Finite Group Databasebeta

← #29576264

Subgroups — #29576264

Order 15616.

686 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455827C211yesmaximal, characteristic
2#21446796C211yesmaximal, characteristic, complemented
3#21444317C211yesmaximal, characteristic, complemented
4#21444244C211yesmaximal, characteristic
5#21443722C211yesmaximal, characteristic, complemented
6#21443652C211yesmaximal, characteristic, complemented
7C42×D4×C61C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9#16840092—21no—
10#16840052C412yescomplemented
11#16839967C412yescomplemented
12#16839913—21no—
13C4×#11758200—22no—
14#16839815C2211yescharacteristic
15#16839815C2211yescharacteristic
16#16839786C2211yescharacteristic
17#16839522—21no—
18#16839522—21no—
19#16839498—22no—
20D4⋊#92418—22no—
21C2×C4×D4×C61—21no—
22C2×C4×D4×C61C2211yescharacteristic
23C22×C42×C61—21no—
24C4×C4⋊C4×C61—21no—
25C4×C4⋊C4×C61C2211yescharacteristic
26C4×C22⋊C4×C61—21no—
27C4×C22⋊C4×C61—22no—
28C43×C61C2211yescharacteristic
29C2×#11758200—22no—
30C2×#11758194—21no—
31#14519777C2×C411yescharacteristic, complemented
32#14519777C2×C411yescharacteristic, complemented
33#14519769—21no—
34#14519756—21no—
35#14519756—21no—
36C4×Dic122—21no—
37C4×Dic122—21no—
38#14519736—21no—
39#14519708—22no—
40C4⋊#92418—21no—
41C4⋊#92418—21no—
42C4⋊#92418—21no—
43C4⋊#92418C2×C412yescomplemented
44#14519700—22no—
45#14519698—22no—
46C22⋊#92418—21no—
47C22⋊#92418—21no—
48C4×#92418—21no—
49C4×#92418—21no—
50C22×D4×C61D411yescharacteristic
51C23×C4×C61—22no—
52C23×C4×C61—21no—
53C4×D4×C61—28no—
54C4×D4×C61—21no—
55C4×D4×C61—21no—
56C4×D4×C61C2×C412yes—
57C4×D4×C61D412yes—
58C2×C4⋊C4×C61—21no—
59C2×C4⋊C4×C61D411yescharacteristic
60C2×C22⋊C4×C61—22no—
61C2×C22⋊C4×C61—21no—
62C2×C42×C61—21no—
63C2×C42×C61—22no—
64C2×C42×C61—21no—
65C2×C42×C61—21no—
66C2×C42×C61—42no—
67C2×C42×C61—42no—
68C2×C42×C61D411yescharacteristic
69C2×C42×C61D411yescharacteristic
70C2×C42×C61C2311yescharacteristic
71#95×C61—22no—
72#95×C61D412yes—
73C24×C61—21no—
74C2×D4×C61—24no—
75C2×D4×C61—21no—
76C2×D4×C61C22⋊C412yes—
77C22×C4×C61—21no—
78C22×C4×C61—28no—
79C22×C4×C61—21no—
80C22×C4×C61—21no—
81C22×C4×C61—22no—
82C22×C4×C61—22no—
83C22×C4×C61—22no—
84C22×C4×C61—44no—
85C22×C4×C61—44no—
86C22×C4×C61—41no—
87C22×C4×C61—41no—
88C22×C4×C61—41no—
89C22×C4×C61—41no—
90C22×C4×C61C2×D411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61C2×D411yescharacteristic
93C2×Dic122—21no—
94C2×Dic122—21no—
95C4⋊C4×C61—24no—
96C4⋊C4×C61—21no—
97C4⋊C4×C61C22⋊C412yes—
98C22⋊C4×C61—28no—
99C22⋊C4×C61—22no—
100C22⋊C4×C61—22no—
101C42×C61—24no—
102C42×C61—21no—
103C42×C61—21no—
104C42×C61—21no—
105C42×C61—42no—
106C42×C61—44no—
107C42×C61—41no—
108C42×C61—41no—
109C42×C61SD1612yescomplemented
110C42×C61C22×C411yescharacteristic
111C42×C61C2×D411yescharacteristic
112C42×C61#4111yescharacteristic
113C42×C61#4111yescharacteristic
114C22⋊Dic61—41no—
115#11758200—44no—
116C4⋊Dic61—21no—
117C4⋊Dic61—21no—
118C4⋊Dic61—21no—
119C4⋊Dic61—21no—
120#11758196—41no—
121#11758196—41no—
122C4×Dic61—41no—
123#11758194—41no—
124#11758194—41no—
125C2×#92418—22no—
126C2×#92418—41no—
127C2×#92418—41no—
128C23×C61—24no—
