Finite Group Databasebeta

← #30601125

Subgroups — #30601125

Order 15616.

490 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 80 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#21462670C211yesmaximal, characteristic
2#21461301C212yesmaximal, complemented
3#21461079C211yesmaximal, characteristic
4#21460670C212yesmaximal, complemented
5#21451022C211yesmaximal, characteristic
6#16840793—24no—
7#16840782C2212yes—
8#16840782C2212yes—
9#16840732—21no—
10C2×C22⋊#92420—21no—
11#16840619—24no—
12#16840605—21no—
13#16840605—21no—
14C2×#14519768C2211yescharacteristic
15C2×D4×Dic61C2211yescharacteristic
16#16839685—21no—
17#16839685—21no—
18#16839665C411yescharacteristic
19#16839634—21no—
20#16839634—21no—
21#16839631C411yescharacteristic
22#16839628C411yescharacteristic
23C4×#11758196C2211yescharacteristic
24C61×#390C411yescharacteristic
25C2×#11758217—22no—
26C22×#92420—22no—
27#14519844—22no—
28#14519844—22no—
29C22⋊#92420—22no—
30C22⋊#92420—22no—
31C22⋊#92420—22no—
32C22⋊#92420—22no—
33#14519832—22no—
34#14519832D414yes—
35C23×Dic61D411yescharacteristic
36C23×Dic61D411yescharacteristic
37#14519768—22no—
38#14519768—22no—
39D4×Dic61—22no—
40D4×Dic61—22no—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61C2×C411yescharacteristic
43C2×C4⋊Dic61C2×C411yescharacteristic
44C2×#11758196—21no—
45C2×#11758196—21no—
46C2×#11758196—21no—
47C2×#11758196—21no—
48C2×C22⋊Dic61—21no—
49C2×C22⋊Dic61—21no—
50C2×C22⋊Dic61D411yescharacteristic
51C2×C22⋊Dic61D411yescharacteristic
52C2×C4×Dic61C2×C411yescharacteristic
53C2×C4×Dic61C2311yescharacteristic
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57C22×D4×C61C2×C411yescharacteristic
58C2×C4⋊C4×C61C2×C411yescharacteristic
59C2×C22⋊C4×C61—21no—
60C2×C22⋊C4×C61—21no—
61C2×C42×C61C2×C411yescharacteristic
62C24×C61C22⋊C411yescharacteristic
63C24×C61C22⋊C411yescharacteristic
64C2×D4×C61—22no—
65C2×D4×C61—22no—
66C2×D4×C61—41no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61C22×C411yescharacteristic
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—81no—
77C22×Dic61—81no—
78C22×Dic61C22⋊C411yescharacteristic
79C22×Dic61C22⋊C411yescharacteristic
80C22×Dic61C2×D411yescharacteristic
81C22×Dic61C2×D411yescharacteristic
82#11758217—82no—
83C2×#92420—24no—
84C2×#92420—42no—
85C2×#92420—82no—
86C4⋊C4×C61—22no—
87C22⋊C4×C61—81no—
88C22⋊C4×C61—81no—
89C42×C61—41no—
90C22⋊Dic61—22no—
91C22⋊Dic61—22no—
92C22⋊Dic61—42no—
93C22⋊Dic61—42no—
94C4⋊Dic61—22no—
95C4⋊Dic61—22no—
96C4⋊Dic61—42no—
97#11758196—42no—
98#11758196—41no—
99#11758196—41no—
100#11758196—81no—
101#11758196—81no—
102C4×Dic61—41no—
103C4×Dic61C2×D412yes—
104C4×Dic61#4112yes—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61—21no—
110C23×C61—41no—
111C23×C61—41no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61#10112yes—
115C23×C61C2×C22⋊C411yescharacteristic
116D4×C61—44no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61C4×D412yes—
126C2×Dic61—22no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—42no—
132C2×Dic61—42no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—81no—
141C2×Dic61—81no—
142C2×Dic61#12011yescharacteristic
143C2×Dic61#12112yes—
144C2×Dic61#12311yescharacteristic
145#92420—44no—
146#92420—82no—
147#9449—611nomaximal, Sylow
148C22×C61—21no—
149C22×C61—21no—
150C22×C61—22no—
151C22×C61—42no—
152C22×C61—42no—
153C22×C61—41no—
154C22×C61—41no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61—81no—
159C22×C61—81no—
160C22×C61#38611yescharacteristic
161C22×C61C2×#10111yescharacteristic
162C22×C61#41311yescharacteristic
163C4×C61—22no—
164C4×C61—81no—
165C4×C61—81no—
166Dic61—22no—
167Dic61—21no—
168Dic61—21no—
169Dic61—42no—
170Dic61—41no—
