Finite Group Databasebeta

← #14654030

Subgroups — #14654030

Order 2816.

982 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622659C211yesmaximal, characteristic
2C2×#10622604C211yesmaximal, characteristic
3#13068546C211yesmaximal, characteristic
4C2×#10622176C211yesmaximal, characteristic, complemented
5C2×#10622166C211yesmaximal, characteristic, complemented
6#13066494C211yesmaximal, characteristic, complemented
7C11×#2627C211yesmaximal, characteristic, complemented
8C23×D44C2211yescharacteristic
9C2×C11×C22⋊Q8C2211yescharacteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C22×#4325—21no—
12C22×(C2×D11)⋊C4—21no—
13C22×(C2×D11)⋊C4—21no—
14C11×#400—21no—
15C11×#398—22no—
16C11×#395—21no—
17C11×#385—21no—
18C11×#381—21no—
19C11×#380C2211yescharacteristic
20C2×C11⋊#95C2211yescharacteristic
21C2×C22⋊(C11⋊C8)C2211yescharacteristic
22C2×C22⋊(C11⋊C8)C2211yescharacteristic
23#10622659—22no—
24#10622659—22no—
25#10622604—22no—
26#10622604—22no—
27C2×#66873—21no—
28C2×#66873—22no—
29#10622176—22no—
30#10622166—22no—
31C24×D11—21no—
32C22×Q8×C11D411yescharacteristic
33C23×C4×C11D411yescharacteristic
34C23×C4×C11D411yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C23×Dic11—21no—
37C22×D44—21no—
38C22×D44—21no—
39C22×D44—21no—
40C22×D44—21no—
41C22×D44—21no—
42C22×D44—44no—
43C22×D44D412yes—
44C11×C22⋊Q8—21no—
45C11×C22⋊Q8—21no—
46C11×C22⋊Q8—21no—
47C11×C22⋊Q8—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C11×C4⋊C4D412yes—
58C2×C11×C22⋊C4—21no—
59C2×C11×C22⋊C4—21no—
60C2×#4325—24no—
61C2×#4325—44no—
62C2×(C2×D11)⋊C4—24no—
63C2×(C2×D11)⋊C4—24no—
64C2×(C2×D11)⋊C4—42no—
65C2×(C2×D11)⋊C4—44no—
66C2×(C2×D11)⋊C4—42no—
67C22×C11⋊C8—21no—
68C22×C11⋊C8—21no—
69C11×#95—22no—
70C11×#95—22no—
71C11×#95—22no—
72C11×#95—21no—
73C11⋊#95—21no—
74C11⋊#95D412yes—
75C22⋊(C11⋊C8)—21no—
76C22⋊(C11⋊C8)—21no—
77C22⋊(C11⋊C8)—21no—
78C22⋊(C11⋊C8)D412yes—
79#66873—24no—
80#66873—44no—
81#9923—111nomaximal, Sylow
82C24×C11C2×D411yescharacteristic
83C23×D11—24no—
84C23×D11—22no—
85C23×D11—42no—
86C23×D11—42no—
87C23×D11—42no—
88C23×D11—41no—
89C23×D11—41no—
90C23×D11—41no—
91C23×D11—41no—
92C23×D11—41no—
93C23×D11—41no—
94C2×Q8×C11—21no—
95C2×Q8×C11—21no—
96C2×Q8×C11—42no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—22no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—42no—
110C22×C4×C11—42no—
111C22×C4×C11SD1612yescomplemented
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11#4111yescharacteristic
118C22×Dic11—22no—
119C22×Dic11—42no—
120C22×Dic11—42no—
121C22×Dic11—41no—
122C22×Dic11—41no—
123C2×D44—24no—
124C2×D44—24no—
125C2×D44—22no—
126C2×D44—22no—
127C2×D44—42no—
128C2×D44—42no—
129C2×D44—44no—
130C2×D44—44no—
131C2×D44—44no—
132C2×D44—44no—
133C2×D44—41no—
134C2×D44—41no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—42no—
138C11×C4⋊C4—41no—
139C11×C4⋊C4—41no—
140C11×C4⋊C4—41no—
141C11×C4⋊C4—41no—
142C11×C4⋊C4—41no—
143C11×C4⋊C4—41no—
144C11×C4⋊C4—82no—
145C11×C22⋊C4—41no—
146C11×C22⋊C4—41no—
147C11×C22⋊C4—41no—
148C11×C22⋊C4—41no—
149#4325—48no—
150(C2×D11)⋊C4—48no—
151(C2×D11)⋊C4—48no—
152C2×C11⋊C8—22no—
153C2×C11⋊C8—42no—
154C2×C11⋊C8—42no—
155C2×C11⋊C8—41no—
156C2×#450—111no—
157#2627D1111yescharacteristic, complemented
158C2×#394—111no—
159#1786—111no—
160C2×#328—111no—
161C2×#324—111no—
162#1294—111no—
163C23×C11—22no—
164C23×C11—22no—
165C23×C11#12011yescharacteristic
166C23×C11#12011yescharacteristic
167C23×C11#12111yescharacteristic
168C23×C11C2×SD1611yescharacteristic
169C23×C11#13511yescharacteristic
