Finite Group Databasebeta

← #29576300

Subgroups — #29576300

Order 15616.

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

normal subgroups only

This group has 474 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#21455859C211yesmaximal, characteristic
2#21448293C211yesmaximal, characteristic
3#21446795C211yesmaximal, characteristic
4#21444317C211yesmaximal, characteristic
5#21444247C211yesmaximal, characteristic
6#21443651C211yesmaximal, characteristic
7C61×#1303C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9C2×C4×Dic122C2211yescharacteristic
10#16840098—21no—
11#16840058C412yescomplemented
12#16839973C412yescomplemented
13#16839920—21no—
14C4×Dic244—22no—
15#16839815C2211yescharacteristic
16#16839667—21no—
17#16839658—21no—
18#16839644—22no—
19C4×#11758196—21no—
20#16839608—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#14519736—21no—
43C2×C4⋊Dic61D411yescharacteristic
44C2×#11758196—21no—
45C2×#11758196—22no—
46C2×C4×Dic61—21no—
47C2×C4×Dic61—21no—
48C2×C4×Dic61—21no—
49C2×C4×Dic61D411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51#14519711—22no—
52C4⋊#92418—21no—
53#14519702—22no—
54#14519702—22no—
55C22⋊#92418—21no—
56C4×#92418—21no—
57#14519684—22no—
58#14519684—22no—
59#14519684—22no—
60C2×M16×C61—21no—
61C2×C4⋊C4×C61—21no—
62C2×C42×C61—21no—
63C2×C42×C61C2311yescharacteristic
64C4⋊C8×C61—21no—
65C4⋊C8×C61—21no—
66C4⋊C8×C61C2×C412yes—
67C22⋊C8×C61—21no—
68C4×C8×C61—21no—
69#95×C61D412yes—
70C22×C4×C61—22no—
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C2×Dic122—21no—
79C2×Dic122—21no—
80C2×Dic122—21no—
81C2×Dic122—42no—
82C2×Dic122C22⋊C412yes—
83M16×C61—41no—
84M16×C61—41no—
85C2×C8×C61—22no—
86C2×C8×C61—41no—
87C4⋊C4×C61—42no—
88C42×C61—41no—
89C42×C61—41no—
90C42×C61C22×C411yescharacteristic
91C42×C61C2×D411yescharacteristic
92C42×C61#4111yescharacteristic
93C42×C61#4111yescharacteristic
94C22⋊Dic61—41no—
95C4⋊Dic61—21no—
96C4⋊Dic61—21no—
97C4⋊Dic61—21no—
98C4⋊Dic61—21no—
99C4⋊Dic61—21no—
100C4⋊Dic61C22⋊C412yes—
101#11758196—22no—
102#11758196—22no—
103#11758196—44no—
104#11758196—41no—
105#11758196—41no—
106C4×Dic61—22no—
107C4×Dic61—22no—
108C4×Dic61—21no—
109C4×Dic61—21no—
110C4×Dic61—21no—
111C4×Dic61—42no—
112C4×Dic61—42no—
113C4×Dic61—41no—
114C4×Dic61Q1612yescomplemented
115C2×#92418—41no—
116Dic244—44no—
117C23×C61#12011yescharacteristic
118C2×C4×C61—22no—
119C2×C4×C61—41no—
120C2×C4×C61—42no—
121C2×C4×C61—42no—
122C2×C4×C61—42no—
123C2×C4×C61C2×C22⋊C411yescharacteristic
124C2×C4×C61C4×D411yescharacteristic
125C2×C4×C61C4×D411yescharacteristic
126C2×C4×C61#12111yescharacteristic
127C2×C4×C61#12111yescharacteristic
128C2×C4×C61#12311yescharacteristic
129C2×C4×C61C2×Q1611yescharacteristic
130C2×C4×C61#13511yescharacteristic
131C2×C4×C61#13711yescharacteristic
132C2×C4×C61#13711yescharacteristic
133C2×Dic61—22no—
134C2×Dic61—22no—
135C2×Dic61—22no—
136C2×Dic61—22no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—42no—
141C2×Dic61—42no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145Dic122—22no—
146Dic122—22no—
147Dic122—42no—
148Dic122—42no—
149Dic122—81no—
150C8×C61—42no—
151C8×C61—81no—
152#92418—81no—
153#9236—611nomaximal, Sylow
154C22×C61—21no—
155C22×C61—21no—
156C22×C61#38611yescharacteristic
157C22×C61#45111yescharacteristic
158C22×C61#45211yescharacteristic
159C4×C61—21no—
160C4×C61—21no—
161C4×C61—21no—
162C4×C61—82no—
163C4×C61#42112yes—
164C4×C61C4×Q1611yescharacteristic
165C4×C61#44111yescharacteristic
166C4×C61#46211yescharacteristic
167C4×C61#46411yescharacteristic
168Dic61—42no—
169Dic61—42no—
170Dic61—42no—
171Dic61—42no—
172Dic61—81no—
173Dic61—81no—
174#3104—611no—
175#2295—611no—
176#1994—611no—
177#1503—611no—
178#1487—611no—
179#1303D6111yescharacteristic
180#1276—611no—
181C2×C61—21no—
182C2×C61—21no—
183C2×C61#187811yescharacteristic
