Finite Group Databasebeta

← #29576290

Subgroups — #29576290

Order 15616.

550 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455827C211yesmaximal, characteristic
2#21448284C211yesmaximal, characteristic
3#21446795C211yesmaximal, characteristic, complemented
4#21444319C211yesmaximal, characteristic, complemented
5#21443720C211yesmaximal, characteristic, complemented
6#21443651C211yesmaximal, characteristic, complemented
7C61×#1486C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9C2×#14519736—21no—
10#16840092—21no—
11#16840052C412yescomplemented
12#16839967C412yescomplemented
13#16839913—21no—
14C4×#11758200—22no—
15#16839815C2211yescharacteristic
16#16839665—21no—
17#16839661—21no—
18#16839655—22no—
19C4×C4⋊Dic61C2211yescharacteristic
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—
29C2×#11758200—22no—
30#14519777C2×C411yescharacteristic
31#14519777C2×C411yescharacteristic
32#14519769—21no—
33#14519756—21no—
34#14519756—21no—
35C4×Dic122—21no—
36C4×Dic122—21no—
37#14519736—21no—
38#14519736—42no—
39#14519736—42no—
40C2×C4⋊Dic61—22no—
41C2×C4⋊Dic61—21no—
42C2×C22⋊Dic61—22no—
43C2×C22⋊Dic61—22no—
44C2×C4×Dic61—21no—
45C2×C4×Dic61—21no—
46C2×C4×Dic61—21no—
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49#14519708—22no—
50C4⋊#92418C2×C412yes—
51#14519700—22no—
52#14519698—22no—
53C22⋊#92418—21no—
54C4×#92418—21no—
55#14519684—22no—
56#14519684D412yes—
57C22×D4×C61D411yescharacteristic
58C23×C4×C61—21no—
59C2×M16×C61—21no—
60C4×D4×C61—21no—
61C4×D4×C61—21no—
62C4×D4×C61C2×C412yes—
63C4×D4×C61D412yes—
64C2×C4⋊C4×C61D411yescharacteristic
65C2×C22⋊C4×C61—21no—
66C2×C42×C61C2311yescharacteristic
67C4⋊C8×C61—21no—
68C4⋊C8×C61—21no—
69C4⋊C8×C61—21no—
70C22⋊C8×C61—21no—
71C4×C8×C61—21no—
72C24×C61—21no—
73C2×D4×C61—21no—
74C2×D4×C61—42no—
75C2×D4×C61C22⋊C412yes—
76C22×C4×C61—21no—
77C22×C4×C61—22no—
78C22×C4×C61—22no—
79C22×C4×C61—41no—
80C22×C4×C61—41no—
81C22×C4×C61—41no—
82C22×C4×C61—41no—
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C22×Dic61—21no—
87C22×Dic61—21no—
88C22×Dic61—22no—
89C2×Dic122—21no—
90C2×Dic122—21no—
91M16×C61—41no—
92M16×C61—41no—
93C2×C8×C61—41no—
94C2×C8×C61—41no—
95C4⋊C4×C61—21no—
96C4⋊C4×C61C22⋊C412yes—
97C22⋊C4×C61—22no—
98C22⋊C4×C61—22no—
99C42×C61C22×C411yescharacteristic
100C42×C61C2×D411yescharacteristic
101C42×C61#4111yescharacteristic
102C42×C61#4111yescharacteristic
103C22⋊Dic61—44no—
104C22⋊Dic61—44no—
105C22⋊Dic61—41no—
106#11758200—44no—
107C4⋊Dic61—21no—
108C4⋊Dic61—21no—
109C4⋊Dic61—21no—
110C4⋊Dic61—21no—
111C4⋊Dic61—44no—
112C4⋊Dic61—42no—
113#11758196—41no—
114#11758196—41no—
115C4×Dic61—21no—
116C4×Dic61—21no—
117C4×Dic61—21no—
118C4×Dic61—42no—
119C4×Dic61—42no—
120C4×Dic61—41no—
121C4×Dic61—41no—
122C4×Dic61—41no—
123C4×Dic61SD1612yescomplemented
124C2×#92418—22no—
125C23×C61—22no—
126C23×C61—42no—
127C23×C61—42no—
