Finite Group Databasebeta

← #14770504

Subgroups — #14770504

Order 2816.

1364 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4339C211yesmaximal, characteristic
2C2×#10622314C212yesmaximal, complemented
3#13069414C212yesmaximal, complemented
4#13069412C212yesmaximal, complemented
5#13069408C212yesmaximal, complemented
6#13068596C211yesmaximal, characteristic, complemented
7#13068595C211yesmaximal, characteristic, complemented
8#13068595C211yesmaximal, characteristic, complemented
9#13068377C211yesmaximal, characteristic, complemented
10#13068373C211yesmaximal, characteristic, complemented
11C11×#1749C211yesmaximal, characteristic, complemented
12C22×#4339C411yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C2×C4×C22⋊D11C411yescharacteristic
15C2×C4×C22⋊D11C411yescharacteristic
16C2×C4×C22⋊D11C2211yescharacteristic
17C2×C4×C22⋊D11C2211yescharacteristic
18C2×#66979C411yescharacteristic
19C4×#4339—28no—
20C2×C4×D44C411yescharacteristic
21C2×C4×D44C2211yescharacteristic
22C2×#66925C411yescharacteristic
23C2×#66925C411yescharacteristic
24C2×C42×D11C2211yescharacteristic
25C2×C42×D11C2211yescharacteristic
26C2×C4×Dic22C411yescharacteristic
27C2×C4×Dic22C2211yescharacteristic
28C2×C11×C22⋊C8C2212yes—
29C2×C11×#97C2212yes—
30C2×C22⋊(C11⋊C8)C2212yes—
31C2×(C2×D11)⋊C8C2212yes—
32C2×(C2×D11)⋊C8C2212yes—
33C2×(C2×D11)⋊C8C2212yes—
34C2×(C2×D11)⋊C8C2212yes—
35C2×#66879C2212yes—
36C2×Dic11⋊C8C2212yes—
37C2×Dic11⋊C8C2212yes—
38C2×C8×Dic11C2212yes—
39C2×C4⋊(C11⋊C8)C2212yes—
40#10622314—28no—
41C11×#336C2211yescharacteristic
42C11×#336C2211yescharacteristic
43#10622162C2211yescharacteristic
44#10622162C2211yescharacteristic
45C23×C4×C11C2×C411yescharacteristic
46C23×C4×C11C2×C411yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C22×C22⋊D11C2×C411yescharacteristic
49C22×C22⋊D11C2×C411yescharacteristic
50C2×#4339—24no—
51C2×#4339—24no—
52C2×#4339—24no—
53C22×D44C2×C411yescharacteristic
54C22×C4×D11C2×C411yescharacteristic
55C22×C4×D11C2×C411yescharacteristic
56C22×C4×D11C2×C411yescharacteristic
57C22×C4×D11C2×C411yescharacteristic
58C22×C4×D11C2311yescharacteristic
59C22×C4×D11C2311yescharacteristic
60C22×Dic22C2×C411yescharacteristic
61C22×C8×C11C2312yes—
62C22×C8×C11C2312yes—
63C2×C42×C11—24no—
64C2×C42×C11C2×C411yescharacteristic
65C2×C42×C11C2×C411yescharacteristic
66C2×C42×C11C2311yescharacteristic
67C2×C42×C11C2311yescharacteristic
68C2×C22⋊Dic11C2×C411yescharacteristic
69C2×C22⋊Dic11C2×C411yescharacteristic
70C4×C22⋊D11—24no—
71C4×C22⋊D11—24no—
72C4×C22⋊D11—24no—
73C4×C22⋊D11—24no—
74C2×(C2×D11)⋊C4C2×C411yescharacteristic
75C2×(C2×D11)⋊C4C2×C411yescharacteristic
76C2×(C2×D11)⋊C4C2×C411yescharacteristic
77C2×(C2×D11)⋊C4C2×C411yescharacteristic
78#66979—24no—
79C2×C4⋊Dic11C2×C411yescharacteristic
80C2×C4⋊Dic11C2×C411yescharacteristic
81C2×Dic11⋊C4C2×C411yescharacteristic
82C2×Dic11⋊C4C2×C411yescharacteristic
