Finite Group Databasebeta

← C89×#22889 #36400737

Subgroups — C89×#22889 #36400737

Order 22784.

1020 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#3002C211yesmaximal, characteristic
2C2×#443×C89C211yesmaximal, characteristic, complemented
3C89×#2933C211yesmaximal, characteristic, complemented
4C2×#421×C89C211yesmaximal, characteristic, complemented
5C89×#2880C211yesmaximal, characteristic, complemented
6C89×#1975C211yesmaximal, characteristic, complemented
7C89×#1937C211yesmaximal, characteristic, complemented
8C89×#1929C211yesmaximal, characteristic, complemented
9C89×#1897C211yesmaximal, characteristic, complemented
10C89×#1876C211yesmaximal, characteristic, complemented
11C89×#1876C211yesmaximal, characteristic, complemented
12C89×#1866C211yesmaximal, characteristic, complemented
13C89×#1855C211yesmaximal, characteristic, complemented
14C89×#1765C211yesmaximal, characteristic, complemented
15C89×#1750C211yesmaximal, characteristic, complemented
16C22×#41×C89C2211yescharacteristic
17C2×#135×C89C2211yescharacteristic
18C2×#135×C89C2211yescharacteristic
19C2×#131×C89C2211yescharacteristic
20C2×#131×C89C2211yescharacteristic
21C2×#131×C89C2211yescharacteristic, complemented
22C22×M16×C89C2211yescharacteristic
23#525×C89C2211yescharacteristic
24C2×#117×C89C2211yescharacteristic
25#452×C89C411yescharacteristic, complemented
26#452×C89C411yescharacteristic, complemented
27#451×C89C411yescharacteristic, complemented
28#450×C89C411yescharacteristic, complemented
29#449×C89C411yescharacteristic, complemented
30#449×C89C411yescharacteristic, complemented
31#448×C89C411yescharacteristic, complemented
32#447×C89C411yescharacteristic, complemented
33#443×C89—24no—
34#436×C89—21no—
35#435×C89—21no—
36#435×C89—21no—
37C8×D4×C89—21no—
38C2×#108×C89C2211yescharacteristic, complemented
39C2×#108×C89C2211yescharacteristic, complemented
40#424×C89C2211yescharacteristic, complemented
41#421×C89—24no—
42C2×#104×C89C2211yescharacteristic
43C2×#104×C89C2211yescharacteristic
44C2×#104×C89C2211yescharacteristic
45C2×#104×C89C2211yescharacteristic
46C2×#104×C89C2211yescharacteristic, complemented
47C2×#104×C89C2211yescharacteristic, complemented
48#416×C89C2211yescharacteristic
49#416×C89C2211yescharacteristic
50#408×C89—21no—
51#408×C89—21no—
52#408×C89C2211yescharacteristic
53#408×C89C2211yescharacteristic
54#408×C89C2211yescharacteristic, complemented
55#407×C89—21no—
56#407×C89C2211yescharacteristic
57C2×C22⋊C8×C89—21no—
58C2×C22⋊C8×C89C2211yescharacteristic
59C2×C22⋊C8×C89C2211yescharacteristic
60#405×C89C2211yescharacteristic, complemented
61C2×#97×C89C2211yescharacteristic, complemented
62C2×C4×C8×C89C2211yescharacteristic, complemented
63#341×C89C2211yescharacteristic, complemented
64#341×C89C2211yescharacteristic, complemented
65#339×C89C2211yescharacteristic, complemented
66#339×C89C2211yescharacteristic, complemented
