Finite Group Databasebeta

← #36554633

Subgroups — #36554633

Order 22784.

894 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19151555C211yesmaximal, characteristic
2#26022877C211yesmaximal, characteristic
3#26022873C211yesmaximal, characteristic
4#26020386C211yesmaximal, characteristic, complemented
5#26020384C211yesmaximal, characteristic, complemented
6#26020384C211yesmaximal, characteristic, complemented
7#26020382C211yesmaximal, characteristic, complemented
8#26020381C211yesmaximal, characteristic, complemented
9#26020379C211yesmaximal, characteristic, complemented
10#26020378C211yesmaximal, characteristic, complemented
11#26019970C211yesmaximal, characteristic
12#26019970C211yesmaximal, characteristic
13#26019967C211yesmaximal, characteristic
14#340×D89C211yesmaximal, characteristic
15C89×#1836C211yesmaximal, characteristic, complemented
16C22×#13083557C2211yescharacteristic
17C22×C8×D89C2211yescharacteristic
18C2×#15667970C2211yescharacteristic
19C2×#15667970C2211yescharacteristic
20C2×#15667969C2211yescharacteristic
21C2×C4⋊C4×D89C2211yescharacteristic
22C2×C4⋊C4×D89C2211yescharacteristic
23#19151555C418yescomplemented
24C2×#15667922C2211yescharacteristic
25C2×C4×#10623494C2211yescharacteristic
26C2×C8×Dic89C2211yescharacteristic
27#19151495—21no—
28#19151495—21no—
29#19151493—21no—
30#19151493—21no—
31#19151472—21no—
32#19151472—21no—
33#19151469—21no—
34#19151469—21no—
35#19151468C2211yescharacteristic
36#19151467C2211yescharacteristic
37#19151467C2211yescharacteristic
38#19151464C2211yescharacteristic
39#19151463C2211yescharacteristic
40#19151463C2211yescharacteristic
41#19151361C2211yescharacteristic
42#19151361C2211yescharacteristic
43#19151361C2211yescharacteristic
44#19151361C2211yescharacteristic
45#19151360C2211yescharacteristic
46#19151360C2211yescharacteristic
47#19151360C2211yescharacteristic
48#19151360C2211yescharacteristic
49#19151360C2211yescharacteristic
50#19151360C2211yescharacteristic
51#19151360C2211yescharacteristic
52#19151360C2211yescharacteristic
53C2×#97×C89C2211yescharacteristic
54#384×C89C2211yescharacteristic
55#382×C89C2211yescharacteristic
56#340×C89C2211yescharacteristic
57#340×C89C2211yescharacteristic
58#340×C89C2211yescharacteristic
59#340×C89C2211yescharacteristic
60C22×C4×D89—21no—
61C22×C4×D89—21no—
62C22×C4×D89C2311yescharacteristic
63C2×#13083557—22no—
64C2×#13083557—22no—
65C2×#13083557C2×C414yes—
66C22×#10623494C2311yescharacteristic
67C22×#10623494C2311yescharacteristic
68C2×C8×D89—22no—
69C2×C8×D89—22no—
70C2×C8×D89C2×C414yes—
71#15667970—22no—
72#15667970—22no—
73#15667970—22no—
74#15667970—22no—
75#15667969C2×C414yes—
76#15667969Q814yes—
77C2×C4⋊Dic89—21no—
78C2×C4⋊Dic89—21no—
79C2×C4⋊Dic89C2311yescharacteristic
80C2×C4⋊Dic89C2311yescharacteristic
81C2×C4⋊Dic89C2311yescharacteristic
82C2×C4⋊Dic89C2311yescharacteristic
83C2×#13083553—21no—
84C2×#13083553—21no—
85C2×#13083553—21no—
