Finite Group Databasebeta

← #36478113

Subgroups — #36478113

Order 22784.

1386 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19151494C211yesmaximal, characteristic
2C2×C4⋊C4×Dic89C211yesmaximal, characteristic
3C2×C4×#13083553C211yesmaximal, characteristic
4#26018518C212yesmaximal
5#26018507C212yesmaximal
6#26018487C212yesmaximal
7#26018483C212yesmaximal
8#26018482C211yesmaximal, characteristic
9#26018481C211yesmaximal, characteristic
10#26018481C211yesmaximal, characteristic
11C89×C4⋊#95C211yesmaximal, characteristic
12C22×C4⋊Dic89C2211yescharacteristic
13C22×C4⋊Dic89C2211yescharacteristic
14C22×#13083553C2211yescharacteristic
15C22×#13083553C2211yescharacteristic
16C22×#13083553C2212yes—
17C22×C4×Dic89C2211yescharacteristic
18C22×C4×Dic89C2211yescharacteristic
19C22×C4×Dic89C2212yes—
20#19151494C418yescomplemented
21C4⋊C4×Dic89—24no—
22C4×#13083553—24no—
23C2×#15667919C2212yes—
24C2×#15667919C2212yes—
25C2×#15667919C2212yes—
26C2×#15667919C2211yescharacteristic
27C2×#15667919C2211yescharacteristic
28C2×#15667919C2212yes—
29C2×#15667919C2212yes—
30C2×#15667919C2212yes—
31C2×#15667919C2212yes—
32C2×#15667919C2212yes—
33C22×C4⋊C4×C89C2211yescharacteristic
34C22×C4⋊C4×C89C2211yescharacteristic
35C22×C42×C89C2211yescharacteristic
36C2×#95×C89C2212yes—
37C2×#95×C89C2212yes—
38C23×Dic89C2312yes—
39C23×Dic89C2311yescharacteristic
40C23×Dic89C2311yescharacteristic
41C23×Dic89C2312yes—
42C23×Dic89C2311yescharacteristic
43C23×Dic89C2311yescharacteristic
44C2×C4⋊Dic89—22no—
45C2×C4⋊Dic89—22no—
46C2×C4⋊Dic89—22no—
47C2×C4⋊Dic89—22no—
48C2×C4⋊Dic89C2×C414yes—
49C2×C4⋊Dic89Q814yes—
50C2×#13083553—22no—
51C2×#13083553—22no—
52C2×#13083553—22no—
53C2×#13083553—22no—
54C2×#13083553—22no—
55C2×#13083553—42no—
56C2×#13083553—42no—
57C2×#13083553C2×C418yes—
58C2×#13083553Q814yes—
59C2×C4×Dic89—24no—
60C2×C4×Dic89—22no—
61C2×C4×Dic89—22no—
62C2×C4×Dic89—22no—
63C2×C4×Dic89—22no—
64C2×C4×Dic89—42no—
65C2×C4×Dic89—42no—
66C2×C4×Dic89C2×C414yes—
67C2×C4×Dic89D414yes—
68#15667919—22no—
69#15667919—22no—
70#15667919—24no—
71#15667919—24no—
72#15667919—24no—
73#15667919—24no—
74#15667919—42no—
75#15667919—42no—
76#15667919—42no—
77#15667919C2×C418yes—
78C23×C4×C89C2312yes—
79C23×C4×C89C2312yes—
80C23×C4×C89C2311yescharacteristic
81C23×C4×C89C2311yescharacteristic
82C23×C4×C89C2311yescharacteristic
83C2×C4⋊C4×C89—22no—
84C2×C4⋊C4×C89—22no—
85C2×C4⋊C4×C89—22no—
86C2×C4⋊C4×C89—22no—
87C2×C4⋊C4×C89—22no—
88C2×C4⋊C4×C89C2×C414yes—
89C2×C42×C89—22no—
90C2×C42×C89—22no—
91C2×C42×C89—22no—
92#95×C89—42no—
93#95×C89—42no—
94C22×Dic89—21no—
