Finite Group Databasebeta

← #14816759

Subgroups — #14816759

Order 2816.

896 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×#10622460C211yesmaximal, characteristic, complemented
2C2×C4×D88C211yesmaximal, characteristic
3#13072488C211yesmaximal, characteristic, complemented
4#13071527C211yesmaximal, characteristic, complemented
5#13070136C211yesmaximal, characteristic, complemented
6#13070099C211yesmaximal, characteristic, complemented
7#13070003C211yesmaximal, characteristic, complemented
8#13069955C211yesmaximal, characteristic, complemented
9#13069349C211yesmaximal, characteristic, complemented
10#13068963C211yesmaximal, characteristic
11#13068963C211yesmaximal, characteristic
12#13068880C211yesmaximal, characteristic, complemented
13#13068880C211yesmaximal, characteristic, complemented
14#13068866C211yesmaximal, characteristic, complemented
15C11×#1916C211yesmaximal, characteristic, complemented
16C22×D88C2211yescharacteristic
17C2×C4×D44C2211yescharacteristic
18C2×C4×D44C2211yescharacteristic
19C2×C4×D44C2211yescharacteristic
20C2×C4×D44C2211yescharacteristic
21C2×#66923C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25C2×#66885C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66882C2211yescharacteristic
34C2×#66881C2211yescharacteristic
35C2×#66881C2211yescharacteristic
36#10622605—21no—
37#10622602—21no—
38#10622602—21no—
39#10622602—21no—
40#10622552C2211yescharacteristic
41#10622552C2211yescharacteristic
42#10622549C2211yescharacteristic
43#10622541C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622541C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622460—24no—
48C4×D88—24no—
49#10622289—21no—
50#10622280—21no—
51#10622280—21no—
52D11×#95—21no—
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55C11×#336C2211yescharacteristic
56C11×#336C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61C22×D44C2311yescharacteristic
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×C4×D11—21no—
65C22×C4×D11—21no—
66C22×C4×D11—21no—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
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)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×D88—22no—
97C2×D88—22no—
98C2×D88Q814yes—
99C4×D44—22no—
100C4×D44—22no—
101C4×D44—22no—
102C4×D44—22no—
103C4×D44—22no—
104C4×D44—41no—
105C4×D44—41no—
106C4×D44—41no—
107#66923—22no—
108#66923—41no—
109C11×C4⋊C8—22no—
110C4×C8×C11—22no—
111C11×#95D411yescharacteristic
112C11×#95D411yescharacteristic
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119#66885—22no—
120#66885—22no—
121#66885—22no—
122#66885—22no—
123#66885—41no—
124#66885D414yes—
125#66882—22no—
126#66882—22no—
127#66882—22no—
128#66881—22no—
129#66881—41no—
130#26370—111nomaximal, Sylow
131C23×D11—21no—
132C23×D11—21no—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44C2×D412yes—
155C2×D44C2×Q812yes—
156C2×D44C2×Q812yes—
157C2×D44#4112yes—
158C2×C4×D11—24no—
159C2×C4×D11—42no—
160C2×C4×D11—42no—
161C2×C4×D11—42no—
162C2×C4×D11—42no—
163C2×C4×D11—42no—
164C2×C4×D11—42no—
165C2×C4×D11—81no—
166C2×C4×D11—81no—
167C2×C4×D11—81no—
168C2×C4×D11—81no—
169C2×C4×D11—81no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11C2×D412yes—
181C2×C8×C11C2×Q812yes—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—41no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—21no—
190(C2×D11)⋊C4—24no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—42no—
194(C2×D11)⋊C4—42no—
195(C2×D11)⋊C4—81no—
196(C2×D11)⋊C4—81no—
197(C2×D11)⋊C4—81no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11C2×D412yes—
209C4⋊Dic11#4112yes—
210Dic11⋊C4—42no—
211Dic11⋊C4—42no—
212Dic11⋊C4—81no—
213Dic11⋊C4—81no—
214Dic11⋊C4—81no—
215Dic11⋊C4—81no—
216D88—28no—
217C2×#478—111no—
218C2×C4×D8—111no—
219#2454—111no—
220#2349—111no—
221#2092—111no—
222#2085—111no—
223#2067—111no—
224#2059—111no—
225#1942—111no—
226#1916D1111yescharacteristic, complemented
227#1879—111no—
228#1879—111no—
229#1864—111no—
230#1864—111no—
231#1862—111no—
