Finite Group Databasebeta

← #29576262

Subgroups — #29576262

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
2C4×D4×Dic61C211yesmaximal, characteristic
3#21446795C211yesmaximal, characteristic, complemented
4#21444319C211yesmaximal, characteristic, complemented
5#21443720C211yesmaximal, characteristic, complemented
6#21443651C211yesmaximal, characteristic, complemented
7C61×#1486C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9C2×D4×Dic61—21no—
10C22×C4×Dic61—21no—
11#16840092—21no—
12#16840052C412yescomplemented
13#16839967C412yescomplemented
14#16839913—21no—
15C4×#11758200—22no—
16#16839815C2211yescharacteristic
17C4⋊C4×Dic61—21no—
18C4×C4⋊Dic61C2211yescharacteristic
19C22⋊C4×Dic61—22no—
20C4×C22⋊Dic61—21no—
21C42×Dic61C2211yescharacteristic
22#16839523—21no—
23#16839523—21no—
24#16839500—22no—
25C2×C4×D4×C61C2211yescharacteristic
26C61×#431C2211yescharacteristic
27C61×#423C2211yescharacteristic
28C61×D4⋊C8—22no—
29C23×Dic61—22no—
30C2×#11758200—22no—
31#14519777C2×C411yescharacteristic, complemented
32#14519777C2×C411yescharacteristic, complemented
33#14519769—21no—
34#14519756—21no—
35#14519756—21no—
36C4×Dic122—21no—
37C4×Dic122—21no—
38D4×Dic61—28no—
39#14519736—21no—
40C2×C4⋊Dic61—21no—
41C2×C22⋊Dic61—22no—
42C2×C4×Dic61—21no—
43C2×C4×Dic61—22no—
44C2×C4×Dic61—21no—
45C2×C4×Dic61—21no—
46C2×C4×Dic61—42no—
47C2×C4×Dic61—42no—
48C2×C4×Dic61D411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50#14519708—22no—
51C4⋊#92418C2×C412yescomplemented
52#14519700—22no—
53#14519698—22no—
54C22⋊#92418—21no—
55C4×#92418—21no—
56#14519684—22no—
57#14519684D412yes—
58C22×D4×C61D411yescharacteristic
59C23×C4×C61—21no—
60C2×M16×C61—21no—
61C4×D4×C61—21no—
62C4×D4×C61—21no—
63C4×D4×C61C2×C412yes—
64C4×D4×C61D412yes—
65C2×C4⋊C4×C61D411yescharacteristic
66C2×C22⋊C4×C61—21no—
67C2×C42×C61C2311yescharacteristic
68C4⋊C8×C61—21no—
69C4⋊C8×C61—21no—
70C4⋊C8×C61—21no—
71C22⋊C8×C61—21no—
72C4×C8×C61—21no—
73C24×C61—21no—
74C2×D4×C61—24no—
75C2×D4×C61—21no—
76C2×D4×C61C22⋊C412yes—
77C22×C4×C61—21no—
78C22×C4×C61—22no—
79C22×C4×C61—22no—
80C22×C4×C61—41no—
81C22×C4×C61—41no—
82C22×C4×C61—41no—
83C22×C4×C61—41no—
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61C2×D411yescharacteristic
87C22×Dic61—21no—
88C22×Dic61—28no—
89C22×Dic61—22no—
90C22×Dic61—21no—
91C22×Dic61—44no—
92C22×Dic61—44no—
93C2×Dic122—21no—
94C2×Dic122—21no—
95M16×C61—41no—
96M16×C61—41no—
97C2×C8×C61—41no—
98C2×C8×C61—41no—
99C4⋊C4×C61—21no—
100C4⋊C4×C61C22⋊C412yes—
101C22⋊C4×C61—22no—
102C22⋊C4×C61—22no—
103C42×C61C22×C411yescharacteristic
104C42×C61C2×D411yescharacteristic
105C42×C61#4111yescharacteristic
106C42×C61#4111yescharacteristic
107C22⋊Dic61—28no—
108C22⋊Dic61—41no—
109#11758200—44no—
110C4⋊Dic61—24no—
111C4⋊Dic61—21no—
112C4⋊Dic61—21no—
113C4⋊Dic61—21no—
114C4⋊Dic61—21no—
115#11758196—41no—
116#11758196—41no—
117C4×Dic61—24no—
118C4×Dic61—21no—
119C4×Dic61—21no—
120C4×Dic61—21no—
121C4×Dic61—42no—
122C4×Dic61—44no—
