Finite Group Databasebeta

← #30604999

Subgroups — #30604999

Order 15616.

470 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 68 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#21461524C211yesmaximal, characteristic, complemented
2#21461072C211yesmaximal, characteristic, complemented
3#21460820C212yesmaximal, complemented
4#21460801C212yesmaximal, complemented
5#21451508C211yesmaximal, characteristic
6C2×D61⋊M16—21no—
7#16840782—21no—
8#16840642—21no—
9#16840642C2212yes—
10#16840608C2212yes—
11#16840606—21no—
12C2×#14519734C2211yescharacteristic
13#16839681C2211yescharacteristic
14#16839676C2211yescharacteristic
15#16839673C411yescharacteristic
16#16839670C411yescharacteristic
17#16839662—21no—
18#16839656—21no—
19#16839650—21no—
20#16839638—21no—
21#16839608C411yescharacteristic
22C2×#124×C61C411yescharacteristic
23C2×#11758213—41no—
24D61⋊M16—24no—
25D61⋊M16—42no—
26C2×#11758217—22no—
27C2×D61⋊C8—41no—
28#14519844—41no—
29C22⋊#92420—22no—
30#14519832—41no—
31C22×C22⋊D61—21no—
32C22×C4×D61D411yescharacteristic
33#14519734—41no—
34#14519734—41no—
35C2×#11758196—21no—
36C2×#11758196D411yescharacteristic
37C2×#11758196C2311yescharacteristic
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61—21no—
41C2×#11758198—21no—
42C2×#11758198C2×C411yescharacteristic
43C2×#11758198D411yescharacteristic
44C2×C4×Dic61—21no—
45C2×C4×Dic61D411yescharacteristic
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684C2×C411yescharacteristic
50#14519684C2×C411yescharacteristic
51C22×Q8×C61C2×C411yescharacteristic
52C22×D4×C61C2×C411yescharacteristic
53#124×C61—41no—
54#124×C61—41no—
55C2×C22⋊C4×C61—21no—
56C2×C22⋊C4×C61—21no—
57C2×C42×C61C2×C411yescharacteristic
58C24×C61—21no—
59C23×D61C22⋊C411yescharacteristic
60C2×Q8×C61—41no—
61C2×Q8×C61—81no—
62C2×D4×C61—41no—
63C2×D4×C61—81no—
64C22×C4×C61—21no—
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22×C411yescharacteristic
68C2×C22⋊D61—42no—
69C2×C22⋊D61—42no—
70C2×C22⋊D61—81no—
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C2×D411yescharacteristic
75C22×Dic61C2×D411yescharacteristic
76C2×C4×D61—22no—
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81#11758217—24no—
82#11758217—42no—
83C2×#92420—42no—
84C2×#92420—42no—
85#11758213—44no—
86D61⋊C8—44no—
87C22⋊C4×C61—42no—
88C22⋊C4×C61—41no—
89C22⋊C4×C61—41no—
90C42×C61—21no—
91C42×C61—21no—
92C22⋊Dic61—42no—
93C22⋊Dic61—41no—
94C22⋊Dic61—41no—
95C22⋊Dic61—81no—
96#11758198—41no—
97#11758198—41no—
98#11758198—81no—
99#11758196—41no—
100#11758196—41no—
101#11758196—81no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C4×Dic61—42no—
105C23×C61—41no—
106C23×C61—41no—
107C23×C61—41no—
108C23×C61—41no—
109C23×C61—41no—
110C23×C61—41no—
111C23×C61—41no—
112C23×C61C2×C22⋊C411yescharacteristic
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—41no—
116C22×D61—41no—
117C22×D61#10412yes—
118Q8×C61—82no—
119D4×C61—82no—
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—41no—
128C2×C4×C61—41no—
129C2×C4×C61#9911yescharacteristic
130C2×C4×C61#9911yescharacteristic
131C22⋊D61—84no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—22no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61AGL(1,ℤ/8)11yescharacteristic
145C2×Dic61#13711yescharacteristic
146C4×D61—22no—
147C4×D61—22no—
148C4×D61—22no—
149C4×D61—22no—
150#92420—44no—
151#92420—82no—
152#11765—611nomaximal, Sylow
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—81no—
156C22×C61—81no—
157C22×C61—81no—
158C22×C61—81no—
159C22×C61—81no—
160C22×C61—81no—
161C22×C61—81no—
162C22×C61C2×#9911yescharacteristic
163C22×C61#41711yescharacteristic
164C22×C61C2×#10411yescharacteristic
165C2×D61—22no—
166C2×D61—41no—
167C2×D61—41no—
168C2×D61—42no—
169C2×D61—81no—
170C4×C61—21no—
171C4×C61—21no—
172C4×C61—41no—
173C4×C61—41no—
174C4×C61—81no—
175Dic61—21no—
176Dic61—21no—
177Dic61—42no—
178Dic61—41no—
179Dic61—41no—
