Finite Group Databasebeta

← #29590911

Subgroups — #29590911

Order 15616.

432 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 87 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#21445902C211yesmaximal, characteristic, complemented
2#21444133C211yesmaximal, characteristic, complemented
3#21443846C212yesmaximal, complemented
4#21443822C212yesmaximal, complemented
5C61×#2598C211yesmaximal, characteristic
6#16839815—21no—
7#16839726—21no—
8#16839531—21no—
9#16839531C2212yes—
10#16839488C2212yes—
11#16839486—21no—
12C2×C4×D4×C61C411yescharacteristic
13C2×#117×C61C2211yescharacteristic
14C61×#400C2211yescharacteristic
15C61×#399C411yescharacteristic
16C61×#394C2211yescharacteristic
17C61×#392C411yescharacteristic
18C61×#388—21no—
19C61×#386—21no—
20C61×#386—21no—
21C61×#385—21no—
22C61×#383C411yescharacteristic
23C2×#11758194—22no—
24C4⋊#92418—41no—
25C22⋊#92418—22no—
26C22⋊#92418—41no—
27C22⋊#92418—41no—
28C4×#92418—41no—
29C22×D4×C61—21no—
30C22×D4×C61C2×C411yescharacteristic
31C23×C4×C61—21no—
32C23×C4×C61D411yescharacteristic
33C4×D4×C61—41no—
34C4×D4×C61—41no—
35#117×C61—41no—
36#117×C61—41no—
37C2×C4⋊C4×C61—21no—
38C2×C4⋊C4×C61C2×C411yescharacteristic
39C2×C4⋊C4×C61D411yescharacteristic
40C2×C4⋊C4×C61C2311yescharacteristic
41C2×C22⋊C4×C61—21no—
42C2×C22⋊C4×C61—21no—
43C2×C22⋊C4×C61—21no—
44C2×C22⋊C4×C61—21no—
45C2×C22⋊C4×C61—21no—
46C2×C22⋊C4×C61C2×C411yescharacteristic
47C2×C22⋊C4×C61D411yescharacteristic
48C2×C42×C61C2×C411yescharacteristic
49C2×C42×C61D411yescharacteristic
50#95×C61—21no—
51#95×C61—21no—
52#95×C61—21no—
53#95×C61—21no—
54#95×C61C2×C411yescharacteristic
55#95×C61C2×C411yescharacteristic
56C24×C61—21no—
57C24×C61C22⋊C411yescharacteristic
58C2×D4×C61—41no—
59C2×D4×C61—42no—
60C2×D4×C61—42no—
61C2×D4×C61—42no—
62C2×D4×C61—81no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—22no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—41no—
70C22×C4×C61—42no—
71C22×C4×C61—81no—
72C22×C4×C61—81no—
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C22⋊C411yescharacteristic
75C22×C4×C61C22⋊C411yescharacteristic
76C22×C4×C61C22×C411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C4⋊C4×C61—41no—
80C4⋊C4×C61—41no—
81C4⋊C4×C61—41no—
82C4⋊C4×C61—81no—
83C22⋊C4×C61—41no—
84C22⋊C4×C61—41no—
85C22⋊C4×C61—42no—
86C22⋊C4×C61—41no—
87C22⋊C4×C61—41no—
88C22⋊C4×C61—42no—
89C22⋊C4×C61—81no—
90C22⋊C4×C61—81no—
91C42×C61—21no—
92C42×C61—21no—
93C42×C61—21no—
94C42×C61—21no—
95#11758194—42no—
96#11758194—42no—
97C2×#92418—42no—
98C2×#92418—42no—
99C23×C61—22no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61—41no—
104C23×C61—41no—
105C23×C61—41no—
106C23×C61—41no—
107C23×C61—41no—
108C23×C61—41no—
109C23×C61—41no—
110C23×C61—41no—
111C23×C61C2×C22⋊C411yescharacteristic
112D4×C61—42no—
113D4×C61—42no—
114D4×C61—84no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—42no—
124C2×C4×C61—42no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—84no—
139C2×C4×C61#9911yescharacteristic
140C2×C4×C61#9911yescharacteristic
141C2×C4×C61#13512yes—
142#92418—82no—
143#92418—82no—
144#11847—611nomaximal, Sylow
145C22×C61—21no—
146C22×C61—21no—
147C22×C61—42no—
148C22×C61—42no—
149C22×C61—42no—
150C22×C61—42no—
151C22×C61—41no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61—81no—
155C22×C61—81no—
156C22×C61—81no—
157C22×C61—81no—
158C22×C61—81no—
159C22×C61C2×#9911yescharacteristic
160C22×C61#41611yescharacteristic
161C22×C61#42111yescharacteristic
162C4×C61—22no—
163C4×C61—21no—
164C4×C61—21no—
165C4×C61—41no—
166C4×C61—41no—
167C4×C61—41no—
168C4×C61—41no—
169C4×C61—81no—
170C4×C61—81no—
171C4×C61—81no—
172#2598D6111yescharacteristic
173#1822—611no—
174#1458—611no—
