Finite Group Databasebeta

← #14646512

Subgroups — #14646512

Order 2816.

614 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
1C4×#66977C211yesmaximal, characteristic
2C2×#10622105C212yesmaximal
3#13066843C211yesmaximal, characteristic
4#13066496C212yesmaximal
5C11×#1797C211yesmaximal, characteristic
6C22×C42×C11C2211yescharacteristic
7C2×#66977C2211yescharacteristic
8C2×C4×Dic22C411yescharacteristic, complemented
9C2×C11×C4⋊C8—21no—
10C2×C11×C22⋊C8C2212yes—
11#10622825C2211yescharacteristic
12#10622823—21no—
13C4×C22⋊Dic11—21no—
14C2×C11⋊#95—21no—
15C2×C11⋊#95—21no—
16C2×C11⋊#95C2212yes—
17C4×C4⋊Dic11C411yescharacteristic, complemented
18#10622546—21no—
19C4×Dic11⋊C4—21no—
20#10622542C411yescharacteristic, complemented
21#10622541C411yescharacteristic, complemented
22C11×#336—21no—
23#10622105—24no—
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C23×C4×C11C2311yescharacteristic
27C23×Dic11—22no—
28C22×Dic22C2×C411yescharacteristic
29C22×C8×C11—22no—
30C2×C42×C11—42no—
31C2×C42×C11C2×C411yescharacteristic
32C2×C42×C11C2×C411yescharacteristic
33C2×C42×C11D411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37C2×C4⋊Dic11C2×C411yescharacteristic
38C2×C4⋊Dic11C2×C411yescharacteristic
39C2×C4⋊Dic11C2×C411yescharacteristic
40#66977—21no—
41#66977—21no—
42#66977D412yes—
43#66977Q812yes—
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4—21no—
47C2×C4×Dic11—21no—
48C2×C4×Dic11—21no—
49C4×Dic22—42no—
50C11×C4⋊C8—42no—
51C11×C22⋊C8—22no—
52C11×C22⋊C8—22no—
53C11⋊#95—24no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—22no—
60C11⋊#95—22no—
61C11⋊#95—42no—
62#8574—111nomaximal, Sylow
63C24×C11C2×D411yescharacteristic
64C22×C4×C11—22no—
65C22×C4×C11—22no—
66C22×C4×C11—22no—
67C22×C4×C11—22no—
68C22×C4×C11—41no—
69C22×C4×C11—41no—
70C22×C4×C11—41no—
71C22×C4×C11—41no—
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11C22×C411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×Q811yescharacteristic
80C22×C4×C11#4111yescharacteristic
81C22×C4×C11#4111yescharacteristic
82C22×Dic11—24no—
83C22×Dic11—21no—
84C22×Dic11—21no—
85C22×Dic11—21no—
86C22×Dic11—21no—
87C22×Dic11—42no—
88C22×Dic11—42no—
89C22×Dic11—42no—
90C22×Dic11—42no—
91C22×Dic11—42no—
92C22×Dic11—42no—
93C2×Dic22—21no—
94C2×Dic22—41no—
95C2×Dic22—41no—
96C2×Dic22C4⋊C412yes—
97C2×C8×C11—42no—
98C2×C8×C11—42no—
99C2×C8×C11—42no—
100C42×C11—22no—
101C42×C11—22no—
102C42×C11—41no—
103C42×C11—41no—
104C22⋊Dic11—22no—
105C22⋊Dic11—22no—
106C22⋊Dic11—42no—
107C4⋊Dic11—21no—
108C4⋊Dic11—41no—
109C4⋊Dic11—41no—
110C4⋊Dic11C4⋊C412yes—
111Dic11⋊C4—22no—
112Dic11⋊C4—22no—
113Dic11⋊C4—42no—
114Dic11⋊C4—42no—
115C4×Dic11—42no—
116C4×Dic11—42no—
117C4×C22⋊Q8—111no—
118#1797D1111yescharacteristic
119C2×#328—112no—
120#1434—111no—
121#1294—112no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11—21no—
126C23×C11C2×C22⋊C411yescharacteristic
