Finite Group Databasebeta

← #14719814

Subgroups — #14719814

Order 2816.

976 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623113C211yesmaximal, characteristic
2#13077656C211yesmaximal, characteristic, complemented
3#13077639C211yesmaximal, characteristic, complemented
4#13066978C214yesmaximal, complemented
5#13066963C214yesmaximal, complemented
6#13066940C211yesmaximal, characteristic, complemented
7#13066928C211yesmaximal, characteristic, complemented
8#13066928C211yesmaximal, characteristic, complemented
9C11×#1461C211yesmaximal, characteristic, complemented
10C2×C4×Q8×C11C2211yescharacteristic
11C2×#67000C411yescharacteristic
12C2×#66999C411yescharacteristic
13#10623113—22no—
14#10623113—22no—
15#10623113—22no—
16#10623113—22no—
17C2×#66949C2212yes—
18C2×#66948C411yescharacteristic
19C2×#66947C2212yes—
20C2×#66941C411yescharacteristic
21C2×#66929C412yes—
22C2×#66928C412yes—
23C2×C4×D44C2211yescharacteristic
24C2×#66925C2211yescharacteristic
25C11×#431C2211yescharacteristic
26C11×#431C2211yescharacteristic
27#10622538C2211yescharacteristic
28#10622538C2211yescharacteristic
29#10622451—22no—
30#10622447—22no—
31#10622339C2214yes—
32D11×C22⋊C8C2214yes—
33#10622301—22no—
34C8×D44—22no—
35C11×#324C2214yes—
36#10622166C2214yes—
37#10622107C2212yes—
38#10622107C2212yes—
39#10622106C2212yes—
40#10622106C2212yes—
41C22×Q8×C11C2×C411yescharacteristic
42C22×D44C2×C411yescharacteristic
43C22×D44C2×C412yes—
44C22×C4×D11C2×C411yescharacteristic
45C22×C4×D11C2312yes—
46C22×Dic22C2×C412yes—
47C4×Q8×C11—21no—
48C4×Q8×C11—21no—
49C4×Q8×C11—21no—
50C4×Q8×C11—21no—
51C2×C11×C4⋊C4C2×C411yescharacteristic
52C2×C11×C4⋊C4C2312yes—
53C2×C42×C11C2×C412yes—
54C2×C42×C11C2311yescharacteristic
55#67000—22no—
56#67000—22no—
57#66999—22no—
58#66999—22no—
59C2×(C2×D11)⋊C4C2×C411yescharacteristic
60C2×(C2×D11)⋊C4C2×C412yes—
61C2×(C2×D11)⋊C4C2×C412yes—
62C2×(C2×D11)⋊C4C2×C412yes—
63C2×(C2×D11)⋊C4C2×C412yes—
64C2×(C2×D11)⋊C4C2×C412yes—
65C2×(C2×D11)⋊C4C2311yescharacteristic
66C2×C4⋊Dic11C2×C411yescharacteristic
67C2×Dic11⋊C4C2×C411yescharacteristic
68C2×Dic11⋊C4C2×C412yes—
69C2×Dic11⋊C4C2×C412yes—
70C2×Dic11⋊C4C2311yescharacteristic
71C2×C4×Dic11C2×C411yescharacteristic
72C2×#4313—24no—
73C2×C8×D11—24no—
74#66949—24no—
75#66949—24no—
76#66948—22no—
77#66948—22no—
78#66947—24no—
79#66947—24no—
80#66941—22no—
81#66941—22no—
82#66929—24no—
83#66929—24no—
84#66928—24no—
85#66928—24no—
86C4×D44D412yes—
87C4×D44D412yes—
88C4×D44D412yes—
89C4×D44D412yes—
90#66925—21no—
91#66925—21no—
92#66925—21no—
93#66925—21no—
94C11×C4⋊C8—21no—
95C11×C4⋊C8—21no—
96C11×C22⋊C8C2312yes—
97C11×C22⋊C8C2312yes—
98C4×C8×C11—21no—
99C4×C8×C11—21no—
100C22⋊(C11⋊C8)C2312yes—
101C22⋊(C11⋊C8)C2312yes—
102(C2×D11)⋊C8—24no—
103(C2×D11)⋊C8—24no—
104C4⋊(C11⋊C8)—21no—
105C4⋊(C11⋊C8)—21no—
106C4×C11⋊C8—21no—