86C2×#13083553—21no—
87C2×#13083553—21no—
88C2×#13083553—21no—
89C2×#13083553D411yescharacteristic
90C2×#13083553D411yescharacteristic
91C4⋊C4×D89—22no—
92C4⋊C4×D89—22no—
93C4⋊C4×D89—22no—
94C4⋊C4×D89—22no—
95C2×#13083551—21no—
96C2×#13083551—21no—
97C2×#13083551D411yescharacteristic
98C2×#13083551D411yescharacteristic
99C2×C4×Dic89—21no—
100C2×C4×Dic89—21no—
101C2×C4×Dic89C2311yescharacteristic
102#15667922C2×C414yescomplemented
103C4×#10623494C2×C414yescomplemented
104C8×Dic89C2×C414yescomplemented
105#15667919—21no—
106#15667919—21no—
107#15667919—21no—
108#15667919—21no—
109#15667919—21no—
110#15667919—21no—
111C22×C8×C89C2311yescharacteristic
112C22×C8×C89C2311yescharacteristic
113C2×C4⋊C4×C89—21no—
114C2×C4⋊C4×C89—21no—
115C2×C4⋊C4×C89C2311yescharacteristic
116C2×C4⋊C4×C89C2311yescharacteristic
117C2×C4⋊C4×C89C2311yescharacteristic
118C2×C4⋊C4×C89C2311yescharacteristic
119C2×C42×C89C2311yescharacteristic
120#97×C89C2×C414yescomplemented
121#95×C89—21no—
122#95×C89—21no—
123C23×D89C2×D411yescharacteristic
124C22×Dic89—21no—
125C22×Dic89—21no—
126C22×Dic89—21no—
127C22×Dic89—21no—
128C22×Dic89C2×D411yescharacteristic
129C22×Dic89C2×D411yescharacteristic
130C22×Dic89C2×D411yescharacteristic
131C2×C4×D89—42no—
132C2×C4×D89—42no—
133C2×C4×D89—81no—
134C2×C4×D89—81no—
135C2×C4×D89—81no—
136C2×C4×D89—81no—
137C2×C4×D89C22×C412yes—
138C2×C4×D89C2×Q812yes—
139C2×C4×D89#4112yes—
140C2×C4×D89#4112yes—
141C2×C4×D89#4112yes—
142C2×C4×D89#4112yes—
143#13083557—28no—
144C2×#10623494—21no—
145C2×#10623494—21no—
146C2×#10623494—21no—
147C2×#10623494—21no—
148C2×#10623494C22×C412yes—
149C2×#10623494C22×C412yes—
150C8×D89—28no—
151C4⋊Dic89—21no—
152C4⋊Dic89—21no—
153C4⋊Dic89—21no—
154C4⋊Dic89—21no—
155C4⋊Dic89—21no—
156C4⋊Dic89—21no—
157C4⋊Dic89—21no—
158C4⋊Dic89—21no—
159C4⋊Dic89—81no—
160C4⋊Dic89—81no—
161#13083553—42no—
162#13083553—42no—
163#13083553—81no—
164#13083553—81no—
165#13083553—81no—
166#13083553—81no—
167#13083553C4⋊C414yes—
168#13083553C4⋊C414yes—
169#13083551—42no—
170#13083551—42no—
171#13083551C4⋊C414yes—
172#13083551C4⋊C414yes—
173C4×Dic89—42no—
174C4×Dic89—42no—
175C4×Dic89C22×C412yes—
176C4×Dic89C2×Q812yes—
177C22×C4×C89—21no—
178C22×C4×C89—21no—
179C22×C4×C89—21no—
180C22×C4×C89—21no—
181C22×C4×C89C2×D411yescharacteristic
182C22×C4×C89C2×D411yescharacteristic
183C22×C4×C89C2411yescharacteristic
184C2×C8×C89—21no—
185C2×C8×C89—21no—
186C2×C8×C89—21no—
187C2×C8×C89—21no—
188C2×C8×C89C22×C412yes—
189C2×C8×C89C22×C412yes—
190C4⋊C4×C89—21no—
191C4⋊C4×C89—21no—
192C4⋊C4×C89—21no—
193C4⋊C4×C89—21no—
194C4⋊C4×C89—21no—
195C4⋊C4×C89—21no—
196C4⋊C4×C89—21no—
197C4⋊C4×C89—21no—
198C4⋊C4×C89—81no—
199C4⋊C4×C89—81no—
200C42×C89C22×C412yes—
201C42×C89C2×Q812yes—
202C23×C89C22×D411yescharacteristic
203C22×D89—21no—
204C22×D89—21no—
205C22×D89—21no—
206C22×D89—21no—
207C22×D89C2×C4⋊C412yes—
208C22×D89#12412yes—
209C22×D89#12412yes—
210C2×C4×C89—21no—
