Finite Group Databasebeta

← #30604228

Subgroups — #30604228

Order 15616.

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

normal subgroups only

This group has 460 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#21461070C211yesmaximal, characteristic, complemented
2#21461050C211yesmaximal, characteristic, complemented
3#21460764C212yesmaximal, complemented
4#21460743C212yesmaximal
5#21450093C211yesmaximal, characteristic
6#16840782—21no—
7#16840778—21no—
8#16840607—21no—
9#16840607—21no—
10#16840605C2212yes—
11#16840605C2212yes—
12C2×#14519736C2211yescharacteristic
13#16839698—21no—
14#16839687—21no—
15#16839650—21no—
16#16839650—21no—
17#16839635C411yescharacteristic
18#16839635C2211yescharacteristic
19#16839625C411yescharacteristic
20#16839618C411yescharacteristic
21#16839618C2211yescharacteristic
22C22×C22⋊C4×C61C411yescharacteristic
23#14519844—41no—
24C4⋊#92420—41no—
25C22⋊#92420—22no—
26C22⋊#92420—22no—
27#14519832—41no—
28C4×#92420—41no—
29#14519736—41no—
30#14519736—41no—
31C2×C4⋊Dic61D411yescharacteristic
32C2×C4⋊Dic61D411yescharacteristic
33C2×#11758196—21no—
34C2×#11758196—21no—
35C2×C22⋊Dic61—21no—
36C2×C22⋊Dic61—21no—
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61C2×C411yescharacteristic
40C2×C22⋊Dic61C2×C411yescharacteristic
41C2×C22⋊Dic61C2×C411yescharacteristic
42C2×C22⋊Dic61C2311yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49C25×C61C2×C411yescharacteristic
50C23×C4×C61C2×C411yescharacteristic
51C23×C4×C61C2×C411yescharacteristic
52C2×C22⋊C4×C61—21no—
53C2×C22⋊C4×C61—21no—
54C2×C22⋊C4×C61—41no—
55C2×C22⋊C4×C61—41no—
56C24×C61—21no—
57C24×C61—22no—
58C24×C61—41no—
59C24×C61—42no—
60C24×C61—41no—
61C24×C61—81no—
62C24×C61C22×C411yescharacteristic
63C22×C4×C61—22no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—41no—
68C22×C4×C61—41no—
69C22×C4×C61—81no—
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22⋊C411yescharacteristic
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61C22⋊C411yescharacteristic
76C22×Dic61C2×D411yescharacteristic
77C22×Dic61C2×D411yescharacteristic
78C2×#92420—42no—
79C2×#92420—42no—
80C22⋊C4×C61—42no—
81C22⋊C4×C61—41no—
82C22⋊C4×C61—41no—
83C22⋊Dic61—22no—
84C22⋊Dic61—41no—
85C22⋊Dic61—41no—
86C22⋊Dic61—42no—
87C22⋊Dic61—42no—
88C22⋊Dic61—41no—
89C22⋊Dic61—81no—
90C22⋊Dic61—81no—
91C4⋊Dic61—41no—
92C4⋊Dic61—41no—
93#11758196—81no—
94#11758196—81no—
95C4×Dic61—21no—
96C4×Dic61—21no—
97C4×Dic61—21no—
98C4×Dic61—21no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61—22no—
102C23×C61—41no—
103C23×C61—41no—
104C23×C61—41no—
105C23×C61—41no—
106C23×C61—41no—
107C23×C61—42no—
108C23×C61—41no—
109C23×C61—41no—
110C23×C61—41no—
111C23×C61—42no—
112C23×C61—82no—
113C23×C61—84no—
114C23×C61—84no—
115C23×C61—82no—
116C23×C61C2×C22⋊C411yescharacteristic
117C23×C61#13112yes—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—42no—
124C2×C4×C61—42no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—82no—
129C2×C4×C61#9911yescharacteristic
130C2×C4×C61#9911yescharacteristic
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145#92420—82no—
146#92420—82no—
147#11542—611nomaximal, Sylow
148C22×C61—21no—
149C22×C61—21no—
150C22×C61—22no—
151C22×C61—42no—
152C22×C61—42no—
153C22×C61—42no—
154C22×C61—42no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61—42no—
158C22×C61—81no—
159C22×C61—81no—
160C22×C61—84no—
161C22×C61—84no—
162C22×C61—81no—
163C22×C61—81no—
164C22×C61#40811yescharacteristic
165C22×C61C2×#9911yescharacteristic
166C22×C61#41311yescharacteristic
167C4×C61—21no—
168C4×C61—21no—
169C4×C61—41no—
170C4×C61—81no—
171Dic61—41no—
172Dic61—41no—
173Dic61—41no—