232C23×C11C22×D411yescharacteristic
233C22×D11—22no—
234C22×D11—22no—
235C22×D11—22no—
236C22×D11—22no—
237C22×D11—41no—
238C22×D11—41no—
239C22×D11—41no—
240C22×D11—41no—
241C22×D11—41no—
242C22×D11—41no—
243C22×D11—41no—
244C22×D11—41no—
245C22×D11—41no—
246C22×D11—41no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
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—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11#13512yes—
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11C22×Q811yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11H(5,𝔽2)11yescharacteristic
270C2×C4×C112−1+411yescharacteristic
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289D44—22no—
290D44—22no—
291D44—22no—
292D44—22no—
293D44—22no—
294D44—41no—
295D44—41no—
296D44C22⋊Q814yes—
297C4×D11—84no—
298C4×D11—84no—
299C4×D11—84no—
300C4×D11—84no—
301C8×C11—22no—
302C8×C11—22no—
303C8×C11—41no—
304C8×C11—41no—
305C22×D8—111no—
306C2×#125—111no—
307C2×C4×D4—111no—
308C2×C4×D4—111no—
309C2×C4×D4—111no—
310C2×C4×D4—111no—
311#478—224no—
312C4×D8—224no—
313C2×#107—111no—
314C2×#107—111no—
315C2×#107—111no—
316C2×#106—111no—
317C2×#106—111no—
318C2×C4⋊C8C2×D1111yescharacteristic
319C2×#102—111no—
320C2×#102—111no—
321C2×#102—111no—
322C2×#102—111no—
323C2×#102—111no—
324C2×#102—111no—
325C2×C4×C8C2×D1111yescharacteristic
326#399—221no—
327#396—221no—
328#390—111no—
329#390—111no—
330#389—111no—
331#389—111no—
332#389—111no—
333#389—111no—
334#385—221no—
335#385—221no—
336#385—221no—
337#382—111no—
338#380—221no—
339#380—221no—
340C4×C4⋊C4C2×D1111yescharacteristic
341C2×#95—221no—
342#340—111no—
343#340—111no—
344#340—111no—
345#340—111no—
346#336C2×D1111yescharacteristic
347#336C2×D1111yescharacteristic
348#336C2×D1111yescharacteristic
349#336C2×D1111yescharacteristic
350C22×C11#52511yescharacteristic
351C22×C11D4211yescharacteristic
352C22×C11D4×Q811yescharacteristic
353C22×C11C2×#13511yescharacteristic
354C22×C11#57511yescharacteristic
355C22×C11#57611yescharacteristic
356C22×C11#57611yescharacteristic
357C2×D11—24no—
358C2×D11—42no—
359C2×D11—42no—
360C2×D11—42no—
361C2×D11—42no—
362C2×D11—42no—
363C2×D11—42no—
364C2×D11—42no—
365C2×D11—42no—
366C2×D11—42no—
367C2×D11—81no—
368C2×D11—81no—
369C2×D11—81no—
370C2×D11—81no—
371C4×C11—22no—
372C4×C11—41no—
373C4×C11—41no—
374C4×C11—41no—
375C4×C11—41no—
376C4×C11—41no—
377C4×C11C2×C22⋊Q811yescharacteristic
378C4×C11#53911yescharacteristic
379C4×C11#54711yescharacteristic
380C4×C11#55411yescharacteristic
381Dic11—42no—
382Dic11—42no—
383Dic11—81no—
384Dic11—81no—
385Dic11—81no—
386Dic11—81no—
387C22×D4—111no—
388C22×D4—111no—
389C23×C4—221no—
390C23×C4—221no—
391C23×C4—221no—
392C23×C4—221no—
393C2×D8—114no—
394C2×D8—222no—
395C2×D8—222no—
396C22×C8C22×D1111yescharacteristic
397C22×C8C22×D1111yescharacteristic
398C22×C8C22×D1111yescharacteristic
399C22×C8C22×D1111yescharacteristic
400#125—222no—
401#125—441no—
402C4×D4—222no—
403C4×D4—222no—
404C4×D4—222no—
405C4×D4—222no—
406C4×D4—222no—
407C4×D4—441no—
408C4×D4—441no—
409C4×D4—441no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4D4411yescharacteristic
423C2×C4⋊C4D4411yescharacteristic
424C2×C22⋊C4—221no—
425C2×C22⋊C4—221no—
426C2×C22⋊C4—221no—
427C2×C22⋊C4—221no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C22⋊C4—221no—
432C2×C42C22×D1111yescharacteristic
433C2×C42C22×D1111yescharacteristic
434C2×C42C22×D1111yescharacteristic
435#107—222no—
436#107—222no—
437#107—222no—
438#106—222no—
439#106—441no—
440C4⋊C8—22no—
441#102—114no—
442#102—222no—
443#102—222no—
444#102—222no—
445#102—222no—
446#102—441no—
447C4×C8—22no—
448#95—221no—
449#95—221no—
450#95—221no—
451#95—221no—
452#95—221no—
453#95—221no—
454#95D4411yescharacteristic
455#95D4411yescharacteristic
456C2×C11#244911yescharacteristic
457C2×C11#310211yescharacteristic
458C2×C11#312211yescharacteristic
459C2×C11#326811yescharacteristic
460C2×C11#328011yescharacteristic
461C2×C11#338011yescharacteristic
462C2×C11#338911yescharacteristic
