Finite Group Databasebeta

← #30605241

Subgroups — #30605241

Order 15616.

400 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 64 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#21461684C211yesmaximal, characteristic
2#21461077C211yesmaximal, characteristic
3#21460819C212yesmaximal, complemented
4#21460803C212yesmaximal, complemented
5#21451741C211yesmaximal, characteristic
6#16840765—21no—
7C2×#14519837—21no—
8#16840732—21no—
9#16840642C2212yes—
10#16840608C2212yes—
11#16840606—21no—
12C2×#14519757C411yescharacteristic
13C2×#14519737C2211yescharacteristic
14#16839693C2211yescharacteristic
15#16839689—21no—
16#16839683C2211yescharacteristic
17#16839677—21no—
18#16839674C411yescharacteristic
19#16839649—21no—
20#16839637—21no—
21#16839624C411yescharacteristic
22C61×#397C411yescharacteristic
23C2×#11758217—22no—
24C2×#11758217—41no—
25#14519844—41no—
26C4⋊#92420—41no—
27#14519837—42no—
28C22⋊#92420—22no—
29C22⋊#92420—41no—
30C22×Dic122C2×C411yescharacteristic
31C22×C22⋊D61D411yescharacteristic
32C23×Dic61D411yescharacteristic
33C22×C4×D61C2×C411yescharacteristic
34#14519757—41no—
35#14519757—41no—
36#14519737—41no—
37#14519737—41no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61—21no—
40C2×#11758196—21no—
41C2×#11758196C2311yescharacteristic
42C2×C22⋊Dic61—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198D411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684C2×C411yescharacteristic
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C22⋊C4×C61—21no—
54C2×C22⋊C4×C61C2×C411yescharacteristic
55#95×C61—21no—
56#95×C61C2×C411yescharacteristic
57C24×C61C22⋊C411yescharacteristic
58C23×D61C22⋊C411yescharacteristic
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22×C411yescharacteristic
63C2×C22⋊D61—21no—
64C2×C22⋊D61—21no—
65C2×C22⋊D61—41no—
66C2×C22⋊D61—41no—
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61—81no—
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C2×D411yescharacteristic
74C22×Dic61C2×D411yescharacteristic
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—81no—
78C2×Dic122—41no—
79C2×Dic122—81no—
80#11758217—42no—
81#11758217—42no—
82#11758217—82no—
83C2×#92420—42no—
84C2×#92420—42no—
85C4⋊C4×C61—41no—
86C22⋊C4×C61—41no—
87C22⋊C4×C61—42no—
88C22⋊Dic61—81no—
89#11758198—41no—
90#11758198—42no—
91#11758198—81no—
92C4⋊Dic61—41no—
93C4⋊Dic61—41no—
94C4⋊Dic61—81no—
95#11758196—41no—
96#11758196—41no—
97#11758196—41no—
98C4×Dic61—21no—
99C4×Dic61—21no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61—41no—
104C23×C61—41no—
105C23×C61C2×C22⋊C411yescharacteristic
106C22×D61—21no—
107C22×D61—21no—
108C22×D61—21no—
109C22×D61—41no—
110C22×D61—41no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C22⋊D61—42no—
122C22⋊D61—42no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—41no—
127C2×Dic61—42no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—81no—
136C2×Dic61#9911yescharacteristic
137C2×Dic61#9911yescharacteristic
138C2×Dic61AGL(1,ℤ/8)11yescharacteristic
139C2×Dic61#13711yescharacteristic
140C4×D61—81no—
141C4×D61—81no—
142Dic122—82no—
143#92420—82no—
144#92420—82no—
145#11834—611nomaximal, Sylow
146C22×C61—21no—
147C22×C61—21no—
148C22×C61—42no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61—41no—
152C22×C61—81no—
153C22×C61C2×#9911yescharacteristic
154C22×C61#41711yescharacteristic
155C22×C61#42111yescharacteristic
156C2×D61—41no—
157C2×D61—41no—
158C2×D61—41no—
159C2×D61—81no—
160C2×D61—81no—
161C4×C61—41no—
162C4×C61—41no—
163C4×C61—81no—
164C4×C61—81no—
165Dic61—21no—
166Dic61—21no—
167Dic61—21no—
168Dic61—21no—
169Dic61—41no—
170Dic61—81no—
171Dic61—81no—
172#2638—611no—
173#1800—611no—
174#1465—611no—
