Finite Group Databasebeta

← #29568492

Subgroups — #29568492

Order 15616.

464 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454186C211yesmaximal, characteristic
2C4×C4⋊#92418C211yesmaximal, characteristic, complemented
3#21443643C212yesmaximal, complemented
4#21443639C212yesmaximal
5C61×#1767C211yesmaximal, characteristic, complemented
6C2×#14519771—21no—
7C2×C4⋊#92418—21no—
8C2×C4×#92418—21no—
9#16839664C411yescharacteristic
10#16839664C411yescharacteristic
11#16839664C2211yescharacteristic
12#16839660C411yescharacteristic
13#16839660C411yescharacteristic
14#16839660C2211yescharacteristic
15#16839653—21no—
16#16839653—21no—
17#16839653—21no—
18#16839517C2212yes—
19C2×C4⋊C8×C61—21no—
20C2×#97×C61—21no—
21C43×C61C2211yescharacteristic
22C61×#336C2212yes—
23C22×D244C2×C411yescharacteristic
24C22×#92418—22no—
25#14519771—42no—
26#14519771—42no—
27C2×C4⋊Dic61C2×C411yescharacteristic
28C2×C4⋊Dic61C2×C411yescharacteristic
29C2×C4⋊Dic61C2×C411yescharacteristic
30C2×#11758196—21no—
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×#11758198—21no—
34C2×#11758198—21no—
35C2×#11758198—21no—
36C2×#11758198—21no—
37C2×#11758198—21no—
38C2×#11758198—21no—
39C4⋊#92418—24no—
40C4×#92418—42no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44C22×C8×C61—22no—
45C2×C42×C61C2×C411yescharacteristic
46C2×C42×C61C2×C411yescharacteristic
47C2×C42×C61D411yescharacteristic
48C2×C42×C61D411yescharacteristic
49C2×C42×C61D411yescharacteristic
50C2×C42×C61D411yescharacteristic
51C2×C42×C61C2311yescharacteristic
52C4⋊C8×C61—24no—
53#97×C61—42no—
54C23×D61—21no—
55C22×C4×C61C22⋊C411yescharacteristic
56C22×C4×C61C22⋊C411yescharacteristic
57C22×C4×C61C22⋊C411yescharacteristic
58C22×C4×C61C22⋊C411yescharacteristic
59C22×C4×C61C22×C411yescharacteristic
60C22×C4×C61C2×D411yescharacteristic
61C22×C4×C61C2×D411yescharacteristic
62C22×Dic61—21no—
63C22×Dic61—21no—
64C22×Dic61—21no—
65C2×D244—22no—
66C2×D244—41no—
67C2×D244—41no—
68C2×C8×C61—24no—
69C2×C8×C61—42no—
70C2×C8×C61—42no—
71C42×C61—22no—
72C42×C61—22no—
73C42×C61—22no—
74C42×C61—21no—
75C42×C61—21no—
76C42×C61—41no—
77C42×C61—41no—
78C42×C61D812yes—
79C42×C61SD1612yes—
80#11758198—42no—
81#11758198—42no—
82#11758198—42no—
83#11758198—42no—
84#11758198—41no—
85#11758198—41no—
86#11758198—41no—
87#11758198—41no—
88C4⋊Dic61—22no—
89C4⋊Dic61—41no—
90C4⋊Dic61—41no—
91#11758196—42no—
92#11758196—42no—
93#11758196—41no—
94#11758196—41no—
95C2×#92418—24no—
96C2×#92418—42no—
97C2×#92418—42no—
98C23×C61C2×C22⋊C411yescharacteristic
99C22×D61—41no—
100C22×D61—41no—
101C22×D61—41no—
102C22×D61—41no—
103C22×D61—41no—
104C22×D61—41no—
105C22×D61—41no—
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#10212yes—
121C2×C4×C61#10212yes—
122C2×C4×C61#10412yes—
123C2×C4×C61#10412yes—
124C2×C4×C61#13112yes—
125C2×C4×C61C2×D811yescharacteristic
126C2×C4×C61C2×SD1611yescharacteristic
127C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C61#13711yescharacteristic
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138D244—82no—
139C8×C61—44no—
140#92418—44no—
141#7686—611nomaximal, Sylow
142C22×C61#40811yescharacteristic
143C22×C61#41011yescharacteristic
144C22×C61#41311yescharacteristic
145C22×C61C2×#10211yescharacteristic
146C22×C61#41711yescharacteristic
147C22×C61C2×#10411yescharacteristic
148C22×C61C2×#10411yescharacteristic
149C2×D61—81no—
150C2×D61—81no—
151C2×D61—81no—
152C2×D61—81no—
153C2×D61—81no—
154C2×D61—81no—
155C2×D61—81no—
156C4×C61—22no—
157C4×C61—22no—
158C4×C61—22no—
159C4×C61—22no—
160C4×C61—21no—
161C4×C61—21no—
162C4×C61—21no—
163C4×C61—21no—
164C4×C61—22no—
165Dic61—81no—
166Dic61—81no—
167Dic61—81no—
168#2860—611no—
169#1767D6111yescharacteristic, complemented
170C4×C4⋊C8—611no—
171#1271—612no—
172#1270—612no—
173C2×C61#147311yescharacteristic
174C2×C61#148311yescharacteristic
175C2×C61#149211yescharacteristic
176C2×C61#150211yescharacteristic
177C2×C61#150911yescharacteristic
178C2×C61#152411yescharacteristic
179C2×C61#154711yescharacteristic
