Finite Group Databasebeta

← #29575245

Subgroups — #29575245

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#21456379C211yesmaximal, characteristic
2#21454565C211yesmaximal, characteristic
3#21444313C211yesmaximal, characteristic
4#21444222C211yesmaximal, characteristic, complemented
5#21443660C211yesmaximal, characteristic, complemented
6#21443657C211yesmaximal, characteristic, complemented
7C61×#1986C211yesmaximal, characteristic, complemented
8C2×#14519785—21no—
9#16840312C2211yescharacteristic
10#16840158C411yescharacteristic, complemented
11#16840136C411yescharacteristic, complemented
12#16840112C411yescharacteristic, complemented
13#16840110C411yescharacteristic, complemented
14#16839993—22no—
15C4×#11758201—22no—
16#16839841—21no—
17#16839835—22no—
18C8×D244—21no—
19#16839815C2211yescharacteristic
20C2×C4⋊#92418C2211yescharacteristic
21#16839730—21no—
22C2×C4×#92418C2211yescharacteristic
23#16839495—22no—
24Q8⋊#92418—21no—
25Q8⋊#92418—21no—
26C61×#533C2211yescharacteristic
27C4×M16×C61C2211yescharacteristic
28C4×C4⋊C4×C61C2211yescharacteristic
29C61×#339—21no—
30C61×#339—21no—
31C2×#11758222—21no—
32C2×#11758201—22no—
33#14519785—42no—
34#14519785—42no—
35C2×#11758189—22no—
36C22×#92418—21no—
37C22×#92418—21no—
38C2×C8×D61—22no—
39#14519777C2×C411yescharacteristic
40#14519774C2×C411yescharacteristic
41#14519765—21no—
42#14519751—21no—
43#14519751D412yes—
44C4×D244—21no—
45C4×D244D412yes—
46#14519708—22no—
47C4⋊#92418—21no—
48C4⋊#92418—21no—
49C4⋊#92418D411yescharacteristic
50C4⋊#92418D411yescharacteristic
51#14519701—22no—
52#14519697—22no—
53C22⋊#92418—21no—
54#14519689—22no—
55#14519689—22no—
56C4×#92418—21no—
57C4×#92418—21no—
58C4×#92418C2×C411yescharacteristic
59C4×#92418C2×C411yescharacteristic
60C2×M16×C61D411yescharacteristic
61C2×M16×C61D411yescharacteristic
62C4⋊Q8×C61C2×C411yescharacteristic
63C4⋊Q8×C61C2×C411yescharacteristic
64#125×C61—21no—
65C22⋊Q8×C61—21no—
66C22⋊Q8×C61—21no—
67C4×Q8×C61—21no—
68C4×Q8×C61—21no—
69#117×C61—21no—
70C2×C4⋊C4×C61—21no—
71C2×C42×C61—21no—
72C2×C42×C61C2311yescharacteristic
73#97×C61—21no—
74C4×C8×C61—21no—
75#95×C61—21no—
76C2×Q8×C61—21no—
77C2×Q8×C61—21no—
78C22×C4×C61—41no—
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61#4111yescharacteristic
82C2×C22⋊D61—22no—
83#11758222—41no—
84#11758222—41no—
85#11758222—41no—
86#11758222—41no—
87C2×D244—21no—
88C2×D244—21no—
89C2×D244C22⋊C412yes—
90C2×C4×D61—22no—
91C2×Dic122—21no—
92M16×C61—21no—
93M16×C61—21no—
94M16×C61—21no—
95M16×C61SD1612yescomplemented
96C2×C8×C61—21no—
97C2×C8×C61—21no—
98C4⋊C4×C61—22no—
99C4⋊C4×C61—21no—
100C4⋊C4×C61—21no—
101C4⋊C4×C61—21no—
102C4⋊C4×C61—21no—
103C4⋊C4×C61—41no—
104C4⋊C4×C61—41no—
105C4⋊C4×C61—41no—
106C22⋊C4×C61—41no—
107C42×C61—41no—
108C42×C61—41no—
109C42×C61—41no—
110C42×C61C22×C411yescharacteristic
111C42×C61C2×D411yescharacteristic
112C42×C61C2×D411yescharacteristic
113C42×C61#4111yescharacteristic
114#11758201—44no—
115#11758198—22no—
116#11758198—22no—
117C4⋊Dic61—21no—
118C4⋊Dic61C22⋊C412yes—
119C2×#92418—21no—
120C2×#92418—21no—
121C2×#92418—21no—
122C2×#92418—21no—
123C2×#92418—42no—
