Finite Group Databasebeta

← #29577271

Subgroups — #29577271

Order 15616.

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

normal subgroups only

This group has 418 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#21457042C211yesmaximal, characteristic
2#21454955C211yesmaximal, characteristic
3#21446770C211yesmaximal, characteristic, complemented
4#21444544C211yesmaximal, characteristic, complemented
5#21444345C211yesmaximal, characteristic
6#21443674C211yesmaximal, characteristic, complemented
7C61×#1290C211yesmaximal, characteristic, complemented
8C2×#14519777C2211yescharacteristic
9#16840296C2211yescharacteristic
10#16840171C412yescomplemented
11#16840122C412yescomplemented
12#16840093—21no—
13#16840076—21no—
14#16840058—21no—
15#16840053—21no—
16#16839891—21no—
17#16839833—21no—
18#16839832—21no—
19C8×C22⋊D61—21no—
20#16839822—21no—
21#16839819C2211yescharacteristic
22#16839787—21no—
23C4×C4⋊Dic61C2211yescharacteristic
24#16839525—21no—
25#16839525—21no—
26#16839510—21no—
27#16839510—21no—
28#16839500—21no—
29#16839497—21no—
30C61×#432C2211yescharacteristic
31C61×#432C2211yescharacteristic
32C2×C4⋊C8×C61C2211yescharacteristic
33C22×Dic122—21no—
34C2×#11758189—21no—
35C2×C8×D61—21no—
36#14519777—21no—
37#14519777—21no—
38#14519777—21no—
39#14519777C2×C412yes—
40#14519771—21no—
41#14519769C2×C411yescharacteristic
42#14519765C2×C411yescharacteristic
43#14519760—21no—
44#14519756D411yescharacteristic
45#14519751D411yescharacteristic
46C4×Dic122D411yescharacteristic
47C4×D244D411yescharacteristic
48C4×C22⋊D61—21no—
49#14519734—21no—
50C2×C4⋊Dic61—21no—
51C2×C4⋊Dic61—21no—
52C2×C4⋊Dic61—21no—
53C2×C4×Dic61—21no—
54#14519711—22no—
55#14519709—22no—
56C4⋊#92418D411yescharacteristic
57C4⋊#92418D411yescharacteristic
58#14519706—21no—
59#14519706—21no—
60#14519702—22no—
61#14519699—22no—
62C22⋊#92418—21no—
63#14519689—21no—
64#14519689—21no—
65#14519688—21no—
66#14519687—21no—
67C8×Dic61—21no—
68#14519684—21no—
69C22×C8×C61D411yescharacteristic
70C22×C8×C61D411yescharacteristic
71C2×C42×C61C2311yescharacteristic
72C4⋊C8×C61—21no—
73C4⋊C8×C61—21no—
74C4⋊C8×C61—21no—
75C4⋊C8×C61—21no—
76C22⋊C8×C61—21no—
77C22⋊C8×C61—21no—
78#97×C61—21no—
79#97×C61C2×C412yes—
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61#4111yescharacteristic
83C2×C22⋊D61—21no—
84C22×Dic61—41no—
85C22×Dic61—41no—
86C2×D244C22⋊C411yescharacteristic
87C2×C4×D61—21no—
88C2×Dic122—22no—
89C2×Dic122—41no—
90C2×Dic122—81no—
91C2×Dic122—81no—
92C2×Dic122C22⋊C411yescharacteristic
93C2×C8×C61—22no—
94C2×C8×C61—21no—
95C2×C8×C61—21no—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C2×C8×C61—41no—
99C42×C61C22×C411yescharacteristic
100C42×C61C2×D411yescharacteristic
101C42×C61C2×D411yescharacteristic
102C42×C61#4111yescharacteristic
103C22⋊Dic61—21no—
104#11758198—21no—
105#11758198—21no—
106#11758198—21no—
107#11758198—21no—
108C4⋊Dic61—22no—
109C4⋊Dic61—22no—
