Finite Group Databasebeta

← #29568624

Subgroups — #29568624

Order 15616.

464 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454158C211yesmaximal, characteristic
2#21445799C211yesmaximal, characteristic
3#21443644C212yesmaximal, complemented
4#21443641C212yesmaximal, complemented
5C61×#1797C211yesmaximal, characteristic
6C2×#14519756C411yescharacteristic
7C2×C4⋊#92418—21no—
8C2×C22⋊#92418—21no—
9#16839668C411yescharacteristic
10#16839668C2211yescharacteristic
11#16839660C411yescharacteristic
12#16839660C2211yescharacteristic
13#16839646—21no—
14#16839646—21no—
15#16839635—21no—
16#16839625—21no—
17#16839622C411yescharacteristic
18#16839517C2212yes—
19C22×C42×C61C2211yescharacteristic
20C2×C4⋊C8×C61—21no—
21C2×C22⋊C8×C61—21no—
22C61×#336C2212yes—
23C22×Dic122C2×C411yescharacteristic
24C22×#92418—22no—
25#14519756—42no—
26C2×C4⋊Dic61C2×C411yescharacteristic
27C2×C4⋊Dic61C2×C411yescharacteristic
28C2×C4⋊Dic61C2×C411yescharacteristic
29C2×#11758196—21no—
30C2×#11758196—21no—
31C2×#11758196—21no—
32C2×C22⋊Dic61—21no—
33C2×C22⋊Dic61—21no—
34C4⋊#92418—42no—
35C22⋊#92418—42no—
36#14519684—21no—
37#14519684—21no—
38#14519684—21no—
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42#14519684—21no—
43C23×C4×C61C2×C411yescharacteristic
44C23×C4×C61D411yescharacteristic
45C23×C4×C61D411yescharacteristic
46C22×C8×C61—22no—
47C2×C42×C61—42no—
48C2×C42×C61C2×C411yescharacteristic
49C2×C42×C61D411yescharacteristic
50C2×C42×C61D411yescharacteristic
51C2×C42×C61C2311yescharacteristic
52C4⋊C8×C61—42no—
53C22⋊C8×C61—42no—
54C24×C61C22⋊C411yescharacteristic
55C22×C4×C61—22no—
56C22×C4×C61—22no—
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61—41no—
60C22×C4×C61—41no—
61C22×C4×C61—41no—
62C22×C4×C61—41no—
63C22×C4×C61—41no—
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61SD1612yes—
68C22×C4×C61Q1612yes—
69C22×C4×C61C22×C411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C2×Dic122—22no—
77C2×Dic122—41no—
78C2×Dic122—41no—
79C2×C8×C61—42no—
80C2×C8×C61—42no—
81C2×C8×C61—42no—
82C42×C61—22no—
83C42×C61—22no—
84C42×C61—41no—
85C42×C61—41no—
86C22⋊Dic61—42no—
87C22⋊Dic61—42no—
88C4⋊Dic61—22no—
89C4⋊Dic61—41no—
90C4⋊Dic61—41no—
91#11758196—42no—
92#11758196—42no—
93#11758196—41no—
94#11758196—41no—
95C2×#92418—42no—
96C2×#92418—42no—
97C2×#92418—42no—
98C23×C61—21no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61#10312yes—
105C23×C61C2×C22⋊C411yescharacteristic
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—42no—
120C2×C4×C61—42no—
121C2×C4×C61—44no—
122C2×C4×C61—42no—
123C2×C4×C61—42no—
124C2×C4×C61#9912yes—
125C2×C4×C61#10312yes—
126C2×C4×C61#13112yes—
127C2×C4×C61C2×SD1611yescharacteristic
128C2×C4×C61C2×Q1611yescharacteristic
129C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C61#13711yescharacteristic
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143Dic122—82no—
144C8×C61—82no—
145#92418—82no—
146#7715—611nomaximal, Sylow
147C22×C61—22no—
148C22×C61—22no—
149C22×C61—22no—
150C22×C61—41no—
151C22×C61—41no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61#40811yescharacteristic
155C22×C61C2×#9911yescharacteristic
156C22×C61#41311yescharacteristic
157C22×C61C2×#10311yescharacteristic
158C22×C61#41711yescharacteristic
159C22×C61#42111yescharacteristic
160C22×C61#42111yescharacteristic
161C4×C61—22no—
162C4×C61—22no—
163C4×C61—21no—
164C4×C61—21no—
165C4×C61—21no—
166C4×C61—22no—
167C4×C61—21no—
168C4×C61—41no—
169Dic61—81no—
170Dic61—81no—
171Dic61—81no—
172Dic61—81no—
173#2855—611no—
174#1797—611no—
175#1797D6111yescharacteristic
176#1272—612no—
177#1271—612no—
178C2×C61—42no—
179C2×C61#146811yescharacteristic
180C2×C61#148111yescharacteristic
181C2×C61#149511yescharacteristic
182C2×C61#151311yescharacteristic
183C2×C61#152011yescharacteristic
184C2×C61#153511yescharacteristic
