Finite Group Databasebeta

← #29568245

Subgroups — #29568245

Order 15616.

510 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 111 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#21448283C211yesmaximal, characteristic
2#21445672C211yesmaximal, characteristic, complemented
3#21443643C212yesmaximal, complemented
4#21443639C212yesmaximal
5C61×#1745C211yesmaximal, characteristic, complemented
6C2×C4×D244C411yescharacteristic
7C2×#14519734—21no—
8C2×C4⋊#92418—21no—
9C2×#14519688—21no—
10#16839664C411yescharacteristic
11#16839664C2211yescharacteristic
12#16839660C411yescharacteristic
13#16839660C2211yescharacteristic
14#16839653—21no—
15#16839653—21no—
16C4×C4⋊Dic61C411yescharacteristic
17C4×#11758198—21no—
18#16839517C2212yes—
19C2×#97×C61—21no—
20C43×C61C2211yescharacteristic
21C61×#336—21no—
22C61×#336C2212yes—
23C22×D244C2×C411yescharacteristic
24C22×C4×D61—21no—
25C22×#92418—22no—
26C4×D244—22no—
27C4×D244—22no—
28#14519734—44no—
29C2×C4⋊Dic61C2×C411yescharacteristic
30C2×C4⋊Dic61C2×C411yescharacteristic
31C2×C4⋊Dic61C2×C411yescharacteristic
32C2×#11758196—21no—
33C2×#11758196—21no—
34C2×#11758198—21no—
35C2×#11758198—21no—
36C2×#11758198—21no—
37C2×#11758198—21no—
38C2×#11758198—21no—
39C2×C4×Dic61—21no—
40C4⋊#92418—24no—
41#14519688—42no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45C22×C8×C61—22no—
46C2×C42×C61C2×C411yescharacteristic
47C2×C42×C61C2×C411yescharacteristic
48C2×C42×C61D411yescharacteristic
49C2×C42×C61D411yescharacteristic
50C2×C42×C61D411yescharacteristic
51C2×C42×C61D411yescharacteristic
52C2×C42×C61C2311yescharacteristic
53#97×C61—24no—
54C23×D61—21no—
55C22×C4×C61C22⋊C411yescharacteristic
56C22×C4×C61C22⋊C411yescharacteristic
57C22×C4×C61C22⋊C411yescharacteristic
58C22×C4×C61C22⋊C411yescharacteristic
59C22×C4×C61C22×C411yescharacteristic
60C22×C4×C61C2×D411yescharacteristic
61C22×C4×C61C2×D411yescharacteristic
62C22×Dic61—21no—
63C22×Dic61—21no—
64C22×Dic61—21no—
65C2×D244—21no—
66C2×D244—41no—
67C2×D244—41no—
68C2×D244M1612yes—
69C2×C4×D61—24no—
70C2×C4×D61—42no—
71C2×C4×D61—42no—
72C2×C8×C61—24no—
73C2×C8×C61—42no—
74C2×C8×C61—42no—
75C42×C61—22no—
76C42×C61—22no—
77C42×C61—21no—
78C42×C61—21no—
79C42×C61—21no—
80C42×C61—22no—
81C42×C61—21no—
82C42×C61—41no—
83C42×C61—41no—
84#11758198—24no—
85#11758198—42no—
86#11758198—42no—
87#11758198—41no—
88#11758198—42no—
89#11758198—41no—
90C4⋊Dic61—21no—
91C4⋊Dic61—41no—
92C4⋊Dic61—41no—
93C4⋊Dic61M1612yes—
94#11758196—42no—
95#11758196—42no—
96C4×Dic61—42no—
97C2×#92418—24no—
98C2×#92418—42no—
99C2×#92418—42no—
100C23×C61C2×C22⋊C411yescharacteristic
101C22×D61—22no—
102C22×D61—41no—
103C22×D61—41no—
104C22×D61—41no—
105C22×D61—41no—
106C22×D61—41no—
107C22×D61—41no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
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—21no—
124C2×C4×C61#10412yes—
125C2×C4×C61#10412yes—
126C2×C4×C61C2×M1611yescharacteristic
127C2×C4×C61C2×M1611yescharacteristic
128C2×C4×C61AGL(1,ℤ/8)12yes—
129C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C61#13711yescharacteristic
131C2×Dic61—22no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140D244—42no—
141D244—42no—
142C4×D61—48no—
143C8×C61—44no—
144#92418—44no—
145#7628—611nomaximal, Sylow
146C22×C61#40711yescharacteristic
147C22×C61#41011yescharacteristic
148C22×C61#41311yescharacteristic
149C22×C61#41711yescharacteristic
150C22×C61#41811yescharacteristic
151C22×C61C2×#10411yescharacteristic
152C22×C61C2×#10411yescharacteristic
153C2×D61—42no—
154C2×D61—42no—
155C2×D61—42no—
156C2×D61—81no—
157C2×D61—81no—
158C2×D61—81no—
159C2×D61—81no—
160C4×C61—21no—
161C4×C61—21no—
162C4×C61—22no—
163C4×C61—22no—
164C4×C61—21no—
165C4×C61—21no—
166C4×C61—22no—
167C4×C61—41no—
168C4×C61—41no—
169Dic61—42no—
170Dic61—81no—
171Dic61—81no—
172#2293—611no—
173#1767—611no—
174#1745D6111yescharacteristic, complemented
175#1271—612no—
176#1270—612no—
177C2×C61#146411yescharacteristic
178C2×C61#148911yescharacteristic
179C2×C61#149011yescharacteristic
180C2×C61#150511yescharacteristic
181C2×C61#150911yescharacteristic
182C2×C61#152411yescharacteristic
