Finite Group Databasebeta

← #29577280

Subgroups — #29577280

Order 15616.

430 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 93 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#21456848C211yesmaximal, characteristic
2#21454960C211yesmaximal, characteristic
3#21446767C211yesmaximal, characteristic, complemented
4#21444535C211yesmaximal, characteristic, complemented
5#21444342C211yesmaximal, characteristic
6#21443688C211yesmaximal, characteristic, complemented
7C61×#1285C211yesmaximal, characteristic, complemented
8C2×#14519777C2211yescharacteristic
9#16840296C2211yescharacteristic
10#16840156C412yescomplemented
11#16840131C412yescomplemented
12#16839973—21no—
13#16839968—21no—
14#16839920—21no—
15#16839903—21no—
16#16839890—21no—
17#16839835—21no—
18#16839830—21no—
19#16839825—21no—
20#16839822—21no—
21#16839819C2211yescharacteristic
22#16839787—21no—
23C2×C4⋊#92418C2211yescharacteristic
24#16839524—21no—
25#16839524—21no—
26#16839507—21no—
27#16839507—21no—
28#16839498—21no—
29#16839495—21no—
30C61×#432C2211yescharacteristic
31C61×#432C2211yescharacteristic
32C4×C4⋊C4×C61C2211yescharacteristic
33C22×Dic122—21no—
34C2×Dic244—22no—
35C2×#11758190—22no—
36C2×#11758189—21no—
37C22×#92418D411yescharacteristic
38C22×#92418D411yescharacteristic
39C2×C8×D61—21no—
40#14519777—21no—
41#14519777—21no—
42#14519777—21no—
43#14519777C2×C412yes—
44#14519771—21no—
45#14519769C2×C411yescharacteristic
46#14519765C2×C411yescharacteristic
47#14519760—21no—
48#14519756D411yescharacteristic
49#14519751D411yescharacteristic
50C4×Dic122D411yescharacteristic
51C4×D244D411yescharacteristic
52C4×C22⋊D61—21no—
53#14519734—21no—
54C2×C4⋊Dic61—21no—
55C2×C4⋊Dic61—21no—
56C4⋊#92418—21no—
57C4⋊#92418—21no—
58C4⋊#92418—21no—
59#14519706—21no—
60#14519706—21no—
61#14519702—22no—
62#14519702—22no—
63C22⋊#92418—21no—
64#14519689—21no—
65#14519689—21no—
66#14519688—21no—
67#14519687—21no—
68C8×Dic61—21no—
69C2×C4⋊C4×C61—21no—
70C2×C42×C61—21no—
71C2×C42×C61C2311yescharacteristic
72C4⋊C8×C61—21no—
73C4⋊C8×C61D411yescharacteristic
74C4⋊C8×C61D411yescharacteristic
75C22⋊C8×C61—21no—
76C22⋊C8×C61—21no—
77#97×C61—21no—
78#97×C61C2×C412yes—
79#95×C61—21no—
80C22×C4×C61—41no—
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61C2×D411yescharacteristic
83C22×C4×C61#4111yescharacteristic
84C2×C22⋊D61—21no—
85C22×Dic61—41no—
86C2×D244C22⋊C411yescharacteristic
87C2×C4×D61—21no—
88C2×Dic122—22no—
89C2×Dic122—41no—
90C2×Dic122—82no—
91C2×Dic122C22⋊C411yescharacteristic
92C2×C8×C61—22no—
93C2×C8×C61—21no—
94C2×C8×C61—21no—
95C4⋊C4×C61—22no—
96C4⋊C4×C61—41no—
97C42×C61—81no—
98C42×C61C22×C411yescharacteristic
99C42×C61C2×D411yescharacteristic
100C42×C61C2×D411yescharacteristic
101C42×C61#4111yescharacteristic
102C22⋊Dic61—21no—
103#11758198—21no—
104#11758198—21no—
105#11758198—21no—
106#11758198—21no—
107C4⋊Dic61—22no—
108C4⋊Dic61—22no—
109C4⋊Dic61—41no—