83C2×Dic11⋊C4C2×C411yescharacteristic
84C2×Dic11⋊C4C2×C411yescharacteristic
85C2×C4×Dic11C2×C411yescharacteristic
86C2×C4×Dic11C2×C411yescharacteristic
87C2×C4×Dic11C2×C411yescharacteristic
88C2×C4×Dic11C2×C411yescharacteristic
89C2×C4×Dic11C2311yescharacteristic
90C2×C4×Dic11C2311yescharacteristic
91C22×C11⋊C8C2312yes—
92C22×C11⋊C8C2312yes—
93C4×D44—24no—
94C4×D44—24no—
95#66925—24no—
96#66925—24no—
97C42×D11—24no—
98C42×D11—24no—
99C4×Dic22—24no—
100C4×Dic22D418yes—
101C11×C22⋊C8—24no—
102C11×#97—24no—
103C22⋊(C11⋊C8)—42no—
104(C2×D11)⋊C8—24no—
105(C2×D11)⋊C8—24no—
106(C2×D11)⋊C8—42no—
107(C2×D11)⋊C8—42no—
108#66879—24no—
109Dic11⋊C8—24no—
110Dic11⋊C8—24no—
111C8×Dic11—24no—
112C4⋊(C11⋊C8)—24no—
113#22532—111nomaximal, Sylow
114C24×C11C22×C411yescharacteristic
115C23×D11C22×C411yescharacteristic
116C23×D11C22×C411yescharacteristic
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—41no—
127C22×C4×C11C22×C411yescharacteristic
128C22×C4×C11C22×C411yescharacteristic
129C22×C4×C11C22×C411yescharacteristic
130C22×C4×C11C22×C411yescharacteristic
131C22×C4×C11C22×C411yescharacteristic
132C22×C4×C11C2411yescharacteristic
133C2×C22⋊D11—22no—
134C2×C22⋊D11—22no—
135C2×C22⋊D11—22no—
136C2×C22⋊D11—22no—
137C2×C22⋊D11—22no—
138C2×C22⋊D11M1614yes—
139C22×Dic11C22×C411yescharacteristic
140C22×Dic11C22×C411yescharacteristic
141C22×Dic11C22×C411yescharacteristic
142C22×Dic11C22×C411yescharacteristic
143C22×Dic11C22×C411yescharacteristic
144C22×Dic11C22×C411yescharacteristic
145#4339—232no—
146C2×D44—22no—
147C2×D44—22no—
148C2×D44—22no—
149C2×C4×D11—22no—
150C2×C4×D11—22no—
151C2×C4×D11—22no—
152C2×C4×D11—22no—
153C2×C4×D11—22no—
154C2×C4×D11—22no—
155C2×C4×D11—22no—
156C2×C4×D11—22no—
157C2×C4×D11—22no—
158C2×C4×D11—22no—
159C2×C4×D11—22no—
160C2×C4×D11—22no—
161C2×C4×D11—22no—
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—41no—
167C2×C4×D11—41no—
168C2×C4×D11M1614yes—
169C2×Dic22—22no—
170C2×Dic22—22no—
171C2×Dic22C22⋊C414yes—
172C2×C8×C11—22no—
173C2×C8×C11—22no—
174C2×C8×C11—22no—
175C2×C8×C11—22no—
176C2×C8×C11—22no—
177C2×C8×C11#4114yescomplemented
178C42×C11—22no—
179C42×C11—22no—
180C42×C11—22no—
181C42×C11C2×D414yes—
182C22⋊Dic11—22no—
183C22⋊Dic11—22no—
184(C2×D11)⋊C4—22no—
185(C2×D11)⋊C4—22no—
186(C2×D11)⋊C4—22no—
187(C2×D11)⋊C4—22no—
188C4⋊Dic11—22no—
189C4⋊Dic11C22⋊C414yes—
190Dic11⋊C4—22no—
191Dic11⋊C4—22no—
192Dic11⋊C4C22⋊C414yes—
193Dic11⋊C4C22⋊C414yes—
194C4×Dic11—22no—
195C4×Dic11—22no—
196C4×Dic11—22no—
197C4×Dic11—22no—
198C4×Dic11C2×D414yes—
199C4×Dic11C2×D414yes—
200C2×C11⋊C8—22no—
201C2×C11⋊C8—22no—
202C2×C11⋊C8—22no—
203C2×C11⋊C8—22no—
204C2×C11⋊C8—22no—
205C2×C11⋊C8—22no—
206C2×C4×#41—111no—
207C2×#446—112no—
208#1955—112no—
209#1955—112no—
210#1954—112no—
211#1797—111no—
212#1797—111no—
213#1797—111no—
214#1749—111no—
215#1749D1111yescharacteristic, complemented
216C4×C22⋊C8—111no—
