Finite Group Databasebeta

← #14796389

Subgroups — #14796389

Order 2816.

998 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622620C211yesmaximal, characteristic, complemented
2C2×C4×#4323C211yesmaximal, characteristic
3#13073565C211yesmaximal, characteristic, complemented
4#13070087C212yesmaximal, complemented
5#13070001C212yesmaximal, complemented
6#13069576C211yesmaximal, characteristic, complemented
7#13069335C211yesmaximal, characteristic, complemented
8#13068964C212yesmaximal
9#13068616C212yesmaximal, complemented
10#13068613C211yesmaximal, characteristic, complemented
11D4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
12C2×C4×D4×C11C2212yes—
13C2×C4×D4×C11C2211yescharacteristic
14C22×C11×C4⋊C4—21no—
15C22×#4323C2211yescharacteristic
16C2×#66950—21no—
17C2×#66950—21no—
18C2×C4×D44C2211yescharacteristic
19C2×#66922C2211yescharacteristic
20C11×#389C2212yes—
21C11×#385—22no—
22C11×#384C2211yescharacteristic
23C11×#380—21no—
24C4×C11×C4⋊C4C2211yescharacteristic
25C2×#66896C2211yescharacteristic
26C2×#66896C2212yes—
27C4×#4323—24no—
28#10622620—24no—
29C2×#66873C2211yescharacteristic
30C2×#66873C2212yes—
31C2×#66871C2211yescharacteristic
32C2×#66871C2212yes—
33#10622552C2212yes—
34#10622548C2212yes—
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36C2×C4⋊(C11⋊C8)C2212yes—
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622290—22no—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42#10622162C2212yes—
43C22×D4×C11C2311yescharacteristic
44C23×C4×C11—21no—
45C23×C4×C11—22no—
46C22×D44C2311yescharacteristic
47C22×C4×D11—21no—
48C22×Dic22—21no—
49C4×D4×C11—24no—
50C4×D4×C11—22no—
51C4×D4×C11—42no—
52C4×D4×C11D414yes—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—44no—
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C11×C4⋊C4D411yescharacteristic
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C22⋊C4—21no—
62C2×C11×C22⋊C4—22no—
63C2×C42×C11C2312yes—
64C2×C42×C11C2311yescharacteristic
65C2×#4323—22no—
66C2×#4323—22no—
67C2×#4323Q814yescomplemented
68C2×(C2×D11)⋊C4—21no—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—22no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—22no—
73C2×C4⋊Dic11—22no—
74C2×C4⋊Dic11C2312yes—
75C2×C4⋊Dic11C2311yescharacteristic
76C22×C11⋊C8C2311yescharacteristic
77C22×C11⋊C8C2312yes—
78C22×C11⋊C8C2311yescharacteristic
79#66950—44no—
80#66950—44no—
81C4×D44—22no—
82C4×D44—22no—
83#66922—22no—
84#66922—22no—
85C11×#95—22no—
86C11×#95D412yes—
87#66896—24no—
88#66896—22no—
89#66873—22no—
90#66873—42no—
91#66871—24no—
92#66871—22no—
93C4⋊(C11⋊C8)—22no—
94C4⋊(C11⋊C8)—42no—
95C4×C11⋊C8—22no—
96#24811—111nomaximal, Sylow
97C24×C11—21no—
98C23×D11—21no—
99C2×D4×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11C2×D412yes—
103C2×D4×C11C2×Q812yes—
104C2×D4×C11#4112yes—
105C22×C4×C11—21no—
106C22×C4×C11—24no—
107C22×C4×C11—22no—
108C22×C4×C11—44no—
109C22×C4×C11—42no—
110C22×C4×C11—42no—
111C22×C4×C11—44no—
112C22×C4×C11—82no—
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2411yescharacteristic
