Finite Group Databasebeta

← #30595545

Subgroups — #30595545

Order 15616.

590 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 590 conjugacy classes of subgroups — too many to draw. Only its 96 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, complemented
2#21461546C211yesmaximal, characteristic, complemented
3#21460638C212yesmaximal, complemented
4#21460635C212yesmaximal, complemented
5C4×#14519748C211yesmaximal, characteristic
6C2×#14519834—21no—
7C2×#14519834—21no—
8C2×#14519832—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519748C411yescharacteristic
13C2×C4×C22⋊D61—21no—
14C2×C42×D61C2211yescharacteristic
15#16839665C2211yescharacteristic
16#16839658C2211yescharacteristic
17#16839650—21no—
18#16839638—21no—
19#16839619C411yescharacteristic
20C4×C4⋊Dic61C411yescharacteristic
21C4×C22⋊Dic61—21no—
22C2×C4×D4×C61C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25#14519834—24no—
26#14519834—42no—
27#14519832—42no—
28C22×C22⋊D61—21no—
29C22×C4×D61C2×C411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C22×C4×D61D411yescharacteristic
32#14519748—22no—
33#14519748—22no—
34C4×C22⋊D61—44no—
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×#11758196—21no—
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61—21no—
41C2×#11758198—21no—
42C2×C4×Dic61—21no—
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61C2311yescharacteristic
46C42×D61—42no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50C22×D4×C61C2×C411yescharacteristic
51C23×C4×C61—21no—
52C4×D4×C61—42no—
53C2×C4⋊C4×C61C2×C411yescharacteristic
54C2×C22⋊C4×C61—21no—
55C2×C42×C61C2×C411yescharacteristic
56C24×C61—21no—
57C23×D61C22⋊C411yescharacteristic
58C2×D4×C61—21no—
59C2×D4×C61—41no—
60C2×D4×C61—41no—
61C2×D4×C61M1612yes—
62C22×C4×C61—21no—
63C22×C4×C61—42no—
64C22×C4×C61—42no—
65C22×C4×C61—42no—
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22×C411yescharacteristic
69C2×C22⋊D61—24no—
70C2×C22⋊D61—42no—
71C2×C22⋊D61—42no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61C2×D411yescharacteristic
76C22×Dic61C2×D411yescharacteristic
77C2×C4×D61—22no—
78C2×C4×D61—22no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—22no—
82C2×C4×D61—22no—
83C2×C4×D61—41no—
84C2×C4×D61—41no—
85C2×C4×D61—41no—
86C2×C4×D61—41no—
87C2×#92420—24no—
88C2×#92420—42no—
89C2×#92420—42no—
90C2×#92420—42no—
91C2×#92420—42no—
92C2×#92420—42no—
93C4⋊C4×C61—41no—
94C22⋊C4×C61—42no—
95C42×C61—22no—
96C22⋊Dic61—24no—
97C22⋊Dic61—42no—
98C22⋊Dic61—42no—
99#11758198—42no—
100C4⋊Dic61—21no—
101C4⋊Dic61—41no—
102C4⋊Dic61M1612yes—
103#11758196—42no—
104C4×Dic61—22no—
105C4×Dic61—41no—
106C4×Dic61—41no—
107C4×Dic61—42no—
108C23×C61—22no—
109C23×C61—41no—
110C23×C61—41no—
111C23×C61—41no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61C2×C22⋊C411yescharacteristic
116C22×D61—21no—
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—21no—
122C22×D61#10412yes—
123D4×C61—42no—
124D4×C61—42no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—84no—
136C2×C4×C61#9912yes—
137C2×C4×C61C2×M1611yescharacteristic
138C2×C4×C61C2×M1611yescharacteristic
139C22⋊D61—48no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—22no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61#13512yes—
154C2×Dic61AGL(1,ℤ/8)12yes—
155C4×D61—44no—
156C4×D61—44no—
157C4×D61—42no—
158C4×D61—42no—
159#92420—44no—
160#92420—82no—
161#7620—611nomaximal, Sylow
162C22×C61—42no—
163C22×C61—42no—
164C22×C61—42no—
165C22×C61—81no—
166C22×C61—81no—
167C22×C61—81no—
168C22×C61—81no—
169C22×C61#40711yescharacteristic
170C22×C61C2×#9911yescharacteristic
171C22×C61#41311yescharacteristic
172C22×C61#41611yescharacteristic
173C22×C61#41811yescharacteristic
174C22×C61C2×#10411yescharacteristic
175C22×C61#42111yescharacteristic
176C2×D61—22no—
177C2×D61—22no—
178C2×D61—22no—
179C2×D61—41no—
180C2×D61—41no—
181C2×D61—41no—
182C2×D61—41no—
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—22no—
186C4×C61—41no—
187C4×C61—81no—
188Dic61—22no—
189Dic61—22no—
190Dic61—41no—
191Dic61—42no—
192Dic61—81no—
193C4×#121—611no—
194#1817—611no—
195#1749—611no—
196#1271—612no—
197#1270—612no—
198C2×C61—82no—
199C2×C61#146511yescharacteristic
200C2×C61#148811yescharacteristic