180Dic61—81no—
181#2610—611no—
182#1742—611no—
183#1464—611no—
184#1354—612no—
185#1345—612no—
186C2×C61—21no—
187C2×C61—21no—
188C2×C61—161no—
189C2×C61#150411yescharacteristic
190C2×C61#212211yescharacteristic
191C2×C61#213211yescharacteristic
192D61—42no—
193C22×M16—1221no—
194C2×#124#692311yescharacteristic
195C2×#117—611no—
196#432—1221no—
197#395—611no—
198#394—611no—
199#393—611no—
200#392—611no—
201#390—1221no—
202#388—1221no—
203#388—1221no—
204#386—1221no—
205#376—611no—
206#343—612no—
207#343—1221no—
208#324—612no—
209#323—1221no—
210C61#1176511yescharacteristic, complemented, Sylow
211C22×Q8C2×#692311yescharacteristic
212C22×D4—1221no—
213C22×D4C2×#692311yescharacteristic
214C23×C4—611no—
215C2×M16—1222no—
216C2×M16—1224no—
217C2×M16—2442no—
218C2×M16—2441no—
219C22×C8—2441no—
220#124—41no—
221#124—41no—
222#117—2441no—
223#117—2441no—
224C2×C4⋊C4—611no—
225C2×C4⋊C4—611no—
226C2×C4⋊C4—1221no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—611no—
230C2×C22⋊C4—611no—
231C2×C22⋊C4—1221no—
232C2×C22⋊C4—1221no—
233C2×C22⋊C4—1221no—
234C2×C22⋊C4—1221no—
235C2×C42—611no—
236C2×C42—1221no—
237C2×C42C2×#692311yescharacteristic
238C4⋊C8—2441no—
239C22⋊C8—1222no—
240#97—2441no—
241#95—611no—
242#95—611no—
243#95—1221no—
244#95—1221no—
245#95—1221no—
246C24—21no—
247C24—611no—
248C2×Q8—41no—
249C2×Q8—81no—
250C2×D4—41no—
251C2×D4—81no—
252C2×D4—4881no—
253C2×D4—2442no—
254C2×D4—2442no—
255C22×C4—21no—
256C22×C4—611no—
257C22×C4—611no—
258C22×C4—611no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—1222no—
262C22×C4—1221no—
263C22×C4—1221no—
264C22×C4—1221no—
265C22×C4—1221no—
266C22×C4C22⋊#692311yescharacteristic
267C22×C4C22⋊#692311yescharacteristic
268C22×C4C22×#692311yescharacteristic
269M16—1224no—
270M16—2442no—
271M16—2444no—
272C2×C8—2442no—
273C2×C8—2444no—
274C2×C8—2442no—
275C4⋊C4—4881no—
276C4⋊C4—2441no—
277C4⋊C4—2441no—
278C22⋊C4—42no—
279C22⋊C4—41no—
280C22⋊C4—41no—
281C22⋊C4—4881no—
282C22⋊C4—4881no—
283C22⋊C4—2441no—
284C22⋊C4—2441no—
285C22⋊C4—2441no—
286C22⋊C4—2441no—
287C22⋊C4—2442no—
288C42—21no—
289C42—21no—
290C42—1221no—
291C42—1221no—
292C42—2442no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23—612no—
301C23—1221no—
302C23—1221no—
303C23—2441no—
304C23—2441no—
305C23C2×C22⋊#692311yescharacteristic
306Q8—82no—
307D4—82no—
308D4—4884no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—611no—
319C2×C4—611no—
320C2×C4—1222no—
321C2×C4—1222no—
322C2×C4—1222no—
323C2×C4—1222no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—1222no—
327C2×C4—1221no—
328C2×C4—1221no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4—2441no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4#1451983511yescharacteristic
337C2×C4#1451983511yescharacteristic
338C8—4882no—
339C8—2444no—
340C22—21no—
341C22—21no—
342C22—81no—
343C22—81no—
344C22—81no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22—81no—
349C22—1222no—
350C22—4881no—
351C22—2442no—
352C22—2441no—
353C22—2441no—
354C22C2×#1451983511yescharacteristic
355C22#1684075311yescharacteristic
356C22D61⋊#10411yescharacteristic
357C4—21no—
358C4—21no—
359C4—41no—
360C4—41no—
361C4—81no—
362C4—1221no—
363C4—1221no—
364C4—4881no—
365C4—2442no—
366C4—2441no—
367C4—2441no—
368C2—21no—
369C2—21no—
370C2—161no—
371C2—2442no—
372C2#2146120511yescharacteristic
373C2#2146207811yescharacteristic
374C2#2146211011yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#124×C61C4
socleC22×C61C2×#99
prime radical#16839670C4
cosocleC2×#11758196C23
hypercenterC2×#124#6923
hypocenterC61#11765
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. #21461524C2semidirect
2. #21461072C2semidirect
3. #21460820C2semidirect
4. #21460801C2semidirect
210. C61#11765semidirect

Maximal subgroups

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

subgroupindex
#214615242
#214610722
#214608202
#214608012
#214515082
#1176561