463D11—44no—
464D11—82no—
465C24—221no—
466C24—221no—
467C2×D4—112no—
468C2×D4—112no—
469C2×D4—112no—
470C2×D4—112no—
471C2×D4—221no—
472C2×D4—221no—
473C2×D4—221no—
474C2×D4—221no—
475C2×D4—221no—
476C2×D4—221no—
477C2×D4—221no—
478C2×D4—221no—
479C22×C4—224no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4—442no—
487C22×C4—442no—
488C22×C4—442no—
489C22×C4—442no—
490C22×C4—442no—
491C22×C4—442no—
492C22×C4—881no—
493C22×C4—881no—
494C22×C4—881no—
495C22×C4—881no—
496C22×C4—881no—
497C22×C4C2×D4411yescharacteristic
498C22×C4C2×D4411yescharacteristic
499C22×C4C2×D4411yescharacteristic
500C22×C4C2×D4411yescharacteristic
501C22×C4C2×D4411yescharacteristic
502C22×C4C2×D4411yescharacteristic
503C22×C4C23×D1111yescharacteristic
504D8—228no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8D4×D1112yes—
516C2×C8Q8×D1112yes—
517C4⋊C4—22no—
518C4⋊C4—41no—
519C4⋊C4—112no—
520C4⋊C4—112no—
521C4⋊C4—221no—
522C4⋊C4—221no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—442no—
532C4⋊C4—442no—
533C4⋊C4—881no—
534C4⋊C4—881no—
535C4⋊C4—881no—
536C4⋊C4—881no—
537C22⋊C4—224no—
538C22⋊C4—442no—
539C22⋊C4—442no—
540C22⋊C4—442no—
541C22⋊C4—442no—
542C22⋊C4—881no—
543C22⋊C4—881no—
544C22⋊C4—881no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—21no—
551C11#2637011yescharacteristic, complemented, Sylow
552C23—222no—
553C23—222no—
554C23—222no—
555C23—222no—
556C23—441no—
557C23—441no—
558C23—441no—
559C23—441no—
560C23—441no—
561C23—441no—
562C23—441no—
563C23—441no—
564C23—441no—
565C23—441no—
566C23C22×D4411yescharacteristic
567D4—114no—
568D4—222no—
569D4—222no—
570D4—222no—
571D4—222no—
572D4—222no—
573D4—441no—
574D4—441no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—222no—
593C2×C4—222no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—884no—
611C2×C4—884no—
612C2×C4—884no—
613C2×C4—884no—
614C2×C4#6695712yes—
615C2×C4C2×D4×D1111yescharacteristic
616C2×C4C2×Q8×D1111yescharacteristic
617C2×C4#41×D1111yescharacteristic
618C2×C4#41×D1111yescharacteristic
619C2×C4#6704211yescharacteristic
620C2×C4#6704311yescharacteristic
621C8—22no—
622C8—22no—
623C8—41no—
624C8—41no—
625C22—224no—
626C22—442no—
627C22—442no—
628C22—442no—
629C22—442no—
630C22—442no—
631C22—442no—
632C22—442no—
633C22—442no—
634C22—442no—
635C22—881no—
636C22—881no—
637C22—881no—
638C22—881no—
639C22#1062305511yescharacteristic
640C22D4×D4411yescharacteristic
641C22Q8×D4411yescharacteristic
642C22C2×#6695711yescharacteristic
643C22#1062327911yescharacteristic
644C22#1062328311yescharacteristic
645C22#1062328311yescharacteristic
646C4—22no—
647C4—41no—
648C4—41no—
649C4—41no—
650C4—41no—
651C4—41no—
652C4—442no—
653C4—442no—
654C4—881no—
655C4—881no—
656C4—881no—
657C4—881no—
658C4D11×C22⋊Q811yescharacteristic
659C4#1062318611yescharacteristic
660C4#1062322111yescharacteristic
661C4#1062323811yescharacteristic
662C2—444no—
663C2—882no—
664C2#1307243011yescharacteristic
665C2#1307863611yescharacteristic
666C2#1307886011yescharacteristic
667C2#1308016111yescharacteristic
668C2#1308030311yescharacteristic
669C2#1308148411yescharacteristic
670C2#1308157611yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1916C2
socleC23×C11C22×D4
prime radicalC22×D88C22
hypercenter#1916D11
hypocenterC11#26370
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1916

Complements

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

NH ≅ G/Ntype
1. C2×#10622460C2semidirect
3. #13072488C2semidirect
4. #13071527C2semidirect
5. #13070136C2semidirect
6. #13070099C2semidirect
7. #13070003C2semidirect
8. #13069955C2semidirect
9. #13069349C2semidirect
12. #13068880C2semidirect
13. #13068880C2semidirect
14. #13068866C2semidirect
15. C11×#1916C2semidirect
226. #1916D11semidirect
551. C11#26370semidirect

Maximal subgroups

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

subgroupindex
C2×#106224602
C2×C4×D882
#130724882
#130715272
#130701362
#130700992
#130700032
#130699552
#130693492
#130689632
#130688802
#130688662
C11×#19162
#2637011