Finite Group Databasebeta

← C89×#22062 #36399910

Subgroups — C89×#22062 #36399910

Order 22784.

900 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#3002C211yesmaximal, characteristic
2C89×#2930C211yesmaximal, characteristic, complemented
3C89×#2879C211yesmaximal, characteristic, complemented
4C89×#1975C211yesmaximal, characteristic, complemented
5C89×#1974C211yesmaximal, characteristic, complemented
6C89×#1938C211yesmaximal, characteristic, complemented
7C89×#1937C211yesmaximal, characteristic, complemented
8C89×#1929C211yesmaximal, characteristic, complemented
9C89×#1929C211yesmaximal, characteristic, complemented
10C89×#1876C211yesmaximal, characteristic, complemented
11C89×#1876C211yesmaximal, characteristic, complemented
12C89×#1871C211yesmaximal, characteristic, complemented
13C89×#1855C211yesmaximal, characteristic, complemented
14C89×#1789C211yesmaximal, characteristic, complemented
15C89×#1753C211yesmaximal, characteristic, complemented
16C22×#41×C89C2211yescharacteristic
17C2×#135×C89C2211yescharacteristic
18C2×#135×C89C2211yescharacteristic
19C2×#131×C89C2211yescharacteristic, complemented
20C22×M16×C89C2211yescharacteristic
21C22×M16×C89C2211yescharacteristic
22#525×C89C2211yescharacteristic
23#452×C89C411yescharacteristic, complemented
24#452×C89C411yescharacteristic, complemented
25#451×C89C411yescharacteristic, complemented
26#450×C89C411yescharacteristic, complemented
27#449×C89C411yescharacteristic, complemented
28#449×C89C411yescharacteristic, complemented
29#448×C89C411yescharacteristic, complemented
30#447×C89C411yescharacteristic, complemented
31#436×C89—21no—
32#436×C89—21no—
33#435×C89—21no—
34#435×C89—21no—
35C2×#108×C89C2211yescharacteristic, complemented
36C2×#108×C89C2211yescharacteristic, complemented
37#424×C89C2211yescharacteristic, complemented
38C2×#104×C89C2211yescharacteristic
39C2×#104×C89C2211yescharacteristic
40C2×#104×C89C2211yescharacteristic
41C2×#104×C89C2211yescharacteristic
42C2×#104×C89C2211yescharacteristic, complemented
43C2×#104×C89C2211yescharacteristic, complemented
44#416×C89C2211yescharacteristic
45#416×C89C2211yescharacteristic
46#408×C89—21no—
47#408×C89—21no—
48#408×C89C2211yescharacteristic
49#408×C89C2211yescharacteristic
50#408×C89C2211yescharacteristic
51#408×C89C2211yescharacteristic
52#408×C89C2211yescharacteristic, complemented
53#407×C89—21no—
54#407×C89—21no—
55#407×C89C2211yescharacteristic
56C2×C22⋊C8×C89C2211yescharacteristic
57#405×C89C2211yescharacteristic, complemented
58C2×#97×C89C2211yescharacteristic, complemented
59C2×C4×C8×C89C2211yescharacteristic, complemented
60C4×C22⋊C4×C89C2211yescharacteristic
61#341×C89C2211yescharacteristic, complemented
62#341×C89C2211yescharacteristic, complemented
63#339×C89C2211yescharacteristic, complemented
64#339×C89C2211yescharacteristic, complemented
65#336×C89C2211yescharacteristic, complemented
66#336×C89C2211yescharacteristic, complemented
67C2×#41×C89—21no—
68C2×#41×C89—21no—
69C2×#41×C89—41no—
70C2×#41×C89—41no—
71C2×#41×C89—41no—
72C2×#41×C89—41no—
73C2×#41×C89C2×C411yescharacteristic
74C2×#41×C89C2×C411yescharacteristic
75C2×#41×C89C2311yescharacteristic
76C2×#41×C89C2311yescharacteristic
77C2×#41×C89C2311yescharacteristic
