Finite Group Databasebeta

← C89×#29437 #36407285

Subgroups — C89×#29437 #36407285

Order 22784.

708 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#2644C211yesmaximal, characteristic, complemented
2C89×#2319C211yesmaximal, characteristic, complemented
3C89×#2086C211yesmaximal, characteristic, complemented
4C89×#2065C211yesmaximal, characteristic, complemented
5C89×#2065C211yesmaximal, characteristic, complemented
6C89×#2054C211yesmaximal, characteristic
7C89×#1970C211yesmaximal, characteristic
8C89×#1941C211yesmaximal, characteristic, complemented
9C89×#1936C211yesmaximal, characteristic, complemented
10C89×#1936C211yesmaximal, characteristic, complemented
11C89×#1926C211yesmaximal, characteristic, complemented
12C89×#1918C211yesmaximal, characteristic, complemented
13C89×#1879C211yesmaximal, characteristic
14C89×#1864C211yesmaximal, characteristic, complemented
15C89×#1768C211yesmaximal, characteristic, complemented
16C22×D8×C89C2211yescharacteristic
17C2×C4×D4×C89C2211yescharacteristic
18C2×#107×C89C2211yescharacteristic
19C2×#106×C89C2211yescharacteristic
20C2×#106×C89C2211yescharacteristic
21C2×C4⋊C8×C89C2211yescharacteristic
22C2×C4⋊C8×C89C2211yescharacteristic
23C2×#102×C89C2211yescharacteristic
24C2×#102×C89C2211yescharacteristic
25C2×#102×C89C2211yescharacteristic
26C2×#102×C89C2211yescharacteristic
27C2×#102×C89C2211yescharacteristic
28C2×#102×C89C2211yescharacteristic
29C2×#97×C89C2211yescharacteristic
30C2×C4×C8×C89C2211yescharacteristic
31#397×C89—21no—
32#397×C89—21no—
33#397×C89—21no—
34#396×C89—21no—
35#390×C89C2211yescharacteristic
36#390×C89C2211yescharacteristic
37#390×C89C2211yescharacteristic
38#390×C89C2211yescharacteristic
39#390×C89C2211yescharacteristic
40#389×C89C2211yescharacteristic
41#389×C89C2211yescharacteristic
42#389×C89C2211yescharacteristic
43#389×C89C2211yescharacteristic
44#389×C89C2211yescharacteristic
45#388×C89—21no—
46#388×C89—21no—
47#381×C89—21no—
48#380×C89—21no—
49C4×C4⋊C4×C89C2211yescharacteristic
50#376×C89C2211yescharacteristic
51#340×C89C2211yescharacteristic
52#340×C89C2211yescharacteristic
53#340×C89C2211yescharacteristic
54#340×C89C2211yescharacteristic
55#340×C89C2211yescharacteristic
56#340×C89C2211yescharacteristic
57#336×C89C2211yescharacteristic
58#336×C89C2211yescharacteristic
59C22×D4×C89C2311yescharacteristic
60C22×D4×C89C2311yescharacteristic
61C23×C4×C89—21no—
62C2×D8×C89—22no—
63C2×D8×C89—22no—
64C2×D8×C89—41no—
65C22×C8×C89C2311yescharacteristic
66C22×C8×C89C2311yescharacteristic
67C22×C8×C89C2311yescharacteristic
68C22×C8×C89C2311yescharacteristic
69C4×D4×C89—22no—
70C4×D4×C89—22no—
71C2×C4⋊C4×C89—21no—
72C2×C4⋊C4×C89—21no—
73C2×C4⋊C4×C89—21no—
74C2×C4⋊C4×C89—21no—
75C2×C4⋊C4×C89—21no—
76C2×C4⋊C4×C89C2311yescharacteristic
77C2×C4⋊C4×C89C2311yescharacteristic
78C2×C4⋊C4×C89C2311yescharacteristic
79C2×C4⋊C4×C89C2311yescharacteristic
80C2×C4⋊C4×C89C2311yescharacteristic
81C2×C4⋊C4×C89C2311yescharacteristic
82C2×C22⋊C4×C89—21no—
83C2×C22⋊C4×C89—21no—
84C2×C22⋊C4×C89—21no—
85C2×C22⋊C4×C89—21no—
86C2×C22⋊C4×C89—21no—
87C2×C22⋊C4×C89—21no—
88C2×C22⋊C4×C89—21no—
89C2×C22⋊C4×C89—21no—
90C2×C22⋊C4×C89—21no—
91C2×C22⋊C4×C89—21no—
92C2×C22⋊C4×C89—21no—
93C2×C42×C89—21no—
94C2×C42×C89C2311yescharacteristic
95C2×C42×C89C2311yescharacteristic
96C2×C42×C89C2311yescharacteristic
97#107×C89—22no—
98#106×C89—22no—
99#106×C89—41no—
100C4⋊C8×C89—22no—
101C4⋊C8×C89—22no—
