Finite Group Databasebeta

← #14645258

Subgroups — #14645258

Order 2816.

1030 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊Q8C211yesmaximal, characteristic
2#13068593C211yesmaximal, characteristic
3#13068593C211yesmaximal, characteristic
4C2×#10622120C211yesmaximal, characteristic, complemented
5C2×#10622185C211yesmaximal, characteristic, complemented
6C2×#10622124C211yesmaximal, characteristic, complemented
7C2×C11×#332C211yesmaximal, characteristic, complemented
8C22×Q8×D11—21no—
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×#66997—21no—
11D11×C4⋊Q8—22no—
12D11×C4⋊Q8—22no—
13D11×C4⋊Q8—22no—
14D11×C4⋊Q8—22no—
15C2×C4⋊C4×D11—21no—
16C2×C4⋊C4×D11C412yes—
17C2×#66941—21no—
18C2×#66941C412yes—
19C2×C42×D11C2211yescharacteristic
20C2×#66922C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×(C2×D11)⋊C8—21no—
24C2×(C2×D11)⋊C8—21no—
25C2×C4⋊(C11⋊C8)C2211yescharacteristic
26C2×C4⋊(C11⋊C8)C2211yescharacteristic
27C11×#332—22no—
28#10622188—21no—
29#10622188—21no—
30#10622185—22no—
31#10622124—22no—
32#10622120—22no—
33C22×Q8×C11—21no—
34C2×Q8×D11—24no—
35C2×Q8×D11—24no—
36C2×Q8×D11—42no—
37C2×Q8×D11—42no—
38C2×Q8×D11—42no—
39C2×Q8×D11—42no—
40C22×C4×D11—22no—
41C22×C4×D11C2×C411yescharacteristic
42C22×C4×D11D411yescharacteristic
43C22×C4×D11D411yescharacteristic
44C22×Dic22—21no—
45C22×Dic22—22no—
46C22×C8×C11—21no—
47C22×C8×C11—21no—
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8D412yes—
51C11×C4⋊Q8D412yes—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4C2×C412yes—
54C2×C42×C11C2311yescharacteristic
55#66997—24no—
56#66997—24no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11C2×C412yes—
59C2×Dic11⋊C4—22no—
60C2×Dic11⋊C4—22no—
61C2×C4×Dic11C2×C411yescharacteristic
62C2×C4×Dic11D411yescharacteristic
63C2×C4×Dic11D411yescharacteristic
64C22×C11⋊C8—21no—
65C22×C11⋊C8—21no—
66C4⋊C4×D11—24no—
67C4⋊C4×D11—24no—
68C4⋊C4×D11—24no—
69C4⋊C4×D11—24no—
70#66941—24no—
71#66941—24no—
72#66941—24no—
73#66941—24no—
74C42×D11—21no—
75C42×D11—21no—
76C42×D11—21no—
77C42×D11—21no—
78#66922—21no—
79#66922—21no—
80#66922D412yes—
81#66922D412yes—
82C11×C4⋊C8—21no—
83C11×C4⋊C8—21no—
84C11×C4⋊C8—21no—
85C11×C4⋊C8—21no—
86(C2×D11)⋊C8—42no—
87(C2×D11)⋊C8—42no—
88C4⋊(C11⋊C8)—21no—
89C4⋊(C11⋊C8)—21no—
90C4⋊(C11⋊C8)—21no—
91C4⋊(C11⋊C8)—21no—
92#8340—111nomaximal, Sylow
93C23×D11C22⋊C411yescharacteristic
94C2×Q8×C11—22no—
95C2×Q8×C11—22no—
96C2×Q8×C11—41no—
97C2×Q8×C11—41no—
98C2×Q8×C11—41no—
99C2×Q8×C11—41no—
100C22×C4×C11—22no—
101C22×C4×C11C22×C411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×Dic11—22no—
105C22×Dic11C22⋊C411yescharacteristic
106C22×Dic11C22⋊C411yescharacteristic
107C22×Dic11C22⋊C411yescharacteristic
108Q8×D11—48no—
109Q8×D11—48no—
110Q8×D11—48no—
111Q8×D11—48no—
112C2×C4×D11—22no—
113C2×C4×D11—28no—
114C2×C4×D11—22no—
115C2×C4×D11—21no—
116C2×C4×D11—21no—
117C2×C4×D11—21no—
118C2×C4×D11—21no—
119C2×C4×D11—21no—
120C2×C4×D11—21no—
121C2×C4×D11—21no—
122C2×C4×D11—21no—
123C2×C4×D11—21no—
124C2×C4×D11—21no—
125C2×C4×D11—44no—
126C2×C4×D11—44no—
127C2×C4×D11D812yes—
128C2×C4×D11SD1612yes—