127C23×C11#12111yescharacteristic
128C23×C11C22⋊Q811yescharacteristic
129C23×C11#13512yes—
130C23×C11#13712yes—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—44no—
150C2×C4×C11—44no—
151C2×C4×C11#9912yes—
152C2×C4×C11#10412yes—
153C2×C4×C11C2×C4⋊C411yescharacteristic
154C2×C4×C11#11711yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11C22⋊Q811yescharacteristic
157C2×Dic11—22no—
158C2×Dic11—22no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—44no—
164C2×Dic11—44no—
165C2×Dic11—44no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—82no—
173C2×Dic11—82no—
174C2×Dic11—82no—
175C2×Dic11—82no—
176Dic22—42no—
177Dic22—42no—
178C8×C11—82no—
179C2×C22⋊Q8—111no—
180C2×C4×Q8—111no—
181C22×C42C2×D1111yescharacteristic
182C2×C4⋊C8—21no—
183C2×C22⋊C8C2×D1112yes—
184#391—111no—
185#389—111no—
186#387—221no—
187#385—221no—
188#380—111no—
189C4×C4⋊C4—111no—
190C4×C4⋊C4—221no—
191C4×C22⋊C4—221no—
192C2×#95—112no—
193C2×#95—221no—
194C2×#95—221no—
195#336—21no—
196#328—224no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—22no—
202C22×C11—22no—
203C22×C11—22no—
204C22×C11—22no—
205C22×C11#38011yescharacteristic
206C22×C11C2×#9911yescharacteristic
207C22×C11#41011yescharacteristic
208C22×C11#41611yescharacteristic
209C22×C11#41911yescharacteristic
210C22×C11C2×#10411yescharacteristic
211C22×C11#42111yescharacteristic
212C22×C11#46412yes—
213C22×C11#47912yes—
214C4×C11—21no—
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—22no—
219C4×C11—22no—
220C4×C11—41no—
221C4×C11—41no—
222Dic11—42no—
223Dic11—42no—
224Dic11—84no—
225Dic11—81no—
226Dic11—81no—
227C22×Q8—111no—
228C23×C4—222no—
229C23×C4D4411yescharacteristic
230C23×C4D4411yescharacteristic
231C23×C4C22×D1111yescharacteristic
232C22×C8—22no—
233C22⋊Q8—112no—
234C22⋊Q8—112no—
235C22⋊Q8—221no—
236C22⋊Q8—221no—
237C4×Q8—442no—
238C2×C4⋊C4—111no—
239C2×C4⋊C4—111no—
240C2×C4⋊C4—111no—
241C2×C4⋊C4—221no—
242C2×C4⋊C4—221no—
243C2×C4⋊C4—221no—
244C2×C22⋊C4—221no—
245C2×C22⋊C4—221no—
246C2×C42—42no—
247C2×C42—221no—
248C2×C42—221no—
249C2×C42C4×D1111yescharacteristic
250C2×C42C4×D1111yescharacteristic
251C2×C42C22⋊D1111yescharacteristic
252C2×C42C22⋊D1111yescharacteristic
253C4⋊C8—42no—
254C22⋊C8—22no—
255C22⋊C8—22no—
256#95—224no—
257#95—221no—
258#95—221no—
259#95—221no—
260#95—221no—
261#95—221no—
262#95—222no—
263#95—222no—
264#95—442no—
265C2×C11—22no—
266C2×C11—22no—
267C2×C11#150011yescharacteristic
268C2×C11#150811yescharacteristic
269C2×C11#151511yescharacteristic
270C2×C11#151611yescharacteristic
271C2×C11#179911yescharacteristic
272C2×C11#180511yescharacteristic
273C2×C11#180611yescharacteristic
274C24C2×D4411yescharacteristic
275C2×Q8—112no—
276C2×Q8—221no—
277C2×Q8—441no—
278C2×Q8—441no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—221no—
288C22×C4—221no—
289C22×C4—224no—
290C22×C4—221no—
291C22×C4—221no—
292C22×C4—442no—
293C22×C4—442no—