78C22×Q8×C89C2×C411yescharacteristic
79C22×D4×C89—21no—
80C22×D4×C89C2×C411yescharacteristic
81C23×C4×C89—21no—
82C23×C4×C89C2311yescharacteristic
83#135×C89—41no—
84#135×C89—41no—
85#135×C89—41no—
86#135×C89—41no—
87C2×Q16×C89C2×C411yescharacteristic
88C2×Q16×C89C2×C411yescharacteristic
89C2×SD16×C89C2×C411yescharacteristic
90C2×SD16×C89C2×C411yescharacteristic
91C2×SD16×C89C2×C411yescharacteristic
92C2×SD16×C89C2×C411yescharacteristic
93C2×D8×C89C2×C411yescharacteristic
94C2×D8×C89C2×C411yescharacteristic
95#131×C89—41no—
96#131×C89—41no—
97C2×M16×C89—21no—
98C2×M16×C89—21no—
99C2×M16×C89—41no—
100C2×M16×C89—41no—
101C2×M16×C89—41no—
102C2×M16×C89—41no—
103C2×M16×C89D411yescharacteristic
104C2×M16×C89D411yescharacteristic
105C2×M16×C89D411yescharacteristic
106C2×M16×C89D411yescharacteristic
107C2×M16×C89C2311yescharacteristic
108C2×M16×C89C2311yescharacteristic
109C2×M16×C89C2311yescharacteristic
110C2×M16×C89C2311yescharacteristic
111C22×C8×C89—21no—
112C22×C8×C89—21no—
113C22×C8×C89C2311yescharacteristic
114C22×C8×C89C2311yescharacteristic
115C22×C8×C89C2311yescharacteristic
116C22×C8×C89C2311yescharacteristic
117#123×C89—21no—
118C22⋊Q8×C89C2×C411yescharacteristic
119C22⋊Q8×C89C2×C411yescharacteristic
120#121×C89C2×C411yescharacteristic
121#121×C89C2×C411yescharacteristic
122#120×C89—21no—
123C4×D4×C89—21no—
124C4×D4×C89—21no—
125#117×C89C2311yescharacteristic
126C2×C22⋊C4×C89—21no—
127C2×C42×C89C2311yescharacteristic
128C2×C42×C89C2311yescharacteristic
129#108×C89—41no—
130#108×C89—41no—
131C4⋊C8×C89—21no—
132C4⋊C8×C89—21no—
133#104×C89—41no—
134#104×C89—41no—
135#104×C89—41no—
136#104×C89—41no—
137#104×C89—41no—
138#104×C89—41no—
139#103×C89C2×C411yescharacteristic
140#103×C89C2×C411yescharacteristic
141#103×C89C2×C411yescharacteristic
142#103×C89C2×C411yescharacteristic
143#102×C89C2×C411yescharacteristic
144#102×C89C2×C411yescharacteristic
145#102×C89C2×C411yescharacteristic
146#102×C89C2×C411yescharacteristic
147C22⋊C8×C89—21no—
148C22⋊C8×C89—21no—
149C22⋊C8×C89—21no—
150C22⋊C8×C89—21no—
151C22⋊C8×C89—21no—
152C22⋊C8×C89—21no—
153C22⋊C8×C89—21no—
154C22⋊C8×C89—21no—
155C22⋊C8×C89—21no—
156C22⋊C8×C89—21no—
157C22⋊C8×C89—21no—
158C22⋊C8×C89—21no—
159C22⋊C8×C89C2×C411yescharacteristic
160C22⋊C8×C89C2×C411yescharacteristic
161C22⋊C8×C89C2×C411yescharacteristic
162C22⋊C8×C89C2×C411yescharacteristic
163#97×C89—21no—
164#97×C89—41no—
165C4×C8×C89—21no—
166C4×C8×C89—41no—
167#95×C89—21no—
168C24×C89—21no—
169C24×C89#4111yescharacteristic
170#41×C89—21no—
171#41×C89—21no—
172#41×C89—21no—
173#41×C89—21no—
174#41×C89—21no—
175#41×C89—21no—
176#41×C89—21no—
177#41×C89—21no—
178#41×C89—21no—
179#41×C89—21no—
180#41×C89—21no—
181#41×C89—21no—
182#41×C89—41no—
183#41×C89—41no—
184#41×C89—41no—
185#41×C89—41no—
186#41×C89—42no—
187#41×C89—42no—
188#41×C89—42no—
189#41×C89—42no—
190C2×Q8×C89—21no—
191C2×Q8×C89—41no—
192C2×Q8×C89—41no—
193C2×Q8×C89C22×C411yescharacteristic
194C2×Q8×C89C22×C411yescharacteristic
195C2×Q8×C89C22×C411yescharacteristic
196C2×D4×C89—21no—
197C2×D4×C89—21no—
198C2×D4×C89—21no—
199C2×D4×C89—21no—
200C2×D4×C89—21no—
201C2×D4×C89—21no—
202C2×D4×C89—21no—
203C2×D4×C89—21no—
204C2×D4×C89—41no—
205C2×D4×C89—41no—