211C2×C4×C89—21no—
212C2×C4×C89—21no—
213C2×C4×C89—21no—
214C2×C4×C89—41no—
215C2×C4×C89—41no—
216C2×C4×C89—41no—
217C2×C4×C89—41no—
218C2×C4×C89—41no—
219C2×C4×C89—41no—
220C2×C4×C89—41no—
221C2×C4×C89—41no—
222C2×C4×C89—41no—
223C2×C4×C89—41no—
224C2×C4×C89—41no—
225C2×C4×C89—41no—
226C2×C4×C89C2×C4⋊C412yes—
227C2×C4×C89C2×C4⋊C412yes—
228C2×C4×C89C23×C411yescharacteristic
229C2×C4×C89C22×Q811yescharacteristic
230C2×C4×C89C2×#4111yescharacteristic
231C2×C4×C89C2×#4111yescharacteristic
232C2×C4×C89C2×#4111yescharacteristic
233C2×C4×C89C2×#4111yescharacteristic
234C2×Dic89—21no—
235C2×Dic89—21no—
236C2×Dic89—21no—
237C2×Dic89—21no—
238C2×Dic89—41no—
239C2×Dic89—41no—
240C2×Dic89—41no—
241C2×Dic89—41no—
242C2×Dic89—41no—
243C2×Dic89—41no—
244C2×Dic89—41no—
245C2×Dic89—41no—
246C2×Dic89—41no—
247C2×Dic89—41no—
248C2×Dic89—41no—
249C2×Dic89—41no—
250C2×Dic89C2×C4⋊C412yes—
251C2×Dic89C2×C4⋊C412yes—
252C2×Dic89C2×C4⋊C412yes—
253C2×Dic89#12412yes—
254C2×Dic89#12412yes—
255C4×D89—84no—
256C4×D89—84no—
257C4×D89#11714yes—
258C4×D89#11714yes—
259C4×D89#12514yes—
260C4×D89#12514yes—
261C8×C89—22no—
262C8×C89—22no—
263#10623494—22no—
264#10623494—22no—
265C22×C89C22×C4⋊C411yescharacteristic
266C22×C89C2×#12411yescharacteristic
267C22×C89C2×#12411yescharacteristic
268C22×C89#57611yescharacteristic
269C22×C89#57711yescharacteristic
270C22×C89#57711yescharacteristic
271C22×C89#57811yescharacteristic
272C2×D89—22no—
273C2×D89—22no—
274C2×D89—22no—
275C2×D89—22no—
276C2×D89—22no—
277C2×D89—22no—
278C2×D89#38214yes—
279C4×C89—22no—
280C4×C89—22no—
281C4×C89—81no—
282C4×C89—81no—
283C4×C89—81no—
284C4×C89—81no—
285C4×C89C2×#11711yescharacteristic
286C4×C89C2×#11711yescharacteristic
287C4×C89C2×#12511yescharacteristic
288C4×C89C2×#12511yescharacteristic
289Dic89—22no—
290Dic89—22no—
291Dic89—81no—
292Dic89—81no—
293Dic89—81no—
294Dic89—81no—
295Dic89#38214yes—
296#20763—891nomaximal, Sylow
297C2×C89C2×#38211yescharacteristic
298C2×C89#291211yescharacteristic
299C2×C89#291311yescharacteristic
300C2×C89#313611yescharacteristic
301C2×C89#313611yescharacteristic
302C2×C89#313711yescharacteristic
303C2×C89#313711yescharacteristic
304D89—24no—
305C2×#405—891no—
306#2317—891no—
307#2317—891no—
308#1836—891no—
309#1836—891no—
310#1836—891no—
311#1836D8911yescharacteristic, complemented
312#1835—891no—
313#1835—891no—
314#1834—891no—
315#1834—891no—
316#1736—891no—
317#1736—891no—
318#1735—891no—
319C2×#340—891no—
320C89#2076311yescharacteristic, complemented, Sylow
321C22×M16—891no—
322C23×C8—891no—
323C2×#117—891no—
324C2×#117—891no—
325C2×#117—891no—
326C22×C4⋊C4—891no—
327C22×C4⋊C4—891no—
328#405—898no—
329C2×#97—891no—
330C2×#97C2×D8911yescharacteristic
331C2×C4×C8—891no—
332C2×C4×C8—891no—
333#389—1781no—
334#389—1781no—
335#389—1781no—
336#389—1781no—
337#385—1781no—
338#385—1781no—
339#385—1781no—
340#385—1781no—
341#384—891no—
342#384—891no—
343#384—891no—
