Finite Group Databasebeta

← #30600046

Subgroups — #30600046

Order 15616.

616 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 92 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#21462296C211yesmaximal, characteristic
2#21461722C212yesmaximal
3D61⋊#324C211yesmaximal, characteristic
4#21460693C212yesmaximal
5#398×D61C211yesmaximal, characteristic
6D61⋊(C22⋊C8)C2212yes—
7#16840711—24no—
8#16840705—21no—
9#16840704C2212yes—
10C4×C22⋊#6923—21no—
11#16840635—24no—
12#16840608—21no—
13#16840607—21no—
14C2×C4⋊C4×D61—21no—
15C2×C4⋊C4×D61C2211yescharacteristic
16C2×C4⋊C4×D61C2211yescharacteristic
17#16839696—21no—
18#16839695—21no—
19#16839694C411yescharacteristic, complemented
20#16839693C411yescharacteristic, complemented
21#16839692C411yescharacteristic, complemented
22#95×D61—21no—
23#95×D61C2211yescharacteristic
24C61×#398C411yescharacteristic, complemented
25C2×D61⋊C8—22no—
26C2×C4⋊#6923D414yes—
27C2×C22⋊#6923—22no—
28C2×C4×#6923—22no—
29#14519834—22no—
30C22⋊#92420—22no—
31(C2×#6923)⋊C4—24no—
32(C2×#6923)⋊C4—22no—
33(C2×#6923)⋊C4—22no—
34C22×C4×D61—21no—
35C22×C4×D61—21no—
36C22×C4×D61D411yescharacteristic
37C22×C4×D61D411yescharacteristic
38C22×C4×D61C2311yescharacteristic
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61C2×C411yescharacteristic
41C2×C4⋊Dic61D411yescharacteristic
42C2×#11758196—21no—
43C2×#11758196—21no—
44C2×#11758196—21no—
45C2×#11758196C2×C411yescharacteristic
46C2×#11758196D411yescharacteristic
47C4⋊C4×D61—22no—
48C4⋊C4×D61—22no—
49C4⋊C4×D61—22no—
50C4⋊C4×D61—22no—
51C4⋊C4×D61—44no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684C2×C411yescharacteristic
57C2×C4⋊C4×C61—21no—
58C2×C4⋊C4×C61C2×C411yescharacteristic
59C2×C4⋊C4×C61C2×C411yescharacteristic
60#95×C61—21no—
61#95×C61C2×C411yescharacteristic
62C23×D61C2×D411yescharacteristic
63C22×#6923—24no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22×C411yescharacteristic
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C2×D411yescharacteristic
74C2×C4×D61—24no—
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—22no—
79C2×C4×D61—22no—
80C2×C4×D61—21no—
81C2×C4×D61—42no—
82C2×C4×D61—42no—
83C2×C4×D61—42no—
84C2×C4×D61—42no—
85C2×C4×D61—41no—
86C2×C4×D61—41no—
87C2×C4×D61—42no—
88C2×C4×D61—42no—
89C2×C4×D61C2×D412yes—
90C2×C4×D61#4112yes—
91C22⋊#6923—42no—
92C22⋊#6923—42no—
93C2×#92420—42no—
94C4⋊#6923—44no—
95C4×#6923—82no—
96D61⋊C8—44no—
97C4⋊C4×C61—22no—
98C4⋊C4×C61—22no—
99C4⋊C4×C61—42no—
100C4⋊Dic61—22no—
101C4⋊Dic61—22no—
102C4⋊Dic61—42no—
103#11758196—22no—
104#11758196—22no—
105#11758196—42no—
106#11758196—42no—
107#11758196—42no—
108C23×C61C2×C22⋊C411yescharacteristic
109C22×D61—22no—
110C22×D61—22no—
111C22×D61#12011yescharacteristic
112C22×D61#12311yescharacteristic
113C22×D61#13512yes—
114C22×D61AGL(1,ℤ/8)12yes—
115C2×#6923—44no—
116C2×#6923—44no—
117C2×#6923—44no—
118C2×C4×C61—22no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61C4×D412yes—
131C2×Dic61—22no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61#12112yes—
144C4×D61—24no—
145C4×D61—42no—
146C4×D61—48no—
147C4×D61—42no—
148C4×D61—42no—
149C4×D61—42no—
150C4×D61—81no—
151C4×D61—82no—
152C4×D61—82no—
153#92420—82no—
154#9026—611nomaximal, Sylow
155C22×C61—21no—
156C22×C61—21no—
157C22×C61#38611yescharacteristic
158C22×C61#41611yescharacteristic
159C22×C61#41811yescharacteristic
160C2×D61—21no—
161C2×D61—21no—
162C2×D61—24no—
163C2×D61—24no—
164C2×D61#44912yes—
165C2×D61#45612yes—
166C2×D61#45812yes—
167C2×D61#48212yes—
168#6923—84no—
169C4×C61—22no—
170C4×C61—42no—
171C4×C61—41no—
172C4×C61—41no—
173C4×C61—81no—
174Dic61—22no—
175Dic61—42no—
176Dic61—41no—
177Dic61—41no—
178Dic61—81no—
179C2×#398—611no—
180#2313—611no—
181#1823—612no—
182C2×#324—611no—
183#1294—612no—
184C2×C61—21no—
185C2×C61—21no—
186C2×C61#187511yescharacteristic
