Finite Group Databasebeta

← #29578025

Subgroups — #29578025

Order 15616.

518 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 99 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#21454860C211yesmaximal, characteristic
2#21451162C211yesmaximal, characteristic
3#21444148C212yesmaximal, complemented
4#21443724C212yesmaximal, complemented
5C61×#1465C211yesmaximal, characteristic
6C22×#11758196C2211yescharacteristic
7#16839840—24no—
8#16839815—21no—
9#16839726—21no—
10#16839726C2212yes—
11#16839695—21no—
12#16839685—21no—
13#16839646—21no—
14#16839642C411yescharacteristic
15#16839642C411yescharacteristic
16#16839635—21no—
17#16839634C411yescharacteristic
18#16839634C411yescharacteristic
19#16839622C2211yescharacteristic
20#16839487—24no—
21C2×C4×D4×C61C2211yescharacteristic
22C61×#407C2212yes—
23C61×#324—21no—
24C61×#323—21no—
25C23×Dic61C2×C411yescharacteristic
26C23×Dic61C2×C411yescharacteristic
27C2×#11758194—22no—
28C2×#11758194—22no—
29C2×C4⋊Dic61—21no—
30C2×#11758196—21no—
31C2×#11758196—21no—
32C2×#11758196—22no—
33C2×#11758196—21no—
34C2×#11758196—22no—
35C2×#11758196—21no—
36C2×C22⋊Dic61—21no—
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61C2×C411yescharacteristic
39C2×C22⋊Dic61C2×C411yescharacteristic
40C4⋊#92418—22no—
41C22⋊#92418—22no—
42C22⋊#92418—22no—
43C22⋊#92418D414yes—
44C4×#92418—22no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50C22×D4×C61C2×C411yescharacteristic
51C23×C4×C61D411yescharacteristic
52C23×C4×C61C2311yescharacteristic
53C2×M16×C61—22no—
54C4×D4×C61—22no—
55C4×D4×C61—22no—
56C2×C4⋊C4×C61D411yescharacteristic
57C2×C22⋊C4×C61C2×C411yescharacteristic
58C2×C22⋊C4×C61D411yescharacteristic
59C2×C42×C61D411yescharacteristic
60C22⋊C8×C61—22no—
61C22⋊C8×C61—22no—
62C24×C61C22⋊C411yescharacteristic
63C24×C61C22×C411yescharacteristic
64C2×D4×C61—22no—
65C2×D4×C61—22no—
66C2×D4×C61—41no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—81no—
70C22×C4×C61—81no—
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C2×D412yes—
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61#4112yes—
78C22×Dic61—21no—
79C22×Dic61—22no—
80C22×Dic61—21no—
81C22×Dic61—21no—
82C22×Dic61—21no—
83C22×Dic61—22no—
84C22×Dic61—42no—
85C22×Dic61—81no—
86M16×C61—82no—
87C2×C8×C61—42no—
88C4⋊C4×C61—22no—
89C22⋊C4×C61—22no—
90C22⋊C4×C61—22no—
91C42×C61—21no—
92C42×C61—21no—
93C22⋊Dic61—42no—
94C22⋊Dic61—41no—
95C22⋊Dic61—41no—
96C22⋊Dic61—81no—
97C4⋊Dic61—81no—
98#11758196—42no—
99#11758196—41no—
100#11758196—42no—
101#11758196—41no—
102#11758196—81no—
103#11758194—82no—
104#11758194—82no—
105C2×#92418—24no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61—21no—
110C23×C61—21no—
111C23×C61—41no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61C2×C22⋊C411yescharacteristic
116C23×C61C4×D412yes—
117D4×C61—44no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—42no—
123C2×C4×C61—41no—
124C2×C4×C61—42no—
125C2×C4×C61—41no—
126C2×C4×C61—42no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—81no—
130C2×C4×C61#10112yes—
131C2×C4×C61#12011yescharacteristic
132C2×C4×C61#12112yes—
133C2×C4×C61#12311yescharacteristic
134C2×Dic61—22no—
135C2×Dic61—24no—
136C2×Dic61—41no—
137C2×Dic61—42no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—82no—
149C8×C61—82no—
150#92418—44no—
151#9518—611nomaximal, Sylow
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—22no—
155C22×C61—22no—
156C22×C61—22no—
157C22×C61—42no—
158C22×C61—42no—
159C22×C61—42no—
160C22×C61—41no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61—81no—
164C22×C61#38611yescharacteristic
165C22×C61C2×#10111yescharacteristic
166C22×C61#41311yescharacteristic
167C4×C61—22no—
168C4×C61—21no—
169C4×C61—22no—
170C4×C61—21no—
171C4×C61—41no—
172C4×C61—41no—
173Dic61—42no—
174Dic61—81no—
175Dic61—81no—
176Dic61—81no—
177#2975—611no—
178#2579—611no—
179#1465D6111yescharacteristic
180#1463—612no—
181#1305—612no—