95C22×Dic89—21no—
96C22×Dic89—21no—
97C22×Dic89—21no—
98C22×Dic89—21no—
99C22×Dic89—21no—
100C22×Dic89—21no—
101C22×Dic89—21no—
102C22×Dic89—21no—
103C22×Dic89—22no—
104C22×Dic89—22no—
105C22×Dic89—22no—
106C22×Dic89—22no—
107C22×Dic89—22no—
108C22×Dic89—21no—
109C22×Dic89—21no—
110C22×Dic89—21no—
111C22×Dic89—21no—
112C22×Dic89—21no—
113C22×Dic89—22no—
114C22×Dic89—22no—
115C22×Dic89—22no—
116C22×Dic89—21no—
117C22×Dic89—21no—
118C22×Dic89—22no—
119C22×Dic89—22no—
120C22×Dic89—22no—
121C22×Dic89—22no—
122C22×Dic89—21no—
123C22×Dic89—21no—
124C22×Dic89—21no—
125C22×Dic89—21no—
126C22×Dic89C22×C414yes—
127C22×Dic89C22×C412yes—
128C22×Dic89C22×C412yes—
129C22×Dic89C2×D412yes—
130C22×Dic89C2×D412yes—
131C22×Dic89C2×Q814yes—
132C22×Dic89C2×Q812yes—
133C22×Dic89C2×Q812yes—
134C22×Dic89#4112yes—
135C22×Dic89#4112yes—
136C4⋊Dic89—28no—
137C4⋊Dic89—28no—
138#13083553—28no—
139#13083553—28no—
140#13083553—48no—
141C4×Dic89—28no—
142C4×Dic89—28no—
143C4×Dic89—48no—
144C24×C89C2411yescharacteristic
145C22×C4×C89—21no—
146C22×C4×C89—21no—
147C22×C4×C89—22no—
148C22×C4×C89—21no—
149C22×C4×C89—21no—
150C22×C4×C89—21no—
151C22×C4×C89—21no—
152C22×C4×C89—22no—
153C22×C4×C89—21no—
154C22×C4×C89—21no—
155C22×C4×C89—21no—
156C22×C4×C89—21no—
157C22×C4×C89—22no—
158C22×C4×C89—22no—
159C22×C4×C89—21no—
160C22×C4×C89—22no—
161C22×C4×C89—22no—
162C22×C4×C89—21no—
163C22×C4×C89—22no—
164C22×C4×C89—22no—
165C22×C4×C89—22no—
166C22×C4×C89—22no—
167C22×C4×C89—22no—
168C22×C4×C89—22no—
169C22×C4×C89—22no—
170C22×C4×C89C22×C414yes—
171C22×C4×C89C22×C412yes—
172C22×C4×C89C2×D412yes—
173C22×C4×C89C2×Q812yes—
174C22×C4×C89C2×Q812yes—
175C22×C4×C89#4112yes—
176C22×C4×C89#4112yes—
177C22×C4×C89#4112yes—
178C22×C4×C89#4112yes—
179C22×C4×C89#4112yes—
180C4⋊C4×C89—28no—
181C4⋊C4×C89—44no—
182C42×C89—44no—
183C23×C89C23×C411yescharacteristic
184C23×C89C22×D411yescharacteristic
185C23×C89C22×Q811yescharacteristic
186C23×C89C22×Q811yescharacteristic
187C23×C89C2×#4111yescharacteristic
188C23×C89C2×#4111yescharacteristic
189C23×C89C2×#4111yescharacteristic
190C23×C89C2×#4111yescharacteristic
191C23×C89C2×#4111yescharacteristic
192C23×C89C2×#4111yescharacteristic
193C23×C89C2×#4111yescharacteristic
194C23×C89H(5,𝔽2)11yescharacteristic
195C23×C89H(5,𝔽2)11yescharacteristic
196C23×C89H(5,𝔽2)11yescharacteristic
197C23×C892−1+411yescharacteristic
198C2×C4×C89—24no—
199C2×C4×C89—24no—
200C2×C4×C89—24no—
201C2×C4×C89—22no—
202C2×C4×C89—22no—
203C2×C4×C89—22no—
204C2×C4×C89—22no—
205C2×C4×C89—22no—
206C2×C4×C89—22no—
207C2×C4×C89—41no—
208C2×C4×C89—41no—