344#384C2×D8911yescharacteristic
345#382—891no—
346#382—891no—
347#382—891no—
348#382C2×D8911yescharacteristic
349#340—891no—
350#340—891no—
351#340—891no—
352#340—891no—
353#340—891no—
354#340—891no—
355#340—891no—
356#340—891no—
357#340—891no—
358#340—891no—
359#340—891no—
360#340—891no—
361#340C2×D8911yescharacteristic
362#340C2×D8911yescharacteristic
363#340C2×D8911yescharacteristic
364#340C2×D8911yescharacteristic
365C23×C4—891no—
366C23×C4—1781no—
367C23×C4—1781no—
368C2×M16—894no—
369C2×M16—1782no—
370C2×M16—1782no—
371C22×C8—891no—
372C22×C8—891no—
373C22×C8—894no—
374C22×C8—1782no—
375C22×C8—1782no—
376C22×C8C22×D8911yescharacteristic
377C22×C8C22×D8911yescharacteristic
378#117—894no—
379#117—894no—
380#117—1782no—
381#117—1782no—
382#117—1782no—
383#117—1782no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—891no—
387C2×C4⋊C4—891no—
388C2×C4⋊C4—891no—
389C2×C4⋊C4—891no—
390C2×C4⋊C4—891no—
391C2×C4⋊C4—891no—
392C2×C4⋊C4—1782no—
393C2×C4⋊C4—1782no—
394C2×C4⋊C4—1782no—
395C2×C4⋊C4—1782no—
396C2×C4⋊C4—1781no—
397C2×C4⋊C4—1781no—
398C2×C4⋊C4—1781no—
399C2×C4⋊C4—1781no—
400C2×C4⋊C4—1781no—
401C2×C4⋊C4—1781no—
402C2×C4⋊C4—1781no—
403C2×C4⋊C4—1781no—
404C2×C4⋊C4C22×D8911yescharacteristic
405C2×C4⋊C4C22×D8911yescharacteristic
406C2×C4⋊C4C22×D8911yescharacteristic
407C2×C4⋊C4C22×D8911yescharacteristic
408C2×C22⋊C4—891no—
409C2×C22⋊C4—891no—
410C2×C22⋊C4—1781no—
411C2×C22⋊C4—1781no—
412C2×C42—891no—
413C2×C42—1781no—
414C2×C42—1781no—
415C2×C42C22×D8911yescharacteristic
416#97—894no—
417#97C4×D8914yescomplemented
418C4×C8—894no—
419C4×C8—894no—
420#95—21no—
421#95—21no—
422#95—1781no—
423#95—1781no—
424#95—1781no—
425#95—1781no—
426#95—1781no—
427#95—1781no—
428C24—891no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—891no—
434C22×C4—892no—
435C22×C4—892no—
436C22×C4—892no—
437C22×C4—892no—
438C22×C4—892no—
439C22×C4—892no—
440C22×C4—891no—
441C22×C4—891no—
442C22×C4—3562no—
443C22×C4—3562no—
444C22×C4—1781no—
445C22×C4—1781no—
446C22×C4—1781no—
447C22×C4—1781no—
448C22×C4—7121no—
449C22×C4—7121no—
450C22×C4—7121no—
451C22×C4—7121no—
452C22×C4D4×D8911yescharacteristic
453C22×C4D4×D8911yescharacteristic
454C22×C4C23×D8911yescharacteristic
455M16—1788no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—892no—
461C2×C8—892no—
462C2×C8—1788no—
463C2×C8—1781no—
464C2×C8—1781no—
465C2×C8—1781no—
466C2×C8—1781no—
467C2×C8C2×C4×D8912yes—
468C2×C8C2×C4×D8912yes—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—81no—
478C4⋊C4—81no—
479C4⋊C4—894no—
480C4⋊C4—894no—
481C4⋊C4—3562no—
482C4⋊C4—3562no—
483C4⋊C4—1781no—
484C4⋊C4—1781no—
485C4⋊C4—1781no—
486C4⋊C4—1781no—
487C4⋊C4—1781no—
488C4⋊C4—1781no—
489C4⋊C4—1781no—
490C4⋊C4—1781no—
491C4⋊C4—7121no—
492C4⋊C4—7121no—
493C4⋊C4—7121no—
494C4⋊C4—7121no—
495C4⋊C4—7121no—
496C4⋊C4—7121no—
497C22⋊C4—894no—
498C22⋊C4—894no—
499C22⋊C4—3562no—
500C22⋊C4—3562no—
501C42—892no—
502C42—892no—
503C42—3562no—
504C42—3562no—
