Finite Group Databasebeta

← #29568348

Subgroups — #29568348

Order 15616.

518 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454158C211yesmaximal, characteristic
2#21445887C211yesmaximal, characteristic
3#21443644C212yesmaximal, complemented
4#21443641C212yesmaximal, complemented
5C2×C61×#336C211yesmaximal, characteristic
6C2×#14519756C411yescharacteristic
7C2×C22⋊#92418—21no—
8#16839668C411yescharacteristic
9#16839668C2211yescharacteristic
10#16839660C411yescharacteristic
11#16839660C2211yescharacteristic
12#16839646—21no—
13#16839646—21no—
14#16839635—21no—
15#16839625—21no—
16#16839622C411yescharacteristic
17#16839517—21no—
18#16839517C2212yes—
19C23×C8×C61—21no—
20C22×C42×C61C2211yescharacteristic
21C61×#336—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—
34C22⋊#92418—42no—
35#14519684—21no—
36#14519684—21no—
37#14519684—21no—
38#14519684—21no—
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42C23×C4×C61C2×C411yescharacteristic
43C23×C4×C61D411yescharacteristic
44C23×C4×C61D411yescharacteristic
45C22×C8×C61—24no—
46C22×C8×C61—22no—
47C22×C8×C61—42no—
48C22×C8×C61—42no—
49C2×C42×C61—42no—
50C2×C42×C61C2×C411yescharacteristic
51C2×C42×C61D411yescharacteristic
52C2×C42×C61D411yescharacteristic
53C2×C42×C61C2311yescharacteristic
54C24×C61C22⋊C411yescharacteristic
55C22×C4×C61—22no—
56C22×C4×C61—22no—
57C22×C4×C61—22no—
58C22×C4×C61—22no—
59C22×C4×C61—22no—
60C22×C4×C61—22no—
61C22×C4×C61—41no—
62C22×C4×C61—41no—
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61SD1612yes—
67C22×C4×C61Q1612yes—
68C22×C4×C61C22×C411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C2×Dic122—22no—
76C2×Dic122—41no—
77C2×Dic122—41no—
78C2×C8×C61—24no—
79C2×C8×C61—48no—
80C2×C8×C61—42no—
81C2×C8×C61—42no—
82C42×C61—41no—
83C42×C61—41no—
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—42no—
94C2×#92418—42no—
95C2×#92418—42no—
96C2×#92418—42no—
97C23×C61—21no—
98C23×C61—21no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61#9912yes—
102C23×C61#10312yes—
103C23×C61#10412yes—
104C23×C61C2×C22⋊C411yescharacteristic
105C2×C4×C61—24no—
106C2×C4×C61—24no—
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—44no—
122C2×C4×C61—44no—
123C2×C4×C61#10312yes—
124C2×C4×C61#13112yes—
125C2×C4×C61C2×SD1611yescharacteristic
126C2×C4×C61C2×Q1611yescharacteristic
127C2×C4×C61#13512yes—
128C2×Dic61—41no—
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—
138C2×Dic61—41no—
139C2×Dic61—41no—
140Dic122—82no—
141C8×C61—44no—
142#92418—82no—
143#7655—611nomaximal, Sylow
144C22×C61—22no—
145C22×C61—22no—
146C22×C61—22no—
147C22×C61—22no—
148C22×C61—22no—
149C22×C61—22no—
150C22×C61#32814yes—
151C22×C61#40811yescharacteristic
152C22×C61C2×#9911yescharacteristic
153C22×C61#41311yescharacteristic
154C22×C61C2×#10311yescharacteristic
155C22×C61#41611yescharacteristic
156C22×C61C2×#10411yescharacteristic
157C22×C61#42111yescharacteristic
158C4×C61—22no—
159C4×C61—21no—
160C4×C61—22no—
161C4×C61—21no—
162C4×C61—22no—
163C4×C61—41no—
164C4×C61—41no—
165Dic61—81no—
166Dic61—81no—
167Dic61—81no—
168Dic61—81no—
169#2855—611no—
170#1817—611no—
171C2×#336D6111yescharacteristic
172#1272—612no—
173#1271—612no—
174C2×C61—24no—
175C2×C61#146811yescharacteristic
176C2×C61#148111yescharacteristic
177C2×C61#149411yescharacteristic
178C2×C61C2×#32811yescharacteristic
179C2×C61#151611yescharacteristic
180C2×C61#153211yescharacteristic
181C2×C61#154211yescharacteristic
182C23×C8—21no—
183C2×C22⋊Q8—611no—
184C22×C42C2×D6111yescharacteristic
185C2×C22⋊C8—1221no—
186#391—611no—
187#391—611no—
188#389—611no—
189#389—611no—