129C2×C4×D11SD1612yes—
130C2×C4×D11Q1612yes—
131C2×Dic22—28no—
132C2×Dic22—22no—
133C2×Dic22—22no—
134C2×Dic22—44no—
135C2×Dic22—44no—
136C2×Dic22—41no—
137C2×Dic22—41no—
138C2×Dic22—41no—
139C2×Dic22—41no—
140C2×C8×C11—41no—
141C2×C8×C11—41no—
142C2×C8×C11—41no—
143C2×C8×C11—41no—
144C2×C8×C11—41no—
145C2×C8×C11—41no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4C22⋊C414yes—
150C42×C11C2×D411yescharacteristic
151C42×C11C2×D411yescharacteristic
152C42×C11C2×D411yescharacteristic
153C42×C11C2×D411yescharacteristic
154C4⋊Dic11—22no—
155C4⋊Dic11—22no—
156C4⋊Dic11—22no—
157C4⋊Dic11C22⋊C414yes—
158Dic11⋊C4—28no—
159Dic11⋊C4—28no—
160C4×Dic11—21no—
161C4×Dic11—21no—
162C4×Dic11—21no—
163C4×Dic11—21no—
164C4×Dic11—21no—
165C4×Dic11—21no—
166C2×C11⋊C8—41no—
167C2×C11⋊C8—41no—
168C2×C11⋊C8—41no—
169C2×C11⋊C8—41no—
170C2×C11⋊C8—41no—
171C2×C11⋊C8—41no—
172C22×C4⋊Q8—111no—
173#1797—111no—
174#1797—111no—
175C2×#332—111no—
176C2×#332—111no—
177C2×#332—111no—
178C2×#332D1111yescharacteristic, complemented
179C23×C11C2×C22⋊C411yescharacteristic
180C22×D11—21no—
181C22×D11—21no—
182C22×D11—21no—
183C22×D11—21no—
184C22×D11#10112yes—
185C22×D11#10212yes—
186C22×D11#10312yes—
187Q8×C11—42no—
188Q8×C11—42no—
189Q8×C11—42no—
190Q8×C11—42no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—24no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11C2×C22⋊C411yescharacteristic
197C2×C4×C11C2×C22⋊C411yescharacteristic
198C2×C4×C11#12011yescharacteristic
199C2×C4×C11#12011yescharacteristic
200C2×C4×C11#12011yescharacteristic
201C2×C4×C11#12011yescharacteristic
202C2×C4×C11C2×D811yescharacteristic
203C2×C4×C11C2×SD1611yescharacteristic
204C2×C4×C11C2×SD1611yescharacteristic
205C2×C4×C11C2×Q1611yescharacteristic
206C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
207C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
208C2×C4×C11#13711yescharacteristic
209C2×C4×C11#13711yescharacteristic
210C2×Dic11—21no—
211C2×Dic11—21no—
212C2×Dic11—21no—
213C2×Dic11—21no—
214C2×Dic11—21no—
215C2×Dic11—21no—
216C2×Dic11—24no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11#10112yes—
220C2×Dic11#10212yes—
221C2×Dic11#10312yes—
222C4×D11—24no—
223C4×D11—24no—
224C4×D11—22no—
225C4×D11—22no—
226C4×D11—22no—
227C4×D11—22no—
228C4×D11—22no—
229C4×D11—22no—
230C4×D11—22no—
231C4×D11—22no—
232C4×D11—416no—
233Dic22—416no—
234Dic22—42no—
235Dic22—42no—
236Dic22—42no—
237Dic22—42no—
238C8×C11—81no—
239C8×C11—81no—
240C11⋊C8—81no—
241C11⋊C8—81no—
242C23×Q8—221no—
243C2×C4⋊Q8—112no—
244C2×C4⋊Q8—111no—
245C2×C4⋊Q8—221no—
246C2×C4⋊Q8—221no—
247C2×C4⋊Q8—222no—
248C2×C4⋊Q8—222no—
249C2×C4⋊Q8—222no—
250C2×C4⋊Q8—222no—
251C2×C4⋊Q8C2×D1111yescharacteristic
252C22×C4⋊C4—112no—
253C22×C4⋊C4—221no—
254C22×C42—111no—
255C2×C4⋊C8—111no—
256C2×C4⋊C8—111no—
257C2×C4⋊C8C2×D1111yescharacteristic
258C2×C4⋊C8C2×D1111yescharacteristic
259C2×C22⋊C8—221no—
260C2×C22⋊C8—221no—
261#336—221no—
262#336—221no—
263#332—22no—
264#332—222no—
265#332—222no—
266#332—222no—
267C22×C11#37911yescharacteristic
268C22×C11C2×#10111yescharacteristic
269C22×C11C2×#10111yescharacteristic