67#336×C89C2211yescharacteristic, complemented
68#336×C89C2211yescharacteristic, complemented
69C2×#41×C89—21no—
70C2×#41×C89—21no—
71C2×#41×C89—22no—
72C2×#41×C89—22no—
73C2×#41×C89—41no—
74C2×#41×C89—41no—
75C2×#41×C89C2×C411yescharacteristic
76C2×#41×C89C2×C411yescharacteristic
77C2×#41×C89C2311yescharacteristic
78C2×#41×C89C2311yescharacteristic
79C2×#41×C89C2311yescharacteristic
80C22×Q8×C89C2×C411yescharacteristic
81C22×D4×C89—21no—
82C22×D4×C89C2×C411yescharacteristic
83C23×C4×C89—21no—
84C23×C4×C89C2311yescharacteristic
85#135×C89—22no—
86#135×C89—22no—
87#135×C89—41no—
88#135×C89—41no—
89C2×Q16×C89C2×C411yescharacteristic
90C2×Q16×C89C2×C411yescharacteristic
91C2×SD16×C89C2×C411yescharacteristic
92C2×SD16×C89C2×C411yescharacteristic
93C2×SD16×C89C2×C411yescharacteristic
94C2×SD16×C89C2×C411yescharacteristic
95C2×D8×C89C2×C411yescharacteristic
96C2×D8×C89C2×C411yescharacteristic
97#131×C89—22no—
98#131×C89—22no—
99#131×C89—22no—
100#131×C89—41no—
101#131×C89—41no—
102#131×C89—41no—
103C2×M16×C89—21no—
104C2×M16×C89—21no—
105C2×M16×C89—21no—
106C2×M16×C89—21no—
107C2×M16×C89—22no—
108C2×M16×C89—41no—
109C2×M16×C89C2311yescharacteristic
110C2×M16×C89C2311yescharacteristic
111C2×M16×C89C2311yescharacteristic
112C2×M16×C89C2311yescharacteristic
113C22×C8×C89—21no—
114C22×C8×C89—21no—
115C22×C8×C89—21no—
116C22×C8×C89—21no—
117C22×C8×C89C2311yescharacteristic
118C22×C8×C89C2311yescharacteristic
119C22×C8×C89C2311yescharacteristic
120C22×C8×C89C2311yescharacteristic
121#123×C89—21no—
122C22⋊Q8×C89C2×C411yescharacteristic
123C22⋊Q8×C89C2×C411yescharacteristic
124#121×C89C2×C411yescharacteristic
125#121×C89C2×C411yescharacteristic
126#120×C89—21no—
127C4×D4×C89—21no—
128C4×D4×C89—21no—
129#117×C89—22no—
130#117×C89—41no—
131#117×C89C2311yescharacteristic
132C2×C4⋊C4×C89—21no—
133C2×C22⋊C4×C89—21no—
134C2×C42×C89C2311yescharacteristic
135C2×C42×C89C2311yescharacteristic
136#108×C89—22no—
137#108×C89—41no—
138C4⋊C8×C89—21no—
139C4⋊C8×C89—21no—
140#104×C89—22no—
141#104×C89—22no—
142#104×C89—22no—
143#104×C89—22no—
144#104×C89—41no—
145#104×C89D414yescomplemented
146#103×C89C2×C411yescharacteristic
147#103×C89C2×C411yescharacteristic
148#103×C89C2×C411yescharacteristic
149#103×C89C2×C411yescharacteristic
150#102×C89C2×C411yescharacteristic
151#102×C89C2×C411yescharacteristic
152#102×C89C2×C411yescharacteristic
153#102×C89C2×C411yescharacteristic
154C22⋊C8×C89—21no—
155C22⋊C8×C89—21no—
156C22⋊C8×C89—21no—
157C22⋊C8×C89—21no—
158C22⋊C8×C89—21no—
159C22⋊C8×C89—21no—
160C22⋊C8×C89—21no—
161C22⋊C8×C89—21no—
162C22⋊C8×C89C2×C411yescharacteristic
163C22⋊C8×C89C2×C411yescharacteristic
164C22⋊C8×C89C2×C411yescharacteristic
165C22⋊C8×C89C2×C411yescharacteristic
166C22⋊C8×C89D411yescharacteristic
167C22⋊C8×C89D411yescharacteristic
168C22⋊C8×C89D411yescharacteristic
169C22⋊C8×C89D411yescharacteristic