175#1353—612no—
176#1345—612no—
177C2×C61—21no—
178C2×C61—21no—
179C2×C61—81no—
180C2×C61—82no—
181C2×C61#151611yescharacteristic
182C2×C61#212011yescharacteristic
183C2×C61#213411yescharacteristic
184C2×C4×D4Dic6111yescharacteristic
185C2×#117C2×D6111yescharacteristic
186#431—1221no—
187#407—1221no—
188#400C2×D6111yescharacteristic
189#399Dic6111yescharacteristic
190#394C2×D6111yescharacteristic
191#392Dic6111yescharacteristic
192#388—21no—
193#386—21no—
194#386—21no—
195#385—21no—
196#383Dic6111yescharacteristic
197#343—612no—
198#343—1221no—
199#324—612no—
200#323—1221no—
201C61#1184711yescharacteristic, complemented, Sylow
202C22×D4—21no—
203C22×D4C2×Dic6111yescharacteristic
204C23×C4—21no—
205C23×C4C22⋊D6111yescharacteristic
206C2×M16—1222no—
207C4×D4—41no—
208C4×D4—41no—
209#117—41no—
210#117—41no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4C2×Dic6111yescharacteristic
213C2×C4⋊C4C22⋊D6111yescharacteristic
214C2×C4⋊C4C22×D6111yescharacteristic
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4C2×Dic6111yescharacteristic
221C2×C22⋊C4C22⋊D6111yescharacteristic
222C2×C42C2×Dic6111yescharacteristic
223C2×C42C22⋊D6111yescharacteristic
224C4⋊C8—2441no—
225C22⋊C8—1222no—
226C22⋊C8—2441no—
227C22⋊C8—2441no—
228C4×C8—2441no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95—21no—
233#95C2×Dic6111yescharacteristic
234#95C2×Dic6111yescharacteristic
235C24—21no—
236C24C22⋊Dic6111yescharacteristic
237C2×D4—41no—
238C2×D4—42no—
239C2×D4—42no—
240C2×D4—42no—
241C2×D4—81no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—22no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—41no—
249C22×C4—42no—
250C22×C4—81no—
251C22×C4—81no—
252C22×C4C22⋊Dic6111yescharacteristic
253C22×C4C22⋊Dic6111yescharacteristic
254C22×C4C22⋊Dic6111yescharacteristic
255C22×C4C22×Dic6111yescharacteristic
256C22×C4C2×C22⋊D6111yescharacteristic
257C22×C4C2×C22⋊D6111yescharacteristic
258M16—2442no—
259M16—2442no—
260C2×C8—2442no—
261C2×C8—2442no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—81no—
266C22⋊C4—41no—
267C22⋊C4—41no—
268C22⋊C4—42no—
269C22⋊C4—41no—
270C22⋊C4—41no—
271C22⋊C4—42no—
272C22⋊C4—81no—
273C22⋊C4—81no—
274C42—21no—
275C42—21no—
276C42—21no—
277C42—21no—
278C23—22no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23C2×C22⋊Dic6111yescharacteristic
291D4—42no—
292D4—42no—
293D4—84no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—84no—
318C2×C4#1451969211yescharacteristic
319C2×C4#1451969211yescharacteristic
320C2×C4#1451979712yes—
321C8—4882no—
322C8—4882no—
323C22—21no—
324C22—21no—
325C22—42no—
326C22—42no—
327C22—42no—
328C22—41no—
329C22—42no—
330C22—41no—
331C22—41no—
332C22—81no—
333C22—81no—
334C22—81no—
335C22—81no—
336C22—81no—
337C22C2×#1451969211yescharacteristic
338C22#1683975811yescharacteristic
339C22#1683977911yescharacteristic
340C4—22no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—81no—
348C4—81no—
349C4—81no—
350C2—21no—
351C2—21no—
352C2—81no—
353C2—82no—
354C2#2144437511yescharacteristic
355C2#2144746011yescharacteristic
356C2#2144751111yescharacteristic
subgroupG/H
centerC22C2×#14519692
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#2598C2
socleC22×C61C2×#99
prime radicalC61×#392C4
cosocleC2×C4⋊C4×C61C23
hypercenter#2598D61
hypocenterC61#11847
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2598

Complements

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

NH ≅ G/Ntype
1. #21445902C2semidirect
2. #21444133C2semidirect
3. #21443846C2semidirect
4. #21443822C2semidirect
201. C61#11847semidirect

Maximal subgroups

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

subgroupindex
#214459022
#214441332
#214438462
#214438222
C61×#25982
#1184761