Finite Group Databasebeta

← #29590785

Subgroups — #29590785

Order 15616.

434 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 83 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#21449078C211yesmaximal, characteristic
2#21445807C211yesmaximal, characteristic
3#21443844C212yesmaximal, complemented
4#21443820C212yesmaximal, complemented
5C61×#1466C211yesmaximal, characteristic
6C2×#14519736C411yescharacteristic, complemented
7C2×#14519692—21no—
8#16839701C411yescharacteristic, complemented
9#16839698C2211yescharacteristic
10#16839692C411yescharacteristic, complemented
11#16839690—21no—
12#16839687C2211yescharacteristic
13#16839676—21no—
14#16839622—21no—
15C4×#11758196—21no—
16C4×C22⋊Dic61—21no—
17C4×C22⋊Dic61C411yescharacteristic, complemented
18#16839529C2212yes—
19C2×C4×D4×C61C2211yescharacteristic
20C61×#432—21no—
21C61×#323—21no—
22C61×#323C2212yes—
23#14519736—41no—
24#14519736—41no—
25C2×C4⋊Dic61—41no—
26C2×C4⋊Dic61C2×C411yescharacteristic
27C2×C4⋊Dic61C2×C411yescharacteristic
28C2×#11758196—21no—
29C2×#11758196—21no—
30C2×C22⋊Dic61—21no—
31C2×C22⋊Dic61—21no—
32C2×C22⋊Dic61—21no—
33C2×C22⋊Dic61—21no—
34C2×C22⋊Dic61—22no—
35C2×C4×Dic61—21no—
36C2×C4×Dic61—21no—
37#14519692—42no—
38#14519684—21no—
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42#14519684—41no—
43#14519684C2×C411yescharacteristic
44#14519684C2×C411yescharacteristic
45C22×D4×C61D411yescharacteristic
46C23×C4×C61C2×C411yescharacteristic
47C23×C4×C61D411yescharacteristic
48C4×D4×C61—41no—
49C4×D4×C61—41no—
50C2×C4⋊C4×C61C2×C411yescharacteristic
51C2×C22⋊C4×C61D411yescharacteristic
52C2×C22⋊C4×C61C2311yescharacteristic
53C2×C42×C61D411yescharacteristic
54C4⋊C8×C61—41no—
55C22⋊C8×C61—22no—
56#97×C61—41no—
57C24×C61C22⋊C411yescharacteristic
58C24×C61C2×D411yescharacteristic
59C2×D4×C61—21no—
60C2×D4×C61—21no—
61C2×D4×C61—41no—
62C2×D4×C61—41no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—42no—
68C22×C4×C61—42no—
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22×C411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—42no—
79C2×C8×C61—42no—
80C4⋊C4×C61—41no—
81C22⋊C4×C61—41no—
82C22⋊C4×C61—41no—
83C42×C61—21no—
84C42×C61—21no—
85C22⋊Dic61—42no—
86C22⋊Dic61—42no—
87C22⋊Dic61—42no—
88C22⋊Dic61—41no—
89C22⋊Dic61—41no—
90C22⋊Dic61—42no—
91C22⋊Dic61—42no—
92C4⋊Dic61—41no—
93C4⋊Dic61—41no—
94C4⋊Dic61—82no—
95#11758196—42no—
96#11758196—42no—
97C4×Dic61—42no—
98C4×Dic61—41no—
99C4×Dic61—41no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61—41no—
106C23×C61—41no—
107C23×C61—41no—
108C23×C61—41no—
109C23×C61C2×C22⋊C411yescharacteristic
110C23×C61AGL(1,ℤ/8)11yescharacteristic
111C23×C61#13711yescharacteristic
112D4×C61—42no—
113D4×C61—42no—
114C2×C4×C61—22no—
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—42no—
122C2×C4×C61—42no—
123C2×C4×C61—42no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—81no—
128C2×C4×C61#9911yescharacteristic
129C2×C4×C61#9911yescharacteristic
130C2×Dic61—22no—
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—41no—
141C2×Dic61—41no—
142C2×Dic61—82no—
143C2×Dic61—82no—
144C2×Dic61—82no—
145C8×C61—82no—
146#11822—611nomaximal, Sylow
147C22×C61—21no—
148C22×C61—21no—
149C22×C61—21no—
150C22×C61—21no—
151C22×C61—41no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61—41no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61—81no—
159C22×C61—81no—
160C22×C61—81no—
161C22×C61C2×#9911yescharacteristic
162C22×C61#41711yescharacteristic
163C22×C61#42111yescharacteristic
164C4×C61—21no—
165C4×C61—41no—
166C4×C61—41no—
167C4×C61—41no—
168C4×C61—41no—
169C4×C61#35212yes—
170Dic61—42no—
171Dic61—81no—
172Dic61—81no—
173Dic61—81no—
174Dic61—162no—
175#2395—611no—
176#1799—611no—
