Finite Group Databasebeta

← #30597819

Subgroups — #30597819

Order 15616.

528 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#21461604C211yesmaximal, characteristic
2C4×#14519844C211yesmaximal, characteristic
3C2×#16840622C212yesmaximal
4#21460697C212yesmaximal
5#21448388C211yesmaximal, characteristic
6C2×#14519844C2212yes—
7C2×#14519844C2212yes—
8C2×#14519832—21no—
9C2×C4×#92420—21no—
10#16840628—21no—
11#16840628—21no—
12#16840622C418yescomplemented
13C2×#14519775C2211yescharacteristic
14C2×Q8×Dic61C411yescharacteristic
15C2×#14519742C411yescharacteristic
16#16839668C411yescharacteristic
17#16839659—21no—
18#16839659—21no—
19#16839631C2211yescharacteristic
20#16839613—21no—
21#16839613—21no—
22C42×Dic61C2211yescharacteristic
23C61×#391C411yescharacteristic
24C22×#92420—22no—
25C22×#92420—22no—
26#14519844—22no—
27#14519844—22no—
28#14519844C2×C414yes—
29#14519844C2×C414yes—
30#14519832—42no—
31C4×#92420—42no—
32C22×Dic122C2×C411yescharacteristic
33#14519775—22no—
34#14519775C2×C414yes—
35Q8×Dic61—42no—
36#14519742—42no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61C2×C411yescharacteristic
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×#11758196—21no—
44C2×C4×Dic61—21no—
45C2×C4×Dic61—21no—
46C2×C4×Dic61C2×C411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51C2×C4×Dic61C2311yescharacteristic
52#14519684—21no—
53#14519684—21no—
54C22×Q8×C61C2×C411yescharacteristic
55C2×C4⋊C4×C61C2×C411yescharacteristic
56C2×C42×C61C2×C411yescharacteristic
57#95×C61—21no—
58#95×C61—21no—
59C2×Q8×C61—21no—
60C2×Q8×C61—41no—
61C2×Q8×C61—41no—
62C2×Q8×C61C4212yes—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22×C411yescharacteristic
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C2×D411yescharacteristic
73C22×Dic61C2×D411yescharacteristic
74C2×Dic122—21no—
75C2×Dic122—41no—
76C2×Dic122—41no—
77C2×Dic122C4212yes—
78C2×#92420—24no—
79C2×#92420—24no—
80C2×#92420—42no—
81C2×#92420—42no—
82C2×#92420—42no—
83C2×#92420—42no—
84C4⋊C4×C61—41no—
85C42×C61—41no—
86C4⋊Dic61—42no—
87C4⋊Dic61—41no—
88#11758196—24no—
89#11758196—24no—
90#11758196—42no—
91#11758196—42no—
92#11758196—41no—
93#11758196—41no—
94C4×Dic61—22no—
95C4×Dic61—22no—
96C4×Dic61—21no—
97C4×Dic61—21no—
98C4×Dic61—22no—
99C4×Dic61—42no—
100C4×Dic61—42no—
101C4×Dic61SD1612yes—
102C4×Dic61Q1612yes—
103C4×Dic61C22×C412yes—
104C4×Dic61#4112yes—
105C23×C61C2×C22⋊C411yescharacteristic
106Q8×C61—42no—
107Q8×C61—42no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—22no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61#10312yes—
122C2×C4×C61C2×C4211yescharacteristic
123C2×C4×C61#11711yescharacteristic
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—22no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61#10012yes—
135C2×Dic61#10312yes—
136C2×Dic61C4×D412yes—
137C2×Dic61C4×D412yes—
138C2×Dic61C2×SD1611yescharacteristic
139C2×Dic61C2×Q1611yescharacteristic
140C2×Dic61#13512yes—
141C2×Dic61AGL(1,ℤ/8)11yescharacteristic
142C2×Dic61#13712yes—
143C2×Dic61#13711yescharacteristic
144Dic122—42no—
145Dic122—42no—
146#92420—44no—
147#92420—44no—
148#8235—611nomaximal, Sylow
149C22×C61C4×C22⋊C411yescharacteristic
150C22×C61C2×#10011yescharacteristic
151C22×C61#41311yescharacteristic
152C22×C61C2×#10311yescharacteristic
153C22×C61#41611yescharacteristic
154C22×C61#41711yescharacteristic
155C22×C61#41911yescharacteristic
156C4×C61—22no—
157C4×C61—21no—
158C4×C61—21no—
159C4×C61—41no—
160C4×C61—42no—
161C4×C61—81no—
162Dic61—22no—
163Dic61—22no—
164Dic61—42no—
165Dic61—81no—
166Dic61C4×SD1612yes—
167Dic61C4×Q1612yes—
168Dic61#44012yes—
169Dic61#44112yes—
170C4×C4⋊Q8—611no—
171#1767—611no—
172C4×C4⋊C8—611no—
173C2×#333—612no—
174#1296—612no—
175C2×C61#154811yescharacteristic
