Finite Group Databasebeta

← #30601136

Subgroups — #30601136

Order 15616.

468 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 82 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
2#21461352C212yesmaximal
3#21461082C211yesmaximal, characteristic
4#21460670C212yesmaximal
5#21450805C211yesmaximal, characteristic
6#16840813—24no—
7#16840782—21no—
8#16840782C2212yes—
9#16840782C2212yes—
10#16840778—21no—
11#16840622—24no—
12#16840607—21no—
13#16840607—21no—
14C2×#14519775C411yescharacteristic
15C2×#14519775C2211yescharacteristic
16C2×Q8×Dic61C2211yescharacteristic
17#16839695—21no—
18#16839695—21no—
19#16839669C411yescharacteristic
20#16839668C411yescharacteristic
21#16839657—21no—
22#16839657—21no—
23C4×#11758196C2211yescharacteristic
24C2×C4⋊Q8×C61C411yescharacteristic
25#14519844—22no—
26#14519844—22no—
27#14519844D414yes—
28C4⋊#92420—22no—
29C22⋊#92420—22no—
30C22⋊#92420—22no—
31#14519832—22no—
32#14519832—22no—
33#14519832—22no—
34C4×#92420—22no—
35C22×Dic122C2×C411yescharacteristic
36#14519775—22no—
37#14519775—22no—
38#14519775—42no—
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×#11758196—21no—
48C2×#11758196—21no—
49C2×C4×Dic61C2×C411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51C2×C4×Dic61D411yescharacteristic
52C2×C4×Dic61C2311yescharacteristic
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57#14519684—21no—
58C22×Q8×C61C2×C411yescharacteristic
59C22×Q8×C61C2×C411yescharacteristic
60C4⋊Q8×C61—42no—
61C2×C4⋊C4×C61—21no—
62C2×C4⋊C4×C61—21no—
63C2×C42×C61C2×C411yescharacteristic
64C2×Q8×C61—22no—
65C2×Q8×C61—22no—
66C2×Q8×C61—22no—
67C2×Q8×C61—41no—
68C2×Q8×C61—41no—
69C2×Q8×C61—41no—
70C22×C4×C61—21no—
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—
86C4⋊C4×C61—42no—
87C4⋊C4×C61—42no—
88C42×C61—41no—
89C4⋊Dic61—22no—
90C4⋊Dic61—22no—
91C4⋊Dic61—22no—
92#11758196—24no—
93#11758196—42no—
94#11758196—42no—
95#11758196—41no—
96#11758196—42no—
97#11758196—41no—
98C4×Dic61—21no—
99C4×Dic61—21no—
100C4×Dic61—21no—
101C4×Dic61—21no—
102C4×Dic61—41no—
103C4×Dic61C2×D412yes—
104C4×Dic61#4112yes—
105C23×C61C2×C22⋊C411yescharacteristic
106Q8×C61—44no—
107Q8×C61—82no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—22no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61#10012yes—
122C2×C4×C61C4×D412yes—
123C2×Dic61—22no—
124C2×Dic61—22no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61#12011yescharacteristic
136C2×Dic61#12112yes—
137C2×Dic61#12311yescharacteristic
138Dic122—82no—
139#92420—44no—
140#92420—82no—
141#9452—611nomaximal, Sylow
142C22×C61—21no—
143C22×C61—21no—
144C22×C61#38611yescharacteristic
145C22×C61C2×#10011yescharacteristic
146C22×C61#41311yescharacteristic
147C4×C61—22no—
148C4×C61—22no—
149C4×C61—42no—
150C4×C61—41no—
151C4×C61—81no—
152Dic61—21no—
153Dic61—22no—
154Dic61—42no—
155Dic61—41no—
156Dic61—41no—
157Dic61—81no—
158Dic61#45612yes—
159#2983—611no—
160#2546—611no—
161#1558—612no—
162#1467—611no—
163#1285—612no—
164C2×C61—21no—
165C2×C61—21no—
166C2×C61#188611yescharacteristic
167C2×C61#190011yescharacteristic
168C2×C61#190911yescharacteristic
169C2×C4⋊Q8—611no—
170C2×C4⋊Q8—611no—