206C2×D4×C89—42no—
207C2×D4×C89—42no—
208C2×D4×C89C22×C411yescharacteristic
209C2×D4×C89C22×C411yescharacteristic
210C2×D4×C89C22×C411yescharacteristic
211C22×C4×C89—21no—
212C22×C4×C89—21no—
213C22×C4×C89—21no—
214C22×C4×C89—21no—
215C22×C4×C89—21no—
216C22×C4×C89—21no—
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—42no—
224C22×C4×C89—42no—
225C22×C4×C89C22×C411yescharacteristic
226C22×C4×C89C22×C411yescharacteristic
227C22×C4×C89C2×D411yescharacteristic
228C22×C4×C89C2×D411yescharacteristic
229C22×C4×C89#4111yescharacteristic
230C22×C4×C89C2411yescharacteristic
231Q16×C89—41no—
232Q16×C89—41no—
233SD16×C89—41no—
234SD16×C89—41no—
235SD16×C89—41no—
236SD16×C89—41no—
237D8×C89—41no—
238D8×C89—41no—
239M16×C89—21no—
240M16×C89—21no—
241M16×C89—21no—
242M16×C89—21no—
243M16×C89—21no—
244M16×C89—21no—
245M16×C89—21no—
246M16×C89—21no—
247M16×C89—41no—
248M16×C89—41no—
249M16×C89—41no—
250M16×C89—41no—
251M16×C89—42no—
252M16×C89—42no—
253C2×C8×C89—21no—
254C2×C8×C89—21no—
255C2×C8×C89—21no—
256C2×C8×C89—21no—
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—42no—
266C2×C8×C89—42no—
267C2×C8×C89C22×C411yescharacteristic
268C2×C8×C89C22×C411yescharacteristic
269C2×C8×C89C22×C411yescharacteristic
270C2×C8×C89C22×C411yescharacteristic
271C2×C8×C89C2×D411yescharacteristic
272C2×C8×C89C2×D411yescharacteristic
273C2×C8×C89C2×D411yescharacteristic
274C2×C8×C89C2×D411yescharacteristic
275C4⋊C4×C89—21no—
276C4⋊C4×C89—21no—
277C4⋊C4×C89C22×C411yescharacteristic
278C4⋊C4×C89C22×C411yescharacteristic
279C22⋊C4×C89—21no—
280C22⋊C4×C89—21no—
281C22⋊C4×C89—21no—
282C22⋊C4×C89—21no—
283C22⋊C4×C89—21no—
284C22⋊C4×C89—42no—
285C42×C89—21no—
286C42×C89—21no—
287C42×C89—21no—
288C42×C89—21no—
289C42×C89—21no—
290C23×C89—21no—
291C23×C89—21no—
292C23×C89—21no—
293C23×C89—21no—
294C23×C89—21no—
295C23×C89—41no—
296C23×C89—41no—
297C23×C89—42no—
298C23×C89—81no—
299C23×C89—81no—
300C23×C89C4×D411yescharacteristic
301C23×C89C4×D411yescharacteristic
302C23×C89C2×#4111yescharacteristic
303Q8×C89—21no—
304Q8×C89—21no—
305Q8×C89—21no—
306Q8×C89—21no—
307Q8×C89—21no—
308Q8×C89—21no—
309Q8×C89—42no—
310D4×C89—21no—
311D4×C89—21no—
312D4×C89—21no—
313D4×C89—21no—
314D4×C89—21no—
315D4×C89—21no—
316D4×C89—42no—
317D4×C89—42no—
318D4×C89—42no—
319D4×C89—41no—
320D4×C89—41no—
321D4×C89—41no—
322D4×C89—41no—
323D4×C89—41no—
324D4×C89—41no—
325D4×C89—81no—
326D4×C89—81no—
327C2×C4×C89—21no—
328C2×C4×C89—21no—
329C2×C4×C89—21no—
330C2×C4×C89—21no—
331C2×C4×C89—21no—
332C2×C4×C89—21no—
333C2×C4×C89—21no—
334C2×C4×C89—21no—
335C2×C4×C89—21no—
336C2×C4×C89—21no—
337C2×C4×C89—22no—
338C2×C4×C89—21no—
339C2×C4×C89—21no—
340C2×C4×C89—21no—
341C2×C4×C89—21no—
342C2×C4×C89—21no—
343C2×C4×C89—42no—
344C2×C4×C89—42no—
345C2×C4×C89—41no—
346C2×C4×C89—42no—
347C2×C4×C89—41no—
348C2×C4×C89—41no—
349C2×C4×C89—41no—
350C2×C4×C89—41no—
351C2×C4×C89—41no—
352C2×C4×C89—41no—
353C2×C4×C89—41no—
354C2×C4×C89—41no—
355C2×C4×C89—41no—
356C2×C4×C89—41no—
357C2×C4×C89C4×D411yescharacteristic
358C2×C4×C89C4×D411yescharacteristic
359C2×C4×C89C23×C411yescharacteristic
360C2×C4×C89C22×D411yescharacteristic
361C2×C4×C89H(5,𝔽2)11yescharacteristic
362C2×C4×C89H(5,𝔽2)11yescharacteristic