170#97×C89—21no—
171#97×C89—41no—
172C4×C8×C89—21no—
173C4×C8×C89—22no—
174C24×C89—21no—
175C24×C89#4111yescharacteristic
176#41×C89—21no—
177#41×C89—21no—
178#41×C89—22no—
179#41×C89—22no—
180#41×C89—21no—
181#41×C89—21no—
182#41×C89—21no—
183#41×C89—21no—
184#41×C89—21no—
185#41×C89—21no—
186#41×C89—21no—
187#41×C89—21no—
188#41×C89—42no—
189#41×C89—42no—
190#41×C89—41no—
191#41×C89—41no—
192#41×C89—42no—
193#41×C89—42no—
194#41×C89C2×D412yes—
195#41×C89#4112yes—
196C2×Q8×C89—21no—
197C2×Q8×C89—22no—
198C2×Q8×C89—41no—
199C2×Q8×C89C22×C411yescharacteristic
200C2×Q8×C89C22×C411yescharacteristic
201C2×Q8×C89C22×C411yescharacteristic
202C2×D4×C89—21no—
203C2×D4×C89—22no—
204C2×D4×C89—21no—
205C2×D4×C89—21no—
206C2×D4×C89—21no—
207C2×D4×C89—21no—
208C2×D4×C89—21no—
209C2×D4×C89—21no—
210C2×D4×C89—21no—
211C2×D4×C89—41no—
212C2×D4×C89—42no—
213C2×D4×C89—42no—
214C2×D4×C89C22×C411yescharacteristic
215C2×D4×C89C22×C411yescharacteristic
216C2×D4×C89C22×C411yescharacteristic
217C22×C4×C89—21no—
218C22×C4×C89—21no—
219C22×C4×C89—21no—
220C22×C4×C89—21no—
221C22×C4×C89—21no—
222C22×C4×C89—21no—
223C22×C4×C89—21no—
224C22×C4×C89—21no—
225C22×C4×C89—21no—
226C22×C4×C89—21no—
227C22×C4×C89—21no—
228C22×C4×C89—21no—
229C22×C4×C89—42no—
230C22×C4×C89—42no—
231C22×C4×C89C22×C411yescharacteristic
232C22×C4×C89C22×C411yescharacteristic
233C22×C4×C89C2×D411yescharacteristic
234C22×C4×C89C2×D411yescharacteristic
235C22×C4×C89#4111yescharacteristic
236C22×C4×C89C2411yescharacteristic
237Q16×C89—22no—
238Q16×C89—41no—
239SD16×C89—22no—
240SD16×C89—22no—
241SD16×C89—41no—
242SD16×C89—41no—
243D8×C89—22no—
244D8×C89—41no—
245M16×C89—21no—
246M16×C89—21no—
247M16×C89—21no—
248M16×C89—21no—
249M16×C89—21no—
250M16×C89—21no—
251M16×C89—21no—
252M16×C89—42no—
253M16×C89—42no—
254M16×C89—42no—
255M16×C89—42no—
256M16×C89C2×D412yes—
257C2×C8×C89—21no—
258C2×C8×C89—21no—
259C2×C8×C89—21no—
260C2×C8×C89—21no—
261C2×C8×C89—21no—
262C2×C8×C89—21no—
263C2×C8×C89—21no—
264C2×C8×C89—21no—
265C2×C8×C89—21no—
266C2×C8×C89—21no—
267C2×C8×C89—21no—
268C2×C8×C89—21no—
269C2×C8×C89—42no—
270C2×C8×C89—42no—
271C2×C8×C89—42no—
272C2×C8×C89—42no—
273C2×C8×C89C22×C411yescharacteristic
274C2×C8×C89C22×C411yescharacteristic
275C2×C8×C89C22×C411yescharacteristic
276C2×C8×C89C22×C411yescharacteristic
277C2×C8×C89C2×D411yescharacteristic
278C2×C8×C89C2×D411yescharacteristic
279C2×C8×C89C2×D411yescharacteristic
280C2×C8×C89C2×D411yescharacteristic
281C4⋊C4×C89—21no—
282C4⋊C4×C89—21no—
283C4⋊C4×C89—42no—
284C4⋊C4×C89C22×C411yescharacteristic
285C4⋊C4×C89C22×C411yescharacteristic
286C22⋊C4×C89—21no—
287C22⋊C4×C89—21no—
288C22⋊C4×C89—21no—
289C22⋊C4×C89—21no—
290C22⋊C4×C89—21no—
291C22⋊C4×C89—42no—
292C42×C89—21no—
293C42×C89—21no—
294C42×C89—21no—
295C42×C89—21no—
296C42×C89C2×D412yes—
297C23×C89—21no—
298C23×C89—21no—
299C23×C89—21no—
300C23×C89—21no—
301C23×C89—21no—
