Finite Group Databasebeta

← #30599287

Subgroups — #30599287

Order 15616.

514 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 114 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#21461676C211yesmaximal, characteristic
2#21461676C211yesmaximal, characteristic
3#21460697C212yesmaximal, complemented
4#21460697C212yesmaximal, complemented
5#21448223C211yesmaximal, characteristic
6C2×#14519844C2212yes—
7C2×#14519844C2212yes—
8C2×#14519834—21no—
9C2×#14519834—21no—
10#16840628—21no—
11#16840628—21no—
12C2×#14519734—21no—
13C2×C42×D61C2211yescharacteristic
14#16839631C2211yescharacteristic
15#16839631C2211yescharacteristic
16#16839626—21no—
17#16839621—21no—
18#16839619C411yescharacteristic
19#16839619C411yescharacteristic
20C4×#11758196—21no—
21C4×C4⋊Dic61C411yescharacteristic
22C4×C4⋊C4×C61C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25#14519844—24no—
26#14519844—24no—
27#14519834—42no—
28#14519834—42no—
29C22×C4×D61C2×C411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C22×C4×D61D411yescharacteristic
32#14519734—42no—
33#14519734—42no—
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×C4×Dic61—21no—
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61C2311yescharacteristic
46C42×D61—24no—
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—22no—
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C2×C4×D61—41no—
74C2×C4×D61—41no—
75C2×C4×D61D812yes—
76C2×C4×D61SD1612yes—
77C2×#92420—42no—
78C2×#92420—42no—
79C2×#92420—42no—
80C2×#92420—42no—
81C2×#92420—42no—
82C2×#92420—42no—
83C4⋊C4×C61—41no—
84C4⋊C4×C61—41no—
85C42×C61—22no—
86C42×C61—42no—
87#11758198—42no—
88#11758198—42no—
89C4⋊Dic61—41no—
90C4⋊Dic61—41no—
91#11758196—41no—
92#11758196—41no—
93#11758196—41no—
94#11758196—41no—
95#11758196—42no—
96#11758196—41no—
97#11758196—41no—
98C4×Dic61—22no—
99C4×Dic61—22no—
100C4×Dic61—42no—
101C4×Dic61#4114yes—
102C23×C61C2×C22⋊C411yescharacteristic
103C22×D61—21no—
104C22×D61—21no—
105C22×D61—21no—
106C22×D61—21no—
107C22×D61—21no—
108C22×D61—21no—
109C22×D61#10212yes—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
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—41no—
123C2×C4×C61#10212yes—
124C2×C4×C61#11712yes—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61#12312yes—
135C2×Dic61#12312yes—
136C2×Dic61C2×D811yescharacteristic
137C2×Dic61C2×SD1611yescharacteristic
138C2×Dic61#13512yes—
139C2×Dic61AGL(1,ℤ/8)11yescharacteristic
140C2×Dic61#13712yes—
141C2×Dic61#13711yescharacteristic
142C4×D61—24no—
143C4×D61—24no—
144C4×D61—44no—
145C4×D61—42no—
146C4×D61—42no—
147#92420—82no—
148#92420—82no—
149#8726—611nomaximal, Sylow
150C22×C61#38111yescharacteristic
151C22×C61#41311yescharacteristic
152C22×C61#41311yescharacteristic
153C22×C61C2×#10211yescharacteristic
154C22×C61#41611yescharacteristic
155C22×C61#41711yescharacteristic
156C22×C61#41911yescharacteristic
157C2×D61—22no—
158C2×D61—22no—
159C2×D61—22no—
160C2×D61—41no—
161C2×D61—41no—
162C2×D61—41no—
163C2×D61—41no—
164C4×C61—22no—
165C4×C61—22no—
166C4×C61—41no—
167C4×C61—81no—
168C4×C61—81no—
169Dic61—41no—
170Dic61—81no—
171Dic61—81no—
172Dic61#48012yes—
173Dic61#48212yes—
174Dic61#48312yes—
175Dic61#48512yes—
176#2285—611no—
177#1797—611no—
178#1797—611no—
179#1296—612no—
180#1296—612no—
181C2×C61#154011yescharacteristic
182C2×C61#154711yescharacteristic
183C2×C61#155411yescharacteristic
184C2×C61#155911yescharacteristic
185C2×C61#182211yescharacteristic
186C2×C61#182311yescharacteristic
187C2×C61#182511yescharacteristic
188D61—42no—
189C2×#117—1221no—
190C22×C42—611no—
191C2×C4⋊C8—612no—
192C2×C4⋊C8—612no—
193C2×C22⋊C8—1221no—