110C4⋊Dic61—41no—
111C4⋊Dic61C22⋊C411yescharacteristic
112C4⋊Dic61C22⋊C411yescharacteristic
113#11758196—21no—
114#11758196—21no—
115#11758196—21no—
116#11758196—21no—
117C4×Dic61—21no—
118C2×#92418—21no—
119C2×#92418—21no—
120C2×#92418—41no—
121C2×#92418—41no—
122C2×#92418—41no—
123Dic244—82no—
124#11758190—82no—
125#11758189—81no—
126C8×D61—81no—
127C23×C61#12111yescharacteristic
128C22×D61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—41no—
134C2×C4×C61—42no—
135C2×C4×C61—81no—
136C2×C4×C61—81no—
137C2×C4×C61C2×C22⋊C411yescharacteristic
138C2×C4×C61C4×D411yescharacteristic
139C2×C4×C61C4×D411yescharacteristic
140C2×C4×C61#12011yescharacteristic
141C2×C4×C61#12111yescharacteristic
142C2×C4×C61#12311yescharacteristic
143C22⋊D61—41no—
144C22⋊D61—41no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—42no—
149C2×Dic61—82no—
150D244—41no—
151C4×D61—41no—
152C4×D61—41no—
153Dic122—41no—
154Dic122—42no—
155Dic122—42no—
156Dic122—82no—
157C8×C61—42no—
158C8×C61—41no—
159C8×C61—41no—
160#92418—41no—
161#92418—41no—
162#92418—81no—
163#9376—611nomaximal, Sylow
164C22×C61—21no—
165C22×C61—21no—
166C22×C61#38611yescharacteristic
167C22×C61#47111yescharacteristic
168C22×C61#47311yescharacteristic
169C2×D61—41no—
170C2×D61—41no—
171C2×D61—41no—
172C4×C61—21no—
173C4×C61—21no—
174C4×C61—21no—
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—82no—
178C4×C61#45511yescharacteristic
179C4×C61#45611yescharacteristic
180Dic61—41no—
181Dic61—41no—
182Dic61—41no—
183Dic61—82no—
184#3218—611no—
185#2992—611no—
186#1987—611no—
187#1556—611no—
188#1509—611no—
189#1290—611no—
190#1285D6111yescharacteristic, complemented
191C2×C61—21no—
192C2×C61—21no—
193C2×C61#188211yescharacteristic
194C2×C61#190811yescharacteristic
195C2×C61#191011yescharacteristic
196D61—81no—
197C2×C4⋊Q8—611no—
198#529—611no—
199#497—612no—
200#491—612no—
201#462—1221no—
202#461—1221no—
203#451—1221no—
204#448—1221no—
205#446—1221no—
206#435—1221no—
207#435—1221no—
208C8×D4—1221no—
209#433—1221no—
210#432—611no—
211#432C2×D6111yescharacteristic
212#432C2×D6111yescharacteristic
213#424—1221no—
214C2×C4⋊C8—611no—
215C4×C4⋊C4C2×D6111yescharacteristic
216#340—1221no—
217#340—1221no—
218#332—1221no—
219#332—1221no—
220#328—1221no—
221#327—1221no—
222C61#937611yescharacteristic, complemented, Sylow
223C22×Q8—1221no—
224C2×Q16—1222no—
225C2×SD16—1222no—
226C2×M16—1221no—
227C22×C8—611no—
228C22×C8—611no—
229C22×C8—1221no—
230C4⋊Q8—612no—
231C4⋊Q8—1221no—
232C4⋊Q8—1221no—
233C4⋊Q8—1221no—
234#126—1221no—
235#125—611no—
236#124—611no—
237#123—1221no—
238C22⋊Q8—611no—
239#121—611no—
240C4×Q8—611no—
241C4×D4—611no—
242C4×D4—1221no—
243#117—1221no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—1221no—
246C2×C4⋊C4—1221no—
247C2×C42—21no—
248C2×C42C22×D6111yescharacteristic
249C4⋊C8—21no—
250C4⋊C8—1221no—
251C4⋊C8—1221no—
252C4⋊C8—1221no—
253C4⋊C8—1221no—
254C4⋊C8—1221no—
