Finite Group Databasebeta

← #30604172

Subgroups — #30604172

Order 15616.

442 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 74 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#21461078C211yesmaximal, characteristic
2#21461074C211yesmaximal, characteristic
3#21460764C212yesmaximal, complemented
4#21460745C212yesmaximal, complemented
5#21448488C211yesmaximal, characteristic
6#16840783—21no—
7#16840733—21no—
8#16840608—21no—
9#16840606—21no—
10#16840605C2212yes—
11#16840605C2212yes—
12C2×#14519760C411yescharacteristic
13C2×C4×C22⋊D61C2211yescharacteristic
14#16839657—21no—
15#16839652—21no—
16#16839643—21no—
17#16839641C411yescharacteristic
18#16839635C2211yescharacteristic
19#16839633—21no—
20#16839625C2211yescharacteristic
21C4×C22⋊Dic61C411yescharacteristic
22C22×C4⋊C4×C61C411yescharacteristic
23C2×#11758213—41no—
24C4⋊#92420—41no—
25#14519834—41no—
26C22⋊#92420—22no—
27C22⋊#92420—22no—
28#14519832—41no—
29C22×C22⋊D61C2×C411yescharacteristic
30C22×C4×D61D411yescharacteristic
31#14519760—22no—
32#14519760—22no—
33C4×C22⋊D61—41no—
34C4×C22⋊D61—41no—
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×#11758196D411yescharacteristic
38C2×C22⋊Dic61C2×C411yescharacteristic
39C2×C22⋊Dic61C2×C411yescharacteristic
40C2×C22⋊Dic61C2311yescharacteristic
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198D411yescharacteristic
44C2×C4×Dic61—21no—
45C2×C4×Dic61D411yescharacteristic
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51C23×C4×C61C2×C411yescharacteristic
52C23×C4×C61C2×C411yescharacteristic
53C23×C4×C61C2×C411yescharacteristic
54C2×C4⋊C4×C61—21no—
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61—41no—
57C2×C4⋊C4×C61—41no—
58C24×C61C22×C411yescharacteristic
59C23×D61C22⋊C411yescharacteristic
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—41no—
66C22×C4×C61—41no—
67C22×C4×C61—41no—
68C22×C4×C61—81no—
69C22×C4×C61—81no—
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61M1612yescomplemented
73C2×C22⋊D61—21no—
74C2×C22⋊D61—21no—
75C2×C22⋊D61—41no—
76C2×C22⋊D61—41no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61C22⋊C411yescharacteristic
80C22×Dic61C2×D411yescharacteristic
81C22×Dic61C2×D411yescharacteristic
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—81no—
85C2×#92420—42no—
86C2×#92420—42no—
87#11758213—82no—
88C4⋊C4×C61—42no—
89C4⋊C4×C61—41no—
90C4⋊C4×C61—41no—
91C22⋊Dic61—21no—
92C22⋊Dic61—41no—
93C22⋊Dic61—41no—
94C22⋊Dic61M1612yescomplemented
95#11758198—24no—
96#11758198—41no—
97#11758198—81no—
98#11758196—24no—
99#11758196—41no—
100#11758196—81no—
101C4×Dic61—21no—
102C4×Dic61—21no—
103C4×Dic61—81no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61—41no—
107C23×C61—41no—
108C23×C61C2×C22⋊C411yescharacteristic
109C23×C61C2×M1611yescharacteristic
110C23×C61C2×M1611yescharacteristic
111C22×D61—21no—
112C22×D61—21no—
113C22×D61—21no—
114C22×D61—41no—
115C22×D61—41no—
116C2×C4×C61—22no—
117C2×C4×C61—21no—
118C2×C4×C61—41no—
119C2×C4×C61—42no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—42no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—81no—
128C2×C4×C61—81no—
129C2×C4×C61—82no—
130C2×C4×C61#9911yescharacteristic
131C2×C4×C61#9911yescharacteristic
132C22⋊D61—42no—
133C22⋊D61—42no—
134C2×Dic61—21no—
135C2×Dic61—22no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C4×D61—42no—
148C4×D61—81no—
149#92420—82no—
150#92420—82no—
151#11528—611nomaximal, Sylow
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61—42no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61#40711yescharacteristic
162C22×C61C2×#9911yescharacteristic
163C22×C61#41311yescharacteristic
164C2×D61—42no—
165C2×D61—41no—
166C2×D61—41no—
167C2×D61—41no—
168C2×D61—81no—
169C4×C61—21no—
170C4×C61—21no—
171C4×C61—41no—
172C4×C61—42no—
173C4×C61—81no—
174Dic61—42no—
175Dic61—41no—
176Dic61—41no—
177Dic61—41no—
178Dic61—81no—