270C22×C11C2×#10211yescharacteristic
271C22×C11C2×#10311yescharacteristic
272C22×C11#41811yescharacteristic
273C22×C11#41911yescharacteristic
274C2×D11—22no—
275C2×D11—22no—
276C2×D11—22no—
277C2×D11—22no—
278C2×D11—22no—
279C2×D11—22no—
280C2×D11#33214yescomplemented
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—44no—
284C4×C11#44711yescharacteristic
285C4×C11#44711yescharacteristic
286C4×C11#44811yescharacteristic
287C4×C11#44811yescharacteristic
288C4×C11#45011yescharacteristic
289C4×C11#45011yescharacteristic
290C4×C11#45111yescharacteristic
291C4×C11#45111yescharacteristic
292Dic11—22no—
293Dic11—22no—
294Dic11—22no—
295Dic11—44no—
296C22×Q8—21no—
297C22×Q8—222no—
298C22×Q8—224no—
299C22×Q8—224no—
300C22×Q8—221no—
301C22×Q8—442no—
302C22×Q8—442no—
303C22×Q8—442no—
304C22×Q8—442no—
305C23×C4—111no—
306C23×C4—111no—
307C23×C4—111no—
308C23×C4—222no—
309C22×C8—21no—
310C22×C8—21no—
311C22×C8—221no—
312C22×C8—221no—
313C4⋊Q8—21no—
314C4⋊Q8—21no—
315C4⋊Q8—112no—
316C4⋊Q8—112no—
317C4⋊Q8—224no—
318C4⋊Q8—224no—
319C4⋊Q8—224no—
320C4⋊Q8—224no—
321C4⋊Q8—224no—
322C4⋊Q8—224no—
323C4⋊Q8—221no—
324C4⋊Q8—221no—
325C4⋊Q8D4412yes—
326C4⋊Q8C22⋊D1112yes—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—112no—
329C2×C4⋊C4—224no—
330C2×C4⋊C4—224no—
331C2×C4⋊C4—224no—
332C2×C4⋊C4—222no—
333C2×C4⋊C4—222no—
334C2×C4⋊C4—221no—
335C2×C4⋊C4—224no—
336C2×C4⋊C4C4×D1112yes—
337C2×C42—111no—
338C2×C42—111no—
339C2×C42—111no—
340C2×C42—221no—
341C2×C42—221no—
342C2×C42—221no—
343C2×C42—221no—
344C2×C42C22×D1111yescharacteristic
345C4⋊C8—21no—
346C4⋊C8—21no—
347C4⋊C8—21no—
348C4⋊C8—21no—
349C4⋊C8—221no—
350C4⋊C8—221no—
351C4⋊C8—221no—
352C4⋊C8—221no—
353C22⋊C8—442no—
354C22⋊C8—442no—
355C2×C11C2×#33211yescharacteristic
356C2×C11#154611yescharacteristic
357C2×C11#154911yescharacteristic
358C2×C11#155611yescharacteristic
359C2×C11#178411yescharacteristic
360C2×C11#178611yescharacteristic
361C2×C11#178711yescharacteristic
362D11—24no—
363C24—111no—
364C2×Q8—22no—
365C2×Q8—22no—
366C2×Q8—41no—
367C2×Q8—41no—
368C2×Q8—41no—
369C2×Q8—41no—
370C2×Q8—228no—
371C2×Q8—222no—
372C2×Q8—222no—
373C2×Q8—444no—
374C2×Q8—444no—
375C2×Q8—448no—
376C2×Q8—448no—
377C2×Q8—448no—
378C2×Q8—448no—
379C2×Q8—441no—
380C2×Q8—441no—
381C2×Q8—441no—
382C2×Q8—441no—
383C22×C4—22no—
384C22×C4—111no—
385C22×C4—111no—
386C22×C4—111no—
387C22×C4—112no—
388C22×C4—112no—
389C22×C4—112no—
390C22×C4—112no—
391C22×C4—222no—
392C22×C4—222no—
393C22×C4—228no—
394C22×C4—221no—
395C22×C4—221no—
396C22×C4—221no—
397C22×C4—221no—
398C22×C4—221no—
399C22×C4—221no—
400C22×C4—221no—
401C22×C4—221no—
402C22×C4—221no—
403C22×C4—221no—
404C22×C4—222no—
405C22×C4—444no—
406C22×C4—444no—
407C22×C4C2×C4×D1111yescharacteristic
408C22×C4D4×D1111yescharacteristic
409C22×C4D4×D1111yescharacteristic
410C2×C8—41no—
411C2×C8—41no—
412C2×C8—41no—
413C2×C8—41no—
414C2×C8—41no—
415C2×C8—41no—
416C2×C8—441no—
417C2×C8—441no—
418C2×C8—441no—
419C2×C8—441no—
420C2×C8—441no—
421C2×C8—441no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—114no—
426C4⋊C4—228no—
427C4⋊C4—228no—
