Finite Group Databasebeta

← #29596317

Subgroups — #29596317

Order 15616.

420 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#427×D61C211yesmaximal, characteristic
2#21447429C211yesmaximal, characteristic
3#21445841C211yesmaximal, characteristic
4#21443926C211yesmaximal, characteristic, complemented
5#21443925C211yesmaximal, characteristic, complemented
6#21443924C211yesmaximal, characteristic, complemented
7C61×#1386C211yesmaximal, characteristic, complemented
8C22×C8×D61C2211yescharacteristic
9#117×D61—21no—
10C2×#14519717C2211yescharacteristic
11#16839800C2211yescharacteristic
12#16839799C411yescharacteristic, complemented
13#16839799C411yescharacteristic, complemented
14#16839798—21no—
15#16839797—21no—
16#107×D61C411yescharacteristic, complemented
17#107×D61C411yescharacteristic, complemented
18C2×#14519709C2211yescharacteristic
19#106×D61—21no—
20#16839619—21no—
21#16839541—21no—
22#16839541—21no—
23#16839524—21no—
24C2×M32×C61C2211yescharacteristic
25C61×#427C2211yescharacteristic
26C2×#106×C61C2211yescharacteristic
27C22×C4×D61D411yescharacteristic
28C22×#92418D411yescharacteristic
29C2×C8×D61—21no—
30C2×C8×D61—21no—
31C2×C8×D61—21no—
32C2×C8×D61—21no—
33C2×C8×D61C2×C411yescharacteristic
34C2×C8×D61C2×C411yescharacteristic
35C2×C8×D61D411yescharacteristic
36C2×C8×D61D411yescharacteristic
37#14519736—21no—
38#14519735—21no—
39#14519735—21no—
40#14519734—41no—
41#14519733—41no—
42C2×C4⋊Dic61—21no—
43C4⋊C4×D61—21no—
44C4⋊C4×D61—21no—
45C2×#11758198—41no—
46C22⋊C4×D61—41no—
47C42×D61—41no—
48#14519717—21no—
49#14519717—21no—
50C2×#11758185—21no—
51#14519711C2×C411yescharacteristic
52#14519711C2×C411yescharacteristic
53#14519710—21no—
54#14519710—21no—
55#14519709—21no—
56#14519709—21no—
57#14519709—21no—
58#14519708—21no—
59#14519708—21no—
60#14519684—41no—
61C22×C8×C61C2311yescharacteristic
62#117×C61—21no—
63C2×C4⋊C4×C61—21no—
64M32×C61—21no—
65M32×C61—21no—
66C2×C16×C61—21no—
67#107×C61C2×C411yescharacteristic
68#107×C61C2×C411yescharacteristic
69#106×C61—21no—
70#106×C61—21no—
71#106×C61—21no—
72C23×D61D811yescharacteristic
73C22×C4×C61—41no—
74C22×C4×C61C2×D411yescharacteristic
75C22×Dic61—41no—
76C22×Dic61D811yescharacteristic
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—41no—
82C2×C4×D61—41no—
83C2×C4×D61C22⋊C411yescharacteristic
84C2×C4×D61C22⋊C411yescharacteristic
85C2×C4×D61SD1611yescharacteristic
86C2×C4×D61SD1611yescharacteristic
87C2×C8×C61C22×C411yescharacteristic
88C2×C8×C61C2×D411yescharacteristic
89C2×C8×C61#4111yescharacteristic
90C2×C8×C61#4111yescharacteristic
91C2×C8×C61#4111yescharacteristic
92C2×C8×C61#4111yescharacteristic
93C4⋊C4×C61—21no—
94C4⋊C4×C61—21no—
95C4⋊C4×C61—41no—
96C4⋊C4×C61—41no—
97C22⋊C4×C61—41no—
98C42×C61—41no—
99C22⋊Dic61—41no—
100#11758198—41no—
101#11758198—41no—
102#11758198—82no—
103C4⋊Dic61—21no—
104C4⋊Dic61—21no—
105C4⋊Dic61—41no—
106C4⋊Dic61—41no—
107#11758196—41no—
108#11758196—41no—
109C4×Dic61—41no—
110C4×Dic61—41no—
111C4×Dic61—41no—
112C2×#92418—21no—
113C2×#92418—21no—
114C2×#92418C22⋊C411yescharacteristic
115C2×#92418C22⋊C411yescharacteristic
116C8×D61—21no—
117C8×D61—21no—
118C8×D61—21no—
119C8×D61—21no—
120C8×D61—21no—
121C8×D61—21no—
