Finite Group Databasebeta

← #14802070

Subgroups — #14802070

Order 2816.

884 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622657C211yesmaximal, characteristic, complemented
2C2×#10622661C211yesmaximal, characteristic
3#13073108C211yesmaximal, characteristic
4#13070097C211yesmaximal, characteristic, complemented
5#13070034C211yesmaximal, characteristic, complemented
6#13070001C211yesmaximal, characteristic, complemented
7#13069931C211yesmaximal, characteristic, complemented
8#13069384C211yesmaximal, characteristic, complemented
9#13069236C211yesmaximal, characteristic, complemented
10#13068971C211yesmaximal, characteristic, complemented
11#13068933C211yesmaximal, characteristic
12#13068796C211yesmaximal, characteristic, complemented
13#13068631C211yesmaximal, characteristic, complemented
14C2×#10622167C211yesmaximal, characteristic, complemented
15C11×#2360C211yesmaximal, characteristic, complemented
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×#4325C2211yescharacteristic
20C2×#66983C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C23×C11⋊C8C2211yescharacteristic
23C11×#391C2211yescharacteristic
24C11×#389—21no—
25C11×#389C2211yescharacteristic
26C11×#387—21no—
27C11×#385—21no—
28C4×C11×C4⋊C4C2211yescharacteristic
29C4×C11×C22⋊C4—21no—
30C4×C11×C22⋊C4C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35#10622661—24no—
36#10622657—24no—
37C2×#66873C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43#10622571—21no—
44#10622571—21no—
45#10622552C2211yescharacteristic
46#10622552C2211yescharacteristic
47#10622549C2211yescharacteristic
48#10622549C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51#10622287—21no—
52#10622287—21no—
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11—21no—
65C23×Dic11—21no—
66C22×D44C2311yescharacteristic
67C11×C22⋊Q8—22no—
68C11×C22⋊Q8D414yes—
69C4×Q8×C11—22no—
70C4×Q8×C11—41no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—41no—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4D411yescharacteristic
82C2×C11×C22⋊C4D411yescharacteristic
83C2×C42×C11—21no—
84C2×C42×C11—21no—
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×#4325—22no—
88C2×#4325—22no—
89C2×#4325—41no—
90#66983—22no—
91#66983—22no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×C4⋊Dic11—22no—
98C2×C4⋊Dic11—22no—
99C2×C4⋊Dic11—21no—
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103C22×C11⋊C8—22no—
104C22×C11⋊C8—22no—
105C22×C11⋊C8—41no—
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C11×#95—21no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95—21no—
114C11×#95D411yescharacteristic
115C11×#95D411yescharacteristic
116#66899—22no—
117#66899—22no—
118#66899—22no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C22⋊(C11⋊C8)—22no—
124#66873—22no—
125#66873—22no—
126#66873—41no—
127#66872—22no—
128#66871—22no—
129#66871—22no—
130C4⋊(C11⋊C8)—22no—
131C4⋊(C11⋊C8)—41no—
132#25210—111nomaximal, Sylow
133C24×C11C2×D411yescharacteristic
134C23×D11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11C2×D412yes—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—42no—
150C22×C4×C11—42no—
151C22×C4×C11—81no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D412yes—
158C22×C4×C11#4112yes—
159C22×C4×C11C2411yescharacteristic
160C2×C22⋊D11—42no—
161C2×C22⋊D11—42no—
162C2×C22⋊D11—42no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—42no—
167C22×Dic11—81no—
168C22×Dic11—81no—
169C2×D44—21no—
170C2×D44—21no—
171C2×D44—21no—
172C2×D44—21no—
173C2×D44—21no—
174C2×D44—21no—
175C11×C4⋊C4—24no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—42no—
181C11×C4⋊C4—42no—
182C11×C4⋊C4—81no—
183C11×C4⋊C4C2×D412yes—
184C11×C4⋊C4#4112yes—
185C11×C22⋊C4—24no—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—22no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11—42no—
193C42×C11—81no—
194#4325—44no—
195(C2×D11)⋊C4—42no—
196(C2×D11)⋊C4—81no—
197(C2×D11)⋊C4—81no—
198(C2×D11)⋊C4—81no—
199(C2×D11)⋊C4—81no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—42no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—44no—
219C2×C11⋊C8#4112yes—
220C2×#484—111no—
221C2×#465—111no—
222#2504—111no—
223#2360D1111yescharacteristic, complemented
224#2085—111no—
225#2074—111no—
