Finite Group Databasebeta

← #30605010

Subgroups — #30605010

Order 15616.

462 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 70 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#21461522C211yesmaximal, characteristic
2#21461068C211yesmaximal, characteristic
3#21460819C212yesmaximal, complemented
4#21460803C212yesmaximal, complemented
5#21451193C211yesmaximal, characteristic
6C2×D61⋊M16—21no—
7#16840733—21no—
8#16840642—21no—
9#16840642C2212yes—
10#16840608C2212yes—
11#16840607—21no—
12C2×#14519757C411yescharacteristic
13C2×C4⋊C4×D61C2211yescharacteristic
14#16839693C2211yescharacteristic
15#16839683C2211yescharacteristic
16#16839682C411yescharacteristic
17#16839661—21no—
18#16839659—21no—
19#16839636—21no—
20#16839633—21no—
21#16839609C411yescharacteristic
22C61×#398C411yescharacteristic
23C2×#11758213—41no—
24C2×#11758213—41no—
25D61⋊M16—24no—
26D61⋊M16—42no—
27C2×#11758217—22no—
28C2×D61⋊C8—41no—
29#14519834—41no—
30C22⋊#92420—22no—
31C22×Dic122C2×C411yescharacteristic
32C22×C4×D61C2×C411yescharacteristic
33C22×C4×D61D411yescharacteristic
34C22×C4×D61D411yescharacteristic
35#14519757—41no—
36#14519757—41no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61D411yescharacteristic
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196D411yescharacteristic
43C2×#11758196C2311yescharacteristic
44C4⋊C4×D61—41no—
45C4⋊C4×D61—41no—
46C2×#11758198—21no—
47C2×#11758198—21no—
48C2×C4×Dic61—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684C2×C411yescharacteristic
53C2×C4⋊C4×C61—21no—
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C4⋊C4×C61C2×C411yescharacteristic
56#95×C61—21no—
57#95×C61C2×C411yescharacteristic
58C23×D61C22⋊C411yescharacteristic
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C22×C411yescharacteristic
64C22×Dic61—21no—
65C22×Dic61—21no—
66C22×Dic61C22⋊C411yescharacteristic
67C22×Dic61C2×D411yescharacteristic
68C22×Dic61C2×D411yescharacteristic
69C2×C4×D61—21no—
70C2×C4×D61—21no—
71C2×C4×D61—22no—
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—81no—
79C2×C4×D61—81no—
80C2×Dic122—41no—
81C2×Dic122—81no—
82#11758217—24no—
83#11758217—42no—
84C2×#92420—42no—
85C2×#92420—42no—
86#11758213—44no—
87#11758213—82no—
88D61⋊C8—44no—
89C4⋊C4×C61—41no—
90C4⋊C4×C61—41no—
91C4⋊C4×C61—42no—
92#11758198—24no—
93#11758198—41no—
94#11758198—41no—
95C4⋊Dic61—41no—
96C4⋊Dic61—42no—
97C4⋊Dic61—81no—
98#11758196—41no—
99#11758196—41no—
100#11758196—41no—
101#11758196—41no—
102#11758196—81no—
103C4×Dic61—81no—
104C23×C61C2×C22⋊C411yescharacteristic
105C22×D61—21no—
106C22×D61—21no—
107C22×D61—22no—
108C22×D61—41no—
109C22×D61#9911yescharacteristic
110C22×D61#9911yescharacteristic
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—22no—
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—41no—
123C2×C4×C61#10412yes—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—22no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61AGL(1,ℤ/8)11yescharacteristic
137C2×Dic61#13711yescharacteristic
138C4×D61—22no—
139C4×D61—22no—
140C4×D61—22no—
141C4×D61—22no—
142C4×D61—42no—
143C4×D61—81no—
144C4×D61—81no—
145C4×D61—81no—
146Dic122—82no—
147#92420—44no—
148#92420—82no—
149#11768—611nomaximal, Sylow
150C22×C61—21no—
151C22×C61—21no—
152C22×C61C2×#9911yescharacteristic
153C22×C61#41711yescharacteristic
154C22×C61C2×#10411yescharacteristic
155C2×D61—21no—
156C2×D61—21no—
157C2×D61—21no—
158C2×D61—21no—
159C2×D61—21no—
160C2×D61—42no—
161C2×D61—42no—
162C2×D61#35612yes—
163C4×C61—22no—
164C4×C61—42no—
165C4×C61—41no—
166C4×C61—41no—
167C4×C61—81no—
168Dic61—21no—
169Dic61—21no—
170Dic61—42no—
171Dic61—41no—
172Dic61—41no—
173Dic61—81no—
174#2583—611no—
175C2×#343—611no—
176#1463—611no—
177#1354—612no—
178#1346—612no—
179C2×C61—21no—
180C2×C61—21no—
