Finite Group Databasebeta

← #30599382

Subgroups — #30599382

Order 15616.

530 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 90 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#21461680C211yesmaximal, characteristic
2#21461056C211yesmaximal, characteristic
3#21460693C212yesmaximal, complemented
4#21460681C212yesmaximal, complemented
5#21448730C211yesmaximal, characteristic
6C2×#14519836—21no—
7D61⋊(C22⋊C8)C2212yes—
8#16840704C2212yes—
9#16840640—21no—
10#16840607—21no—
11#16840606—21no—
12C2×C4×D244—21no—
13C2×C4×D244C2211yescharacteristic
14#16839660—21no—
15#16839633—21no—
16#16839633—21no—
17#16839628C411yescharacteristic, complemented
18#16839621C411yescharacteristic, complemented
19#16839621C2211yescharacteristic
20#95×D61C411yescharacteristic, complemented
21#95×D61C2211yescharacteristic
22C4×C4⋊C4×C61C411yescharacteristic, complemented
23C2×D61⋊C8—22no—
24C2×C4⋊#6923—22no—
25C2×C22⋊#6923—22no—
26#14519836—42no—
27#14519834—22no—
28C22⋊#92420—22no—
29(C2×#6923)⋊C4—22no—
30C22×D244D411yescharacteristic
31C22×C4×D61—21no—
32C22×C4×D61—21no—
33C22×C4×D61C2×C411yescharacteristic
34C22×C4×D61C2311yescharacteristic
35C4×D244—22no—
36C4×D244—22no—
37C4×D244—44no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61D411yescharacteristic
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198D411yescharacteristic
45C2×#11758198D411yescharacteristic
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684C2×C411yescharacteristic
50#14519684C2×C411yescharacteristic
51C2×C4⋊C4×C61—21no—
52C2×C42×C61—21no—
53C2×C42×C61C2×C411yescharacteristic
54#95×C61C2×C411yescharacteristic
55#95×C61C2×C411yescharacteristic
56C23×D61C22⋊C411yescharacteristic
57C23×D61C2×D411yescharacteristic
58C22×#6923—42no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C22×C411yescharacteristic
64C22×Dic61—21no—
65C22×Dic61—21no—
66C22×Dic61C22⋊C411yescharacteristic
67C22×Dic61C2×D411yescharacteristic
68C2×D244—22no—
69C2×D244—22no—
70C2×D244SD1612yes—
71C2×D244Q1612yes—
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61—42no—
75C2×C4×D61—42no—
76C2×C4×D61—42no—
77C2×C4×D61—42no—
78C2×C4×D61—81no—
79C2×C4×D61—81no—
80C2×C4×D61—81no—
81C2×C4×D61—81no—
82C2×C4×D61#4112yes—
83C2×C4×D61#4112yes—
84C22⋊#6923—42no—
85C22⋊#6923—42no—
86C2×#92420—42no—
87C4⋊#6923—82no—
88D61⋊C8—82no—
89C4⋊C4×C61—42no—
90C42×C61—21no—
91C42×C61—21no—
92C42×C61—42no—
93#11758198—22no—
94#11758198—22no—
95#11758198—42no—
96#11758198—42no—
97C4⋊Dic61—22no—
98C4⋊Dic61—42no—
99#11758196—81no—
100#11758196—81no—
101C23×C61C2×C22⋊C411yescharacteristic
102C22×D61—21no—
103C22×D61—21no—
104C22×D61—41no—
105C22×D61—41no—
106C22×D61—41no—
107C22×D61—41no—
108C22×D61#10312yes—
109C22×D61#12312yes—
110C22×D61C2×SD1611yescharacteristic
111C22×D61C2×Q1611yescharacteristic
112C22×D61AGL(1,ℤ/8)12yes—
113C2×#6923—82no—
114C2×#6923—82no—
115C2×#6923—82no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—22no—
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#10312yes—
128C2×C4×C61#11711yescharacteristic
129C2×C4×C61#11711yescharacteristic
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—41no—
139C2×Dic61#12312yes—
140D244—24no—
141D244—24no—
142C4×D61—42no—
143C4×D61—42no—
144C4×D61—81no—
145C4×D61—81no—
146C4×D61—84no—
147C4×D61—84no—
148#92420—82no—
149#8761—611nomaximal, Sylow
150C22×C61—21no—
151C22×C61—21no—
152C22×C61#38111yescharacteristic
153C22×C61C2×#10311yescharacteristic
154C22×C61#41811yescharacteristic
155C2×D61—22no—
156C2×D61—22no—
157C2×D61—22no—
158C2×D61—42no—
159C2×D61—41no—
160C2×D61—41no—
161C2×D61—42no—
162C2×D61—41no—
163C2×D61—41no—
164C2×D61—42no—
165C2×D61#48112yes—
166C2×D61#48412yes—
167#6923—162no—
168C4×C61—22no—
169C4×C61—21no—
170C4×C61—21no—
171C4×C61—42no—
172C4×C61—41no—
173C4×C61—81no—
174Dic61—22no—
175Dic61—41no—
176Dic61—81no—
177Dic61—81no—
178#2349—611no—
179#1799—611no—
180#1459—611no—
181#1294—612no—
182#1289—612no—
183C2×C61—21no—
184C2×C61—21no—
185C2×C61#182411yescharacteristic
