Finite Group Databasebeta

← #30601791

Subgroups — #30601791

Order 15616.

498 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461752C211yesmaximal, characteristic
2C4×#14519844C211yesmaximal, characteristic
3C2×#16840622C212yesmaximal
4C2×#16840621C212yesmaximal
5#21454194C211yesmaximal, characteristic
6C2×#14519844—21no—
7C2×#14519844C2212yes—
8C2×#14519844C2212yes—
9C2×C4⋊#92420—21no—
10C2×C4×#92420—21no—
11#16840628—21no—
12#16840622—24no—
13#16840621—24no—
14C2×#14519776C2211yescharacteristic
15C2×#14519775C2211yescharacteristic
16#16839669C411yescharacteristic
17#16839668C411yescharacteristic
18#16839667C411yescharacteristic
19#16839666—21no—
20#16839666—21no—
21#16839626—21no—
22#16839626—21no—
23C42×Dic61C2211yescharacteristic
24C61×#391C411yescharacteristic
25C22×#92420—22no—
26C22×#92420—22no—
27#14519844—22no—
28#14519844—22no—
29#14519844—22no—
30#14519844—42no—
31#14519844D414yes—
32C4⋊#92420—42no—
33C4×#92420—42no—
34C22×Dic122—21no—
35C22×Dic122C2×C411yescharacteristic
36#14519776—22no—
37#14519776—22no—
38#14519775—22no—
39#14519775—22no—
40C2×C4⋊Dic61C2×C411yescharacteristic
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×#11758196—21no—
44C2×C4×Dic61C2×C411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49C2×C4×Dic61C2311yescharacteristic
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56C22×Q8×C61C2×C411yescharacteristic
57C2×C4⋊C4×C61C2×C411yescharacteristic
58C2×C42×C61C2×C411yescharacteristic
59#95×C61—21no—
60#95×C61—21no—
61C2×Q8×C61—22no—
62C2×Q8×C61—41no—
63C2×Q8×C61—41no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22×C411yescharacteristic
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C2×D411yescharacteristic
74C22×Dic61C2×D411yescharacteristic
75C2×Dic122—22no—
76C2×Dic122—42no—
77C2×Dic122—42no—
78C2×Dic122—41no—
79C2×Dic122—41no—
80C2×Dic122—41no—
81C2×Dic122—41no—
82C2×#92420—24no—
83C2×#92420—42no—
84C2×#92420—42no—
85C2×#92420—42no—
86C2×#92420—42no—
87C2×#92420—42no—
88C4⋊C4×C61—22no—
89C42×C61—41no—
90C4⋊Dic61—22no—
91#11758196—42no—
92#11758196—41no—
93#11758196—41no—
94#11758196—41no—
95#11758196—41no—
96C4×Dic61—22no—
97C4×Dic61—21no—
98C4×Dic61—21no—
99C4×Dic61—41no—
100C4×Dic61SD1612yes—
101C4×Dic61SD1612yes—
102C4×Dic61Q1612yes—
103C4×Dic61Q1612yes—
104C4×Dic61C2×D412yes—
105C4×Dic61#4112yes—
106C23×C61C2×C22⋊C411yescharacteristic
107Q8×C61—82no—
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—41no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61#10312yes—
121C2×C4×C61#10312yes—
122C2×C4×C61C4×D412yes—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61#10312yes—
134C2×Dic61#10312yes—
135C2×Dic61#12112yes—
136C2×Dic61#12411yescharacteristic
137C2×Dic61#12711yescharacteristic
138C2×Dic61C2×SD1611yescharacteristic
139C2×Dic61C2×SD1611yescharacteristic
140C2×Dic61C2×Q1611yescharacteristic
141C2×Dic61C2×Q1611yescharacteristic
142C2×Dic61#13512yes—
143C2×Dic61AGL(1,ℤ/8)11yescharacteristic
144C2×Dic61#13711yescharacteristic
145Dic122—82no—
146Dic122—82no—
147Dic122—82no—
148#92420—44no—
149#92420—82no—
150#9697—611nomaximal, Sylow
151C22×C61#39011yescharacteristic
152C22×C61#41311yescharacteristic
153C22×C61#41311yescharacteristic
154C22×C61C2×#10311yescharacteristic
155C22×C61C2×#10311yescharacteristic
156C22×C61#41611yescharacteristic
157C22×C61#41711yescharacteristic
158C4×C61—22no—
159C4×C61—22no—
160C4×C61—22no—
161C4×C61—81no—
162C4×C61—81no—
163Dic61—22no—
164Dic61—22no—
165Dic61—81no—
166Dic61—81no—
167Dic61#46312yes—
168Dic61#46412yes—
169Dic61#48711yescharacteristic
170Dic61#48711yescharacteristic
171Dic61#49211yescharacteristic
172Dic61#49411yescharacteristic
173#2862—611no—
174#1842—611no—
175C4×C4⋊C8—611no—
