Finite Group Databasebeta

← #29575246

Subgroups — #29575246

Order 15616.

500 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456374C211yesmaximal, characteristic
2#21454563C211yesmaximal, characteristic
3#21446762C211yesmaximal, characteristic, complemented
4#21444223C211yesmaximal, characteristic, complemented
5#21443660C211yesmaximal, characteristic, complemented
6#21443655C211yesmaximal, characteristic, complemented
7C61×#1502C211yesmaximal, characteristic
8C2×#14519784—21no—
9#16840319C2211yescharacteristic
10#16840158C411yescharacteristic, complemented
11#16840134C411yescharacteristic, complemented
12#16840114C411yescharacteristic, complemented
13#16840108C411yescharacteristic, complemented
14#16839989—22no—
15C4×#11758200—22no—
16#16839840—21no—
17#16839834—22no—
18D4×#92418—21no—
19C2×C4⋊#92418C2211yescharacteristic
20#16839729—21no—
21C4×#11758194C2211yescharacteristic
22C2×C4×#92418C2211yescharacteristic
23#16839522—21no—
24#16839522—21no—
25#16839494—21no—
26#16839494—21no—
27C61×#532C2211yescharacteristic
28C61×#431C2211yescharacteristic
29C4×C4⋊C4×C61C2211yescharacteristic
30C61×#327—22no—
31C2×#11758200—22no—
32#14519784—42no—
33#14519784—42no—
34C2×#11758194—22no—
35C2×#11758194D411yescharacteristic
36C2×#11758194D411yescharacteristic
37C22×#92418—22no—
38C22×#92418—21no—
39C22×#92418—21no—
40#14519777C2×C411yescharacteristic
41#14519777C2×C411yescharacteristic
42#14519769—21no—
43#14519756—21no—
44#14519756—21no—
45C4×Dic122—21no—
46C4×Dic122—21no—
47#14519736—21no—
48#14519708—22no—
49C4⋊#92418—21no—
50C4⋊#92418D411yescharacteristic
51C4⋊#92418D411yescharacteristic
52#14519700—22no—
53#14519698—22no—
54C22⋊#92418—22no—
55C22⋊#92418—22no—
56#14519688—21no—
57C4×#92418—21no—
58C4×#92418—21no—
59C4×#92418C2×C411yescharacteristic
60C4×#92418C2×C411yescharacteristic
61C2×#41×C61—21no—
62C4⋊Q8×C61C2×C411yescharacteristic
63#127×C61C2×C411yescharacteristic
64#124×C61—21no—
65#121×C61—21no—
66#121×C61D412yes—
67C4×D4×C61—21no—
68C4×D4×C61D412yes—
69C2×C4⋊C4×C61—21no—
70C2×C42×C61—21no—
71C2×C42×C61C2311yescharacteristic
72C4⋊C8×C61—21no—
73C22⋊C8×C61—21no—
74C4×C8×C61—21no—
75#95×C61—21no—
76#41×C61—41no—
77#41×C61—41no—
78#41×C61—41no—
79#41×C61—41no—
80C2×Q8×C61—21no—
81C2×D4×C61—22no—
82C2×D4×C61—21no—
83C2×D4×C61—21no—
84C2×D4×C61C22⋊C412yes—
85C22×C4×C61—22no—
86C22×C4×C61—41no—
87C22×C4×C61C2×D411yescharacteristic
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61#4111yescharacteristic
90C2×Dic122—21no—
91C2×Dic122—21no—
92C2×C8×C61—41no—
93C4⋊C4×C61—21no—
94C4⋊C4×C61—22no—
95C4⋊C4×C61—41no—
96C4⋊C4×C61C22⋊C412yes—
97C22⋊C4×C61—22no—
98C22⋊C4×C61—22no—
99C42×C61—41no—
100C42×C61—41no—
101C42×C61C22×C411yescharacteristic
102C42×C61C2×D411yescharacteristic
103C42×C61C2×D411yescharacteristic
104C42×C61#4111yescharacteristic
105C22⋊Dic61—41no—
106#11758200—44no—
107C4⋊Dic61—21no—
108C4⋊Dic61—21no—
109C4⋊Dic61—21no—
110C4⋊Dic61—21no—
111#11758196—41no—
112#11758196—41no—
113C4×Dic61—41no—
114#11758194—21no—
115#11758194—21no—
116#11758194—21no—
117#11758194—44no—
118#11758194SD1612yescomplemented
119C2×#92418—21no—
120C2×#92418—21no—
121C2×#92418—21no—
122C2×#92418—21no—