186C2×C61#182711yescharacteristic
187C2×C61#182811yescharacteristic
188D61—22no—
189D61—22no—
190D61—42no—
191C2×C4×D4—611no—
192C2×C4×D4—1221no—
193C2×#99—1221no—
194C2×C22⋊C8—612no—
195#389—1221no—
196#385—1221no—
197#385—1221no—
198#382—611no—
199#380—611no—
200#380—611no—
201#380—612no—
202C4×C4⋊C4#692311yescharacteristic, complemented
203C2×#95—611no—
204C2×#95—611no—
205#342—1221no—
206#324—1221no—
207#323—1221no—
208C61#876111yescharacteristic, complemented, Sylow
209C22×D4—611no—
210C23×C4—611no—
211C23×C4—611no—
212C23×C4—1221no—
213C23×C4—1221no—
214C22×C8—1222no—
215C4×D4—1222no—
216C4×D4—1222no—
217C4×D4—2444no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—611no—
220C2×C4⋊C4—1221no—
221C2×C4⋊C4—1221no—
222C2×C4⋊C4—1222no—
223C2×C4⋊C4—1221no—
224C2×C22⋊C4—611no—
225C2×C22⋊C4—611no—
226C2×C22⋊C4—1221no—
227C2×C22⋊C4—1221no—
228C2×C22⋊C4—1222no—
229C2×C42—21no—
230C2×C42C2×#692311yescharacteristic
231#99—2442no—
232C22⋊C8—1222no—
233C22⋊C8—1222no—
234#95—611no—
235#95—611no—
236#95—1221no—
237#95—1221no—
238#95—1222no—
239#95—1221no—
240#95C2×#692311yescharacteristic
241#95C2×#692311yescharacteristic
242C24—611no—
243C24—611no—
244C2×D4—612no—
245C2×D4—612no—
246C2×D4—1222no—
247C2×D4—1222no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—611no—
251C22×C4—612no—
252C22×C4—612no—
253C22×C4—611no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4—4881no—
259C22×C4—4881no—
260C22×C4—4881no—
261C22×C4—4881no—
262C22×C4—2442no—
263C22×C4—2442no—
264C22×C4—2442no—
265C22×C4—2442no—
266C22×C4—2442no—
267C22×C4C22⋊#692311yescharacteristic
268C22×C4C22⋊#692311yescharacteristic
269C22×C4C22×#692311yescharacteristic
270C2×C8—4882no—
271C2×C8—2442no—
272C4⋊C4—42no—
273C4⋊C4—1222no—
274C4⋊C4—4881no—
275C4⋊C4—4881no—
276C4⋊C4—4882no—
277C4⋊C4—2442no—
278C22⋊C4—1222no—
279C22⋊C4—1222no—
280C22⋊C4—2442no—
281C22⋊C4—2442no—
282C22⋊C4—2442no—
283C22⋊C4—2442no—
284C42—21no—
285C42—21no—
286C42—42no—
287C23—612no—
288C23—611no—
289C23—611no—
290C23—612no—
291C23—612no—
292C23—1221no—
293C23—1221no—
294C23—2441no—
295C23—2441no—
296C23—2441no—
297C23—2441no—
298C23C2×C22⋊#692311yescharacteristic
299D4—1224no—
300D4—1224no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—22no—
304C2×C4—21no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—612no—
313C2×C4—1221no—
314C2×C4—4881no—
315C2×C4—4881no—
316C2×C4—4884no—
317C2×C4—4884no—
318C2×C4—4882no—
319C2×C4—4882no—
320C2×C4—4882no—
321C2×C4—2442no—
322C2×C4—2442no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4—2441no—
327C2×C4—2441no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4#1451984012yes—
332C2×C4#1451985611yescharacteristic
333C2×C4#1451985611yescharacteristic
334C8—4882no—
335C22—21no—
336C22—21no—
337C22—612no—
338C22—612no—
339C22—1222no—
340C22—1222no—
341C22—1222no—
342C22—2442no—
343C22—2441no—
344C22—2441no—
345C22—2442no—
346C22—2442no—
347C22—2441no—
348C22—2441no—
349C22#1684070511yescharacteristic
350C22C2×#1451984011yescharacteristic
351C22#1684075411yescharacteristic
352C4—22no—
353C4—21no—
354C4—21no—
355C4—42no—
356C4—41no—
357C4—81no—
358C4—1222no—
359C4—9762no—
360C4—4881no—
361C4—4881no—
362C4—2441no—
363C2—21no—
364C2—21no—
365C2—1222no—
366C2—1222no—
367C2—2442no—
368C2#2146172311yescharacteristic
369C2#2146172811yescharacteristic
370C2#2146173111yescharacteristic
subgroupG/H
centerC22#16840705
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC4×C4⋊C4×C61C4
socleC22×C61#381
prime radicalC22×D244D4
cosocleC22×C4×D61C23
hypercenterC4×C4⋊C4#6923
hypocenterC61#8761
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #21460693C2semidirect
4. #21460681C2semidirect
17. #16839628C4semidirect
18. #16839621C4semidirect
20. #95×D61C4semidirect
22. C4×C4⋊C4×C61C4semidirect
202. C4×C4⋊C4#6923semidirect
208. C61#8761semidirect

Maximal subgroups

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

subgroupindex
#214616802
#214610562
#214606932
#214606812
#214487302
#876161