Finite Group Databasebeta

← #30604312

Subgroups — #30604312

Order 15616.

444 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 72 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#21461075C211yesmaximal, characteristic
2#21461055C211yesmaximal, characteristic
3#21460750C212yesmaximal, complemented
4#21460749C212yesmaximal, complemented
5#21450812C211yesmaximal, characteristic
6#16840732—21no—
7C2×C22⋊#92420—21no—
8#16840607C2212yes—
9#16840607C2212yes—
10#16840605—21no—
11#16840605—21no—
12C2×#14519775C411yescharacteristic
13C2×#14519764C411yescharacteristic
14C2×D4×Dic61C2211yescharacteristic
15#16839690—21no—
16#16839690—21no—
17#16839669C2211yescharacteristic
18#16839668C2211yescharacteristic
19#16839620—21no—
20#16839620—21no—
21C4×#11758196C411yescharacteristic
22C2×#124×C61C411yescharacteristic
23C2×#11758217—41no—
24C22×#92420—41no—
25C22⋊#92420—22no—
26C22⋊#92420—22no—
27C22⋊#92420—41no—
28C22⋊#92420—41no—
29C22×Dic122C2×C411yescharacteristic
30C23×Dic61D411yescharacteristic
31C23×Dic61D411yescharacteristic
32#14519775—41no—
33#14519775—41no—
34#14519764—42no—
35D4×Dic61—41no—
36D4×Dic61—41no—
37C2×C4⋊Dic61C2311yescharacteristic
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61D411yescharacteristic
44C2×C22⋊Dic61D411yescharacteristic
45C2×C4×Dic61C2×C411yescharacteristic
46C2×C4×Dic61C2×C411yescharacteristic
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52C22×Q8×C61C2×C411yescharacteristic
53C22×D4×C61C2×C411yescharacteristic
54#124×C61—42no—
55C2×C22⋊C4×C61—21no—
56C2×C22⋊C4×C61—21no—
57C2×C42×C61C2×C411yescharacteristic
58C24×C61C22⋊C411yescharacteristic
59C24×C61C22⋊C411yescharacteristic
60C2×Q8×C61—22no—
61C2×Q8×C61—41no—
62C2×Q8×C61—41no—
63C2×D4×C61—22no—
64C2×D4×C61—22no—
65C2×D4×C61—41no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61C22×C411yescharacteristic
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—42no—
76C22×Dic61—42no—
77C22×Dic61C22⋊C411yescharacteristic
78C22×Dic61C22⋊C411yescharacteristic
79C22×Dic61C2×D411yescharacteristic
80C22×Dic61C2×D411yescharacteristic
81C2×Dic122—22no—
82C2×Dic122—41no—
83C2×Dic122—41no—
84#11758217—82no—
85C2×#92420—42no—
86C2×#92420—42no—
87C2×#92420—82no—
88C22⋊C4×C61—42no—
89C22⋊C4×C61—42no—
90C42×C61—41no—
91C22⋊Dic61—41no—
92C22⋊Dic61—41no—
93C22⋊Dic61—42no—
94C22⋊Dic61—42no—
95C4⋊Dic61—41no—
96#11758196—42no—
97#11758196—42no—
98#11758196—41no—
99#11758196—41no—
100C4×Dic61—21no—
101C4×Dic61—21no—
102C4×Dic61—41no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61—41no—
109C23×C61—41no—
110C23×C61—41no—
111C23×C61—41no—
112C23×C61#10012yes—
113C23×C61C2×C22⋊C411yescharacteristic
114Q8×C61—82no—
115D4×C61—44no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61#13112yes—
125C2×Dic61—22no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—42no—
130C2×Dic61—42no—
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—41no—
140C2×Dic61—81no—
141C2×Dic61—81no—
142C2×Dic61#9911yescharacteristic
143C2×Dic61#9911yescharacteristic
144Dic122—82no—
145#92420—82no—
146#92420—82no—
147#11564—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#40811yescharacteristic
161C22×C61C2×#9911yescharacteristic
162C22×C61C2×#10011yescharacteristic
163C4×C61—22no—
164C4×C61—81no—
165C4×C61—81no—
166Dic61—21no—
167Dic61—41no—
168Dic61—41no—
169Dic61—41no—
170Dic61—81no—
171Dic61—81no—
172Dic61#35412yes—