124C2×#92418—41no—
125C2×#92418—41no—
126C2×#92418—41no—
127#11758189—44no—
128C8×D61—44no—
129C23×C61#12111yescharacteristic
130C22×D61—22no—
131Q8×C61—42no—
132Q8×C61—41no—
133Q8×C61—41no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—41no—
137C2×C4×C61—42no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—81no—
141C2×C4×C61—81no—
142C2×C4×C61C2×C22⋊C411yescharacteristic
143C2×C4×C61C4×D411yescharacteristic
144C2×C4×C61C4×D411yescharacteristic
145C2×C4×C61#12011yescharacteristic
146C2×C4×C61#12111yescharacteristic
147C2×C4×C61#12311yescharacteristic
148C2×C4×C61C2×SD1611yescharacteristic
149C2×C4×C61#13511yescharacteristic
150C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C61#13711yescharacteristic
152C22⋊D61—42no—
153C22⋊D61—42no—
154C2×Dic61—22no—
155D244—42no—
156D244—41no—
157D244—41no—
158D244—41no—
159D244—41no—
160C4×D61—42no—
161C4×D61—42no—
162Dic122—41no—
163Dic122—41no—
164C8×C61—22no—
165C8×C61—41no—
166#92418—22no—
167#92418—41no—
168#92418—41no—
169#92418—41no—
170#92418—81no—
171#9055—611nomaximal, Sylow
172C22×C61—21no—
173C22×C61—21no—
174C22×C61#38611yescharacteristic
175C22×C61#46111yescharacteristic
176C22×C61#46311yescharacteristic
177C2×D61—42no—
178C2×D61—42no—
179C2×D61—42no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—21no—
183C4×C61—82no—
184C4×C61—81no—
185C4×C61—81no—
186C4×C61C4×SD1611yescharacteristic
187C4×C61#44011yescharacteristic
188C4×C61#44311yescharacteristic
189C4×C61#44411yescharacteristic
190C4×C61#45011yescharacteristic
191C4×C61#45211yescharacteristic
192Dic61—42no—
193#3167—611no—
194#2935—611no—
195#1986D6111yescharacteristic, complemented
196#1502—611no—
197#1481—611no—
198#1279—611no—
199#1278—611no—
200C2×C61—21no—
201C2×C61—21no—
202C2×C61#187611yescharacteristic
203C2×C61#187711yescharacteristic
204C2×C61#188411yescharacteristic
205D61—82no—
206C2×#131—1221no—
207#533C2×D6111yescharacteristic
208#532—611no—
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#431—611no—
219C2×C4⋊C8—611no—
220#408—1221no—
221C4×M16C2×D6111yescharacteristic
222C2×C4×C8—611no—
223C4×C4⋊C4C2×D6111yescharacteristic
224#339—21no—
225#339—21no—
226#327—1222no—
227Q8⋊C8—1221no—
228Q8⋊C8—1221no—
229C61#905511yescharacteristic, complemented, Sylow
230C2×#41—1221no—
231C2×SD16—1222no—
232#131—2442no—
233#131—2442no—
234C2×M16—1222no—
235C2×M16C22⋊D6111yescharacteristic
236C2×M16C22⋊D6111yescharacteristic
237C22×C8—1222no—
238C22×C8—1221no—
239C22×C8—1221no—
240C4⋊Q8—611no—
241C4⋊Q8C4×D6111yescharacteristic
242C4⋊Q8C4×D6111yescharacteristic
243#127—611no—
244#125—21no—
245#124—1221no—
246C22⋊Q8—21no—
247C22⋊Q8—21no—
248#121—612no—
249#121—1221no—
250C4×Q8—21no—
251C4×Q8—21no—
252C4×D4—612no—
253C4×D4—1221no—
254#117—21no—
255C2×C4⋊C4—21no—
256C2×C42—21no—
257C2×C42C22×D6111yescharacteristic
258#106—1222no—
259C4⋊C8—611no—
260C4⋊C8—611no—
261C4⋊C8—1221no—
262C4⋊C8—1221no—
263#103—1222no—
264#102—1222no—
265C22⋊C8—1222no—
266C22⋊C8—1222no—
267C22⋊C8—1221no—
268#97—21no—
269C4×C8—21no—
270C4×C8—611no—
271C4×C8—611no—
272C4×C8—1221no—
273C4×C8—1221no—
274#95—21no—
275#41—2441no—
276#41—2441no—