194C2×C22⋊C8—1221no—
195#384—611no—
196#384—611no—
197#382—1221no—
198#380—611no—
199#380—611no—
200#380—1221no—
201C4×C4⋊C4—611no—
202C4×C4⋊C4—1221no—
203C4×C4⋊C4#692311yescharacteristic
204#336—1221no—
205#336—1221no—
206C61#872611yescharacteristic, complemented, Sylow
207C23×C4—611no—
208C23×C4—611no—
209C23×C4—611no—
210C22×C8—1222no—
211C22×C8—1222no—
212#117—2442no—
213#117—2442no—
214C2×C4⋊C4—611no—
215C2×C4⋊C4—611no—
216C2×C4⋊C4—1221no—
217C2×C4⋊C4—1221no—
218C2×C4⋊C4—1221no—
219C2×C4⋊C4—1221no—
220C2×C4⋊C4C2×#692311yescharacteristic
221C2×C4⋊C4C2×#692311yescharacteristic
222C2×C22⋊C4—1221no—
223C2×C22⋊C4—1221no—
224C2×C42—21no—
225C2×C42—611no—
226C2×C42—611no—
227C2×C42—611no—
228C2×C42—1224no—
229C2×C42—1221no—
230C2×C42C2×#692311yescharacteristic
231C4⋊C8—1224no—
232C4⋊C8—1224no—
233C22⋊C8—2442no—
234C22⋊C8—2442no—
235#95—21no—
236#95—1221no—
237#95—1221no—
238#95—1221no—
239C24—611no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—611no—
243C22×C4—611no—
244C22×C4—612no—
245C22×C4—612no—
246C22×C4—611no—
247C22×C4—1222no—
248C22×C4—1222no—
249C22×C4—1221no—
250C22×C4—1222no—
251C22×C4—1222no—
252C22×C4—1221no—
253C22×C4—1222no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—2441no—
257C22×C4—2441no—
258C22×C4C22⋊#692311yescharacteristic
259C22×C4C22⋊#692311yescharacteristic
260C22×C4C22×#692311yescharacteristic
261C2×C8—2442no—
262C2×C8—2442no—
263C2×C8—2442no—
264C2×C8—2442no—
265C2×C8—2442no—
266C2×C8—2442no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—2441no—
270C4⋊C4—2441no—
271C4⋊C4—2442no—
272C4⋊C4—2441no—
273C4⋊C4—2441no—
274C4⋊C4—2441no—
275C4⋊C4—2441no—
276C4⋊C4—2441no—
277C4⋊C4—2441no—
278C22⋊C4—2442no—
279C22⋊C4—2442no—
280C42—22no—
281C42—42no—
282C42—614no—
283C42—1222no—
284C42—1222no—
285C42—2442no—
286C23—612no—
287C23—1221no—
288C23—1221no—
289C23—1221no—
290C23—1221no—
291C23—1221no—
292C23—1221no—
293C23C2×C22⋊#692311yescharacteristic
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
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—41no—
307C2×C4—612no—
308C2×C4—612no—
309C2×C4—611no—
310C2×C4—611no—
311C2×C4—612no—
312C2×C4—611no—
313C2×C4—611no—
314C2×C4—612no—
315C2×C4—1224no—
316C2×C4—1224no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—2444no—
321C2×C4—2442no—
322C2×C4—2442no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4—2441no—
327C2×C4—2441no—
328C2×C4—2441no—
329C2×C4#1451983912yes—
330C2×C4#1451985612yes—
331C8—4882no—
332C8—4882no—
333C22—1222no—
334C22—1222no—
335C22—1222no—
336C22—2441no—
337C22—2441no—
338C22—2441no—
339C22—2441no—
340C22#1684070511yescharacteristic
341C22#1684074811yescharacteristic
342C22#1684074811yescharacteristic
343C22C2×#1451983911yescharacteristic
344C22#1684075211yescharacteristic
345C22#1684075311yescharacteristic
346C22#1684075511yescharacteristic
347C4—22no—
348C4—22no—
349C4—41no—
350C4—81no—
351C4—81no—
352C4—612no—
353C4—612no—
354C4—612no—
355C4—612no—
356C4—4881no—
357C4—4881no—
358C4—2441no—
359C2—2442no—
360C2#2146131611yescharacteristic
361C2#2146133011yescharacteristic
362C2#2146134411yescharacteristic
363C2#2146135411yescharacteristic
364C2#2146172011yescharacteristic
365C2#2146172211yescharacteristic
366C2#2146172411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC4×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC4×C4⋊C4#6923
hypocenterC61#8726
LCSG ▷ C22×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. #21460697C2semidirect
4. #21460697C2semidirect
206. C61#8726semidirect

Maximal subgroups

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

subgroupindex
#214616762
#214606972
#214482232
#872661