302C23×C89—41no—
303C23×C89—41no—
304C23×C89—42no—
305C23×C89—42no—
306C23×C89—81no—
307C23×C89C4×D411yescharacteristic
308C23×C89C4×D411yescharacteristic
309C23×C89C2×#4111yescharacteristic
310Q8×C89—21no—
311Q8×C89—21no—
312Q8×C89—21no—
313Q8×C89—21no—
314Q8×C89—21no—
315Q8×C89—42no—
316Q8×C89C4×D412yes—
317D4×C89—22no—
318D4×C89—22no—
319D4×C89—21no—
320D4×C89—21no—
321D4×C89—21no—
322D4×C89—21no—
323D4×C89—21no—
324D4×C89—42no—
325D4×C89—42no—
326D4×C89—42no—
327D4×C89—42no—
328D4×C89—41no—
329D4×C89—41no—
330D4×C89—41no—
331D4×C89—41no—
332D4×C89—81no—
333D4×C89C4×D412yes—
334C2×C4×C89—21no—
335C2×C4×C89—21no—
336C2×C4×C89—21no—
337C2×C4×C89—21no—
338C2×C4×C89—21no—
339C2×C4×C89—21no—
340C2×C4×C89—21no—
341C2×C4×C89—21no—
342C2×C4×C89—22no—
343C2×C4×C89—21no—
344C2×C4×C89—22no—
345C2×C4×C89—21no—
346C2×C4×C89—21no—
347C2×C4×C89—21no—
348C2×C4×C89—21no—
349C2×C4×C89—21no—
350C2×C4×C89—21no—
351C2×C4×C89—22no—
352C2×C4×C89—42no—
353C2×C4×C89—42no—
354C2×C4×C89—42no—
355C2×C4×C89—41no—
356C2×C4×C89—41no—
357C2×C4×C89—41no—
358C2×C4×C89—41no—
359C2×C4×C89—41no—
360C2×C4×C89—41no—
361C2×C4×C89—41no—
362C2×C4×C89—41no—
363C2×C4×C89—41no—
364C2×C4×C89C4×D411yescharacteristic
365C2×C4×C89C4×D411yescharacteristic
366C2×C4×C89C23×C411yescharacteristic
367C2×C4×C89C22×D411yescharacteristic
368C2×C4×C89C22×D411yescharacteristic
369C2×C4×C89C2×#4111yescharacteristic
370C2×C4×C89H(5,𝔽2)11yescharacteristic
371C2×C4×C89H(5,𝔽2)11yescharacteristic
372C8×C89—21no—
373C8×C89—21no—
374C8×C89—21no—
375C8×C89—21no—
376C8×C89—21no—
377C8×C89—21no—
378C8×C89—22no—
379C8×C89—21no—
380C8×C89—21no—
381C8×C89—41no—
382C8×C89—41no—
383C8×C89—41no—
384C22×C89—21no—
385C22×C89—21no—
386C22×C89—21no—
387C22×C89—21no—
388C22×C89—22no—
389C22×C89—21no—
390C22×C89—21no—
391C22×C89—21no—
392C22×C89—21no—
393C22×C89—41no—
394C22×C89—41no—
395C22×C89—41no—
396C22×C89—41no—
397C22×C89—41no—
398C22×C89—41no—
399C22×C89—41no—
400C22×C89—41no—
401C22×C89—81no—
402C22×C89—81no—
403C22×C89—84no—
404C22×C89C2×C4×D411yescharacteristic
405C22×C89#54611yescharacteristic
406C22×C89#55111yescharacteristic
407C4×C89—21no—
408C4×C89—21no—
409C4×C89—22no—
410C4×C89—42no—
411C4×C89—41no—
412C4×C89—41no—
413C4×C89—41no—
414C4×C89—41no—
415C4×C89—81no—
416C4×C89C2×C4×D411yescharacteristic
417C4×C89#51811yescharacteristic
418C4×C89D4211yescharacteristic
419C4×C89#54611yescharacteristic
420#22889C8911yesmaximal, characteristic, direct product factor, Sylow
421C2×C89—21no—
422C2×C89—21no—
423C2×C89—41no—
424C2×C89—41no—
425C2×C89—42no—
426C2×C89—81no—
427C2×C89—81no—
428C2×C89#235811yescharacteristic
429C2×C89#295511yescharacteristic
430C2×C89#295711yescharacteristic
431#3002C2×C8911yescharacteristic
432C2×#443C2×C8911yescharacteristic, complemented
433#2933C2×C8911yescharacteristic, complemented
434C2×#421C2×C8911yescharacteristic, complemented
