Finite Group Databasebeta

← #30604306

Subgroups — #30604306

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#21461059C211yesmaximal, characteristic
3#21460746C212yesmaximal, complemented
4#21460745C212yesmaximal, complemented
5#21450124C211yesmaximal, characteristic
6#16840778—21no—
7#16840732—21no—
8#16840607—21no—
9#16840605—21no—
10#16840605C2212yes—
11#16840605C2212yes—
12C2×#14519758C411yescharacteristic
13C2×D4×Dic61C2211yescharacteristic
14C22×#11758196C411yescharacteristic
15#16839695—21no—
16#16839690—21no—
17#16839657—21no—
18#16839625C2211yescharacteristic
19#16839623C2211yescharacteristic
20#16839620—21no—
21#16839620C411yescharacteristic
22C2×#123×C61C411yescharacteristic
23C2×#11758217—41no—
24C4⋊#92420—41no—
25C22⋊#92420—22no—
26C22⋊#92420—22no—
27C22⋊#92420—41no—
28C4×#92420—41no—
29C23×Dic61C2×C411yescharacteristic
30C23×Dic61C2×C411yescharacteristic
31C23×Dic61D411yescharacteristic
32#14519758—42no—
33D4×Dic61—41no—
34D4×Dic61—41no—
35C2×C4⋊Dic61D411yescharacteristic
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196—41no—
41C2×#11758196—41no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61C2×C411yescharacteristic
44C2×C22⋊Dic61D411yescharacteristic
45C2×C22⋊Dic61C2311yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52C22×D4×C61C2×C411yescharacteristic
53C23×C4×C61C2×C411yescharacteristic
54#123×C61—42no—
55C2×C4⋊C4×C61—21no—
56C2×C22⋊C4×C61—21no—
57C2×C22⋊C4×C61C2×C411yescharacteristic
58C24×C61C22⋊C411yescharacteristic
59C24×C61C22×C411yescharacteristic
60C2×D4×C61—22no—
61C2×D4×C61—22no—
62C2×D4×C61—41no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—22no—
66C22×C4×C61—41no—
67C22×C4×C61—41no—
68C22×C4×C61C22⋊C411yescharacteristic
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—22no—
76C22×Dic61—42no—
77C22×Dic61—42no—
78C22×Dic61—41no—
79C22×Dic61—41no—
80C22×Dic61C22⋊C411yescharacteristic
81C22×Dic61C22⋊C411yescharacteristic
82C22×Dic61C2×D411yescharacteristic
83C22×Dic61C2×D411yescharacteristic
84#11758217—82no—
85C2×#92420—42no—
86C2×#92420—42no—
87C4⋊C4×C61—42no—
88C22⋊C4×C61—42no—
89C22⋊C4×C61—41no—
90C22⋊Dic61—41no—
91C22⋊Dic61—41no—
92C22⋊Dic61—42no—
93C22⋊Dic61—41no—
94C4⋊Dic61—41no—
95#11758196—42no—
96#11758196—42no—
97#11758196—42no—
98#11758196—41no—
99#11758196—41no—
100C4×Dic61—21no—
101C4×Dic61—21no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—41no—
108C23×C61—41no—
109C23×C61—41no—
110C23×C61—41no—
111C23×C61C2×C22⋊C411yescharacteristic
112C23×C61#13112yes—
113D4×C61—44no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—82no—
123C2×C4×C61#10012yes—
124C2×Dic61—22no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—42no—
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—82no—
142C2×Dic61#9911yescharacteristic
143C2×Dic61#9911yescharacteristic
144#92420—82no—
145#92420—82no—
146#11562—611nomaximal, Sylow
147C22×C61—21no—
148C22×C61—21no—
149C22×C61—22no—
150C22×C61—42no—
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#40811yescharacteristic
160C22×C61C2×#9911yescharacteristic
161C22×C61C2×#10011yescharacteristic
162C4×C61—22no—
163C4×C61—81no—
164C4×C61—81no—
165Dic61—21no—
166Dic61—41no—
167Dic61—41no—
168Dic61—41no—
169Dic61—81no—
170Dic61—81no—
171Dic61#35212yes—
172#2486—611no—
173#1465—611no—
174#1460—611no—
175#1317—612no—
176#1317—612no—
177C2×C61—21no—
178C2×C61—21no—
179C2×C61—42no—
180C2×C61—81no—
