Finite Group Databasebeta

← #14802069

Subgroups — #14802069

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×#10622497C211yesmaximal, characteristic, complemented
2C2×#10622477C211yesmaximal, characteristic
3#13073105C211yesmaximal, characteristic
4#13071620C211yesmaximal, characteristic, complemented
5#13070038C211yesmaximal, characteristic, complemented
6#13070001C211yesmaximal, characteristic, complemented
7#13069935C211yesmaximal, characteristic, complemented
8#13069385C211yesmaximal, characteristic, complemented
9#13069235C211yesmaximal, characteristic, complemented
10#13068970C211yesmaximal, characteristic, complemented
11#13068932C211yesmaximal, characteristic
12#13068795C211yesmaximal, characteristic, complemented
13#13068628C211yesmaximal, characteristic, complemented
14D11×#340C211yesmaximal, characteristic, complemented
15C11×#2085C211yesmaximal, characteristic, complemented
16C22×#4314C2211yescharacteristic
17C22×C8×D11C2211yescharacteristic
18C2×#66950C2211yescharacteristic
19C2×#66948C2211yescharacteristic
20C2×C4⋊C4×D11C2211yescharacteristic
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C11×#389C2211yescharacteristic
26C11×#382C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×(C2×D11)⋊C8C2211yescharacteristic
29C2×#66880C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31#10622602—21no—
32#10622601C2211yescharacteristic
33#10622590C2211yescharacteristic
34C4⋊C4×Dic11C2211yescharacteristic
35#10622587C2211yescharacteristic
36#10622586—21no—
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42#10622552C2211yescharacteristic
43C4×(C2×D11)⋊C4C2211yescharacteristic
44C2×C4⋊(C11⋊C8)C2211yescharacteristic
45#10622497—24no—
46#10622477—24no—
47#10622288—21no—
48#10622288—21no—
49#10622279—21no—
50#10622278—21no—
51#10622278—21no—
52#10622267—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#336C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×D44—21no—
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×C4×D11—21no—
65C22×C4×D11C2311yescharacteristic
66C22×Dic22C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4D411yescharacteristic
82C2×(C2×D11)⋊C4D411yescharacteristic
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C2×#4314—22no—
95C2×#4314—22no—
96C2×#4314—41no—
97C2×C8×D11—22no—
98C2×C8×D11—22no—
99C2×C8×D11—41no—
100#66950—22no—
101#66950D414yes—
102#66948—22no—
103#66948—22no—
104C4⋊C4×D11—22no—
105C4⋊C4×D11—22no—
106C4⋊C4×D11—22no—
107C4⋊C4×D11—41no—
108C4×Dic22—22no—
109C4×Dic22—41no—
110C11×#107—22no—
111C11×#106—22no—
112C11×#95—21no—
113C11×#95—21no—
114C11×#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95D411yescharacteristic
121C11⋊#95D411yescharacteristic
122#66885—22no—
123(C2×D11)⋊C8—22no—
124#66880—22no—
125Dic11⋊C8—22no—
126#66874—22no—
127#66874—22no—
128#66873—22no—
129#66873—41no—
130#66871—22no—
131C4⋊(C11⋊C8)—41no—
132#25210—111nomaximal, Sylow
133C23×D11—21no—
134C23×D11C2×D411yescharacteristic
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2411yescharacteristic
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11C2×D411yescharacteristic
146C22×Dic11C2×D411yescharacteristic
147C22×Dic11C2×D411yescharacteristic
148C2×D44—21no—
149C2×D44—21no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—42no—
155C2×D44—42no—
156C2×D44—42no—
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—42no—
162C2×C4×D11—42no—
163C2×C4×D11—42no—
164C2×C4×D11—81no—
165C2×C4×D11—81no—
166C2×C4×D11—81no—
167C2×C4×D11C2×D412yes—
168C2×C4×D11#4112yes—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×Dic22—21no—
173C2×Dic22—21no—
174C2×Dic22C2×D412yes—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11#4112yes—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—81no—
189C11×C4⋊C4C2×D412yes—
190C42×C11—21no—
191C42×C11—21no—
192(C2×D11)⋊C4—24no—
193(C2×D11)⋊C4—22no—
194(C2×D11)⋊C4—22no—
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—24no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11#4112yes—
205Dic11⋊C4—42no—
206Dic11⋊C4—42no—
207Dic11⋊C4—42no—
208C4×Dic11—21no—
209C4×Dic11—21no—
