Finite Group Databasebeta

← #29584768

Subgroups — #29584768

Order 15616.

402 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21446613C211yesmaximal, characteristic
2#21445816C211yesmaximal, characteristic
3#21445816C211yesmaximal, characteristic
4#21443702C211yesmaximal, characteristic, complemented
5#21443702C211yesmaximal, characteristic, complemented
6#21443654C211yesmaximal, characteristic, complemented
7C61×#1834C211yesmaximal, characteristic, complemented
8C2×C4×D244C2211yescharacteristic
9C2×C4⋊#92418C2211yescharacteristic
10C2×C4⋊#92418C2211yescharacteristic
11C2×C4⋊#92418C2211yescharacteristic
12C2×#14519697—21no—
13C2×#14519697—21no—
14C2×#14519689—21no—
15C2×#14519689—21no—
16#16839524—21no—
17#16839524—21no—
18C2×C4×C8×C61C2211yescharacteristic
19C61×#384C2211yescharacteristic
20C61×#384C2211yescharacteristic
21C61×#340—21no—
22C61×#340—21no—
23C22×D244D411yescharacteristic
24C22×C4×D61—21no—
25C22×#92418—21no—
26C22×#92418—21no—
27C22×#92418—21no—
28C4×D244—21no—
29C4×D244—21no—
30C4×D244—21no—
31C4×D244—21no—
32C2×C4⋊Dic61D411yescharacteristic
33C2×#11758198—21no—
34C4⋊#92418—21no—
35C4⋊#92418—21no—
36C4⋊#92418—21no—
37C4⋊#92418—21no—
38C4⋊#92418—21no—
39C4⋊#92418—21no—
40#14519697—42no—
41#14519697—42no—
42#14519689—42no—
43#14519689—42no—
44C22×C8×C61D411yescharacteristic
45C22×C8×C61D411yescharacteristic
46C2×C4⋊C4×C61—21no—
47C2×C4⋊C4×C61—21no—
48C2×C4⋊C4×C61—21no—
49C2×C4⋊C4×C61—21no—
50C2×C4⋊C4×C61—21no—
51C2×C4⋊C4×C61—21no—
52C2×C42×C61C2311yescharacteristic
53C4×C8×C61—21no—
54C4×C8×C61—21no—
55C23×D61—21no—
56C22×C4×C61—41no—
57C22×C4×C61—41no—
58C22×C4×C61C2×D411yescharacteristic
59C22×C4×C61C2×D411yescharacteristic
60C22×C4×C61#4111yescharacteristic
61C22×Dic61—21no—
62C2×D244—21no—
63C2×D244—21no—
64C2×D244—21no—
65C2×D244—21no—
66C2×D244—21no—
67C2×D244SD1612yes—
68C2×C4×D61—41no—
69C2×C4×D61—41no—
70C2×C4×D61—41no—
71C2×C4×D61—41no—
72C2×C4×D61—41no—
73C2×C4×D61—41no—
74C2×C8×C61—21no—
75C2×C8×C61—21no—
76C2×C8×C61—21no—
77C2×C8×C61—21no—
78C2×C8×C61—21no—
79C2×C8×C61—21no—
80C4⋊C4×C61—41no—
81C4⋊C4×C61—41no—
82C4⋊C4×C61—41no—
83C4⋊C4×C61—41no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—41no—
86C4⋊C4×C61—41no—
87C4⋊C4×C61—41no—
88C4⋊C4×C61—81no—
89C4⋊C4×C61—81no—
90C42×C61#4111yescharacteristic
91C42×C61#4111yescharacteristic
92C42×C61#4111yescharacteristic
93C42×C61#4111yescharacteristic
94#11758198—41no—
95#11758198—41no—
96C4⋊Dic61—21no—
97C4⋊Dic61—21no—
98C2×#92418—41no—
99C2×#92418—41no—
100C2×#92418—41no—
101C2×#92418—41no—
102C2×#92418—41no—
103C2×#92418—41no—
104C2×#92418—41no—
105C2×#92418—41no—
106C2×#92418—41no—
107C23×C61#12111yescharacteristic
108C22×D61—22no—
109C22×D61—41no—
110C22×D61—41no—
111C22×D61—41no—
112C22×D61—41no—
113C22×D61—41no—
114C22×D61—41no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—81no—
118C2×C4×C61—81no—
119C2×C4×C61—81no—
120C2×C4×C61—81no—
121C2×C4×C61—81no—
122C2×C4×C61—81no—
123C2×C4×C61#12311yescharacteristic
124C2×C4×C61#12311yescharacteristic
125C2×C4×C61#12311yescharacteristic
