Finite Group Databasebeta

← #29576272

Subgroups — #29576272

Order 15616.

566 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 115 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#21455859C211yesmaximal, characteristic
2C4×#14519742C211yesmaximal, characteristic
3#21446795C211yesmaximal, characteristic
4#21444317C211yesmaximal, characteristic
5#21444247C211yesmaximal, characteristic
6#21443651C211yesmaximal, characteristic
7C61×#1303C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9C2×C4×Dic122C2211yescharacteristic
10C2×#14519742—21no—
11#16840098—21no—
12#16840058C412yescomplemented
13#16839973C412yescomplemented
14#16839920—21no—
15C4×Dic244—22no—
16#16839815C2211yescharacteristic
17C4⋊C4×Dic61—21no—
18C4×#11758196—21no—
19#16839613—22no—
20C42×Dic61—21no—
21C42×Dic61C2211yescharacteristic
22#16839523—21no—
23#16839523—21no—
24#16839498—22no—
25#16839492—22no—
26C61×#431C2211yescharacteristic
27C61×#423C2211yescharacteristic
28C4×C4⋊C4×C61C2211yescharacteristic
29C22×Dic122D411yescharacteristic
30C2×Dic244—22no—
31#14519777C2×C411yescharacteristic
32#14519777C2×C411yescharacteristic
33#14519769—21no—
34#14519756—21no—
35#14519756—21no—
36C4×Dic122—21no—
37C4×Dic122—21no—
38C4×Dic122—21no—
39C4×Dic122—21no—
40C4×Dic122C2×C412yes—
41C4×Dic122D412yes—
42#14519742—28no—
43#14519736—21no—
44C2×C4⋊Dic61D411yescharacteristic
45C2×#11758196—22no—
46C2×#11758196—21no—
47C2×C4×Dic61—22no—
48C2×C4×Dic61—21no—
49C2×C4×Dic61—21no—
50C2×C4×Dic61—22no—
51C2×C4×Dic61—21no—
52C2×C4×Dic61D411yescharacteristic
53C2×C4×Dic61D411yescharacteristic
54#14519711—22no—
55C4⋊#92418—21no—
56#14519702—22no—
57#14519702—22no—
58C22⋊#92418—21no—
59C4×#92418—21no—
60#14519684—22no—
61C2×M16×C61—21no—
62C2×C4⋊C4×C61—21no—
63C2×C42×C61—21no—
64C2×C42×C61C2311yescharacteristic
65C4⋊C8×C61—21no—
66C4⋊C8×C61—21no—
67C4⋊C8×C61C2×C412yes—
68C22⋊C8×C61—21no—
69C4×C8×C61—21no—
70#95×C61D412yes—
71C22×C4×C61—22no—
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C2×Dic122—21no—
80C2×Dic122—24no—
81C2×Dic122—21no—
82C2×Dic122—21no—
83C2×Dic122C22⋊C412yes—
84M16×C61—41no—
85M16×C61—41no—
86C2×C8×C61—22no—
87C2×C8×C61—41no—
88C4⋊C4×C61—24no—
89C42×C61—41no—
90C42×C61—41no—
91C42×C61C22×C411yescharacteristic
92C42×C61C2×D411yescharacteristic
93C42×C61#4111yescharacteristic
94C42×C61#4111yescharacteristic
95C22⋊Dic61—41no—
96C4⋊Dic61—21no—
97C4⋊Dic61—21no—
98C4⋊Dic61—21no—
99C4⋊Dic61—21no—
100C4⋊Dic61—21no—
101C4⋊Dic61C22⋊C412yes—
102#11758196—28no—
103#11758196—22no—
104#11758196—22no—
105#11758196—41no—
106#11758196—41no—
107C4×Dic61—28no—
108C4×Dic61—24no—
109C4×Dic61—22no—
110C4×Dic61—22no—
111C4×Dic61—21no—
112C4×Dic61—21no—
113C4×Dic61—21no—
114C4×Dic61—42no—
115C4×Dic61—44no—
116C4×Dic61—41no—
117C4×Dic61Q1612yescomplemented
118C2×#92418—41no—