210C4×Dic11—42no—
211C4×Dic11—81no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218#4314—44no—
219C8×D11—44no—
220C2×#484—111no—
221C2×#465—111no—
222#2504—111no—
223#2360—111no—
224#2085D1111yescharacteristic, complemented
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×C11C22×D411yescharacteristic
236C22×D11—21no—
237C22×D11—21no—
238C22×D11—21no—
239C22×D11—21no—
240C22×D11—41no—
241C22×D11—41no—
242C22×D11—41no—
243C22×D11—41no—
244C22×D11—41no—
245C22×D11—41no—
246C22×D11—41no—
247C22×D11#12112yes—
248C22×D11#13512yes—
249C22×D11#13712yes—
250C2×C4×C11—22no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11H(5,𝔽2)11yescharacteristic
273C2×C4×C112−1+411yescharacteristic
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11#12112yes—
292D44—41no—
293D44—41no—
294D44—41no—
295D44—41no—
296D44—84no—
297C4×D11—22no—
298C4×D11—22no—
299C4×D11—22no—
300C4×D11—22no—
301C4×D11—84no—
302C4×D11—84no—
303Dic22—22no—
304Dic22—22no—
305Dic22—41no—
306Dic22—41no—
307C8×C11—22no—
308C8×C11—41no—
309C11⋊C8—41no—
310C11⋊C8—41no—
311C22×SD16—111no—
312C23×C8—111no—
313C2×C22⋊Q8—111no—
314C2×#121—111no—
315C2×C4×Q8—111no—
316C22×C4⋊C4—111no—
317C22×C4⋊C4—111no—
318#484—224no—
319#465—224no—
320C2×#107—111no—
321C2×#107C2×D1111yescharacteristic
322C2×#106C2×D1111yescharacteristic
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#391—111no—
335#390—111no—
336#390—111no—
337#389—221no—
338#389C2×D1111yescharacteristic
339#387—221no—
340#386—221no—
341#386—221no—
342#385—221no—
343#382—111no—
344#382C2×D1111yescharacteristic
345C4×C4⋊C4—111no—
346C4×C22⋊C4—111no—
347C4×C22⋊C4—221no—
348#340—111no—
349#340—111no—
350#340—111no—
351#340—111no—
352#340C2×D1111yescharacteristic
353#340C2×D1111yescharacteristic
354#336—111no—
355#336C2×D1111yescharacteristic
356C22×C11C2×#12111yescharacteristic
357C22×C11#54611yescharacteristic
358C22×C11#54711yescharacteristic
359C22×C11C2×#13511yescharacteristic
360C22×C11C2×#13711yescharacteristic
361C22×C11#57611yescharacteristic
362C22×C11#57711yescharacteristic
363C2×D11—22no—
364C2×D11—22no—
365C2×D11—22no—
366C2×D11—22no—
367C2×D11—22no—
368C2×D11—22no—
369C2×D11—81no—
370C2×D11—81no—
371C2×D11—81no—
372C2×D11—81no—
373C2×D11—81no—
374C2×D11—81no—
375C2×D11—81no—
376C2×D11#46414yes—
377C4×C11—41no—
378C4×C11—42no—
379C4×C11—41no—
380C4×C11—81no—
381C4×C11—81no—
382C4×C11—81no—
383C4×C11#52911yescharacteristic
384C4×C11#53911yescharacteristic
385C4×C11#54611yescharacteristic
386C4×C11#54711yescharacteristic
387Dic11—22no—
388Dic11—41no—
389Dic11—41no—
390Dic11—42no—
391Dic11—42no—
392Dic11—81no—
393C22×Q8—111no—
394C22×D4—111no—
395C22×D4—221no—
396C23×C4—111no—
397C23×C4—221no—
398C23×C4—221no—
399C2×SD16—222no—
400C2×SD16—222no—
401C2×SD16—441no—
402C22×C8—111no—
403C22×C8—111no—
404C22×C8—222no—
405C22×C8—222no—
406C22×C8—441no—
407C22×C8C22×D1111yescharacteristic
408C22×C8C22×D1111yescharacteristic
409C22⋊Q8—114no—
410C22⋊Q8—222no—
411#121—222no—
412#121—222no—
413C4×Q8—222no—
414C4×Q8—441no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—222no—
419C2×C4⋊C4—222no—
420C2×C4⋊C4—222no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4—441no—
426C2×C4⋊C4C22×D1111yescharacteristic
427C2×C4⋊C4C22×D1111yescharacteristic
428C2×C4⋊C4C22×D1111yescharacteristic
429C2×C4⋊C4C22×D1111yescharacteristic
430C2×C22⋊C4—111no—
431C2×C22⋊C4—111no—
432C2×C22⋊C4—221no—
433C2×C22⋊C4—221no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4—221no—
436C2×C22⋊C4—221no—
437C2×C22⋊C4—221no—
438C2×C42—111no—
439C2×C42—221no—
440C2×C42—221no—
441C2×C42C22×D1111yescharacteristic
442#107—22no—
443#107—222no—
444#106—22no—
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—111no—
458#95—111no—
459#95—221no—
460#95—221no—
461#95—221no—
462#95—221no—
463#95—221no—
464C2×C11#242511yescharacteristic
465C2×C11C2×#46411yescharacteristic
466C2×C11#304511yescharacteristic
467C2×C11#329711yescharacteristic
468C2×C11#332011yescharacteristic
469C2×C11#333711yescharacteristic
470C2×C11#334611yescharacteristic
471D11—24no—
472D11—161no—
473C24—111no—
474C24—221no—