126C2×C4×C61#12411yescharacteristic
127C2×C4×C61#12611yescharacteristic
128C2×C4×C61#12611yescharacteristic
129C2×C4×C61C2×SD1611yescharacteristic
130C2×C4×C61#13511yescharacteristic
131C2×C4×C61#13511yescharacteristic
132C2×C4×C61#13511yescharacteristic
133C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C61#13711yescharacteristic
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140D244—22no—
141D244—22no—
142D244—41no—
143D244—41no—
144C4×D61—81no—
145C4×D61—81no—
146C4×D61—81no—
147C4×D61—81no—
148C8×C61—41no—
149C8×C61—41no—
150#92418—81no—
151#92418—81no—
152#92418—81no—
153#10625—611nomaximal, Sylow
154C22×C61#39711yescharacteristic
155C22×C61#46311yescharacteristic
156C22×C61#46311yescharacteristic
157C22×C61#46511yescharacteristic
158C22×C61#46811yescharacteristic
159C22×C61#47211yescharacteristic
160C22×C61#47311yescharacteristic
161C2×D61—42no—
162C2×D61—42no—
163C2×D61—42no—
164C2×D61—81no—
165C2×D61—81no—
166C2×D61—81no—
167C2×D61—81no—
168C4×C61—21no—
169C4×C61—21no—
170C4×C61—161no—
171C4×C61—161no—
172C4×C61#48111yescharacteristic
173C4×C61#48211yescharacteristic
174C4×C61#48211yescharacteristic
175C4×C61#48211yescharacteristic
176C4×C61#48311yescharacteristic
177C4×C61#48511yescharacteristic
178C4×C61#48811yescharacteristic
179C4×C61#49011yescharacteristic
180Dic61—81no—
181#1954—611no—
182#1834D6111yescharacteristic, complemented
183#1802—611no—
184#1802—611no—
185#1296—611no—
186#1296—611no—
187#1277—611no—
188C2×C61#167711yescharacteristic
189C2×C61#167911yescharacteristic
190C2×C61#169711yescharacteristic
191C2×C61#169911yescharacteristic
192C2×C61#207311yescharacteristic
193C2×C61#207711yescharacteristic
194C2×C61#207811yescharacteristic
195D61—82no—
196C2×C4×D4—611no—
197C2×C4⋊C8—611no—
198C2×C4⋊C8—611no—
199C2×C4⋊C8—611no—
200C2×#102—1221no—
201C2×#102—1221no—
202C2×C22⋊C8—1221no—
203C2×C22⋊C8—1221no—
204C2×C4×C8C2×D6111yescharacteristic
205#384C2×D6111yescharacteristic
206#384C2×D6111yescharacteristic
207#340—21no—
208#340—21no—
209#340—1221no—
210#340—1221no—
211C61#1062511yescharacteristic, complemented, Sylow
212C22×D4—611no—
213C23×C4—1221no—
214C22×C8—1221no—
215C22×C8—1221no—
216C22×C8—1221no—
217C22×C8C22⋊D6111yescharacteristic
218C22×C8C22⋊D6111yescharacteristic
219C4×D4—1221no—
220C4×D4—1221no—
221C4×D4—1221no—
222C4×D4—1221no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—611no—
230C2×C22⋊C4—1221no—
231C2×C42C22×D6111yescharacteristic
232C4⋊C8—1221no—
233C4⋊C8—1221no—
234C4⋊C8—1221no—
235C4⋊C8—1221no—
236C4⋊C8—1221no—
237C4⋊C8—1221no—
238#102—2442no—
239#102—2442no—
240C22⋊C8—2442no—
241C22⋊C8—2442no—
242C4×C8—21no—
243C4×C8—21no—
244C24—1221no—
245C2×D4—612no—
246C2×D4—1221no—
247C2×D4—1221no—
248C2×D4—1221no—
249C2×D4—1221no—
250C2×D4—1221no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—1221no—
254C22×C4—2441no—
255C22×C4—2441no—
256C22×C4—2441no—
257C22×C4—2441no—
258C22×C4—2441no—
259C22×C4—2441no—
260C22×C4D4×D6111yescharacteristic
261C22×C4#1175822411yescharacteristic
262C22×C4C2×C22⋊D6111yescharacteristic