171C2×C4⋊Q8#692311yescharacteristic
172C2×C4×Q8—611no—
173#446—1224no—
174#432—612no—
175#432—612no—
176#432—1221no—
177#431—1221no—
178#398—1221no—
179#398—1221no—
180#391—611no—
181#391—611no—
182#389—1221no—
183#389—1221no—
184C4×C4⋊C4—611no—
185#333—1224no—
186#324—1221no—
187#324—1221no—
188C61#945211yescharacteristic, complemented, Sylow
189C22×Q8—611no—
190C22×Q8C2×#692311yescharacteristic
191C22×Q8C2×#692311yescharacteristic
192C4⋊Q8—42no—
193C4⋊Q8—1222no—
194C4⋊Q8—1222no—
195C4⋊Q8—2442no—
196C4×Q8—1222no—
197C4×Q8—1222no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—611no—
201C2×C4⋊C4—611no—
202C2×C4⋊C4—611no—
203C2×C4⋊C4—1221no—
204C2×C4⋊C4—1221no—
205C2×C4⋊C4—1221no—
206C2×C4⋊C4—1221no—
207C2×C4⋊C4—1221no—
208C2×C42—611no—
209C2×C42—611no—
210C2×C42—611no—
211C2×C42—611no—
212C2×C42C2×#692311yescharacteristic
213C4⋊C8—614no—
214C4⋊C8—1222no—
215C4⋊C8—1222no—
216C4⋊C8—1222no—
217C22⋊C8—1222no—
218C22⋊C8—1222no—
219#97—1222no—
220#97—1222no—
221#97—1222no—
222C4×C8—1222no—
223#95—1221no—
224#95—1221no—
225#95—1221no—
226#95—1221no—
227#95—1221no—
228C2×Q8—22no—
229C2×Q8—22no—
230C2×Q8—22no—
231C2×Q8—41no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×Q8—1222no—
235C2×Q8—2441no—
236C2×Q8—2441no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—611no—
240C22×C4—611no—
241C22×C4—611no—
242C22×C4—611no—
243C22×C4—1221no—
244C22×C4—1221no—
245C22×C4C22⋊#692311yescharacteristic
246C22×C4C22⋊#692311yescharacteristic
247C22×C4C22×#692311yescharacteristic
248C2×C8—1224no—
249C2×C8—2442no—
250C4⋊C4—42no—
251C4⋊C4—42no—
252C4⋊C4—1222no—
253C4⋊C4—1222no—
254C4⋊C4—1224no—
255C4⋊C4—1222no—
256C4⋊C4—2442no—
257C4⋊C4—2441no—
258C4⋊C4—2442no—
259C4⋊C4—2441no—
260C4⋊C4—2442no—
261C42—41no—
262C42—612no—
263C42—612no—
264C42—1221no—
265C42—1221no—
266C42—1221no—
267C42—1221no—
268C42—2441no—
269C23C2×C22⋊#692311yescharacteristic
270Q8—44no—
271Q8—82no—
272Q8—4882no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—22no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—611no—
287C2×C4—612no—
288C2×C4—611no—
289C2×C4—1222no—
290C2×C4—1222no—
291C2×C4—1221no—
292C2×C4—1221no—
293C2×C4—2441no—
294C2×C4—2441no—
295C2×C4—2441no—
296C2×C4—2441no—
297C2×C4—2441no—
298C2×C4—2441no—
299C2×C4—2441no—
300C2×C4—2441no—
301C2×C4#1451983712yes—
302C2×C4D4×#692312yes—
303C8—4882no—
304C8—2444no—
305C22—21no—
306C22—21no—
307C22#1684071011yescharacteristic
308C22C2×#1451983711yescharacteristic
309C22#1684074911yescharacteristic
310C4—22no—
311C4—22no—
312C4—42no—
313C4—41no—
314C4—81no—
315C4—612no—
316C4—1221no—
317C4—1222no—
318C4—4881no—
319C4—2442no—
320C4—2441no—
321C4—2441no—
322C2—21no—
323C2—21no—
324C2#2146182511yescharacteristic
325C2#2146184411yescharacteristic
326C2#2146186111yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C4⋊Q8×C61C4
socleC22×C61#386
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×C4⋊Q8#6923
hypocenterC61#9452
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
188. C61#9452semidirect

Maximal subgroups

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

subgroupindex
#214627152
#214613522
#214610822
#214606702
#214508052
#945261