170C23×C11AGL(1,ℤ/8)11yescharacteristic
171C23×C11#13711yescharacteristic
172C22×D11—24no—
173C22×D11—42no—
174C22×D11—44no—
175C22×D11—44no—
176C22×D11—44no—
177C22×D11—44no—
178C22×D11—44no—
179C22×D11—42no—
180C22×D11—42no—
181C22×D11—42no—
182C22×D11—42no—
183C22×D11—42no—
184C22×D11—44no—
185C22×D11—82no—
186C22×D11—82no—
187C22×D11—82no—
188C22×D11—82no—
189C22×D11—82no—
190C22×D11—81no—
191C22×D11—81no—
192C22×D11—82no—
193C22×D11—81no—
194C22×D11—81no—
195Q8×C11—42no—
196Q8×C11—81no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—42no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—81no—
221C2×C4×C11#12011yescharacteristic
222C2×C4×C11#12111yescharacteristic
223C2×C4×C11#12111yescharacteristic
224C2×C4×C11#12711yescharacteristic
225C2×Dic11—42no—
226C2×Dic11—42no—
227C2×Dic11—42no—
228C2×Dic11—82no—
229C2×Dic11—82no—
230D44—24no—
231D44—24no—
232D44—42no—
233D44—44no—
234D44—42no—
235D44—44no—
236C11⋊C8—42no—
237C11⋊C8—81no—
238C23×D4—111no—
239C22×SD16—221no—
240C2×C22⋊Q8C2×D1111yescharacteristic
241C22×C4⋊C4C2×D1111yescharacteristic
242C22×C22⋊C4—221no—
243C22×C22⋊C4—221no—
244#450—222no—
245#450—222no—
246C2×#102—221no—
247C2×#102—222no—
248C2×C22⋊C8—111no—
249C2×C22⋊C8—111no—
250#400—21no—
251#398—22no—
252#395—21no—
253#394—222no—
254#394—222no—
255#385—21no—
256#381—21no—
257#380C2×D1111yescharacteristic
258C2×#95—111no—
259#328—222no—
260#324—222no—
261C22×C11—22no—
262C22×C11—22no—
263C22×C11—22no—
264C22×C11—22no—
265C22×C11—21no—
266C22×C11—21no—
267C22×C11—21no—
268C22×C11—21no—
269C22×C11#39211yescharacteristic
270C22×C11#44811yescharacteristic
271C22×C11#44911yescharacteristic
272C22×C11#45011yescharacteristic
273C22×C11#45211yescharacteristic
274C22×C11#45412yes—
275C22×C11B(4,𝔽2)12yes—
276C22×C11#46511yescharacteristic
277C22×C11#46811yescharacteristic
278C2×D11—44no—
279C2×D11—44no—
280C2×D11—44no—
281C2×D11—82no—
282C2×D11—82no—
283C2×D11—84no—
284C2×D11—84no—
285C2×D11—84no—
286C2×D11—84no—
287C2×D11—82no—
288C2×D11—82no—
289C4×C11—21no—
290C4×C11—21no—
291C4×C11—21no—
292C4×C11—21no—
293C4×C11—42no—
294C4×C11—82no—
295C4×C11—81no—
296C4×C11—81no—
297C4×C11—81no—
298Dic11—82no—
299C25—221no—
300C22×Q8C22⋊D1111yescharacteristic
301C22×D4—112no—
302C22×D4—221no—
303C22×D4—221no—
304C22×D4—221no—
305C22×D4—221no—
306C22×D4—221no—
307C22×D4—444no—
308C23×C4—221no—
309C23×C4C22⋊D1111yescharacteristic
310C23×C4C22⋊D1111yescharacteristic
311C23×C4C22×D1111yescharacteristic
312C2×SD16—224no—
313C2×SD16—444no—
314C22×C8—221no—
315C22×C8—221no—
316C22⋊Q8—21no—
317C22⋊Q8—21no—
318C22⋊Q8—21no—
319C22⋊Q8—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4C22⋊D1111yescharacteristic
329C2×C4⋊C4C22⋊D1112yes—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—224no—
333C2×C22⋊C4—224no—
334C2×C22⋊C4—442no—
335C2×C22⋊C4—444no—
336C2×C22⋊C4—442no—
337#102—224no—
338#102—444no—
339C22⋊C8—112no—
340C22⋊C8—221no—
341C22⋊C8—221no—
342C22⋊C8—221no—
343#95—22no—
344#95—22no—
345#95—22no—
346#95—21no—
347#95—112no—
348#95—221no—
349C2×C11—21no—
350C2×C11—21no—
351C2×C11—21no—
352C2×C11—21no—
353C2×C11#159712yes—
354C2×C11#159912yes—
355C2×C11#200011yescharacteristic
356C2×C11#200311yescharacteristic
357C2×C11#202111yescharacteristic
358D11—84no—
359C24—224no—
360C24—222no—
361C24—442no—
362C24—442no—
363C24—442no—
364C24—441no—
365C24—441no—
366C24—441no—
367C24—441no—
368C24—441no—
369C24—441no—
370C24C2×C22⋊D1111yescharacteristic
371C2×Q8—21no—
372C2×Q8—21no—
373C2×Q8—42no—
374C2×D4—224no—