475C2×Q8—112no—
476C2×Q8—221no—
477C2×Q8—221no—
478C2×Q8—221no—
479C2×Q8—221no—
480C2×Q8—221no—
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—111no—
495C22×C4—112no—
496C22×C4—112no—
497C22×C4—111no—
498C22×C4—111no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4—221no—
506C22×C4—442no—
507C22×C4—442no—
508C22×C4—442no—
509C22×C4—881no—
510C22×C4—881no—
511C22×C4—881no—
512C22×C4D4×D1111yescharacteristic
513C22×C4D4×D1111yescharacteristic
514C22×C4C23×D1111yescharacteristic
515SD16—444no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—221no—
522C2×C8—221no—
523C2×C8—221no—
524C2×C8—221no—
525C2×C8—221no—
526C2×C8—221no—
527C2×C8—444no—
528C2×C8#434312yes—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—81no—
537C4⋊C4—112no—
538C4⋊C4—224no—
539C4⋊C4—221no—
540C4⋊C4—221no—
541C4⋊C4—221no—
542C4⋊C4—442no—
543C4⋊C4—442no—
544C4⋊C4—442no—
545C4⋊C4D4×D1112yes—
546C22⋊C4—222no—
547C22⋊C4—222no—
548C22⋊C4—224no—
549C22⋊C4—442no—
550C22⋊C4—881no—
551C22⋊C4—881no—
552C22⋊C4—881no—
553C22⋊C4—881no—
554C42—21no—
555C42—21no—
556C42—221no—
557C42—221no—
558C42—442no—
559C42—881no—
560C11#2521011yescharacteristic, complemented, Sylow
561C23—112no—
562C23—112no—
563C23—112no—
564C23—221no—
565C23—221no—
566C23—221no—
567C23—221no—
568C23—441no—
569C23—441no—
570C23—441no—
571C23—441no—
572C23—441no—
573C23—441no—
574C23—441no—
575C23C2×D4×D1111yescharacteristic
576Q8—222no—
577Q8—222no—
578Q8—441no—
579Q8—441no—
580D4—441no—
581D4—441no—
582D4—441no—
583D4—441no—
584D4—884no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—22no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—112no—
604C2×C4—221no—
605C2×C4—221no—
606C2×C4—222no—
607C2×C4—222no—
608C2×C4—222no—
609C2×C4—222no—
610C2×C4—221no—
611C2×C4—221no—
612C2×C4—221no—
613C2×C4—221no—
614C2×C4—221no—
615C2×C4—221no—
616C2×C4—222no—
617C2×C4—222no—
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—884no—
627C2×C4C2×D4×D1111yescharacteristic
628C2×C4C2×#434311yescharacteristic
629C2×C4#6704011yescharacteristic
630C2×C4#41×D1111yescharacteristic
631C2×C4#41×D1111yescharacteristic
632C2×C4#6704211yescharacteristic
633C8—22no—
634C8—41no—
635C8—441no—
636C8—441no—
637C22—114no—
638C22—222no—
639C22—222no—
640C22—222no—
641C22—222no—
642C22—222no—
643C22—222no—
644C22—881no—
645C22—881no—
646C22—881no—
647C22—881no—
648C22—881no—
649C22—881no—
650C22—881no—
651C22D11×#12111yescharacteristic
652C22#1062318511yescharacteristic
653C22#1062325711yescharacteristic
654C22D11×#13511yescharacteristic
655C22#1062330111yescharacteristic
656C22#1062330511yescharacteristic
657C22D11×#13711yescharacteristic
658C4—42no—
659C4—41no—
660C4—41no—
661C4—81no—
662C4—81no—
663C4—81no—
664C4—222no—
665C4—441no—
666C4—442no—
667C4—442no—
668C4—441no—
669C4—881no—
670C4#1062316111yescharacteristic
671C4#1062316211yescharacteristic
672C4#1062322211yescharacteristic
673C4#1062322311yescharacteristic
674C2—224no—
675C2—1761no—
676C2#1307216011yescharacteristic
677C2D11×#46411yescharacteristic
678C2#1307815611yescharacteristic
679C2#1308046911yescharacteristic
680C2#1308079011yescharacteristic
681C2#1308099411yescharacteristic
682C2#1308110011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2085C2
socleC23×C11C22×D4
prime radicalC2×#66948C22
hypercenter#2085D11
hypocenterC11#25210
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2085

Complements

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

NH ≅ G/Ntype
1. C2×#10622497C2semidirect
4. #13071620C2semidirect
5. #13070038C2semidirect
6. #13070001C2semidirect
7. #13069935C2semidirect
8. #13069385C2semidirect
9. #13069235C2semidirect
10. #13068970C2semidirect
12. #13068795C2semidirect
13. #13068628C2semidirect
14. D11×#340C2semidirect
15. C11×#2085C2semidirect
224. #2085D11semidirect
560. C11#25210semidirect

Maximal subgroups

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

subgroupindex
C2×#106224972
C2×#106224772
#130731052
#130716202
#130700382
#130700012
#130699352
#130693852
#130692352
#130689702
#130689322
#130687952
#130686282
D11×#3402
C11×#20852
#2521011