110C4⋊Dic61—22no—
111C4⋊Dic61—41no—
112C4⋊Dic61—41no—
113C4⋊Dic61—41no—
114C4⋊Dic61C22⋊C411yescharacteristic
115C4⋊Dic61C22⋊C411yescharacteristic
116#11758196—21no—
117#11758196—21no—
118#11758196—21no—
119#11758196—21no—
120C4×Dic61—21no—
121C4×Dic61—81no—
122C2×#92418—21no—
123C2×#92418—21no—
124#11758189—81no—
125C8×D61—81no—
126C23×C61#12111yescharacteristic
127C22×D61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—41no—
133C2×C4×C61C2×C22⋊C411yescharacteristic
134C2×C4×C61C4×D411yescharacteristic
135C2×C4×C61C4×D411yescharacteristic
136C2×C4×C61#12011yescharacteristic
137C2×C4×C61#12111yescharacteristic
138C2×C4×C61#12311yescharacteristic
139C22⋊D61—41no—
140C22⋊D61—41no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—42no—
145C2×Dic61—42no—
146C2×Dic61—81no—
147C2×Dic61—81no—
148C2×Dic61—81no—
149C2×Dic61—81no—
150D244—41no—
151C4×D61—41no—
152C4×D61—41no—
153Dic122—41no—
154Dic122—82no—
155Dic122—82no—
156C8×C61—42no—
157C8×C61—41no—
158C8×C61—41no—
159C8×C61—81no—
160#92418—41no—
161#92418—41no—
162#9375—611nomaximal, Sylow
163C22×C61—21no—
164C22×C61—21no—
165C22×C61#38611yescharacteristic
166C22×C61#47111yescharacteristic
167C22×C61#47211yescharacteristic
168C2×D61—41no—
169C2×D61—41no—
170C2×D61—41no—
171C4×C61—21no—
172C4×C61—21no—
173C4×C61—21no—
174C4×C61—21no—
175C4×C61—21no—
176C4×C61#45511yescharacteristic
177C4×C61#45611yescharacteristic
178Dic61—41no—
179Dic61—41no—
180Dic61—41no—
181Dic61—82no—
182Dic61—82no—
183#3238—611no—
184#2992—611no—
185#1988—611no—
186#1558—611no—
187#1509—611no—
188#1290D6111yescharacteristic, complemented
189#1285—611no—
190C2×C61—21no—
191C2×C61—21no—
192C2×C61#188211yescharacteristic
193C2×C61#190711yescharacteristic
194C2×C61#190911yescharacteristic
195D61—81no—
196C2×C4⋊Q8—611no—
197#529—611no—
198#501—612no—
199#489—612no—
200#483—1221no—
201#480—1221no—
202#477—1221no—
203#476—1221no—
204#446—1221no—
205#435—1221no—
206#435—1221no—
207C8×D4—1221no—
208#433—1221no—
209#432—611no—
210#432C2×D6111yescharacteristic
211#432C2×D6111yescharacteristic
212#424—1221no—
213C2×C4⋊C8C2×D6111yescharacteristic
214C4×C4⋊C4—611no—
215#340—1221no—
216#340—1221no—
217#333—1221no—
218#333—1221no—
219#328—1221no—
220#327—1221no—
221C61#937511yescharacteristic, complemented, Sylow
222C22×Q8—1221no—
223C2×M16—1221no—
224C22×C8—1221no—
225C22×C8D24411yescharacteristic
226C22×C8D24411yescharacteristic
227C4⋊Q8—612no—
228C4⋊Q8—1221no—
229C4⋊Q8—1221no—
230C4⋊Q8—1221no—
231#126—1221no—
232#125—611no—
233#124—611no—
234#123—1221no—
235C22⋊Q8—611no—
236#121—611no—
237C4×Q8—611no—
238C4×D4—611no—
239C4×D4—1221no—
240#117—1221no—
241C2×C4⋊C4—1221no—
242C2×C4⋊C4—1221no—
243C2×C4⋊C4—1221no—
244C2×C42—1221no—
245C2×C42C22×D6111yescharacteristic
246#107—1222no—
247#106—1222no—
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8—21no—
251C4⋊C8—21no—
252C4⋊C8—611no—
253C4⋊C8—611no—
254C4⋊C8—1221no—
255C4⋊C8—1221no—