217C23×C11—21no—
218C23×C11—21no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11C2×M1612yes—
224C23×C11C23×C411yescharacteristic
225C22×D11—21no—
226C22×D11—21no—
227C22×D11—21no—
228C22×D11—21no—
229C22×D11—21no—
230C22×D11—21no—
231C22×D11—21no—
232C22×D11—21no—
233C22×D11—21no—
234C22×D11—21no—
235C22×D11—21no—
236C22×D11—21no—
237C22×D11C2×M1612yes—
238C22×D11C2×M1612yes—
239C2×C4×C11—28no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—44no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11C2×C22⋊C412yes—
255C2×C4×C11C2×C22⋊C412yes—
256C2×C4×C11C2×M1612yes—
257C2×C4×C11#13112yes—
258C2×C4×C11C22×D412yes—
259C2×C4×C11C2×#4112yes—
260C2×C4×C11H(5,𝔽2)11yescharacteristic
261C2×C4×C112−1+411yescharacteristic
262C22⋊D11—28no—
263C22⋊D11—28no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11C2×C22⋊C412yes—
277C2×Dic11C2×C22⋊C412yes—
278C2×Dic11C2×C22⋊C412yes—
279C2×Dic11C2×C22⋊C412yes—
280C2×Dic11C2×M1612yes—
281C2×Dic11C2×M1612yes—
282D44—28no—
283C4×D11—28no—
284C4×D11—28no—
285C4×D11—44no—
286C4×D11—44no—
287C4×D11—42no—
288C4×D11—42no—
289C4×D11—42no—
290C4×D11—42no—
291Dic22—28no—
292C8×C11—24no—
293C8×C11—42no—
294C11⋊C8—42no—
295C11⋊C8—42no—
296C22×#41—111no—
297C4×#41—228no—
298C2×C4×Q8—111no—
299C2×C4×Q8—111no—
300C2×C4×D4—111no—
301C2×C4×D4—111no—
302C2×C4×D4—111no—
303C2×C4×D4—111no—
304C2×C4×D4—111no—
305C2×C4×D4—111no—
306C2×#117—111no—
307C2×#117—111no—
308C2×#117—111no—
309C22×C42—111no—
310C22×C42—111no—
311C22×C42C2×D1111yescharacteristic
312#446—228no—
313C2×C4⋊C8—112no—
314C2×C4⋊C8—112no—
315C2×C4⋊C8—112no—
316C2×C22⋊C8—112no—
317C2×C22⋊C8—112no—
318C2×C22⋊C8—112no—
319C2×C22⋊C8—112no—
320C2×C22⋊C8—112no—
321C2×C22⋊C8C2×D1112yes—
322C2×#97—112no—
323C2×#97C2×D1112yes—
324C2×C4×C8—112no—
325#336—111no—
326#336—111no—
327#336C2×D1111yescharacteristic
328#336C2×D1111yescharacteristic
329C22×C11—22no—
330C22×C11—22no—
331C22×C11—22no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11C22×C22⋊C411yescharacteristic
337C22×C11C4×#4111yescharacteristic
338C22×C11#52011yescharacteristic
339C22×C11C22×M1611yescharacteristic
340C22×C11C22×M1611yescharacteristic
341C22×C11C2×#13111yescharacteristic
342C22×C11#56811yescharacteristic
343C2×D11—22no—
344C2×D11—22no—
345C2×D11—22no—
346C2×D11—22no—
347C2×D11—22no—
348C2×D11—22no—
349C2×D11—41no—
350C2×D11—41no—
351C2×D11—41no—
352C2×D11—41no—
353C2×D11—41no—
354C2×D11—41no—
355C2×D11—41no—
356C2×D11—41no—
357C4×C11—22no—
358C4×C11—22no—
359C4×C11—22no—
360C4×C11—22no—
361C4×C11—41no—
362C4×C11#54812yes—
363C4×C11#55012yes—
364Dic11—22no—
365Dic11—22no—
366Dic11—22no—
367Dic11—41no—
368Dic11—41no—
369Dic11#40714yes—
370C2×#41—224no—
371C2×#41—224no—
372C2×#41—224no—
373C22×Q8—111no—
374C22×D4—111no—
375C22×D4—111no—
376C22×D4—111no—
377C23×C4—111no—
378C23×C4—111no—
379C23×C4—111no—
380C23×C4—111no—
381C23×C4—111no—
382C23×C4—111no—
