Finite Group Databasebeta

← #29578355

Subgroups — #29578355

Order 15616.

398 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21446780C211yesmaximal, characteristic
2#21446741C211yesmaximal, characteristic
3#21446583C211yesmaximal, characteristic
4C8×C4⋊Dic61C211yesmaximal, characteristic
5C2×#16839509C211yesmaximal, characteristic
6#21443703C211yesmaximal, characteristic
7C61×#1277C211yesmaximal, characteristic
8C2×#14519777C2211yescharacteristic
9C2×#14519709—21no—
10C2×C4⋊#92418C2211yescharacteristic
11C2×#14519702—21no—
12C2×#14519702—21no—
13C2×C8×Dic61—21no—
14#16839632C2211yescharacteristic
15C4×C4⋊Dic61C2211yescharacteristic
16#16839525—21no—
17#16839525—21no—
18#16839525—21no—
19#16839516—21no—
20#16839509C414yescomplemented
21C2×C4⋊C8×C61C2211yescharacteristic
22C2×C4⋊C8×C61C2211yescharacteristic
23C2×C4×C8×C61C2211yescharacteristic
24C22×Dic122—21no—
25C22×#92418—21no—
26#14519777—21no—
27#14519777—21no—
28#14519777—21no—
29#14519777C2×C412yes—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61D411yescharacteristic
36C2×C4⋊Dic61D411yescharacteristic
37C2×C4×Dic61—21no—
38#14519709—42no—
39C4⋊#92418—21no—
40C4⋊#92418C2×C412yes—
41#14519702—42no—
42#14519702—42no—
43C8×Dic61—42no—
44#14519684—21no—
45C22×C8×C61—21no—
46C22×C8×C61—21no—
47C22×C8×C61D411yescharacteristic
48C22×C8×C61D411yescharacteristic
49C2×C42×C61C2311yescharacteristic
50C4⋊C8×C61—21no—
51C4⋊C8×C61—21no—
52C4⋊C8×C61—21no—
53C4⋊C8×C61C2×C412yes—
54C4×C8×C61—21no—
55C4×C8×C61—21no—
56C22×C4×C61C2×D411yescharacteristic
57C22×C4×C61C2×D411yescharacteristic
58C22×C4×C61#4111yescharacteristic
59C22×Dic61—21no—
60C22×Dic61—21no—
61C22×Dic61—41no—
62C22×Dic61—41no—
63C2×Dic122—22no—
64C2×Dic122—41no—
65C2×Dic122—41no—
66C2×Dic122—41no—
67C2×Dic122—41no—
68C2×Dic122—41no—
69C2×C8×C61—21no—
70C2×C8×C61—21no—
71C2×C8×C61—22no—
72C2×C8×C61—21no—
73C2×C8×C61—21no—
74C2×C8×C61—21no—
75C2×C8×C61—41no—
76C2×C8×C61—41no—
77C2×C8×C61—41no—
78C2×C8×C61—41no—
79C2×C8×C61—41no—
80C2×C8×C61SD1612yes—
81C42×C61C22×C411yescharacteristic
82C42×C61#4111yescharacteristic
83C42×C61#4111yescharacteristic
84C42×C61#4111yescharacteristic
85C4⋊Dic61—21no—
86C4⋊Dic61—21no—
87C4⋊Dic61—22no—
88C4⋊Dic61—22no—
89C4⋊Dic61—41no—
90C4⋊Dic61—41no—
91C4⋊Dic61—41no—
92C4⋊Dic61—41no—
93C4⋊Dic61—41no—
94C4⋊Dic61—41no—
95C4⋊Dic61—81no—
96C4⋊Dic61D812yes—
97C4⋊Dic61SD1612yes—
98C4×Dic61—41no—
99C4×Dic61—41no—
100C2×#92418—22no—
101C2×#92418—41no—
102C2×#92418—41no—
103C23×C61#12111yescharacteristic
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61#11711yescharacteristic
107C2×C4×C61C4×D411yescharacteristic
108C2×C4×C61C4×D411yescharacteristic
109C2×C4×C61#12311yescharacteristic
110C2×C4×C61#12411yescharacteristic
111C2×C4×C61#12611yescharacteristic
112C2×C4×C61C2×D811yescharacteristic
113C2×C4×C61C2×SD1611yescharacteristic
