Finite Group Databasebeta

← #14656077

Subgroups — #14656077

Order 2816.

744 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622640C211yesmaximal, characteristic, complemented
2C2×#10622456C211yesmaximal, characteristic
3#13073534C211yesmaximal, characteristic, complemented
4#13069422C211yesmaximal, characteristic, complemented
5C2×#10622097C211yesmaximal, characteristic, complemented
6#13066500C211yesmaximal, characteristic, complemented
7C2×C11×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C11C2211yescharacteristic
9C2×#66999—21no—
10C22×#4325—21no—
11C22×D88—21no—
12C2×#66927C2211yescharacteristic
13C2×C4×D44C2211yescharacteristic
14C2×C11×C4⋊C8C2211yescharacteristic
15C2×C4×C8×C11C2211yescharacteristic
16C2×#66885—21no—
17C2×#66885—22no—
18#10622640—22no—
19#10622640—22no—
20#10622607—22no—
21#10622600—21no—
22C2×#66873—21no—
23#10622552—21no—
24#10622548C2211yescharacteristic
25#10622541—21no—
26C2×C4⋊(C11⋊C8)C2211yescharacteristic
27#10622456—22no—
28#10622456—22no—
29C11×Q8⋊C8—22no—
30#10622097—22no—
31C22×Q8×C11D411yescharacteristic
32C22×D44—21no—
33C22×D44—21no—
34C22×D44—21no—
35C22×D44D411yescharacteristic
36C22×C4×D11—21no—
37C22×C8×C11—21no—
38C22×C8×C11—21no—
39C4×Q8×C11—21no—
40C4×Q8×C11—21no—
41C4×Q8×C11—21no—
42C4×Q8×C11—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4D411yescharacteristic
45C2×C42×C11—21no—
46C2×C42×C11C2311yescharacteristic
47#66999—42no—
48#66999—42no—
49C2×#4325—24no—
50C2×#4325—42no—
51C2×#4325—42no—
52C2×(C2×D11)⋊C4—22no—
53C2×(C2×D11)⋊C4—21no—
54C2×(C2×D11)⋊C4—22no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11D411yescharacteristic
58C2×C4⋊Dic11D412yes—
59C2×Dic11⋊C4—22no—
60C22×C11⋊C8—21no—
61C2×D88—24no—
62C2×D88—42no—
63C2×D88—42no—
64#66927—21no—
65#66927—21no—
66#66927—21no—
67#66927D412yes—
68C4×D44—21no—
69C4×D44—21no—
70C4×D44—21no—
71C4×D44—21no—
72C11×C4⋊C8—21no—
73C11×C4⋊C8D412yes—
74C4×C8×C11—21no—
75C4×C8×C11—21no—
76C11⋊#95—22no—
77#66885—24no—
78#66885—44no—
79#66873—24no—
80C4⋊(C11⋊C8)—21no—
81C4⋊(C11⋊C8)D412yes—
82#10229—111nomaximal, Sylow
83C23×D11—21no—
84C23×D11—41no—
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C2×Q8×C11—21no—
88C2×Q8×C11—21no—
89C2×Q8×C11—21no—
90C2×Q8×C11D812yescomplemented
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×Dic11—21no—
97C22×Dic11—22no—
98C2×D44—21no—
99C2×D44—22no—
100C2×D44—22no—
101C2×D44—21no—
102C2×D44—22no—
103C2×D44—21no—
104C2×D44—21no—
105C2×D44—21no—
106C2×D44—42no—
107C2×D44—42no—
108C2×D44—41no—
109C2×D44—41no—
110C2×D44—41no—
111C2×D44—41no—
112C2×D44—41no—
113C2×D44—41no—
114C2×D44—41no—
115C2×D44—41no—
116C2×D44—41no—
117C2×D44—41no—
118C2×D44—41no—
119C2×D44SD1612yescomplemented
120C2×C4×D11—41no—
121C2×C4×D11—41no—
122C2×C4×D11—41no—
123C2×C4×D11—41no—
124C2×C4×D11—41no—
125C2×C4×D11—41no—
126C2×C8×C11—22no—
127C2×C8×C11—22no—
128C2×C8×C11—41no—
129C2×C8×C11—41no—
130C2×C8×C11—41no—
131C2×C8×C11—41no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—41no—