209C2×C4×C89—41no—
210C2×C4×C89—42no—
211C2×C4×C89—42no—
212C2×C4×C89—41no—
213C2×C4×C89—42no—
214C2×C4×C89—42no—
215C2×C4×C89—41no—
216C2×C4×C89—41no—
217C2×C4×C89—41no—
218C2×C4×C89—41no—
219C2×C4×C89—42no—
220C2×C4×C89—42no—
221C2×C4×C89—42no—
222C2×C4×C89—42no—
223C2×C4×C89—42no—
224C2×C4×C89—42no—
225C2×C4×C89—42no—
226C2×C4×C89#11714yes—
227C2×C4×C89C4×D414yes—
228C2×C4×C89C4×Q814yes—
229C2×C4×C89C22⋊Q814yes—
230C2×C4×C89#12314yes—
231C2×C4×C89#12514yes—
232C2×C4×C89#12614yes—
233C2×Dic89—22no—
234C2×Dic89—22no—
235C2×Dic89—22no—
236C2×Dic89—22no—
237C2×Dic89—22no—
238C2×Dic89—22no—
239C2×Dic89—22no—
240C2×Dic89—22no—
241C2×Dic89—22no—
242C2×Dic89—22no—
243C2×Dic89—22no—
244C2×Dic89—22no—
245C2×Dic89—24no—
246C2×Dic89—22no—
247C2×Dic89—24no—
248C2×Dic89—22no—
249C2×Dic89—24no—
250C2×Dic89—22no—
251C2×Dic89—24no—
252C2×Dic89—22no—
253C2×Dic89—22no—
254C2×Dic89—22no—
255C2×Dic89—24no—
256C2×Dic89—24no—
257C2×Dic89—42no—
258C2×Dic89—42no—
259C2×Dic89—41no—
260C2×Dic89—41no—
261C2×Dic89—41no—
262C2×Dic89—41no—
263C2×Dic89—41no—
264C2×Dic89—42no—
265C2×Dic89—42no—
266C2×Dic89—41no—
267C2×Dic89—41no—
268C2×Dic89—41no—
269C2×Dic89—42no—
270C2×Dic89—42no—
271C2×Dic89—42no—
272C2×Dic89—42no—
273C2×Dic89C4×Q814yes—
274C2×Dic89C22⋊Q814yes—
275C22×C89C2×#11711yescharacteristic
276C22×C89C2×C4×D411yescharacteristic
277C22×C89C2×C4×Q811yescharacteristic
278C22×C89C2×C4×Q811yescharacteristic
279C22×C89C4×#4111yescharacteristic
280C22×C89#51811yescharacteristic
281C22×C89#52011yescharacteristic
282C22×C89C2×C22⋊Q811yescharacteristic
283C22×C89C2×C22⋊Q811yescharacteristic
284C22×C89C2×#12311yescharacteristic
285C22×C89#52511yescharacteristic
286C22×C89C2×#12511yescharacteristic
287C22×C89C2×#12611yescharacteristic
288C22×C89#52911yescharacteristic
289C22×C89#53311yescharacteristic
290C22×C89#53511yescharacteristic
291C22×C89#53711yescharacteristic
292C22×C89#54011yescharacteristic
293C22×C89#54211yescharacteristic
294C22×C89#55211yescharacteristic
295C22×C89#55311yescharacteristic
296C22×C89#55311yescharacteristic
297C22×C89#55311yescharacteristic
298C22×C89#55411yescharacteristic
299C22×C89#55411yescharacteristic
300C22×C89#55411yescharacteristic
301C22×C89#55411yescharacteristic
302C22×C89#55511yescharacteristic
303C22×C89#55611yescharacteristic
304C22×C89#55711yescharacteristic
305C22×C89#55711yescharacteristic
306C22×C89Q8211yescharacteristic
307C22×C89#55911yescharacteristic
308C22×C89#55911yescharacteristic
309C22×C89#55911yescharacteristic
310C4×C89—44no—
311C4×C89—42no—
312C4×C89—42no—
313C4×C89—82no—