114C2×C4×C61C2×SD1611yescharacteristic
115C2×C4×C61#13511yescharacteristic
116C2×C4×C61#13511yescharacteristic
117C2×C4×C61#13511yescharacteristic
118C2×C4×C61#13711yescharacteristic
119C2×C4×C61#13711yescharacteristic
120C2×Dic61—22no—
121C2×Dic61—22no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—42no—
127C2×Dic61—81no—
128C2×Dic61—81no—
129C2×Dic61—81no—
130C2×Dic61—81no—
131C2×Dic61—81no—
132Dic122—42no—
133Dic122—42no—
134Dic122—81no—
135Dic122—81no—
136C8×C61—22no—
137C8×C61—42no—
138C8×C61—41no—
139C8×C61—81no—
140#92418—42no—
141#9565—611nomaximal, Sylow
142C22×C61#38811yescharacteristic
143C22×C61#46111yescharacteristic
144C22×C61#46411yescharacteristic
145C22×C61#46511yescharacteristic
146C22×C61#46611yescharacteristic
147C22×C61#47111yescharacteristic
148C22×C61#47311yescharacteristic
149C4×C61—21no—
150C4×C61—21no—
151C4×C61C4×D811yescharacteristic
152C4×C61C4×SD1611yescharacteristic
153C4×C61C4×SD1611yescharacteristic
154C4×C61#44111yescharacteristic
155C4×C61#48311yescharacteristic
156C4×C61#48511yescharacteristic
157C4×C61#48611yescharacteristic
158C4×C61#48811yescharacteristic
159Dic61—42no—
160Dic61—42no—
161Dic61—82no—
162Dic61—161no—
163#1990—611no—
164#1981—611no—
165#1948—611no—
166C8×C4⋊C4—611no—
167C2×#332—611no—
168#1296—611no—
169#1277D6111yescharacteristic
170C2×C61#167111yescharacteristic
171C2×C61#167311yescharacteristic
172C2×C61#168011yescharacteristic
173C2×C61#168211yescharacteristic
174C2×C61#192711yescharacteristic
175C2×C61#193011yescharacteristic
176C2×C61#193411yescharacteristic
177C2×C4⋊Q8—611no—
178C2×#106—1221no—
179C2×C4⋊C8—611no—
180C2×C4⋊C8C2×D6111yescharacteristic
181C2×C4⋊C8C2×D6111yescharacteristic
182C2×#103—1221no—
183C2×#103—1221no—
184C2×C4×C8—1221no—
185C2×C4×C8C2×D6111yescharacteristic
186#384—611no—
187C4×C4⋊C4—611no—
188#340—1221no—
189#340—1221no—
190#340—1221no—
191#336—1221no—
192#332—614no—
193C61#956511yescharacteristic, complemented, Sylow
194C22×Q8—1221no—
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—1221no—
198C22×C8D24411yescharacteristic
199C22×C8D24411yescharacteristic
200C4⋊Q8—612no—
201C4⋊Q8—1221no—
202C4⋊Q8—1221no—
203C4⋊Q8—1221no—
204C2×C4⋊C4—611no—
205C2×C4⋊C4—611no—
206C2×C4⋊C4—1221no—
207C2×C4⋊C4—1221no—
208C2×C4⋊C4—1221no—
209C2×C4⋊C4—1221no—
210C2×C4⋊C4—1221no—
211C2×C42—1221no—
212C2×C42C22×D6111yescharacteristic
213#106—2442no—
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—612no—
218C4⋊C8—1221no—
219C4⋊C8C4×D6112yes—
220#103—2442no—
221#103—2442no—
222C4×C8—21no—
223C4×C8—21no—
224C4×C8—2442no—
225#95—1221no—
226C2×Q8—1222no—
227C2×Q8—2441no—
228C2×Q8—2441no—
229C2×Q8—2441no—
230C2×Q8—2441no—
231C2×Q8—2441no—
232C22×C4—1221no—
233C22×C4—1221no—
234C22×C4—2441no—
235C22×C4—2441no—
236C22×C4C2×D24411yescharacteristic
237C22×C4D4×D6111yescharacteristic
238C22×C4#1175822611yescharacteristic