174Dic61—41no—
175Dic61—81no—
176Dic61—81no—
177#2482—611no—
178#1464—611no—
179#1458—611no—
180#1326—612no—
181#1316—612no—
182C2×C61—21no—
183C2×C61—21no—
184C2×C61—42no—
185C2×C61—82no—
186C2×C61#146811yescharacteristic
187C2×C61#212011yescharacteristic
188C2×C61#212211yescharacteristic
189C2×#117—611no—
190C22×C22⋊C4#692311yescharacteristic
191#432—1221no—
192#431—1221no—
193#399—1221no—
194#397—1221no—
195#388—1221no—
196#388—1221no—
197#385—611no—
198#385—611no—
199#381—611no—
200#379—611no—
201#379—611no—
202#324—1221no—
203#324—1221no—
204#323—612no—
205#323—612no—
206C61#1154211yescharacteristic, complemented, Sylow
207C25C2×#692311yescharacteristic
208C23×C4C2×#692311yescharacteristic
209C23×C4C2×#692311yescharacteristic
210#117—2441no—
211#117—2441no—
212C2×C4⋊C4—611no—
213C2×C4⋊C4—611no—
214C2×C4⋊C4—1221no—
215C2×C4⋊C4—1221no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—41no—
219C2×C22⋊C4—41no—
220C2×C22⋊C4—611no—
221C2×C22⋊C4—611no—
222C2×C22⋊C4—611no—
223C2×C22⋊C4—611no—
224C2×C22⋊C4—1221no—
225C2×C22⋊C4—1221no—
226C2×C22⋊C4—1221no—
227C2×C22⋊C4—1221no—
228C2×C42—611no—
229C2×C42—611no—
230C4⋊C8—2441no—
231C4⋊C8—2441no—
232C22⋊C8—1222no—
233C22⋊C8—1222no—
234#97—2441no—
235C4×C8—2441no—
236#95—1221no—
237#95—1221no—
238#95—1221no—
239#95—1221no—
240C24—21no—
241C24—22no—
242C24—41no—
243C24—42no—
244C24—41no—
245C24—81no—
246C24C22×#692311yescharacteristic
247C22×C4—22no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—81no—
254C22×C4—611no—
255C22×C4—611no—
256C22×C4—611no—
257C22×C4—611no—
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4C22⋊#692311yescharacteristic
261C22×C4C22⋊#692311yescharacteristic
262C2×C8—2442no—
263C2×C8—2442no—
264C4⋊C4—4881no—
265C4⋊C4—4881no—
266C4⋊C4—2441no—
267C4⋊C4—2441no—
268C22⋊C4—42no—
269C22⋊C4—41no—
270C22⋊C4—41no—
271C22⋊C4—1222no—
272C22⋊C4—4881no—
273C22⋊C4—4881no—
274C22⋊C4—2441no—
275C22⋊C4—2441no—
276C22⋊C4—2442no—
277C22⋊C4—2442no—
278C22⋊C4—2441no—
279C42—1221no—
280C42—1221no—
281C42—1221no—
282C42—1221no—
283C23—21no—
284C23—21no—
285C23—22no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23—42no—
292C23—42no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—82no—
297C23—84no—
298C23—84no—
299C23—82no—
300C23C2×C22⋊#692311yescharacteristic
301C23#1451986412yes—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—82no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—1221no—
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#1451983511yescharacteristic
328C2×C4#1451983511yescharacteristic
329C8—4882no—
330C8—4882no—
331C22—21no—
332C22—21no—
333C22—22no—
334C22—42no—
335C22—42no—
336C22—42no—
337C22—42no—
338C22—41no—
339C22—41no—
340C22—42no—
341C22—81no—
342C22—81no—
343C22—84no—
344C22—84no—
345C22—81no—
346C22—81no—
347C22#1684073511yescharacteristic
348C22C2×#1451983511yescharacteristic
349C22#1684074911yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—81no—
354C4—4881no—
355C4—4881no—
356C4—2441no—
357C4—2441no—
358C4—2441no—
359C4—2441no—
360C2—21no—
361C2—21no—
362C2—42no—
363C2—82no—
364C2#2146108411yescharacteristic
365C2#2146207011yescharacteristic
366C2#2146207811yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
FittingC22×C22⋊C4×C61C4
socleC22×C61C2×#99
prime radicalC25×C61C2×C4
cosocleC2×C22⋊Dic61C23
hypercenterC22×C22⋊C4#6923
hypocenterC61#11542
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #21461070C2semidirect
2. #21461050C2semidirect
3. #21460764C2semidirect
206. C61#11542semidirect

Maximal subgroups

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

subgroupindex
#214610702
#214610502
#214607642
#214607432
#214500932
#1154261