383C23×C4C4×D1111yescharacteristic
384C23×C4C4×D1111yescharacteristic
385C23×C4C22×D1111yescharacteristic
386C22×C8—112no—
387C22×C8—112no—
388C22×C8C22×D1112yes—
389C22×C8C22×D1112yes—
390C4×Q8—118no—
391C4×Q8—224no—
392C4×D4—224no—
393C4×D4—224no—
394C4×D4—224no—
395C4×D4—224no—
396C4×D4—224no—
397C4×D4—224no—
398#117—224no—
399#117—224no—
400#117—224no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—111no—
407C2×C22⋊C4—111no—
408C2×C22⋊C4—111no—
409C2×C22⋊C4—111no—
410C2×C22⋊C4—111no—
411C2×C22⋊C4—111no—
412C2×C22⋊C4—111no—
413C2×C42—24no—
414C2×C42—111no—
415C2×C42—111no—
416C2×C42—111no—
417C2×C42—111no—
418C2×C42—111no—
419C2×C42—111no—
420C2×C42—224no—
421C2×C42—224no—
422C2×C42C4×D1111yescharacteristic
423C2×C42C4×D1111yescharacteristic
424C2×C42C22×D1111yescharacteristic
425C2×C42C22×D1111yescharacteristic
426C4⋊C8—224no—
427C4⋊C8—224no—
428C4⋊C8—224no—
429C22⋊C8—24no—
430C22⋊C8—224no—
431C22⋊C8—224no—
432C22⋊C8—442no—
433C22⋊C8—442no—
434C22⋊C8—442no—
435#97—24no—
436#97—224no—
437C4×C8—224no—
438C2×C11—42no—
439C2×C11#234111yescharacteristic
440C2×C11C2×#40711yescharacteristic
441C2×C11#288011yescharacteristic
442C2×C11#296511yescharacteristic
443C2×C11#297011yescharacteristic
444C2×C11#298911yescharacteristic
445C2×C11#299011yescharacteristic
446D11—42no—
447D11—42no—
448C24—111no—
449C24—111no—
450C24C2×C4×D1111yescharacteristic
451#41—2232no—
452C2×Q8—114no—
453C2×Q8—222no—
454C2×Q8—222no—
455C2×D4—114no—
456C2×D4—222no—
457C2×D4—222no—
458C2×D4—222no—
459C2×D4—222no—
460C2×D4—222no—
461C2×D4—222no—
462C2×D4—222no—
463C2×D4—222no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—41no—
474C22×C4—111no—
475C22×C4—111no—
476C22×C4—111no—
477C22×C4—111no—
478C22×C4—114no—
479C22×C4—111no—
480C22×C4—111no—
481C22×C4—222no—
482C22×C4—222no—
483C22×C4—222no—
484C22×C4—222no—
485C22×C4—222no—
486C22×C4—222no—
487C22×C4—222no—
488C22×C4—222no—
489C22×C4—222no—
490C22×C4—222no—
491C22×C4—222no—
492C22×C4—222no—
493C22×C4—222no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—441no—
499C22×C4—441no—
500C22×C4C2×C4×D1111yescharacteristic
501C22×C4C2×C4×D1111yescharacteristic
502C22×C4C2×C4×D1111yescharacteristic
503C22×C4C2×C4×D1111yescharacteristic
504C22×C4C2×C4×D1111yescharacteristic
505C22×C4C23×D1111yescharacteristic
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—22no—
509C2×C8—22no—
510C2×C8—22no—
511C2×C8—222no—
512C2×C8—222no—
513C2×C8—222no—
514C2×C8—222no—
515C2×C8—222no—
516C2×C8—222no—
517C2×C8#433914yescomplemented
518C4⋊C4—114no—
519C4⋊C4—114no—
520C4⋊C4—114no—
521C4⋊C4—222no—
522C4⋊C4—222no—
523C4⋊C4—222no—
524C22⋊C4—222no—
525C22⋊C4—222no—
526C22⋊C4—222no—
527C22⋊C4—222no—
528C22⋊C4—222no—
529C22⋊C4—222no—
530C42—22no—
531C42—22no—
532C42—22no—
533C42—114no—
534C42—114no—
535C42—222no—
536C42—222no—
537C42—222no—
538C42—222no—
539C42D4×D1114yes—