226#2067—111no—
227#2055—111no—
228#1949—111no—
229#1925—111no—
230#1880—111no—
231#1874—111no—
232#1850—111no—
233#1805—111no—
234C2×#340—111no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11#12112yes—
240C23×C11#13512yes—
241C23×C11#13712yes—
242C23×C11C22×D411yescharacteristic
243C22×D11—41no—
244C22×D11—41no—
245C22×D11—41no—
246C22×D11—41no—
247C22×D11—41no—
248C22×D11—41no—
249C22×D11—41no—
250Q8×C11—22no—
251Q8×C11—22no—
252Q8×C11—41no—
253Q8×C11—41no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—22no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—84no—
285C2×C4×C11#12112yes—
286C2×C4×C11C22×D411yescharacteristic
287C2×C4×C11C2×#4111yescharacteristic
288C2×C4×C11C2×#4111yescharacteristic
289C2×C4×C11C2×#4111yescharacteristic
290C2×C4×C11H(5,𝔽2)11yescharacteristic
291C2×C4×C112−1+411yescharacteristic
292C22⋊D11—84no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—84no—
303D44—41no—
304D44—41no—
305D44—41no—
306D44—41no—
307C11⋊C8—22no—
308C11⋊C8—41no—
309C11⋊C8—41no—
310C11⋊C8—41no—
311C22×SD16—111no—
312C23×C8—111no—
313C2×C22⋊Q8C2×D1111yescharacteristic
314C2×#121—111no—
315C2×C4×Q8C2×D1111yescharacteristic
316C22×C4⋊C4—111no—
317C22×C4⋊C4C2×D1111yescharacteristic
318#484—224no—
319#465—224no—
320C2×#107—111no—
321C2×#107—111no—
322C2×#106—111no—
323C2×C4⋊C8—111no—
324C2×C4⋊C8—111no—
325C2×#103—111no—
326C2×#103—111no—
327C2×#103—111no—
328C2×#102—111no—
329C2×#102—111no—
330C2×#102—111no—
331C2×C22⋊C8—111no—
332#397—221no—
333#397—221no—
334#391C2×D1111yescharacteristic
335#390—111no—
336#390—111no—
337#389—21no—
338#389C2×D1111yescharacteristic
339#387—21no—
340#386—221no—
341#386—221no—
342#385—21no—
343#382—111no—
344#382—111no—
345C4×C4⋊C4C2×D1111yescharacteristic
346C4×C22⋊C4—21no—
347C4×C22⋊C4C2×D1111yescharacteristic
348#340—111no—
349#340—111no—
350#340—111no—
351#340—111no—
352#340—111no—
353#340—111no—
354#336—111no—
355#336—111no—
356C22×C11—22no—
357C22×C11—22no—
358C22×C11—22no—
359C22×C11—22no—
360C22×C11—22no—
361C22×C11—22no—
362C22×C11#46414yes—
363C22×C11C2×#12111yescharacteristic
364C22×C11#54611yescharacteristic
365C22×C11#54711yescharacteristic
366C22×C11C2×#13511yescharacteristic
367C22×C11C2×#13711yescharacteristic
368C22×C11#57611yescharacteristic
369C22×C11#57711yescharacteristic
370C2×D11—81no—
371C2×D11—81no—
372C2×D11—81no—
373C2×D11—81no—
374C2×D11—81no—
375C2×D11—81no—
376C2×D11—81no—
377C4×C11—22no—
378C4×C11—41no—
379C4×C11—41no—
380C4×C11—42no—
381C4×C11—41no—
382C4×C11—42no—
383C4×C11—42no—
384C4×C11—41no—
385C4×C11—81no—
386C4×C11#52911yescharacteristic
387C4×C11#53911yescharacteristic
388C4×C11#54611yescharacteristic
389C4×C11#54711yescharacteristic
390Dic11—81no—
391Dic11—81no—
392Dic11—81no—
393C22×Q8C22×D1111yescharacteristic
394C22×D4—111no—
395C22×D4—221no—
396C23×C4—21no—
397C23×C4—221no—
398C23×C4C22×D1111yescharacteristic
399C2×SD16—222no—
400C2×SD16—222no—
401C2×SD16—441no—
402C22×C8—111no—
403C22×C8—111no—
404C22×C8—111no—
405C22×C8—111no—
406C22×C8—222no—
407C22×C8—222no—
408C22×C8—441no—
409C22⋊Q8—22no—
410C22⋊Q8D4414yes—
411#121—222no—
412#121—222no—
413C4×Q8—22no—
414C4×Q8—41no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—41no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—222no—
425C2×C4⋊C4—222no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4C22×D1111yescharacteristic
428C2×C4⋊C4C22×D1111yescharacteristic
429C2×C4⋊C4C22×D1111yescharacteristic
430C2×C22⋊C4—21no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4—221no—
433C2×C22⋊C4—221no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4—221no—
436C2×C22⋊C4C22⋊D1111yescharacteristic
437C2×C22⋊C4C22⋊D1111yescharacteristic
438C2×C42—21no—
439C2×C42—21no—
440C2×C42C22×D1111yescharacteristic
441C2×C42C22×D1111yescharacteristic
442#107—222no—
443#107—222no—
444#106—222no—
445C4⋊C8—222no—
446C4⋊C8—441no—
447#103—222no—
448#103—222no—
449#103—222no—
450#102—222no—
451#102—222no—
452#102—441no—
453C22⋊C8—222no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95—221no—
459#95—221no—
460#95—221no—
461#95—221no—
462#95C22⋊D1111yescharacteristic
463#95C22⋊D1111yescharacteristic
464C2×C11—24no—
465C2×C11#242511yescharacteristic
466C2×C11C2×#46411yescharacteristic
467C2×C11#304511yescharacteristic