128C23×C61—41no—
129C23×C61—41no—
130C23×C61#12011yescharacteristic
131D4×C61—22no—
132D4×C61—22no—
133D4×C61—42no—
134C2×C4×C61—22no—
135C2×C4×C61—22no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—42no—
140C2×C4×C61—42no—
141C2×C4×C61—42no—
142C2×C4×C61—42no—
143C2×C4×C61C2×C22⋊C411yescharacteristic
144C2×C4×C61C4×D411yescharacteristic
145C2×C4×C61C4×D411yescharacteristic
146C2×C4×C61#12111yescharacteristic
147C2×C4×C61#12111yescharacteristic
148C2×C4×C61#12311yescharacteristic
149C2×C4×C61C2×SD1611yescharacteristic
150C2×C4×C61#13511yescharacteristic
151C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C61#13711yescharacteristic
153C2×Dic61—22no—
154C2×Dic61—22no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—42no—
160C2×Dic61—42no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—42no—
164Dic122—42no—
165Dic122—81no—
166C8×C61—81no—
167C8×C61—81no—
168#92418—42no—
169#9235—611nomaximal, Sylow
170C22×C61—21no—
171C22×C61—21no—
172C22×C61—42no—
173C22×C61—42no—
174C22×C61—42no—
175C22×C61—82no—
176C22×C61—82no—
177C22×C61#38611yescharacteristic
178C22×C61#45011yescharacteristic
179C22×C61#45211yescharacteristic
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—21no—
183C4×C61—42no—
184C4×C61#42112yes—
185C4×C61C4×SD1611yescharacteristic
186C4×C61#44011yescharacteristic
187C4×C61#46111yescharacteristic
188C4×C61#46311yescharacteristic
189Dic61—42no—
190Dic61—42no—
191Dic61—82no—
192Dic61—81no—
193Dic61—81no—
194#3101—611no—
195#2293—611no—
196#1994—611no—
197#1503—611no—
198#1486D6111yescharacteristic
199#1303—611no—
200#1276—611no—
201C2×C61—21no—
202C2×C61—21no—
203C2×C61—82no—
204C2×C61#187711yescharacteristic
205C2×C61#189711yescharacteristic
206C2×C61#190611yescharacteristic
207#533—611no—
208C2×C4×D4C2×D6111yescharacteristic
209C2×#117—1221no—
210#483—1221no—
211#476—612no—
212#461—612no—
213#450—1221no—
214C4×SD16—1222no—
215#431—611no—
216#431C2×D6111yescharacteristic
217#423C2×D6111yescharacteristic
218#390—1221no—
219#389—1221no—
220#388—1222no—
221C4×C4⋊C4—611no—
222C4×C22⋊C4—1221no—
223C43—611no—
224#339—1221no—
225#339—1221no—
226#328—1222no—
227D4⋊C8—22no—
228C61#923511yescharacteristic, complemented, Sylow
229C22×D4D24411yescharacteristic
230C23×C4—21no—
231C2×SD16—1222no—
232C2×M16—21no—
233C4⋊Q8—611no—
234C4⋊Q8—611no—
235#125—1221no—
236C22⋊Q8—1221no—
237C22⋊Q8—1221no—
238C4×Q8—1221no—
239C4×Q8—1221no—
240C4×D4—21no—
241C4×D4—21no—
242C4×D4C4×D6112yes—
243C4×D4C22⋊D6112yes—
244#117—1221no—
245#117—2442no—
246#117—2442no—
247C2×C4⋊C4—1222no—
248C2×C4⋊C4—1221no—
249C2×C4⋊C4D24411yescharacteristic
250C2×C22⋊C4—21no—
251C2×C22⋊C4—1222no—
252C2×C22⋊C4—1222no—
253C2×C42—611no—
254C2×C42—611no—
255C2×C42—1221no—
256C2×C42—1221no—
257C2×C42—1221no—
258C2×C42C22×D6111yescharacteristic
259#106—1222no—
260C4⋊C8—21no—
261C4⋊C8—21no—
262C4⋊C8—21no—