435#2880C2×C8911yescharacteristic, complemented
436#1975C2×C8911yescharacteristic, complemented
437#1937C2×C8911yescharacteristic, complemented
438#1929C2×C8911yescharacteristic, complemented
439#1897C2×C8911yescharacteristic, complemented
440#1876C2×C8911yescharacteristic, complemented
441#1876C2×C8911yescharacteristic, complemented
442#1866C2×C8911yescharacteristic, complemented
443#1855C2×C8911yescharacteristic, complemented
444#1765C2×C8911yescharacteristic, complemented
445#1750C2×C8911yescharacteristic, complemented
446C89#2288911yescharacteristic, direct product factor, Sylow
447C22×#41C22×C8911yescharacteristic
448C2×#135C22×C8911yescharacteristic
449C2×#135C22×C8911yescharacteristic
450C2×#131C22×C8911yescharacteristic
451C2×#131C22×C8911yescharacteristic
452C2×#131C22×C8911yescharacteristic, complemented
453C22×M16C22×C8911yescharacteristic
454#525C22×C8911yescharacteristic
455C2×#117C22×C8911yescharacteristic
456#452C4×C8911yescharacteristic, complemented
457#452C4×C8911yescharacteristic, complemented
458#451C4×C8911yescharacteristic, complemented
459#450C4×C8911yescharacteristic, complemented
460#449C4×C8911yescharacteristic, complemented
461#449C4×C8911yescharacteristic, complemented
462#448C4×C8911yescharacteristic, complemented
463#447C4×C8911yescharacteristic, complemented
464#443—24no—
465#436—21no—
466#435—21no—
467#435—21no—
468C8×D4—21no—
469C2×#108C22×C8911yescharacteristic, complemented
470C2×#108C22×C8911yescharacteristic, complemented
471#424C22×C8911yescharacteristic, complemented
472#421—24no—
473C2×#104C22×C8911yescharacteristic
474C2×#104C22×C8911yescharacteristic
475C2×#104C22×C8911yescharacteristic
476C2×#104C22×C8911yescharacteristic
477C2×#104C22×C8911yescharacteristic, complemented
478C2×#104C22×C8911yescharacteristic, complemented
479#416C22×C8911yescharacteristic
480#416C22×C8911yescharacteristic
481#408—21no—
482#408—21no—
483#408C22×C8911yescharacteristic
484#408C22×C8911yescharacteristic
485#408C22×C8911yescharacteristic, complemented
486#407—21no—
487#407C22×C8911yescharacteristic
488C2×C22⋊C8—21no—
489C2×C22⋊C8C22×C8911yescharacteristic
490C2×C22⋊C8C22×C8911yescharacteristic
491#405C22×C8911yescharacteristic, complemented
492C2×#97C22×C8911yescharacteristic, complemented
493C2×C4×C8C22×C8911yescharacteristic, complemented
494#341C22×C8911yescharacteristic, complemented
495#341C22×C8911yescharacteristic, complemented
496#339C22×C8911yescharacteristic, complemented
497#339C22×C8911yescharacteristic, complemented
498#336C22×C8911yescharacteristic, complemented
499#336C22×C8911yescharacteristic, complemented
500C2×#41—21no—
501C2×#41—21no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41C2×C4×C8911yescharacteristic
507C2×#41C2×C4×C8911yescharacteristic
508C2×#41C23×C8911yescharacteristic
509C2×#41C23×C8911yescharacteristic
510C2×#41C23×C8911yescharacteristic