107C4×C11⋊C8—21no—
108#17388—111nomaximal, Sylow
109C23×D11C22×C411yescharacteristic
110C23×D11C22×C412yes—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C22×C4×C11C22×C412yes—
116C22×C4×C11C22×C412yes—
117C22×C4×C11C22×C411yescharacteristic
118C22×C4×C11C22×C411yescharacteristic
119C22×C4×C11C2411yescharacteristic
120C22×Dic11C22×C411yescharacteristic
121C22×Dic11C22×C411yescharacteristic
122C22×Dic11C22×C411yescharacteristic
123C22×Dic11C22×C412yes—
124C2×D44—24no—
125C2×D44—22no—
126C2×D44—22no—
127C2×D44—82no—
128C2×D44C22⋊C412yes—
129C2×D44C22⋊C412yes—
130C2×C4×D11—21no—
131C2×C4×D11—21no—
132C2×C4×D11—22no—
133C2×C4×D11—22no—
134C2×C4×D11—82no—
135C2×C4×D11C2×D414yes—
136C2×C4×D11C2×D414yes—
137C2×Dic22—24no—
138C2×Dic22—82no—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C42×C11—22no—
146C42×C11—22no—
147C42×C11C2×D411yescharacteristic
148C42×C11C2×D411yescharacteristic
149C42×C11C2×D411yescharacteristic
150C42×C11C2×D411yescharacteristic
151(C2×D11)⋊C4—24no—
152(C2×D11)⋊C4—24no—
153(C2×D11)⋊C4—24no—
154(C2×D11)⋊C4—24no—
155(C2×D11)⋊C4—21no—
156(C2×D11)⋊C4—21no—
157(C2×D11)⋊C4—21no—
158(C2×D11)⋊C4—21no—
159(C2×D11)⋊C4C22⋊C414yes—
160(C2×D11)⋊C4C22⋊C414yes—
161C4⋊Dic11C22⋊C412yes—
162C4⋊Dic11C22⋊C412yes—
163Dic11⋊C4—24no—
164Dic11⋊C4—24no—
165Dic11⋊C4—21no—
166Dic11⋊C4—21no—
167Dic11⋊C4—21no—
168Dic11⋊C4—21no—
169C4×Dic11—21no—
170C4×Dic11—21no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—22no—
173#4313—84no—
174C8×D11—84no—
175C2×#542—111no—
176#2975—111no—
177#2972—111no—
178#1472—114no—
179#1468—114no—
180#1461—111no—
181#1461D1111yescharacteristic, complemented
182#1458—111no—
183#1458—111no—
184C23×C11C23×C411yescharacteristic
185C22×D11—22no—
186C22×D11—22no—
187C22×D11—21no—
188C22×D11—21no—
189C22×D11—21no—
190C22×D11—42no—
191C22×D11—42no—
192C22×D11—41no—
193C22×D11—41no—
194C22×D11C2×C22⋊C414yes—
195Q8×C11—42no—
196Q8×C11—42no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—42no—
204C2×C4×C11C2×C22⋊C411yescharacteristic
205C2×C4×C11C2×C22⋊C411yescharacteristic
206C2×C4×C11C2×C22⋊C411yescharacteristic
207C2×C4×C11C2×C22⋊C411yescharacteristic
208C2×C4×C11#13112yes—
209C2×C4×C11#13112yes—
210C2×C4×C11C22×D411yescharacteristic
211C2×C4×C11C22×D411yescharacteristic
212C2×Dic11—21no—
213C2×Dic11—21no—
214C2×Dic11—21no—
215C2×Dic11—21no—
216C2×Dic11—21no—
217C2×Dic11—42no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220C2×Dic11C2×C22⋊C414yes—
221D44—24no—
222D44—24no—
223D44—84no—
224C4×D11—44no—
225C4×D11—44no—
226C4×D11—42no—
227C4×D11—42no—
228Dic22—84no—
229C8×C11—42no—
230C8×C11—42no—
231C11⋊C8—42no—
232C11⋊C8—42no—
233#542—222no—
234#542—222no—
235#542—222no—
236#542—222no—
237C2×C4⋊Q8—111no—
238C2×#126—112no—
239C2×#124—111no—
240C2×#124—112no—
241C2×#123—112no—
242C2×C22⋊Q8—111no—
243C2×C22⋊Q8—112no—
244C2×#121—111no—