182C2×C61—21no—
183C2×C61—21no—
184C2×C61—42no—
185C2×C61—81no—
186C2×C61#189111yescharacteristic
187C2×C61#190111yescharacteristic
188C2×C61#191311yescharacteristic
189C2×C4×D4C2×D6111yescharacteristic
190C22×C4⋊C4—611no—
191#436—1224no—
192#431—1221no—
193#407—612no—
194#407—1221no—
195#407C2×D6112yes—
196#398—1221no—
197#396—1221no—
198#387—1221no—
199#386—611no—
200#386—611no—
201#385—611no—
202#385—611no—
203#385—1221no—
204#380—611no—
205#324—21no—
206#324—1224no—
207#323—21no—
208C61#951811yescharacteristic, complemented, Sylow
209C22×D4C4×D6111yescharacteristic
210C23×C4—611no—
211C23×C4—611no—
212C23×C4D24411yescharacteristic
213C23×C4C22×D6111yescharacteristic
214C2×M16—22no—
215C2×M16—1222no—
216C2×M16—1222no—
217C4×D4—22no—
218C4×D4—22no—
219C2×C4⋊C4—1221no—
220C2×C4⋊C4—1221no—
221C2×C4⋊C4—1221no—
222C2×C4⋊C4—1221no—
223C2×C4⋊C4—1222no—
224C2×C4⋊C4—1222no—
225C2×C4⋊C4—1221no—
226C2×C4⋊C4C22⋊D6111yescharacteristic
227C2×C22⋊C4—611no—
228C2×C22⋊C4—611no—
229C2×C22⋊C4—1221no—
230C2×C22⋊C4—1221no—
231C2×C22⋊C4C4×D6111yescharacteristic
232C2×C22⋊C4C22⋊D6111yescharacteristic
233C2×C42D24411yescharacteristic
234C4⋊C8—1222no—
235C22⋊C8—22no—
236C22⋊C8—22no—
237C22⋊C8—614no—
238C22⋊C8—1222no—
239C22⋊C8—1222no—
240C4×C8—1222no—
241#95—1221no—
242#95—1221no—
243#95—1221no—
244#95—1221no—
245#95—1221no—
246C24#1175819811yescharacteristic
247C24C2×C4×D6111yescharacteristic
248C2×D4—22no—
249C2×D4—22no—
250C2×D4—41no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—81no—
254C22×C4—81no—
255C22×C4—1221no—
256C22×C4—1222no—
257C22×C4—1222no—
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—4881no—
262C22×C4—2442no—
263C22×C4#1175819811yescharacteristic
264C22×C4#1175819811yescharacteristic
265C22×C4#1175819811yescharacteristic
266C22×C4C2×D24411yescharacteristic
267C22×C4D4×D6112yes—
268C22×C4#1175822412yes—
269C22×C4C2×C22⋊D6111yescharacteristic
270M16—82no—
271M16—4882no—
272M16—4882no—
273C2×C8—42no—
274C2×C8—1224no—
275C4⋊C4—22no—
276C4⋊C4—4881no—
277C4⋊C4—4881no—
278C4⋊C4—2442no—
279C4⋊C4—2441no—
280C4⋊C4—2442no—
281C4⋊C4—2441no—
282C22⋊C4—22no—
283C22⋊C4—22no—
284C22⋊C4—4881no—
285C22⋊C4—2442no—
286C22⋊C4—2441no—
287C22⋊C4—2441no—
288C42—21no—
289C42—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23C2×#1175819811yescharacteristic
300C23#1451973712yes—
301D4—44no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—41no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—81no—
314C2×C4—1222no—
315C2×C4—1224no—
316C2×C4—4882no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4—2441no—
327C2×C4—2442no—
328C2×C4—2441no—
329C2×C4#1451969512yes—
330C2×C4#1451974711yescharacteristic
331C2×C4#1451974912yes—
332C2×C4#1451976111yescharacteristic
333C8—82no—
334C8—2444no—
335C22—21no—
336C22—21no—
337C22—22no—
338C22—22no—
339C22—22no—
340C22—42no—
341C22—42no—
342C22—42no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—81no—
347C22#1683963911yescharacteristic
348C22C2×#1451969511yescharacteristic
349C22#1683974411yescharacteristic
350C4—22no—
351C4—22no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—4881no—
357C4—4881no—
358C4—4881no—
359C4—2442no—
360C2—21no—
361C2—21no—
362C2—42no—
363C2—81no—
364C2#2144623511yescharacteristic
365C2#2144628511yescharacteristic
366C2#2144635911yescharacteristic
subgroupG/H
centerC22#16839639
commutatorC24×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1465C2
socleC22×C61#386
prime radicalC22×D4×C61C2×C4
cosocleC23×C4×C61C23
hypercenter#1465D61
hypocenterC61#9518
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1465

Complements

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

NH ≅ G/Ntype
3. #21444148C2semidirect
4. #21443724C2semidirect
208. C61#9518semidirect

Maximal subgroups

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

subgroupindex
#214548602
#214511622
#214441482
#214437242
C61×#14652
#951861