123C4×Dic61—41no—
124C4×Dic61—41no—
125C4×Dic61—41no—
126C4×Dic61SD1612yescomplemented
127C2×#92418—22no—
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—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—42no—
143C2×C4×C61—42no—
144C2×C4×C61—42no—
145C2×C4×C61—42no—
146C2×C4×C61C2×C22⋊C411yescharacteristic
147C2×C4×C61C4×D411yescharacteristic
148C2×C4×C61C4×D411yescharacteristic
149C2×C4×C61#12111yescharacteristic
150C2×C4×C61#12111yescharacteristic
151C2×C4×C61#12311yescharacteristic
152C2×C4×C61C2×SD1611yescharacteristic
153C2×C4×C61#13511yescharacteristic
154C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C61#13711yescharacteristic
156C2×Dic61—22no—
157C2×Dic61—22no—
158C2×Dic61—22no—
159C2×Dic61—22no—
160C2×Dic61—24no—
161C2×Dic61—416no—
162C2×Dic61—41no—
163C2×Dic61—42no—
164C2×Dic61—42no—
165C2×Dic61—41no—
166C2×Dic61—41no—
167C2×Dic61—41no—
168Dic122—42no—
169Dic122—81no—
170C8×C61—81no—
171C8×C61—81no—
172#92418—42no—
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—21no—
185C4×C61—21no—
186C4×C61—21no—
187C4×C61—42no—
188C4×C61C2×#10412yes—
189C4×C61C4×SD1611yescharacteristic
190C4×C61#44011yescharacteristic
191C4×C61#46111yescharacteristic
192C4×C61#46311yescharacteristic
193Dic61—24no—
194Dic61—42no—
195Dic61—44no—
196Dic61—81no—
197Dic61—81no—
198#3101—611no—
199C42×D4—611no—
200#1994—611no—
201#1503—611no—
202#1486D6111yescharacteristic
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—1221no—
213C2×C4×D4C2×D6111yescharacteristic
214C22×C42—1221no—
215#483—1221no—
216#476—612no—
217#461—612no—
218#450—1221no—
219C4×SD16—1222no—
220#431—611no—
221#431C2×D6111yescharacteristic
222#423C2×D6111yescharacteristic
223C4×C4⋊C4—611no—
224C4×C4⋊C4—1221no—
225C4×C22⋊C4—1222no—
226C4×C22⋊C4—1221no—
227C43—611no—
228#339—1221no—
229#339—1221no—
230#328—1222no—
231D4⋊C8—22no—
232C61#923111yescharacteristic, complemented, Sylow
233C22×D4D24411yescharacteristic
234C23×C4—21no—
235C23×C4—1222no—
236C2×SD16—1222no—
237C2×M16—21no—
238C4⋊Q8—611no—
239C4⋊Q8—611no—
240#125—1221no—
241C22⋊Q8—1221no—
242C22⋊Q8—1221no—
243C4×Q8—1221no—
244C4×Q8—1221no—
245C4×D4—21no—
246C4×D4—21no—
247C4×D4—1228no—
248C4×D4C4×D6112yes—
249C4×D4C22⋊D6112yes—
250#117—1221no—
251C2×C4⋊C4—1221no—
252C2×C4⋊C4D24411yescharacteristic
253C2×C22⋊C4—21no—
254C2×C22⋊C4—1222no—
255C2×C42—611no—
256C2×C42—611no—
257C2×C42—1221no—
258C2×C42—1222no—
259C2×C42—1221no—
260C2×C42—1221no—
261C2×C42—2442no—
262C2×C42—2442no—
263C2×C42C22×D6111yescharacteristic
264#106—1222no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8—612no—
269#103—1222no—
270#102—1222no—
271C22⋊C8—21no—
272C22⋊C8—1221no—
273C4×C8—21no—
274C4×C8—1221no—
275#95—612no—
276#95—1222no—
277C24—21no—
278C2×Q8—1221no—
279C2×Q8—1221no—
280C2×D4—24no—
281C2×D4—21no—
282C2×D4#1175819812yes—
283C22×C4—21no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—1221no—
291C22×C4—1228no—
292C22×C4—1222no—
293C22×C4—1221no—
294C22×C4—2444no—
295C22×C4—2444no—