245C2×C4×Q8C2×D1111yescharacteristic
246C2×C4×D4—111no—
247C2×#117—111no—
248#436—222no—
249#436—222no—
250C8×D4—222no—
251C8×D4—222no—
252#431—111no—
253#431—111no—
254#431C2×D1111yescharacteristic
255#431C2×D1111yescharacteristic
256#407—114no—
257C2×C22⋊C8—114no—
258#324—114no—
259#324—112no—
260#324—112no—
261#324C2×D1114yes—
262#323—112no—
263#323—112no—
264C22×C11—21no—
265C22×C11—21no—
266C22×C11C22×C22⋊C411yescharacteristic
267C22×C11C2×#13111yescharacteristic
268C22×C11C2×#13111yescharacteristic
269C2×D11—24no—
270C2×D11—24no—
271C2×D11—24no—
272C2×D11—41no—
273C2×D11—41no—
274C2×D11—41no—
275C2×D11—82no—
276C2×D11—82no—
277C2×D11—81no—
278C2×D11—81no—
279C4×C11—21no—
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—42no—
284C4×C11—42no—
285C4×C11#40812yes—
286C4×C11#40812yes—
287Dic11—24no—
288Dic11—41no—
289Dic11—41no—
290Dic11—41no—
291C22×Q8—112no—
292C22×Q8C4×D1111yescharacteristic
293C22×D4—111no—
294C22×D4—112no—
295C23×C4—112no—
296C23×C4—111no—
297C2×M16—224no—
298C22×C8—224no—
299C4⋊Q8—222no—
300C4⋊Q8—222no—
301#126—224no—
302#126—224no—
303#124—224no—
304#124—224no—
305#124—222no—
306#124—222no—
307#123—224no—
308#123—224no—
309C22⋊Q8—224no—
310C22⋊Q8—224no—
311C22⋊Q8—222no—
312C22⋊Q8—222no—
313#121—222no—
314#121—222no—
315C4×Q8—21no—
316C4×Q8—21no—
317C4×Q8—21no—
318C4×Q8—21no—
319C4×D4—112no—
320C4×D4—112no—
321C4×D4—112no—
322C4×D4—112no—
323#117—221no—
324#117—221no—
325#117—221no—
326#117—221no—
327C2×C4⋊C4—111no—
328C2×C4⋊C4—111no—
329C2×C4⋊C4—112no—
330C2×C4⋊C4—112no—
331C2×C4⋊C4—111no—
332C2×C4⋊C4C4×D1111yescharacteristic
333C2×C4⋊C4C22×D1112yes—
334C2×C22⋊C4—112no—
335C2×C22⋊C4—111no—
336C2×C22⋊C4—112no—
337C2×C22⋊C4—112no—
338C2×C22⋊C4—112no—
339C2×C22⋊C4—112no—
340C2×C22⋊C4—111no—
341C2×C42—111no—
342C2×C42C4×D1112yes—
343C2×C42C22×D1111yescharacteristic
344C4⋊C8—21no—
345C4⋊C8—21no—
346C4⋊C8—221no—
347C4⋊C8—221no—
348C22⋊C8—112no—
349C22⋊C8—112no—
350C22⋊C8—224no—
351C22⋊C8—224no—
352C22⋊C8C22×D1112yes—
353C22⋊C8C22×D1112yes—
354C4×C8—21no—
355C4×C8—21no—
356C4×C8—221no—
357C4×C8—221no—
358C2×C11—21no—
359C2×C11—21no—
360C2×C11C2×#40811yescharacteristic
361C2×C11#288311yescharacteristic
362C2×C11#288911yescharacteristic
363D11—44no—
364D11—81no—
365C24—112no—
366C24—111no—
367C2×Q8—21no—
368C2×Q8—21no—
369C2×Q8—22no—
370C2×Q8—22no—
371C2×Q8—224no—
372C2×Q8—882no—
373C2×D4—112no—
374C2×D4—112no—
375C2×D4—224no—
376C2×D4—222no—
377C2×D4—222no—
378C2×D4—882no—
379C22×C4—112no—
380C22×C4—114no—
381C22×C4—114no—
382C22×C4—111no—
383C22×C4—111no—
384C22×C4—111no—
385C22×C4—221no—
386C22×C4—221no—
387C22×C4—222no—
388C22×C4—222no—
389C22×C4—882no—
390C22×C4C2×C4×D1112yes—
391C22×C4C2×C4×D1112yes—
392C22×C4C2×C4×D1111yescharacteristic
393C22×C4C2×C4×D1111yescharacteristic
394C22×C4C23×D1111yescharacteristic
395M16—884no—