118C22×Dic11—21no—
119C22×Dic11—22no—
120C2×D44—21no—
121C2×D44—21no—
122C2×D44—21no—
123C2×D44—21no—
124C2×D44—21no—
125C2×D44C2×Q812yes—
126C2×C4×D11—42no—
127C2×C4×D11—42no—
128C2×C4×D11—42no—
129C2×Dic22—42no—
130C2×Dic22—42no—
131C2×Dic22—42no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—44no—
137C11×C4⋊C4—42no—
138C11×C4⋊C4—81no—
139C11×C4⋊C4D814yescomplemented
140C11×C4⋊C4C2×D412yes—
141C11×C22⋊C4—24no—
142C11×C22⋊C4—44no—
143C42×C11—22no—
144C42×C11—22no—
145C42×C11C2×D412yes—
146C42×C11#4112yes—
147#4323—28no—
148(C2×D11)⋊C4—44no—
149(C2×D11)⋊C4—42no—
150(C2×D11)⋊C4—44no—
151C4⋊Dic11—22no—
152C4⋊Dic11—21no—
153C4⋊Dic11—22no—
154C4⋊Dic11—21no—
155C4⋊Dic11—44no—
156C4⋊Dic11—42no—
157C4⋊Dic11—44no—
158C2×C11⋊C8—21no—
159C2×C11⋊C8—21no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—21no—
162C2×C11⋊C8—21no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—21no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8C2×Q812yes—
167C2×#474—111no—
168C2×C4×D8—111no—
169#2542—111no—
170D4×C4⋊C4D1111yescharacteristic, complemented
171#2083—112no—
172#2067—112no—
173#1990—111no—
174#1939—111no—
175#1879—112no—
176#1802—111no—
177#1802—112no—
178C23×C11—22no—
179C23×C11—22no—
180C23×C11—22no—
181C23×C11—41no—
182C23×C11—41no—
183C23×C11—41no—
184C23×C11—41no—
185C23×C11C22×D411yescharacteristic
186C22×D11—22no—
187C22×D11—41no—
188C22×D11—41no—
189C22×D11—41no—
190C22×D11—41no—
191C22×D11—41no—
192C22×D11—41no—
193D4×C11—22no—
194D4×C11—22no—
195D4×C11—22no—
196D4×C11C22⋊Q814yescomplemented
197C2×C4×C11—22no—
198C2×C4×C11—21no—
199C2×C4×C11—22no—
200C2×C4×C11—21no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—48no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—88no—
212C2×C4×C11#12112yes—
213C2×C4×C11#12112yes—
214C2×C4×C11C2×D814yes—
215C2×C4×C11C2×D812yes—
216C2×C4×C11AGL(1,ℤ/8)12yes—
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11C22×Q811yescharacteristic
219C2×C4×C11C2×#4111yescharacteristic
220C2×C4×C11C2×#4111yescharacteristic
221C2×C4×C11H(5,𝔽2)11yescharacteristic
222C2×C4×C112−1+411yescharacteristic
223C2×Dic11—42no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—42no—
227C2×Dic11—41no—
228C2×Dic11—42no—
229D44—22no—
230D44—22no—
231D44—41no—
232D44—41no—
233C4×D11—84no—
234Dic22—84no—
235C11⋊C8—22no—
236C11⋊C8—41no—
237C11⋊C8—42no—
238C22×D8—111no—
239C2×C4⋊Q8—111no—
240C2×C22⋊Q8—221no—
241C2×C22⋊Q8—221no—
242C2×C4×D4—111no—
243C2×C4×D4C2×D1112yes—
244C2×C4×D4C2×D1111yescharacteristic
245C22×C4⋊C4—21no—
246#474—224no—
247C4×D8—224no—
248C2×#107—112no—
249C2×#107—111no—
250C2×C4⋊C8—111no—
251C2×C4⋊C8—112no—
252C2×#102—111no—
253C2×#102—112no—
254C2×#102—111no—
255C2×#102—112no—
256C2×C4×C8—111no—
257#399—222no—
258#390—112no—
259#389C2×D1112yes—
260#385—22no—
261#384—112no—
262#384C2×D1111yescharacteristic
263#380—21no—
264C4×C4⋊C4C2×D1111yescharacteristic
265#340—112no—
266#340—112no—
267#340—112no—
268#336—112no—
269C22×C11—24no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11—42no—
273C22×C11—42no—
