Finite Group Databasebeta

← #30598861

Subgroups — #30598861

Order 15616.

492 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461752C211yesmaximal, characteristic
2C4×C4⋊#92420C211yesmaximal, characteristic
3C2×Q8⋊#92420C212yesmaximal
4#21460655C212yesmaximal
5#21448294C211yesmaximal, characteristic
6C2×#14519844—21no—
7C2×#14519844—21no—
8C2×C4⋊#92420—21no—
9C2×C4⋊#92420C2212yes—
10C2×C4×#92420C2212yes—
11#16840628—21no—
12Q8⋊#92420—24no—
13C2×Q8×Dic61C2211yescharacteristic
14#16839669C411yescharacteristic
15#16839660C411yescharacteristic
16#16839658C411yescharacteristic
17#16839647—21no—
18#16839645—21no—
19C4⋊C4×Dic61C2211yescharacteristic
20#16839613—21no—
21#16839607—21no—
22C42×Dic61C2211yescharacteristic
23C61×#391C411yescharacteristic
24C22×#92420—22no—
25C22×#92420—22no—
26#14519844—42no—
27#14519844—42no—
28C4⋊#92420—24no—
29C4⋊#92420—22no—
30C4⋊#92420—22no—
31C4×#92420—22no—
32C4×#92420—22no—
33Q8×Dic61—21no—
34Q8×Dic61—21no—
35Q8×Dic61D412yes—
36Q8×Dic61Q812yes—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61C2×C411yescharacteristic
39C2×C4⋊Dic61C2×C411yescharacteristic
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×C4×Dic61—21no—
43C2×C4×Dic61—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—
55C22×Q8×C61C2×C411yescharacteristic
56C2×C4⋊C4×C61C2×C411yescharacteristic
57C2×C42×C61C2×C411yescharacteristic
58#95×C61—21no—
59#95×C61—21no—
60C2×Q8×C61—21no—
61C2×Q8×C61—22no—
62C2×Q8×C61—22no—
63C2×Q8×C61C4⋊C412yes—
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×#92420—24no—
76C2×#92420—42no—
77C2×#92420—42no—
78C2×#92420—42no—
79C2×#92420—42no—
80C2×#92420—42no—
81C4⋊C4×C61—22no—
82C42×C61—22no—
83C4⋊Dic61—21no—
84C4⋊Dic61—22no—
85C4⋊Dic61—22no—
86C4⋊Dic61—22no—
87C4⋊Dic61C4⋊C412yes—
88#11758196—42no—
89#11758196—42no—
90C4×Dic61—22no—
91C4×Dic61—22no—
92C4×Dic61—22no—
93C4×Dic61—22no—
94C4×Dic61—21no—
95C4×Dic61—21no—
96C4×Dic61—41no—
97C4×Dic61—41no—
98C4×Dic61—41no—
99C4×Dic61SD1612yes—
100C4×Dic61Q1612yes—
101C4×Dic61C2×D411yescharacteristic
102C4×Dic61C2×Q811yescharacteristic
103C4×Dic61#4111yescharacteristic
104C4×Dic61#4111yescharacteristic
105C23×C61C2×C22⋊C411yescharacteristic
106Q8×C61—24no—
107Q8×C61—42no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—22no—
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#10312yes—
120C2×C4×C61C2×C4⋊C411yescharacteristic
121C2×C4×C61#11711yescharacteristic
122C2×C4×C61#13112yes—
123C2×C4×C61#13112yes—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—22no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61#10312yes—
137C2×Dic61#10412yes—
138C2×Dic61#12111yescharacteristic
139C2×Dic61#12111yescharacteristic
140C2×Dic61C22⋊Q811yescharacteristic
141C2×Dic61C22⋊Q811yescharacteristic
142C2×Dic61C2×SD1611yescharacteristic
143C2×Dic61C2×Q1611yescharacteristic
144C2×Dic61AGL(1,ℤ/8)11yescharacteristic
145C2×Dic61#13711yescharacteristic
146#92420—44no—
147#92420—82no—
148#8568—611nomaximal, Sylow
149C22×C61#38011yescharacteristic
150C22×C61#40811yescharacteristic
151C22×C61#40811yescharacteristic
152C22×C61C2×#10311yescharacteristic
153C22×C61#41711yescharacteristic
154C22×C61C2×#10411yescharacteristic
155C22×C61#42111yescharacteristic
156C4×C61—22no—
157C4×C61—42no—
158C4×C61—41no—
159C4×C61—81no—
160C4×C61#42412yes—
161C4×C61#43312yes—
162Dic61—21no—
163Dic61—21no—
164Dic61—22no—
165Dic61—22no—
166Dic61—42no—
167Dic61—81no—
168Dic61#46011yescharacteristic
169Dic61#46211yescharacteristic
170Dic61#47511yescharacteristic
171Dic61#47711yescharacteristic
172#2295—611no—
173#1842—611no—
174C4×C4⋊C8—611no—
175C2×Q8⋊C8—612no—
176#1279—612no—