511C22×Q8C2×C4×C8911yescharacteristic
512C22×D4—21no—
513C22×D4C2×C4×C8911yescharacteristic
514C23×C4—21no—
515C23×C4C23×C8911yescharacteristic
516#135—22no—
517#135—22no—
518#135—41no—
519#135—41no—
520C2×Q16C2×C4×C8911yescharacteristic
521C2×Q16C2×C4×C8911yescharacteristic
522C2×SD16C2×C4×C8911yescharacteristic
523C2×SD16C2×C4×C8911yescharacteristic
524C2×SD16C2×C4×C8911yescharacteristic
525C2×SD16C2×C4×C8911yescharacteristic
526C2×D8C2×C4×C8911yescharacteristic
527C2×D8C2×C4×C8911yescharacteristic
528#131—22no—
529#131—22no—
530#131—22no—
531#131—41no—
532#131—41no—
533#131—41no—
534C2×M16—21no—
535C2×M16—21no—
536C2×M16—21no—
537C2×M16—21no—
538C2×M16—22no—
539C2×M16—41no—
540C2×M16C23×C8911yescharacteristic
541C2×M16C23×C8911yescharacteristic
542C2×M16C23×C8911yescharacteristic
543C2×M16C23×C8911yescharacteristic
544C22×C8—21no—
545C22×C8—21no—
546C22×C8—21no—
547C22×C8—21no—
548C22×C8C23×C8911yescharacteristic
549C22×C8C23×C8911yescharacteristic
550C22×C8C23×C8911yescharacteristic
551C22×C8C23×C8911yescharacteristic
552#123—21no—
553C22⋊Q8C2×C4×C8911yescharacteristic
554C22⋊Q8C2×C4×C8911yescharacteristic
555#121C2×C4×C8911yescharacteristic
556#121C2×C4×C8911yescharacteristic
557#120—21no—
558C4×D4—21no—
559C4×D4—21no—
560#117—22no—
561#117—41no—
562#117C23×C8911yescharacteristic
563C2×C4⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C42C23×C8911yescharacteristic
566C2×C42C23×C8911yescharacteristic
567#108—22no—
568#108—41no—
569C4⋊C8—21no—
570C4⋊C8—21no—
571#104—22no—
572#104—22no—
573#104—22no—
574#104—22no—
575#104—41no—
576#104D4×C8914yescomplemented
577#103C2×C4×C8911yescharacteristic
578#103C2×C4×C8911yescharacteristic
579#103C2×C4×C8911yescharacteristic
580#103C2×C4×C8911yescharacteristic
581#102C2×C4×C8911yescharacteristic
582#102C2×C4×C8911yescharacteristic
583#102C2×C4×C8911yescharacteristic
584#102C2×C4×C8911yescharacteristic
585C22⋊C8—21no—
586C22⋊C8—21no—
587C22⋊C8—21no—
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8—21no—
591C22⋊C8—21no—
592C22⋊C8—21no—
593C22⋊C8C2×C4×C8911yescharacteristic
594C22⋊C8C2×C4×C8911yescharacteristic
595C22⋊C8C2×C4×C8911yescharacteristic
596C22⋊C8C2×C4×C8911yescharacteristic
597C22⋊C8D4×C8911yescharacteristic
598C22⋊C8D4×C8911yescharacteristic
599C22⋊C8D4×C8911yescharacteristic
600C22⋊C8D4×C8911yescharacteristic
601#97—21no—
602#97—41no—
603C4×C8—21no—
604C4×C8—22no—
605C24—21no—
606C24#41×C8911yescharacteristic
607#41—21no—
608#41—21no—
609#41—22no—
610#41—22no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—21no—
619#41—42no—
620#41—42no—
621#41—41no—
622#41—41no—
623#41—42no—
624#41—42no—
625#41C2×D4×C8912yes—
626#41#41×C8912yes—
627C2×Q8—21no—
628C2×Q8—22no—
629C2×Q8—41no—
630C2×Q8C22×C4×C8911yescharacteristic
631C2×Q8C22×C4×C8911yescharacteristic
632C2×Q8C22×C4×C8911yescharacteristic
633C2×D4—21no—