181C2×C61#150411yescharacteristic
182C2×C61#212111yescharacteristic
183C2×C61C2×#35611yescharacteristic
184D61—22no—
185D61—41no—
186C22×M16—1221no—
187C2×C22⋊Q8—611no—
188C22×C4⋊C4—611no—
189#407—1221no—
190#398—611no—
191#398#692311yescharacteristic
192#395—611no—
193#395—611no—
194#389—1221no—
195#389—1221no—
196#385—1221no—
197#385—1221no—
198C4×C22⋊C4—611no—
199#343—612no—
200#343—1221no—
201#324—612no—
202#324—1221no—
203C61#1176811yescharacteristic, complemented, Sylow
204C22×Q8—611no—
205C23×C4—611no—
206C23×C4—611no—
207C23×C4—611no—
208C2×M16—1222no—
209C2×M16—1224no—
210C2×M16—2441no—
211C2×M16—2442no—
212C2×M16—2441no—
213C22×C8—2441no—
214C22⋊Q8—2441no—
215C22⋊Q8—2441no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—611no—
218C2×C4⋊C4—611no—
219C2×C4⋊C4—611no—
220C2×C4⋊C4—1221no—
221C2×C4⋊C4—1221no—
222C2×C4⋊C4—1221no—
223C2×C4⋊C4—1221no—
224C2×C4⋊C4—2441no—
225C2×C4⋊C4—2441no—
226C2×C4⋊C4C2×#692311yescharacteristic
227C2×C4⋊C4C2×#692311yescharacteristic
228C2×C22⋊C4—1221no—
229C2×C22⋊C4—1221no—
230C2×C42—1221no—
231C22⋊C8—1222no—
232C22⋊C8—2441no—
233#95—21no—
234#95—611no—
235#95—1221no—
236#95—1221no—
237#95—1221no—
238#95C2×#692311yescharacteristic
239C24—611no—
240C2×Q8—4881no—
241C2×Q8—2441no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—611no—
245C22×C4—611no—
246C22×C4—611no—
247C22×C4—1221no—
248C22×C4—1221no—
249C22×C4—1221no—
250C22×C4—1221no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—1222no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4—4881no—
259C22×C4—4881no—
260C22×C4C22⋊#692311yescharacteristic
261C22×C4C22⋊#692311yescharacteristic
262C22×C4C22×#692311yescharacteristic
263M16—1224no—
264M16—4882no—
265M16—2442no—
266M16—2444no—
267C2×C8—2442no—
268C2×C8—2444no—
269C2×C8—2442no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—42no—
273C4⋊C4—4881no—
274C4⋊C4—4881no—
275C4⋊C4—2441no—
276C4⋊C4—2441no—
277C4⋊C4—2441no—
278C4⋊C4—2441no—
279C4⋊C4—2441no—
280C4⋊C4—2442no—
281C22⋊C4—1224no—
282C22⋊C4—2441no—
283C22⋊C4—2441no—
284C42—4881no—
285C23—611no—
286C23—611no—
287C23—1222no—
288C23—1221no—
289C23—1221no—
290C23—2441no—
291C23C2×C22⋊#692311yescharacteristic
292Q8—4882no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—22no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
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—1222no—
309C2×C4—1222no—
310C2×C4—1222no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—1222no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—4881no—
317C2×C4—4881no—
318C2×C4—4881no—
319C2×C4—2442no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4—2441no—
327C2×C4#1451984112yes—
328C8—4882no—
329C8—2444no—
330C22—21no—
331C22—21no—
332C22—612no—
333C22—1221no—
334C22—1221no—
335C22—1221no—
336C22—1221no—
337C22—1221no—
338C22—2442no—
339C22—2442no—
340C22D61⋊#9911yescharacteristic
341C22#1684075311yescharacteristic
342C22C2×#1451984111yescharacteristic
343C4—22no—
344C4—42no—
345C4—41no—
346C4—41no—
347C4—81no—
348C4—1221no—
349C4—1221no—
350C4—4881no—
351C4—2442no—
352C4—2441no—
353C4—2441no—
354C2—21no—
355C2—21no—
356C2—1222no—
357C2—2441no—
358C2#2146120411yescharacteristic
359C2#2146207711yescharacteristic
360C2D61⋊#35611yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#398C4
socleC22×C61C2×#99
prime radicalC23×D61C22⋊C4
cosocleC2×#11758196C23
hypercenter#398#6923
hypocenterC61#11768
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #398

Complements

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

NH ≅ G/Ntype
3. #21460819C2semidirect
4. #21460803C2semidirect
203. C61#11768semidirect

Maximal subgroups

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

subgroupindex
#214615222
#214610682
#214608192
#214608032
#214511932
#1176861