255C4⋊C8D24411yescharacteristic
256C4⋊C8D24411yescharacteristic
257#103—1222no—
258#103—1222no—
259C22⋊C8—21no—
260C22⋊C8—21no—
261C22⋊C8—1221no—
262C22⋊C8—1221no—
263C22⋊C8—1221no—
264#97—21no—
265#97—1221no—
266#97—1221no—
267#97C4×D6112yes—
268C4×C8—1221no—
269#95—21no—
270C2×Q8—611no—
271C2×Q8—1222no—
272C2×Q8—4882no—
273C2×Q8—2441no—
274C2×D4—611no—
275C2×D4—1221no—
276C22×C4—41no—
277C22×C4—1221no—
278C22×C4—2441no—
279C22×C4#1175822211yescharacteristic
280C22×C4D4×D6111yescharacteristic
281C22×C4D4×D6111yescharacteristic
282Q16—4882no—
283SD16—4882no—
284M16—4881no—
285C2×C8—22no—
286C2×C8—21no—
287C2×C8—21no—
288C2×C8—1221no—
289C2×C8—1221no—
290C2×C8—4881no—
291C2×C8—2441no—
292C2×C8—2441no—
293C2×C8—2441no—
294C4⋊C4—22no—
295C4⋊C4—41no—
296C4⋊C4—611no—
297C4⋊C4—611no—
298C4⋊C4—1221no—
299C4⋊C4—1221no—
300C4⋊C4—1221no—
301C4⋊C4—1221no—
302C4⋊C4—1222no—
303C4⋊C4—1222no—
304C4⋊C4—2441no—
305C4⋊C4—2441no—
306C22⋊C4—1221no—
307C22⋊C4—1221no—
308C22⋊C4—1221no—
309C22⋊C4—1221no—
310C22⋊C4—1221no—
311C42—81no—
312C42—1221no—
313C42C2×C4×D6111yescharacteristic
314C42C2×D24411yescharacteristic
315C42D4×D6111yescharacteristic
316C42#1175822611yescharacteristic
317C23—1221no—
318C23#1451975011yescharacteristic
319Q8—4882no—
320Q8—2442no—
321Q8—2442no—
322Q8—2441no—
323D4—2441no—
324D4—2441no—
325D4—2441no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—4882no—
338C2×C4—2442no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4C22⋊C4×D6111yescharacteristic
342C2×C4#1451973911yescharacteristic
343C2×C4C4×D24411yescharacteristic
344C2×C4#1451974711yescharacteristic
345C2×C4#1451975211yescharacteristic
346C2×C4#1451976211yescharacteristic
347C8—42no—
348C8—41no—
349C8—41no—
350C8—4881no—
351C8—2441no—
352C8—2441no—
353C22—21no—
354C22—21no—
355C22—2441no—
356C22—2441no—
357C22—2441no—
358C22#1683964011yescharacteristic
359C22#1684002411yescharacteristic
360C22#1684003611yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—82no—
367C4—4882no—
368C4—2441no—
369C4—2441no—
370C4—2441no—
371C4#1683994111yescharacteristic
372C4#1683994611yescharacteristic
373C2—21no—
374C2—21no—
375C2—4881no—
376C2#2144618911yescharacteristic
377C2#2144633511yescharacteristic
378C2#2144634511yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1285C2
socleC22×C61#386
prime radical#14519751D4
cosocleC2×C42×C61C23
hypercenter#1285D61
hypocenterC61#9376
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1285

Complements

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

NH ≅ G/Ntype
3. #21446767C2semidirect
4. #21444535C2semidirect
6. #21443688C2semidirect
7. C61×#1285C2semidirect
10. #16840156C4semidirect
11. #16840131C4semidirect
190. #1285D61semidirect
222. C61#9376semidirect

Maximal subgroups

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

subgroupindex
#214568482
#214549602
#214467672
#214445352
#214443422
#214436882
C61×#12852
#937661