176C2×#333—612no—
177C2×#332—612no—
178C2×C61#154211yescharacteristic
179C2×C61#154211yescharacteristic
180C2×C61#155011yescharacteristic
181C2×C61#155011yescharacteristic
182C2×C61#195611yescharacteristic
183C2×C61#196711yescharacteristic
184C2×C61#198311yescharacteristic
185C2×C4⋊Q8—611no—
186C2×C4⋊Q8—611no—
187C2×C4⋊C8—612no—
188C2×C4⋊C8—612no—
189C2×C4⋊C8—1221no—
190C2×C4⋊C8—1221no—
191C2×C4×C8—1221no—
192#391—611no—
193#391—611no—
194#391—611no—
195#391—1221no—
196#391—1221no—
197#391#692311yescharacteristic
198#382—1221no—
199#382—1221no—
200C43—611no—
201#336—1221no—
202#333—1224no—
203#332—1224no—
204C61#969711yescharacteristic, complemented, Sylow
205C22×Q8—611no—
206C22×Q8—1221no—
207C22×Q8C2×#692311yescharacteristic
208C22×C8—1222no—
209C22×C8—1222no—
210C4⋊Q8—1222no—
211C4⋊Q8—1222no—
212C4⋊Q8—1222no—
213C4⋊Q8—1222no—
214C2×C4⋊C4—611no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4—1221no—
217C2×C4⋊C4—1221no—
218C2×C4⋊C4C2×#692311yescharacteristic
219C2×C42—611no—
220C2×C42—611no—
221C2×C42—611no—
222C2×C42—611no—
223C2×C42—611no—
224C2×C42—611no—
225C2×C42C2×#692311yescharacteristic
226C4⋊C8—614no—
227C4⋊C8—1222no—
228C4⋊C8—1222no—
229C4⋊C8—1222no—
230C4⋊C8—2442no—
231C4⋊C8—2442no—
232C4×C8—2442no—
233#95—21no—
234#95—21no—
235#95—1221no—
236#95—1221no—
237#95—1221no—
238#95—1221no—
239#95—1221no—
240#95—1221no—
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—1222no—
245C2×Q8—2441no—
246C2×Q8—2441no—
247C2×Q8—2442no—
248C2×Q8—2442no—
249C2×Q8—2441no—
250C2×Q8—2441no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—611no—
254C22×C4—611no—
255C22×C4—611no—
256C22×C4—611no—
257C22×C4—1221no—
258C22×C4—1221no—
259C22×C4C22⋊#692311yescharacteristic
260C22×C4C22⋊#692311yescharacteristic
261C22×C4C22×#692311yescharacteristic
262C2×C8—1224no—
263C2×C8—2442no—
264C2×C8—2442no—
265C2×C8—2442no—
266C2×C8—2442no—
267C2×C8—2442no—
268C4⋊C4—22no—
269C4⋊C4—1222no—
270C4⋊C4—2441no—
271C4⋊C4—2441no—
272C4⋊C4—2442no—
273C4⋊C4—2441no—
274C4⋊C4—2441no—
275C42—41no—
276C42—612no—
277C42—612no—
278C42—612no—
279C42—612no—
280C42—612no—
281C42—612no—
282C42—1221no—
283C42—1222no—
284C42—1221no—
285C42—2441no—
286C23C2×C22⋊#692311yescharacteristic
287Q8—82no—
288Q8—4882no—
289Q8—4882no—
290Q8—4882no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—612no—
304C2×C4—611no—
305C2×C4—611no—
306C2×C4—611no—
307C2×C4—611no—
308C2×C4—611no—
309C2×C4—611no—
310C2×C4—612no—
311C2×C4—611no—
312C2×C4—611no—
313C2×C4—612no—
314C2×C4—612no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4#1451984012yes—
326C2×C4#1451984012yes—
327C2×C4D4×#692312yes—
328C8—4882no—
329C8—2444no—
330C22#1684071411yescharacteristic
331C22#1684074811yescharacteristic
332C22#1684074911yescharacteristic
333C22C2×#1451984011yescharacteristic
334C22C2×#1451984011yescharacteristic
335C22#1684075211yescharacteristic
336C22#1684075311yescharacteristic
337C4—22no—
338C4—22no—
339C4—22no—
340C4—81no—
341C4—81no—
342C4—611no—
343C4—611no—
344C4—611no—
345C4—611no—
346C4—612no—
347C4—612no—
348C4—1222no—
349C4—1222no—
350C4—4881no—
351C4—4881no—
352C2#2146132011yescharacteristic
353C2#2146132111yescharacteristic
354C2#2146133611yescharacteristic
355C2#2146133711yescharacteristic
356C2#2146194611yescharacteristic
357C2#2146196311yescharacteristic
358C2#2146198711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#391C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#391#6923
hypocenterC61#9697
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
204. C61#9697semidirect

Maximal subgroups

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

subgroupindex
#214617522
C4×#145198442
C2×#168406222
C2×#168406212
#214541942
#969761