129C23×C61—22no—
130C23×C61—42no—
131C23×C61—41no—
132C23×C61—41no—
133C23×C61#12011yescharacteristic
134D4×C61—24no—
135D4×C61—22no—
136D4×C61#10414yes—
137C2×C4×C61—22no—
138C2×C4×C61—22no—
139C2×C4×C61—22no—
140C2×C4×C61—22no—
141C2×C4×C61—22no—
142C2×C4×C61—24no—
143C2×C4×C61—22no—
144C2×C4×C61—41no—
145C2×C4×C61—416no—
146C2×C4×C61—41no—
147C2×C4×C61—42no—
148C2×C4×C61—42no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—42no—
153C2×C4×C61—42no—
154C2×C4×C61—42no—
155C2×C4×C61—42no—
156C2×C4×C61C2×C22⋊C411yescharacteristic
157C2×C4×C61C4×D411yescharacteristic
158C2×C4×C61C4×D411yescharacteristic
159C2×C4×C61#12111yescharacteristic
160C2×C4×C61#12111yescharacteristic
161C2×C4×C61#12311yescharacteristic
162C2×C4×C61C2×SD1611yescharacteristic
163C2×C4×C61#13511yescharacteristic
164C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C61#13711yescharacteristic
166C2×Dic61—41no—
167C2×Dic61—41no—
168Dic122—42no—
169Dic122—81no—
170#92418—42no—
171#92418—81no—
172#92418—81no—
173#9231—611nomaximal, Sylow
174C22×C61—21no—
175C22×C61—21no—
176C22×C61—24no—
177C22×C61—44no—
178C22×C61—44no—
179C22×C61—42no—
180C22×C61—42no—
181C22×C61#38611yescharacteristic
182C22×C61#45011yescharacteristic
183C22×C61#45211yescharacteristic
184C4×C61—24no—
185C4×C61—21no—
186C4×C61—21no—
187C4×C61—21no—
188C4×C61—42no—
189C4×C61—44no—
190C4×C61—42no—
191C4×C61C2×#10412yes—
192C4×C61C4×SD1611yescharacteristic
193C4×C61#44011yescharacteristic
194C4×C61#46111yescharacteristic
195C4×C61#46311yescharacteristic
196Dic61—81no—
197Dic61—81no—
198#3101—611no—
199C42×D4D6111yescharacteristic
200#1994—611no—
201#1503—611no—
202#1486—611no—
203#1303—611no—
204#1276—611no—
205C2×C61—21no—
206C2×C61—21no—
207C2×C61—44no—
208C2×C61#187711yescharacteristic
209C2×C61#189611yescharacteristic
210C2×C61#190611yescharacteristic
211#533—611no—
212C2×C4×D4—21no—
213C2×C4×D4C2×D6111yescharacteristic
214C22×C42—21no—
215#483—1221no—
216#476—612no—
217#461—612no—
218#450—1221no—
219C4×SD16—1222no—
220#431—611no—
221#431—611no—
222#423—611no—
223C4×C4⋊C4—21no—
224C4×C4⋊C4C2×D6111yescharacteristic
225C4×C22⋊C4—21no—
226C4×C22⋊C4—22no—
227C43C2×D6111yescharacteristic
228#339—1221no—
229#339—1221no—
230#328—1222no—
231D4⋊C8—1222no—
232C61#923111yescharacteristic, complemented, Sylow
233C22×D4C22⋊D6111yescharacteristic
234C23×C4—22no—
235C23×C4—21no—
236C2×SD16—1222no—
237C2×M16—1221no—
238C4⋊Q8—611no—
239C4⋊Q8—611no—
240#125—1221no—
241C22⋊Q8—1221no—
242C22⋊Q8—1221no—
243C4×Q8—1221no—
244C4×Q8—1221no—
245C4×D4—28no—
246C4×D4—21no—
247C4×D4—21no—
248C4×D4C4×D6112yes—
249C4×D4D24412yes—
250#117—1221no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4C22⋊D6111yescharacteristic
253C2×C22⋊C4—22no—
254C2×C22⋊C4—21no—
255C2×C42—21no—
256C2×C42—22no—
257C2×C42—21no—
258C2×C42—21no—
259C2×C42—42no—
260C2×C42—42no—
261C2×C42C22⋊D6111yescharacteristic
262C2×C42C22⋊D6111yescharacteristic
263C2×C42C22×D6111yescharacteristic
264#106—1222no—
265C4⋊C8—612no—
266C4⋊C8—1221no—
267C4⋊C8—1221no—
268C4⋊C8—1221no—
269#103—1222no—
270#102—1222no—
271C22⋊C8—1221no—
272C22⋊C8—1221no—
273C4×C8—1221no—
274C4×C8—1221no—
275#95—22no—
276#95C22⋊D6112yes—
277C24—21no—
