Finite Group Databasebeta

← C2×#26020556 #36555619

Subgroups — C2×#26020556 #36555619

Order 22784.

2270 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#15667988C211yesmaximal, characteristic
2C22×C4⋊C4×D89C211yesmaximal, characteristic
3C22×#15667936C211yesmaximal, characteristic, complemented
4C22×#15667924C211yesmaximal, characteristic
5#26020556C218yesmaximal, direct product factor
6C2×#19151361C211yesmaximal, characteristic, complemented
7C2×#19151360C211yesmaximal, characteristic, complemented
8C22×#103×C89C211yesmaximal, characteristic, complemented
9C23×C4×D89—21no—
10C23×C4×D89C2211yescharacteristic
11C23×#10623494C2211yescharacteristic
12C2×#15667988—22no—
13C2×#15667988—24no—
14C2×#15667988C418yescomplemented
15C2×#15667988C2214yes—
16C22×C4⋊Dic89C2211yescharacteristic
17C22×C4⋊Dic89C2211yescharacteristic
18C22×#13083553—21no—
19C22×#13083553—21no—
20C2×C4⋊C4×D89—24no—
21C2×C4⋊C4×D89—24no—
22C2×C4⋊C4×D89—22no—
23C2×C4⋊C4×D89C2214yes—
24C22×#13083551—21no—
25C2×#15667936—24no—
26C2×#15667936C2214yescomplemented
27C2×#15667924—24no—
28C2×#15667924C2214yes—
29#19151361C2214yescomplemented
30#19151360C2214yescomplemented
31C23×Q8×C89C2211yescharacteristic
32C23×C8×C89C2211yescharacteristic
33C22×C4⋊C4×C89C2211yescharacteristic
34C2×#103×C89—24no—
35C2×#103×C89C2214yescomplemented
36C24×D89D411yescharacteristic
37C23×Dic89—21no—
38C23×Dic89—21no—
39C23×Dic89D411yescharacteristic
40C22×C4×D89—28no—
41C22×C4×D89—24no—
42C22×C4×D89—22no—
43C22×C4×D89—22no—
44C22×C4×D89—22no—
45C22×C4×D89—22no—
46C22×C4×D89—44no—
47C22×C4×D89—44no—
48C22×C4×D89C2×C414yes—
49C22×C4×D89D412yes—
50C22×C4×D89D414yes—
51C22×C4×D89C2312yes—
52C22×#10623494—22no—
53C22×#10623494—22no—
54C22×#10623494—22no—
55C22×#10623494C2312yes—
56#15667988—216no—
57#15667988—28no—
58#15667988C2×C4116yescomplemented
59C2×C4⋊Dic89—21no—
60C2×C4⋊Dic89—22no—
61C2×C4⋊Dic89—21no—
62C2×C4⋊Dic89—22no—
63C2×C4⋊Dic89C2×C414yescomplemented
64C2×C4⋊Dic89D414yes—
65C2×C4⋊Dic89C2312yes—
66C2×C4⋊Dic89C2312yes—
67C2×#13083553—28no—
68C2×#13083553—28no—
69C2×#13083553—24no—
70C2×#13083553—24no—
71C4⋊C4×D89—216no—
72C4⋊C4×D89—28no—
73C4⋊C4×D89—28no—
74C2×#13083551—28no—
75C2×#13083551—24no—
76#15667936—28no—
77#15667924—28no—
78C22×Q8×C89—22no—
79C22×Q8×C89—21no—
80C22×Q8×C89—22no—
81C22×Q8×C89—22no—
82C22×Q8×C89—22no—
83C22×Q8×C89—22no—
84C22×Q8×C89C2×C414yescomplemented
85C22×Q8×C89C2312yes—
86C23×C4×C89—21no—
87C23×C4×C89—21no—
88C23×C4×C89C2311yescharacteristic
89C22×C8×C89—22no—
90C22×C8×C89—22no—
91C22×C8×C89—22no—
92C22×C8×C89C2312yes—
93C2×C4⋊C4×C89—21no—
94C2×C4⋊C4×C89—22no—
95C2×C4⋊C4×C89D414yes—
96C2×C4⋊C4×C89C2312yes—
97#103×C89—28no—
98C23×D89—22no—
99C23×D89—22no—
100C23×D89—22no—
101C23×D89—22no—
102C23×D89C22⋊C414yes—
103C23×D89SD1614yes—
104C23×D89Q1614yes—
105C23×D89C2×D412yes—
106C22×Dic89—22no—
