Finite Group Databasebeta

← #30595416

Subgroups — #30595416

Order 15616.

522 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461709C211yesmaximal, characteristic
2C4×C22⋊#92420C211yesmaximal, characteristic
3#21460640C212yesmaximal, complemented
4#21460638C212yesmaximal, complemented
5#21448347C211yesmaximal, characteristic
6C2×C22⋊#92420—21no—
7C2×C22⋊#92420—21no—
8C2×C4×#92420—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519756C411yescharacteristic
13C2×#14519742C411yescharacteristic
14C22×C4×Dic61C2211yescharacteristic
15#16839667C2211yescharacteristic
16#16839658C2211yescharacteristic
17#16839644—21no—
18#16839634—21no—
19C4⋊C4×Dic61C411yescharacteristic
20#16839613—21no—
21C22⋊C4×Dic61—21no—
22C61×#380C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25C22⋊#92420—24no—
26C22⋊#92420—42no—
27C4×#92420—42no—
28C22×Dic122C2×C411yescharacteristic
29C23×Dic61D411yescharacteristic
30C23×Dic61D411yescharacteristic
31#14519756—22no—
32#14519756C814yescomplemented
33#14519742—42no—
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×C22⋊Dic61—21no—
39C2×C4×Dic61—21no—
40C2×C4×Dic61—21no—
41C2×C4×Dic61—42no—
42C2×C4×Dic61C2×C411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61C2311yescharacteristic
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50C23×C4×C61C2×C411yescharacteristic
51C2×C4⋊C4×C61C2×C411yescharacteristic
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C22⋊C4×C61—21no—
54#95×C61—21no—
55C24×C61C22⋊C411yescharacteristic
56C22×C4×C61—21no—
57C22×C4×C61—21no—
58C22×C4×C61—41no—
59C22×C4×C61—41no—
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C2×C812yes—
62C22×C4×C61M1612yes—
63C22×C4×C61C22×C411yescharacteristic
64C22×Dic61—21no—
65C22×Dic61—21no—
66C22×Dic61—22no—
67C22×Dic61—22no—
68C22×Dic61—22no—
69C22×Dic61—22no—
70C22×Dic61—41no—
71C22×Dic61—41no—
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C2×D411yescharacteristic
75C22×Dic61C2×D411yescharacteristic
76C2×Dic122—21no—
77C2×Dic122—41no—
78C2×Dic122—41no—
79C2×Dic122C2×C812yes—
80C2×#92420—24no—
81C2×#92420—42no—
82C2×#92420—42no—
83C2×#92420—42no—
84C2×#92420—42no—
85C2×#92420—42no—
86C4⋊C4×C61—41no—
87C4⋊C4×C61—41no—
88C22⋊C4×C61—42no—
89C22⋊Dic61—24no—
90C4⋊Dic61—21no—
91C4⋊Dic61C2×C812yes—
92#11758196—24no—
93#11758196—42no—
94#11758196—42no—
95C4×Dic61—22no—
96C4×Dic61—22no—
97C4×Dic61—41no—
98C4×Dic61—41no—
99C4×Dic61—42no—
100C4×Dic61—42no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61C22⋊C812yes—
108C23×C61C2×C22⋊C411yescharacteristic
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—42no—
114C2×C4×C61—42no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61C22⋊C812yes—
122C2×C4×C61C22×C811yescharacteristic
123C2×C4×C61C2×M1611yescharacteristic
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—22no—
133C2×Dic61—22no—
134C2×Dic61—44no—
135C2×Dic61—44no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61#9912yes—
141C2×Dic61#10412yes—
142C2×Dic61#13512yes—
143C2×Dic61#13712yes—
144Dic122—42no—
145Dic122—42no—
146#92420—44no—
147#92420—82no—
148#7583—611nomaximal, Sylow
149C22×C61—22no—
150C22×C61—22no—
151C22×C61—22no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61—41no—
155C22×C61—41no—
156C22×C61C2×C22⋊C811yescharacteristic
157C22×C61C2×#9911yescharacteristic
158C22×C61#41311yescharacteristic
159C22×C61#41611yescharacteristic
160C22×C61#41911yescharacteristic
161C22×C61C2×#10411yescharacteristic
162C22×C61#42111yescharacteristic
163C4×C61—21no—
164C4×C61—21no—
165C4×C61—22no—
166C4×C61—81no—
167C4×C61—81no—
168Dic61—22no—
169Dic61—22no—
170Dic61—22no—
171Dic61—22no—
172Dic61—42no—
173Dic61—42no—
174C4×C22⋊Q8—611no—
175#1817—611no—
176C4×C22⋊C8—611no—