540C11#2253211yescharacteristic, complemented, Sylow
541C23—21no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—112no—
548C23—112no—
549C23—221no—
550C23—221no—
551C23—221no—
552C23—221no—
553C23—221no—
554C23—221no—
555C23—221no—
556C23—221no—
557C23—221no—
558C23—221no—
559C23—221no—
560C23—221no—
561C23M16×D1112yes—
562C23C22×C4×D1111yescharacteristic
563Q8—228no—
564D4—228no—
565D4—228no—
566D4—228no—
567C2×C4—28no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—44no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—112no—
583C2×C4—112no—
584C2×C4—112no—
585C2×C4—112no—
586C2×C4—112no—
587C2×C4—112no—
588C2×C4—228no—
589C2×C4—228no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—221no—
601C2×C4—221no—
602C2×C4—444no—
603C2×C4—444no—
604C2×C4—442no—
605C2×C4—442no—
606C2×C4—442no—
607C2×C4—442no—
608C2×C4C22⋊C4×D1112yes—
609C2×C4C22⋊C4×D1112yes—
610C2×C4M16×D1112yes—
611C2×C4#6696012yes—
612C2×C4C2×#433912yes—
613C2×C4C2×D4×D1112yes—
614C2×C4#6704211yescharacteristic
615C2×C4#6704311yescharacteristic
616C8—24no—
617C8—42no—
618C8—442no—
619C8—442no—
620C22—22no—
621C22—22no—
622C22—22no—
623C22—41no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—222no—
628C22—222no—
629C22—222no—
630C22—222no—
631C22—222no—
632C22—222no—
633C22—441no—
634C22—441no—
635C22—441no—
636C22—441no—
637C22—441no—
638C22—441no—
639C22—441no—
640C22—441no—
641C22C4×#433911yescharacteristic
642C22C2×C22⋊C4×D1111yescharacteristic
643C22#1062305411yescharacteristic
644C22C2×M16×D1111yescharacteristic
645C22C2×M16×D1111yescharacteristic
646C22C2×#6696011yescharacteristic
647C22#1062327611yescharacteristic
648C4—22no—
649C4—22no—
650C4—22no—
651C4—22no—
652C4—41no—
653C4—114no—
654C4—222no—
655C4—222no—
656C4—222no—
657C4—441no—
658C4—441no—
659C4#1062308312yes—
660C4#1062308412yes—
661C2—42no—
662C2—442no—
663C2—442no—
664C2#1307145611yescharacteristic
665C2D11×#40711yescharacteristic
666C2#1307706611yescharacteristic
667C2#1307757811yescharacteristic
668C2#1307762711yescharacteristic
669C2#1307773511yescharacteristic
670C2#1307774311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1749C2
prime radicalC22×#4339C4
cosocleC22×C4×C11C24
hypercenter#1749D11
hypocenterC11#22532
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1749

Complements

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

NH ≅ G/Ntype
2. C2×#10622314C2semidirect
3. #13069414C2semidirect
4. #13069412C2semidirect
5. #13069408C2semidirect
6. #13068596C2semidirect
7. #13068595C2semidirect
8. #13068595C2semidirect
9. #13068377C2semidirect
10. #13068373C2semidirect
11. C11×#1749C2semidirect
177. C2×C8×C11#41semidirect
215. #1749D11semidirect
517. C2×C8#4339semidirect
540. C11#22532semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43392
C2×#106223142
#130694142
#130694122
#130694082
#130685962
#130685952
#130683772
#130683732
C11×#17492
#2253211