Finite Group Databasebeta

← #29577472

Subgroups — #29577472

Order 15616.

526 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 93 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#21451194C211yesmaximal, characteristic
2#21448419C211yesmaximal, characteristic
3#21444340C211yesmaximal, characteristic
4#21444338C211yesmaximal, characteristic
5#21444148C211yesmaximal, characteristic
6#21443705C211yesmaximal, characteristic
7C61×#1297C211yesmaximal, characteristic
8C2×#14519756C2211yescharacteristic
9C22×#11758196C2211yescharacteristic
10#16839726C2211yescharacteristic
11#16839694C412yescomplemented
12#16839683C412yescomplemented
13#16839660—22no—
14#16839646—22no—
15#16839644—22no—
16#16839637—21no—
17#16839637—21no—
18#16839623—21no—
19#16839620—21no—
20C4×C22⋊Dic61C2211yescharacteristic
21#16839500—22no—
22#16839498—22no—
23#16839487—22no—
24C61×#407C2211yescharacteristic
25C4×C22⋊C4×C61C2211yescharacteristic
26C4×C22⋊C4×C61C2211yescharacteristic
27C22×Dic122C2×C411yescharacteristic
28C23×Dic61D411yescharacteristic
29C23×Dic61D411yescharacteristic
30C2×#11758194—21no—
31#14519756—21no—
32#14519756—21no—
33#14519756—21no—
34#14519756—21no—
35C2×C4⋊Dic61—22no—
36C2×C4⋊Dic61—22no—
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×#11758196—22no—
44C2×#11758196C2×C412yes—
45C2×#11758196D412yes—
46C2×C22⋊Dic61—21no—
47C2×C22⋊Dic61—21no—
48C2×C4×Dic61—21no—
49C22⋊#92418—21no—
50C22⋊#92418—21no—
51#14519684—22no—
52#14519684—24no—
53#14519684—22no—
54#14519684—22no—
55#14519684D412yes—
56C23×C4×C61C2311yescharacteristic
57C2×M16×C61—21no—
58C2×C22⋊C4×C61—21no—
59C2×C22⋊C4×C61—21no—
60C2×C42×C61—21no—
61C2×C42×C61—21no—
62C22⋊C8×C61—21no—
63C22⋊C8×C61—21no—
64#95×C61C2×C412yes—
65#95×C61D412yes—
66C24×C61C2×D411yescharacteristic
67C22×C4×C61—22no—
68C22×C4×C61—22no—
69C22×C4×C61—81no—
70C22×C4×C61C22×C411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61#4111yescharacteristic
75C22×C4×C61#4111yescharacteristic
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—21no—
82C22×Dic61—22no—
83C22×Dic61—42no—
84C22×Dic61—81no—
85C22×Dic61C22⋊C412yes—
86C22×Dic61C22⋊C412yes—
87C2×Dic122—21no—
88C2×Dic122—21no—
89C2×Dic122—81no—
90M16×C61—81no—
91C2×C8×C61—41no—
92C22⋊C4×C61—24no—
93C22⋊C4×C61—42no—
94C42×C61—81no—
95C42×C61—81no—
96C22⋊Dic61—42no—
97C22⋊Dic61—41no—
98C22⋊Dic61—41no—
99C4⋊Dic61—21no—
100C4⋊Dic61—21no—
101C4⋊Dic61—44no—
102C4⋊Dic61—82no—
103#11758196—22no—
104#11758196—22no—
105#11758196—22no—
106#11758196—22no—
107#11758196—41no—
108#11758196—41no—
109#11758196—82no—
110C4×Dic61—81no—
111#11758194—81no—
112C2×#92418—41no—
113C23×C61—22no—
114C23×C61—22no—
115C23×C61—41no—
116C23×C61C2×C22⋊C411yescharacteristic
117C23×C61#12011yescharacteristic
118C23×C61#12311yescharacteristic
119C2×C4×C61—24no—
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—42no—
127C2×C4×C61—42no—
128C2×C4×C61—42no—
129C2×C4×C61—42no—
130C2×C4×C61—42no—
131C2×C4×C61C4×D411yescharacteristic
132C2×C4×C61C4×D411yescharacteristic
133C2×C4×C61#12111yescharacteristic
134C2×C4×C61#12111yescharacteristic
135C2×Dic61—22no—
136C2×Dic61—22no—
137C2×Dic61—22no—
138C2×Dic61—22no—
139C2×Dic61—42no—
140C2×Dic61—42no—
141C2×Dic61—42no—
142C2×Dic61—42no—
143C2×Dic61—42no—
144C2×Dic61—42no—
145C2×Dic61—42no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—42no—
149C2×Dic61—42no—
150C2×Dic61—81no—
151Dic122—81no—
152Dic122—81no—
153C8×C61—81no—
154#92418—81no—
155#9412—611nomaximal, Sylow
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—44no—
164C22×C61#38611yescharacteristic
165C22×C61#42112yes—
166C22×C61#45612yes—
167C4×C61—21no—
168C4×C61—21no—
169C4×C61—21no—
170C4×C61—21no—
171C4×C61—44no—
172C4×C61—82no—
173Dic61—42no—
174Dic61—42no—
175Dic61—82no—
176Dic61—81no—
177Dic61—81no—
178#2583—611no—
179#2313—611no—
180#1508—611no—
181#1508—611no—
182#1463—611no—
183#1297—611no—
