Finite Group Databasebeta

← #14653293

Subgroups — #14653293

Order 2816.

606 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622651C211yesmaximal, characteristic
2#13069452C211yesmaximal, characteristic, complemented
3#13068643C211yesmaximal, characteristic, complemented
4C22⋊C4×C11⋊C8C211yesmaximal, characteristic, complemented
5#13067184C211yesmaximal, characteristic, complemented
6#13067183C211yesmaximal, characteristic, complemented
7C11×#1964C211yesmaximal, characteristic, complemented
8C2×C11×#121C2211yescharacteristic
9C22×#4323C411yescharacteristic, complemented
10C2×#66983C2211yescharacteristic
11C23×C11⋊C8C2211yescharacteristic
12C2×C11×#99—22no—
13C11×#380C2211yescharacteristic
14C4×C11×C22⋊C4C2211yescharacteristic
15C2×#66896C411yescharacteristic, complemented
16#10622825C2211yescharacteristic
17C2×C22⋊(C11⋊C8)C2211yescharacteristic
18#10622651—21no—
19#10622651—21no—
20#10622651—21no—
21#10622651—21no—
22C2×#66873C411yescharacteristic, complemented
23C2×#66871—21no—
24C2×#66871C411yescharacteristic, complemented
25C2×#66870—22no—
26C2×C4×C11⋊C8—21no—
27#10622175—22no—
28#10622167—21no—
29#10622162—21no—
30#10622089—22no—
31C22×D4×C11—21no—
32C22×D4×C11C2×C411yescharacteristic
33C23×C4×C11C2311yescharacteristic
34C22×C22⋊D11—21no—
35C22×D44C2×C411yescharacteristic
36C11×#121—21no—
37C11×#121—21no—
38C11×#121—21no—
39C11×#121—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4C2×C411yescharacteristic
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4D412yes—
45C2×C42×C11—21no—
46C2×C22⋊Dic11—21no—
47C2×#4323—21no—
48C2×#4323—21no—
49C2×#4323—42no—
50#66983—21no—
51#66983—21no—
52#66983—21no—
53#66983—21no—
54C2×(C2×D11)⋊C4—21no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11C2×C411yescharacteristic
57C22×C11⋊C8—21no—
58C22×C11⋊C8—42no—
59C22×C11⋊C8C2×C411yescharacteristic
60C22×C11⋊C8C2×C411yescharacteristic
61C22×C11⋊C8D411yescharacteristic
62C22×C11⋊C8D411yescharacteristic
63C22×C11⋊C8D411yescharacteristic
64C22×C11⋊C8D411yescharacteristic
65C11×#99—44no—
66C11×#95—21no—
67C11×#95—21no—
68#66896—21no—
69#66896—21no—
70C11⋊#95—21no—
71C22⋊(C11⋊C8)—21no—
72C22⋊(C11⋊C8)D412yes—
73#66873—21no—
74#66873—21no—
75#66871—21no—
76#66871—21no—
77#66871—42no—
78#66870—44no—
79C4×C11⋊C8—42no—
80#9783—111nomaximal, Sylow
81C24×C11—21no—
82C24×C11C2×D411yescharacteristic
83C23×D11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—41no—
87C2×D4×C11—41no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—42no—
91C2×D4×C11—42no—
92C22×C4×C11—22no—
93C22×C4×C11—21no—
94C22×C4×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11C22×C411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11#4111yescharacteristic
102C22×C4×C11#4111yescharacteristic
103C2×C22⋊D11—41no—
104C2×C22⋊D11—41no—
105C2×C22⋊D11—42no—
106C2×C22⋊D11—42no—
107C22×Dic11—21no—
108C22×Dic11—41no—
109C2×D44—21no—
110C2×D44—21no—
111C2×D44—41no—
112C2×D44—41no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C22⋊C4—22no—
118C11×C22⋊C4—41no—
119C11×C22⋊C4—41no—
120C11×C22⋊C4—42no—
121C11×C22⋊C4D814yescomplemented
122C42×C11—41no—
123C42×C11—41no—
124C22⋊Dic11—42no—
125#4323—42no—
126#4323—42no—
127(C2×D11)⋊C4—41no—
128(C2×D11)⋊C4—41no—
129C4⋊Dic11—21no—
130C4⋊Dic11—21no—
131C4⋊Dic11—41no—
132C4⋊Dic11—41no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—41no—
138C2×C11⋊C8—41no—
139C2×C11⋊C8—41no—
140C2×C11⋊C8—41no—
141C2×C11⋊C8—41no—
142C2×C11⋊C8C22⋊C411yescharacteristic
143C2×C11⋊C8C22⋊C411yescharacteristic
144C2×C11⋊C8C22⋊C411yescharacteristic
145C2×C11⋊C8C22⋊C411yescharacteristic