135C11×C4⋊C4—41no—
136C42×C11—41no—
137C42×C11—41no—
138C42×C11C2×D411yescharacteristic
139C42×C11C2×D411yescharacteristic
140C42×C11C2×D411yescharacteristic
141C42×C11#4111yescharacteristic
142#4325—48no—
143(C2×D11)⋊C4—44no—
144(C2×D11)⋊C4—41no—
145(C2×D11)⋊C4—41no—
146(C2×D11)⋊C4—82no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11—42no—
150C4⋊Dic11—41no—
151C4⋊Dic11—41no—
152C4⋊Dic11—41no—
153C4⋊Dic11—41no—
154Dic11⋊C4—44no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—41no—
157C2×C11⋊C8—41no—
158D88—48no—
159C2×#460—111no—
160C2×#459—111no—
161#2538—111no—
162#1957—111no—
163C2×Q8⋊C8D1111yescharacteristic, complemented
164C2×D4⋊C8—111no—
165#1296—111no—
166C23×C11#12011yescharacteristic
167C22×D11—22no—
168C22×D11—41no—
169C22×D11—41no—
170C22×D11—41no—
171C22×D11—41no—
172C22×D11—41no—
173C22×D11—41no—
174C22×D11—42no—
175C22×D11—81no—
176C22×D11—81no—
177C22×D11—81no—
178C22×D11—81no—
179C22×D11—81no—
180C22×D11—81no—
181Q8×C11—22no—
182Q8×C11—22no—
183Q8×C11—41no—
184Q8×C11—41no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—22no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11#12011yescharacteristic
194C2×C4×C11#12011yescharacteristic
195C2×C4×C11#12111yescharacteristic
196C2×C4×C11#12111yescharacteristic
197C2×C4×C11#12111yescharacteristic
198C2×C4×C11#12711yescharacteristic
199C2×C4×C11C2×D811yescharacteristic
200C2×C4×C11C2×SD1611yescharacteristic
201C2×C4×C11#13511yescharacteristic
202C2×C4×C11#13511yescharacteristic
203C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
204C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
205C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
206C2×C4×C11#13711yescharacteristic
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—41no—
212C2×Dic11—42no—
213D44—22no—
214D44—22no—
215D44—44no—
216D44—42no—
217D44—42no—
218D44—42no—
219D44—41no—
220D44—42no—
221D44—41no—
222D44—82no—
223D44—81no—
224D44—81no—
225D44—81no—
226D44—81no—
227C4×D11—81no—
228C4×D11—81no—
229C4×D11—81no—
230C4×D11—81no—
231C8×C11—42no—
232C8×C11—42no—
233C11⋊C8—42no—
234C22×SD16—221no—
235C22×D8—221no—
236C2×#127—111no—
237C2×C22⋊Q8—221no—
238C2×C4×Q8C2×D1111yescharacteristic
239C2×C4×D4—111no—
240#460—222no—
241#460—222no—
242#459—222no—
243#459—222no—
244C2×C4⋊C8—111no—
245C2×C4⋊C8C2×D1111yescharacteristic
246C2×#102—221no—
247C2×#102—221no—
248C2×#102—222no—
249C2×C4×C8C2×D1111yescharacteristic
250#396—222no—
251#390—221no—
252#389—221no—
253#384—111no—
254#380—221no—
255Q8⋊C8—22no—
256D4⋊C8—222no—
257C22×C11#39211yescharacteristic
258C22×C11#44711yescharacteristic
259C22×C11#44811yescharacteristic
260C22×C11#44911yescharacteristic
261C22×C11#44911yescharacteristic
262C22×C11#45311yescharacteristic
263C22×C11#45411yescharacteristic
264C2×D11—42no—
265C2×D11—42no—
266C2×D11—42no—
267C2×D11—81no—
268C2×D11—81no—
269C2×D11—81no—
270C2×D11—81no—
271C2×D11—82no—
272C2×D11—82no—
273C2×D11—82no—
274C2×D11—161no—
