Finite Group Databasebeta

← #30605469

Subgroups — #30605469

Order 15616.

452 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 76 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#21461682C211yesmaximal, characteristic
2#21461060C211yesmaximal, characteristic
3#21460816C212yesmaximal, complemented
4#21460815C212yesmaximal, complemented
5#21450131C211yesmaximal, characteristic
6#16840778—21no—
7C2×#14519836—21no—
8#16840704—21no—
9#16840640C2212yes—
10#16840606—21no—
11#16840606C2212yes—
12C2×#14519739C2211yescharacteristic
13C2×C4⋊C4×D61C411yescharacteristic, complemented
14#16839701C411yescharacteristic, complemented
15#16839699C2211yescharacteristic
16#16839697C2211yescharacteristic
17#16839659—21no—
18#16839640—21no—
19#16839636—21no—
20#16839621—21no—
21#16839621C411yescharacteristic, complemented
22C61×#400C411yescharacteristic, complemented
23C2×C4⋊#6923—41no—
24C2×C22⋊#6923—22no—
25C4⋊#92420—41no—
26#14519836—42no—
27C22⋊#92420—22no—
28C4×#92420—41no—
29(C2×#6923)⋊C4—41no—
30C22×D244D411yescharacteristic
31C22×C4×D61—21no—
32C22×C4×D61C2×C411yescharacteristic
33C22×C4×D61D411yescharacteristic
34#14519739—41no—
35#14519739—41no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196—21no—
41C4⋊C4×D61—41no—
42C4⋊C4×D61—41no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198D411yescharacteristic
47C2×#11758198C2311yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49#14519684—21no—
50#14519684—21no—
51#14519684C2×C411yescharacteristic
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C4⋊C4×C61C2×C411yescharacteristic
54#95×C61—21no—
55#95×C61—21no—
56#95×C61C2×C411yescharacteristic
57C23×D61C22⋊C411yescharacteristic
58C23×D61C2×D411yescharacteristic
59C22×#6923—42no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22×C411yescharacteristic
65C22×Dic61—21no—
66C22×Dic61—21no—
67C22×Dic61C22⋊C411yescharacteristic
68C22×Dic61C2×D411yescharacteristic
69C2×D244—41no—
70C2×D244—41no—
71C2×D244SD1612yes—
72C2×D244Q1612yes—
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—42no—
78C2×C4×D61—42no—
79C2×C4×D61—42no—
80C2×C4×D61—81no—
81C2×C4×D61—81no—
82C22⋊#6923—42no—
83C22⋊#6923—42no—
84C2×#92420—42no—
85C4⋊#6923—82no—
86C4⋊C4×C61—41no—
87C4⋊C4×C61—41no—
88#11758198—41no—
89#11758198—41no—
90#11758198—42no—
91#11758198—81no—
92#11758198—81no—
93C4⋊Dic61—41no—
94C4⋊Dic61—81no—
95#11758196—42no—
96#11758196—41no—
97#11758196—41no—
98#11758196—81no—
99C4×Dic61—21no—
100C4×Dic61—21no—
101C23×C61C2×C22⋊C411yescharacteristic
102C22×D61—21no—
103C22×D61—21no—
104C22×D61—21no—
105C22×D61—21no—
106C22×D61—41no—
107C22×D61—41no—
108C22×D61—41no—
109C22×D61—41no—
110C22×D61#10312yes—
111C22×D61C2×SD1611yescharacteristic
112C22×D61C2×Q1611yescharacteristic
113C2×#6923—82no—
114C2×#6923—82no—
115C2×#6923—82no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
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—41no—
127C2×C4×C61—41no—
128C2×C4×C61#10312yes—
129C2×Dic61—22no—
130C2×Dic61—21no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61#9911yescharacteristic
139C2×Dic61#9911yescharacteristic
140D244—42no—
141D244—42no—
142C4×D61—42no—
143C4×D61—42no—
144C4×D61—42no—
145C4×D61—81no—
146C4×D61—84no—
147#92420—82no—
148#11899—611nomaximal, Sylow
149C22×C61—21no—
150C22×C61—21no—
151C22×C61C2×#9911yescharacteristic
152C22×C61C2×#10311yescharacteristic
153C22×C61#42111yescharacteristic
154C2×D61—21no—
155C2×D61—22no—
156C2×D61—21no—
157C2×D61—42no—
158C2×D61—41no—
159C2×D61—41no—
160C2×D61—41no—
161C2×D61—41no—
162C2×D61—42no—
163C2×D61—41no—
164C2×D61—41no—
165C2×D61—81no—
166#6923—162no—
167C4×C61—22no—
168C4×C61—41no—
169C4×C61—41no—
170C4×C61—81no—
171C4×C61—81no—
172Dic61—21no—
173Dic61—41no—
174Dic61—81no—
175Dic61—81no—
176Dic61#35212yes—
177#2487—611no—
178#1799—611no—
179#1460—611no—
180#1352—612no—
181#1352—612no—
182C2×C61—21no—
183C2×C61—21no—
