Finite Group Databasebeta

← #30601124

Subgroups — #30601124

Order 15616.

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

normal subgroups only

This group has 486 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#21462715C211yesmaximal, characteristic, complemented
2#21461298C212yesmaximal
3#21461082C211yesmaximal, characteristic, complemented
4#21460670C212yesmaximal, complemented
5#21450798C211yesmaximal, characteristic
6#16840813—24no—
7#16840782—21no—
8#16840782C2212yes—
9#16840782C2212yes—
10#16840778—21no—
11#16840617—24no—
12#16840607—21no—
13#16840607—21no—
14C2×#14519775C411yescharacteristic
15C2×#14519764C2211yescharacteristic
16C2×Q8×Dic61C2211yescharacteristic
17#16839685—21no—
18#16839685—21no—
19#16839668C411yescharacteristic
20#16839665C411yescharacteristic
21#16839656—21no—
22#16839656—21no—
23C4×#11758196C2211yescharacteristic
24C2×#124×C61C411yescharacteristic
25#14519844—22no—
26#14519844—22no—
27#14519844—22no—
28C4⋊#92420—22no—
29C22⋊#92420—22no—
30C22⋊#92420—22no—
31#14519832—22no—
32#14519832—22no—
33#14519832D414yes—
34C4×#92420—22no—
35C22×Dic122C2×C411yescharacteristic
36#14519775—42no—
37#14519764—22no—
38#14519764—22no—
39Q8×Dic61—22no—
40Q8×Dic61—22no—
41C2×C4⋊Dic61C2×C411yescharacteristic
42C2×C4⋊Dic61D411yescharacteristic
43C2×C4⋊Dic61D411yescharacteristic
44C2×#11758196—21no—
45C2×#11758196—21no—
46C2×#11758196—21no—
47C2×C22⋊Dic61—21no—
48C2×C22⋊Dic61—21no—
49C2×C22⋊Dic61—21no—
50C2×C22⋊Dic61—21no—
51C2×C4×Dic61C2×C411yescharacteristic
52C2×C4×Dic61D411yescharacteristic
53C2×C4×Dic61D411yescharacteristic
54C2×C4×Dic61C2311yescharacteristic
55#14519684—21no—
56#14519684—21no—
57#14519684—21no—
58C22×Q8×C61C2×C411yescharacteristic
59C22×D4×C61C2×C411yescharacteristic
60#124×C61—42no—
61C2×C22⋊C4×C61—21no—
62C2×C22⋊C4×C61—21no—
63C2×C42×C61C2×C411yescharacteristic
64C24×C61—21no—
65C2×Q8×C61—22no—
66C2×Q8×C61—22no—
67C2×Q8×C61—41no—
68C2×D4×C61—22no—
69C2×D4×C61—41no—
70C2×D4×C61—41no—
71C22×C4×C61—21no—
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C22×C411yescharacteristic
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61C22⋊C411yescharacteristic
78C22×Dic61C22⋊C411yescharacteristic
79C22×Dic61C2×D411yescharacteristic
80C22×Dic61C2×D411yescharacteristic
81C2×Dic122—22no—
82C2×Dic122—41no—
83C2×Dic122—41no—
84C2×#92420—24no—
85C2×#92420—42no—
86C22⋊C4×C61—42no—
87C22⋊C4×C61—42no—
88C42×C61—41no—
89C22⋊Dic61—42no—
90C22⋊Dic61—42no—
91C22⋊Dic61—41no—
92C22⋊Dic61—42no—
93C22⋊Dic61—41no—
94C4⋊Dic61—22no—
95C4⋊Dic61—22no—
96C4⋊Dic61—22no—
97#11758196—42no—
98#11758196—42no—
99#11758196—42no—
100C4×Dic61—21no—
101C4×Dic61—21no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C4×Dic61—41no—
105C4×Dic61C2×D412yes—
106C4×Dic61#4112yes—
107C23×C61—41no—
108C23×C61—41no—
109C23×C61—41no—
110C23×C61—41no—
111C23×C61—41no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61C2×C22⋊C411yescharacteristic
115Q8×C61—44no—
116D4×C61—82no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61#10012yes—
128C2×C4×C61C4×D412yes—
129C2×Dic61—22no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61#12011yescharacteristic
142C2×Dic61#12112yes—
143C2×Dic61#12311yescharacteristic
144Dic122—82no—
145#92420—44no—
146#92420—82no—
147#9448—611nomaximal, Sylow
148C22×C61—21no—
149C22×C61—21no—
150C22×C61—81no—
151C22×C61—81no—
152C22×C61—81no—
153C22×C61—81no—
154C22×C61—81no—
155C22×C61—81no—
156C22×C61—81no—
157C22×C61#38611yescharacteristic
158C22×C61C2×#10011yescharacteristic
159C22×C61#41311yescharacteristic
160C4×C61—22no—
161C4×C61—22no—
162C4×C61—41no—
163C4×C61—81no—