314C4×C89#38718yes—
315Dic89—24no—
316Dic89—24no—
317Dic89—42no—
318Dic89—44no—
319Dic89—44no—
320Dic89—42no—
321#14041—891nomaximal, Sylow
322C2×C89C2×#38711yescharacteristic
323C2×C89C4×C22⋊Q811yescharacteristic
324C2×C89#232411yescharacteristic
325C2×C89#235511yescharacteristic
326C2×C89#235711yescharacteristic
327C2×C89#236911yescharacteristic
328C2×C89#237011yescharacteristic
329C2×C89#248511yescharacteristic
330C2×C89#248711yescharacteristic
331C2×C89#250711yescharacteristic
332C2×C89#250911yescharacteristic
333C2×C89#251111yescharacteristic
334C2×C89#251311yescharacteristic
335C2×C89#258011yescharacteristic
336C2×C89#258211yescharacteristic
337C2×#389—891no—
338C2×C4×C4⋊C4—891no—
339C2×C4×C4⋊C4—891no—
340#1445—892no—
341#1442—892no—
342#1436—892no—
343#1436—892no—
344C4⋊#95—891no—
345C4⋊#95—891no—
346C4⋊#95—891no—
347C4⋊#95D8911yescharacteristic
348C89#1404111yescharacteristic, complemented, Sylow
349C22×C4⋊C4—892no—
350C22×C4⋊C4—891no—
351C22×C4⋊C4—891no—
352C22×C4⋊C4—891no—
353C22×C4⋊C4—891no—
354C22×C4⋊C4C2×D8911yescharacteristic
355C22×C4⋊C4C2×D8911yescharacteristic
356C22×C42—891no—
357C22×C42—891no—
358C22×C42—892no—
359C22×C42C2×D8911yescharacteristic
360#389—898no—
361C4×C4⋊C4—1784no—
362C4×C4⋊C4—1784no—
363C2×#95—892no—
364C2×#95—892no—
365C2×#95—892no—
366C2×#95—892no—
367C2×#95—892no—
368C2×#95—892no—
369C2×#95—892no—
370C2×#95—891no—
371C2×#95—892no—
372C2×#95—891no—
373C2×#95C2×D8912yes—
374C2×#95C2×D8912yes—
375C23×C4—891no—
376C23×C4—891no—
377C23×C4—892no—
378C23×C4—891no—
379C23×C4—891no—
380C23×C4—892no—
381C23×C4C22×D8912yes—
382C23×C4C22×D8912yes—
383C23×C4C22×D8911yescharacteristic
384C23×C4C22×D8911yescharacteristic
385C23×C4C22×D8911yescharacteristic
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—898no—
392C2×C4⋊C4—894no—
393C2×C4⋊C4—894no—
394C2×C4⋊C4—894no—
395C2×C4⋊C4—3562no—
396C2×C4⋊C4—3562no—
397C2×C4⋊C4—1782no—
398C2×C4⋊C4—1782no—
399C2×C4⋊C4—1782no—
400C2×C4⋊C4—1782no—
401C2×C4⋊C4—1782no—
402C2×C4⋊C4—1782no—
403C2×C4⋊C4—1782no—
404C2×C4⋊C4—1782no—
405C2×C4⋊C4—1782no—
406C2×C4⋊C4C4×D8914yes—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—894no—
411C2×C42—894no—
412C2×C42—3562no—
413C2×C42—3562no—
414C2×C42—1784no—
415C2×C42—1782no—
416C2×C42—1782no—
417C2×C42—1782no—
418C2×C42—1782no—
419#95—42no—
420#95—42no—
421#95—898no—
422#95—3562no—
423#95—3562no—
424#95—3562no—
425#95—1782no—
426#95—1782no—
427#95—1784no—
428#95—1784no—
429#95—1784no—
430#95—1784no—
431C24C23×D8911yescharacteristic
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—892no—
458C22×C4—892no—