294C22×C4—442no—
295C22×C4—442no—
296C22×C4—442no—
297C22×C4—442no—
298C22×C4(C2×D11)⋊C411yescharacteristic
299C22×C4(C2×D11)⋊C411yescharacteristic
300C22×C4(C2×D11)⋊C411yescharacteristic
301C22×C4(C2×D11)⋊C411yescharacteristic
302C22×C4C2×C4×D1111yescharacteristic
303C22×C4D4×D1111yescharacteristic
304C22×C4#434111yescharacteristic
305C22×C4Q8×D1111yescharacteristic
306C22×C4#434311yescharacteristic
307C22×C4C2×C22⋊D1111yescharacteristic
308C2×C8—42no—
309C2×C8—42no—
310C2×C8—42no—
311C4⋊C4—112no—
312C4⋊C4—221no—
313C4⋊C4—222no—
314C4⋊C4—222no—
315C4⋊C4—441no—
316C4⋊C4—441no—
317C4⋊C4—442no—
318C4⋊C4—442no—
319C22⋊C4—222no—
320C22⋊C4—222no—
321C22⋊C4—442no—
322C42—22no—
323C42—22no—
324C42—41no—
325C42—41no—
326C42—442no—
327C42—442no—
328C11#857411yescharacteristic, complemented, Sylow
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23#6694811yescharacteristic
334C23#6695011yescharacteristic
335C23#6695712yes—
336C23#6696212yes—
337C23C2×(C2×D11)⋊C411yescharacteristic
338Q8—442no—
339Q8—442no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—44no—
359C2×C4—44no—
360C2×C4—222no—
361C2×C4—222no—
362C2×C4—441no—
363C2×C4—441no—
364C2×C4—441no—
365C2×C4—441no—
366C2×C4—444no—
367C2×C4—444no—
368C2×C4—444no—
369C2×C4—441no—
370C2×C4—441no—
371C2×C4—441no—
372C2×C4—441no—
373C2×C4—441no—
374C2×C4—441no—
375C2×C4—882no—
376C2×C4—882no—
377C2×C4—882no—
378C2×C4—882no—
379C2×C4#6687012yes—
380C2×C4#6688912yes—
381C2×C4C4⋊C4×D1111yescharacteristic
382C2×C4#6694511yescharacteristic
383C2×C4#6699111yescharacteristic
384C2×C4#6699911yescharacteristic
385C8—82no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—22no—
391C22—22no—
392C22—22no—
393C22—22no—
394C22#1062244212yes—
395C22#1062245812yes—
396C22C2×#6687011yescharacteristic
397C22#1062260011yescharacteristic
398C22#1062261911yescharacteristic
399C22#1062272611yescharacteristic
400C22#1062273311yescharacteristic
401C22C2×#6688911yescharacteristic
402C22#1062275211yescharacteristic
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—22no—
408C4—22no—
409C4—41no—
410C4—41no—
411C4—442no—
412C4—442no—
413C4—884no—
414C4—881no—
415C4—881no—
416C2—22no—
417C2—22no—
418C2#1306710311yescharacteristic
419C2#1306713711yescharacteristic
420C2#1306716811yescharacteristic
421C2#1306717311yescharacteristic
422C2#1306860111yescharacteristic
423C2#1306863211yescharacteristic
424C2#1306863311yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1797C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#1797D11
hypocenterC11#8574
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
8. C2×C4×Dic22C4semidirect
17. C4×C4⋊Dic11C4semidirect
20. #10622542C4semidirect
21. #10622541C4semidirect
328. C11#8574semidirect

Maximal subgroups

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

subgroupindex
C4×#669772
C2×#106221052
#130668432
#130664962
C11×#17972
#857411