102#102×C89—22no—
103#102×C89—22no—
104#102×C89—22no—
105#102×C89—22no—
106#102×C89—41no—
107#102×C89—41no—
108#97×C89—41no—
109C4×C8×C89—41no—
110#95×C89—21no—
111#95×C89—21no—
112#95×C89—21no—
113#95×C89—21no—
114#95×C89—21no—
115#95×C89—21no—
116#95×C89D411yescharacteristic
117#95×C89D411yescharacteristic
118#95×C89D411yescharacteristic
119#95×C89D411yescharacteristic
120C24×C89—21no—
121C24×C89—21no—
122C2×D4×C89—21no—
123C2×D4×C89—21no—
124C2×D4×C89—21no—
125C2×D4×C89—21no—
126C2×D4×C89—21no—
127C2×D4×C89—21no—
128C2×D4×C89—21no—
129C2×D4×C89—21no—
130C2×D4×C89—21no—
131C2×D4×C89—21no—
132C2×D4×C89—21no—
133C2×D4×C89#4112yes—
134C22×C4×C89—21no—
135C22×C4×C89—24no—
136C22×C4×C89—21no—
137C22×C4×C89—21no—
138C22×C4×C89—21no—
139C22×C4×C89—21no—
140C22×C4×C89—21no—
141C22×C4×C89—81no—
142C22×C4×C89—81no—
143C22×C4×C89C2×D411yescharacteristic
144C22×C4×C89C2×D411yescharacteristic
145C22×C4×C89C2×D411yescharacteristic
146C22×C4×C89C2×D411yescharacteristic
147C22×C4×C89C2×D411yescharacteristic
148C22×C4×C89C2×D411yescharacteristic
149C22×C4×C89C2411yescharacteristic
150D8×C89—44no—
151C2×C8×C89—21no—
152C2×C8×C89—21no—
153C2×C8×C89—21no—
154C2×C8×C89—21no—
155C2×C8×C89—21no—
156C2×C8×C89—21no—
157C2×C8×C89—21no—
158C2×C8×C89—21no—
159C2×C8×C89—21no—
160C2×C8×C89—21no—
161C2×C8×C89#4112yes—
162C2×C8×C89#4112yes—
163C4⋊C4×C89—21no—
164C4⋊C4×C89—21no—
165C4⋊C4×C89—21no—
166C4⋊C4×C89—21no—
167C4⋊C4×C89—21no—
168C4⋊C4×C89—21no—
169C4⋊C4×C89—21no—
170C4⋊C4×C89—21no—
171C4⋊C4×C89—21no—
172C4⋊C4×C89—21no—
173C4⋊C4×C89—21no—
174C4⋊C4×C89—81no—
175C4⋊C4×C89—81no—
176C4⋊C4×C89—81no—
177C4⋊C4×C89—81no—
178C4⋊C4×C89—81no—
179C4⋊C4×C89#4112yes—
180C22⋊C4×C89—24no—
181C22⋊C4×C89—81no—
182C22⋊C4×C89—81no—
183C22⋊C4×C89—81no—
184C22⋊C4×C89—81no—
185C22⋊C4×C89—81no—
186C22⋊C4×C89—81no—
187C22⋊C4×C89—81no—
188C22⋊C4×C89—81no—
189C22⋊C4×C89—81no—
190C22⋊C4×C89—81no—
191C42×C89—21no—
192C42×C89—21no—
193C42×C89—21no—
194C42×C89—21no—
195C42×C89—21no—
196C42×C89—21no—
197C42×C89—81no—
198C23×C89—22no—
199C23×C89—41no—
200C23×C89—41no—
201C23×C89—41no—
202C23×C89—41no—
203C23×C89—41no—
204C23×C89—41no—
205C23×C89—41no—
206C23×C89—41no—
207C23×C89—41no—
208C23×C89—41no—
209C23×C89—41no—
210C23×C89—41no—
211C23×C89—41no—
212C23×C89C22×D411yescharacteristic
213D4×C89—22no—
214D4×C89—22no—
215D4×C89—41no—
216D4×C89—41no—
217D4×C89—41no—
218D4×C89—41no—
219D4×C89—41no—
220D4×C89—41no—
221C2×C4×C89—21no—
222C2×C4×C89—21no—
223C2×C4×C89—22no—
224C2×C4×C89—21no—
225C2×C4×C89—21no—
226C2×C4×C89—21no—
227C2×C4×C89—21no—
228C2×C4×C89—21no—
229C2×C4×C89—21no—
230C2×C4×C89—21no—
231C2×C4×C89—21no—
232C2×C4×C89—21no—
233C2×C4×C89—21no—
234C2×C4×C89—21no—
235C2×C4×C89—21no—
236C2×C4×C89—21no—
237C2×C4×C89—21no—
238C2×C4×C89—21no—
239C2×C4×C89—21no—
240C2×C4×C89—41no—
241C2×C4×C89—41no—
242C2×C4×C89—41no—
243C2×C4×C89—41no—
244C2×C4×C89—41no—
245C2×C4×C89—41no—
246C2×C4×C89—41no—
247C2×C4×C89—41no—
248C2×C4×C89—41no—
249C2×C4×C89—41no—
250C2×C4×C89—41no—
251C2×C4×C89—41no—
252C2×C4×C89—41no—
253C2×C4×C89—41no—
254C2×C4×C89—41no—
255C2×C4×C89—41no—
256C2×C4×C89—41no—
257C2×C4×C89—84no—
258C2×C4×C89C2×#4111yescharacteristic
259C2×C4×C89C2×#4111yescharacteristic
260C2×C4×C89C2×#4111yescharacteristic
261C2×C4×C89C2×#4111yescharacteristic
262C2×C4×C89H(5,𝔽2)11yescharacteristic
263C2×C4×C892−1+411yescharacteristic
264C8×C89—22no—
265C8×C89—22no—