123C2×#92418—21no—
124C2×#92418—21no—
125C2×#92418—42no—
126C2×#92418—44no—
127C2×#92418—41no—
128C2×#92418—41no—
129C23×C61—22no—
130C23×C61#12111yescharacteristic
131Q8×C61—41no—
132Q8×C61—41no—
133D4×C61—42no—
134D4×C61—42no—
135D4×C61—42no—
136D4×C61—41no—
137D4×C61—41no—
138D4×C61—41no—
139D4×C61—41no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—22no—
143C2×C4×C61—41no—
144C2×C4×C61—42no—
145C2×C4×C61—42no—
146C2×C4×C61—42no—
147C2×C4×C61—81no—
148C2×C4×C61—81no—
149C2×C4×C61C2×C22⋊C411yescharacteristic
150C2×C4×C61C4×D411yescharacteristic
151C2×C4×C61C4×D411yescharacteristic
152C2×C4×C61#12011yescharacteristic
153C2×C4×C61#12111yescharacteristic
154C2×C4×C61#12311yescharacteristic
155C2×C4×C61C2×SD1611yescharacteristic
156C2×C4×C61#13511yescharacteristic
157C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C61#13711yescharacteristic
159C2×Dic61—41no—
160C2×Dic61—41no—
161Dic122—42no—
162Dic122—41no—
163Dic122—41no—
164C8×C61—81no—
165#92418—22no—
166#92418—22no—
167#92418—41no—
168#92418—41no—
169#92418—41no—
170#92418—41no—
171#9055—611nomaximal, Sylow
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—42no—
175C22×C61—42no—
176C22×C61—42no—
177C22×C61#38611yescharacteristic
178C22×C61#46111yescharacteristic
179C22×C61#46311yescharacteristic
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—21no—
183C4×C61—42no—
184C4×C61—82no—
185C4×C61C4×SD1611yescharacteristic
186C4×C61#44011yescharacteristic
187C4×C61#44311yescharacteristic
188C4×C61#44411yescharacteristic
189C4×C61#45011yescharacteristic
190C4×C61#45211yescharacteristic
191Dic61—81no—
192Dic61—81no—
193#3167—611no—
194#2935—611no—
195#1986—611no—
196#1502D6111yescharacteristic
197#1481—611no—
198#1279—611no—
199#1278—611no—
200C2×C61—21no—
201C2×C61—21no—
202C2×C61—82no—
203C2×C61#187611yescharacteristic
204C2×C61#187711yescharacteristic
205C2×C61#188411yescharacteristic
206C2×#131—1221no—
207#533—611no—
208#532C2×D6111yescharacteristic
209#498—611no—
210#492—611no—
211#487—611no—
212#486—611no—
213#465—1222no—
214C4×SD16—1222no—
215#436—1221no—
216#435—1222no—
217C8×D4—1221no—
218#431C2×D6111yescharacteristic
219C2×C4⋊C8—611no—
220#408—1221no—
221C4×M16—611no—
222C2×C4×C8—611no—
223C4×C4⋊C4C2×D6111yescharacteristic
224#339—1221no—
225#339—1221no—
226#327—22no—
227Q8⋊C8—1221no—
228Q8⋊C8—1221no—
229C61#905511yescharacteristic, complemented, Sylow
230C2×#41—21no—
231C2×SD16—1222no—
232#131—2442no—
233#131—2442no—
234C2×M16—611no—
235C2×M16—611no—
236C2×M16—1222no—
237C22×C8—1222no—
238C22×C8—1221no—
239C22×C8—1221no—
240C4⋊Q8—611no—
241C4⋊Q8—611no—
242C4⋊Q8C4×D6111yescharacteristic
243#127C4×D6111yescharacteristic
244#125—1221no—
245#124—21no—
246C22⋊Q8—1221no—
247C22⋊Q8—1221no—
248#121—21no—
249#121C22⋊D6112yes—
250C4×Q8—1221no—
251C4×Q8—1221no—
252C4×D4—21no—
253C4×D4D24412yes—
254#117—1221no—
255C2×C4⋊C4—21no—
256C2×C42—21no—
257C2×C42C22×D6111yescharacteristic
258#106—1222no—
259C4⋊C8—21no—
260C4⋊C8—611no—
261C4⋊C8—611no—
262C4⋊C8—1221no—
263#103—1222no—
264#102—1222no—
265C22⋊C8—21no—
266C22⋊C8—1222no—
267C22⋊C8—1222no—
268#97—1221no—
269C4×C8—21no—
270C4×C8—611no—
271C4×C8—611no—
272C4×C8—1221no—
273C4×C8—1221no—