183C2×C61#155711yescharacteristic
184D61—82no—
185C2×C4×D4—611no—
186C2×#117—1221no—
187C2×C4⋊C8—1221no—
188C2×#97—21no—
189C2×#97—1221no—
190#390—611no—
191#390—611no—
192#389—611no—
193#389—611no—
194#388—1221no—
195#388—1221no—
196C4×C4⋊C4—611no—
197C4×C22⋊C4—1221no—
198C43C2×D6111yescharacteristic
199#336—21no—
200#336—612no—
201#336C2×D6112yes—
202C61#762811yescharacteristic, complemented, Sylow
203C22×D4—611no—
204C23×C4—1221no—
205C22×C8—22no—
206C22×C8—1222no—
207C4×D4—1222no—
208C4×D4—1222no—
209#117—2444no—
210C2×C4⋊C4—611no—
211C2×C4⋊C4—611no—
212C2×C4⋊C4—611no—
213C2×C4⋊C4—1221no—
214C2×C4⋊C4—1221no—
215C2×C22⋊C4—1221no—
216C2×C22⋊C4—1221no—
217C2×C22⋊C4—1221no—
218C2×C22⋊C4—1221no—
219C2×C22⋊C4—1221no—
220C2×C42—1221no—
221C2×C42C4×D6111yescharacteristic
222C2×C42C4×D6111yescharacteristic
223C2×C42D24411yescharacteristic
224C2×C42D24411yescharacteristic
225C2×C42C22⋊D6111yescharacteristic
226C2×C42C22⋊D6111yescharacteristic
227C2×C42C22×D6111yescharacteristic
228C4⋊C8—1224no—
229#97—24no—
230#97—2442no—
231#95—1221no—
232#95—1221no—
233#95—1221no—
234C24—1221no—
235C2×D4—612no—
236C2×D4—1221no—
237C2×D4—2441no—
238C2×D4—2441no—
239C22×C4—1224no—
240C22×C4—1221no—
241C22×C4—1221no—
242C22×C4—1221no—
243C22×C4—2442no—
244C22×C4—2442no—
245C22×C4#1175819811yescharacteristic
246C22×C4#1175819811yescharacteristic
247C22×C4#1175819811yescharacteristic
248C22×C4#1175819811yescharacteristic
249C22×C4C2×C4×D6111yescharacteristic
250C22×C4C2×D24411yescharacteristic
251C22×C4C2×C22⋊D6111yescharacteristic
252C2×C8—24no—
253C2×C8—42no—
254C2×C8—42no—
255C2×C8—1224no—
256C2×C8—2442no—
257C2×C8—2442no—
258C4⋊C4—612no—
259C4⋊C4—1221no—
260C4⋊C4—2441no—
261C4⋊C4—2441no—
262C4⋊C4—2442no—
263C4⋊C4—2442no—
264C22⋊C4—1224no—
265C22⋊C4—2442no—
266C22⋊C4—2441no—
267C22⋊C4—2442no—
268C22⋊C4—2442no—
269C22⋊C4—2441no—
270C42—21no—
271C42—22no—
272C42—22no—
273C42—21no—
274C42—21no—
275C42—22no—
276C42—21no—
277C42—41no—
278C42—41no—
279C42—2442no—
280C23—1222no—
281C23—2441no—
282C23—2441no—
283C23—2441no—
284C23—2441no—
285C23—2441no—
286C23—2441no—
287C23C2×#1175819811yescharacteristic
288D4—2442no—
289D4—2442no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
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—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—1222no—
307C2×C4—2448no—
308C2×C4—2441no—
309C2×C4—2441no—
310C2×C4—2441no—
311C2×C4—2441no—
312C2×C4—2441no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4#1451970312yes—
317C2×C4#1451970512yes—
318C2×C4M16×D6111yescharacteristic
319C2×C4M16×D6111yescharacteristic
320C2×C4#1451980212yes—
321C2×C4#1451980511yescharacteristic
322C2×C4#1451981011yescharacteristic
323C8—44no—
324C8—2444no—
325C22—4881no—
326C22—4881no—
327C22—4881no—
328C22—4881no—
329C22—2442no—
330C22—2442no—
331C22—2442no—
332C22#1683972511yescharacteristic
333C22#1683973511yescharacteristic
334C22#1683974411yescharacteristic
335C22#1683976411yescharacteristic
336C22#1683976611yescharacteristic
337C22C2×#1451970311yescharacteristic
338C22C2×#1451970511yescharacteristic
339C4—21no—
340C4—21no—
341C4—22no—
342C4—22no—
343C4—22no—
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—4881no—
349C4—4881no—
350C4—2442no—
351C2—4882no—
352C2#2144415111yescharacteristic
353C2#2144425911yescharacteristic
354C2#2144426111yescharacteristic
355C2#2144432611yescharacteristic
356C2#2144434511yescharacteristic
357C2#2144440811yescharacteristic
358C2#2144454211yescharacteristic
subgroupG/H
centerC23C2×#11758198
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1745C2
socleC23×C61C2×C22⋊C4
prime radicalC22×D244C2×C4
cosocleC2×C42×C61C23
hypercenter#1745D61
hypocenterC61#7628
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C43 ◁ #1745

Complements

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

NH ≅ G/Ntype
2. #21445672C2semidirect
3. #21443643C2semidirect
5. C61×#1745C2semidirect
174. #1745D61semidirect
202. C61#7628semidirect

Maximal subgroups

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

subgroupindex
#214482832
#214456722
#214436432
#214436392
C61×#17452
#762861