Finite Group Databasebeta

← #30605224

Subgroups — #30605224

Order 15616.

420 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 70 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#21461683C211yesmaximal, characteristic
2#21461074C211yesmaximal, characteristic
3#21460818C212yesmaximal, complemented
4#21460803C212yesmaximal, complemented
5#21449076C211yesmaximal, characteristic
6#16840765—21no—
7C2×#14519837—21no—
8#16840733—21no—
9#16840642C2212yes—
10#16840608C2212yes—
11#16840605—21no—
12C2×C4×C22⋊D61C2211yescharacteristic
13#16839700C2211yescharacteristic
14#16839697C411yescharacteristic
15#16839693C2211yescharacteristic
16#16839690—21no—
17#16839688C411yescharacteristic
18#16839677—21no—
19C4×#11758196—21no—
20C4×#11758198—21no—
21C4×C22⋊Dic61C411yescharacteristic
22C2×#117×C61C411yescharacteristic
23C2×#11758213—41no—
24C2×#11758217—22no—
25#14519844—41no—
26C4⋊#92420—41no—
27#14519837—42no—
28#14519834—41no—
29C22⋊#92420—22no—
30C22×C22⋊D61D411yescharacteristic
31C22×C4×D61D411yescharacteristic
32C4×C22⋊D61—41no—
33C4×C22⋊D61—41no—
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×#11758196C2311yescharacteristic
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61D411yescharacteristic
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198C2×C411yescharacteristic
42C2×C4×Dic61—21no—
43C2×C4×Dic61D411yescharacteristic
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684C2×C411yescharacteristic
49#14519684C2×C411yescharacteristic
50C23×C4×C61C2×C411yescharacteristic
51#117×C61—41no—
52#117×C61—41no—
53C2×C4⋊C4×C61C2×C411yescharacteristic
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C22⋊C4×C61—21no—
56C2×C42×C61—21no—
57C24×C61C22⋊C411yescharacteristic
58C23×D61C22⋊C411yescharacteristic
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—42no—
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22×C411yescharacteristic
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68C2×C22⋊D61—41no—
69C2×C22⋊D61—41no—
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C2×D411yescharacteristic
74C22×Dic61C2×D411yescharacteristic
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—42no—
78#11758217—42no—
79#11758217—42no—
80C2×#92420—42no—
81C2×#92420—42no—
82#11758213—82no—
83C4⋊C4×C61—41no—
84C4⋊C4×C61—41no—
85C22⋊C4×C61—42no—
86C42×C61—41no—
87C42×C61—41no—
88C22⋊Dic61—41no—
89C22⋊Dic61—42no—
90#11758198—41no—
91#11758198—42no—
92#11758198—42no—
93#11758196—41no—
94#11758196—42no—
95#11758196—41no—
96#11758196—41no—
97C4×Dic61—21no—
98C4×Dic61—21no—
99C4×Dic61—42no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61—41no—
104C23×C61—41no—
105C23×C61C2×C22⋊C411yescharacteristic
106C22×D61—21no—
107C22×D61—21no—
108C22×D61—21no—
109C22×D61—41no—
110C22×D61—41no—
111C2×C4×C61—22no—
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×C61—41no—
122C2×C4×C61#9911yescharacteristic
123C2×C4×C61#9911yescharacteristic
124C22⋊D61—42no—
125C22⋊D61—42no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—22no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61AGL(1,ℤ/8)11yescharacteristic
139C2×Dic61#13711yescharacteristic
140C4×D61—42no—
141C4×D61—81no—
142#92420—82no—
143#92420—82no—
144#11830—611nomaximal, Sylow
145C22×C61—21no—
146C22×C61—21no—
147C22×C61—41no—
148C22×C61—41no—
149C22×C61—41no—
150C22×C61—81no—
151C22×C61—81no—
152C22×C61C2×#9911yescharacteristic
153C22×C61#41711yescharacteristic
154C22×C61#42111yescharacteristic
155C2×D61—42no—
156C2×D61—41no—
157C2×D61—41no—
158C2×D61—41no—
159C2×D61—81no—
160C4×C61—21no—
161C4×C61—41no—
162C4×C61—81no—
163C4×C61—81no—
164C4×C61#35212yes—
165Dic61—21no—
166Dic61—21no—
167Dic61—42no—
168Dic61—41no—
169Dic61—41no—
170Dic61—81no—
171#2395—611no—