396C2×C8—22no—
397C2×C8—22no—
398C2×C8—222no—
399C2×C8—222no—
400C2×C8—884no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—112no—
406C4⋊C4—112no—
407C4⋊C4—224no—
408C4⋊C4—224no—
409C4⋊C4—221no—
410C4⋊C4—221no—
411C4⋊C4—221no—
412C4⋊C4—221no—
413C22⋊C4—114no—
414C22⋊C4—114no—
415C22⋊C4—224no—
416C22⋊C4—224no—
417C22⋊C4—224no—
418C22⋊C4—224no—
419C22⋊C4—221no—
420C22⋊C4—221no—
421C22⋊C4—221no—
422C22⋊C4—221no—
423C42—22no—
424C42—22no—
425C42—221no—
426C42—221no—
427C42D4×D1111yescharacteristic
428C42D4×D1111yescharacteristic
429C42D4×D1111yescharacteristic
430C42D4×D1111yescharacteristic
431C11#1738811yescharacteristic, complemented, Sylow
432C23—114no—
433C23—222no—
434C23—222no—
435C23—221no—
436C23—221no—
437C23—221no—
438C23—442no—
439C23—442no—
440C23—441no—
441C23—441no—
442C23C22×C4×D1111yescharacteristic
443Q8—42no—
444Q8—42no—
445Q8—884no—
446D4—224no—
447D4—224no—
448D4—884no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—114no—
457C2×C4—221no—
458C2×C4—221no—
459C2×C4—221no—
460C2×C4—221no—
461C2×C4—221no—
462C2×C4—444no—
463C2×C4—444no—
464C2×C4—442no—
465C2×C4—442no—
466C2×C4—442no—
467C2×C4—441no—
468C2×C4—441no—
469C2×C4C22⋊C4×D1111yescharacteristic
470C2×C4C22⋊C4×D1111yescharacteristic
471C2×C4C22⋊C4×D1111yescharacteristic
472C2×C4C22⋊C4×D1111yescharacteristic
473C2×C4#6695412yes—
474C2×C4#6696012yes—
475C2×C4C2×D4×D1111yescharacteristic
476C2×C4C2×D4×D1111yescharacteristic
477C8—42no—
478C8—42no—
479C8—442no—
480C8—442no—
481C22—21no—
482C22—21no—
483C22—224no—
484C22—224no—
485C22—224no—
486C22—441no—
487C22—441no—
488C22—441no—
489C22—882no—
490C22—882no—
491C22—881no—
492C22—881no—
493C22C2×C22⋊C4×D1111yescharacteristic
494C22C2×#6695411yescharacteristic
495C22C2×#6696011yescharacteristic
496C4—21no—
497C4—21no—
498C4—21no—
499C4—21no—
500C4—42no—
501C4—42no—
502C4—224no—
503C4—441no—
504C4—441no—
505C4—441no—
506C4#1062234012yes—
507C4#1062234012yes—
508C2—21no—
509C2—21no—
510C2—444no—
511C2—881no—
512C2C2×#1062234011yescharacteristic
513C2#1307707511yescharacteristic
514C2#1307709611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1461C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#66948C4
cosocleC22×C4×C11C24
hypercenter#1461D11
hypocenterC11#17388
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1461

Complements

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

NH ≅ G/Ntype
2. #13077656C2semidirect
3. #13077639C2semidirect
4. #13066978C2semidirect
5. #13066963C2semidirect
6. #13066940C2semidirect
7. #13066928C2semidirect
8. #13066928C2semidirect
9. C11×#1461C2semidirect
181. #1461D11semidirect
431. C11#17388semidirect

Maximal subgroups

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

subgroupindex
C2×#106231132
#130776562
#130776392
#130669782
#130669632
#130669402
#130669282
C11×#14612
#1738811