173#2547—611no—
174#1465—611no—
175#1459—611no—
176#1319—612no—
177#1319—612no—
178C2×C61—21no—
179C2×C61—21no—
180C2×C61—42no—
181C2×C61—81no—
182C2×C61#147111yescharacteristic
183C2×C61C2×#35411yescharacteristic
184C2×C61#213511yescharacteristic
185C2×C4⋊Q8—611no—
186C2×#124—611no—
187C2×#124#692311yescharacteristic
188C2×C4×D4—611no—
189#407—1221no—
190C2×C22⋊C8—1221no—
191#397—1221no—
192#397—1221no—
193#391—611no—
194#391—611no—
195#380—1221no—
196#380—1221no—
197C4×C4⋊C4—611no—
198#324—612no—
199#324—612no—
200#323—1221no—
201#323—1221no—
202C61#1156411yescharacteristic, complemented, Sylow
203C22×Q8—611no—
204C22×Q8C2×#692311yescharacteristic
205C22×D4C2×#692311yescharacteristic
206C23×C4—611no—
207C23×C4—611no—
208C2×M16—2441no—
209C22×C8—2441no—
210C4⋊Q8—2441no—
211C4⋊Q8—2441no—
212#124—42no—
213#124—2442no—
214C4×D4—2441no—
215C4×D4—2441no—
216C2×C4⋊C4—611no—
217C2×C4⋊C4—1221no—
218C2×C4⋊C4—1221no—
219C2×C4⋊C4—1221no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—611no—
223C2×C22⋊C4—611no—
224C2×C22⋊C4—1221no—
225C2×C22⋊C4—1221no—
226C2×C42—611no—
227C2×C42—611no—
228C2×C42C2×#692311yescharacteristic
229C22⋊C8—1222no—
230C22⋊C8—1222no—
231C22⋊C8—2441no—
232C22⋊C8—2441no—
233#95—1221no—
234#95—1221no—
235#95—1221no—
236#95—1221no—
237#95—1221no—
238C24C22⋊#692311yescharacteristic
239C24C22⋊#692311yescharacteristic
240C2×Q8—22no—
241C2×Q8—41no—
242C2×Q8—41no—
243C2×Q8—1222no—
244C2×Q8—2441no—
245C2×Q8—2441no—
246C2×D4—22no—
247C2×D4—22no—
248C2×D4—41no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—611no—
252C22×C4—611no—
253C22×C4—611no—
254C22×C4—611no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—2442no—
262C22×C4—2442no—
263C22×C4C22×#692311yescharacteristic
264M16—4882no—
265C2×C8—4882no—
266C2×C8—2442no—
267C2×C8—2442no—
268C4⋊C4—2441no—
269C4⋊C4—2441no—
270C4⋊C4—2441no—
271C4⋊C4—2442no—
272C4⋊C4—2442no—
273C22⋊C4—42no—
274C22⋊C4—42no—
275C22⋊C4—2441no—
276C22⋊C4—2441no—
277C22⋊C4—2442no—
278C22⋊C4—2442no—
279C42—41no—
280C42—1221no—
281C42—1221no—
282C42—2441no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23—41no—
292C23#1451983712yes—
293C23C2×C22⋊#692311yescharacteristic
294Q8—82no—
295Q8—4882no—
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—611no—
307C2×C4—1222no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—4881no—
312C2×C4—4881no—
313C2×C4—2442no—
314C2×C4—2442no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4#1451986412yes—
325C8—4882no—
326C8—4882no—
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#1684073511yescharacteristic
340C22D61⋊#9911yescharacteristic
341C22C2×#1451983711yescharacteristic
342C4—22no—
343C4—81no—
344C4—81no—
345C4—612no—
346C4—1221no—
347C4—4881no—
348C4—4881no—
349C4—2441no—
350C4—2441no—
351C4—2441no—
352C2—21no—
353C2—21no—
354C2—42no—
355C2—81no—
356C2#2146109511yescharacteristic
357C2D61⋊#35411yescharacteristic
358C2#2146212211yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#124×C61C4
socleC22×C61C2×#99
prime radicalC22×D4×C61C2×C4
cosocleC2×C4⋊Dic61C23
hypercenterC2×#124#6923
hypocenterC61#11564
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
3. #21460750C2semidirect
4. #21460749C2semidirect
202. C61#11564semidirect

Maximal subgroups

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

subgroupindex
#214610752
#214610552
#214607502
#214607492
#214508122
#1156461