176C2×C61#155011yescharacteristic
177C2×C61#155111yescharacteristic
178C2×C61#155411yescharacteristic
179C2×C61C4×#10011yescharacteristic
180C2×C61C4×#10311yescharacteristic
181C2×C61#176311yescharacteristic
182C2×C4⋊Q8—611no—
183C2×C4×Q8—611no—
184C2×C4×Q8—611no—
185C2×C4⋊C8—612no—
186C2×C4⋊C8—612no—
187C2×#97—1221no—
188C2×C4×C8—1221no—
189#391—611no—
190#391#692311yescharacteristic
191#389—1221no—
192#389—1221no—
193#384—611no—
194C4×C4⋊C4—1221no—
195C4×C4⋊C4—1221no—
196C43—611no—
197#336—1221no—
198#336—1221no—
199#333—618no—
200C61#823511yescharacteristic, complemented, Sylow
201C22×Q8—611no—
202C22×Q8C2×#692311yescharacteristic
203C22×C8—1222no—
204C22×C8—1222no—
205C4⋊Q8—614no—
206C4⋊Q8—1222no—
207C4×Q8—2442no—
208C4×Q8—2442no—
209C2×C4⋊C4—611no—
210C2×C4⋊C4—1221no—
211C2×C4⋊C4—1221no—
212C2×C4⋊C4—1221no—
213C2×C4⋊C4—1221no—
214C2×C4⋊C4—1221no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4C2×#692311yescharacteristic
217C2×C42—611no—
218C2×C42—611no—
219C2×C42—611no—
220C2×C42—611no—
221C2×C42—611no—
222C2×C42—611no—
223C2×C42—1221no—
224C2×C42—1221no—
225C2×C42C2×#692311yescharacteristic
226C4⋊C8—614no—
227C4⋊C8—614no—
228C4⋊C8—1222no—
229C4⋊C8—1222no—
230#97—2442no—
231C4×C8—2442no—
232#95—21no—
233#95—21no—
234#95—1221no—
235#95—1221no—
236C2×Q8—21no—
237C2×Q8—41no—
238C2×Q8—41no—
239C2×Q8—612no—
240C2×Q8—1221no—
241C2×Q8—2441no—
242C2×Q8—2441no—
243C2×Q8C4×#692312yes—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—611no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—611no—
250C22×C4—1221no—
251C22×C4—1221no—
252C22×C4C22⋊#692311yescharacteristic
253C22×C4C22⋊#692311yescharacteristic
254C22×C4C22×#692311yescharacteristic
255C2×C8—1224no—
256C2×C8—1224no—
257C2×C8—2442no—
258C2×C8—2442no—
259C2×C8—2442no—
260C2×C8—2442no—
261C4⋊C4—41no—
262C4⋊C4—1224no—
263C4⋊C4—1224no—
264C4⋊C4—2441no—
265C4⋊C4—2442no—
266C4⋊C4—2441no—
267C4⋊C4—2441no—
268C4⋊C4—2442no—
269C4⋊C4—2442no—
270C42—41no—
271C42—612no—
272C42—612no—
273C42—612no—
274C42—612no—
275C42—1221no—
276C42—1221no—
277C42—1222no—
278C42—1222no—
279C42—1222no—
280C42—2442no—
281C42—2442no—
282C23C2×C22⋊#692311yescharacteristic
283Q8—42no—
284Q8—42no—
285Q8—2442no—
286Q8—2442no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—22no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—611no—
301C2×C4—611no—
302C2×C4—612no—
303C2×C4—611no—
304C2×C4—611no—
305C2×C4—612no—
306C2×C4—612no—
307C2×C4—612no—
308C2×C4—612no—
309C2×C4—612no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1222no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4#1451984012yes—
321C2×C4C2×C4×#692311yescharacteristic
322C2×C4#1451985611yescharacteristic
323C8—2444no—
324C8—2444no—
325C22C4×C22⋊#692311yescharacteristic
326C22D61⋊#10011yescharacteristic
327C22#1684074911yescharacteristic
328C22C2×#1451984011yescharacteristic
329C22#1684075211yescharacteristic
330C22#1684075311yescharacteristic
331C22#1684075511yescharacteristic
332C4—21no—
333C4—21no—
334C4—22no—
335C4—42no—
336C4—41no—
337C4—81no—
338C4—612no—
339C4—612no—
340C4—612no—
341C4—612no—
342C4—1222no—
343C4—1222no—
344C4—4881no—
345C4—2442no—
346C2#2146133311yescharacteristic
347C2#2146133711yescharacteristic
348C2#2146133911yescharacteristic
349C2#2146134511yescharacteristic
350C2#2146156911yescharacteristic
351C2C4×#1451984011yescharacteristic
352C2#2146159111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#391C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#391#6923
hypocenterC61#8235
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
12. #16840622C4semidirect
200. C61#8235semidirect

Maximal subgroups

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

subgroupindex
#214616042
C4×#145198442
C2×#168406222
#214606972
#214483882
#823561