266C8×C89—41no—
267C8×C89—41no—
268C22×C89—42no—
269C22×C89—42no—
270C22×C89—42no—
271C22×C89—81no—
272C22×C89—81no—
273C22×C89—81no—
274C22×C89—81no—
275C22×C89—81no—
276C22×C89—81no—
277C22×C89—81no—
278C22×C89—81no—
279C22×C89—81no—
280C22×C89—81no—
281C22×C89—81no—
282C22×C89#52511yescharacteristic
283C22×C89#53211yescharacteristic
284C22×C89#53711yescharacteristic
285C22×C89#57611yescharacteristic
286C22×C89#57611yescharacteristic
287C22×C89#57711yescharacteristic
288C22×C89#57711yescharacteristic
289C4×C89—41no—
290C4×C89—42no—
291C4×C89—41no—
292C4×C89—41no—
293C4×C89—41no—
294C4×C89—41no—
295C4×C89—41no—
296C4×C89—81no—
297C4×C89—81no—
298C4×C89—81no—
299C4×C89—81no—
300C4×C89—81no—
301C4×C89#55111yescharacteristic
302C4×C89#55211yescharacteristic
303C4×C89#55311yescharacteristic
304C4×C89#55611yescharacteristic
305#29437C8911yesmaximal, characteristic, direct product factor, Sylow
306C2×C89—82no—
307C2×C89—161no—
308C2×C89#260111yescharacteristic
309C2×C89#311811yescharacteristic
310C2×C89#311911yescharacteristic
311C2×C89#317311yescharacteristic
312C2×C89#317611yescharacteristic
313C2×C89#325711yescharacteristic
314C2×C89#325711yescharacteristic
315#2644C2×C8911yescharacteristic, complemented
316#2319C2×C8911yescharacteristic, complemented
317#2086C2×C8911yescharacteristic, complemented
318#2065C2×C8911yescharacteristic, complemented
319#2065C2×C8911yescharacteristic, complemented
320#2054C2×C8911yescharacteristic
321#1970C2×C8911yescharacteristic
322#1941C2×C8911yescharacteristic, complemented
323#1936C2×C8911yescharacteristic, complemented
324#1936C2×C8911yescharacteristic, complemented
325#1926C2×C8911yescharacteristic, complemented
326#1918C2×C8911yescharacteristic, complemented
327#1879C2×C8911yescharacteristic
328#1864C2×C8911yescharacteristic, complemented
329#1768C2×C8911yescharacteristic, complemented
330C89#2943711yescharacteristic, direct product factor, Sylow
331C22×D8C22×C8911yescharacteristic
332C2×C4×D4C22×C8911yescharacteristic
333C2×#107C22×C8911yescharacteristic
334C2×#106C22×C8911yescharacteristic
335C2×#106C22×C8911yescharacteristic
336C2×C4⋊C8C22×C8911yescharacteristic
337C2×C4⋊C8C22×C8911yescharacteristic
338C2×#102C22×C8911yescharacteristic
339C2×#102C22×C8911yescharacteristic
340C2×#102C22×C8911yescharacteristic
341C2×#102C22×C8911yescharacteristic
342C2×#102C22×C8911yescharacteristic
343C2×#102C22×C8911yescharacteristic
344C2×#97C22×C8911yescharacteristic
345C2×C4×C8C22×C8911yescharacteristic
346#397—21no—
347#397—21no—
348#397—21no—
349#396—21no—
350#390C22×C8911yescharacteristic
351#390C22×C8911yescharacteristic
352#390C22×C8911yescharacteristic
353#390C22×C8911yescharacteristic
354#390C22×C8911yescharacteristic
355#389C22×C8911yescharacteristic
356#389C22×C8911yescharacteristic
357#389C22×C8911yescharacteristic
358#389C22×C8911yescharacteristic
359#389C22×C8911yescharacteristic
360#388—21no—
361#388—21no—
362#381—21no—
363#380—21no—
364C4×C4⋊C4C22×C8911yescharacteristic
365#376C22×C8911yescharacteristic
366#340C22×C8911yescharacteristic
367#340C22×C8911yescharacteristic
368#340C22×C8911yescharacteristic
369#340C22×C8911yescharacteristic
370#340C22×C8911yescharacteristic
371#340C22×C8911yescharacteristic
372#336C22×C8911yescharacteristic
373#336C22×C8911yescharacteristic
374C22×D4C23×C8911yescharacteristic
375C22×D4C23×C8911yescharacteristic
376C23×C4—21no—
377C2×D8—22no—
378C2×D8—22no—