107C22×Dic89—22no—
108C22×Dic89—24no—
109C22×Dic89—24no—
110C22×Dic89—22no—
111C22×Dic89—22no—
112C22×Dic89—42no—
113C22×Dic89—42no—
114C22×Dic89—42no—
115C22×Dic89—42no—
116C22×Dic89C22⋊C414yes—
117C22×Dic89C2×D412yes—
118C2×C4×D89—28no—
119C2×C4×D89—28no—
120C2×C4×D89—24no—
121C2×C4×D89—28no—
122C2×C4×D89—28no—
123C2×C4×D89—24no—
124C2×C4×D89—22no—
125C2×C4×D89—22no—
126C2×C4×D89—22no—
127C2×C4×D89—22no—
128C2×C4×D89—216no—
129C2×C4×D89—48no—
130C2×C4×D89—432no—
131C2×C4×D89—48no—
132C2×C4×D89C22⋊C418yes—
133C2×C4×D89C22×C414yes—
134C2×C4×D89C2×D414yes—
135C2×#10623494—22no—
136C2×#10623494—22no—
137C2×#10623494—22no—
138C2×#10623494—44no—
139C4⋊Dic89—24no—
140C4⋊Dic89—24no—
141C4⋊Dic89—22no—
142C4⋊Dic89—22no—
143C4⋊Dic89C22×C414yescomplemented
144C4⋊Dic89C2×D414yes—
145#13083553—216no—
146#13083553—216no—
147#13083551—216no—
148C24×C89C2×D411yescharacteristic
149C2×Q8×C89—24no—
150C2×Q8×C89—22no—
151C2×Q8×C89—28no—
152C2×Q8×C89—28no—
153C2×Q8×C89—22no—
154C2×Q8×C89—22no—
155C2×Q8×C89—22no—
156C2×Q8×C89—22no—
157C2×Q8×C89—42no—
158C2×Q8×C89—44no—
159C2×Q8×C89—44no—
160C2×Q8×C89—42no—
161C2×Q8×C89C22×C414yescomplemented
162C22×C4×C89—24no—
163C22×C4×C89—24no—
164C22×C4×C89—22no—
165C22×C4×C89—22no—
166C22×C4×C89—42no—
167C22×C4×C89—42no—
168C22×C4×C89—42no—
169C22×C4×C89—42no—
170C22×C4×C89C22×C412yes—
171C22×C4×C89C2×D411yescharacteristic
172C22×C4×C89C2×D412yes—
173C22×C4×C89C2×D412yes—
174C22×C4×C89C2×D412yes—
175C22×C4×C89#4112yes—
176C22×C4×C89#4112yes—
177C22×C4×C89C2411yescharacteristic
178C2×C8×C89—22no—
179C2×C8×C89—22no—
180C2×C8×C89—22no—
181C2×C8×C89—44no—
182C4⋊C4×C89—24no—
183C4⋊C4×C89—22no—
184C4⋊C4×C89C2×D414yes—
185C23×C89C2×C22⋊C412yes—
186C23×C89#12012yes—
187C23×C89#12312yes—
188C23×C89C2×SD1612yes—
189C23×C89C2×Q1612yes—
190C23×C89AGL(1,ℤ/8)12yes—
191C23×C89#13712yes—
192C23×C89C22×D411yescharacteristic
193C22×D89—22no—
194C22×D89—22no—
195C22×D89—22no—
196C22×D89—22no—
197C22×D89—28no—
198C22×D89—28no—
199C22×D89—28no—
200C22×D89—28no—
201C22×D89—28no—
202C22×D89—28no—
203C22×D89#103116yescomplemented
204C22×D89C2×C22⋊C414yes—
205C22×D89C2×SD1614yes—
206C22×D89C2×Q1614yes—
207Q8×C89—24no—
208Q8×C89—24no—
209Q8×C89—42no—
210Q8×C89—42no—
211Q8×C89—48no—
212C2×C4×C89—24no—
213C2×C4×C89—24no—
214C2×C4×C89—42no—
215C2×C4×C89—42no—
216C2×C4×C89—42no—
217C2×C4×C89—42no—
218C2×C4×C89—48no—
219C2×C4×C89—48no—
220C2×C4×C89C2×C22⋊C412yes—
221C2×C4×C89C4×D414yes—
222C2×C4×C89C4×D414yes—
223C2×C4×C89#12012yes—
224C2×C4×C89#12114yes—
225C2×C4×C89#12114yes—
226C2×C4×C89#12312yes—
227C2×C4×C89C23×C411yescharacteristic
228C2×C4×C89C22×D411yescharacteristic
229C2×C4×C89C22×D411yescharacteristic
230C2×C4×C89C22×D411yescharacteristic
231C2×C4×C89C2×#4111yescharacteristic
232C2×C4×C89C2×#4111yescharacteristic
233C2×Dic89—22no—
234C2×Dic89—22no—
235C2×Dic89—28no—
236C2×Dic89—24no—