634C2×D4—22no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—41no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4C22×C4×C8911yescharacteristic
646C2×D4C22×C4×C8911yescharacteristic
647C2×D4C22×C4×C8911yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4C22×C4×C8911yescharacteristic
663C22×C4C22×C4×C8911yescharacteristic
664C22×C4C2×D4×C8911yescharacteristic
665C22×C4C2×D4×C8911yescharacteristic
666C22×C4#41×C8911yescharacteristic
667C22×C4C24×C8911yescharacteristic
668Q16—22no—
669Q16—41no—
670SD16—22no—
671SD16—22no—
672SD16—41no—
673SD16—41no—
674D8—22no—
675D8—41no—
676M16—21no—
677M16—21no—
678M16—21no—
679M16—21no—
680M16—21no—
681M16—21no—
682M16—21no—
683M16—42no—
684M16—42no—
685M16—42no—
686M16—42no—
687M16C2×D4×C8912yes—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—42no—
701C2×C8—42no—
702C2×C8—42no—
703C2×C8—42no—
704C2×C8C22×C4×C8911yescharacteristic
705C2×C8C22×C4×C8911yescharacteristic
706C2×C8C22×C4×C8911yescharacteristic
707C2×C8C22×C4×C8911yescharacteristic
708C2×C8C2×D4×C8911yescharacteristic
709C2×C8C2×D4×C8911yescharacteristic
710C2×C8C2×D4×C8911yescharacteristic
711C2×C8C2×D4×C8911yescharacteristic
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—42no—
715C4⋊C4C22×C4×C8911yescharacteristic
716C4⋊C4C22×C4×C8911yescharacteristic
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—42no—
723C42—21no—
724C42—21no—
725C42—21no—
726C42—21no—
727C42C2×D4×C8912yes—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—81no—
738C23C4×D4×C8911yescharacteristic
739C23C4×D4×C8911yescharacteristic
740C23C2×#41×C8911yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—21no—
744Q8—21no—
745Q8—21no—
746Q8—42no—
747Q8C4×D4×C8912yes—
748D4—22no—
749D4—22no—
750D4—21no—
751D4—21no—
752D4—21no—
753D4—21no—
754D4—21no—
755D4—42no—
756D4—42no—
757D4—42no—
758D4—42no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—41no—
763D4—81no—
764D4C4×D4×C8912yes—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4C4×D4×C8911yescharacteristic
796C2×C4C4×D4×C8911yescharacteristic
797C2×C4C23×C4×C8911yescharacteristic
798C2×C4C22×D4×C8911yescharacteristic
799C2×C4C22×D4×C8911yescharacteristic
800C2×C4C2×#41×C8911yescharacteristic
801C2×C4H(5,𝔽2)×C8911yescharacteristic
802C2×C4H(5,𝔽2)×C8911yescharacteristic
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C8—21no—
808C8—21no—
809C8—22no—
810C8—21no—
811C8—21no—
812C8—41no—
813C8—41no—
814C8—41no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—22no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—81no—
833C22—81no—
834C22—84no—
835C22C2×C4×D4×C8911yescharacteristic
836C22#546×C8911yescharacteristic
837C22#551×C8911yescharacteristic
838C4—21no—
839C4—21no—
840C4—22no—
841C4—42no—
842C4—41no—
843C4—41no—
844C4—41no—
845C4—41no—
846C4—81no—
847C4C2×C4×D4×C8911yescharacteristic
848C4#518×C8911yescharacteristic
849C4D42×C8911yescharacteristic
850C4#546×C8911yescharacteristic
