Finite Group Databasebeta

← #14767656

Subgroups — #14767656

Order 2816.

818 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079061C211yesmaximal, characteristic
2#13077328C211yesmaximal, characteristic, complemented
3#13077327C211yesmaximal, characteristic, complemented
4#13069448C211yesmaximal, characteristic, complemented
5#13068941C214yesmaximal, complemented
6#13068940C214yesmaximal, complemented
7#13068756C211yesmaximal, characteristic, complemented
8#13068368C211yesmaximal, characteristic, complemented
9C11×#1963C211yesmaximal, characteristic, complemented
10C11×#532C2211yescharacteristic
11C2×#67003C2214yes—
12C2×#67001C2212yes—
13C2×#66960C2212yes—
14#10623008C2211yescharacteristic
15C11×#423C2211yescharacteristic
16C2×C11×#104C2214yes—
17C11×#376C2211yescharacteristic
18#10622847C2212yes—
19#10622742C2212yes—
20#10622699C412yescomplemented
21#10622687C412yescomplemented
22#10622673C412yescomplemented
23#10622671C412yescomplemented
24#10622625—21no—
25#10622625—21no—
26D4×C11⋊C8—21no—
27D4×C11⋊C8—21no—
28C2×#66869C2214yes—
29#10622537C2211yescharacteristic
30C2×#66867C2211yescharacteristic
31C2×C4×C11⋊C8C2211yescharacteristic
32#10622451—21no—
33#10622451—21no—
34#10622447—21no—
35#10622447—21no—
36#10622196C2214yes—
37#10622162C2212yes—
38#10622162C2212yes—
39C2×C11×#41C2312yes—
40C2×#4339C2312yes—
41C2×C11×M16C2312yes—
42C11×C4⋊Q8C2×C411yescharacteristic
43C11×#127C2×C411yescharacteristic
44C11×#124C2×C412yes—
45C11×#121—21no—
46C11×#121—21no—
47C4×D4×C11—21no—
48C4×D4×C11—21no—
49C2×C42×C11C2312yes—
50C2×C42×C11C2311yescharacteristic
51#67003—44no—
52#67003—44no—
53#67001—44no—
54C2×#4326C2×C414yes—
55C2×#4325C2×C414yes—
56C2×#4324C2×C414yes—
57C2×#4323C2×C414yes—
58#66983—21no—
59#66983—21no—
60C2×#4318—22no—
61C2×#4318C2312yes—
62C22×C11⋊C8—22no—
63C22×C11⋊C8C2312yes—
64C22×C11⋊C8C2311yescharacteristic
65C22×C11⋊C8C2311yescharacteristic
66#66960—44no—
67C2×#4313—22no—
68C2×C8×D11—22no—
69#66928C2×C412yes—
70#66927C2×C411yescharacteristic
71C4×D44—21no—
72C4×D44—21no—
73#66922C2×C411yescharacteristic
74C11×C4⋊C8—21no—
75C11×C4⋊C8—21no—
76C11×#104—44no—
77C11×#95—21no—
78C11×#95—21no—
79C22⋊(C11⋊C8)—22no—
80C22⋊(C11⋊C8)—22no—
81(C2×D11)⋊C8—22no—
82(C2×D11)⋊C8—22no—
83#66869—44no—
84C4⋊(C11⋊C8)—21no—
85C4⋊(C11⋊C8)—21no—
86#66867C2×C412yes—
87#66867C2×C412yes—
88C4×C11⋊C8D411yescharacteristic
89C4×C11⋊C8D411yescharacteristic
90C4×C11⋊C8D411yescharacteristic
91C4×C11⋊C8D411yescharacteristic
92#22281—111nomaximal, Sylow
93C11×#41—24no—
94C11×#41—24no—
95C2×Q8×C11C22×C412yes—
96C2×D4×C11—22no—
97C2×D4×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11C22×C412yes—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11#4111yescharacteristic
103C22×C4×C11#4111yescharacteristic
104C22×C4×C11C2411yescharacteristic
105C2×C22⋊D11—22no—
106#4339—24no—
107#4339—24no—
108C2×D44—21no—
109C2×D44—21no—
110C2×D44C22×C412yes—
111C2×C4×D11—22no—
112C2×Dic22C22×C412yes—
113C11×M16—24no—
114C2×C8×C11—22no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—21no—
117C11×C22⋊C4—22no—
118C11×C22⋊C4—22no—
119C42×C11—22no—
120C42×C11—22no—
121C42×C11C22×C411yescharacteristic
122C42×C11C22×C411yescharacteristic
123C42×C11C2×D411yescharacteristic
124C42×C11C2×D411yescharacteristic