187C2×C61#188611yescharacteristic
188C2×C61#189011yescharacteristic
189D61—22no—
190D61#160914yes—
191C22×C4⋊C4—611no—
192C22×C4⋊C4—611no—
193C22×C4⋊C4—1221no—
194C2×C22⋊C8—612no—
195#398—611no—
196#398—611no—
197#398—611no—
198#398—1221no—
199#398—1221no—
200#398#692311yescharacteristic, complemented
201#387—1224no—
202#381—1221no—
203#380—612no—
204C4×C22⋊C4—1221no—
205C2×#95—611no—
206C2×#95—1221no—
207#340—1224no—
208#324—1221no—
209#324—1221no—
210C61#902611yescharacteristic, complemented, Sylow
211C23×C4—611no—
212C23×C4—611no—
213C23×C4—611no—
214C23×C4—1221no—
215C23×C4—1221no—
216C22×C8—1222no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—611no—
219C2×C4⋊C4—611no—
220C2×C4⋊C4—611no—
221C2×C4⋊C4—611no—
222C2×C4⋊C4—614no—
223C2×C4⋊C4—1222no—
224C2×C4⋊C4—1222no—
225C2×C4⋊C4—1222no—
226C2×C4⋊C4—1222no—
227C2×C4⋊C4—1221no—
228C2×C4⋊C4—1221no—
229C2×C4⋊C4—1221no—
230C2×C4⋊C4—1221no—
231C2×C4⋊C4—2444no—
232C2×C4⋊C4C2×#692311yescharacteristic
233C2×C4⋊C4C2×#692311yescharacteristic
234C2×C22⋊C4—1222no—
235C2×C42—1222no—
236C22⋊C8—1222no—
237C22⋊C8—1222no—
238#95—21no—
239#95—611no—
240#95—1221no—
241#95—1221no—
242#95—1221no—
243#95—1222no—
244#95—1222no—
245#95—1224no—
246#95—1221no—
247#95C2×#692311yescharacteristic
248C24—611no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—611no—
252C22×C4—612no—
253C22×C4—612no—
254C22×C4—611no—
255C22×C4—611no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4—1222no—
261C22×C4—1222no—
262C22×C4—1224no—
263C22×C4—1221no—
264C22×C4—1224no—
265C22×C4—1221no—
266C22×C4—2442no—
267C22×C4—2441no—
268C22×C4—2441no—
269C22×C4—2442no—
270C22×C4—2442no—
271C22×C4—2442no—
272C22×C4—2442no—
273C22×C4—2442no—
274C22×C4C22⋊#692311yescharacteristic
275C22×C4C22⋊#692311yescharacteristic
276C22×C4C22×#692311yescharacteristic
277C2×C8—2442no—
278C2×C8—2444no—
279C4⋊C4—22no—
280C4⋊C4—22no—
281C4⋊C4—42no—
282C4⋊C4—1222no—
283C4⋊C4—1222no—
284C4⋊C4—1222no—
285C4⋊C4—1222no—
286C4⋊C4—2442no—
287C4⋊C4—2442no—
288C4⋊C4—2442no—
289C4⋊C4—2442no—
290C4⋊C4—2444no—
291C22⋊C4—2442no—
292C22⋊C4—2442no—
293C42—4882no—
294C23—611no—
295C23—611no—
296C23—612no—
297C23—612no—
298C23—1222no—
299C23—1222no—
300C23C2×C22⋊#692311yescharacteristic
301C2×C4—22no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—612no—
314C2×C4—1224no—
315C2×C4—1222no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—4881no—
321C2×C4—4882no—
322C2×C4—4882no—
323C2×C4—2442no—
324C2×C4—2442no—
325C2×C4—2442no—
326C2×C4—2442no—
327C2×C4—2448no—
328C2×C4—2441no—
329C2×C4—2444no—
330C2×C4—2444no—
331C2×C4—2444no—
332C2×C4—2441no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4D4×#692312yes—
339C8—4882no—
340C22—21no—
341C22—21no—
342C22—612no—
343C22—612no—
344C22—612no—
345C22—612no—
346C22—1224no—
347C22—1224no—
348C22—1221no—
349C22—1221no—
350C22#1684071011yescharacteristic
351C22#1684075211yescharacteristic
352C22#1684075411yescharacteristic
353C4—22no—
354C4—42no—
355C4—41no—
356C4—41no—
357C4—81no—
358C4—1222no—
359C4—4884no—
360C4—4881no—
361C4—2442no—
362C4—2441no—
363C4—2441no—
364C2—21no—
365C2—21no—
366C2—614no—
367C2—1222no—
368C2#2146180711yescharacteristic
369C2#2146182511yescharacteristic
370C2#2146182911yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#398C4
socleC22×C61#386
prime radicalC23×D61C2×D4
cosocleC22×C4×D61C23
hypercenter#398#6923
hypocenterC61#9026
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #398

Complements

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

NH ≅ G/Ntype
19. #16839694C4semidirect
20. #16839693C4semidirect
21. #16839692C4semidirect
24. C61×#398C4semidirect
200. #398#6923semidirect
210. C61#9026semidirect

Maximal subgroups

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

subgroupindex
#214622962
#214617222
D61⋊#3242
#214606932
#398×D612
#902661