263C4⋊C8—612no—
264#103—1222no—
265#102—1222no—
266C22⋊C8—21no—
267C22⋊C8—1221no—
268C4×C8—21no—
269C4×C8—1221no—
270#95—612no—
271#95—1222no—
272C24—21no—
273C2×Q8—1221no—
274C2×Q8—1221no—
275C2×D4—21no—
276C2×D4—42no—
277C2×D4#1175819812yes—
278C22×C4—21no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—1221no—
286C22×C4—1221no—
287C22×C4—1222no—
288C22×C4C2×D24411yescharacteristic
289C22×C4D4×D6111yescharacteristic
290C22×C4D4×D6111yescharacteristic
291SD16—2444no—
292M16—41no—
293M16—41no—
294C2×C8—41no—
295C2×C8—41no—
296C2×C8—1222no—
297C4⋊C4—21no—
298C4⋊C4—1221no—
299C4⋊C4—1221no—
300C4⋊C4—1221no—
301C4⋊C4—1221no—
302C4⋊C4—2442no—
303C4⋊C4—2444no—
304C4⋊C4—2441no—
305C4⋊C4—2441no—
306C4⋊C4#1175819812yes—
307C22⋊C4—22no—
308C22⋊C4—22no—
309C22⋊C4—2444no—
310C22⋊C4—2444no—
311C22⋊C4—2441no—
312C42—612no—
313C42—1221no—
314C42—1221no—
315C42—1221no—
316C42—2442no—
317C42—2442no—
318C42—2441no—
319C42—2441no—
320C42—2441no—
321C42C2×C4×D6111yescharacteristic
322C42#1175822411yescharacteristic
323C42#1175822411yescharacteristic
324C42C2×C22⋊D6111yescharacteristic
325C23—22no—
326C23—42no—
327C23—42no—
328C23—41no—
329C23—41no—
330C23#1451974711yescharacteristic
331Q8—4881no—
332Q8—2442no—
333D4—22no—
334D4—22no—
335D4—42no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—1222no—
346C2×C4—1222no—
347C2×C4—2442no—
348C2×C4—2442no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4—2442no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4C2×#1175819811yescharacteristic
357C2×C4#1451973711yescharacteristic
358C2×C4#1451973711yescharacteristic
359C2×C4#1451974911yescharacteristic
360C2×C4#1451974911yescharacteristic
361C2×C4#1451976111yescharacteristic
362C2×C4SD16×D6111yescharacteristic
363C2×C4#1451979611yescharacteristic
364C2×C4#1451980111yescharacteristic
365C2×C4#1451980611yescharacteristic
366C8—81no—
367C8—81no—
368C8—2442no—
369C22—21no—
370C22—21no—
371C22—42no—
372C22—42no—
373C22—42no—
374C22—82no—
375C22—82no—
376C22#1683963911yescharacteristic
377C22#1683991411yescharacteristic
378C22#1683992511yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—42no—
383C4—4882no—
384C4—4881no—
385C4—4881no—
386C4—2442no—
387C4—2442no—
388C4#1683977812yes—
389C4#1683985311yescharacteristic
390C4#1683985911yescharacteristic
391C4#1683996511yescharacteristic
392C4#1683997511yescharacteristic
393C2—21no—
394C2—21no—
395C2—82no—
396C2#2144615111yescharacteristic
397C2#2144626511yescharacteristic
398C2#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#9235
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
11. #16840052C4semidirect
12. #16839967C4semidirect
123. C4×Dic61SD16semidirect
228. C61#9235semidirect

Maximal subgroups

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

subgroupindex
#214558272
#214482842
#214467952
#214443192
#214437202
#214436512
C61×#14862
#923561