Finite Group Databasebeta

← #29567136

Subgroups — #29567136

Order 15616.

464 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839488C211yesmaximal, characteristic
2#21444072C211yesmaximal, characteristic
3C2×C61×#343C211yesmaximal, characteristic
4C22×C4⋊Dic61C411yescharacteristic
5C2×C22⋊#92418—21no—
6C2×#14519684—21no—
7C2×#14519684—21no—
8C2×#14519684C411yescharacteristic
9#16839488—21no—
10#16839488C412yescomplemented
11C22×M16×C61—21no—
12C22×C4⋊C4×C61C2211yescharacteristic
13C61×#343—21no—
14C61×#343C412yescomplemented
15C23×Dic61—21no—
16C23×Dic61—21no—
17C22×#92418—41no—
18C2×C4⋊Dic61—41no—
19C2×C4⋊Dic61—42no—
20C22⋊#92418—22no—
21C22⋊#92418—41no—
22#14519684—42no—
23#14519684—41no—
24#14519684—41no—
25#14519684—41no—
26C23×C4×C61C2×C411yescharacteristic
27C23×C4×C61D411yescharacteristic
28C23×C4×C61D411yescharacteristic
29C2×M16×C61—22no—
30C2×M16×C61—22no—
31C2×M16×C61—22no—
32C2×M16×C61—41no—
33C2×M16×C61—41no—
34C2×M16×C61—41no—
35C22×C8×C61—41no—
36C2×C4⋊C4×C61—41no—
37C2×C4⋊C4×C61—41no—
38C2×C4⋊C4×C61C2×C411yescharacteristic
39C2×C4⋊C4×C61C2×C411yescharacteristic
40C2×C4⋊C4×C61D411yescharacteristic
41C2×C4⋊C4×C61Q811yescharacteristic
42C24×C61C22⋊C411yescharacteristic
43C22×C4×C61—21no—
44C22×C4×C61—21no—
45C22×C4×C61—21no—
46C22×C4×C61—21no—
47C22×C4×C61—21no—
48C22×C4×C61—21no—
49C22×C4×C61—21no—
50C22×C4×C61—21no—
51C22×C4×C61—41no—
52C22×C4×C61—41no—
53C22×C4×C61—41no—
54C22×C4×C61—41no—
55C22×C4×C61C4211yescharacteristic
56C22×C4×C61C22⋊C411yescharacteristic
57C22×C4×C61C22⋊C411yescharacteristic
58C22×C4×C61C4⋊C411yescharacteristic
59C22×C4×C61C4⋊C411yescharacteristic
60C22×C4×C61C4⋊C411yescharacteristic
61C22×C4×C61D811yescharacteristic
62C22×C4×C61SD1611yescharacteristic
63C22×C4×C61SD1611yescharacteristic
64C22×C4×C61Q1611yescharacteristic
65C22×Dic61—22no—
66C22×Dic61—22no—
67C22×Dic61—41no—
68C22×Dic61—41no—
69C22×Dic61—41no—
70C22×Dic61—41no—
71C22×Dic61—41no—
72C22×Dic61—41no—
73C22×Dic61—41no—
74C22×Dic61—41no—
75C22×Dic61—41no—
76C22×Dic61—41no—
77C22×Dic61—41no—
78C22×Dic61—41no—
79M16×C61—24no—
80M16×C61—42no—
81M16×C61—42no—
82M16×C61—42no—
83C2×C8×C61—42no—
84C2×C8×C61—42no—
85C2×C8×C61—42no—
86C4⋊C4×C61—41no—
87C4⋊C4×C61—41no—
88C4⋊C4×C61—41no—
89C4⋊C4×C61—41no—
90C4⋊Dic61—42no—
91C4⋊Dic61—42no—
92C2×#92418—42no—
93C2×#92418—81no—
94C2×#92418—81no—
95C23×C61—21no—
96C23×C61—21no—
97C23×C61—21no—
98C23×C61—21no—
99C23×C61#9511yescharacteristic
100C23×C61#9911yescharacteristic
101C23×C61#9911yescharacteristic
102C23×C61#10211yescharacteristic
103C23×C61#10311yescharacteristic
104C23×C61#10411yescharacteristic
105C23×C61#10411yescharacteristic
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—42no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—81no—
132C2×C4×C61#10211yescharacteristic
133C2×C4×C61#10311yescharacteristic
134C2×C4×C61#10611yescharacteristic
135C2×C4×C61#10711yescharacteristic
136C2×Dic61—42no—
137C2×Dic61—42no—
138C2×Dic61—42no—
139C2×Dic61—42no—
140C2×Dic61—42no—
141C2×Dic61—42no—
142C2×Dic61—81no—
143C2×Dic61—81no—
144C2×Dic61—81no—
145C2×Dic61—81no—
146C2×Dic61—81no—
147C2×Dic61—81no—
148C2×Dic61—81no—
149C2×Dic61—81no—
150C8×C61—44no—
151#92418—82no—
152#7251—611nomaximal, Sylow
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—21no—
164C22×C61—21no—
165C22×C61#32711yescharacteristic
166C22×C61#32711yescharacteristic
167C22×C61#32811yescharacteristic
168C22×C61#32811yescharacteristic
169C22×C61#33911yescharacteristic
170C22×C61#34011yescharacteristic
171C22×C61#34211yescharacteristic
172C22×C61AΣL(1,𝔽16)11yescharacteristic
173C22×C61#35211yescharacteristic
174C22×C61#35511yescharacteristic
175C22×C61#35611yescharacteristic
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—41no—
181C4×C61—41no—
182C4×C61—41no—
183C4×C61—41no—
184Dic61—82no—
185Dic61—82no—
186C2×#343D6111yescharacteristic
187C2×#324—611no—
188#1441—611no—
189C2×C61—21no—
190C2×C61—21no—
191C2×C61—21no—
192C2×C61—21no—
193C2×C61#129411yescharacteristic
194C2×C61#134511yescharacteristic
195C2×C61#134611yescharacteristic
196C2×C61#135311yescharacteristic