256#103—1222no—
257#102—1222no—
258C22⋊C8—21no—
259C22⋊C8—21no—
260C22⋊C8—1221no—
261C22⋊C8—1221no—
262C22⋊C8—1221no—
263#97—21no—
264#97—1221no—
265#97—1221no—
266#97C4×D6112yes—
267C4×C8—1221no—
268#95—1221no—
269C2×Q8—611no—
270C2×Q8—1222no—
271C2×Q8—4881no—
272C2×Q8—4881no—
273C2×Q8—2441no—
274C2×D4—611no—
275C2×D4—1221no—
276C22×C4—1221no—
277C22×C4—2441no—
278C22×C4—2441no—
279C22×C4C2×D24411yescharacteristic
280C22×C4D4×D6111yescharacteristic
281C22×C4#1175822611yescharacteristic
282M16—4881no—
283C2×C8—22no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—1221no—
290C2×C8—1221no—
291C2×C8—4881no—
292C4⋊C4—611no—
293C4⋊C4—611no—
294C4⋊C4—1222no—
295C4⋊C4—1221no—
296C4⋊C4—1221no—
297C4⋊C4—1221no—
298C4⋊C4—1221no—
299C4⋊C4—1222no—
300C4⋊C4—1222no—
301C4⋊C4—2441no—
302C4⋊C4—2441no—
303C4⋊C4—2441no—
304C22⋊C4—1221no—
305C22⋊C4—1221no—
306C22⋊C4—1221no—
307C22⋊C4—1221no—
308C22⋊C4—1221no—
309C42—1221no—
310C42—4881no—
311C42C2×C4×D6111yescharacteristic
312C42#1175822211yescharacteristic
313C42D4×D6111yescharacteristic
314C42D4×D6111yescharacteristic
315C23—1221no—
316C23#1451975211yescharacteristic
317Q8—4882no—
318Q8—4882no—
319Q8—2441no—
320D4—2441no—
321D4—2441no—
322D4—2441no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—41no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—4881no—
332C2×C4—4881no—
333C2×C4—4881no—
334C2×C4—4881no—
335C2×C4—2442no—
336C2×C4—2442no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4C22⋊C4×D6111yescharacteristic
340C2×C4#1451973911yescharacteristic
341C2×C4C4×D24411yescharacteristic
342C2×C4#1451974711yescharacteristic
343C2×C4#1451975011yescharacteristic
344C2×C4#1451976211yescharacteristic
345C8—42no—
346C8—41no—
347C8—41no—
348C8—81no—
349C8—2441no—
350C8—2441no—
351C22—21no—
352C22—21no—
353C22—2441no—
354C22—2441no—
355C22—2441no—
356C22#1683964011yescharacteristic
357C22#1684002611yescharacteristic
358C22#1684003311yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—4882no—
365C4—4882no—
366C4—2441no—
367C4—2441no—
368C4—2441no—
369C4#1683994211yescharacteristic
370C4#1683994711yescharacteristic
371C2—21no—
372C2—21no—
373C2—4881no—
374C2#2144618711yescharacteristic
375C2#2144632611yescharacteristic
376C2#2144634011yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1290C2
socleC22×C61#386
prime radical#14519751D4
cosocleC2×C42×C61C23
hypercenter#1290D61
hypocenterC61#9375
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1290

Complements

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

NH ≅ G/Ntype
3. #21446770C2semidirect
4. #21444544C2semidirect
6. #21443674C2semidirect
7. C61×#1290C2semidirect
10. #16840171C4semidirect
11. #16840122C4semidirect
188. #1290D61semidirect
221. C61#9375semidirect

Maximal subgroups

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

subgroupindex
#214570422
#214549552
#214467702
#214445442
#214443452
#214436742
C61×#12902
#937561