363C2×C4×C89H(5,𝔽2)11yescharacteristic
364C2×C4×C89H(5,𝔽2)11yescharacteristic
365C8×C89—21no—
366C8×C89—21no—
367C8×C89—21no—
368C8×C89—21no—
369C8×C89—21no—
370C8×C89—21no—
371C8×C89—21no—
372C8×C89—21no—
373C8×C89—41no—
374C8×C89—41no—
375C8×C89—41no—
376C8×C89—41no—
377C22×C89—21no—
378C22×C89—21no—
379C22×C89—21no—
380C22×C89—21no—
381C22×C89—21no—
382C22×C89—21no—
383C22×C89—21no—
384C22×C89—21no—
385C22×C89—41no—
386C22×C89—41no—
387C22×C89—41no—
388C22×C89—41no—
389C22×C89—41no—
390C22×C89—41no—
391C22×C89—41no—
392C22×C89—41no—
393C22×C89—41no—
394C22×C89—81no—
395C22×C89—81no—
396C22×C89—84no—
397C22×C89C2×C4×D411yescharacteristic
398C22×C89#53811yescharacteristic
399C22×C89#53811yescharacteristic
400C4×C89—21no—
401C4×C89—21no—
402C4×C89—42no—
403C4×C89—41no—
404C4×C89—41no—
405C4×C89—41no—
406C4×C89—41no—
407C4×C89—41no—
408C4×C89—81no—
409C4×C89#51811yescharacteristic
410C4×C89#51811yescharacteristic
411C4×C89#53411yescharacteristic
412C4×C89#53511yescharacteristic
413#22062C8911yesmaximal, characteristic, direct product factor, Sylow
414C2×C89—21no—
415C2×C89—21no—
416C2×C89—41no—
417C2×C89—41no—
418C2×C89—81no—
419C2×C89—81no—
420C2×C89—81no—
421C2×C89#232111yescharacteristic
422C2×C89#295611yescharacteristic
423C2×C89#295711yescharacteristic
424#3002C2×C8911yescharacteristic
425#2930C2×C8911yescharacteristic, complemented
426#2879C2×C8911yescharacteristic, complemented
427#1975C2×C8911yescharacteristic, complemented
428#1974C2×C8911yescharacteristic, complemented
429#1938C2×C8911yescharacteristic, complemented
430#1937C2×C8911yescharacteristic, complemented
431#1929C2×C8911yescharacteristic, complemented
432#1929C2×C8911yescharacteristic, complemented
433#1876C2×C8911yescharacteristic, complemented
434#1876C2×C8911yescharacteristic, complemented
435#1871C2×C8911yescharacteristic, complemented
436#1855C2×C8911yescharacteristic, complemented
437#1789C2×C8911yescharacteristic, complemented
438#1753C2×C8911yescharacteristic, complemented
439C89#2206211yescharacteristic, direct product factor, Sylow
440C22×#41C22×C8911yescharacteristic
441C2×#135C22×C8911yescharacteristic
442C2×#135C22×C8911yescharacteristic
443C2×#131C22×C8911yescharacteristic, complemented
444C22×M16C22×C8911yescharacteristic
445C22×M16C22×C8911yescharacteristic
446#525C22×C8911yescharacteristic
447#452C4×C8911yescharacteristic, complemented
448#452C4×C8911yescharacteristic, complemented
449#451C4×C8911yescharacteristic, complemented
450#450C4×C8911yescharacteristic, complemented
451#449C4×C8911yescharacteristic, complemented
452#449C4×C8911yescharacteristic, complemented
453#448C4×C8911yescharacteristic, complemented
454#447C4×C8911yescharacteristic, complemented
455#436—21no—
456#436—21no—
457#435—21no—
458#435—21no—
459C2×#108C22×C8911yescharacteristic, complemented
460C2×#108C22×C8911yescharacteristic, complemented
461#424C22×C8911yescharacteristic, complemented
462C2×#104C22×C8911yescharacteristic
463C2×#104C22×C8911yescharacteristic
464C2×#104C22×C8911yescharacteristic
465C2×#104C22×C8911yescharacteristic
466C2×#104C22×C8911yescharacteristic, complemented
467C2×#104C22×C8911yescharacteristic, complemented
468#416C22×C8911yescharacteristic
469#416C22×C8911yescharacteristic
