Finite Group Databasebeta

← #30595420

Subgroups — #30595420

Order 15616.

510 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 112 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#21461746C211yesmaximal, characteristic, complemented
2C4×C4⋊#92420C211yesmaximal, characteristic, complemented
3#21460640C212yesmaximal, complemented
4#21460636C212yesmaximal
5#21448358C211yesmaximal, characteristic
6C2×C4⋊#92420—21no—
7C2×C4×#92420—21no—
8#16840628—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519765C411yescharacteristic
13C2×#14519742C411yescharacteristic
14C2×#14519739C411yescharacteristic
15#16839667C2211yescharacteristic
16#16839663C2211yescharacteristic
17#16839651—21no—
18#16839651—21no—
19#16839609—21no—
20#16839609—21no—
21C42×Dic61C2211yescharacteristic
22C61×#382C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25C4⋊#92420—24no—
26C4×#92420—42no—
27C22×Dic122C2×C411yescharacteristic
28C22×D244C2×C411yescharacteristic
29C22×C4×D61—21no—
30#14519765—22no—
31#14519765C814yescomplemented
32#14519742—42no—
33#14519739—42no—
34C2×#11758196—21no—
35C2×#11758198—21no—
36C2×#11758198—21no—
37C2×#11758198—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×C4×Dic61—21no—
41C2×C4×Dic61C2×C411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61C2311yescharacteristic
47#14519684—21no—
48#14519684—21no—
49C2×C4⋊C4×C61C2×C411yescharacteristic
50C2×C4⋊C4×C61C2×C411yescharacteristic
51C2×C42×C61C2×C411yescharacteristic
52#95×C61—21no—
53#95×C61—21no—
54C23×D61—21no—
55C22×C4×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61C22⋊C411yescharacteristic
58C22×C4×C61C22⋊C411yescharacteristic
59C22×C4×C61C22×C411yescharacteristic
60C22×Dic61—21no—
61C22×Dic61C22⋊C411yescharacteristic
62C22×Dic61C22⋊C411yescharacteristic
63C22×Dic61C2×D411yescharacteristic
64C22×Dic61C2×D411yescharacteristic
65C2×D244—21no—
66C2×D244—41no—
67C2×D244—41no—
68C2×D244C2×C812yes—
69C2×C4×D61—42no—
70C2×C4×D61—42no—
71C2×C4×D61—42no—
72C2×Dic122—21no—
73C2×Dic122—41no—
74C2×Dic122—41no—
75C2×Dic122C2×C812yes—
76C2×#92420—24no—
77C2×#92420—42no—
78C2×#92420—42no—
79C2×#92420—42no—
80C2×#92420—42no—
81C2×#92420—42no—
82C4⋊C4×C61—41no—
83C4⋊C4×C61—41no—
84C42×C61C2×C812yes—
85C42×C61M1612yes—
86#11758198—24no—
87#11758198—24no—
88#11758198—42no—
89#11758198—42no—
90#11758198—41no—
91#11758198—41no—
92#11758196—42no—
93C4×Dic61—22no—
94C4×Dic61—22no—
95C4×Dic61—22no—
96C4×Dic61—21no—
97C4×Dic61—21no—
98C4×Dic61—41no—
99C4×Dic61—41no—
100C4×Dic61—42no—
101C23×C61C2×C22⋊C411yescharacteristic
102C22×D61—22no—
103C22×D61—41no—
104C22×D61—41no—
105C22×D61—41no—
106C22×D61—41no—
107C22×D61—41no—
108C22×D61—41no—
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—41no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61C22⋊C812yes—
122C2×C4×C61C22⋊C812yes—
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—21no—
132C2×Dic61—21no—
133C2×Dic61—22no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61#10012yes—
137C2×Dic61#10412yes—
138C2×Dic61#13512yes—
139C2×Dic61AGL(1,ℤ/8)11yescharacteristic
140C2×Dic61#13711yescharacteristic
141D244—42no—
142D244—42no—
143C4×D61—84no—
144Dic122—42no—
145Dic122—42no—
146#92420—44no—
147#92420—82no—
148#7584—611nomaximal, Sylow
149C22×C61C2×C22⋊C811yescharacteristic
150C22×C61#41011yescharacteristic
151C22×C61C2×#10011yescharacteristic
152C22×C61#41611yescharacteristic
153C22×C61#41711yescharacteristic
154C22×C61C2×#10411yescharacteristic
155C22×C61#42111yescharacteristic
156C2×D61—42no—
157C2×D61—42no—
158C2×D61—42no—
159C2×D61—81no—
160C2×D61—81no—
161C2×D61—81no—
162C2×D61—81no—
163C4×C61—21no—
164C4×C61—21no—
165C4×C61—22no—
166C4×C61—22no—
167C4×C61—81no—
168C4×C61—81no—
169Dic61—22no—
170Dic61—21no—
171Dic61—21no—
172Dic61—22no—
173Dic61—22no—
174Dic61—42no—
175C4×#124—611no—
176#1839—611no—
177C4×C4⋊C8—611no—
178#1272—612no—
179#1270—612no—
180C2×C61#146011yescharacteristic
181C2×C61#147611yescharacteristic