274#95—21no—
275#41—41no—
276#41—41no—
277#41—41no—
278#41—41no—
279C2×Q8—21no—
280C2×Q8—1221no—
281C2×Q8—1221no—
282C2×D4—22no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4#1175819812yes—
286C22×C4—22no—
287C22×C4—41no—
288C22×C4D4×D6111yescharacteristic
289C22×C4#1175822411yescharacteristic
290C22×C4C2×C22⋊D6111yescharacteristic
291SD16—2444no—
292M16—612no—
293M16—1221no—
294M16—1221no—
295M16—1221no—
296M16—2444no—
297C2×C8—41no—
298C2×C8—1221no—
299C2×C8—1221no—
300C2×C8—1221no—
301C2×C8—1221no—
302C2×C8—1221no—
303C2×C8—1221no—
304C2×C8—2442no—
305C2×C8—2444no—
306C2×C8—2441no—
307C2×C8—2441no—
308C4⋊C4—21no—
309C4⋊C4—22no—
310C4⋊C4—41no—
311C4⋊C4—1221no—
312C4⋊C4—1221no—
313C4⋊C4—1221no—
314C4⋊C4—1221no—
315C4⋊C4—2441no—
316C4⋊C4—2441no—
317C4⋊C4#1175819812yes—
318C22⋊C4—22no—
319C22⋊C4—22no—
320C22⋊C4—2441no—
321C42—41no—
322C42—41no—
323C42—2441no—
324C42C2×C4×D6111yescharacteristic
325C42C2×D24411yescharacteristic
326C42D4×D6111yescharacteristic
327C42#1175822411yescharacteristic
328C23—22no—
329C23#1451974911yescharacteristic
330Q8—41no—
331Q8—41no—
332Q8—2442no—
333Q8—2441no—
334Q8—2441no—
335D4—42no—
336D4—42no—
337D4—42no—
338D4—41no—
339D4—41no—
340D4—41no—
341D4—41no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—22no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4C2×#1175819811yescharacteristic
354C2×C4#1451973711yescharacteristic
355C2×C4#1451973711yescharacteristic
356C2×C4#1451974711yescharacteristic
357C2×C4#1451974911yescharacteristic
358C2×C4#1451976111yescharacteristic
359C2×C4SD16×D6111yescharacteristic
360C2×C4#1451979611yescharacteristic
361C2×C4#1451980111yescharacteristic
362C2×C4#1451980611yescharacteristic
363C8—81no—
364C8—1222no—
365C8—1222no—
366C8—2441no—
367C8—2441no—
368C8—2441no—
369C8—2441no—
370C22—21no—
371C22—21no—
372C22—42no—
373C22—42no—
374C22—42no—
375C22#1683963911yescharacteristic
376C22#1683996511yescharacteristic
377C22#1683997511yescharacteristic
378C4—21no—
379C4—21no—
380C4—21no—
381C4—42no—
382C4—82no—
383C4—4881no—
384C4—4881no—
385C4#1683985311yescharacteristic
386C4#1683985911yescharacteristic
387C4#1683987611yescharacteristic
388C4#1683988111yescharacteristic
389C4#1683991411yescharacteristic
390C4#1683992511yescharacteristic
391C2—21no—
392C2—21no—
393C2—82no—
394C2#2144614411yescharacteristic
395C2#2144615111yescharacteristic
396C2#2144620011yescharacteristic
subgroupG/H
centerC2×C4#14519747
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1502C2
socleC22×C61#386
prime radicalC61×#532C22
cosocleC2×C42×C61C23
hypercenter#1502D61
hypocenterC61#9055
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1502

Complements

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

NH ≅ G/Ntype
3. #21446762C2semidirect
4. #21444223C2semidirect
5. #21443660C2semidirect
6. #21443655C2semidirect
10. #16840158C4semidirect
11. #16840134C4semidirect
12. #16840114C4semidirect
13. #16840108C4semidirect
118. #11758194SD16semidirect
229. C61#9055semidirect

Maximal subgroups

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

subgroupindex
#214563742
#214545632
#214467622
#214442232
#214436602
#214436552
C61×#15022
#905561