184C2×C61#189711yescharacteristic
185C2×C61#190611yescharacteristic
186#533—611no—
187C2×C4×Q8—611no—
188#484—1221no—
189#477—612no—
190#462—612no—
191#451—1221no—
192C4×Q16—1222no—
193#431—611no—
194#431C2×D6111yescharacteristic
195#423C2×D6111yescharacteristic
196#391—1221no—
197#389—1221no—
198#387—1222no—
199C4×C4⋊C4—1221no—
200C4×C4⋊C4C2×D6111yescharacteristic
201#376—1221no—
202C43—611no—
203#339—1221no—
204#339—1221no—
205#328—1222no—
206Q8⋊C8—1222no—
207C61#923611yescharacteristic, complemented, Sylow
208C22×Q8—611no—
209C2×Q16—1222no—
210C2×M16—21no—
211C4⋊Q8—611no—
212C4⋊Q8—611no—
213#125—1221no—
214C22⋊Q8—1221no—
215C22⋊Q8—1221no—
216C4×Q8—612no—
217C4×Q8—612no—
218C4×Q8—1221no—
219C4×Q8—1221no—
220C4×Q8—1221no—
221C4×Q8—1221no—
222#117—1221no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—611no—
225C2×C4⋊C4—1221no—
226C2×C4⋊C4—1222no—
227C2×C42—21no—
228C2×C42—611no—
229C2×C42—611no—
230C2×C42—1221no—
231C2×C42—1221no—
232C2×C42—1221no—
233C2×C42C22×D6111yescharacteristic
234#107—1222no—
235C4⋊C8—21no—
236C4⋊C8—21no—
237C4⋊C8—1221no—
238C4⋊C8C4×D6112yes—
239#103—1222no—
240#103—1222no—
241C22⋊C8—21no—
242C22⋊C8—1221no—
243C4×C8—21no—
244C4×C8—1221no—
245#95—1222no—
246#95—1222no—
247#95—1222no—
248#95D24412yes—
249C2×Q8—612no—
250C2×Q8—1221no—
251C2×Q8—1221no—
252C2×Q8—1221no—
253C2×Q8—2442no—
254C22×C4—22no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4—1221no—
259C22×C4C2×D24411yescharacteristic
260C22×C4D4×D6111yescharacteristic
261C22×C4D4×D6111yescharacteristic
262Q16—2444no—
263M16—41no—
264M16—41no—
265C2×C8—22no—
266C2×C8—41no—
267C2×C8—2441no—
268C4⋊C4—42no—
269C4⋊C4—612no—
270C4⋊C4—1222no—
271C4⋊C4—1222no—
272C4⋊C4—1221no—
273C4⋊C4—1221no—
274C4⋊C4—1221no—
275C4⋊C4—1221no—
276C4⋊C4—1221no—
277C4⋊C4—2444no—
278C4⋊C4—2441no—
279C4⋊C4—2441no—
280C22⋊C4—2441no—
281C42—41no—
282C42—41no—
283C42—612no—
284C42—1222no—
285C42—1222no—
286C42—1221no—
287C42—1221no—
288C42—1221no—
289C42—2442no—
290C42—2442no—
291C42—2441no—
292C42C2×C4×D6111yescharacteristic
293C42#1175822211yescharacteristic
294C42D4×D6111yescharacteristic
295C42#1175822611yescharacteristic
296C23#1451974711yescharacteristic
297Q8—1222no—
298Q8—1222no—
299Q8—4881no—
300Q8—2442no—
301Q8—2442no—
302C2×C4—22no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—1222no—
308C2×C4—1222no—
309C2×C4—1222no—
310C2×C4—1222no—
311C2×C4—2441no—
312C2×C4—2441no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4—2442no—
317C2×C4—2442no—
318C2×C4—2441no—
319C2×C4C22⋊C4×D6111yescharacteristic
320C2×C4#1451973911yescharacteristic
321C2×C4C4×D24411yescharacteristic
322C2×C4#1451975011yescharacteristic
323C2×C4#1451975211yescharacteristic
324C2×C4#1451976211yescharacteristic
325C2×C4Q16×D6111yescharacteristic
326C2×C4#1451979611yescharacteristic
327C2×C4#1451980611yescharacteristic
328C2×C4#1451980611yescharacteristic
329C8—42no—
330C8—81no—
331C8—4881no—
332C22—21no—
333C22—21no—
334C22#1683964011yescharacteristic
335C22#1683991911yescharacteristic
336C22#1683992511yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—82no—
341C4—4881no—
342C4—4881no—
343C4—2442no—
344C4—2442no—
345C4—2442no—
346C4—2442no—
347C4#1683977712yes—
348C4#1683985611yescharacteristic
349C4#1683986811yescharacteristic
350C4#1683997111yescharacteristic
351C4#1683998311yescharacteristic
352C2—21no—
353C2—21no—
354C2#2144616111yescharacteristic
355C2#2144626611yescharacteristic
356C2#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#9236
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
11. #16840058C4semidirect
12. #16839973C4semidirect
114. C4×Dic61Q16semidirect
207. C61#9236semidirect

Maximal subgroups

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

subgroupindex
#214558592
#214482932
#214467952
#214443172
#214442472
#214436512
C61×#13032
#923661