277#41—2441no—
278#41—2441no—
279C2×Q8—21no—
280C2×Q8—21no—
281C2×Q8—1221no—
282C2×D4—612no—
283C2×D4—1222no—
284C2×D4—1221no—
285C2×D4—1221no—
286C22×C4—41no—
287C22×C4—1222no—
288C22×C4D4×D6111yescharacteristic
289C22×C4#1175822411yescharacteristic
290C22×C4C2×C22⋊D6111yescharacteristic
291SD16—2444no—
292M16—21no—
293M16—21no—
294M16—21no—
295M16—2444no—
296M16#1175820112yescomplemented
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—1221no—
300C2×C8—1221no—
301C2×C8—1221no—
302C2×C8—1221no—
303C2×C8—2444no—
304C2×C8—2442no—
305C2×C8—2441no—
306C2×C8—2441no—
307C2×C8—2441no—
308C4⋊C4—22no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—612no—
317C4⋊C4—1221no—
318C22⋊C4—41no—
319C22⋊C4—1222no—
320C22⋊C4—1222no—
321C42—41no—
322C42—41no—
323C42—41no—
324C42C2×C4×D6111yescharacteristic
325C42#1175822211yescharacteristic
326C42D4×D6111yescharacteristic
327C42D4×D6111yescharacteristic
328C23—1222no—
329C23#1451974811yescharacteristic
330Q8—42no—
331Q8—41no—
332Q8—41no—
333Q8—2441no—
334Q8—2441no—
335D4—2442no—
336D4—2442no—
337D4—2442no—
338D4—2441no—
339D4—2441no—
340D4—2441no—
341D4—2441no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—1222no—
351C2×C4—2442no—
352C2×C4—2442no—
353C2×C4C22⋊C4×D6111yescharacteristic
354C2×C4#1451973711yescharacteristic
355C2×C4C4×C22⋊D6111yescharacteristic
356C2×C4#1451974511yescharacteristic
357C2×C4#1451975011yescharacteristic
358C2×C4#1451975911yescharacteristic
359C2×C4C2×#1175820111yescharacteristic
360C2×C4#1451979711yescharacteristic
361C2×C4#1451980211yescharacteristic
362C2×C4#1451980811yescharacteristic
363C8—22no—
364C8—41no—
365C8—1222no—
366C8—4881no—
367C8—2441no—
368C8—2441no—
369C8—2441no—
370C22—21no—
371C22—21no—
372C22—2442no—
373C22—2442no—
374C22—2442no—
375C22#1683963811yescharacteristic
376C22#1683996411yescharacteristic
377C22#1683997411yescharacteristic
378C4—21no—
379C4—21no—
380C4—21no—
381C4—82no—
382C4—81no—
383C4—81no—
384C4—2442no—
385C4C4×#1175820111yescharacteristic
386C4#1683986011yescharacteristic
387C4#1683987611yescharacteristic
388C4#1683988111yescharacteristic
389C4#1683991211yescharacteristic
390C4#1683992211yescharacteristic
391C2—21no—
392C2—21no—
393C2—4882no—
394C2#2144614311yescharacteristic
395C2#2144615611yescharacteristic
396C2#2144619911yescharacteristic
subgroupG/H
centerC2×C4#14519745
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1986C2
socleC22×C61#386
prime radical#16840312C22
cosocleC2×C42×C61C23
hypercenter#1986D61
hypocenterC61#9055
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1986

Complements

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

NH ≅ G/Ntype
4. #21444222C2semidirect
5. #21443660C2semidirect
6. #21443657C2semidirect
7. C61×#1986C2semidirect
10. #16840158C4semidirect
11. #16840136C4semidirect
12. #16840112C4semidirect
13. #16840110C4semidirect
95. M16×C61SD16semidirect
195. #1986D61semidirect
229. C61#9055semidirect
296. M16#11758201semidirect

Maximal subgroups

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

subgroupindex
#214563792
#214545652
#214443132
#214442222
#214436602
#214436572
C61×#19862
#905561