Finite Group Databasebeta

← #30598936

Subgroups — #30598936

Order 15616.

496 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461752C211yesmaximal, characteristic
2#21461735C211yesmaximal, characteristic
3C2×#16840621C212yesmaximal
4#21460697C212yesmaximal
5#21448390C211yesmaximal, characteristic
6C2×#14519844—21no—
7C2×#14519844C2212yes—
8C2×#14519844C2212yes—
9C2×C4⋊#92420—21no—
10#16840628—21no—
11#16840628—21no—
12#16840621—24no—
13C2×#14519776C2211yescharacteristic
14C2×#14519742—21no—
15#16839666—21no—
16#16839660C411yescharacteristic
17#16839657—21no—
18#16839631C2211yescharacteristic
19C4⋊C4×Dic61C411yescharacteristic
20C4⋊C4×Dic61C411yescharacteristic
21#16839613—21no—
22C42×Dic61C2211yescharacteristic
23C61×#389C411yescharacteristic
24C22×#92420—22no—
25C22×#92420—22no—
26#14519844—22no—
27#14519844—22no—
28#14519844—22no—
29#14519844—22no—
30#14519844—42no—
31C4⋊#92420—42no—
32C22×Dic122—21no—
33#14519776—21no—
34#14519776—21no—
35#14519776D412yes—
36#14519776Q812yes—
37#14519742—44no—
38C2×C4⋊Dic61C2×C411yescharacteristic
39C2×C4⋊Dic61C2×C411yescharacteristic
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—
54#14519684—21no—
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61C2×C411yescharacteristic
57C2×C4⋊C4×C61C2×C411yescharacteristic
58C2×C42×C61C2×C411yescharacteristic
59#95×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22×C411yescharacteristic
65C22×Dic61—21no—
66C22×Dic61—21no—
67C22×Dic61C22⋊C411yescharacteristic
68C22×Dic61C22⋊C411yescharacteristic
69C22×Dic61C2×D411yescharacteristic
70C22×Dic61C2×D411yescharacteristic
71C2×Dic122—22no—
72C2×Dic122—22no—
73C2×Dic122—42no—
74C2×Dic122—42no—
75C2×#92420—42no—
76C2×#92420—42no—
77C2×#92420—42no—
78C2×#92420—42no—
79C2×#92420—42no—
80C2×#92420—42no—
81C4⋊C4×C61—21no—
82C4⋊C4×C61—42no—
83C4⋊C4×C61—41no—
84C4⋊C4×C61C4⋊C412yes—
85C42×C61—41no—
86C4⋊Dic61—21no—
87C4⋊Dic61—41no—
88C4⋊Dic61C4⋊C412yes—
89#11758196—22no—
90#11758196—22no—
91#11758196—42no—
92#11758196—41no—
93#11758196—42no—
94#11758196—41no—
95C4×Dic61—22no—
96C4×Dic61—22no—
97C4×Dic61—21no—
98C4×Dic61—22no—
99C4×Dic61—21no—
100C4×Dic61—42no—
101C4×Dic61—42no—
102C4×Dic61SD1612yes—
103C4×Dic61Q1612yes—
104C4×Dic61C2×D411yescharacteristic
105C4×Dic61C2×Q811yescharacteristic
106C4×Dic61#4111yescharacteristic
107C4×Dic61#4111yescharacteristic
108C23×C61C2×C22⋊C411yescharacteristic
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—22no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61#10312yes—
123C2×C4×C61C2×C4⋊C411yescharacteristic
124C2×C4×C61#11711yescharacteristic
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—22no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61#10112yes—
136C2×Dic61#10312yes—
137C2×Dic61#12111yescharacteristic
138C2×Dic61#12111yescharacteristic
139C2×Dic61C22⋊Q811yescharacteristic
140C2×Dic61C22⋊Q811yescharacteristic
141C2×Dic61C2×SD1611yescharacteristic
142C2×Dic61C2×Q1611yescharacteristic
143C2×Dic61#13512yes—
144C2×Dic61AGL(1,ℤ/8)11yescharacteristic
145C2×Dic61AGL(1,ℤ/8)12yes—
146C2×Dic61#13711yescharacteristic
147Dic122—44no—
148Dic122—44no—
149#92420—82no—
150#92420—82no—
151#8591—611nomaximal, Sylow
152C22×C61#38011yescharacteristic
153C22×C61C2×#10111yescharacteristic
154C22×C61#41311yescharacteristic
155C22×C61C2×#10311yescharacteristic
156C22×C61#41611yescharacteristic
157C22×C61#41711yescharacteristic
158C22×C61#41811yescharacteristic
159C4×C61—22no—
160C4×C61—21no—
161C4×C61—21no—
162C4×C61—42no—
163C4×C61—41no—
164C4×C61—81no—
165Dic61—22no—
166Dic61—22no—
167Dic61—42no—
168Dic61—81no—
169Dic61#46011yescharacteristic
170Dic61#46211yescharacteristic
171Dic61#46312yes—
172Dic61#47511yescharacteristic
173Dic61#47711yescharacteristic
174Dic61#47812yes—
175C4×C4⋊Q8—611no—
176#1842—611no—
177#1831—611no—
178C2×#332—612no—
179#1296—612no—