184#1297D6111yescharacteristic
185C2×C61—22no—
186C2×C61—22no—
187C2×C61—41no—
188C2×C61#188611yescharacteristic
189C2×C61#189711yescharacteristic
190C2×C61#191311yescharacteristic
191C2×C22⋊Q8—611no—
192C22×C4⋊C4—611no—
193#407—611no—
194#407C2×D6111yescharacteristic
195#398—612no—
196#395—612no—
197#389—1222no—
198#387—1222no—
199#387—1222no—
200#385—1221no—
201#385—1221no—
202#381—1221no—
203#380—1221no—
204C4×C22⋊C4—611no—
205C4×C22⋊C4C2×D6111yescharacteristic
206C4×C22⋊C4C2×D6111yescharacteristic
207#328—1222no—
208#328—1222no—
209#324—1222no—
210C61#941211yescharacteristic, complemented, Sylow
211C22×Q8—611no—
212C23×C4—611no—
213C23×C4—611no—
214C23×C4C22×D6111yescharacteristic
215C2×M16—21no—
216C2×M16—1221no—
217C22⋊Q8—1221no—
218C22⋊Q8—1221no—
219C22⋊Q8—1221no—
220C22⋊Q8—1221no—
221C2×C4⋊C4—612no—
222C2×C4⋊C4—612no—
223C2×C4⋊C4—611no—
224C2×C4⋊C4—1221no—
225C2×C4⋊C4—1221no—
226C2×C4⋊C4—1221no—
227C2×C4⋊C4—1221no—
228C2×C4⋊C4—1222no—
229C2×C4⋊C4—1222no—
230C2×C4⋊C4—1222no—
231C2×C4⋊C4—1221no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—1221no—
235C2×C22⋊C4—1221no—
236C2×C42—21no—
237C2×C42—21no—
238C2×C42—1221no—
239C22⋊C8—21no—
240C22⋊C8—21no—
241C22⋊C8—1221no—
242C22⋊C8—1221no—
243#95—612no—
244#95—1222no—
245#95—1222no—
246#95—1222no—
247#95—1224no—
248#95C4×D6112yes—
249#95D24412yes—
250C24D4×D6111yescharacteristic
251C2×Q8—1221no—
252C2×Q8—1221no—
253C2×Q8—4881no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—81no—
257C22×C4—612no—
258C22×C4—612no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4—1221no—
264C22×C4—1221no—
265C22×C4—1222no—
266C22×C4—4881no—
267C22×C4—2442no—
268C22×C4C2×C4×D6111yescharacteristic
269C22×C4C2×D24411yescharacteristic
270C22×C4#1175822211yescharacteristic
271C22×C4D4×D6111yescharacteristic
272C22×C4D4×D6111yescharacteristic
273C22×C4#1175822611yescharacteristic
274M16—81no—
275M16—4881no—
276C2×C8—41no—
277C2×C8—2441no—
278C4⋊C4—1222no—
279C4⋊C4—1222no—
280C4⋊C4—1222no—
281C4⋊C4—1222no—
282C4⋊C4—1221no—
283C4⋊C4—1221no—
284C4⋊C4—4882no—
285C4⋊C4—4882no—
286C4⋊C4—2444no—
287C4⋊C4—2441no—
288C4⋊C4—2441no—
289C22⋊C4—24no—
290C22⋊C4—42no—
291C22⋊C4—2442no—
292C22⋊C4—2441no—
293C22⋊C4—2441no—
294C42—81no—
295C42—81no—
296C42—4881no—
297C23—22no—
298C23—22no—
299C23—41no—
300C23C22⋊C4×D6111yescharacteristic
301C23#1451974711yescharacteristic
302C23#1451976211yescharacteristic
303Q8—4881no—
304Q8—4881no—
305C2×C4—24no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—1222no—
318C2×C4—1222no—
319C2×C4—1222no—
320C2×C4—1222no—
321C2×C4—4881no—
322C2×C4—2442no—
323C2×C4—2442no—
324C2×C4—2442no—
325C2×C4—2442no—
326C2×C4—2442no—
327C2×C4—2441no—
328C2×C4—2441no—
329C2×C4—2442no—
330C2×C4—2442no—
331C2×C4—2442no—
332C2×C4—2442no—
333C2×C4#1451973911yescharacteristic
334C2×C4C4×D24411yescharacteristic
335C2×C4#1451975011yescharacteristic
336C2×C4#1451975211yescharacteristic
337C8—81no—
338C8—4881no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—44no—
347C22#1683964011yescharacteristic
348C22#1683977712yes—
349C22#1683994612yes—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—44no—
355C4—82no—
356C4—4882no—
357C4—4881no—
358C4—4881no—
359C4—2442no—
360C4—2442no—
361C2—22no—
362C2—22no—
363C2—41no—
364C2#2144621111yescharacteristic
365C2#2144626611yescharacteristic
366C2#2144636011yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1297C2
socleC22×C61#386
prime radicalC24×C61C2×D4
cosocleC23×C4×C61C23
hypercenter#1297D61
hypocenterC61#9412
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1297

Complements

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

NH ≅ G/Ntype
11. #16839694C4semidirect
12. #16839683C4semidirect
210. C61#9412semidirect

Maximal subgroups

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

subgroupindex
#214511942
#214484192
#214443402
#214443382
#214441482
#214437052
C61×#12972
#941261