172#1800—611no—
173#1465—611no—
174#1353—612no—
175#1346—612no—
176C2×C61—21no—
177C2×C61—21no—
178C2×C61—81no—
179C2×C61#151311yescharacteristic
180C2×C61C2×#35211yescharacteristic
181C2×C61#213211yescharacteristic
182D61—81no—
183C2×C4×D4—611no—
184C2×#117#692311yescharacteristic
185#423—1221no—
186C2×#100—1221no—
187#407—1221no—
188#400—611no—
189#399—611no—
190#398—611no—
191#397—611no—
192#397—1221no—
193#394—1221no—
194C4×C4⋊C4—1221no—
195C4×C22⋊C4—611no—
196C4×C22⋊C4—1221no—
197#343—612no—
198#324—612no—
199#323—1221no—
200C61#1183011yescharacteristic, complemented, Sylow
201C22×D4—611no—
202C23×C4—611no—
203C23×C4C2×#692311yescharacteristic
204C2×M16—1222no—
205C2×M16—2441no—
206C4×D4—2441no—
207C4×D4—2441no—
208#117—41no—
209#117—41no—
210C2×C4⋊C4—611no—
211C2×C4⋊C4—1221no—
212C2×C4⋊C4—1221no—
213C2×C4⋊C4C2×#692311yescharacteristic
214C2×C4⋊C4C2×#692311yescharacteristic
215C2×C22⋊C4—21no—
216C2×C22⋊C4—611no—
217C2×C22⋊C4—611no—
218C2×C22⋊C4—1221no—
219C2×C22⋊C4—1221no—
220C2×C22⋊C4—1221no—
221C2×C42—21no—
222C2×C42—611no—
223C2×C42—1221no—
224C4⋊C8—2441no—
225C4⋊C8—2441no—
226#100—2442no—
227C22⋊C8—1222no—
228C22⋊C8—2441no—
229#95—611no—
230#95—611no—
231#95—1221no—
232#95—1221no—
233#95—1221no—
234#95—1221no—
235C24—611no—
236C24C22⋊#692311yescharacteristic
237C2×D4—1221no—
238C2×D4—1221no—
239C2×D4—2441no—
240C2×D4—2441no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—42no—
246C22×C4—611no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—1221no—
250C22×C4—1221no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4—2442no—
254C22×C4C22⋊#692311yescharacteristic
255C22×C4C22×#692311yescharacteristic
256M16—4882no—
257M16—2442no—
258M16—2442no—
259C2×C8—2442no—
260C2×C8—2442no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—2441no—
264C4⋊C4—2441no—
265C4⋊C4—2441no—
266C4⋊C4—2442no—
267C22⋊C4—42no—
268C22⋊C4—2441no—
269C22⋊C4—2442no—
270C22⋊C4—2442no—
271C22⋊C4—2441no—
272C22⋊C4—2442no—
273C42—41no—
274C42—41no—
275C42—1221no—
276C42—1221no—
277C42—2442no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—41no—
282C23—41no—
283C23—1221no—
284C23—1221no—
285C23—1221no—
286C23—2441no—
287C23—2441no—
288C23C2×C22⋊#692311yescharacteristic
289D4—2442no—
290D4—2442no—
291C2×C4—22no—
292C2×C4—21no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—611no—
303C2×C4—611no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—1222no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—4881no—
310C2×C4—2441no—
311C2×C4—2441no—
312C2×C4—2441no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2442no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4#1451983511yescharacteristic
319C2×C4#1451983511yescharacteristic
320C8—4882no—
321C8—4882no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—81no—
328C22—81no—
329C22—4881no—
330C22—2442no—
331C22—2441no—
332C22—2441no—
333C22—2441no—
334C22C2×#1451983511yescharacteristic
335C22#1684075311yescharacteristic
336C22#1684075911yescharacteristic
337C4—21no—
338C4—41no—
339C4—81no—
340C4—81no—
341C4—1221no—
342C4—1221no—
343C4—4881no—
344C4—2442no—
345C4—2441no—
346C4—2441no—
347C4#1684066412yes—
348C2—21no—
349C2—21no—
350C2—81no—
351C2—4881no—
352C2#2146123411yescharacteristic
353C2C2×#1684066411yescharacteristic
354C2#2146211011yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#117×C61C4
socleC22×C61C2×#99
prime radicalC22×C22⋊D61D4
cosocleC2×#11758196C23
hypercenterC2×#117#6923
hypocenterC61#11830
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
3. #21460818C2semidirect
4. #21460803C2semidirect
200. C61#11830semidirect

Maximal subgroups

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

subgroupindex
#214616832
#214610742
#214608182
#214608032
#214490762
#1183061