180C2×C61#154211yescharacteristic
181C2×C61#154911yescharacteristic
182C2×C61#155211yescharacteristic
183C2×C61#155711yescharacteristic
184C2×C61#180111yescharacteristic
185C2×C61#180311yescharacteristic
186C2×C61#180411yescharacteristic
187C2×C4⋊Q8—611no—
188C2×C4×Q8—1221no—
189C2×C4⋊C8—612no—
190C2×C4⋊C8—612no—
191C2×C4⋊C8—1221no—
192C2×C4⋊C8—1221no—
193#391—1221no—
194#389—611no—
195#389—1221no—
196#389#692311yescharacteristic
197#384—611no—
198C4×C4⋊C4—611no—
199C4×C4⋊C4—611no—
200C4×C4⋊C4—1221no—
201C43—611no—
202#336—1221no—
203#336—1221no—
204#332—1224no—
205C61#859111yescharacteristic, complemented, Sylow
206C22×Q8—1221no—
207C22×C8—1222no—
208C22×C8—1222no—
209C4⋊Q8—612no—
210C4⋊Q8—612no—
211C4⋊Q8—1221no—
212C4⋊Q8—1221no—
213C4×Q8—2444no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—611no—
216C2×C4⋊C4—611no—
217C2×C4⋊C4—1221no—
218C2×C4⋊C4—1221no—
219C2×C4⋊C4—1221no—
220C2×C4⋊C4—1221no—
221C2×C4⋊C4C2×#692311yescharacteristic
222C2×C4⋊C4C2×#692311yescharacteristic
223C2×C42—611no—
224C2×C42—611no—
225C2×C42—611no—
226C2×C42—611no—
227C2×C42—611no—
228C2×C42—611no—
229C2×C42—1221no—
230C2×C42—1221no—
231C2×C42C2×#692311yescharacteristic
232C4⋊C8—1222no—
233C4⋊C8—1222no—
234C4⋊C8—1222no—
235C4⋊C8—1222no—
236C4⋊C8—2442no—
237C4⋊C8—2442no—
238#95—21no—
239#95—1221no—
240#95—1221no—
241#95—1221no—
242C2×Q8—1222no—
243C2×Q8—1222no—
244C2×Q8—2442no—
245C2×Q8—2442no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—611no—
249C22×C4—611no—
250C22×C4—611no—
251C22×C4—611no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4C22⋊#692311yescharacteristic
255C22×C4C22⋊#692311yescharacteristic
256C22×C4C22×#692311yescharacteristic
257C2×C8—2442no—
258C2×C8—2442no—
259C2×C8—2442no—
260C2×C8—2442no—
261C2×C8—2442no—
262C2×C8—2442no—
263C4⋊C4—21no—
264C4⋊C4—41no—
265C4⋊C4—42no—
266C4⋊C4—612no—
267C4⋊C4—1222no—
268C4⋊C4—1222no—
269C4⋊C4—1221no—
270C4⋊C4—2441no—
271C4⋊C4—2442no—
272C4⋊C4—2441no—
273C4⋊C4—2441no—
274C4⋊C4—2442no—
275C4⋊C4C4⋊#692312yes—
276C42—41no—
277C42—612no—
278C42—612no—
279C42—611no—
280C42—611no—
281C42—611no—
282C42—611no—
283C42—1221no—
284C42—1222no—
285C42—1222no—
286C42—1221no—
287C42—1222no—
288C42—2442no—
289C42—2442no—
290C23C2×C22⋊#692311yescharacteristic
291Q8—2444no—
292Q8—2444no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—611no—
307C2×C4—611no—
308C2×C4—611no—
309C2×C4—611no—
310C2×C4—611no—
311C2×C4—611no—
312C2×C4—612no—
313C2×C4—611no—
314C2×C4—611no—
315C2×C4—612no—
316C2×C4—612no—
317C2×C4—612no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1222no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4—2441no—
327C2×C4—2441no—
328C2×C4#1451984012yes—
329C2×C4C2×C4⋊#692311yescharacteristic
330C2×C4#1451985611yescharacteristic
331C8—4882no—
332C8—4882no—
333C22#1684070411yescharacteristic
334C22D61⋊#10111yescharacteristic
335C22#1684074911yescharacteristic
336C22C2×#1451984011yescharacteristic
337C22#1684075211yescharacteristic
338C22#1684075311yescharacteristic
339C22#1684075411yescharacteristic
340C4—22no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—42no—
345C4—81no—
346C4—611no—
347C4—611no—
348C4—611no—
349C4—611no—
350C4—612no—
351C4—612no—
352C4—1222no—
353C4—1222no—
354C4—4881no—
355C4—2442no—
356C2#2146132111yescharacteristic
357C2#2146133511yescharacteristic
358C2#2146134111yescharacteristic
359C2#2146135111yescharacteristic
360C2#2146168611yescharacteristic
361C2#2146168811yescharacteristic
362C2#2146168911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#389C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#389#6923
hypocenterC61#8591
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
205. C61#8591semidirect

Maximal subgroups

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

subgroupindex
#214617522
#214617352
C2×#168406212
#214606972
#214483902
#859161