125#4326—44no—
126#4325—44no—
127#4324—44no—
128#4323—44no—
129(C2×D11)⋊C4—22no—
130(C2×D11)⋊C4—22no—
131C4⋊Dic11—21no—
132C4⋊Dic11—21no—
133#4318—24no—
134#4318—44no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—22no—
139C2×C11⋊C8—22no—
140C2×C11⋊C8—44no—
141C2×C11⋊C8C22×C414yes—
142C2×C11⋊C8C2×D411yescharacteristic
143C2×C11⋊C8C2×D411yescharacteristic
144C2×C11⋊C8C2×D411yescharacteristic
145C2×C11⋊C8C2×D411yescharacteristic
146#4313—44no—
147C8×D11—44no—
148#3150—111no—
149#2931—111no—
150#2931—111no—
151#1963—111no—
152#1963D1111yescharacteristic, complemented
153#1876—114no—
154#1876—114no—
155#1838—111no—
156#1746—111no—
157C23×C11—22no—
158C23×C11C2×#4111yescharacteristic
159C22×D11—22no—
160Q8×C11—24no—
161D4×C11—24no—
162D4×C11—42no—
163D4×C11—42no—
164D4×C11—44no—
165C2×C4×C11—22no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11C4×D411yescharacteristic
174C2×C4×C11C4×D411yescharacteristic
175C2×C4×C11C4×D411yescharacteristic
176C2×C4×C11C4×D411yescharacteristic
177C2×C4×C11C23×C411yescharacteristic
178C2×C4×C11C22×D411yescharacteristic
179C2×C4×C11H(5,𝔽2)12yes—
180C2×C4×C11H(5,𝔽2)12yes—
181C22⋊D11—44no—
182C2×Dic11—22no—
183D44—24no—
184D44—42no—
185D44—42no—
186C4×D11—42no—
187C4×D11—42no—
188Dic22—24no—
189C8×C11—42no—
190C11⋊C8—24no—
191C11⋊C8—21no—
192C11⋊C8—21no—
193C11⋊C8—21no—
194C11⋊C8—21no—
195C11⋊C8—42no—
196C2×#135—114no—
197C2×#131—112no—
198C2×#131—112no—
199#532—111no—
200#532C2×D1111yescharacteristic
201#497—112no—
202#497—112no—
203#496—112no—
204#496—112no—
205#436—221no—
206#436—221no—
207#436—221no—
208#436—221no—
209C8×D4—221no—
210C8×D4—221no—
211C8×D4—221no—
212C8×D4—221no—
213#423—111no—
214#423C2×D1111yescharacteristic
215C2×#104—114no—
216C2×#104C2×D1114yes—
217#408—112no—
218#408—112no—
219C2×#97—111no—
220C2×C4×C8—111no—
221#376C2×D1111yescharacteristic
222#341—114no—
223#336—112no—
224#336—112no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—42no—
228C22×C11—42no—
229C22×C11—42no—
230C22×C11C2×C4×D411yescharacteristic
231C22×C11#54012yes—
232C2×D11—42no—
233C2×D11—42no—
234C2×D11—42no—
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—21no—
238C4×C11—21no—
239C4×C11—42no—
240C4×C11—82no—
241C4×C11#51812yes—
242C4×C11#53511yescharacteristic
243C4×C11#53511yescharacteristic
244Dic11—42no—
245C2×#41—112no—
246C2×#41C22×D1112yes—
247#135—444no—
248#135—444no—
249C2×Q16—114no—
250C2×SD16—114no—
251C2×SD16—114no—
252C2×D8—114no—
253#131—444no—
254#131—444no—
255C2×M16—112no—
256C2×M16—222no—
257C2×M16—222no—
258C2×M16C22×D1112yes—
259C22×C8—111no—
260C22×C8—111no—
261C22×C8—112no—
262C22×C8—222no—
263C22×C8—222no—
264C4⋊Q8—111no—
265C4⋊Q8C4×D1111yescharacteristic
266#127—111no—
267#127C4×D1111yescharacteristic
268#124—112no—
269#124C4×D1112yes—
270#121—21no—
271#121—21no—
272#121—221no—
273#121—221no—
274C4×D4—21no—
275C4×D4—21no—
276C4×D4—221no—
277C4×D4—221no—
278C2×C42C22×D1112yes—
279C2×C42C22×D1111yescharacteristic
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8—221no—
283C4⋊C8—221no—
284#104—44no—
285#104—444no—
286C22⋊C8—222no—
287C22⋊C8—222no—
288C22⋊C8—222no—
289C22⋊C8—222no—
290#97—112no—
291#97—112no—
292C4×C8—111no—
293C4×C8—111no—
294C4×C8—111no—
295C4×C8—111no—
296#95—21no—