179#2322—611no—
180#1466—611no—
181#1465—611no—
182#1326—612no—
183#1317—612no—
184C2×C61—21no—
185C2×C61—21no—
186C2×C61—41no—
187C2×C61—41no—
188C2×C61#146511yescharacteristic
189C2×C61#212111yescharacteristic
190C2×C61#212311yescharacteristic
191D61—81no—
192C2×#123—611no—
193C2×C4×D4—611no—
194C22×C4⋊C4#692311yescharacteristic
195#432—1221no—
196#407—1221no—
197#389—1221no—
198#388—1221no—
199#387—1221no—
200#386—611no—
201#385—611no—
202#385—1221no—
203#381—611no—
204C4×C22⋊C4—611no—
205#324—1221no—
206#323—612no—
207#323—612no—
208#323—1221no—
209C61#1152811yescharacteristic, complemented, Sylow
210C22×D4—611no—
211C23×C4—611no—
212C23×C4C2×#692311yescharacteristic
213C23×C4C2×#692311yescharacteristic
214C23×C4C2×#692311yescharacteristic
215C2×M16—2441no—
216#123—1222no—
217#123—1222no—
218C4×D4—2441no—
219C4×D4—2441no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—41no—
223C2×C4⋊C4—41no—
224C2×C4⋊C4—611no—
225C2×C4⋊C4—1221no—
226C2×C4⋊C4—1221no—
227C2×C22⋊C4—611no—
228C2×C22⋊C4—611no—
229C2×C22⋊C4—611no—
230C2×C22⋊C4—611no—
231C2×C22⋊C4—1221no—
232C2×C22⋊C4—1221no—
233C2×C42—611no—
234C2×C42—1221no—
235C4⋊C8—2441no—
236C22⋊C8—1222no—
237C22⋊C8—1222no—
238C22⋊C8—2441no—
239#97—2441no—
240#95—1221no—
241#95—1221no—
242#95—1221no—
243#95—1221no—
244#95—1221no—
245C24—611no—
246C24C22×#692311yescharacteristic
247C2×D4—1221no—
248C2×D4—1221no—
249C2×D4—2441no—
250C2×D4—2441no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—81no—
260C22×C4—81no—
261C22×C4—611no—
262C22×C4—611no—
263C22×C4—611no—
264C22×C4—1221no—
265C22×C4—1221no—
266C22×C4—1221no—
267C22×C4—1221no—
268C22×C4—4881no—
269C22×C4#1175821312yescomplemented
270C22×C4C22⋊#692311yescharacteristic
271C22×C4C22⋊#692311yescharacteristic
272M16—4882no—
273C2×C8—2442no—
274C2×C8—2442no—
275C4⋊C4—42no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—1224no—
279C4⋊C4—4881no—
280C4⋊C4—2441no—
281C22⋊C4—612no—
282C22⋊C4—1224no—
283C22⋊C4—1221no—
284C22⋊C4—4881no—
285C22⋊C4—2441no—
286C22⋊C4—2441no—
287C22⋊C4—2441no—
288C42—1221no—
289C42—1221no—
290C42—4881no—
291C23—21no—
292C23—21no—
293C23—41no—
294C23—41no—
295C23—1221no—
296C23—1221no—
297C23—1221no—
298C23—2441no—
299C23—2441no—
300C23C2×C22⋊#692311yescharacteristic
301C23D61⋊M1611yescharacteristic
302C23C2×#1175821311yescharacteristic
303D4—2442no—
304D4—2442no—
305C2×C4—22no—
306C2×C4—21no—
307C2×C4—41no—
308C2×C4—42no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—82no—
319C2×C4—1222no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—4881no—
326C2×C4—2442no—
327C2×C4—2441no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4—2441no—
333C2×C4—2441no—
334C2×C4#1451983511yescharacteristic
335C2×C4#1451983511yescharacteristic
336C8—4882no—
337C8—4882no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—42no—
345C22—41no—
346C22—41no—
347C22—4881no—
348C22—2442no—
349C22—2441no—
350C22—2441no—
351C22—2441no—
352C22#1684073311yescharacteristic
353C22C2×#1451983511yescharacteristic
354C22#1684074811yescharacteristic
355C4—21no—
356C4—21no—
357C4—41no—
358C4—42no—
359C4—81no—
360C4—4881no—
361C4—2442no—
362C4—2441no—
363C4—2441no—
364C4—2441no—
365C2—21no—
366C2—21no—
367C2—41no—
368C2—41no—
369C2—4881no—
370C2#2146107411yescharacteristic
371C2#2146207411yescharacteristic
372C2#2146208111yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
FittingC22×C4⋊C4×C61C4
socleC22×C61C2×#99
prime radicalC22×C22⋊D61C2×C4
cosocleC2×C22⋊Dic61C23
hypercenterC22×C4⋊C4#6923
hypocenterC61#11528
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #21460764C2semidirect
4. #21460745C2semidirect
72. C22×C4×C61M16semidirect
94. C22⋊Dic61M16semidirect
209. C61#11528semidirect
269. C22×C4#11758213semidirect

Maximal subgroups

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

subgroupindex
#214610782
#214610742
#214607642
#214607452
#214484882
#1152861