119Dic244—44no—
120C23×C61#12011yescharacteristic
121C2×C4×C61—22no—
122C2×C4×C61—24no—
123C2×C4×C61—41no—
124C2×C4×C61—42no—
125C2×C4×C61—42no—
126C2×C4×C61C2×C22⋊C411yescharacteristic
127C2×C4×C61C4×D411yescharacteristic
128C2×C4×C61C4×D411yescharacteristic
129C2×C4×C61#12111yescharacteristic
130C2×C4×C61#12111yescharacteristic
131C2×C4×C61#12311yescharacteristic
132C2×C4×C61C2×Q1611yescharacteristic
133C2×C4×C61#13511yescharacteristic
134C2×C4×C61#13711yescharacteristic
135C2×C4×C61#13711yescharacteristic
136C2×Dic61—22no—
137C2×Dic61—24no—
138C2×Dic61—22no—
139C2×Dic61—22no—
140C2×Dic61—22no—
141C2×Dic61—22no—
142C2×Dic61—22no—
143C2×Dic61—41no—
144C2×Dic61—42no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148Dic122—24no—
149Dic122—22no—
150Dic122—42no—
151Dic122—81no—
152Dic122#10414yes—
153C8×C61—42no—
154C8×C61—81no—
155#92418—81no—
156#9232—611nomaximal, Sylow
157C22×C61—21no—
158C22×C61—21no—
159C22×C61#38611yescharacteristic
160C22×C61#45111yescharacteristic
161C22×C61#45211yescharacteristic
162C4×C61—21no—
163C4×C61—21no—
164C4×C61—21no—
165C4×C61—44no—
166C4×C61C2×#10412yes—
167C4×C61C4×Q1611yescharacteristic
168C4×C61#44111yescharacteristic
169C4×C61#46211yescharacteristic
170C4×C61#46411yescharacteristic
171Dic61—24no—
172Dic61—24no—
173Dic61—42no—
174Dic61—42no—
175Dic61—81no—
176Dic61—81no—
177#3104—611no—
178C42×Q8—611no—
179#1994—611no—
180#1503—611no—
181#1487—611no—
182#1303D6111yescharacteristic
183#1276—611no—
184C2×C61—21no—
185C2×C61—21no—
186C2×C61#187811yescharacteristic
187C2×C61#189611yescharacteristic
188C2×C61#190611yescharacteristic
189#533—611no—
190C2×C4×Q8—611no—
191C2×C4×Q8—1221no—
192#484—1221no—
193#477—612no—
194#462—612no—
195#451—1221no—
196C4×Q16—1222no—
197#431—611no—
198#431C2×D6111yescharacteristic
199#423C2×D6111yescharacteristic
200C4×C4⋊C4—1221no—
201C4×C4⋊C4—1221no—
202C4×C4⋊C4—1222no—
203C4×C4⋊C4C2×D6111yescharacteristic
204C43—611no—
205C43—1221no—
206#339—1221no—
207#339—1221no—
208#328—1222no—
209Q8⋊C8—1222no—
210C61#923211yescharacteristic, complemented, Sylow
211C22×Q8—611no—
212C2×Q16—1222no—
213C2×M16—21no—
214C4⋊Q8—611no—
215C4⋊Q8—611no—
216#125—1221no—
217C22⋊Q8—1221no—
218C22⋊Q8—1221no—
219C4×Q8—612no—
220C4×Q8—612no—
221C4×Q8—1228no—
222C4×Q8—1221no—
223C4×Q8—1221no—
224C4×Q8—1221no—
225C4×Q8—1221no—
226#117—1221no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—611no—
229C2×C4⋊C4—1222no—
230C2×C4⋊C4—1221no—
231C2×C42—21no—
232C2×C42—611no—
233C2×C42—611no—
234C2×C42—1222no—
235C2×C42—1221no—
236C2×C42—1221no—
237C2×C42—1222no—
238C2×C42—1221no—
239C2×C42C22×D6111yescharacteristic
240#107—1222no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—1221no—
244C4⋊C8C4×D6112yes—
245#103—1222no—
246#103—1222no—
247C22⋊C8—21no—
248C22⋊C8—1221no—
249C4×C8—21no—