182C2×C61#147711yescharacteristic
183C2×C61#150911yescharacteristic
184C2×C61#152111yescharacteristic
185C2×C61#152711yescharacteristic
186C2×C61#155111yescharacteristic
187D61—82no—
188C2×#124—611no—
189C2×C4×Q8—611no—
190C2×C4×D4—611no—
191C2×C4⋊C8—1221no—
192C2×C4×C8—1221no—
193#391—611no—
194#390—611no—
195#388—1221no—
196#388—1221no—
197#382#692311yescharacteristic
198C4×C22⋊C4—1221no—
199C4×C22⋊C4—1221no—
200C43—611no—
201#336—612no—
202#336—612no—
203#336—1221no—
204#336—1221no—
205C61#758411yescharacteristic, complemented, Sylow
206C22×Q8—611no—
207C22×D4—611no—
208C23×C4—1221no—
209C22×C8—1222no—
210C22×C8—1222no—
211#124—614no—
212#124—1222no—
213C4×Q8—2442no—
214C4×D4—2442no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4C2×#692311yescharacteristic
217C2×C4⋊C4C2×#692311yescharacteristic
218C2×C22⋊C4—1221no—
219C2×C22⋊C4—1221no—
220C2×C22⋊C4—1221no—
221C2×C22⋊C4—1221no—
222C2×C22⋊C4—1221no—
223C2×C42—611no—
224C2×C42—611no—
225C2×C42—611no—
226C2×C42—611no—
227C2×C42—611no—
228C2×C42—611no—
229C2×C42—1221no—
230C2×C42C2×#692311yescharacteristic
231C4⋊C8—1224no—
232C4×C8—2442no—
233#95—21no—
234#95—21no—
235#95—1221no—
236#95—1221no—
237C24—1221no—
238C2×Q8—612no—
239C2×Q8—1221no—
240C2×Q8—2441no—
241C2×Q8—2441no—
242C2×D4—612no—
243C2×D4—1221no—
244C2×D4—2441no—
245C2×D4—2441no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—611no—
249C22×C4—611no—
250C22×C4—611no—
251C22×C4—611no—
252C22×C4—1221no—
253C22×C4—2442no—
254C22×C4—2442no—
255C22×C4—2442no—
256C22×C4C22⋊#692311yescharacteristic
257C22×C4C22⋊#692311yescharacteristic
258C22×C4C22×#692311yescharacteristic
259C2×C8—1224no—
260C2×C8—2442no—
261C2×C8—2442no—
262C2×C8—2442no—
263C2×C8—2442no—
264C2×C8—2442no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—2442no—
268C22⋊C4—1224no—
269C22⋊C4—1224no—
270C22⋊C4—2442no—
271C22⋊C4—2442no—
272C22⋊C4—2441no—
273C22⋊C4—2441no—
274C42—1221no—
275C42—1222no—
276C42—1222no—
277C42—1221no—
278C42—1222no—
279C42—2441no—
280C42—2441no—
281C42—2442no—
282C42D61⋊C812yes—
283C42#1175821312yes—
284C23—1222no—
285C23—2441no—
286C23—2441no—
287C23—2441no—
288C23—2441no—
289C23—2441no—
290C23—2441no—
291C23C2×C22⋊#692311yescharacteristic
292Q8—2442no—
293Q8—2442no—
294D4—2442no—
295D4—2442no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—612no—
309C2×C4—612no—
310C2×C4—611no—
311C2×C4—611no—
312C2×C4—612no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—1222no—
322C2×C4—4884no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4#1451983412yes—
326C2×C4#1451983412yes—
327C2×C4C2×D61⋊C811yescharacteristic
328C2×C4C2×#1175821311yescharacteristic
329C8—4882no—
330C8—2444no—
331C22—4881no—
332C22—4881no—
333C22—4881no—
334C22—4881no—
335C22—2442no—
336C22—2442no—
337C22—2442no—
338C22C2×#1451983411yescharacteristic
339C22#1684074311yescharacteristic
340C22D61⋊#10011yescharacteristic
341C22#1684075211yescharacteristic
342C22#1684075311yescharacteristic
343C22D61⋊#10411yescharacteristic
344C22#1684075911yescharacteristic
345C4—21no—
346C4—21no—
347C4—22no—
348C4—22no—
349C4—81no—
350C4—81no—
351C4—1222no—
352C4—1222no—
353C4—1222no—
354C4—1221no—
355C4—1221no—
356C4—2442no—
357C2—4882no—
358C2#2146106011yescharacteristic
359C2#2146111211yescharacteristic
360C2#2146111611yescharacteristic
361C2#2146122211yescharacteristic
362C2#2146126211yescharacteristic
363C2#2146127911yescharacteristic
364C2#2146133911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#382C4
socleC23×C61C2×C22⋊C4
prime radicalC22×D244C2×C4
cosocleC2×C4×Dic61C23
hypercenter#382#6923
hypocenterC61#7584
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
1. #21461746C2semidirect
2. C4×C4⋊#92420C2semidirect
3. #21460640C2semidirect
31. #14519765C8semidirect
205. C61#7584semidirect

Maximal subgroups

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

subgroupindex
#214617462
C4×C4⋊#924202
#214606402
#214606362
#214483582
#758461