197C2×C61#135411yescharacteristic
198C2×C61#139011yescharacteristic
199C2×C61#139411yescharacteristic
200C22×M16—21no—
201C22×C4⋊C4—611no—
202C22×C4⋊C4C2×D6111yescharacteristic
203C2×C22⋊C8—1221no—
204C2×#95—611no—
205C2×#95—1221no—
206C2×#95—1221no—
207#343—21no—
208#343Dic6112yescomplemented
209#324—612no—
210#324—1221no—
211C61#725111yescharacteristic, complemented, Sylow
212C23×C4—1221no—
213C23×C4—1221no—
214C23×C4C4×D6111yescharacteristic
215C23×C4D24411yescharacteristic
216C23×C4C22⋊D6111yescharacteristic
217C2×M16—22no—
218C2×M16—22no—
219C2×M16—22no—
220C2×M16—41no—
221C2×M16—41no—
222C2×M16—41no—
223C22×C8—41no—
224C22×C8—2441no—
225C2×C4⋊C4—41no—
226C2×C4⋊C4—41no—
227C2×C4⋊C4—2441no—
228C2×C4⋊C4—2442no—
229C2×C4⋊C4Dic12211yescharacteristic
230C2×C4⋊C4C4×D6111yescharacteristic
231C2×C4⋊C4C2×Dic6111yescharacteristic
232C2×C4⋊C4C22⋊D6111yescharacteristic
233C22⋊C8—1222no—
234C22⋊C8—2441no—
235#95—2441no—
236#95—2442no—
237#95—2441no—
238#95—2441no—
239C24#1175819811yescharacteristic
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—1222no—
253C22×C4—1222no—
254C22×C4—2441no—
255C22×C4—2441no—
256C22×C4—2441no—
257C22×C4—2441no—
258C22×C4—2441no—
259C22×C4—2441no—
260C22×C4—2441no—
261C22×C4—2441no—
262C22×C4—2441no—
263C22×C4—2441no—
264C22×C4—2441no—
265C22×C4—2441no—
266C22×C4C4×Dic6111yescharacteristic
267C22×C4#1175819611yescharacteristic
268C22×C4#1175819611yescharacteristic
269C22×C4C4⋊Dic6111yescharacteristic
270C22×C4#1175819811yescharacteristic
271C22×C4#1175819911yescharacteristic
272C22×C4#1175820011yescharacteristic
273C22×C4#1175820111yescharacteristic
274C22×C4#1175820211yescharacteristic
275C22×C4C22⋊Dic6111yescharacteristic
276M16—24no—
277M16—42no—
278M16—42no—
279M16—42no—
280C2×C8—42no—
281C2×C8—42no—
282C2×C8—42no—
283C2×C8—4881no—
284C2×C8—4881no—
285C2×C8—2442no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—2442no—
291C4⋊C4—2442no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23#1451968411yescharacteristic
297C23#1451969111yescharacteristic
298C23#1451969111yescharacteristic
299C23#1451969711yescharacteristic
300C23#1451970011yescharacteristic
301C23#1451970511yescharacteristic
302C23#1451970511yescharacteristic
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—42no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—81no—
329C2×C4—4881no—
330C2×C4—4881no—
331C2×C4—4881no—
332C2×C4—4881no—
333C2×C4—4881no—
334C2×C4—4881no—
335C2×C4—4881no—
336C2×C4—4881no—
337C2×C4—2442no—
338C2×C4—2442no—
339C2×C4—2442no—
340C2×C4—2442no—
341C2×C4—2442no—
342C2×C4—2442no—
343C2×C4#1451969811yescharacteristic
344C2×C4#1451970111yescharacteristic
345C2×C4#1451970811yescharacteristic
346C2×C4#1451971011yescharacteristic
347C8—44no—
348C8—4882no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22#1683949511yescharacteristic
362C22#1683949511yescharacteristic
363C22#1683949811yescharacteristic
364C22#1683949811yescharacteristic
365C22#1683952211yescharacteristic
366C22#1683952411yescharacteristic
367C22#1683952811yescharacteristic
368C22#1683955011yescharacteristic
369C22#1683955311yescharacteristic
370C22#1683955811yescharacteristic
371C22#1683956011yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—4882no—
381C4—4882no—
382C2—21no—
383C2—21no—
384C2—21no—
385C2—21no—
386C2#2144369811yescharacteristic
387C2#2144382111yescharacteristic
388C2#2144382411yescharacteristic
389C2#2144384511yescharacteristic
390C2#2144384811yescharacteristic
391C2#2144393811yescharacteristic
392C2#2144394511yescharacteristic
subgroupG/H
centerC23#14519691
commutatorC22×C4×C61C42
FrattiniC22×C4⋊C4C2×D61
FittingC2×C61×#343C2
socleC23×C61#99
prime radicalC24×C61C22⋊C4
cosocleC22×C4⋊C4×C61C22
hypercenterC2×#343D61
hypocenterC61#7251
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C24 ◁ C22×C4⋊C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
10. #16839488C4semidirect
14. C61×#343C4semidirect
208. #343Dic61semidirect
211. C61#7251semidirect

Maximal subgroups

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

subgroupindex
C2×#168394882
#214440722
C2×C61×#3432
#725161