146C2×#466—111no—
147#1964—111no—
148#1964D1111yescharacteristic, complemented
149#1808—111no—
150C8×C22⋊C4—111no—
151#1519—111no—
152#1519—111no—
153C23×C11—41no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11—42no—
157C23×C11—81no—
158C23×C11—81no—
159C23×C11C4×D411yescharacteristic
160C23×C11#12111yescharacteristic
161C23×C11#12711yescharacteristic
162C23×C11C2×D812yes—
163C23×C11#13512yes—
164C22×D11—41no—
165C22×D11—42no—
166C22×D11—81no—
167C22×D11—81no—
168D4×C11—41no—
169D4×C11—41no—
170D4×C11—81no—
171D4×C11—82no—
172D4×C11—81no—
173D4×C11—81no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—24no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—41no—
187C2×C4×C11—42no—
188C2×C4×C11—81no—
189C2×C4×C11—81no—
190C2×C4×C11—81no—
191C2×C4×C11C2×C22⋊C411yescharacteristic
192C2×C4×C11C4×D411yescharacteristic
193C2×C4×C11#12111yescharacteristic
194C2×C4×C11#12411yescharacteristic
195C22⋊D11—82no—
196C22⋊D11—81no—
197C22⋊D11—81no—
198C2×Dic11—41no—
199C2×Dic11—42no—
200C2×Dic11—81no—
201C2×Dic11—81no—
202C2×Dic11—81no—
203D44—41no—
204D44—41no—
205D44—81no—
206C11⋊C8—21no—
207C11⋊C8—21no—
208C11⋊C8—21no—
209C11⋊C8—42no—
210C11⋊C8#9912yescomplemented
211C22×D8—111no—
212C23×C8—111no—
213C2×#121—111no—
214C2×#121C2×D1111yescharacteristic
215#466—221no—
216#466—221no—
217#466—221no—
218#466—221no—
219C2×#107—111no—
220C2×#107—221no—
221C2×#102—111no—
222C2×#102—111no—
223C2×#99—22no—
224C2×#99—222no—
225C2×C22⋊C8—111no—
226C2×C4×C8—221no—
227#380—111no—
228#380C2×D1111yescharacteristic
229C4×C22⋊C4C2×D1111yescharacteristic
230#340—221no—
231#336—221no—
232#327—222no—
233#327—222no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—21no—
237C22×C11—21no—
238C22×C11—21no—
239C22×C11—21no—
240C22×C11—42no—
241C22×C11—42no—
242C22×C11—81no—
243C22×C11—81no—
244C22×C11—81no—
245C22×C11—162no—
246C22×C11#39011yescharacteristic
247C22×C11C4×D812yes—
248C22×C11#46612yes—
249C22×C11#49311yescharacteristic
250C22×C11#49511yescharacteristic
251C2×D11—81no—
252C2×D11—81no—
253C2×D11—81no—
254C2×D11—162no—
255C4×C11—21no—
256C4×C11—21no—
257C4×C11—21no—
258C4×C11—44no—
259C4×C11—81no—
260C4×C11—161no—
261C4×C11C2×#9911yescharacteristic
262C4×C11#41011yescharacteristic
263Dic11—81no—
264Dic11—161no—
265C22×D4—21no—
266C22×D4—111no—
267C22×D4—221no—
268C22×D4C4×D1111yescharacteristic
269C23×C4C22×D1111yescharacteristic
270C2×D8—221no—
271C2×D8—221no—
272C2×D8—442no—
273C22×C8—111no—
274C22×C8—111no—
275C22×C8—111no—
276C22×C8—111no—
277C22×C8—111no—
278C22×C8—111no—
279C22×C8—221no—
280C22×C8—442no—
281#121—21no—
282#121—21no—
283#121—21no—
284#121—21no—
285#121—221no—
286#121—221no—
287#121—221no—
288#121—221no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—111no—
291C2×C4⋊C4—221no—
292C2×C4⋊C4C4×D1111yescharacteristic
293C2×C22⋊C4—21no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—221no—
296C2×C22⋊C4—221no—
297C2×C22⋊C4C22⋊D1112yes—
298C2×C42—21no—
299#107—221no—
300#107—221no—
301#107—442no—
302#102—221no—
303#102—221no—
304#102—221no—
305#102—221no—
306#99—44no—
307#99—444no—
308C22⋊C8—112no—
309C22⋊C8—221no—
310C4×C8—442no—
311#95—21no—
312#95—21no—
313#95—221no—
314C2×C11—21no—
315C2×C11—22no—
316C2×C11—22no—
317C2×C11—21no—
318C2×C11—161no—
319C2×C11#196411yescharacteristic
320C2×C11#197011yescharacteristic
321C2×C11#197611yescharacteristic
322D11—161no—
323C24—21no—
324C24—221no—
325C24C2×C22⋊D1111yescharacteristic
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—41no—
329C2×D4—41no—
330C2×D4—42no—
331C2×D4—41no—