164Dic61—22no—
165Dic61—21no—
166Dic61—21no—
167Dic61—42no—
168Dic61—41no—
169Dic61—41no—
170Dic61—81no—
171#2983—611no—
172#2545—611no—
173#1533—612no—
174#1467—611no—
175#1285—612no—
176C2×C61—21no—
177C2×C61—21no—
178C2×C61—161no—
179C2×C61#188411yescharacteristic
180C2×C61#190011yescharacteristic
181C2×C61#191211yescharacteristic
182C2×C4⋊Q8—611no—
183C2×#124—611no—
184C2×#124#692311yescharacteristic
185C2×C4×Q8—611no—
186#446—1224no—
187#432—612no—
188#432—612no—
189#432—1221no—
190#431—1221no—
191#396—1221no—
192#396—1221no—
193#391—611no—
194#390—611no—
195#388—1221no—
196#388—1221no—
197C4×C4⋊C4—611no—
198#329—1224no—
199#324—1221no—
200#324—1221no—
201C61#944811yescharacteristic, complemented, Sylow
202C22×Q8—611no—
203C22×Q8C2×#692311yescharacteristic
204C22×D4C2×#692311yescharacteristic
205C4⋊Q8—2442no—
206#124—42no—
207#124—1222no—
208#124—1222no—
209C4×Q8—1222no—
210C4×Q8—1222no—
211C2×C4⋊C4—611no—
212C2×C4⋊C4—611no—
213C2×C4⋊C4—611no—
214C2×C4⋊C4—1221no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4—1221no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
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×C42C2×#692311yescharacteristic
228C4⋊C8—1222no—
229C4⋊C8—1222no—
230C4⋊C8—1222no—
231C4⋊C8—1222no—
232C22⋊C8—1222no—
233C22⋊C8—1222no—
234#97—614no—
235#97—1222no—
236#97—1222no—
237C4×C8—1222no—
238#95—1221no—
239#95—1221no—
240#95—1221no—
241C24—21no—
242C2×Q8—22no—
243C2×Q8—22no—
244C2×Q8—41no—
245C2×Q8—1222no—
246C2×Q8—2441no—
247C2×Q8—2441no—
248C2×D4—22no—
249C2×D4—41no—
250C2×D4—41no—
251C22×C4—21no—
252C22×C4—611no—
253C22×C4—611no—
254C22×C4—611no—
255C22×C4—611no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4C22⋊#692311yescharacteristic
259C22×C4C22⋊#692311yescharacteristic
260C22×C4C22×#692311yescharacteristic
261C2×C8—1224no—
262C2×C8—2442no—
263C4⋊C4—1222no—
264C4⋊C4—1222no—
265C4⋊C4—1222no—
266C4⋊C4—2442no—
267C4⋊C4—2442no—
268C4⋊C4—2442no—
269C22⋊C4—42no—
270C22⋊C4—42no—
271C22⋊C4—2441no—
272C22⋊C4—2442no—
273C22⋊C4—2441no—
274C22⋊C4—2442no—
275C22⋊C4—2442no—
276C42—41no—
277C42—612no—
278C42—612no—
279C42—1221no—
280C42—1221no—
281C42—1221no—
282C42—1221no—
283C42—2441no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23C2×C22⋊#692311yescharacteristic
292Q8—44no—
293Q8—4882no—
294D4—82no—
295C2×C4—21no—
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—611no—
306C2×C4—612no—
307C2×C4—611no—
308C2×C4—1222no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—2441no—
312C2×C4—2441no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4#1451983712yes—
321C2×C4D4×#692312yes—
322C8—4882no—
323C8—2444no—
324C22—21no—
325C22—21no—
326C22—81no—
327C22—81no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22—81no—
332C22—81no—
333C22#1684071011yescharacteristic
334C22C2×#1451983711yescharacteristic
335C22#1684074911yescharacteristic
336C4—22no—
337C4—22no—
338C4—41no—
339C4—81no—
340C4—1222no—
341C4—1221no—
342C4—1221no—
343C4—4881no—
344C4—2442no—
345C4—2441no—
346C4—2441no—
347C2—21no—
348C2—21no—
349C2—161no—
350C2#2146182311yescharacteristic
351C2#2146184411yescharacteristic
352C2#2146186711yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#124×C61C4
socleC22×C61#386
prime radicalC22×D4×C61C2×C4
cosocleC2×C4×Dic61C23
hypercenterC2×#124#6923
hypocenterC61#9448
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. #21462715C2semidirect
3. #21461082C2semidirect
4. #21460670C2semidirect
201. C61#9448semidirect

Maximal subgroups

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

subgroupindex
#214627152
#214612982
#214610822
#214606702
#214507982
#944861