379C2×D8—41no—
380C22×C8C23×C8911yescharacteristic
381C22×C8C23×C8911yescharacteristic
382C22×C8C23×C8911yescharacteristic
383C22×C8C23×C8911yescharacteristic
384C4×D4—22no—
385C4×D4—22no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4C23×C8911yescharacteristic
392C2×C4⋊C4C23×C8911yescharacteristic
393C2×C4⋊C4C23×C8911yescharacteristic
394C2×C4⋊C4C23×C8911yescharacteristic
395C2×C4⋊C4C23×C8911yescharacteristic
396C2×C4⋊C4C23×C8911yescharacteristic
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C42—21no—
409C2×C42C23×C8911yescharacteristic
410C2×C42C23×C8911yescharacteristic
411C2×C42C23×C8911yescharacteristic
412#107—22no—
413#106—22no—
414#106—41no—
415C4⋊C8—22no—
416C4⋊C8—22no—
417#102—22no—
418#102—22no—
419#102—22no—
420#102—22no—
421#102—41no—
422#102—41no—
423#97—41no—
424C4×C8—41no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95D4×C8911yescharacteristic
432#95D4×C8911yescharacteristic
433#95D4×C8911yescharacteristic
434#95D4×C8911yescharacteristic
435C24—21no—
436C24—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4#41×C8912yes—
449C22×C4—21no—
450C22×C4—24no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—81no—
457C22×C4—81no—
458C22×C4C2×D4×C8911yescharacteristic
459C22×C4C2×D4×C8911yescharacteristic
460C22×C4C2×D4×C8911yescharacteristic
461C22×C4C2×D4×C8911yescharacteristic
462C22×C4C2×D4×C8911yescharacteristic
463C22×C4C2×D4×C8911yescharacteristic
464C22×C4C24×C8911yescharacteristic
465D8—44no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8#41×C8912yes—
477C2×C8#41×C8912yes—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—81no—
490C4⋊C4—81no—
491C4⋊C4—81no—
492C4⋊C4—81no—
493C4⋊C4—81no—
494C4⋊C4#41×C8912yes—
495C22⋊C4—24no—
496C22⋊C4—81no—
497C22⋊C4—81no—
498C22⋊C4—81no—
499C22⋊C4—81no—
500C22⋊C4—81no—
501C22⋊C4—81no—
502C22⋊C4—81no—
503C22⋊C4—81no—
504C22⋊C4—81no—
505C22⋊C4—81no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—21no—
512C42—81no—
513C23—22no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23C22×D4×C8911yescharacteristic
528D4—22no—
529D4—22no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—84no—
573C2×C4C2×#41×C8911yescharacteristic
574C2×C4C2×#41×C8911yescharacteristic
575C2×C4C2×#41×C8911yescharacteristic
576C2×C4C2×#41×C8911yescharacteristic
577C2×C4H(5,𝔽2)×C8911yescharacteristic
578C2×C42−1+4×C8911yescharacteristic
579C8—22no—
580C8—22no—
581C8—41no—
582C8—41no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22#525×C8911yescharacteristic
598C22#532×C8911yescharacteristic
599C22#537×C8911yescharacteristic
600C22#576×C8911yescharacteristic
601C22#576×C8911yescharacteristic
602C22#577×C8911yescharacteristic
603C22#577×C8911yescharacteristic
604C4—41no—
605C4—42no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—81no—
612C4—81no—
613C4—81no—
614C4—81no—
615C4—81no—
616C4#551×C8911yescharacteristic
617C4#552×C8911yescharacteristic
618C4#553×C8911yescharacteristic
619C4#556×C8911yescharacteristic
620C2—82no—
621C2—161no—
622C2C89×#260111yescharacteristic
623C2C89×#311811yescharacteristic
624C2C89×#311911yescharacteristic
625C2C89×#317311yescharacteristic
626C2C89×#317611yescharacteristic
627C2C89×#325711yescharacteristic
628C2C89×#325711yescharacteristic
subgroupG/H
center, socleC23×C89C22×D4
commutator, Frattini, cosocleC22×C4C24×C89
prime radicalC22×D8×C89C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C89 ◁ #376×C89 ◁ G

