Finite Group Databasebeta

← #29577788

Subgroups — #29577788

Order 15616.

598 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#21454843C211yesmaximal, characteristic
2#21445905C212yesmaximal, complemented
3#21445807C211yesmaximal, characteristic
4#21443686C212yesmaximal, complemented
5C61×#2486C211yesmaximal, characteristic
6D4×#92418—24no—
7#16839815—21no—
8C2×#14519692—21no—
9C2×C22⋊#92418—21no—
10C2×C22⋊#92418C2212yes—
11#16839622C2212yes—
12#16839529—21no—
13#16839524—24no—
14C2×#123×C61—21no—
15C2×C4×D4×C61C2211yescharacteristic
16C22×C4⋊C4×C61C2211yescharacteristic
17C61×#398C412yescomplemented
18C61×#397C412yescomplemented
19C61×#389—21no—
20C61×#381—21no—
21C61×#380—21no—
22C61×#380C2211yescharacteristic
23C22×#92418—22no—
24C22×#92418D414yes—
25C2×C4⋊Dic61—22no—
26C2×C22⋊Dic61—22no—
27C4⋊#92418—22no—
28#14519692—42no—
29C22⋊#92418—22no—
30C22⋊#92418—22no—
31C22⋊#92418—22no—
32C4×#92418—22no—
33#14519684—22no—
34C22×D4×C61D411yescharacteristic
35C23×C4×C61—21no—
36C23×C4×C61D411yescharacteristic
37C23×C4×C61C2311yescharacteristic
38#123×C61—42no—
39#123×C61—42no—
40C4×D4×C61—22no—
41C4×D4×C61—22no—
42C2×C4⋊C4×C61—22no—
43C2×C4⋊C4×C61—22no—
44C2×C4⋊C4×C61—22no—
45C2×C4⋊C4×C61—21no—
46C2×C4⋊C4×C61—21no—
47C2×C4⋊C4×C61C2×C412yes—
48C2×C4⋊C4×C61C2×C411yescharacteristic
49C2×C22⋊C4×C61—22no—
50C2×C22⋊C4×C61—21no—
51C2×C22⋊C4×C61C2×C411yescharacteristic
52C2×C22⋊C4×C61D411yescharacteristic
53C2×C42×C61D411yescharacteristic
54#95×C61—22no—
55#95×C61—22no—
56#95×C61C2×C412yes—
57C24×C61C22⋊C411yescharacteristic
58C24×C61C2×D411yescharacteristic
59C2×D4×C61—22no—
60C2×D4×C61—22no—
61C2×D4×C61D812yes—
62C2×D4×C61SD1612yes—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—22no—
66C22×C4×C61—22no—
67C22×C4×C61—42no—
68C22×C4×C61—42no—
69C22×C4×C61—42no—
70C22×C4×C61—41no—
71C22×C4×C61—41no—
72C22×C4×C61—42no—
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C22⋊C411yescharacteristic
75C22×C4×C61C22⋊C411yescharacteristic
76C22×C4×C61C22×C411yescharacteristic
77C22×C4×C61C2×D412yes—
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61#4112yes—
80C22×Dic61—42no—
81C4⋊C4×C61—22no—
82C4⋊C4×C61—24no—
83C4⋊C4×C61—42no—
84C4⋊C4×C61—44no—
85C4⋊C4×C61—41no—
86C4⋊C4×C61—41no—
87C22⋊C4×C61—22no—
88C22⋊C4×C61—22no—
89C22⋊C4×C61—44no—
90C22⋊C4×C61—41no—
91C22⋊C4×C61—41no—
92C42×C61—21no—
93C42×C61—21no—
94C22⋊Dic61—42no—
95C22⋊Dic61—42no—
96C4⋊Dic61—44no—
97C2×#92418—24no—
98C2×#92418—44no—
99C2×#92418—82no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—41no—
103C23×C61—41no—
104C23×C61—41no—
105C23×C61—41no—
106C23×C61#10212yes—
107C23×C61C2×C22⋊C411yescharacteristic
108C23×C61#12112yes—
109C23×C61C2×D811yescharacteristic
110C23×C61C2×SD1611yescharacteristic
111C23×C61#13512yes—
112D4×C61—24no—
113D4×C61—24no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—24no—
117C2×C4×C61—22no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—41no—
121C2×C4×C61—42no—
122C2×C4×C61—42no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—42no—
126C2×C4×C61—42no—
127C2×C4×C61—42no—
128C2×C4×C61—42no—
129C2×C4×C61—42no—
130C2×C4×C61—42no—
131C2×C4×C61—81no—
132C2×C4×C61—82no—
133C2×C4×C61—82no—
134C2×C4×C61#10212yes—
135C2×C4×C61C4×D412yes—
136C2×C4×C61#12011yescharacteristic
137C2×C4×C61#12311yescharacteristic
138C2×Dic61—82no—
139C2×Dic61—82no—
140C2×Dic61—82no—
141#92418—44no—
142#9470—611nomaximal, Sylow
143C22×C61—22no—
144C22×C61—21no—
145C22×C61—22no—
146C22×C61—21no—
147C22×C61—22no—
148C22×C61—41no—
149C22×C61—41no—
150C22×C61—42no—
151C22×C61—42no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61—81no—
155C22×C61#38611yescharacteristic
156C22×C61C2×#10211yescharacteristic
157C22×C61#41611yescharacteristic
158C22×C61#46512yes—
159C22×C61#46612yes—
160C4×C61—21no—
161C4×C61—22no—
162C4×C61—22no—
163C4×C61—41no—
164C4×C61—41no—
165C4×C61—82no—
166C4×C61—82no—
167C4×C61#45812yes—
168Dic61—162no—
169#2972—611no—
170#2486D6111yescharacteristic
171#1823—612no—
172#1799—611no—
173#1289—612no—
174C2×C61—22no—
175C2×C61—21no—