122C8×D61—21no—
123C8×D61—21no—
124C16×C61—41no—
125#11758185—41no—
126C23×C61C2×D811yescharacteristic
127C22×D61—21no—
128C22×D61—21no—
129C22×D61—22no—
130C22×D61—41no—
131C22×D61#10211yescharacteristic
132C22×D61#10211yescharacteristic
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—81no—
136C2×C4×C61—81no—
137C2×C4×C61—81no—
138C2×C4×C61C2×C22⋊C411yescharacteristic
139C2×C4×C61#12311yescharacteristic
140C2×C4×C61#12311yescharacteristic
141C2×C4×C61C2×SD1611yescharacteristic
142C2×C4×C61#13711yescharacteristic
143C2×C4×C61#13711yescharacteristic
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—81no—
149C2×Dic61—81no—
150C2×Dic61—81no—
151C2×Dic61#10211yescharacteristic
152C2×Dic61#10211yescharacteristic
153C4×D61—21no—
154C4×D61—21no—
155C4×D61—21no—
156C4×D61—21no—
157C4×D61—21no—
158C4×D61—21no—
159C4×D61—21no—
160C4×D61—21no—
161C4×D61—82no—
162C4×D61—82no—
163C8×C61#11711yescharacteristic
164C8×C61#11711yescharacteristic
165C8×C61#12311yescharacteristic
166C8×C61#12311yescharacteristic
167#92418—21no—
168#92418—21no—
169#12870—611nomaximal, Sylow
170C22×C61—21no—
171C22×C61—21no—
172C22×C61C2×#10211yescharacteristic
173C22×C61#48011yescharacteristic
174C22×C61#48011yescharacteristic
175C2×D61—21no—
176C2×D61—21no—
177C2×D61—21no—
178C2×D61—21no—
179C2×D61—21no—
180C2×D61—42no—
181C2×D61—42no—
182C2×D61#36012yes—
183C4×C61—81no—
184C4×C61—81no—
185C4×C61—161no—
186C4×C61#38111yescharacteristic
187C4×C61#41911yescharacteristic
188C4×C61#48311yescharacteristic
189C4×C61#48311yescharacteristic
190Dic61—21no—
191Dic61—21no—
192Dic61—81no—
193Dic61—81no—
194Dic61—161no—
195C2×#427—611no—
196#2112—611no—
197#1807—611no—
198#1386—611no—
199#1386—611no—
200#1386—611no—
201#1386D6111yescharacteristic, complemented
202C2×C61—21no—
203C2×C61—21no—
204C2×C61#182311yescharacteristic
205C2×C61C2×#36011yescharacteristic
206C2×C61#214511yescharacteristic
207D61—22no—
208D61—41no—
209C23×C8—611no—
210C2×#117—1221no—
211C2×M32—611no—
212C2×M32C2×D6111yescharacteristic
213#427—611no—
214#427—611no—
215#427—611no—
216#427—1221no—
217#427—1221no—
218#427C2×D6111yescharacteristic
219C2×#107—611no—
220C2×#107—611no—
221C2×#106—611no—
222C2×#106—1221no—
223C2×#106C2×D6111yescharacteristic
224#380—1221no—
225C22⋊C16—1221no—
226C22⋊C16—1221no—
227#340—1221no—
228C61#1287011yescharacteristic, complemented, Sylow
229C23×C4—611no—
230C22×C8—611no—
231C22×C8—611no—
232C22×C8—611no—
233C22×C8—611no—
234C22×C8—611no—
235C22×C8—1221no—
236C22×C8—1221no—
237C22×C8—1221no—
238C22×C8—1221no—
239C22×C8C22×D6111yescharacteristic
240#117—21no—
241#117—1221no—
242#117—1221no—
243#117—1221no—
244#117—2441no—
245#117—2441no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—1221no—
248C2×C4⋊C4—1221no—
249C2×C4⋊C4—1221no—
250C2×C22⋊C4—2441no—
251C2×C22⋊C4—2441no—
252C2×C42—2441no—
253M32—21no—
254M32—21no—
255M32—1221no—
256M32—1221no—
257C2×C16—21no—
258C2×C16—1221no—
259#107—611no—
260#107—611no—
261#107—1221no—
262#107—1221no—
263#107C4×D6111yescharacteristic
264#107C4×D6111yescharacteristic
265#106—21no—
266#106—21no—
267#106—21no—
268#106—1221no—
269#106—1221no—
270#106—1221no—
271#106—1221no—
272#106—1221no—
273#95—2441no—