459C22×C4—892no—
460C22×C4—892no—
461C22×C4—892no—
462C22×C4—892no—
463C22×C4—894no—
464C22×C4—892no—
465C22×C4—892no—
466C22×C4—894no—
467C22×C4—1781no—
468C22×C4—1782no—
469C22×C4—1782no—
470C22×C4—1782no—
471C22×C4—1781no—
472C22×C4—1781no—
473C22×C4—1781no—
474C22×C4—1781no—
475C22×C4—1782no—
476C22×C4—1782no—
477C22×C4—1782no—
478C22×C4—1782no—
479C22×C4—1782no—
480C22×C4—1781no—
481C22×C4—1781no—
482C22×C4—1781no—
483C22×C4—1782no—
484C22×C4—1782no—
485C22×C4—1781no—
486C22×C4—1782no—
487C22×C4—1782no—
488C22×C4—1781no—
489C22×C4—1781no—
490C22×C4—1781no—
491C22×C4—1781no—
492C22×C4—1781no—
493C22×C4—1781no—
494C22×C4—1781no—
495C22×C4—1781no—
496C22×C4—1781no—
497C22×C4—1781no—
498C22×C4—1781no—
499C22×C4C2×C4×D8914yes—
500C22×C4C2×C4×D8912yes—
501C22×C4D4×D8912yes—
502C22×C4Q8×D8912yes—
503C22×C4Q8×D8912yes—
504C22×C4#1308357312yes—
505C22×C4#1308357312yes—
506C22×C4#1308357412yes—
507C22×C4#1308357412yes—
508C22×C4#1308357512yes—
509C4⋊C4—28no—
510C4⋊C4—44no—
511C4⋊C4—3568no—
512C4⋊C4—1788no—
513C4⋊C4—1788no—
514C4⋊C4—1788no—
515C4⋊C4—1788no—
516C42—44no—
517C42—3568no—
518C42—1788no—
519C42—1788no—
520C23C22×C4×D8911yescharacteristic
521C23C2×D4×D8911yescharacteristic
522C23C2×Q8×D8911yescharacteristic
523C23C2×Q8×D8911yescharacteristic
524C23#41×D8911yescharacteristic
525C23#41×D8911yescharacteristic
526C23C2×#1308357311yescharacteristic
527C23C2×#1308357311yescharacteristic
528C23C2×#1308357411yescharacteristic
529C23C2×#1308357411yescharacteristic
530C23C2×#1308357511yescharacteristic
531C23#1566805711yescharacteristic
532C23#1566805711yescharacteristic
533C23#1566805811yescharacteristic
534C23#1566805911yescharacteristic
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—42no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—41no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—894no—
564C2×C4—894no—
565C2×C4—3562no—
566C2×C4—3561no—
567C2×C4—3561no—
568C2×C4—3561no—
569C2×C4—3561no—
570C2×C4—3561no—
571C2×C4—3562no—
572C2×C4—3562no—
573C2×C4—3561no—
574C2×C4—3561no—
575C2×C4—3561no—
576C2×C4—3562no—
577C2×C4—3562no—
578C2×C4—3562no—
579C2×C4—3562no—
580C2×C4—3562no—
581C2×C4—1782no—
582C2×C4—1784no—
583C2×C4—1784no—
584C2×C4—1784no—
585C2×C4—1782no—
586C2×C4—1784no—
587C2×C4—1782no—
588C2×C4—1784no—
589C2×C4—1782no—
590C2×C4—1784no—
591C2×C4—1782no—
592C2×C4—1782no—
593C2×C4—1782no—
594C2×C4—1782no—
595C2×C4—1782no—
596C2×C4—1782no—
597C2×C4—1782no—
598C2×C4—1782no—
599C2×C4—1782no—
600C2×C4—1782no—
601C2×C4—1782no—
602C2×C4—1782no—
603C2×C4—1782no—
604C2×C4—1782no—
605C2×C4#1566796914yes—