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—21no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—21no—
269C2×C8—2441no—
270C2×C8—2441no—
271C2×C8—2441no—
272C2×C8—2441no—
273C2×C8—2441no—
274C2×C8—2441no—
275C2×C8—2441no—
276C2×C8—2441no—
277C2×C8—2441no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—81no—
287C4⋊C4—81no—
288C4⋊C4—1221no—
289C4⋊C4—1221no—
290C22⋊C4—2441no—
291C22⋊C4—2441no—
292C42#1175822211yescharacteristic
293C42#1175822211yescharacteristic
294C42#1175822611yescharacteristic
295C42#1175822611yescharacteristic
296C23—1222no—
297C23—2441no—
298C23—2441no—
299C23—2441no—
300C23—2441no—
301C23—2441no—
302C23—2441no—
303C23#1451974811yescharacteristic
304D4—1222no—
305D4—1222no—
306D4—2441no—
307D4—2441no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—4881no—
317C2×C4—4881no—
318C2×C4—4881no—
319C2×C4—4881no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4#1451976011yescharacteristic
324C2×C4#1451976211yescharacteristic
325C2×C4#1451976211yescharacteristic
326C2×C4#1451976611yescharacteristic
327C2×C4#1451977211yescharacteristic
328C2×C4#1451977211yescharacteristic
329C2×C4SD16×D6111yescharacteristic
330C2×C4#1451979711yescharacteristic
331C2×C4#1451979711yescharacteristic
332C2×C4#1451979811yescharacteristic
333C2×C4#1451980211yescharacteristic
334C2×C4#1451980211yescharacteristic
335C2×C4#1451980411yescharacteristic
336C2×C4#1451980611yescharacteristic
337C8—41no—
338C8—41no—
339C8—4881no—
340C8—4881no—
341C8—4881no—
342C22—4881no—
343C22—4881no—
344C22—4881no—
345C22—4881no—
346C22—2442no—
347C22—2442no—
348C22—2442no—
349C22#1683968811yescharacteristic
350C22#1683997411yescharacteristic
351C22#1683997411yescharacteristic
352C22#1683998811yescharacteristic
353C22#1684000511yescharacteristic
354C22#1684002911yescharacteristic
355C22#1684003411yescharacteristic
356C4—21no—
357C4—21no—
358C4—161no—
359C4—161no—
360C4—4881no—
361C4#1684008211yescharacteristic
362C4#1684008611yescharacteristic
363C4#1684008611yescharacteristic
364C4#1684008811yescharacteristic
365C4#1684009411yescharacteristic
366C4#1684010611yescharacteristic
367C4#1684011911yescharacteristic
368C4#1684012811yescharacteristic
369C2—4882no—
370C2#2144522511yescharacteristic
371C2#2144523911yescharacteristic
372C2#2144534911yescharacteristic
373C2#2144536311yescharacteristic
374C2#2144723311yescharacteristic
375C2#2144725311yescharacteristic
376C2#2144726011yescharacteristic
subgroupG/H
centerC23#14519748
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1834C2
socleC23×C61#121
prime radicalC22×D244D4
hypercenter#1834D61
hypocenterC61#10625
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1834

Complements

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

NH ≅ G/Ntype
4. #21443702C2semidirect
5. #21443702C2semidirect
6. #21443654C2semidirect
7. C61×#1834C2semidirect
182. #1834D61semidirect
211. C61#10625semidirect

Maximal subgroups

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

subgroupindex
#214466132
#214458162
#214437022
#214436542
C61×#18342
#1062561