239C2×C8—21no—
240C2×C8—21no—
241C2×C8—21no—
242C2×C8—22no—
243C2×C8—21no—
244C2×C8—21no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—41no—
250C2×C8—1222no—
251C2×C8—2441no—
252C2×C8—2441no—
253C2×C8#1175819012yes—
254C4⋊C4—612no—
255C4⋊C4—612no—
256C4⋊C4—1221no—
257C4⋊C4—1221no—
258C4⋊C4—1222no—
259C4⋊C4—1222no—
260C4⋊C4—4881no—
261C4⋊C4—2441no—
262C4⋊C4—2441no—
263C4⋊C4—2441no—
264C4⋊C4—2441no—
265C4⋊C4—2441no—
266C4⋊C4—2441no—
267C42—2441no—
268C42—2441no—
269C42C2×C4×D6111yescharacteristic
270C42#1175822211yescharacteristic
271C42#1175822411yescharacteristic
272C42#1175822411yescharacteristic
273C23#1451975211yescharacteristic
274Q8—4881no—
275Q8—4881no—
276Q8—2442no—
277Q8—2442no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—1222no—
281C2×C4—1222no—
282C2×C4—4881no—
283C2×C4—4881no—
284C2×C4—4881no—
285C2×C4—4881no—
286C2×C4—4881no—
287C2×C4—2442no—
288C2×C4—2441no—
289C2×C4—2441no—
290C2×C4—2441no—
291C2×C4—2441no—
292C2×C4#1451973511yescharacteristic
293C2×C4#1451973711yescharacteristic
294C2×C4C4×D24411yescharacteristic
295C2×C4#1451976111yescharacteristic
296C2×C4#1451976311yescharacteristic
297C2×C4#1451977211yescharacteristic
298C2×C4D8×D6111yescharacteristic
299C2×C4SD16×D6111yescharacteristic
300C2×C4C2×#1175819011yescharacteristic
301C2×C4#1451979811yescharacteristic
302C2×C4#1451979911yescharacteristic
303C2×C4#1451980011yescharacteristic
304C2×C4#1451981011yescharacteristic
305C2×C4#1451981011yescharacteristic
306C8—22no—
307C8—42no—
308C8—41no—
309C8—81no—
310C8—2442no—
311C22#1683965411yescharacteristic
312C22#1683996811yescharacteristic
313C22#1683998511yescharacteristic
314C22#1683999211yescharacteristic
315C22#1683999911yescharacteristic
316C22#1684002611yescharacteristic
317C22#1684003811yescharacteristic
318C4—21no—
319C4—21no—
320C4—9761no—
321C4—4882no—
322C4—2442no—
323C4—2442no—
324C4#1683984211yescharacteristic
325C4#1683984711yescharacteristic
326C4C4×#1175819011yescharacteristic
327C4#1683987011yescharacteristic
328C4#1684009311yescharacteristic
329C4#1684010411yescharacteristic
330C4#1684010711yescharacteristic
331C4#1684011811yescharacteristic
332C2#2144519511yescharacteristic
333C2#2144520911yescharacteristic
334C2#2144525011yescharacteristic
335C2#2144526411yescharacteristic
336C2#2144645411yescharacteristic
337C2#2144647511yescharacteristic
338C2#2144650311yescharacteristic
subgroupG/H
centerC23#14519752
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1277C2
socle, prime radicalC23×C61#121
cosocleC2×C42×C61C23
hypercenter#1277D61
hypocenterC61#9565
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
20. #16839509C4semidirect
193. C61#9565semidirect

Maximal subgroups

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

subgroupindex
#214467802
#214467412
#214465832
C8×C4⋊Dic612
C2×#168395092
#214437032
C61×#12772
#956561