177#1466D6111yescharacteristic
178#1352—612no—
179#1344—612no—
180C2×C61—21no—
181C2×C61—21no—
182C2×C61—41no—
183C2×C61—41no—
184C2×C61—81no—
185C2×C61#151311yescharacteristic
186C2×C61C2×#35211yescharacteristic
187C2×C61#212611yescharacteristic
188C2×C4×D4C2×D6111yescharacteristic
189C2×#117—611no—
190#432—21no—
191C2×#99—1221no—
192#400—611no—
193#399—611no—
194#398—611no—
195#397—611no—
196#397—1221no—
197#394—1221no—
198#380—1221no—
199C4×C4⋊C4—1221no—
200C4×C22⋊C4—611no—
201C4×C22⋊C4—1221no—
202#342—612no—
203#323—21no—
204#323C2×D6112yes—
205C61#1182211yescharacteristic, complemented, Sylow
206C22×D4D24411yescharacteristic
207C23×C4C4×D6111yescharacteristic
208C23×C4D24411yescharacteristic
209C4×D4—41no—
210C4×D4—41no—
211#117—2441no—
212#117—2441no—
213C2×C4⋊C4—611no—
214C2×C4⋊C4—611no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4—1221no—
217C2×C4⋊C4—2441no—
218C2×C4⋊C4C4×D6111yescharacteristic
219C2×C22⋊C4—1221no—
220C2×C22⋊C4—1221no—
221C2×C22⋊C4—1221no—
222C2×C22⋊C4—1221no—
223C2×C22⋊C4—1222no—
224C2×C22⋊C4C22⋊D6111yescharacteristic
225C2×C22⋊C4C22×D6111yescharacteristic
226C2×C42—1221no—
227C2×C42—1221no—
228C2×C42C22⋊D6111yescharacteristic
229C4⋊C8—41no—
230#99—2442no—
231C22⋊C8—22no—
232#97—41no—
233#95—611no—
234#95—611no—
235#95—1221no—
236#95—1221no—
237#95—1221no—
238#95—1221no—
239#95—2441no—
240C24#1175819811yescharacteristic
241C24C2×D24411yescharacteristic
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—41no—
245C2×D4—41no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—2442no—
257C22×C4#1175819811yescharacteristic
258C22×C4#1175819811yescharacteristic
259C22×C4#1175819811yescharacteristic
260C22×C4C2×C4×D6111yescharacteristic
261C22×C4C2×C22⋊D6111yescharacteristic
262C2×C8—42no—
263C4⋊C4—41no—
264C4⋊C4—4882no—
265C4⋊C4—2441no—
266C4⋊C4—2441no—
267C4⋊C4—2442no—
268C4⋊C4—2442no—
269C22⋊C4—41no—
270C22⋊C4—41no—
271C22⋊C4—2442no—
272C22⋊C4—2442no—
273C22⋊C4—2442no—
274C22⋊C4—2442no—
275C22⋊C4—2442no—
276C22⋊C4—2441no—
277C22⋊C4—2441no—
278C42—21no—
279C42—21no—
280C42—2442no—
281C42—2441no—
282C42—2441no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23—41no—
292C23C2×#1175819811yescharacteristic
293C23#1451980511yescharacteristic
294C23#1451981011yescharacteristic
295D4—42no—
296D4—42no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—81no—
311C2×C4—1222no—
312C2×C4—4882no—
313C2×C4—4882no—
314C2×C4—4882no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4#1451969111yescharacteristic
327C2×C4#1451969111yescharacteristic
328C8—82no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—81no—
341C22—81no—
342C22—81no—
343C22C2×#1451969111yescharacteristic
344C22#1683976411yescharacteristic
345C22#1683977811yescharacteristic
346C4—21no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4—9762no—
352C4—4881no—
353C4—4881no—
354C4—4881no—
355C4—2442no—
356C4#1683955312yes—
357C2—21no—
358C2—21no—
359C2—41no—
360C2—41no—
361C2—81no—
362C2#2144436311yescharacteristic
363C2C2×#1683955311yescharacteristic
364C2#2144748211yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1466C2
socleC22×C61C2×#99
prime radicalC22×D4×C61D4
cosocleC2×C22⋊C4×C61C23
hypercenter#1466D61
hypocenterC61#11822
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1466

Complements

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

NH ≅ G/Ntype
3. #21443844C2semidirect
4. #21443820C2semidirect
6. C2×#14519736C4semidirect
8. #16839701C4semidirect
10. #16839692C4semidirect
17. C4×C22⋊Dic61C4semidirect
205. C61#11822semidirect

Maximal subgroups

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

subgroupindex
#214490782
#214458072
#214438442
#214438202
C61×#14662
#1182261