297#95—21no—
298C2×C11—22no—
299C2×C11—82no—
300C2×C11#232811yescharacteristic
301C2×C11#295511yescharacteristic
302C2×C11#295511yescharacteristic
303D11—82no—
304#41—24no—
305#41—24no—
306#41—224no—
307#41—224no—
308C2×Q8—112no—
309C2×Q8C2×C4×D1112yes—
310C2×D4—22no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—112no—
314C2×D4—222no—
315C2×D4—221no—
316C2×D4—221no—
317C2×D4C2×C4×D1112yes—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—222no—
321C22×C4#434111yescharacteristic
322C22×C4#434111yescharacteristic
323C22×C4C23×D1111yescharacteristic
324Q16—444no—
325SD16—444no—
326SD16—444no—
327D8—444no—
328M16—24no—
329M16—224no—
330M16—444no—
331M16—444no—
332C2×C8—22no—
333C2×C8—114no—
334C2×C8—111no—
335C2×C8—111no—
336C2×C8—111no—
337C2×C8—111no—
338C2×C8—222no—
339C2×C8—222no—
340C2×C8—222no—
341C2×C8—222no—
342C2×C8—222no—
343C2×C8—444no—
344C2×C8—444no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—221no—
348C4⋊C4—221no—
349C22⋊C4—22no—
350C22⋊C4—22no—
351C22⋊C4—222no—
352C22⋊C4—222no—
353C42—22no—
354C42—22no—
355C42C2×C4×D1111yescharacteristic
356C42C2×C4×D1111yescharacteristic
357C42D4×D1111yescharacteristic
358C42D4×D1111yescharacteristic
359C11#2228111yescharacteristic, complemented, Sylow
360C23—22no—
361C23—222no—
362C23C2×#434111yescharacteristic
363Q8—24no—
364Q8—224no—
365D4—24no—
366D4—42no—
367D4—42no—
368D4—44no—
369D4—224no—
370D4—442no—
371D4—442no—
372D4—444no—
373C2×C4—22no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—222no—
382C2×C4—442no—
383C2×C4—442no—
384C2×C4(C22⋊D11)⋊C411yescharacteristic
385C2×C4(C22⋊D11)⋊C411yescharacteristic
386C2×C4(C22⋊D11)⋊C411yescharacteristic
387C2×C4(C22⋊D11)⋊C411yescharacteristic
388C2×C4C22×C4×D1111yescharacteristic
389C2×C4C2×D4×D1111yescharacteristic
390C2×C4#6703712yes—
391C2×C4#6704212yes—
392C8—42no—
393C8—221no—
394C8—221no—
395C8—224no—
396C8—221no—
397C8—221no—
398C8—442no—
399C22—21no—
400C22—21no—
401C22—42no—
402C22—42no—
403C22—42no—
404C22—442no—
405C22—442no—
406C22—442no—
407C22C2×(C22⋊D11)⋊C411yescharacteristic
408C22#1062315012yes—
409C4—21no—
410C4—21no—
411C4—21no—
412C4—21no—
413C4—42no—
414C4—82no—
415C4—442no—
416C4#1062307612yes—
417C4#1062320511yescharacteristic
418C4#1062324611yescharacteristic
419C2—22no—
420C2—82no—
421C2—882no—
422C2#1307134011yescharacteristic
423C2#1307751511yescharacteristic
424C2#1307751511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1963C2
socleC22×C11C2×C4×D4
prime radical#13079061C2
cosocleC22×C4×C11C24
hypercenter#1963D11
hypocenterC11#22281
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1963

Complements

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

NH ≅ G/Ntype
2. #13077328C2semidirect
3. #13077327C2semidirect
4. #13069448C2semidirect
5. #13068941C2semidirect
6. #13068940C2semidirect
7. #13068756C2semidirect
8. #13068368C2semidirect
9. C11×#1963C2semidirect
20. #10622699C4semidirect
21. #10622687C4semidirect
22. #10622673C4semidirect
23. #10622671C4semidirect
152. #1963D11semidirect
359. C11#22281semidirect

Maximal subgroups

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

subgroupindex
#130790612
#130773282
#130773272
#130694482
#130689412
#130689402
#130687562
#130683682
C11×#19632
#2228111