177#1272—612no—
178#1271—612no—
179C2×C61—42no—
180C2×C61#145911yescharacteristic
181C2×C61#147611yescharacteristic
182C2×C61#147911yescharacteristic
183C2×C61#150811yescharacteristic
184C2×C61#151611yescharacteristic
185C2×C61#152911yescharacteristic
186C2×C61#155411yescharacteristic
187C2×C22⋊Q8—611no—
188C2×C4×Q8—611no—
189C22×C42—611no—
190C2×C22⋊C8—1221no—
191C2×C22⋊C8—1221no—
192C2×C4×C8—1221no—
193#391—611no—
194#389—611no—
195#387—1221no—
196#385—1221no—
197#380#692311yescharacteristic
198C4×C4⋊C4—611no—
199C4×C4⋊C4—1221no—
200C4×C22⋊C4—1221no—
201#336—612no—
202#336—612no—
203#336—1221no—
204C61#758311yescharacteristic, complemented, Sylow
205C22×Q8—611no—
206C23×C4—611no—
207C23×C4—611no—
208C23×C4C2×#692311yescharacteristic
209C22×C8—1222no—
210C22×C8—1222no—
211C22⋊Q8—614no—
212C22⋊Q8—1222no—
213C4×Q8—2442no—
214C2×C4⋊C4—611no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4—1221no—
217C2×C4⋊C4—1221no—
218C2×C4⋊C4C2×#692311yescharacteristic
219C2×C4⋊C4C2×#692311yescharacteristic
220C2×C22⋊C4—21no—
221C2×C22⋊C4—1221no—
222C2×C42—611no—
223C2×C42—611no—
224C2×C42—611no—
225C2×C42—611no—
226C2×C42—1221no—
227C2×C42—1221no—
228C2×C42—2442no—
229C22⋊C8—1224no—
230C22⋊C8—2442no—
231C4×C8—2442no—
232#95—21no—
233#95—1221no—
234#95—1221no—
235#95—1221no—
236#95—1221no—
237C24C22⋊#692311yescharacteristic
238C2×Q8—612no—
239C2×Q8—1221no—
240C2×Q8—2441no—
241C2×Q8—2441no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—611no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—611no—
250C22×C4—1222no—
251C22×C4—1222no—
252C22×C4—1222no—
253C22×C4—1222no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—2441no—
257C22×C4—2441no—
258C22×C4D61⋊C812yes—
259C22×C4#1175821312yes—
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—41no—
269C4⋊C4—41no—
270C4⋊C4—612no—
271C4⋊C4—1224no—
272C4⋊C4—1221no—
273C4⋊C4—2442no—
274C4⋊C4—2442no—
275C22⋊C4—42no—
276C22⋊C4—1224no—
277C42—1222no—
278C42—1222no—
279C42—2441no—
280C42—2441no—
281C42—2442no—
282C42—2442no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23#1451983412yes—
290C23C2×C22⋊#692311yescharacteristic
291Q8—2442no—
292Q8—2442no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—612no—
306C2×C4—612no—
307C2×C4—612no—
308C2×C4—612no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1222no—
318C2×C4—1222no—
319C2×C4—2444no—
320C2×C4—2444no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4#1451983412yes—
326C2×C4C2×D61⋊C811yescharacteristic
327C2×C4C2×#1175821311yescharacteristic
328C8—4882no—
329C8—2444no—
330C22—22no—
331C22—22no—
332C22—22no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22C2×#1451983411yescharacteristic
338C22D61⋊#9911yescharacteristic
339C22#1684074911yescharacteristic
340C22#1684075211yescharacteristic
341C22#1684075511yescharacteristic
342C22D61⋊#10411yescharacteristic
343C22#1684076011yescharacteristic
344C4—22no—
345C4—21no—
346C4—21no—
347C4—81no—
348C4—81no—
349C4—1222no—
350C4—1222no—
351C4—1222no—
352C4—1222no—
353C4—2442no—
354C4—2442no—
355C2—42no—
356C2#2146105711yescharacteristic
357C2#2146111211yescharacteristic
358C2#2146112311yescharacteristic
359C2#2146121711yescharacteristic
360C2#2146124411yescharacteristic
361C2#2146128511yescharacteristic
362C2#2146134511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#380C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#380#6923
hypocenterC61#7583
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #21460640C2semidirect
4. #21460638C2semidirect
32. #14519756C8semidirect
204. C61#7583semidirect

Maximal subgroups

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

subgroupindex
#214617092
C4×C22⋊#924202
#214606402
#214606382
#214483472
#758361