176C2×C61—21no—
177C2×C61—22no—
178C2×C61—42no—
179C2×C61#189011yescharacteristic
180C2×C61#189311yescharacteristic
181C2×C61#190911yescharacteristic
182C2×#123—21no—
183C2×C4×D4C2×D6111yescharacteristic
184C22×C4⋊C4C2×D6111yescharacteristic
185C8×D4—1224no—
186#431—1221no—
187C2×#99—1221no—
188C2×C22⋊C8—612no—
189C2×C22⋊C8—1221no—
190#398Dic6112yescomplemented
191#397Dic6112yescomplemented
192#389—21no—
193#381—21no—
194#380—21no—
195#380—612no—
196#380C2×D6111yescharacteristic
197#342—1221no—
198#340—1224no—
199C61#947011yescharacteristic, complemented, Sylow
200C22×D4C22⋊D6111yescharacteristic
201C23×C4—21no—
202C23×C4C22⋊D6111yescharacteristic
203C23×C4C22×D6111yescharacteristic
204C22×C8—614no—
205C22×C8—1222no—
206#123—42no—
207#123—42no—
208C4×D4—22no—
209C4×D4—22no—
210C2×C4⋊C4—22no—
211C2×C4⋊C4—22no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—1222no—
216C2×C4⋊C4C2×Dic6112yes—
217C2×C4⋊C4C2×Dic6111yescharacteristic
218C2×C22⋊C4—22no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—1222no—
221C2×C22⋊C4C2×Dic6111yescharacteristic
222C2×C22⋊C4C22⋊D6111yescharacteristic
223C2×C42C22⋊D6111yescharacteristic
224C4⋊C8—1222no—
225#99—2442no—
226C22⋊C8—1222no—
227C22⋊C8—1222no—
228C22⋊C8—1222no—
229C4×C8—1222no—
230#95—22no—
231#95—22no—
232#95—1222no—
233#95C2×Dic6112yes—
234C24C22⋊Dic6111yescharacteristic
235C24C2×C22⋊D6111yescharacteristic
236C2×D4—22no—
237C2×D4—22no—
238C2×D4#1175819912yes—
239C2×D4#1175820012yes—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—42no—
250C22×C4—2442no—
251C22×C4C22⋊Dic6111yescharacteristic
252C22×C4C22⋊Dic6111yescharacteristic
253C22×C4C22⋊Dic6111yescharacteristic
254C22×C4D4×D6112yes—
255C22×C4#1175822412yes—
256C22×C4C22×Dic6111yescharacteristic
257C22×C4C2×C22⋊D6111yescharacteristic
258C2×C8—1224no—
259C2×C8—4882no—
260C2×C8—2444no—
261C4⋊C4—22no—
262C4⋊C4—24no—
263C4⋊C4—42no—
264C4⋊C4—44no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—2444no—
268C22⋊C4—22no—
269C22⋊C4—22no—
270C22⋊C4—44no—
271C22⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—2442no—
274C22⋊C4—2442no—
275C42—21no—
276C42—21no—
277C23—21no—
278C23—21no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23#1451969812yes—
284C23C2×C22⋊Dic6111yescharacteristic
285C23#1451974912yes—
286C23C2×#1175819911yescharacteristic
287C23C2×#1175820011yescharacteristic
288C23#1451979712yes—
289D4—24no—
290D4—24no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—24no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—42no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—81no—
309C2×C4—82no—
310C2×C4—82no—
311C2×C4—4882no—
312C2×C4—4882no—
313C2×C4—4882no—
314C2×C4#1451969812yes—
315C2×C4D4×Dic6112yes—
316C2×C4#1451974511yescharacteristic
317C2×C4#1451975811yescharacteristic
318C8—2444no—
319C22—21no—
320C22—22no—
321C22—21no—
322C22—22no—
323C22—22no—
324C22—41no—
325C22—41no—
326C22—42no—
327C22—42no—
328C22—41no—
329C22—41no—
330C22—81no—
331C22#1683964211yescharacteristic
332C22C2×#1451969811yescharacteristic
333C22#1683975811yescharacteristic
334C22#1683998912yes—
335C22#1683999612yes—
336C4—21no—
337C4—22no—
338C4—22no—
339C4—41no—
340C4—41no—
341C4—82no—
342C4—82no—
343C4—9762no—
344C4#1683995112yes—
345C2—21no—
346C2—22no—
347C2—21no—
348C2—22no—
349C2—42no—
350C2#2144623311yescharacteristic
351C2#2144624811yescharacteristic
352C2#2144634211yescharacteristic
subgroupG/H
centerC22#16839642
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#2486C2
socleC22×C61#386
prime radicalC22×D4×C61D4
cosocleC23×C4×C61C23
hypercenter#2486D61
hypocenterC61#9470
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2486

Complements

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

NH ≅ G/Ntype
2. #21445905C2semidirect
4. #21443686C2semidirect
17. C61×#398C4semidirect
18. C61×#397C4semidirect
190. #398Dic61semidirect
191. #397Dic61semidirect
199. C61#9470semidirect

Maximal subgroups

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

subgroupindex
#214548432
#214459052
#214458072
#214436862
C61×#24862
#947061