332C2×D4—41no—
333C2×D4—42no—
334C2×D4—221no—
335C2×D4—221no—
336C2×D4—441no—
337C2×D4—441no—
338C2×D4—442no—
339C2×D4—441no—
340C2×D4—441no—
341C2×D4—442no—
342C22×C4—22no—
343C22×C4—21no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4—221no—
348C22×C4—441no—
349C22×C4C2×C4×D1111yescharacteristic
350C22×C4#433911yescharacteristic
351C22×C4D4×D1111yescharacteristic
352C22×C4D4×D1111yescharacteristic
353C22×C4D4×D1111yescharacteristic
354C22×C4#434111yescharacteristic
355D8—442no—
356D8—442no—
357C2×C8—111no—
358C2×C8—111no—
359C2×C8—111no—
360C2×C8—111no—
361C2×C8—222no—
362C2×C8—222no—
363C2×C8—222no—
364C2×C8—222no—
365C2×C8—441no—
366C2×C8—441no—
367C2×C8—441no—
368C2×C8—441no—
369C2×C8—441no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—221no—
375C4⋊C4—221no—
376C4⋊C4—441no—
377C4⋊C4—441no—
378C22⋊C4—22no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C22⋊C4—42no—
382C22⋊C4—441no—
383C22⋊C4—441no—
384C22⋊C4—442no—
385C22⋊C4#432314yescomplemented
386C42—41no—
387C42—41no—
388C11#978311yescharacteristic, complemented, Sylow
389C23—41no—
390C23—41no—
391C23—41no—
392C23—42no—
393C23—81no—
394C23—81no—
395C23—441no—
396C23—442no—
397C23—881no—
398C23—881no—
399C23C4×C22⋊D1111yescharacteristic
400C23C2×#432312yes—
401C23#6699211yescharacteristic
402C23#6699311yescharacteristic
403C23#6700312yes—
404D4—41no—
405D4—41no—
406D4—81no—
407D4—82no—
408D4—81no—
409D4—81no—
410D4—441no—
411D4—441no—
412D4—881no—
413D4—882no—
414D4—881no—
415D4—881no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—24no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—42no—
430C2×C4—81no—
431C2×C4—81no—
432C2×C4—81no—
433C2×C4—441no—
434C2×C4—442no—
435C2×C4—881no—
436C2×C4—881no—
437C2×C4—881no—
438C2×C4C22⋊C4×D1111yescharacteristic
439C2×C4(C22⋊D11)⋊C411yescharacteristic
440C2×C4#6693711yescharacteristic
441C2×C4#6693811yescharacteristic
442C8—112no—
443C8—221no—
444C8—221no—
445C8—221no—
446C8—442no—
447C22—21no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—42no—
454C22—42no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22—162no—
459C22—881no—
460C22—881no—
461C22—881no—
462C22—1762no—
463C22#1062257011yescharacteristic
464C22C4×#432312yes—
465C22#1062265112yes—
466C22#1062267211yescharacteristic
467C22#1062268611yescharacteristic
468C4—21no—
469C4—21no—
470C4—21no—
471C4—44no—
472C4—81no—
473C4—161no—
474C4—881no—
475C4—1761no—
476C4#1062235311yescharacteristic
477C4D11×#9911yescharacteristic
478C2—22no—
479C2—21no—
480C2—22no—
481C2—21no—
482C2—161no—
483C2—1761no—
484C2#1306945011yescharacteristic
485C2#1306948111yescharacteristic
486C2#1306951111yescharacteristic
subgroupG/H
centerC22#10622570
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1964C2
socleC22×C11#390
prime radicalC2×#10622651C2
cosocleC23×C4×C11C23
hypercenter#1964D11
hypocenterC11#9783
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1964

Complements

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

NH ≅ G/Ntype
2. #13069452C2semidirect
3. #13068643C2semidirect
4. C22⋊C4×C11⋊C8C2semidirect
5. #13067184C2semidirect
6. #13067183C2semidirect
7. C11×#1964C2semidirect
9. C22×#4323C4semidirect
15. C2×#66896C4semidirect
22. C2×#66873C4semidirect
24. C2×#66871C4semidirect
121. C11×C22⋊C4D8semidirect
148. #1964D11semidirect
210. C11⋊C8#99semidirect
385. C22⋊C4#4323semidirect
388. C11#9783semidirect

Maximal subgroups

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

subgroupindex
C2×#106226512
#130694522
#130686432
C22⋊C4×C11⋊C82
#130671842
#130671832
C11×#19642
#978311