacteristic
253#95—21no—
254#95D24412yes—
255#41—4882no—
256C2×Q8—1221no—
257C2×Q8—1221no—
258C2×Q8—1221no—
259C2×D4—1221no—
260C2×D4—1221no—
261C2×D4—1221no—
262C2×D4—2441no—
263C22×C4—22no—
264C22×C4—2441no—
265C22×C4C2×D24411yescharacteristic
266C22×C4#1175822211yescharacteristic
267C22×C4C2×C22⋊D6111yescharacteristic
268SD16—2442no—
269SD16—2442no—
270C2×C8—22no—
271C2×C8—22no—
272C2×C8—22no—
273C2×C8—22no—
274C2×C8—22no—
275C2×C8—2441no—
276C2×C8—2441no—
277C2×C8#1175819811yescharacteristic
278C2×C8#1175819811yescharacteristic
279C2×C8#1175819811yescharacteristic
280C2×C8#1175819811yescharacteristic
281C4⋊C4—1221no—
282C4⋊C4—1221no—
283C4⋊C4—1221no—
284C4⋊C4—1221no—
285C4⋊C4—1221no—
286C4⋊C4—1221no—
287C4⋊C4—2441no—
288C4⋊C4—2441no—
289C22⋊C4—2441no—
290C22⋊C4—2441no—
291C22⋊C4—2441no—
292C42—22no—
293C42—22no—
294C42—2441no—
295C42C2×C4×D6111yescharacteristic
296C42C2×D24411yescharacteristic
297C42C2×D24411yescharacteristic
298C42#1175822211yescharacteristic
299C23—2441no—
300C23#1451975111yescharacteristic
301Q8—4881no—
302Q8—4881no—
303Q8—2441no—
304Q8—2441no—
305D4—4881no—
306D4—4881no—
307D4—4882no—
308D4—2441no—
309D4—2441no—
310C2×C4—22no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—24no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—4882no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4C2×#1175819811yescharacteristic
322C2×C4C4×D24411yescharacteristic
323C2×C4C4×D24411yescharacteristic
324C2×C4#1451975111yescharacteristic
325C2×C4#1451976511yescharacteristic
326C2×C4#1451977411yescharacteristic
327C8—24no—
328C8—21no—
329C8—21no—
330C8—4881no—
331C8—4881no—
332C8#1451970512yes—
333C8#1451970512yes—
334C22—21no—
335C22—21no—
336C22—4881no—
337C22—4881no—
338C22—4881no—
339C22#1683966411yescharacteristic
340C22#1684002512yes—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—44no—
347C4—4881no—
348C4—4881no—
349C4—4881no—
350C4C2×#1451970511yescharacteristic
351C4C2×#1451970511yescharacteristic
352C2—22no—
353C2—9761no—
354C2#2144664711yescharacteristic
355C2#2144671711yescharacteristic
356C2#2144672211yescharacteristic
subgroupG/H
centerC22#16839664
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1726C2
socleC22×C61#390
prime radical#16840312C22
cosocleC2×C42×C61C23
hypercenter#1726D61
hypocenterC61#9761
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1726

Complements

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

NH ≅ G/Ntype
2. #21444582C2semidirect
3. #21444433C2semidirect
5. #21444330C2semidirect
7. C61×#1726C2semidirect
10. #16840160C4semidirect
11. #16840135C4semidirect
12. #16840113C4semidirect
13. #16840109C4semidirect
175. #1726D61semidirect
209. C61#9761semidirect

Maximal subgroups

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

subgroupindex
#214563782
#214445822
#214444332
#214444292
#214443302
#214443262
C61×#17262
#976161