274C22×C11—42no—
275C22×C11—42no—
276C22×C11C2×#12111yescharacteristic
277C22×C11#54611yescharacteristic
278C22×C11D4×Q811yescharacteristic
279C22×C11C22×D811yescharacteristic
280C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
281C22×C11#57711yescharacteristic
282C22×C11#57811yescharacteristic
283C2×D11—42no—
284C2×D11—42no—
285C2×D11—42no—
286C2×D11—81no—
287C2×D11—81no—
288C2×D11—81no—
289C2×D11—81no—
290C4×C11—24no—
291C4×C11—22no—
292C4×C11—42no—
293C4×C11—42no—
294C4×C11—82no—
295C4×C11#45914yes—
296C4×C11C2×C22⋊Q811yescharacteristic
297C4×C11#53711yescharacteristic
298C4×C11#55211yescharacteristic
299C4×C11#55411yescharacteristic
300Dic11—82no—
301Dic11—81no—
302C22×Q8—221no—
303C22×D4—111no—
304C22×D4C22×D1111yescharacteristic
305C23×C4—21no—
306C23×C4—22no—
307C23×C4—221no—
308C2×D8—114no—
309C2×D8—222no—
310C2×D8—222no—
311C22×C8—111no—
312C22×C8—112no—
313C22×C8—111no—
314C4⋊Q8—222no—
315C4⋊Q8—222no—
316C22⋊Q8—444no—
317C22⋊Q8—444no—
318C4×D4—24no—
319C4×D4—22no—
320C4×D4—42no—
321C4×D4—222no—
322C4×D4—222no—
323C4×D4D4414yes—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4—111no—
329C2×C4⋊C4—112no—
330C2×C4⋊C4—222no—
331C2×C4⋊C4—222no—
332C2×C4⋊C4—221no—
333C2×C4⋊C4C22⋊D1111yescharacteristic
334C2×C4⋊C4C22⋊D1111yescharacteristic
335C2×C4⋊C4C22×D1112yes—
336C2×C4⋊C4C22×D1111yescharacteristic
337C2×C22⋊C4—21no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—221no—
340C2×C22⋊C4—222no—
341C2×C22⋊C4—222no—
342C2×C42C22×D1112yes—
343C2×C42C22×D1111yescharacteristic
344#107—222no—
345#107—224no—
346C4⋊C8—222no—
347C4⋊C8—442no—
348#102—222no—
349#102—224no—
350#102—222no—
351#102—442no—
352C4×C8—222no—
353#95—22no—
354#95C22⋊D1112yes—
355C2×C11—44no—
356C2×C11#241711yescharacteristic
357C2×C11C2×#45911yescharacteristic
358C2×C11#304611yescharacteristic
359C2×C11#329411yescharacteristic
360C2×C11#333011yescharacteristic
361C2×C11Q8×D811yescharacteristic
362C2×C11#338411yescharacteristic
363D11—82no—
364C24—21no—
365C24—221no—
366C2×Q8—442no—
367C2×Q8—442no—
368C2×Q8—442no—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—112no—
373C2×D4—221no—
374C2×D4—221no—
375C2×D4—221no—
376C2×D4—221no—
377C2×D4—221no—
378C2×D4C2×D4412yes—
379C2×D4#434112yes—
380C2×D4Q8×D1112yes—
381C22×C4—21no—
382C22×C4—24no—
383C22×C4—22no—
384C22×C4—44no—
385C22×C4—42no—
386C22×C4—42no—
387C22×C4—44no—
388C22×C4—82no—
389C22×C4—222no—
390C22×C4—221no—
391C22×C4—442no—
392C22×C4—442no—
393C22×C4—442no—
394C22×C4C2×C22⋊D1112yes—
395C22×C4C2×C22⋊D1111yescharacteristic
396C22×C4C2×C22⋊D1112yes—
397C22×C4C2×C22⋊D1111yescharacteristic
398C22×C4C23×D1111yescharacteristic
399D8—228no—
400C2×C8—112no—
401C2×C8—221no—
402C2×C8—221no—
403C2×C8—221no—
404C2×C8—222no—
405C2×C8—222no—
406C2×C8—221no—
407C2×C8—222no—
408C2×C8—221no—
409C4⋊C4—22no—
410C4⋊C4—21no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—44no—
414C4⋊C4—42no—
415C4⋊C4—81no—
416C4⋊C4—221no—
417C4⋊C4—222no—
418C4⋊C4—221no—
419C4⋊C4—222no—
420C4⋊C4—444no—
421C4⋊C4—442no—
422C4⋊C4—444no—