237C2×Dic89—24no—
238C2×Dic89—42no—
239C2×Dic89—42no—
240C2×Dic89—42no—
241C2×Dic89—42no—
242C2×Dic89—48no—
243C2×Dic89—48no—
244C2×Dic89C2×C22⋊C414yes—
245C4×D89—24no—
246C4×D89—24no—
247C4×D89—24no—
248C4×D89—24no—
249C4×D89—216no—
250C4×D89—432no—
251C8×C89—42no—
252#10623494—42no—
253C22×C89#38614yes—
254C22×C89C2×#10314yes—
255C22×C89#41714yes—
256C22×C89#45014yes—
257C22×C89#45114yes—
258C22×C89#48314yes—
259C22×C89#48414yes—
260C22×C89C22×C22⋊C411yescharacteristic
261C22×C89C2×#12011yescharacteristic
262C22×C89C2×#12311yescharacteristic
263C22×C89C22×SD1611yescharacteristic
264C22×C89C22×Q1611yescharacteristic
265C22×C89C2×AGL(1,ℤ/8)11yescharacteristic
266C22×C89C2×#13711yescharacteristic
267C2×D89—24no—
268C2×D89—24no—
269C2×D89—24no—
270C2×D89—232no—
271C2×D89—24no—
272C2×D89—24no—
273C2×D89—24no—
274C2×D89C2×#10318yescomplemented
275C4×C89—44no—
276C4×C89—44no—
277C4×C89#38614yes—
278C4×C89C2×C4×D411yescharacteristic
279C4×C89C2×C4×D411yescharacteristic
280C4×C89C2×#12111yescharacteristic
281C4×C89C2×#12111yescharacteristic
282Dic89—24no—
283Dic89—44no—
284Dic89—44no—
285C2×#1872—891nomaximal, Sylow
286C2×C89#187218yescomplemented
287C2×C89C2×#38611yescharacteristic
288C2×C89C22×#10311yescharacteristic
289C2×C89C2×#41711yescharacteristic
290C2×C89C2×#45011yescharacteristic
291C2×C89C2×#45111yescharacteristic
292C2×C89C2×#48311yescharacteristic
293C2×C89C2×#48411yescharacteristic
294D89—28no—
295C22×C22⋊Q8—891no—
296C23×C4⋊C4—891no—
297C22×#103—891no—
298C22×#103D8911yescharacteristic, complemented
299C22×C22⋊C8—891no—
300#1872—898no—
301C2×#340—891no—
302C2×#340—891no—
303C89C2×#187211yescharacteristic, complemented, Sylow
304C23×Q8C2×D8911yescharacteristic
305C24×C4—891no—
306C24×C4—1781no—
307C23×C8—891no—
308C23×C8C2×D8911yescharacteristic
309C2×C22⋊Q8—898no—
310C2×C22⋊Q8—894no—
311C2×C22⋊Q8—1782no—
312C2×C22⋊Q8—1784no—
313C22×C4⋊C4—891no—
314C22×C4⋊C4—891no—
315C22×C4⋊C4—894no—
316C22×C4⋊C4—1784no—
317C22×C4⋊C4—1782no—
318C22×C4⋊C4—1781no—
319C22×C4⋊C4—1781no—
320C22×C4⋊C4—1784no—
321C22×C4⋊C4C2×D8911yescharacteristic
322C22×C22⋊C4—1781no—
323C2×#103—24no—
324C2×#103—894no—
325C2×#103—1784no—
326C2×#103C2×D8914yescomplemented
327C2×C22⋊C8—894no—
328C2×C22⋊C8—1784no—
329#340—894no—
330#340—894no—
331C25—891no—
332C22×Q8—21no—
333C22×Q8—22no—
334C22×Q8—22no—
335C22×Q8—22no—
336C22×Q8—22no—
337C22×Q8—22no—
338C22×Q8C4×D8914yescomplemented
339C22×Q8C22×D8912yes—
340C23×C4—21no—
341C23×C4—21no—
342C23×C4—891no—
343C23×C4—894no—
344C23×C4—892no—
345C23×C4—894no—
346C23×C4—892no—
347C23×C4—3564no—
348C23×C4—3564no—
349C23×C4—1784no—
350C23×C4—1788no—
351C23×C4—1781no—
352C23×C4—1781no—
353C23×C4—1782no—
354C23×C4—1782no—
355C23×C4—1782no—
356C23×C4—1782no—
357C23×C4C22×D8911yescharacteristic
358C22×C8—22no—
359C22×C8—22no—
360C22×C8—22no—
361C22×C8—892no—
