Finite Group Databasebeta

← #30599253

Subgroups — #30599253

Order 15616.

544 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 100 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
2#21460995C211yesmaximal, characteristic
3#21460692C212yesmaximal
4#21460692C212yesmaximal
5#21448215C211yesmaximal, characteristic
6C2×#14519834C2212yes—
7C2×(C2×#6923)⋊C4—21no—
8C2×(C2×#6923)⋊C4—21no—
9C2×(C2×#6923)⋊C4C2212yes—
10#16840628—21no—
11#16840628—21no—
12C2×C42×D61C2211yescharacteristic
13#16839629—21no—
14#16839627C411yescharacteristic, complemented
15#16839627C411yescharacteristic, complemented
16#16839624—21no—
17#16839619C2211yescharacteristic
18#16839619C2211yescharacteristic
19C4×C4⋊Dic61C411yescharacteristic, complemented
20C4×#11758198—21no—
21#16839608—21no—
22C4×C4⋊C4×C61C411yescharacteristic, complemented
23C23×#6923—22no—
24C22×#92420—22no—
25#14519834—24no—
26(C2×#6923)⋊C4—24no—
27(C2×#6923)⋊C4—24no—
28(C2×#6923)⋊C4—42no—
29C22×C4×D61D411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C22×C4×D61C2311yescharacteristic
32C2×C4⋊Dic61C2×C411yescharacteristic
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×#11758198—21no—
35C2×#11758198—21no—
36C2×C4×Dic61—21no—
37C2×C4×Dic61C2×C411yescharacteristic
38C2×C4×Dic61D411yescharacteristic
39C2×C4×Dic61D411yescharacteristic
40C42×D61—24no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48C2×C4⋊C4×C61C2×C411yescharacteristic
49C2×C4⋊C4×C61C2×C411yescharacteristic
50C2×C42×C61—21no—
51C2×C42×C61C2×C411yescharacteristic
52#95×C61—21no—
53C23×D61C2×D411yescharacteristic
54C22×#6923—24no—
55C22×#6923—42no—
56C22×#6923—42no—
57C22×#6923—42no—
58C22×#6923—42no—
59C22×#6923—42no—
60C22×#6923—42no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22×C411yescharacteristic
66C22×Dic61—21no—
67C22×Dic61—21no—
68C22×Dic61C22⋊C411yescharacteristic
69C22×Dic61C22⋊C411yescharacteristic
70C22×Dic61C2×D411yescharacteristic
71C2×C4×D61—22no—
72C2×C4×D61—22no—
73C2×C4×D61—22no—
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—22no—
77C2×C4×D61—41no—
78C2×C4×D61—41no—
79C2×C4×D61—41no—
80C2×C4×D61#4114yes—
81C2×#92420—42no—
82C2×#92420—42no—
83C2×#92420—42no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—41no—
86C42×C61—22no—
87C42×C61—42no—
88#11758198—42no—
89#11758198—41no—
90#11758198—41no—
91C4⋊Dic61—41no—
92C4⋊Dic61—41no—
93C4×Dic61—22no—
94C4×Dic61—22no—
95C4×Dic61—22no—
96C4×Dic61—42no—
97C23×C61C2×C22⋊C411yescharacteristic
98C22×D61—21no—
99C22×D61—21no—
100C22×D61—21no—
101C22×D61—21no—
102C22×D61#12312yes—
103C22×D61#13512yes—
104C22×D61AGL(1,ℤ/8)11yescharacteristic
105C22×D61#13711yescharacteristic
106C2×#6923—44no—
107C2×#6923—44no—
108C2×#6923—44no—
109C2×#6923—82no—
110C2×#6923—82no—
111C2×#6923—82no—
112C2×#6923—82no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61#10412yes—
127C2×C4×C61#11712yes—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61#12312yes—
143C4×D61—44no—
144C4×D61—44no—
145C4×D61—42no—
146C4×D61—42no—
147#92420—82no—
148#8714—611nomaximal, Sylow
149C22×C61#38111yescharacteristic
150C22×C61#41011yescharacteristic
151C22×C61#41011yescharacteristic
152C22×C61#41611yescharacteristic
153C22×C61#41711yescharacteristic
154C22×C61C2×#10411yescharacteristic
155C22×C61#42111yescharacteristic
156C2×D61—22no—
157C2×D61—22no—
158C2×D61—22no—
159C2×D61—21no—
160C2×D61—21no—
161C2×D61—21no—
162C2×D61—21no—
163C2×D61—22no—
164C2×D61#48212yes—
165C2×D61#48512yes—
166#6923—84no—
167C4×C61—22no—
168C4×C61—22no—
169C4×C61—41no—
170C4×C61—81no—
171C4×C61—81no—
172Dic61—22no—
173Dic61—41no—
174Dic61—41no—
175Dic61—81no—
176Dic61—81no—
177#2283—611no—
178#1817—611no—
179#1434—611no—
180#1294—612no—
181#1294—612no—
182C2×C61#150011yescharacteristic
183C2×C61#150911yescharacteristic
184C2×C61#151211yescharacteristic
185C2×C61#152111yescharacteristic
186C2×C61#182011yescharacteristic