423C4⋊C4#432314yescomplemented
424C4⋊C4C2×D4412yes—
425C22⋊C4—24no—
426C22⋊C4—44no—
427C22⋊C4—444no—
428C22⋊C4—442no—
429C22⋊C4—444no—
430C42—22no—
431C42—22no—
432C42C2×D4412yes—
433C42#433912yes—
434C11#2481111yescharacteristic, complemented, Sylow
435C23—22no—
436C23—22no—
437C23—22no—
438C23—41no—
439C23—41no—
440C23—41no—
441C23—41no—
442C23—222no—
443C23—441no—
444C23—441no—
445C23—441no—
446C23—441no—
447C23—441no—
448C23—441no—
449C23C22×C22⋊D1111yescharacteristic
450Q8—884no—
451D4—22no—
452D4—22no—
453D4—22no—
454D4—222no—
455D4—222no—
456D4—441no—
457D4—441no—
458D4#6695014yescomplemented
459C2×C4—22no—
460C2×C4—21no—
461C2×C4—22no—
462C2×C4—21no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—48no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—88no—
474C2×C4—441no—
475C2×C4—442no—
476C2×C4—442no—
477C2×C4—441no—
478C2×C4—442no—
479C2×C4—441no—
480C2×C4—884no—
481C2×C4#6698312yes—
482C2×C4#6698312yes—
483C2×C4C2×#432314yes—
484C2×C4C2×#432312yes—
485C2×C4#6700212yes—
486C2×C4C22×D4411yescharacteristic
487C2×C4C2×#433911yescharacteristic
488C2×C4C2×#434111yescharacteristic
489C2×C4#6703711yescharacteristic
490C2×C4C2×Q8×D1111yescharacteristic
491C2×C4#6704011yescharacteristic
492C8—222no—
493C8—441no—
494C8—442no—
495C22—24no—
496C22—42no—
497C22—42no—
498C22—42no—
499C22—42no—
500C22—42no—
501C22—42no—
502C22—442no—
503C22—442no—
504C22—442no—
505C22—881no—
506C22—881no—
507C22—881no—
508C22—881no—
509C22C2×#6698311yescharacteristic
510C22C22×#432311yescharacteristic
511C22#1062333711yescharacteristic
512C22Q8×C22⋊D1111yescharacteristic
513C22C2×#6700211yescharacteristic
514C22#1062336711yescharacteristic
515C22#1062336911yescharacteristic
516C4—24no—
517C4—22no—
518C4—42no—
519C4—42no—
520C4—82no—
521C4—881no—
522C4—882no—
523C4#1062262814yes—
524C4C2×#6695011yescharacteristic
525C4#1062304111yescharacteristic
526C4#1062304211yescharacteristic
527C4#1062304411yescharacteristic
528C2—44no—
529C2—882no—
530C2#1307206111yescharacteristic
531C2C2×#1062262811yescharacteristic
532C2#1307816611yescharacteristic
533C2#1308042911yescharacteristic
534C2#1308092111yescharacteristic
535C2Q8×#432311yescharacteristic
536C2#1308151511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingD4×C11×C4⋊C4C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenterD4×C4⋊C4D11
hypocenterC11#24811
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#10622620C2semidirect
3. #13073565C2semidirect
4. #13070087C2semidirect
5. #13070001C2semidirect
6. #13069576C2semidirect
7. #13069335C2semidirect
9. #13068616C2semidirect
10. #13068613C2semidirect
11. D4×C11×C4⋊C4C2semidirect
67. C2×#4323Q8semidirect
139. C11×C4⋊C4D8semidirect
170. D4×C4⋊C4D11semidirect
196. D4×C11C22⋊Q8semidirect
423. C4⋊C4#4323semidirect
434. C11#24811semidirect
458. D4#66950semidirect

Maximal subgroups

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

subgroupindex
C2×#106226202
C2×C4×#43232
#130735652
#130700872
#130700012
#130695762
#130693352
#130689642
#130686162
#130686132
D4×C11×C4⋊C42
#2481111