180D61—161no—
181C2×#126—1221no—
182C2×C4⋊C8—21no—
183C2×C4⋊C8—1221no—
184C2×#97—21no—
185C2×C4×C8—1221no—
186#390—611no—
187#390—611no—
188#390—611no—
189#389—611no—
190#389—611no—
191#389—611no—
192#388—1221no—
193#388—1221no—
194#388—1221no—
195C43C2×D6111yescharacteristic
196#336—612no—
197#336C2×D6112yes—
198C61#768611yescharacteristic, complemented, Sylow
199C22×D4—611no—
200C22×C8—22no—
201C22×C8—1222no—
202#126—2442no—
203#126—2442no—
204C2×C4⋊C4—611no—
205C2×C4⋊C4—611no—
206C2×C4⋊C4—611no—
207C2×C4⋊C4—1221no—
208C2×C4⋊C4—1221no—
209C2×C4⋊C4—1221no—
210C2×C22⋊C4—1221no—
211C2×C22⋊C4—1221no—
212C2×C22⋊C4—1221no—
213C2×C22⋊C4—1221no—
214C2×C22⋊C4—1221no—
215C2×C22⋊C4—1221no—
216C2×C42C4×D6111yescharacteristic
217C2×C42C4×D6111yescharacteristic
218C2×C42D24411yescharacteristic
219C2×C42D24411yescharacteristic
220C2×C42C22⋊D6111yescharacteristic
221C2×C42C22⋊D6111yescharacteristic
222C2×C42C22×D6111yescharacteristic
223C4⋊C8—24no—
224C4⋊C8—1224no—
225#97—42no—
226C4×C8—2442no—
227#95—1221no—
228#95—1221no—
229#95—1221no—
230C24—1221no—
231C2×D4—1222no—
232C2×D4—2441no—
233C2×D4—2441no—
234C22×C4—1221no—
235C22×C4—1221no—
236C22×C4—1221no—
237C22×C4#1175819811yescharacteristic
238C22×C4#1175819811yescharacteristic
239C22×C4#1175819811yescharacteristic
240C22×C4#1175819811yescharacteristic
241C22×C4C2×C4×D6111yescharacteristic
242C22×C4C2×D24411yescharacteristic
243C22×C4C2×C22⋊D6111yescharacteristic
244C2×C8—24no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—1224no—
248C2×C8—2442no—
249C2×C8—2442no—
250C4⋊C4—1222no—
251C4⋊C4—2441no—
252C4⋊C4—2441no—
253C4⋊C4—2442no—
254C4⋊C4—2442no—
255C4⋊C4—2441no—
256C4⋊C4—2441no—
257C22⋊C4—2441no—
258C22⋊C4—2442no—
259C22⋊C4—2442no—
260C22⋊C4—2442no—
261C22⋊C4—2442no—
262C22⋊C4—2441no—
263C22⋊C4—2441no—
264C22⋊C4—2441no—
265C42—21no—
266C42—22no—
267C42—22no—
268C42—22no—
269C42—21no—
270C42—41no—
271C42—41no—
272C42#1175819912yes—
273C42#1175820112yes—
274C23—2441no—
275C23—2441no—
276C23—2441no—
277C23—2441no—
278C23—2441no—
279C23—2441no—
280C23—2441no—
281C23C2×#1175819811yescharacteristic
282D4—4882no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—2441no—
298C2×C4—2441no—
299C2×C4—2441no—
300C2×C4—2441no—
301C2×C4—2441no—
302C2×C4—2441no—
303C2×C4—2441no—
304C2×C4—2441no—
305C2×C4—2441no—
306C2×C4#1451969712yes—
307C2×C4#1451969712yes—
308C2×C4#1451970312yes—
309C2×C4#1451970512yes—
310C2×C4#1451978512yes—
311C2×C4C2×#1175819911yescharacteristic
312C2×C4C2×#1175820111yescharacteristic
313C2×C4#1451980511yescharacteristic
314C2×C4#1451981011yescharacteristic
315C8—44no—
316C8—2444no—
317C22—4881no—
318C22—4881no—
319C22—4881no—
320C22—4881no—
321C22—4881no—
322C22—4881no—
323C22—4881no—
324C22#1683973011yescharacteristic
325C22#1683973511yescharacteristic
326C22#1683974411yescharacteristic
327C22C2×#1451969711yescharacteristic
328C22#1683976411yescharacteristic
329C22C2×#1451970311yescharacteristic
330C22C2×#1451970511yescharacteristic
331C4—22no—
332C4—22no—
333C4—22no—
334C4—22no—
335C4—22no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—4881no—
341C4—4881no—
342C4—4881no—
343C2—9761no—
344C2#2144418911yescharacteristic
345C2#2144423311yescharacteristic
346C2#2144426911yescharacteristic
347C2#2144431311yescharacteristic
348C2#2144434511yescharacteristic
349C2#2144440511yescharacteristic
350C2#2144449711yescharacteristic
subgroupG/H
centerC23C2×#11758198
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1767C2
socleC23×C61C2×C22⋊C4
prime radicalC22×D244C2×C4
cosocleC2×C42×C61C23
hypercenter#1767D61
hypocenterC61#7686
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C43 ◁ #1767

Complements

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

NH ≅ G/Ntype
2. C4×C4⋊#92418C2semidirect
3. #21443643C2semidirect
5. C61×#1767C2semidirect
169. #1767D61semidirect
198. C61#7686semidirect

Maximal subgroups

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

subgroupindex
#214541862
C4×C4⋊#924182
#214436432
#214436392
C61×#17672
#768661