250C4×C8—1221no—
251#95—1222no—
252#95D24412yes—
253C2×Q8—612no—
254C2×Q8—1224no—
255C2×Q8—1221no—
256C2×Q8—1221no—
257C2×Q8—1221no—
258C22×C4—22no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4C2×D24411yescharacteristic
264C22×C4D4×D6111yescharacteristic
265C22×C4D4×D6111yescharacteristic
266Q16—2444no—
267M16—41no—
268M16—41no—
269C2×C8—22no—
270C2×C8—41no—
271C2×C8—2441no—
272C4⋊C4—24no—
273C4⋊C4—612no—
274C4⋊C4—1228no—
275C4⋊C4—1222no—
276C4⋊C4—1222no—
277C4⋊C4—1221no—
278C4⋊C4—1221no—
279C4⋊C4—1221no—
280C4⋊C4—1221no—
281C4⋊C4—1221no—
282C4⋊C4—2441no—
283C4⋊C4—2441no—
284C22⋊C4—2441no—
285C42—41no—
286C42—41no—
287C42—612no—
288C42—1224no—
289C42—1228no—
290C42—1222no—
291C42—1222no—
292C42—1221no—
293C42—1221no—
294C42—1221no—
295C42—2442no—
296C42—2444no—
297C42—2441no—
298C42C2×C4×D6111yescharacteristic
299C42#1175822211yescharacteristic
300C42D4×D6111yescharacteristic
301C42#1175822611yescharacteristic
302C23#1451974711yescharacteristic
303Q8—614no—
304Q8—1224no—
305Q8—1222no—
306Q8—4881no—
307Q8—2442no—
308C2×C4—22no—
309C2×C4—24no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—1222no—
314C2×C4—1224no—
315C2×C4—1222no—
316C2×C4—1222no—
317C2×C4—1222no—
318C2×C4—1222no—
319C2×C4—1222no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2442no—
324C2×C4—2441no—
325C2×C4C22⋊C4×D6111yescharacteristic
326C2×C4#1451973911yescharacteristic
327C2×C4C4×D24411yescharacteristic
328C2×C4#1451975011yescharacteristic
329C2×C4#1451975211yescharacteristic
330C2×C4#1451976211yescharacteristic
331C2×C4Q16×D6111yescharacteristic
332C2×C4#1451979611yescharacteristic
333C2×C4#1451980611yescharacteristic
334C2×C4#1451980611yescharacteristic
335C8—42no—
336C8—81no—
337C8—4881no—
338C22—21no—
339C22—21no—
340C22#1683964011yescharacteristic
341C22#1683991911yescharacteristic
342C22#1683992511yescharacteristic
343C4—21no—
344C4—21no—
345C4—21no—
346C4—44no—
347C4—1224no—
348C4—1224no—
349C4—4881no—
350C4—4881no—
351C4—2442no—
352C4—2442no—
353C4#104×D6112yes—
354C4#1683985611yescharacteristic
355C4#1683986811yescharacteristic
356C4#1683997111yescharacteristic
357C4#1683998311yescharacteristic
358C2—21no—
359C2—21no—
360C2#2144616111yescharacteristic
361C2#2144626111yescharacteristic
362C2#2144632111yescharacteristic
subgroupG/H
centerC2×C4#14519750
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1303C2
socleC22×C61#386
prime radicalC23×C61#120
cosocleC2×C42×C61C23
hypercenter#1303D61
hypocenterC61#9232
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
12. #16840058C4semidirect
13. #16839973C4semidirect
117. C4×Dic61Q16semidirect
210. C61#9232semidirect

Maximal subgroups

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

subgroupindex
#214558592
C4×#145197422
#214467952
#214443172
#214442472
#214436512
C61×#13032
#923261