275C2×D11—161no—
276C2×D11—161no—
277C2×D11—161no—
278C4×C11—21no—
279C4×C11—21no—
280C4×C11—42no—
281C4×C11—81no—
282C4×C11#44711yescharacteristic
283C4×C11#44911yescharacteristic
284C4×C11#45011yescharacteristic
285C4×C11#45211yescharacteristic
286C4×C11#46511yescharacteristic
287C4×C11#46611yescharacteristic
288C4×C11#46811yescharacteristic
289C4×C11#46911yescharacteristic
290Dic11—82no—
291Dic11—81no—
292C22×Q8D4411yescharacteristic
293C22×D4—111no—
294C22×D4—221no—
295C22×D4—221no—
296C22×D4—221no—
297C23×C4—221no—
298C2×SD16—224no—
299C2×SD16—442no—
300C2×SD16—442no—
301C2×D8—224no—
302C2×D8—442no—
303C2×D8—442no—
304C22×C8—21no—
305C22×C8—21no—
306C22×C8—221no—
307#127—112no—
308#127—221no—
309#127—221no—
310#127—221no—
311C22⋊Q8—442no—
312C22⋊Q8—442no—
313C4×Q8—21no—
314C4×Q8—21no—
315C4×Q8—21no—
316C4×Q8—21no—
317C4×D4—221no—
318C4×D4—221no—
319C4×D4—221no—
320C4×D4—221no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—111no—
323C2×C4⋊C4—112no—
324C2×C4⋊C4—222no—
325C2×C4⋊C4—221no—
326C2×C4⋊C4—221no—
327C2×C4⋊C4D4411yescharacteristic
328C2×C22⋊C4—222no—
329C2×C22⋊C4—221no—
330C2×C22⋊C4—222no—
331C2×C42—21no—
332C2×C42C22×D1111yescharacteristic
333C4⋊C8—21no—
334C4⋊C8—112no—
335C4⋊C8—221no—
336C4⋊C8C22⋊D1112yes—
337#102—224no—
338#102—224no—
339#102—444no—
340C4×C8—21no—
341C4×C8—21no—
342#95—222no—
343C2×C11#162111yescharacteristic
344C2×C11#162211yescharacteristic
345C2×C11#162711yescharacteristic
346C2×C11#162811yescharacteristic
347C2×C11#199911yescharacteristic
348C2×C11#200011yescharacteristic
349C2×C11#200611yescharacteristic
350D11—82no—
351D11—162no—
352C24—221no—
353C24—441no—
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8D8812yescomplemented
360C2×D4—112no—
361C2×D4—222no—
362C2×D4—221no—
363C2×D4—222no—
364C2×D4—221no—
365C2×D4—221no—
366C2×D4—221no—
367C2×D4—221no—
368C2×D4—222no—
369C2×D4—442no—
370C2×D4—442no—
371C2×D4—441no—
372C2×D4—441no—
373C2×D4—441no—
374C2×D4—441no—
375C2×D4—441no—
376C2×D4—441no—
377C2×D4—441no—
378C2×D4—441no—
379C2×D4—441no—
380C2×D4—441no—
381C2×D4—441no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—221no—
385C22×C4—222no—
386C22×C4—441no—
387C22×C4—441no—
388C22×C4—441no—
389C22×C4—441no—
390C22×C4—441no—
391C22×C4—441no—
392C22×C4C2×D4411yescharacteristic
393C22×C4D4×D1111yescharacteristic
394C22×C4D4×D1111yescharacteristic
395SD16—448no—
396D8—448no—
397C2×C8—22no—
398C2×C8—22no—
399C2×C8—41no—
400C2×C8—41no—
401C2×C8—41no—
402C2×C8—41no—
403C2×C8—222no—
404C2×C8—441no—
405C2×C8—441no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C4⋊C4—221no—
411C4⋊C4—221no—
412C4⋊C4—442no—
413C4⋊C4—444no—
414C4⋊C4—441no—
415C4⋊C4—441no—
416C4⋊C4—441no—
417C4⋊C4—441no—
418C22⋊C4—444no—
419C22⋊C4—441no—
420C22⋊C4—441no—
421C22⋊C4—882no—
422C42—41no—
423C42—41no—
424C42#433911yescharacteristic
425C42D4×D1111yescharacteristic
426C42D4×D1111yescharacteristic
427C42C2×C22⋊D1111yescharacteristic
428C11#1022911yescharacteristic, complemented, Sylow
