Finite Group Databasebeta

← #30595413

Subgroups — #30595413

Order 15616.

522 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 110 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#21461711C211yesmaximal, characteristic
2C4×#14519834C211yesmaximal, characteristic
3#21460640C212yesmaximal, complemented
4#21460637C212yesmaximal, complemented
5C4×#14519757C211yesmaximal, characteristic
6C2×#14519834—21no—
7C2×#14519834—21no—
8C2×C4×#92420—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519757C411yescharacteristic
13C2×C4×Dic122C411yescharacteristic
14C2×C42×D61C2211yescharacteristic
15#16839667C2211yescharacteristic
16#16839661C2211yescharacteristic
17#16839647—21no—
18#16839636—21no—
19#16839619C411yescharacteristic
20C4×C4⋊Dic61—21no—
21C4×#11758198—21no—
22C4×C4⋊C4×C61C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25#14519834—24no—
26#14519834—42no—
27C4×#92420—42no—
28C22×Dic122C2×C411yescharacteristic
29C22×C4×D61C2×C411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C22×C4×D61D411yescharacteristic
32#14519757—22no—
33#14519757C814yescomplemented
34C4×Dic122—42no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×#11758196—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×C4×Dic61—21no—
42C2×C4×Dic61D411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61C2311yescharacteristic
45C42×D61—42no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50C2×C4⋊C4×C61C2×C411yescharacteristic
51C2×C4⋊C4×C61C2×C411yescharacteristic
52C2×C42×C61—21no—
53C2×C42×C61C2×C411yescharacteristic
54#95×C61—21no—
55C23×D61C22⋊C411yescharacteristic
56C22×C4×C61—21no—
57C22×C4×C61—21no—
58C22×C4×C61C22⋊C411yescharacteristic
59C22×C4×C61C22⋊C411yescharacteristic
60C22×C4×C61C22×C411yescharacteristic
61C22×Dic61—21no—
62C22×Dic61—21no—
63C22×Dic61C22⋊C411yescharacteristic
64C22×Dic61C2×D411yescharacteristic
65C22×Dic61C2×D411yescharacteristic
66C2×C4×D61—22no—
67C2×C4×D61—22no—
68C2×C4×D61—22no—
69C2×C4×D61—22no—
70C2×C4×D61—41no—
71C2×C4×D61—41no—
72C2×C4×D61—41no—
73C2×C4×D61—41no—
74C2×C4×D61C2×C812yes—
75C2×C4×D61M1612yes—
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—21no—
87C4⋊C4×C61—41no—
88C4⋊C4×C61C2×C812yes—
89C42×C61—22no—
90C42×C61—42no—
91#11758198—24no—
92#11758198—42no—
93C4⋊Dic61—24no—
94C4⋊Dic61—42no—
95C4⋊Dic61—41no—
96#11758196—42no—
97C4×Dic61—22no—
98C4×Dic61—41no—
99C4×Dic61—41no—
100C4×Dic61—42no—
101C23×C61C2×C22⋊C411yescharacteristic
102C22×D61—21no—
103C22×D61—21no—
104C22×D61—21no—
105C22×D61—21no—
106C22×D61—21no—
107C22×D61—21no—
108C22×D61C22⋊C812yes—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—22no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61#9912yes—
122C2×C4×C61#10412yes—
123C2×C4×C61C22×C811yescharacteristic
124C2×C4×C61C2×M1611yescharacteristic
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—22no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61C22⋊C812yes—
138C2×Dic61#13512yes—
139C2×Dic61#13712yes—
140C4×D61—42no—
141C4×D61—42no—
142C4×D61—44no—
143C4×D61—44no—
144Dic122—42no—
145Dic122—42no—
146#92420—44no—
147#92420—82no—
148#7583—611nomaximal, Sylow
149C22×C61C2×C22⋊C811yescharacteristic
150C22×C61C2×#9911yescharacteristic
151C22×C61#41311yescharacteristic
152C22×C61#41611yescharacteristic
153C22×C61#41911yescharacteristic
154C22×C61C2×#10411yescharacteristic
155C22×C61#42111yescharacteristic
156C2×D61—22no—
157C2×D61—22no—
158C2×D61—22no—
159C2×D61—41no—
160C2×D61—41no—
161C2×D61—41no—
162C2×D61—41no—
163C4×C61—21no—
164C4×C61—21no—