181C2×C61#147111yescharacteristic
182C2×C61C2×#35211yescharacteristic
183C2×C61#212311yescharacteristic
184C2×#123—611no—
185C2×#123#692311yescharacteristic
186C2×C4×D4—611no—
187C22×C4⋊C4—611no—
188#431—1221no—
189#407—1221no—
190#398—1221no—
191#397—1221no—
192#389—1221no—
193#381—611no—
194#381—611no—
195#380—611no—
196#380—1221no—
197#324—1221no—
198#323—612no—
199#323—612no—
200#323—1221no—
201C61#1156211yescharacteristic, complemented, Sylow
202C22×D4C2×#692311yescharacteristic
203C23×C4—611no—
204C23×C4—611no—
205C23×C4—611no—
206C23×C4C2×#692311yescharacteristic
207C2×M16—2441no—
208#123—42no—
209#123—2442no—
210C4×D4—2441no—
211C4×D4—2441no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—611no—
214C2×C4⋊C4—1221no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4—1221no—
217C2×C4⋊C4—1221no—
218C2×C4⋊C4—2441no—
219C2×C4⋊C4—2441no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—611no—
222C2×C22⋊C4—611no—
223C2×C22⋊C4—611no—
224C2×C22⋊C4—1221no—
225C2×C22⋊C4C2×#692311yescharacteristic
226C2×C42—611no—
227C4⋊C8—2441no—
228C22⋊C8—1222no—
229C22⋊C8—1222no—
230C22⋊C8—2441no—
231C4×C8—2441no—
232#95—1221no—
233#95—1221no—
234#95—1221no—
235#95—1221no—
236#95—1221no—
237C24C22⋊#692311yescharacteristic
238C24C22×#692311yescharacteristic
239C2×D4—22no—
240C2×D4—22no—
241C2×D4—41no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—22no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—611no—
250C22×C4—611no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—1222no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4—2442no—
259C22×C4—2442no—
260C22×C4—2441no—
261C22×C4—2441no—
262C22×C4C22⋊#692311yescharacteristic
263M16—4882no—
264C2×C8—2442no—
265C2×C8—2442no—
266C4⋊C4—42no—
267C4⋊C4—2441no—
268C4⋊C4—2441no—
269C4⋊C4—2441no—
270C4⋊C4—2442no—
271C4⋊C4—2442no—
272C4⋊C4—2442no—
273C22⋊C4—42no—
274C22⋊C4—41no—
275C22⋊C4—2441no—
276C22⋊C4—2441no—
277C22⋊C4—2442no—
278C22⋊C4—2441no—
279C42—1221no—
280C42—1221no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23C2×C22⋊#692311yescharacteristic
291C23#1451986412yes—
292D4—44no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—82no—
302C2×C4—611no—
303C2×C4—611no—
304C2×C4—1222no—
305C2×C4—1221no—
306C2×C4—1221no—
307C2×C4—1221no—
308C2×C4—4881no—
309C2×C4—4882no—
310C2×C4—2442no—
311C2×C4—2442no—
312C2×C4—2442no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4#1451983712yes—
323C8—4882no—
324C8—4882no—
325C22—21no—
326C22—21no—
327C22—22no—
328C22—42no—
329C22—42no—
330C22—42no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—81no—
337C22#1684073511yescharacteristic
338C22D61⋊#9911yescharacteristic
339C22C2×#1451983711yescharacteristic
340C4—22no—
341C4—81no—
342C4—81no—
343C4—612no—
344C4—1221no—
345C4—4881no—
346C4—4881no—
347C4—2441no—
348C4—2441no—
349C4—2441no—
350C2—21no—
351C2—21no—
352C2—42no—
353C2—81no—
354C2#2146109511yescharacteristic
355C2D61⋊#35211yescharacteristic
356C2#2146208211yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
FittingC2×#123×C61C4
socleC22×C61C2×#99
prime radicalC22×D4×C61C2×C4
cosocleC2×C22⋊Dic61C23
hypercenterC2×#123#6923
hypocenterC61#11562
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
3. #21460746C2semidirect
4. #21460745C2semidirect
201. C61#11562semidirect

Maximal subgroups

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

subgroupindex
#214610752
#214610592
#214607462
#214607452
#214501242
#1156261