278C2×Q8—1221no—
279C2×Q8—1221no—
280C2×D4—24no—
281C2×D4—21no—
282C2×D4#1175819812yes—
283C22×C4—21no—
284C22×C4—28no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—44no—
291C22×C4—44no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4C2×C22⋊D6111yescharacteristic
297C22×C4C2×C22⋊D6111yescharacteristic
298C22×C4C2×C22⋊D6111yescharacteristic
299SD16—2444no—
300M16—2441no—
301M16—2441no—
302C2×C8—1222no—
303C2×C8—2441no—
304C2×C8—2441no—
305C4⋊C4—24no—
306C4⋊C4—21no—
307C4⋊C4—1221no—
308C4⋊C4—1221no—
309C4⋊C4—1221no—
310C4⋊C4—1221no—
311C4⋊C4—2441no—
312C4⋊C4—2441no—
313C4⋊C4#1175819812yes—
314C22⋊C4—28no—
315C22⋊C4—22no—
316C22⋊C4—22no—
317C22⋊C4—2441no—
318C42—24no—
319C42—21no—
320C42—21no—
321C42—21no—
322C42—44no—
323C42—42no—
324C42—41no—
325C42—41no—
326C42—2441no—
327C42#1175820012yescomplemented
328C42C2×C4×D6111yescharacteristic
329C42C2×D24411yescharacteristic
330C42#1175822211yescharacteristic
331C42#1175822211yescharacteristic
332C23—24no—
333C23—22no—
334C23—42no—
335C23—41no—
336C23—41no—
337C23#1451974611yescharacteristic
338Q8—4881no—
339Q8—2442no—
340D4—24no—
341D4—22no—
342D4#1451970514yes—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—24no—
349C2×C4—22no—
350C2×C4—41no—
351C2×C4—416no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4C2×#1175819811yescharacteristic
365C2×C4C4×C22⋊D6111yescharacteristic
366C2×C4C4×C22⋊D6111yescharacteristic
367C2×C4#1451975111yescharacteristic
368C2×C4#1451975111yescharacteristic
369C2×C4#1451976011yescharacteristic
370C2×C4C2×#1175820011yescharacteristic
371C2×C4#1451979711yescharacteristic
372C2×C4#1451980311yescharacteristic
373C2×C4#1451980711yescharacteristic
374C8—4881no—
375C8—4881no—
376C8—2442no—
377C22—21no—
378C22—21no—
379C22—24no—
380C22—44no—
381C22—44no—
382C22—42no—
383C22—42no—
384C22#1683964111yescharacteristic
385C22#1683991311yescharacteristic
386C22#1683992411yescharacteristic
387C4—24no—
388C4—21no—
389C4—21no—
390C4—21no—
391C4—42no—
392C4—44no—
393C4—42no—
394C4—4881no—
395C4—4881no—
396C4C2×#1451970512yes—
397C4C4×#1175820011yescharacteristic
398C4#1683986211yescharacteristic
399C4#1683996711yescharacteristic
400C4#1683997711yescharacteristic
401C2—21no—
402C2—21no—
403C2—44no—
404C2#2144615311yescharacteristic
405C2#2144626211yescharacteristic
406C2#2144632011yescharacteristic
subgroupG/H
centerC2×C4#14519751
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC42×D4×C61C2
socleC22×C61#386
prime radicalC22×D4×C61D4
cosocleC2×C42×C61C23
hypercenterC42×D4D61
hypocenterC61#9231
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C42×D4

Complements

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

NH ≅ G/Ntype
2. #21446796C2semidirect
3. #21444317C2semidirect
5. #21443722C2semidirect
6. #21443652C2semidirect
10. #16840052C4semidirect
11. #16839967C4semidirect
31. #14519777C2×C4semidirect
32. #14519777C2×C4semidirect
43. C4⋊#92418C2×C4semidirect
109. C42×C61SD16semidirect
232. C61#9231semidirect
327. C42#11758200semidirect

Maximal subgroups

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

subgroupindex
#214558272
#214467962
#214443172
#214442442
#214437222
#214436522
C42×D4×C612
#923161