362C22×C8—1782no—
363C22×C8—1782no—
364C22×C8—1782no—
365C22×C8C22×D8912yes—
366C22⋊Q8—8916no—
367C22⋊Q8—1788no—
368C22⋊Q8—17816no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—894no—
372C2×C4⋊C4—894no—
373C2×C4⋊C4—892no—
374C2×C4⋊C4—892no—
375C2×C4⋊C4—1788no—
376C2×C4⋊C4—17816no—
377C2×C4⋊C4—1784no—
378C2×C4⋊C4—1784no—
379C2×C4⋊C4—1788no—
380C2×C4⋊C4—1788no—
381C2×C4⋊C4—1781no—
382C2×C4⋊C4—1782no—
383C2×C4⋊C4—1781no—
384C2×C4⋊C4—1782no—
385C2×C4⋊C4—1788no—
386C2×C4⋊C4C22⋊D8914yes—
387C2×C4⋊C4C22×D8912yes—
388C2×C22⋊C4—1784no—
389C2×C22⋊C4—1788no—
390#103—28no—
391#103—1788no—
392C22⋊C8—1788no—
393C24—894no—
394C24—894no—
395C24—892no—
396C24—894no—
397C24—1782no—
398C24—1782no—
399C24—1782no—
400C24—1782no—
401C24D4×D8911yescharacteristic
402C2×Q8—22no—
403C2×Q8—24no—
404C2×Q8—28no—
405C2×Q8—28no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—42no—
411C2×Q8—44no—
412C2×Q8—44no—
413C2×Q8—42no—
414C2×Q8C2×C4×D8914yescomplemented
415C22×C4—24no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—24no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—892no—
424C22×C4—894no—
425C22×C4—894no—
426C22×C4—894no—
427C22×C4—898no—
428C22×C4—3568no—
429C22×C4—3568no—
430C22×C4—35632no—
431C22×C4—3562no—
432C22×C4—3562no—
433C22×C4—3562no—
434C22×C4—3562no—
435C22×C4—17816no—
436C22×C4—1784no—
437C22×C4—1782no—
438C22×C4—1782no—
439C22×C4—1784no—
440C22×C4—1782no—
441C22×C4—1782no—
442C22×C4—1788no—
443C22×C4—1788no—
444C22×C4—1784no—
445C22×C4—1788no—
446C22×C4—1788no—
447C22×C4—1784no—
448C22×C4—1782no—
449C22×C4—1782no—
450C22×C4—1782no—
451C22×C4—1782no—
452C22×C4C2×C4×D8912yes—
453C22×C4D4×D8912yes—
454C22×C4D4×D8911yescharacteristic
455C22×C4D4×D8912yes—
456C22×C4C2×C22⋊D8912yes—
457C22×C4#1308357312yes—
458C22×C4#1308357412yes—
459C22×C4C23×D8911yescharacteristic
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—44no—
464C2×C8—3564no—
465C2×C8—1782no—
466C2×C8—1782no—
467C2×C8—1782no—
468C4⋊C4—24no—
469C4⋊C4—22no—
470C4⋊C4—894no—
471C4⋊C4—894no—
472C4⋊C4—17816no—
473C4⋊C4—17816no—
474C4⋊C4—1784no—
475C4⋊C4—1782no—
476C4⋊C4—1782no—
477C4⋊C4—1784no—
478C4⋊C4C2×C22⋊D8914yes—
479C22⋊C4—17816no—
480C23—894no—
481C23—8916no—
482C23—894no—
483C23—894no—
484C23—1782no—
485C23—1782no—
486C23—1788no—
487C23—1788no—
488C23—1788no—
489C23—1788no—
490C23—1788no—
491C23—1782no—
492C23—1782no—
493C23—1788no—
494C23C22⋊C4×D8912yes—
495C23#1566798012yes—
496C23#1566799412yes—
497C23SD16×D8912yes—
498C23Q16×D8912yes—
499C23#1566803912yes—
500C23#1566804412yes—
501C23C2×D4×D8911yescharacteristic
502Q8—24no—
503Q8—24no—
504Q8—48no—
505Q8—42no—
506Q8—42no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—42no—
510C2×C4—48no—
511C2×C4—48no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—894no—
516C2×C4—35632no—
517C2×C4—3562no—
518C2×C4—3562no—
519C2×C4—3562no—
520C2×C4—3568no—