187C2×C61#182511yescharacteristic
188C2×C61#182611yescharacteristic
189D61—22no—
190D61—22no—
191C22×C42—611no—
192C2×C22⋊C8—612no—
193#383—1221no—
194#382—611no—
195#382—611no—
196#381—1221no—
197#380—611no—
198#380—611no—
199C4×C4⋊C4—611no—
200C4×C4⋊C4#692311yescharacteristic, complemented
201C4×C22⋊C4—1221no—
202#376—1221no—
203C2×#95—612no—
204C2×#95—1221no—
205C2×#95—1221no—
206#336—1221no—
207#336—1221no—
208C61#871411yescharacteristic, complemented, Sylow
209C23×C4—611no—
210C23×C4—611no—
211C23×C4—611no—
212C23×C4—1222no—
213C22×C8—1222no—
214C2×C4⋊C4—611no—
215C2×C4⋊C4—611no—
216C2×C4⋊C4C2×#692311yescharacteristic
217C2×C4⋊C4C2×#692311yescharacteristic
218C2×C22⋊C4—1221no—
219C2×C22⋊C4—1221no—
220C2×C42—21no—
221C2×C42—611no—
222C2×C42—611no—
223C2×C42—611no—
224C2×C42—1224no—
225C2×C42—1221no—
226C2×C42C2×#692311yescharacteristic
227C22⋊C8—1224no—
228#95—21no—
229#95—1221no—
230#95—1221no—
231#95—1221no—
232#95—1221no—
233#95—1221no—
234#95—1221no—
235#95—1224no—
236#95—1224no—
237#95—1221no—
238#95—2442no—
239C24—611no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—611no—
243C22×C4—614no—
244C22×C4—611no—
245C22×C4—611no—
246C22×C4—1221no—
247C22×C4—1222no—
248C22×C4—1222no—
249C22×C4—1222no—
250C22×C4—1221no—
251C22×C4—1222no—
252C22×C4—1224no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—2441no—
256C22×C4—2441no—
257C22×C4—2441no—
258C22×C4—2442no—
259C22×C4—2442no—
260C22×C4—2442no—
261C22×C4—2442no—
262C22×C4—2442no—
263C22×C4—2442no—
264C22×C4C22⋊#692311yescharacteristic
265C22×C4C22⋊#692311yescharacteristic
266C22×C4C22×#692311yescharacteristic
267C2×C8—2442no—
268C2×C8—2442no—
269C2×C8—2442no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—2441no—
273C4⋊C4—2441no—
274C22⋊C4—2442no—
275C22⋊C4—2441no—
276C22⋊C4—2441no—
277C42—22no—
278C42—42no—
279C42—1222no—
280C42—1222no—
281C42—1222no—
282C42—2442no—
283C23—612no—
284C23—612no—
285C23—611no—
286C23—611no—
287C23—1221no—
288C23—1221no—
289C23—1221no—
290C23—1221no—
291C23C2×C22⋊#692311yescharacteristic
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—612no—
306C2×C4—1221no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—4882no—
315C2×C4—4882no—
316C2×C4—4882no—
317C2×C4—4882no—
318C2×C4—2444no—
319C2×C4—2444no—
320C2×C4—2442no—
321C2×C4—2442no—
322C2×C4—2444no—
323C2×C4—2444no—
324C2×C4—2444no—
325C2×C4—2441no—
326C2×C4—2441no—
327C2×C4—2441no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4#1451984112yes—
332C2×C4#1451985612yes—
333C8—4882no—
334C22—612no—
335C22—612no—
336C22—1222no—
337C22—1222no—
338C22—1222no—
339C22—1222no—
340C22—1221no—
341C22—1221no—
342C22—1221no—
343C22—1221no—
344C22#1684070511yescharacteristic
345C22#1684074111yescharacteristic
346C22#1684074111yescharacteristic
347C22#1684075211yescharacteristic
348C22#1684075311yescharacteristic
349C22C2×#1451984111yescharacteristic
350C22#1684076111yescharacteristic
351C4—22no—
352C4—22no—
353C4—41no—
354C4—81no—
355C4—81no—
356C4—1222no—
357C4—4884no—
358C4—4881no—
359C4—4881no—
360C4—2441no—
361C4—2441no—
362C2—1222no—
363C2—1222no—
364C2#2146119011yescharacteristic
365C2#2146122111yescharacteristic
366C2#2146123211yescharacteristic
367C2#2146126311yescharacteristic
368C2#2146171611yescharacteristic
369C2#2146172411yescharacteristic
370C2#2146172511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC4×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C2×D4
cosocleC22×C4×D61C23
hypercenterC4×C4⋊C4#6923
hypocenterC61#8714
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
14. #16839627C4semidirect
15. #16839627C4semidirect
19. C4×C4⋊Dic61C4semidirect
22. C4×C4⋊C4×C61C4semidirect
200. C4×C4⋊C4#6923semidirect
208. C61#8714semidirect

Maximal subgroups

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

subgroupindex
#214617112
#214609952
#214606922
#214482152
#871461