505C42C2×C4×D8912yes—
506C42Q8×D8912yes—
507C23—892no—
508C23—892no—
509C23—892no—
510C23—1781no—
511C23—1781no—
512C23—1781no—
513C23—1781no—
514C23C2×D4×D8911yescharacteristic
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—892no—
532C2×C4—892no—
533C2×C4—892no—
534C2×C4—894no—
535C2×C4—894no—
536C2×C4—894no—
537C2×C4—894no—
538C2×C4—892no—
539C2×C4—892no—
540C2×C4—3561no—
541C2×C4—3561no—
542C2×C4—3561no—
543C2×C4—3561no—
544C2×C4—3561no—
545C2×C4—3561no—
546C2×C4—3561no—
547C2×C4—3561no—
548C2×C4—3561no—
549C2×C4—3561no—
550C2×C4—3561no—
551C2×C4—3561no—
552C2×C4—1781no—
553C2×C4—1781no—
554C2×C4—1781no—
555C2×C4—1781no—
556C2×C4—7124no—
557C2×C4—7124no—
558C2×C4C4⋊C4×D8912yes—
559C2×C4C4⋊C4×D8912yes—
560C2×C4C22×C4×D8911yescharacteristic
561C2×C4C2×Q8×D8911yescharacteristic
562C2×C4#41×D8911yescharacteristic
563C2×C4#41×D8911yescharacteristic
564C2×C4#41×D8911yescharacteristic
565C2×C4#41×D8911yescharacteristic
566C8—22no—
567C8—22no—
568C8—1782no—
569C8—1782no—
570C22—894no—
571C22—1782no—
572C22—1782no—
573C22—1782no—
574C22—1782no—
575C22—1782no—
576C22—1782no—
577C22C2×C4⋊C4×D8911yescharacteristic
578C22#124×D8911yescharacteristic
579C22#124×D8911yescharacteristic
580C22#1915240211yescharacteristic
581C22#1915240711yescharacteristic
582C22#1915240811yescharacteristic
583C22#1915241411yescharacteristic
584C4—22no—
585C4—22no—
586C4—81no—
587C4—81no—
588C4—81no—
589C4—81no—
590C4—894no—
591C4—1782no—
592C4—1782no—
593C4—7121no—
594C4—7121no—
595C4—7121no—
596C4—7121no—
597C4#117×D8911yescharacteristic
598C4#117×D8911yescharacteristic
599C4#125×D8911yescharacteristic
600C4#125×D8911yescharacteristic
601C2—1784no—
602C2#382×D8911yescharacteristic
603C2#2602884611yescharacteristic
604C2#2602885111yescharacteristic
605C2#2603060311yescharacteristic
606C2#2603060711yescharacteristic
607C2#2603061411yescharacteristic
608C2#2603061811yescharacteristic
subgroupG/H
centerC23C2×D4×D89
commutatorC2×C4×C89C23×C4
FrattiniC22×C4C23×D89
FittingC89×#1836C2
socleC23×C89C22×D4
prime radicalC23×D89C2×D4
cosocleC22×C4×C89C24
hypercenter#1836D89
hypocenterC89#20763
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1836

Complements

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

NH ≅ G/Ntype
4. #26020386C2semidirect
5. #26020384C2semidirect
6. #26020384C2semidirect
7. #26020382C2semidirect
8. #26020381C2semidirect
9. #26020379C2semidirect
10. #26020378C2semidirect
15. C89×#1836C2semidirect
23. #19151555C4semidirect
102. #15667922C2×C4semidirect
103. C4×#10623494C2×C4semidirect
104. C8×Dic89C2×C4semidirect
120. #97×C89C2×C4semidirect
311. #1836D89semidirect
320. C89#20763semidirect
417. #97C4×D89semidirect

Maximal subgroups

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

subgroupindex
C2×#191515552
#260228772
#260228732
#260203862
#260203842
#260203822
#260203812
#260203792
#260203782
#260199702
#260199672
#340×D892
C89×#18362
#2076389