165C4×C61—22no—
166C4×C61—22no—
167C4×C61—42no—
168C4×C61—81no—
169Dic61—22no—
170Dic61—22no—
171Dic61—22no—
172Dic61—42no—
173Dic61—81no—
174C4×C22⋊Q8—611no—
175#1817—611no—
176C4×C22⋊C8—611no—
177#1272—612no—
178#1271—612no—
179C2×C61#145911yescharacteristic
180C2×C61#147611yescharacteristic
181C2×C61#147911yescharacteristic
182C2×C61#150811yescharacteristic
183C2×C61#151611yescharacteristic
184C2×C61#152911yescharacteristic
185C2×C61#155411yescharacteristic
186D61—42no—
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—611no—
198C4×C4⋊C4—1221no—
199C4×C4⋊C4#692311yescharacteristic
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×C4—611no—
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—1221no—
221C2×C22⋊C4—1221no—
222C2×C42—21no—
223C2×C42—611no—
224C2×C42—611no—
225C2×C42—611no—
226C2×C42—1221no—
227C2×C42—2442no—
228C2×C42C2×#692311yescharacteristic
229C22⋊C8—1224no—
230C22⋊C8—2442no—
231C4×C8—2442no—
232#95—21no—
233#95—1221no—
234#95—1221no—
235#95—1221no—
236#95—1221no—
237C24—611no—
238C2×Q8—612no—
239C2×Q8—1221no—
240C2×Q8—2441no—
241C2×Q8—2441no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—611no—
245C22×C4—611no—
246C22×C4—611no—
247C22×C4—612no—
248C22×C4—612no—
249C22×C4—1222no—
250C22×C4—1222no—
251C22×C4—1221no—
252C22×C4—1222no—
253C22×C4—1222no—
254C22×C4—1221no—
255C22×C4—2441no—
256C22×C4—2441no—
257C22×C4—2441no—
258C22×C4—2441no—
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—21no—
269C4⋊C4—41no—
270C4⋊C4—1224no—
271C4⋊C4—2441no—
272C4⋊C4—2442no—
273C4⋊C4—2442no—
274C4⋊C4D61⋊C812yes—
275C22⋊C4—1224no—
276C22⋊C4—2442no—
277C42—22no—
278C42—42no—
279C42—1222no—
280C42—2441no—
281C42—2441no—
282C42—2442no—
283C23—612no—
284C23—1221no—
285C23—1221no—
286C23—1221no—
287C23—1221no—
288C23—1221no—
289C23—1221no—
290C23C2×C22⋊#692311yescharacteristic
291Q8—2442no—
292Q8—2442no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—22no—
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—1221no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1222no—
315C2×C4—2442no—
316C2×C4—2442no—
317C2×C4—2444no—
318C2×C4—2444no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4#1451983612yes—
325C2×C4#1451984112yes—
326C2×C4C2×D61⋊C811yescharacteristic
327C2×C4D61⋊M1611yescharacteristic
328C8—4882no—
329C8—2444no—
330C22—1222no—
331C22—1222no—
332C22—1222no—
333C22—2441no—
334C22—2441no—
335C22—2441no—
336C22—2441no—
337C22D61⋊(C22⋊C8)11yescharacteristic
338C22C2×#1451983611yescharacteristic
339C22#1684074811yescharacteristic
340C22#1684075211yescharacteristic
341C22#1684075511yescharacteristic
342C22C2×#1451984111yescharacteristic
343C22#1684075911yescharacteristic
344C4—21no—
345C4—21no—
346C4—22no—
347C4—22no—
348C4—42no—
349C4—81no—
350C4—1222no—
351C4—1222no—
352C4—1222no—
353C4—4881no—
354C4—2442no—
355C2—2442no—
356C2#2146105611yescharacteristic
357C2#2146111111yescharacteristic
358C2#2146112211yescharacteristic
359C2#2146121811yescharacteristic
360C2#2146124711yescharacteristic
361C2#2146128411yescharacteristic
362C2#2146134411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC4×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC4×C4⋊C4#6923
hypocenterC61#7583
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #21460640C2semidirect
4. #21460637C2semidirect
33. #14519757C8semidirect
204. C61#7583semidirect

Maximal subgroups

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

subgroupindex
#214617112
C4×#145198342
#214606402
#214606372
C4×#145197572
#758361