175#1354—612no—
176#1346—612no—
177C2×C61—21no—
178C2×C61—21no—
179C2×C61—81no—
180C2×C61#151311yescharacteristic
181C2×C61#212111yescharacteristic
182C2×C61#213511yescharacteristic
183D61—81no—
184C2×C22⋊Q8—611no—
185C2×C4×D4—611no—
186#423—1221no—
187C2×#100—1221no—
188#407—1221no—
189#398—611no—
190#397—1221no—
191#397#692311yescharacteristic
192#395—611no—
193#394—1221no—
194#393—611no—
195#387—1221no—
196#385—1221no—
197#381—611no—
198#343—612no—
199#324—612no—
200#323—1221no—
201C61#1183411yescharacteristic, complemented, Sylow
202C22×Q8—611no—
203C22×D4—611no—
204C23×C4—611no—
205C23×C4—611no—
206C2×M16—1222no—
207C2×M16—2441no—
208C22⋊Q8—2441no—
209C22⋊Q8—2441no—
210C4×D4—2441no—
211C4×D4—2441no—
212C2×C4⋊C4—611no—
213C2×C4⋊C4—1221no—
214C2×C4⋊C4—1221no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4C2×#692311yescharacteristic
217C2×C22⋊C4—21no—
218C2×C22⋊C4—611no—
219C2×C22⋊C4—1221no—
220C2×C22⋊C4—1221no—
221C2×C22⋊C4—1221no—
222C2×C22⋊C4C2×#692311yescharacteristic
223C2×C42—611no—
224C4⋊C8—2441no—
225C4⋊C8—2441no—
226#100—2442no—
227C22⋊C8—1222no—
228C22⋊C8—2441no—
229#95—21no—
230#95—611no—
231#95—1221no—
232#95—1221no—
233#95—1221no—
234#95—1221no—
235#95C2×#692311yescharacteristic
236C24—611no—
237C24C22⋊#692311yescharacteristic
238C2×Q8—4881no—
239C2×Q8—2441no—
240C2×D4—1221no—
241C2×D4—1221no—
242C2×D4—2441no—
243C2×D4—2441no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—611no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—1221no—
250C22×C4—1221no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—4881no—
256C22×C4—4881no—
257C22×C4C22⋊#692311yescharacteristic
258C22×C4C22×#692311yescharacteristic
259M16—4882no—
260M16—2442no—
261M16—2442no—
262C2×C8—2442no—
263C2×C8—2442no—
264C4⋊C4—41no—
265C4⋊C4—4881no—
266C4⋊C4—2441no—
267C4⋊C4—2441no—
268C4⋊C4—2441no—
269C4⋊C4—2441no—
270C4⋊C4—2441no—
271C22⋊C4—41no—
272C22⋊C4—42no—
273C22⋊C4—4881no—
274C22⋊C4—4881no—
275C22⋊C4—2441no—
276C22⋊C4—2442no—
277C42—1221no—
278C42—1221no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—41no—
283C23—41no—
284C23—1221no—
285C23—1221no—
286C23—1221no—
287C23—2441no—
288C23—2441no—
289C23C2×C22⋊#692311yescharacteristic
290Q8—4882no—
291D4—2442no—
292D4—2442no—
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—41no—
302C2×C4—41no—
303C2×C4—611no—
304C2×C4—611no—
305C2×C4—611no—
306C2×C4—611no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—4881no—
311C2×C4—4881no—
312C2×C4—4881no—
313C2×C4—2441no—
314C2×C4—2442no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4—2441no—
322C8—4882no—
323C8—4882no—
324C22—21no—
325C22—21no—
326C22—42no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—81no—
331C22—4881no—
332C22—4881no—
333C22—2441no—
334C22—2441no—
335C22—2441no—
336C22D61⋊#9911yescharacteristic
337C22#1684075311yescharacteristic
338C22#1684076011yescharacteristic
339C4—41no—
340C4—41no—
341C4—81no—
342C4—81no—
343C4—1221no—
344C4—1221no—
345C4—1221no—
346C4—1221no—
347C4—4881no—
348C4—4881no—
349C4—2441no—
350C2—21no—
351C2—21no—
352C2—81no—
353C2—4881no—
354C2#2146123511yescharacteristic
355C2#2146207711yescharacteristic
356C2#2146212211yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#397C4
socleC22×C61C2×#99
prime radicalC22×C22⋊D61D4
cosocleC2×#11758196C23
hypercenter#397#6923
hypocenterC61#11834
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #397

Complements

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

NH ≅ G/Ntype
3. #21460819C2semidirect
4. #21460803C2semidirect
201. C61#11834semidirect

Maximal subgroups

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

subgroupindex
#214616842
#214610772
#214608192
#214608032
#214517412
#1183461