185C2×C61#155011yescharacteristic
186C2×C22⋊Q8—611no—
187C22×C42C2×D6111yescharacteristic
188C2×C4⋊C8—21no—
189C2×C4⋊C8—1221no—
190C2×C22⋊C8—21no—
191C2×C22⋊C8—1221no—
192#391—611no—
193#391—611no—
194#389—611no—
195#389—611no—
196#387—1221no—
197#387—1221no—
198#385—1221no—
199#381—1221no—
200#380—611no—
201#336—612no—
202#336C2×D6112yes—
203C61#771511yescharacteristic, complemented, Sylow
204C22×Q8—611no—
205C23×C4C4×D6111yescharacteristic
206C23×C4D24411yescharacteristic
207C23×C4C22⋊D6111yescharacteristic
208C22×C8—22no—
209C22×C8—1222no—
210C22⋊Q8—2442no—
211C2×C4⋊C4—611no—
212C2×C4⋊C4—611no—
213C2×C4⋊C4—611no—
214C2×C4⋊C4—1221no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4—1221no—
217C2×C22⋊C4—1221no—
218C2×C22⋊C4—1221no—
219C2×C42—42no—
220C2×C42C4×D6111yescharacteristic
221C2×C42D24411yescharacteristic
222C2×C42C22⋊D6111yescharacteristic
223C2×C42C22×D6111yescharacteristic
224C4⋊C8—42no—
225C4⋊C8—2442no—
226C22⋊C8—42no—
227C22⋊C8—2442no—
228#95—1221no—
229#95—1221no—
230#95—1221no—
231#95—1221no—
232#95—1221no—
233#95—1221no—
234#95—1221no—
235C24#1175819811yescharacteristic
236C2×Q8—1222no—
237C2×Q8—2441no—
238C2×Q8—2441no—
239C22×C4—21no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—21no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—1221no—
249C22×C4—1221no—
250C22×C4—1221no—
251C22×C4—1221no—
252C22×C4#1175819811yescharacteristic
253C22×C4#1175819811yescharacteristic
254C22×C4#1175819811yescharacteristic
255C22×C4#1175820012yes—
256C22×C4#1175820212yes—
257C22×C4C2×C4×D6111yescharacteristic
258C22×C4C2×D24411yescharacteristic
259C22×C4C2×C22⋊D6111yescharacteristic
260C2×C8—42no—
261C2×C8—42no—
262C2×C8—42no—
263C2×C8—2442no—
264C2×C8—2442no—
265C2×C8—2442no—
266C4⋊C4—1222no—
267C4⋊C4—2441no—
268C4⋊C4—2441no—
269C4⋊C4—2442no—
270C4⋊C4—2441no—
271C4⋊C4—2442no—
272C4⋊C4—2441no—
273C22⋊C4—2442no—
274C22⋊C4—2442no—
275C42—22no—
276C42—22no—
277C42—41no—
278C42—41no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23#1451970012yes—
286C23C2×#1175819811yescharacteristic
287Q8—4882no—
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—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—44no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—2441no—
307C2×C4—2441no—
308C2×C4—2441no—
309C2×C4—2441no—
310C2×C4—2441no—
311C2×C4—2441no—
312C2×C4—2441no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4#1451969112yes—
319C2×C4#1451970012yes—
320C2×C4#1451978312yes—
321C2×C4C2×#1175820011yescharacteristic
322C2×C4C2×#1175820211yescharacteristic
323C2×C4#1451980511yescharacteristic
324C2×C4#1451981011yescharacteristic
325C8—82no—
326C8—4882no—
327C22—22no—
328C22—22no—
329C22—22no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22#1683972811yescharacteristic
335C22C2×#1451969111yescharacteristic
336C22#1683974411yescharacteristic
337C22C2×#1451970011yescharacteristic
338C22#1683976411yescharacteristic
339C22#1683977811yescharacteristic
340C22#1683978011yescharacteristic
341C4—21no—
342C4—21no—
343C4—21no—
344C4—22no—
345C4—21no—
346C4—22no—
347C4—22no—
348C4—41no—
349C4—4881no—
350C4—4881no—
351C4—4881no—
352C4—4881no—
353C2—42no—
354C2#2144416511yescharacteristic
355C2#2144422111yescharacteristic
356C2#2144428511yescharacteristic
357C2#2144436311yescharacteristic
358C2#2144439011yescharacteristic
359C2#2144445111yescharacteristic
360C2#2144451011yescharacteristic
subgroupG/H
centerC23C2×#11758198
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1797C2
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1797D61
hypocenterC61#7715
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
3. #21443644C2semidirect
4. #21443641C2semidirect
203. C61#7715semidirect

Maximal subgroups

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

subgroupindex
#214541582
#214457992
#214436442
#214436412
C61×#17972
#771561