Finite Group Databasebeta

← #30599386

Subgroups — #30599386

Order 15616.

472 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 80 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#21461679C211yesmaximal, characteristic
2#21461054C211yesmaximal, characteristic
3#21460693C212yesmaximal, complemented
4#21460681C212yesmaximal, complemented
5#21448762C211yesmaximal, characteristic
6C2×#14519835—21no—
7D61⋊(C22⋊C8)C2212yes—
8#16840704C2212yes—
9#16840640—21no—
10#16840608—21no—
11#16840605—21no—
12C2×C4×C22⋊D61C2211yescharacteristic
13#16839650—21no—
14#16839646—21no—
15#16839638—21no—
16#16839629C411yescharacteristic, complemented
17#16839625C411yescharacteristic, complemented
18#16839621C2211yescharacteristic
19C4×#11758198—21no—
20#16839607C411yescharacteristic, complemented
21#95×D61C2211yescharacteristic
22C4×C22⋊C4×C61C411yescharacteristic, complemented
23C2×D61⋊C8—22no—
24C2×C4⋊#6923—22no—
25C2×C22⋊#6923—22no—
26#14519835—42no—
27#14519834—22no—
28C22⋊#92420—22no—
29(C2×#6923)⋊C4—22no—
30C22×C22⋊D61D411yescharacteristic
31C22×C4×D61—21no—
32C22×C4×D61C2311yescharacteristic
33C4×C22⋊D61—22no—
34C4×C22⋊D61—22no—
35C2×#11758196—21no—
36C2×#11758196D411yescharacteristic
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61D411yescharacteristic
39C2×#11758198—21no—
40C2×#11758198D411yescharacteristic
41C2×C4×Dic61—21no—
42C2×C4×Dic61C2×C411yescharacteristic
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684C2×C411yescharacteristic
49#14519684C2×C411yescharacteristic
50C23×C4×C61C2×C411yescharacteristic
51C2×C22⋊C4×C61—21no—
52C2×C42×C61—21no—
53#95×C61C2×C411yescharacteristic
54#95×C61C2×C411yescharacteristic
55C24×C61C22⋊C411yescharacteristic
56C23×D61C2×D411yescharacteristic
57C22×#6923—42no—
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—81no—
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22×C411yescharacteristic
65C2×C22⋊D61—22no—
66C2×C22⋊D61—22no—
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C2×D411yescharacteristic
74C2×C4×D61—42no—
75C2×C4×D61—41no—
76C2×C4×D61—41no—
77C2×C4×D61—81no—
78C2×C4×D61—81no—
79C2×C4×D61#4112yes—
80C2×C4×D61#4112yes—
81C22⋊#6923—42no—
82C22⋊#6923—42no—
83C2×#92420—42no—
84C4⋊#6923—82no—
85D61⋊C8—82no—
86C22⋊C4×C61—42no—
87C42×C61—81no—
88C22⋊Dic61—22no—
89C22⋊Dic61—81no—
90#11758198—22no—
91#11758198—42no—
92#11758196—22no—
93#11758196—81no—
94C4×Dic61—21no—
95C4×Dic61—21no—
96C4×Dic61—42no—
97C23×C61—21no—
98C23×C61—21no—
99C23×C61—21no—
100C23×C61—41no—
101C23×C61—41no—
102C23×C61C2×C22⋊C411yescharacteristic
103C22×D61—41no—
104C22×D61—41no—
105C22×D61#12312yes—
106C22×D61#13512yes—
107C22×D61AGL(1,ℤ/8)11yescharacteristic
108C22×D61#13711yescharacteristic
109C2×#6923—82no—
110C2×#6923—82no—
111C2×#6923—82no—
112C2×C4×C61—22no—
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—41no—
120C2×C4×C61—41no—
121C2×C4×C61—81no—
122C2×C4×C61—81no—
123C2×C4×C61#11711yescharacteristic
124C2×C4×C61#11711yescharacteristic
125C22⋊D61—42no—
126C22⋊D61—42no—
127C2×Dic61—21no—
128C2×Dic61—21no—
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×Dic61—41no—
139C2×Dic61#12312yes—
140C4×D61—42no—
141C4×D61—42no—
142C4×D61—82no—
143C4×D61—82no—
144#92420—82no—
145#8762—611nomaximal, Sylow
146C22×C61—21no—
147C22×C61—21no—
148C22×C61—41no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61—81no—
152C22×C61—81no—
153C22×C61#38111yescharacteristic
154C22×C61#41611yescharacteristic
155C22×C61#41711yescharacteristic
156C2×D61—22no—
157C2×D61—22no—
158C2×D61—41no—
159C2×D61—41no—
160C2×D61—42no—
161C2×D61#48212yes—
162C2×D61#48512yes—
163#6923—162no—
164C4×C61—21no—
165C4×C61—21no—
166C4×C61—42no—
167C4×C61—41no—
168C4×C61—81no—
169Dic61—22no—
170Dic61—41no—
171Dic61—41no—
172Dic61—81no—
173Dic61—81no—
174#2353—611no—
175#1799—611no—
176#1459—611no—