Complements

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

NH ≅ G/Ntype
1. C89×#2644C2semidirect
2. C89×#2319C2semidirect
3. C89×#2086C2semidirect
4. C89×#2065C2semidirect
5. C89×#2065C2semidirect
8. C89×#1941C2semidirect
9. C89×#1936C2semidirect
10. C89×#1936C2semidirect
11. C89×#1926C2semidirect
12. C89×#1918C2semidirect
14. C89×#1864C2semidirect
15. C89×#1768C2semidirect
305. #29437C89direct (N × H)
315. #2644C2×C89semidirect
316. #2319C2×C89semidirect
317. #2086C2×C89semidirect
318. #2065C2×C89semidirect
319. #2065C2×C89semidirect
322. #1941C2×C89semidirect
323. #1936C2×C89semidirect
324. #1936C2×C89semidirect
325. #1926C2×C89semidirect
326. #1918C2×C89semidirect
328. #1864C2×C89semidirect
329. #1768C2×C89semidirect
330. C89#29437direct (N × H)

Maximal subgroups

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

subgroupindex
C89×#26442
C89×#23192
C89×#20862
C89×#20652
C89×#20542
C89×#19702
C89×#19412
C89×#19362
C89×#19262
C89×#19182
C89×#18792
C89×#18642
C89×#17682
#2943789