177C2×C61#148111yescharacteristic
178C2×C61#148311yescharacteristic
179C2×C61#149311yescharacteristic
180C2×C61#149511yescharacteristic
181C2×C61#179811yescharacteristic
182C2×C61#180311yescharacteristic
183C2×C61#180611yescharacteristic
184C2×C4×Q8—611no—
185C2×C4⋊C8—612no—
186C2×C4⋊C8—1221no—
187C2×C4⋊C8—1221no—
188C2×C4⋊C8—1221no—
189C2×C4×C8—612no—
190#391—611no—
191#391#692311yescharacteristic
192#389—611no—
193#389—611no—
194#387—1221no—
195#387—1221no—
196C4×C4⋊C4—611no—
197C4×C4⋊C4—1221no—
198#376—1221no—
199C43—611no—
200#336—1221no—
201Q8⋊C8—1224no—
202C61#856811yescharacteristic, complemented, Sylow
203C22×Q8C2×#692311yescharacteristic
204C22×C8—1222no—
205C22×C8—1222no—
206C4×Q8—612no—
207C4×Q8—612no—
208C4×Q8—1221no—
209C4×Q8—1221no—
210C2×C4⋊C4—611no—
211C2×C4⋊C4—611no—
212C2×C4⋊C4—1221no—
213C2×C4⋊C4—1221no—
214C2×C4⋊C4—1221no—
215C2×C4⋊C4C2×#692311yescharacteristic
216C2×C42—611no—
217C2×C42—611no—
218C2×C42—611no—
219C2×C42—611no—
220C2×C42—611no—
221C2×C42—611no—
222C2×C42—1221no—
223C2×C42—1221no—
224C2×C42C2×#692311yescharacteristic
225C4⋊C8—1222no—
226C4⋊C8—1222no—
227C4⋊C8—1224no—
228C4⋊C8—2442no—
229C4⋊C8—2442no—
230C4×C8—1222no—
231C4×C8—1222no—
232#95—21no—
233#95—21no—
234#95—1221no—
235#95—1221no—
236#95—1221no—
237#95—1221no—
238#95—1221no—
239C2×Q8—21no—
240C2×Q8—22no—
241C2×Q8—22no—
242C2×Q8C4⋊#692312yes—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—611no—
246C22×C4—611no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—1221no—
250C22×C4—1221no—
251C22×C4C22⋊#692311yescharacteristic
252C22×C4C22⋊#692311yescharacteristic
253C22×C4C22×#692311yescharacteristic
254C2×C8—1224no—
255C2×C8—2442no—
256C2×C8—2442no—
257C2×C8—2442no—
258C2×C8—2442no—
259C2×C8—2442no—
260C4⋊C4—22no—
261C4⋊C4—612no—
262C4⋊C4—1222no—
263C4⋊C4—1222no—
264C4⋊C4—1221no—
265C4⋊C4—1222no—
266C4⋊C4—2442no—
267C4⋊C4—2442no—
268C42—22no—
269C42—612no—
270C42—612no—
271C42—611no—
272C42—611no—
273C42—611no—
274C42—611no—
275C42—1222no—
276C42—1221no—
277C42—1221no—
278C42—1222no—
279C42—1222no—
280C42—1222no—
281C42—2441no—
282C42—2441no—
283C42—2441no—
284C23C2×C22⋊#692311yescharacteristic
285Q8—24no—
286Q8—42no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—22no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—611no—
299C2×C4—611no—
300C2×C4—611no—
301C2×C4—611no—
302C2×C4—611no—
303C2×C4—611no—
304C2×C4—611no—
305C2×C4—611no—
306C2×C4—612no—
307C2×C4—612no—
308C2×C4—1221no—
309C2×C4—1221no—
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
323C2×C4#1451986412yes—
324C2×C4#1451986412yes—
325C8—4882no—
326C8—2444no—
327C22#1684070411yescharacteristic
328C22#1684073511yescharacteristic
329C22#1684073611yescharacteristic
330C22C2×#1451984011yescharacteristic
331C22#1684075311yescharacteristic
332C22D61⋊#10411yescharacteristic
333C22#1684076111yescharacteristic
334C4—22no—
335C4—42no—
336C4—41no—
337C4—81no—
338C4—611no—
339C4—611no—
340C4—611no—
341C4—611no—
342C4—1222no—
343C4—1222no—
344C4—1221no—
345C4—1221no—
346C4—4881no—
347C4—2442no—
348C4#1684076812yes—
349C4#1684078612yes—
350C2#2146112811yescharacteristic
351C2#2146113511yescharacteristic
352C2#2146116711yescharacteristic
353C2#2146117611yescharacteristic
354C2#2146167711yescharacteristic
355C2#2146168811yescharacteristic
356C2#2146169411yescharacteristic
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#8568
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
202. C61#8568semidirect

Maximal subgroups

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

subgroupindex
#214617522
C4×C4⋊#924202
C2×Q8⋊#924202
#214606552
#214482942
#856861