274C24—611no—
275C22×C4—41no—
276C22×C4—611no—
277C22×C4—611no—
278C22×C4—611no—
279C22×C4—611no—
280C22×C4—611no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4—1221no—
285C22×C4—2441no—
286C22×C4—2441no—
287C22×C4—2441no—
288C22×C4D4×D6111yescharacteristic
289C2×C8—611no—
290C2×C8—611no—
291C2×C8—1221no—
292C2×C8—1221no—
293C2×C8—1221no—
294C2×C8—1221no—
295C2×C8—1221no—
296C2×C8—1221no—
297C2×C8—1221no—
298C2×C8—1221no—
299C2×C8—1221no—
300C2×C8—1221no—
301C2×C8C2×C4×D6111yescharacteristic
302C2×C8#1175822211yescharacteristic
303C2×C8#1175822211yescharacteristic
304C2×C8D4×D6111yescharacteristic
305C2×C8#1175822411yescharacteristic
306C2×C8#1175822611yescharacteristic
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—1221no—
312C4⋊C4—1221no—
313C4⋊C4—2441no—
314C4⋊C4—2441no—
315C4⋊C4—2441no—
316C4⋊C4—2441no—
317C22⋊C4—41no—
318C22⋊C4—4882no—
319C22⋊C4—2441no—
320C22⋊C4—2441no—
321C22⋊C4—2441no—
322C42—41no—
323C42—2441no—
324C42—2441no—
325C42—2441no—
326C16—41no—
327C16—2441no—
328C23—611no—
329C23—611no—
330C23—1222no—
331C23—1221no—
332C23—1221no—
333C23—2441no—
334C23D8×D6111yescharacteristic
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—611no—
341C2×C4—611no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—4882no—
353C2×C4—4882no—
354C2×C4—4881no—
355C2×C4—4881no—
356C2×C4—4881no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4C22⋊C4×D6111yescharacteristic
360C2×C4#1451975911yescharacteristic
361C2×C4#1451976211yescharacteristic
362C2×C4SD16×D6111yescharacteristic
363C2×C4#1451980611yescharacteristic
364C2×C4#1451980911yescharacteristic
365C8—1221no—
366C8—1221no—
367C8#1451973411yescharacteristic
368C8#1451973511yescharacteristic
369C8#1451975911yescharacteristic
370C8#1451976211yescharacteristic
371C22—21no—
372C22—21no—
373C22—612no—
374C22—1221no—
375C22—1221no—
376C22—1221no—
377C22—1221no—
378C22—1221no—
379C22—2442no—
380C22—2442no—
381C22#102×D6111yescharacteristic
382C22#1684007411yescharacteristic
383C22#1684007711yescharacteristic
384C4—81no—
385C4—81no—
386C4—161no—
387C4—1221no—
388C4—1221no—
389C4—9761no—
390C4—4881no—
391C4—4881no—
392C4#1683962411yescharacteristic
393C4#1683976911yescharacteristic
394C4#1684009111yescharacteristic
395C4#1684009411yescharacteristic
396C2—21no—
397C2—21no—
398C2—1222no—
399C2—2441no—
400C2#2144590411yescharacteristic
401C2#360×D6111yescharacteristic
402C2#2144755311yescharacteristic
subgroupG/H
centerC22#102×D61
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC61×#1386C2
socleC22×C61C2×#102
prime radicalC23×D61D8
cosocleC22×C8×C61C23
hypercenter#1386D61
hypocenterC61#12870
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1386

Complements

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

NH ≅ G/Ntype
4. #21443926C2semidirect
5. #21443925C2semidirect
6. #21443924C2semidirect
7. C61×#1386C2semidirect
12. #16839799C4semidirect
13. #16839799C4semidirect
16. #107×D61C4semidirect
17. #107×D61C4semidirect
201. #1386D61semidirect
228. C61#12870semidirect

Maximal subgroups

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

subgroupindex
#427×D612
#214474292
#214458412
#214439262
#214439252
#214439242
C61×#13862
#1287061