190#387—1221no—
191#387—1221no—
192#385—1221no—
193#381—1221no—
194#380—611no—
195#336—21no—
196#336—612no—
197#336—1221no—
198#336C2×D6112yes—
199C61#765511yescharacteristic, complemented, Sylow
200C22×Q8—611no—
201C23×C4C4×D6111yescharacteristic
202C23×C4D24411yescharacteristic
203C23×C4C22⋊D6111yescharacteristic
204C22×C8—24no—
205C22×C8—22no—
206C22×C8—42no—
207C22×C8—42no—
208C22×C8—1222no—
209C22⋊Q8—2442no—
210C2×C4⋊C4—611no—
211C2×C4⋊C4—611no—
212C2×C4⋊C4—611no—
213C2×C4⋊C4—1221no—
214C2×C4⋊C4—1221no—
215C2×C4⋊C4—1221no—
216C2×C22⋊C4—1221no—
217C2×C22⋊C4—1221no—
218C2×C42—42no—
219C2×C42C4×D6111yescharacteristic
220C2×C42D24411yescharacteristic
221C2×C42C22⋊D6111yescharacteristic
222C2×C42C22×D6111yescharacteristic
223C22⋊C8—2442no—
224#95—1221no—
225#95—1221no—
226#95—1221no—
227#95—1221no—
228#95—1221no—
229#95—1221no—
230#95—1221no—
231C24#1175819811yescharacteristic
232C2×Q8—1222no—
233C2×Q8—2441no—
234C2×Q8—2441no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4—1221no—
244C22×C4—1221no—
245C22×C4—1221no—
246C22×C4—1221no—
247C22×C4#1175819811yescharacteristic
248C22×C4#1175819811yescharacteristic
249C22×C4#1175819811yescharacteristic
250C22×C4#1175820012yes—
251C22×C4#1175820212yes—
252C22×C4C2×C4×D6111yescharacteristic
253C22×C4C2×D24411yescharacteristic
254C22×C4C2×C22⋊D6111yescharacteristic
255C2×C8—24no—
256C2×C8—42no—
257C2×C8—48no—
258C2×C8—42no—
259C2×C8—2442no—
260C2×C8—2442no—
261C2×C8—2442no—
262C4⋊C4—1222no—
263C4⋊C4—2441no—
264C4⋊C4—2441no—
265C4⋊C4—2442no—
266C4⋊C4—2442no—
267C4⋊C4—2442no—
268C22⋊C4—2442no—
269C22⋊C4—2442no—
270C42—41no—
271C42—41no—
272C42—41no—
273C42—41no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23#1451969112yes—
279C23#1451970012yes—
280C23#1451970512yes—
281C23C2×#1175819811yescharacteristic
282Q8—4882no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—24no—
289C2×C4—24no—
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—44no—
300C2×C4—44no—
301C2×C4—2441no—
302C2×C4—2441no—
303C2×C4—2441no—
304C2×C4—2441no—
305C2×C4—2441no—
306C2×C4—2441no—
307C2×C4—2441no—
308C2×C4—2441no—
309C2×C4—2441no—
310C2×C4—2441no—
311C2×C4—2441no—
312C2×C4—2441no—
313C2×C4#1451970012yes—
314C2×C4#1451978312yes—
315C2×C4C2×#1175820011yescharacteristic
316C2×C4C2×#1175820211yescharacteristic
317C2×C4#1451979912yes—
318C8—44no—
319C8—4882no—
320C22—22no—
321C22—22no—
322C22—22no—
323C22—22no—
324C22—22no—
325C22—22no—
326C22#1683949814yes—
327C22#1683972811yescharacteristic
328C22C2×#1451969111yescharacteristic
329C22#1683974411yescharacteristic
330C22C2×#1451970011yescharacteristic
331C22#1683975911yescharacteristic
332C22C2×#1451970511yescharacteristic
333C22#1683977811yescharacteristic
334C4—22no—
335C4—22no—
336C4—21no—
337C4—22no—
338C4—21no—
339C4—41no—
340C4—41no—
341C4—4881no—
342C4—4881no—
343C4—4881no—
344C4—4881no—
345C2—24no—
346C2#2144416511yescharacteristic
347C2#2144422111yescharacteristic
348C2#2144428011yescharacteristic
349C2C2×#1683949811yescharacteristic
350C2#2144437611yescharacteristic
351C2#2144443711yescharacteristic
352C2#2144447711yescharacteristic
subgroupG/H
centerC23C2×#11758198
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC2×C61×#336C2
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C42×C61C23
hypercenterC2×#336D61
hypocenterC61#7655
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
3. #21443644C2semidirect
4. #21443641C2semidirect
199. C61#7655semidirect

Maximal subgroups

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

subgroupindex
#214541582
#214458872
#214436442
#214436412
C2×C61×#3362
#765561