171Dic61—41no—
172Dic61—81no—
173#2973—611no—
174#2566—611no—
175#1534—612no—
176#1466—611no—
177#1285—612no—
178C2×C61—21no—
179C2×C61—21no—
180C2×C61—42no—
181C2×C61—81no—
182C2×C61#188411yescharacteristic
183C2×C61#190111yescharacteristic
184C2×C61#191111yescharacteristic
185C2×#125—611no—
186C2×C4×D4—611no—
187#435—1224no—
188#432—612no—
189#432—612no—
190#407—1221no—
191C2×C22⋊C8—1221no—
192#396—1221no—
193#396—1221no—
194#390—611no—
195#390#692311yescharacteristic
196#385—1221no—
197#385—1221no—
198#384—611no—
199#382—611no—
200C4×C4⋊C4—611no—
201#330—1224no—
202#323—1221no—
203#323—1221no—
204C61#944911yescharacteristic, complemented, Sylow
205C22×D4C2×#692311yescharacteristic
206C23×C4—611no—
207C23×C4—611no—
208C2×M16—1222no—
209C22×C8—1222no—
210#125—1222no—
211#125—1222no—
212C4×D4—1222no—
213C4×D4—1222no—
214C2×C4⋊C4—611no—
215C2×C4⋊C4—611no—
216C2×C4⋊C4—1221no—
217C2×C4⋊C4—1221no—
218C2×C4⋊C4—1221no—
219C2×C4⋊C4—1221no—
220C2×C4⋊C4—1221no—
221C2×C4⋊C4C2×#692311yescharacteristic
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—611no—
225C2×C22⋊C4—611no—
226C2×C22⋊C4—1221no—
227C2×C22⋊C4—1221no—
228C2×C42—611no—
229C2×C42—611no—
230C2×C42C2×#692311yescharacteristic
231C4⋊C8—1222no—
232C4⋊C8—1222no—
233C22⋊C8—1222no—
234C22⋊C8—1222no—
235C22⋊C8—1222no—
236C22⋊C8—1222no—
237#97—614no—
238#97—1222no—
239#95—1221no—
240#95—1221no—
241#95—1221no—
242C24C22⋊#692311yescharacteristic
243C24C22⋊#692311yescharacteristic
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—41no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—611no—
250C22×C4—611no—
251C22×C4—611no—
252C22×C4—611no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4—1221no—
259C22×C4—4881no—
260C22×C4—4881no—
261C22×C4C22×#692311yescharacteristic
262M16—4882no—
263C2×C8—1224no—
264C2×C8—4882no—
265C2×C8—2442no—
266C4⋊C4—22no—
267C4⋊C4—1222no—
268C4⋊C4—1222no—
269C4⋊C4—4881no—
270C4⋊C4—4881no—
271C4⋊C4—2441no—
272C4⋊C4—2441no—
273C4⋊C4—2442no—
274C4⋊C4—2442no—
275C22⋊C4—81no—
276C22⋊C4—81no—
277C22⋊C4—1222no—
278C22⋊C4—1222no—
279C22⋊C4—2442no—
280C22⋊C4—2442no—
281C42—41no—
282C42—612no—
283C42—612no—
284C42—2441no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23#1451983812yes—
295C23C2×C22⋊#692311yescharacteristic
296D4—44no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—611no—
306C2×C4—612no—
307C2×C4—611no—
308C2×C4—1222no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—4881no—
312C2×C4—4881no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2442no—
316C2×C4—2442no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4D4×#692312yes—
325C8—4882no—
326C8—2444no—
327C22—21no—
328C22—21no—
329C22—22no—
330C22—42no—
331C22—42no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—81no—
338C22—81no—
339C22#1684071011yescharacteristic
340C22C2×#1451983811yescharacteristic
341C22#1684074911yescharacteristic
342C4—22no—
343C4—81no—
344C4—81no—
345C4—1222no—
346C4—1221no—
347C4—1221no—
348C4—4881no—
349C4—2442no—
350C4—2441no—
351C4—2441no—
352C2—21no—
353C2—21no—
354C2—42no—
355C2—81no—
356C2#2146182011yescharacteristic
357C2#2146184611yescharacteristic
358C2#2146186511yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#390C4
socleC22×C61#386
prime radicalC22×D4×C61C2×C4
cosocleC2×C4×Dic61C23
hypercenter#390#6923
hypocenterC61#9449
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #390

Complements

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

NH ≅ G/Ntype
2. #21461301C2semidirect
4. #21460670C2semidirect
204. C61#9449semidirect

Maximal subgroups

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

subgroupindex
#214626702
#214613012
#214610792
#214606702
#214510222
#944961