468C2×C11#329711yescharacteristic
469C2×C11#332011yescharacteristic
470C2×C11#333711yescharacteristic
471C2×C11#334611yescharacteristic
472D11—161no—
473C24—221no—
474C24C2×C22⋊D1111yescharacteristic
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8C2×D4412yes—
481C2×D4—221no—
482C2×D4—221no—
483C2×D4—221no—
484C2×D4—221no—
485C2×D4—221no—
486C2×D4—221no—
487C2×D4—442no—
488C2×D4—442no—
489C2×D4—442no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—81no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—442no—
505C22×C4—881no—
506C22×C4—881no—
507C22×C4C2×D4412yes—
508C22×C4#433912yes—
509C22×C4C2×C22⋊D1111yescharacteristic
510C22×C4C2×C22⋊D1111yescharacteristic
511C22×C4C2×C22⋊D1111yescharacteristic
512C22×C4C2×C22⋊D1111yescharacteristic
513C22×C4C2×C22⋊D1111yescharacteristic
514C22×C4C23×D1111yescharacteristic
515SD16—444no—
516C2×C8—112no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C2×C8—221no—
523C2×C8—221no—
524C2×C8—221no—
525C2×C8—221no—
526C2×C8—221no—
527C2×C8—221no—
528C2×C8—444no—
529C4⋊C4—24no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—42no—
535C4⋊C4—42no—
536C4⋊C4—81no—
537C4⋊C4—221no—
538C4⋊C4—221no—
539C4⋊C4—221no—
540C4⋊C4—221no—
541C4⋊C4—221no—
542C4⋊C4—221no—
543C4⋊C4—442no—
544C4⋊C4C2×D4412yes—
545C4⋊C4#434112yes—
546C22⋊C4—24no—
547C22⋊C4—22no—
548C22⋊C4—22no—
549C22⋊C4—442no—
550C22⋊C4—881no—
551C22⋊C4—881no—
552C22⋊C4—881no—
553C22⋊C4—881no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—21no—
558C42—42no—
559C42—81no—
560C11#2521011yescharacteristic, complemented, Sylow
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—441no—
566C23—441no—
567C23—441no—
568C23—441no—
569C23—441no—
570C23—441no—
571C23—441no—
572C23#6698312yes—
573C23#6699512yes—
574C23#6700312yes—
575C23C22×C22⋊D1111yescharacteristic
576Q8—22no—
577Q8—22no—
578Q8—41no—
579Q8—41no—
580D4—441no—
581D4—441no—
582D4—441no—
583D4—441no—
584D4—884no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—84no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4—441no—
624C2×C4—441no—
625C2×C4—884no—
626C2×C4#6698312yes—
627C2×C4C22×D4411yescharacteristic
628C2×C4C2×#433911yescharacteristic
629C2×C4C2×#434111yescharacteristic
630C2×C4#6703711yescharacteristic
631C2×C4#41×D1111yescharacteristic
632C2×C4#6704311yescharacteristic
633C8—222no—
634C8—441no—
635C8—441no—
636C8—441no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—881no—
644C22—881no—
645C22—881no—
646C22—881no—
647C22—881no—
648C22—881no—
649C22—881no—
650C22#1062264114yes—
651C22C2×#6698311yescharacteristic
652C22#1062333711yescharacteristic
653C22C2×#6699511yescharacteristic
654C22C2×#6700311yescharacteristic
655C22#1062335511yescharacteristic
656C22#1062336611yescharacteristic
657C22#1062336811yescharacteristic
658C4—22no—
659C4—41no—
660C4—42no—
661C4—42no—
662C4—41no—
663C4—42no—
664C4—41no—
665C4—41no—
666C4—81no—
667C4—881no—
668C4—881no—
669C4—881no—
670C4#1062306911yescharacteristic
671C4#1062308511yescharacteristic
672C4#1062308611yescharacteristic
673C4#1062309511yescharacteristic
674C2—24no—
675C2—1761no—
676C2#1307216111yescharacteristic
677C2C2×#1062264111yescharacteristic
678C2#1307815511yescharacteristic
679C2#1308046611yescharacteristic
680C2#1308078711yescharacteristic
681C2#1308099511yescharacteristic
682C2#1308109511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2360C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenter#2360D11
hypocenterC11#25210
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2360

Complements

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

NH ≅ G/Ntype
1. C2×#10622657C2semidirect
4. #13070097C2semidirect
5. #13070034C2semidirect
6. #13070001C2semidirect
7. #13069931C2semidirect
8. #13069384C2semidirect
9. #13069236C2semidirect
10. #13068971C2semidirect
12. #13068796C2semidirect
13. #13068631C2semidirect
14. C2×#10622167C2semidirect
15. C11×#2360C2semidirect
223. #2360D11semidirect
560. C11#25210semidirect

Maximal subgroups

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

subgroupindex
C2×#106226572
C2×#106226612
#130731082
#130700972
#130700342
#130700012
#130699312
#130693842
#130692362
#130689712
#130689332
#130687962
#130686312
C2×#106221672
C11×#23602
#2521011