429C23—222no—
430C23—441no—
431C23—441no—
432C23—441no—
433C23—441no—
434C23—441no—
435C23—441no—
436C23—442no—
437C23—881no—
438C23—881no—
439C23—881no—
440C23—881no—
441C23—881no—
442C23—881no—
443C23#6693511yescharacteristic
444Q8—22no—
445Q8—22no—
446Q8—41no—
447Q8—41no—
448D4—222no—
449D4—222no—
450D4—444no—
451D4—442no—
452D4—441no—
453D4—442no—
454D4—442no—
455D4—442no—
456D4—441no—
457D4—882no—
458D4—881no—
459D4—881no—
460D4—881no—
461D4—881no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—22no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—441no—
471C2×C4—442no—
472C2×C4—441no—
473C2×C4—441no—
474C2×C4—442no—
475C2×C4—442no—
476C2×C4—881no—
477C2×C4—881no—
478C2×C4—881no—
479C2×C4—881no—
480C2×C4#6693511yescharacteristic
481C2×C4#6693711yescharacteristic
482C2×C4#6693711yescharacteristic
483C2×C4C2×D8811yescharacteristic
484C2×C4#6695711yescharacteristic
485C2×C4#6696111yescharacteristic
486C2×C4#6696111yescharacteristic
487C2×C4SD16×D1111yescharacteristic
488C2×C4#6696711yescharacteristic
489C2×C4#6697111yescharacteristic
490C2×C4#6697211yescharacteristic
491C2×C4#6698311yescharacteristic
492C2×C4#6699011yescharacteristic
493C2×C4#6699311yescharacteristic
494C8—42no—
495C8—42no—
496C8—442no—
497C22—442no—
498C22—442no—
499C22—442no—
500C22—881no—
501C22—881no—
502C22—881no—
503C22—881no—
504C22—882no—
505C22—882no—
506C22—882no—
507C22—1761no—
508C22—1761no—
509C22—1761no—
510C22—1761no—
511C22#1062234511yescharacteristic
512C22#1062234711yescharacteristic
513C22#1062241911yescharacteristic
514C22#1062242411yescharacteristic
515C22#1062243511yescharacteristic
516C22#1062244011yescharacteristic
517C22#1062257311yescharacteristic
518C4—21no—
519C4—21no—
520C4—42no—
521C4—81no—
522C4—881no—
523C4—882no—
524C4#1062234511yescharacteristic
525C4#1062234711yescharacteristic
526C4#1062242011yescharacteristic
527C4#1062242511yescharacteristic
528C4#1062272811yescharacteristic
529C4#1062274811yescharacteristic
530C4#1062278211yescharacteristic
531C4#1062280011yescharacteristic
532C2—882no—
533C2—1762no—
534C2#1306768311yescharacteristic
535C2#1306769111yescharacteristic
536C2#1306772111yescharacteristic
537C2#1306772911yescharacteristic
538C2#1306961411yescharacteristic
539C2#1306961811yescharacteristic
540C2#1306965911yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×Q8⋊C8C2
socleC23×C11#120
prime radicalC2×#10622456C2
hypercenterC2×Q8⋊C8D11
hypocenterC11#10229
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#10622640C2semidirect
3. #13073534C2semidirect
4. #13069422C2semidirect
5. C2×#10622097C2semidirect
6. #13066500C2semidirect
7. C2×C11×Q8⋊C8C2semidirect
90. C2×Q8×C11D8semidirect
119. C2×D44SD16semidirect
163. C2×Q8⋊C8D11semidirect
359. C2×Q8D88semidirect
428. C11#10229semidirect

Maximal subgroups

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

subgroupindex
C2×#106226402
C2×#106224562
#130735342
#130694222
C2×#106220972
#130665002
C2×C11×Q8⋊C82
#1022911