375C2×D4—224no—
376C2×D4—222no—
377C2×D4—222no—
378C2×D4—442no—
379C2×D4—442no—
380C2×D4—444no—
381C2×D4—444no—
382C2×D4—444no—
383C2×D4—444no—
384C2×D4—441no—
385C2×D4—441no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—42no—
399C22×C4—42no—
400C22×C4—222no—
401C22×C4—442no—
402C22×C4—442no—
403C22×C4—441no—
404C22×C4—441no—
405C22×C4#432512yescomplemented
406C22×C4D4×D1111yescharacteristic
407C22×C4D4×D1111yescharacteristic
408C22×C4D4×D1111yescharacteristic
409C22×C4#434111yescharacteristic
410C22×C4C2×C22⋊D1111yescharacteristic
411C22×C4C2×C22⋊D1111yescharacteristic
412SD16—448no—
413C2×C8—222no—
414C2×C8—442no—
415C2×C8—442no—
416C2×C8—441no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—42no—
420C4⋊C4—41no—
421C4⋊C4—41no—
422C4⋊C4—41no—
423C4⋊C4—41no—
424C4⋊C4—41no—
425C4⋊C4—41no—
426C4⋊C4—82no—
427C22⋊C4—41no—
428C22⋊C4—41no—
429C22⋊C4—41no—
430C22⋊C4—41no—
431C22⋊C4—448no—
432C22⋊C4—448no—
433C11#992311yescharacteristic, complemented, Sylow
434C23—22no—
435C23—22no—
436C23—224no—
437C23—442no—
438C23—444no—
439C23—444no—
440C23—444no—
441C23—444no—
442C23—444no—
443C23—442no—
444C23—442no—
445C23—442no—
446C23—444no—
447C23—442no—
448C23—442no—
449C23—882no—
450C23—882no—
451C23—882no—
452C23—882no—
453C23—882no—
454C23—881no—
455C23—881no—
456C23—882no—
457C23—881no—
458C23—881no—
459C23#6699011yescharacteristic
460C23#6699211yescharacteristic
461C23C2×#432511yescharacteristic
462C23#6699511yescharacteristic
463C23#6700211yescharacteristic
464C23#6700311yescharacteristic
465C23#6700611yescharacteristic
466Q8—42no—
467Q8—81no—
468D4—224no—
469D4—224no—
470D4—442no—
471D4—444no—
472D4—442no—
473D4—444no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—81no—
498C2×C4—442no—
499C2×C4—442no—
500C2×C4—442no—
501C2×C4—882no—
502C2×C4—882no—
503C2×C4#6699011yescharacteristic
504C2×C4#6699111yescharacteristic
505C2×C4#6699211yescharacteristic
506C2×C4#6699311yescharacteristic
507C8—442no—
508C8—881no—
509C22—22no—
510C22—22no—
511C22—22no—
512C22—22no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—444no—
518C22—444no—
519C22—444no—
520C22—882no—
521C22—882no—
522C22—884no—
523C22—884no—
524C22—884no—
525C22—884no—
526C22—882no—
527C22—882no—
528C22#1062265911yescharacteristic
529C22#1062266011yescharacteristic
530C22#1062266111yescharacteristic
531C22#1062266211yescharacteristic
532C22#1062283611yescharacteristic
533C22#1062284011yescharacteristic
534C22#1062285111yescharacteristic
535C22#1062285712yes—
536C22#1062285812yes—
537C4—21no—
538C4—21no—
539C4—21no—
540C4—21no—
541C4—42no—
542C4—82no—
543C4—81no—
544C4—81no—
545C4—81no—
546C4—882no—
547C2—21no—
548C2—21no—
549C2—21no—
550C2—21no—
551C2—884no—
552C2#1306754512yes—
553C2#1306755612yes—
554C2#1306961711yescharacteristic
555C2#1306963611yescharacteristic
556C2#1306974011yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#2627C2
socleC23×C11#120
prime radicalC23×D44C22
hypercenter#2627D11
hypocenterC11#9923
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2627

Complements

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

NH ≅ G/Ntype
4. C2×#10622176C2semidirect
5. C2×#10622166C2semidirect
6. #13066494C2semidirect
7. C11×#2627C2semidirect
111. C22×C4×C11SD16semidirect
157. #2627D11semidirect
405. C22×C4#4325semidirect
433. C11#9923semidirect

Maximal subgroups

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

subgroupindex
C2×#106226592
C2×#106226042
#130685462
C2×#106221762
C2×#106221662
#130664942
C11×#26272
#992311