184C2×C61#152011yescharacteristic
185C2×C61C2×#35211yescharacteristic
186C2×C61#212811yescharacteristic
187D61—41no—
188D61—42no—
189D61—41no—
190C2×C4×D4—611no—
191C22×C4⋊C4—611no—
192#431—1221no—
193C2×#99—1221no—
194#400—611no—
195#400#692311yescharacteristic, complemented
196#399—611no—
197#399—611no—
198#389—1221no—
199#386—1221no—
200#385—1221no—
201#380—611no—
202#380—1221no—
203#380—1221no—
204#342—612no—
205#323—612no—
206#323—1221no—
207C61#1189911yescharacteristic, complemented, Sylow
208C22×D4—611no—
209C23×C4—611no—
210C23×C4—611no—
211C23×C4—1221no—
212C4×D4—2441no—
213C4×D4—2441no—
214C2×C4⋊C4—611no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4—1221no—
217C2×C4⋊C4—1221no—
218C2×C4⋊C4—1221no—
219C2×C4⋊C4—2441no—
220C2×C4⋊C4—2441no—
221C2×C4⋊C4—2441no—
222C2×C4⋊C4C2×#692311yescharacteristic
223C2×C4⋊C4C2×#692311yescharacteristic
224C2×C22⋊C4—611no—
225C2×C22⋊C4—611no—
226C2×C22⋊C4—1221no—
227C2×C22⋊C4—1221no—
228C2×C22⋊C4—1221no—
229C2×C22⋊C4—1222no—
230C2×C42—611no—
231C4⋊C8—2441no—
232#99—2442no—
233C22⋊C8—1222no—
234C4×C8—2441no—
235#95—21no—
236#95—21no—
237#95—611no—
238#95—1221no—
239#95—1221no—
240#95—2441no—
241#95C2×#692311yescharacteristic
242C24—611no—
243C24—611no—
244C2×D4—612no—
245C2×D4—612no—
246C2×D4—2441no—
247C2×D4—2441no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—611no—
251C22×C4—611no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4—4881no—
259C22×C4—4881no—
260C22×C4—2442no—
261C22×C4—2442no—
262C22×C4—2442no—
263C22×C4—2442no—
264C22×C4C22⋊#692311yescharacteristic
265C22×C4C22⋊#692311yescharacteristic
266C22×C4C22×#692311yescharacteristic
267C2×C8—2442no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—4881no—
271C4⋊C4—4881no—
272C4⋊C4—4882no—
273C4⋊C4—2441no—
274C4⋊C4—2441no—
275C4⋊C4—2441no—
276C4⋊C4—2442no—
277C22⋊C4—4881no—
278C22⋊C4—4881no—
279C22⋊C4—2441no—
280C22⋊C4—2441no—
281C22⋊C4—2442no—
282C22⋊C4—2442no—
283C22⋊C4—2442no—
284C42—1221no—
285C42—1221no—
286C23—612no—
287C23—611no—
288C23—611no—
289C23—1221no—
290C23—1221no—
291C23—1221no—
292C23—1221no—
293C23—2441no—
294C23—2441no—
295C23—2441no—
296C23—2441no—
297C23C2×C22⋊#692311yescharacteristic
298D4—2442no—
299D4—2442no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—611no—
313C2×C4—611no—
314C2×C4—1222no—
315C2×C4—1221no—
316C2×C4—4881no—
317C2×C4—4884no—
318C2×C4—4882no—
319C2×C4—4882no—
320C2×C4—4882no—
321C2×C4—2442no—
322C2×C4—2442no—
323C2×C4—2442no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4—2441no—
327C2×C4—2441no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4#1451984012yes—
332C8—4882no—
333C22—21no—
334C22—21no—
335C22—1221no—
336C22—1221no—
337C22—1222no—
338C22—4881no—
339C22—2441no—
340C22—2441no—
341C22—2442no—
342C22—2442no—
343C22—2441no—
344C22—2441no—
345C22—2441no—
346C22—2441no—
347C22D61⋊#9911yescharacteristic
348C22C2×#1451984011yescharacteristic
349C22#1684075911yescharacteristic
350C4—22no—
351C4—41no—
352C4—41no—
353C4—81no—
354C4—81no—
355C4—612no—
356C4—1221no—
357C4—9762no—
358C4—4881no—
359C4—4881no—
360C4—2441no—
361C2—21no—
362C2—21no—
363C2—2441no—
364C2—2441no—
365C2—2442no—
366C2#2146125711yescharacteristic
367C2D61⋊#35211yescharacteristic
368C2#2146209911yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#400C4
socleC22×C61C2×#99
prime radicalC22×D244D4
cosocleC2×#11758198C23
hypercenter#400#6923
hypocenterC61#11899
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #400

Complements

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

NH ≅ G/Ntype
3. #21460816C2semidirect
4. #21460815C2semidirect
13. C2×C4⋊C4×D61C4semidirect
14. #16839701C4semidirect
21. #16839621C4semidirect
22. C61×#400C4semidirect
195. #400#6923semidirect
207. C61#11899semidirect

Maximal subgroups

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

subgroupindex
#214616822
#214610602
#214608162
#214608152
#214501312
#1189961