296C22×C4C2×D24411yescharacteristic
297C22×C4D4×D6111yescharacteristic
298C22×C4D4×D6111yescharacteristic
299SD16—2444no—
300M16—41no—
301M16—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—1222no—
305C4⋊C4—21no—
306C4⋊C4—1224no—
307C4⋊C4—1221no—
308C4⋊C4—1221no—
309C4⋊C4—1221no—
310C4⋊C4—1221no—
311C4⋊C4—2441no—
312C4⋊C4—2441no—
313C4⋊C4#1175819812yes—
314C22⋊C4—22no—
315C22⋊C4—22no—
316C22⋊C4—1228no—
317C22⋊C4—2441no—
318C42—612no—
319C42—1224no—
320C42—1221no—
321C42—1221no—
322C42—1221no—
323C42—2444no—
324C42—2442no—
325C42—2441no—
326C42—2441no—
327C42—2441no—
328C42C2×C4×D6111yescharacteristic
329C42#1175822411yescharacteristic
330C42#1175822411yescharacteristic
331C42C2×C22⋊D6111yescharacteristic
332C23—24no—
333C23—22no—
334C23—42no—
335C23—41no—
336C23—41no—
337C23#1451974711yescharacteristic
338Q8—4881no—
339Q8—2442no—
340D4—24no—
341D4—22no—
342D4#1451970314yes—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—1222no—
353C2×C4—1222no—
354C2×C4—1222no—
355C2×C4—1222no—
356C2×C4—1224no—
357C2×C4—24416no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2442no—
362C2×C4—2442no—
363C2×C4—2441no—
364C2×C4C2×#1175819811yescharacteristic
365C2×C4#1451973711yescharacteristic
366C2×C4#1451973711yescharacteristic
367C2×C4#1451974911yescharacteristic
368C2×C4#1451974911yescharacteristic
369C2×C4#1451976111yescharacteristic
370C2×C4SD16×D6111yescharacteristic
371C2×C4#1451979611yescharacteristic
372C2×C4#1451980111yescharacteristic
373C2×C4#1451980611yescharacteristic
374C8—81no—
375C8—81no—
376C8—2442no—
377C22—21no—
378C22—21no—
379C22—24no—
380C22—44no—
381C22—44no—
382C22—42no—
383C22—42no—
384C22#1683963911yescharacteristic
385C22#1683991411yescharacteristic
386C22#1683992511yescharacteristic
387C4—21no—
388C4—21no—
389C4—21no—
390C4—42no—
391C4—1224no—
392C4—4881no—
393C4—4881no—
394C4—2442no—
395C4—2444no—
396C4C2×#1451970312yes—
397C4#1683985311yescharacteristic
398C4#1683985911yescharacteristic
399C4#1683996511yescharacteristic
400C4#1683997511yescharacteristic
401C2—21no—
402C2—21no—
403C2—44no—
404C2#2144615111yescharacteristic
405C2#2144626011yescharacteristic
406C2#2144631811yescharacteristic
subgroupG/H
centerC2×C4#14519749
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1486C2
socleC22×C61#386
prime radicalC22×D4×C61D4
cosocleC2×C42×C61C23
hypercenter#1486D61
hypocenterC61#9231
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1486

Complements

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

NH ≅ G/Ntype
3. #21446795C2semidirect
4. #21444319C2semidirect
5. #21443720C2semidirect
6. #21443651C2semidirect
12. #16840052C4semidirect
13. #16839967C4semidirect
31. #14519777C2×C4semidirect
32. #14519777C2×C4semidirect
51. C4⋊#92418C2×C4semidirect
126. C4×Dic61SD16semidirect
232. C61#9231semidirect

Maximal subgroups

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

subgroupindex
#214558272
C4×D4×Dic612
#214467952
#214443192
#214437202
#214436512
C61×#14862
#923161