201C2×C61#149011yescharacteristic
202C2×C61#150111yescharacteristic
203C2×C61#151011yescharacteristic
204C2×C61#153211yescharacteristic
205C2×C61#155311yescharacteristic
206D61—42no—
207C2×#121—611no—
208C2×C4×D4—1221no—
209C2×C4×D4#692311yescharacteristic
210C22×C42—611no—
211C2×C22⋊C8—1221no—
212C2×C22⋊C8—1221no—
213C2×#97—1221no—
214#390—611no—
215#389—611no—
216#388—1221no—
217#386—1221no—
218#380—611no—
219C4×C4⋊C4—611no—
220C4×C22⋊C4—1221no—
221#336—612no—
222#336—612no—
223#336—1221no—
224C61#762011yescharacteristic, complemented, Sylow
225C22×D4—1221no—
226C22×D4C2×#692311yescharacteristic
227C23×C4—21no—
228C23×C4—611no—
229C23×C4—611no—
230C23×C4—611no—
231C22×C8—1222no—
232C22×C8—1222no—
233#121—1222no—
234#121—1222no—
235C4×D4—42no—
236C4×D4—2444no—
237C2×C4⋊C4—611no—
238C2×C4⋊C4—611no—
239C2×C4⋊C4—1221no—
240C2×C4⋊C4C2×#692311yescharacteristic
241C2×C22⋊C4—21no—
242C2×C22⋊C4—1221no—
243C2×C22⋊C4—1221no—
244C2×C22⋊C4—1221no—
245C2×C22⋊C4—1221no—
246C2×C42—611no—
247C2×C42—611no—
248C2×C42—611no—
249C2×C42—1221no—
250C2×C42—2442no—
251C2×C42C2×#692311yescharacteristic
252C22⋊C8—1224no—
253C22⋊C8—2442no—
254#97—2442no—
255#95—1221no—
256#95—1221no—
257#95—1221no—
258C24—21no—
259C24—611no—
260C2×D4—21no—
261C2×D4—41no—
262C2×D4—41no—
263C2×D4—1224no—
264C2×D4—2442no—
265C2×D4—2442no—
266C2×D4#1175821312yes—
267C22×C4—21no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—42no—
271C22×C4—611no—
272C22×C4—611no—
273C22×C4—611no—
274C22×C4—1222no—
275C22×C4—1222no—
276C22×C4—1222no—
277C22×C4—1221no—
278C22×C4—1222no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4—2441no—
283C22×C4—2441no—
284C22×C4—2441no—
285C22×C4—2441no—
286C22×C4C22⋊#692311yescharacteristic
287C22×C4C22⋊#692311yescharacteristic
288C22×C4C22×#692311yescharacteristic
289C2×C8—1224no—
290C2×C8—2442no—
291C2×C8—2442no—
292C2×C8—2442no—
293C2×C8—2442no—
294C2×C8—2442no—
295C4⋊C4—41no—
296C4⋊C4—612no—
297C4⋊C4—1221no—
298C4⋊C4—2441no—
299C4⋊C4—2442no—
300C22⋊C4—42no—
301C22⋊C4—1224no—
302C22⋊C4—2442no—
303C22⋊C4—2442no—
304C22⋊C4—2442no—
305C42—22no—
306C42—1222no—
307C42—2441no—
308C42—2441no—
309C42—2442no—
310C23—22no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—612no—
318C23—1221no—
319C23—1221no—
320C23—1221no—
321C23—1221no—
322C23—1221no—
323C23—1221no—
324C23C2×C22⋊#692311yescharacteristic
325D4—42no—
326D4—42no—
327D4—2448no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—84no—
339C2×C4—612no—
340C2×C4—612no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1222no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—2444no—
350C2×C4—2442no—
351C2×C4—2442no—
352C2×C4—2444no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4—2441no—
357C2×C4—2441no—
358C2×C4#1451983512yes—
359C2×C4D61⋊M1611yescharacteristic
360C2×C4C2×#1175821311yescharacteristic
361C8—4882no—
362C8—2444no—
363C22—42no—
364C22—42no—
365C22—42no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22—81no—
370C22—1222no—
371C22—1222no—
372C22—1222no—
373C22—2441no—
374C22—2441no—
375C22—2441no—
376C22—2441no—
377C22#1684073311yescharacteristic
378C22C2×#1451983511yescharacteristic
379C22#1684074811yescharacteristic
380C22#1684075211yescharacteristic
381C22#1684075411yescharacteristic
382C22D61⋊#10411yescharacteristic
383C22#1684076011yescharacteristic
384C4—21no—
385C4—21no—
386C4—22no—
387C4—41no—
388C4—81no—
389C4—1222no—
390C4—1222no—
391C4—4881no—
392C4—2441no—
393C4—2442no—
394C2—82no—
395C2—2442no—
396C2#2146107411yescharacteristic
397C2#2146115111yescharacteristic
398C2#2146115911yescharacteristic
399C2#2146119411yescharacteristic
400C2#2146122411yescharacteristic
401C2#2146129411yescharacteristic
402C2#2146134211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C4×D4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519748C4
cosocleC2×C4×Dic61C23
hypercenterC2×C4×D4#6923
hypocenterC61#7620
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #21461711C2semidirect
2. #21461546C2semidirect
3. #21460638C2semidirect
4. #21460635C2semidirect
224. C61#7620semidirect

Maximal subgroups

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

subgroupindex
#214617112
#214615462
#214606382
#214606352
C4×#145197482
#762061