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—42no—
856C2—81no—
857C2—81no—
858C2C89×#235811yescharacteristic
859C2C89×#295511yescharacteristic
860C2C89×#295711yescharacteristic
subgroupG/H
centerC2×C4×C89C22×D4
commutatorC2×C4C23×C4×C89
Frattini, cosocleC22×C4C24×C89
socleC22×C89C2×C4×D4
prime radicalC89×#3002C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C89 ◁ C2×C22⋊C8×C89 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#443×C89C2semidirect
3. C89×#2933C2semidirect
4. C2×#421×C89C2semidirect
5. C89×#2880C2semidirect
6. C89×#1975C2semidirect
7. C89×#1937C2semidirect
8. C89×#1929C2semidirect
9. C89×#1897C2semidirect
10. C89×#1876C2semidirect
11. C89×#1876C2semidirect
12. C89×#1866C2semidirect
13. C89×#1855C2semidirect
14. C89×#1765C2semidirect
15. C89×#1750C2semidirect
21. C2×#131×C89C22semidirect
25. #452×C89C4semidirect
26. #452×C89C4semidirect
27. #451×C89C4semidirect
28. #450×C89C4semidirect
29. #449×C89C4semidirect
30. #449×C89C4semidirect
31. #448×C89C4semidirect
32. #447×C89C4semidirect
38. C2×#108×C89C22semidirect
39. C2×#108×C89C22semidirect
40. #424×C89C22semidirect
46. C2×#104×C89C22semidirect
47. C2×#104×C89C22semidirect
54. #408×C89C22semidirect
60. #405×C89C22semidirect
61. C2×#97×C89C22semidirect
62. C2×C4×C8×C89C22semidirect
63. #341×C89C22semidirect
64. #341×C89C22semidirect
65. #339×C89C22semidirect
66. #339×C89C22semidirect
67. #336×C89C22semidirect
68. #336×C89C22semidirect
145. #104×C89D4semidirect
420. #22889C89direct (N × H)
432. C2×#443C2×C89semidirect
433. #2933C2×C89semidirect
434. C2×#421C2×C89semidirect
435. #2880C2×C89semidirect
436. #1975C2×C89semidirect
437. #1937C2×C89semidirect
438. #1929C2×C89semidirect
439. #1897C2×C89semidirect
440. #1876C2×C89semidirect
441. #1876C2×C89semidirect
442. #1866C2×C89semidirect
443. #1855C2×C89semidirect
444. #1765C2×C89semidirect
445. #1750C2×C89semidirect
446. C89#22889direct (N × H)
452. C2×#131C22×C89semidirect
456. #452C4×C89semidirect
457. #452C4×C89semidirect
458. #451C4×C89semidirect
459. #450C4×C89semidirect
460. #449C4×C89semidirect
461. #449C4×C89semidirect
462. #448C4×C89semidirect
463. #447C4×C89semidirect
469. C2×#108C22×C89semidirect
470. C2×#108C22×C89semidirect
471. #424C22×C89semidirect
477. C2×#104C22×C89semidirect
478. C2×#104C22×C89semidirect
485. #408C22×C89semidirect
491. #405C22×C89semidirect
492. C2×#97C22×C89semidirect
493. C2×C4×C8C22×C89semidirect
494. #341C22×C89semidirect
495. #341C22×C89semidirect
496. #339C22×C89semidirect
497. #339C22×C89semidirect
498. #336C22×C89semidirect
499. #336C22×C89semidirect
576. #104D4×C89semidirect

Maximal subgroups

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

subgroupindex
C89×#30022
C2×#443×C892
C89×#29332
C2×#421×C892
C89×#28802
C89×#19752
C89×#19372
C89×#19292
C89×#18972
C89×#18762
C89×#18662
C89×#18552
C89×#17652
C89×#17502
#2288989