177#1294—612no—
178#1289—612no—
179C2×C61—21no—
180C2×C61—21no—
181C2×C61—81no—
182C2×C61#182511yescharacteristic
183C2×C61#182711yescharacteristic
184C2×C61#182811yescharacteristic
185D61—22no—
186D61—22no—
187C2×C4×D4—611no—
188C2×#99—1221no—
189C2×C22⋊C8—612no—
190#388—1221no—
191#387—1221no—
192#386—1221no—
193#383—611no—
194#381—611no—
195#380—611no—
196#380—612no—
197C4×C22⋊C4—1221no—
198C4×C22⋊C4#692311yescharacteristic, complemented
199#376—611no—
200C2×#95—611no—
201#342—1221no—
202#324—1221no—
203#323—1221no—
204C61#876211yescharacteristic, complemented, Sylow
205C22×D4—611no—
206C23×C4—611no—
207C23×C4—1221no—
208C23×C4C2×#692311yescharacteristic
209C22×C8—1222no—
210C4×D4—1222no—
211C4×D4—1222no—
212C2×C4⋊C4—611no—
213C2×C4⋊C4—1221no—
214C2×C4⋊C4—1222no—
215C2×C22⋊C4—21no—
216C2×C22⋊C4—611no—
217C2×C22⋊C4—611no—
218C2×C22⋊C4—1221no—
219C2×C22⋊C4—1221no—
220C2×C22⋊C4—1222no—
221C2×C42—21no—
222C2×C42—611no—
223C2×C42—1221no—
224#99—2442no—
225C22⋊C8—1222no—
226C22⋊C8—1222no—
227#95—611no—
228#95—611no—
229#95—1221no—
230#95—1221no—
231#95—1221no—
232#95—1221no—
233#95—1222no—
234#95—1221no—
235#95C2×#692311yescharacteristic
236#95C2×#692311yescharacteristic
237C24—611no—
238C24C22⋊#692311yescharacteristic
239C2×D4—1221no—
240C2×D4—1222no—
241C2×D4—1222no—
242C2×D4—1221no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—81no—
248C22×C4—611no—
249C22×C4—612no—
250C22×C4—612no—
251C22×C4—611no—
252C22×C4—611no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—4881no—
256C22×C4—4881no—
257C22×C4—2442no—
258C22×C4—2441no—
259C22×C4—2441no—
260C22×C4—2442no—
261C22×C4C22⋊#692311yescharacteristic
262C22×C4C22×#692311yescharacteristic
263C2×C8—4882no—
264C2×C8—2442no—
265C4⋊C4—1222no—
266C4⋊C4—4881no—
267C4⋊C4—4882no—
268C22⋊C4—42no—
269C22⋊C4—1222no—
270C22⋊C4—1222no—
271C22⋊C4—4881no—
272C22⋊C4—2442no—
273C22⋊C4—2442no—
274C22⋊C4—2442no—
275C42—81no—
276C42—1221no—
277C42—1221no—
278C42—2442no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—41no—
283C23—41no—
284C23—612no—
285C23—612no—
286C23—611no—
287C23—611no—
288C23—2441no—
289C23—2441no—
290C23C2×C22⋊#692311yescharacteristic
291D4—2442no—
292D4—2442no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—612no—
305C2×C4—1221no—
306C2×C4—1221no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—4882no—
310C2×C4—4882no—
311C2×C4—4882no—
312C2×C4—4882no—
313C2×C4—4882no—
314C2×C4—2442no—
315C2×C4—2442no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4#1451985611yescharacteristic
325C2×C4#1451985611yescharacteristic
326C8—4882no—
327C22—21no—
328C22—21no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—81no—
333C22—81no—
334C22—612no—
335C22—612no—
336C22—1222no—
337C22—1222no—
338C22—2441no—
339C22—2441no—
340C22—2442no—
341C22#1684070511yescharacteristic
342C22#1684075211yescharacteristic
343C22#1684075311yescharacteristic
344C4—21no—
345C4—21no—
346C4—42no—
347C4—41no—
348C4—81no—
349C4—1222no—
350C4—9762no—
351C4—4881no—
352C4—4881no—
353C4—2441no—
354C4—2441no—
355C2—21no—
356C2—21no—
357C2—81no—
358C2—1222no—
359C2—1222no—
360C2#2146172411yescharacteristic
361C2#2146172811yescharacteristic
362C2#2146173011yescharacteristic
subgroupG/H
centerC22#16840705
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC4×C22⋊C4×C61C4
socleC22×C61#381
prime radicalC22×C22⋊D61D4
cosocleC22×C4×D61C23
hypercenterC4×C22⋊C4#6923
hypocenterC61#8762
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #21460693C2semidirect
4. #21460681C2semidirect
16. #16839629C4semidirect
17. #16839625C4semidirect
20. #16839607C4semidirect
22. C4×C22⋊C4×C61C4semidirect
198. C4×C22⋊C4#6923semidirect
204. C61#8762semidirect

Maximal subgroups

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

subgroupindex
#214616792
#214610542
#214606932
#214606812
#214487622
#876261