606C2×C4#1566797214yes—
607C2×C4#1566797714yes—
608C2×C4#1566799014yes—
609C2×C4#1566799414yes—
610C2×C4#1566800214yes—
611C2×C4#1566800514yes—
612C22C2×#1566796911yescharacteristic
613C22C2×#1566797211yescharacteristic
614C22C4×Q8×D8911yescharacteristic
615C22C2×#1566797711yescharacteristic
616C22C4×#1308357511yescharacteristic
617C22#1915207011yescharacteristic
618C22#1915207711yescharacteristic
619C22C22⋊Q8×D8911yescharacteristic
620C22C2×#1566799011yescharacteristic
621C22C2×#1566799411yescharacteristic
622C22#1915211111yescharacteristic
623C22C2×#1566800211yescharacteristic
624C22C2×#1566800511yescharacteristic
625C22#1915212711yescharacteristic
626C22#1915215311yescharacteristic
627C22#1915216411yescharacteristic
628C22#1915217711yescharacteristic
629C22#1915220211yescharacteristic
630C22#1915221711yescharacteristic
631C22#1915229011yescharacteristic
632C22#1915229211yescharacteristic
633C22#1915229511yescharacteristic
634C22#1915229611yescharacteristic
635C22#1915230311yescharacteristic
636C22#1915230411yescharacteristic
637C22#1915230611yescharacteristic
638C22#1915230911yescharacteristic
639C22#1915231211yescharacteristic
640C22#1915231611yescharacteristic
641C22#1915232511yescharacteristic
642C22#1915232611yescharacteristic
643C22#1915232811yescharacteristic
644C22#1915233111yescharacteristic
645C22#1915233111yescharacteristic
646C22#1915233311yescharacteristic
647C4—44no—
648C4—42no—
649C4—42no—
650C4—82no—
651C4—3562no—
652C4—3564no—
653C4—3562no—
654C4—3564no—
655C4—1784no—
656C4—1784no—
657C4#1915148018yes—
658C2C2×#1915148011yescharacteristic
659C2#2602279011yescharacteristic
660C2#2602294811yescharacteristic
661C2#2602320511yescharacteristic
662C2#2602322111yescharacteristic
663C2#2602333811yescharacteristic
664C2#2602335311yescharacteristic
665C2#2602455111yescharacteristic
666C2#2602456511yescharacteristic
667C2#2602477511yescharacteristic
668C2#2602479711yescharacteristic
669C2#2602482911yescharacteristic
670C2#2602485111yescharacteristic
671C2#2602561211yescharacteristic
672C2#2602562411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D89
commutatorC23×C89C23×C4
FittingC89×C4⋊#95C2
socle, prime radical, cosocleC24×C89C24
hypercenterC4⋊#95D89
hypocenterC89#14041
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
20. #19151494C4semidirect
348. C89#14041semidirect

Maximal subgroups

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

subgroupindex
C2×#191514942
C2×C4⋊C4×Dic892
C2×C4×#130835532
#260185182
#260185072
#260184872
#260184832
#260184822
#260184812
C89×C4⋊#952
#1404189