521C2×C4—3568no—
522C2×C4—3562no—
523C2×C4—1784no—
524C2×C4—1784no—
525C2×C4—1788no—
526C2×C4—1782no—
527C2×C4—1782no—
528C2×C4—17816no—
529C2×C4—1784no—
530C2×C4—1784no—
531C2×C4—1784no—
532C2×C4—1784no—
533C2×C4C22⋊C4×D8912yes—
534C2×C4#1566797214yes—
535C2×C4C4×C22⋊D8914yes—
536C2×C4#1566798012yes—
537C2×C4#1566798314yes—
538C2×C4#1566798514yes—
539C2×C4#1566799412yes—
540C2×C4C22×C4×D8911yescharacteristic
541C2×C4C2×D4×D8911yescharacteristic
542C2×C4C2×D4×D8911yescharacteristic
543C2×C4C22×C22⋊D8911yescharacteristic
544C2×C4C2×#1308357311yescharacteristic
545C2×C4C2×#1308357411yescharacteristic
546C8—42no—
547C8—3562no—
548C22—898no—
549C22—1784no—
550C22—1784no—
551C22—1784no—
552C22—1784no—
553C22—1784no—
554C22—17832no—
555C22—1784no—
556C22#1915147414yes—
557C22#103×D8914yes—
558C22#1915159814yes—
559C22#1915174714yes—
560C22#1915175214yes—
561C22#1915192714yes—
562C22#1915193214yes—
563C22C2×C22⋊C4×D8911yescharacteristic
564C22C2×#1566798011yescharacteristic
565C22C2×#1566799411yescharacteristic
566C22C2×SD16×D8911yescharacteristic
567C22C2×Q16×D8911yescharacteristic
568C22C2×#1566803911yescharacteristic
569C22C2×#1566804411yescharacteristic
570C4—44no—
571C4—44no—
572C4—3564no—
573C4—3564no—
574C4—1784no—
575C4#1915147414yes—
576C4C2×#1566797211yescharacteristic
577C4C2×C4×C22⋊D8911yescharacteristic
578C4C2×#1566798311yescharacteristic
579C4C2×#1566798511yescharacteristic
580C2—1788no—
581C2#2602055618yesdirect product factor
582C2C2×#1915147411yescharacteristic
583C2C2×#103×D8911yescharacteristic
584C2C2×#1915159811yescharacteristic
585C2C2×#1915174711yescharacteristic
586C2C2×#1915175211yescharacteristic
587C2C2×#1915192711yescharacteristic
588C2C2×#1915193211yescharacteristic
subgroupG/H
centerC24D4×D89
commutatorC2×C4×C89C23×C4
FrattiniC22×C4C23×D89
FittingC22×#103×C89C2
socleC24×C89C2×D4
prime radicalC24×D89D4
cosocleC22×C4×C89C24
hypercenterC22×#103D89
hypocenterC89C2×#1872
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
3. C22×#15667936C2semidirect
5. #26020556C2direct (N × H)
6. C2×#19151361C2semidirect
7. C2×#19151360C2semidirect
8. C22×#103×C89C2semidirect
14. C2×#15667988C4semidirect
26. C2×#15667936C22semidirect
29. #19151361C22semidirect
30. #19151360C22semidirect
35. C2×#103×C89C22semidirect
58. #15667988C2×C4semidirect
63. C2×C4⋊Dic89C2×C4semidirect
84. C22×Q8×C89C2×C4semidirect
143. C4⋊Dic89C22×C4semidirect
161. C2×Q8×C89C22×C4semidirect
203. C22×D89#103semidirect
274. C2×D89C2×#103semidirect
286. C2×C89#1872semidirect
298. C22×#103D89semidirect
303. C89C2×#1872semidirect
326. C2×#103C2×D89semidirect
338. C22×Q8C4×D89semidirect
414. C2×Q8C2×C4×D89semidirect
581. C2#26020556direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#156679882
C22×C4⋊C4×D892
C22×#156679362
C22×#156679242
#260205562
C2×#191513612
C2×#191513602
C22×#103×C892
C2×#187289