428C4⋊C4—222no—
429C4⋊C4—222no—
430C4⋊C4—222no—
431C4⋊C4(C2×D11)⋊C414yes—
432C42—221no—
433C42—221no—
434C42—221no—
435C42—221no—
436C42—221no—
437C42—221no—
438C42C2×D4411yescharacteristic
439C42D4×D1111yescharacteristic
440C42D4×D1111yescharacteristic
441C42C2×C22⋊D1111yescharacteristic
442C11#834011yescharacteristic, complemented, Sylow
443C23—112no—
444C23—112no—
445C23—112no—
446C23—221no—
447C23—221no—
448C23—221no—
449C23—221no—
450C23C22⋊C4×D1111yescharacteristic
451Q8—42no—
452Q8—42no—
453Q8—42no—
454Q8—42no—
455Q8—4416no—
456Q8—442no—
457Q8—442no—
458Q8—442no—
459Q8—442no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—24no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—112no—
466C2×C4—112no—
467C2×C4—112no—
468C2×C4—224no—
469C2×C4—224no—
470C2×C4—221no—
471C2×C4—221no—
472C2×C4—221no—
473C2×C4—221no—
474C2×C4—221no—
475C2×C4—221no—
476C2×C4—222no—
477C2×C4—222no—
478C2×C4—222no—
479C2×C4—222no—
480C2×C4—222no—
481C2×C4—222no—
482C2×C4—222no—
483C2×C4—222no—
484C2×C4—224no—
485C2×C4—4416no—
486C2×C4—442no—
487C2×C4—442no—
488C2×C4C22⋊C4×D1111yescharacteristic
489C2×C4#6693511yescharacteristic
490C2×C4#6693511yescharacteristic
491C2×C4D8×D1111yescharacteristic
492C2×C4#6696411yescharacteristic
493C2×C4SD16×D1111yescharacteristic
494C2×C4SD16×D1111yescharacteristic
495C2×C4#6696711yescharacteristic
496C2×C4#6696811yescharacteristic
497C2×C4Q16×D1111yescharacteristic
498C2×C4#6697111yescharacteristic
499C2×C4C2×(C2×D11)⋊C411yescharacteristic
500C2×C4#6699011yescharacteristic
501C2×C4#6699011yescharacteristic
502C8—81no—
503C8—81no—
504C8—881no—
505C8—881no—
506C22—114no—
507C22—222no—
508C22—222no—
509C22—222no—
510C22—222no—
511C22—222no—
512C22—222no—
513C22D11×#10111yescharacteristic
514C22D11×#10111yescharacteristic
515C22D11×#10211yescharacteristic
516C22#1062238311yescharacteristic
517C22D11×#10311yescharacteristic
518C22#1062241511yescharacteristic
519C22#1062256811yescharacteristic
520C4—21no—
521C4—21no—
522C4—44no—
523C4—222no—
524C4—222no—
525C4—222no—
526C4—444no—
527C4#1062238611yescharacteristic
528C4#1062238911yescharacteristic
529C4#1062241911yescharacteristic
530C4#1062242111yescharacteristic
531C4#1062276911yescharacteristic
532C4#1062278211yescharacteristic
533C4#1062278311yescharacteristic
534C4#1062279911yescharacteristic
535C2—224no—
536C2D11×#33211yescharacteristic
537C2#1306728611yescharacteristic
538C2#1306729911yescharacteristic
539C2#1306733111yescharacteristic
540C2#1306853811yescharacteristic
541C2#1306854511yescharacteristic
542C2#1306854911yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#332C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC2×C42×C11C23
hypercenterC2×#332D11
hypocenterC11#8340
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
4. C2×#10622120C2semidirect
5. C2×#10622185C2semidirect
6. C2×#10622124C2semidirect
7. C2×C11×#332C2semidirect
178. C2×#332D11semidirect
280. C2×D11#332semidirect
442. C11#8340semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C4⋊Q82
#130685932
C2×#106221202
C2×#106221852
C2×#106221242
C2×C11×#3322
#834011