470#408—21no—
471#408—21no—
472#408C22×C8911yescharacteristic
473#408C22×C8911yescharacteristic
474#408C22×C8911yescharacteristic
475#408C22×C8911yescharacteristic
476#408C22×C8911yescharacteristic, complemented
477#407—21no—
478#407—21no—
479#407C22×C8911yescharacteristic
480C2×C22⋊C8C22×C8911yescharacteristic
481#405C22×C8911yescharacteristic, complemented
482C2×#97C22×C8911yescharacteristic, complemented
483C2×C4×C8C22×C8911yescharacteristic, complemented
484C4×C22⋊C4C22×C8911yescharacteristic
485#341C22×C8911yescharacteristic, complemented
486#341C22×C8911yescharacteristic, complemented
487#339C22×C8911yescharacteristic, complemented
488#339C22×C8911yescharacteristic, complemented
489#336C22×C8911yescharacteristic, complemented
490#336C22×C8911yescharacteristic, complemented
491C2×#41—21no—
492C2×#41—21no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—41no—
497C2×#41C2×C4×C8911yescharacteristic
498C2×#41C2×C4×C8911yescharacteristic
499C2×#41C23×C8911yescharacteristic
500C2×#41C23×C8911yescharacteristic
501C2×#41C23×C8911yescharacteristic
502C22×Q8C2×C4×C8911yescharacteristic
503C22×D4—21no—
504C22×D4C2×C4×C8911yescharacteristic
505C23×C4—21no—
506C23×C4C23×C8911yescharacteristic
507#135—41no—
508#135—41no—
509#135—41no—
510#135—41no—
511C2×Q16C2×C4×C8911yescharacteristic
512C2×Q16C2×C4×C8911yescharacteristic
513C2×SD16C2×C4×C8911yescharacteristic
514C2×SD16C2×C4×C8911yescharacteristic
515C2×SD16C2×C4×C8911yescharacteristic
516C2×SD16C2×C4×C8911yescharacteristic
517C2×D8C2×C4×C8911yescharacteristic
518C2×D8C2×C4×C8911yescharacteristic
519#131—41no—
520#131—41no—
521C2×M16—21no—
522C2×M16—21no—
523C2×M16—41no—
524C2×M16—41no—
525C2×M16—41no—
526C2×M16—41no—
527C2×M16D4×C8911yescharacteristic
528C2×M16D4×C8911yescharacteristic
529C2×M16D4×C8911yescharacteristic
530C2×M16D4×C8911yescharacteristic
531C2×M16C23×C8911yescharacteristic
532C2×M16C23×C8911yescharacteristic
533C2×M16C23×C8911yescharacteristic
534C2×M16C23×C8911yescharacteristic
535C22×C8—21no—
536C22×C8—21no—
537C22×C8C23×C8911yescharacteristic
538C22×C8C23×C8911yescharacteristic
539C22×C8C23×C8911yescharacteristic
540C22×C8C23×C8911yescharacteristic
541#123—21no—
542C22⋊Q8C2×C4×C8911yescharacteristic
543C22⋊Q8C2×C4×C8911yescharacteristic
544#121C2×C4×C8911yescharacteristic
545#121C2×C4×C8911yescharacteristic
546#120—21no—
547C4×D4—21no—
548C4×D4—21no—
549#117C23×C8911yescharacteristic
550C2×C22⋊C4—21no—
551C2×C42C23×C8911yescharacteristic
552C2×C42C23×C8911yescharacteristic
553#108—41no—
554#108—41no—
555C4⋊C8—21no—
556C4⋊C8—21no—
557#104—41no—
558#104—41no—
559#104—41no—
560#104—41no—
561#104—41no—
562#104—41no—
563#103C2×C4×C8911yescharacteristic
564#103C2×C4×C8911yescharacteristic
565#103C2×C4×C8911yescharacteristic
566#103C2×C4×C8911yescharacteristic
567#102C2×C4×C8911yescharacteristic
568#102C2×C4×C8911yescharacteristic
569#102C2×C4×C8911yescharacteristic
570#102C2×C4×C8911yescharacteristic
571C22⋊C8—21no—
572C22⋊C8—21no—
573C22⋊C8—21no—
574C22⋊C8—21no—
575C22⋊C8—21no—
576C22⋊C8—21no—
577C22⋊C8—21no—
578C22⋊C8—21no—
579C22⋊C8—21no—
580C22⋊C8—21no—
581C22⋊C8—21no—
582C22⋊C8—21no—
583C22⋊C8C2×C4×C8911yescharacteristic
584C22⋊C8C2×C4×C8911yescharacteristic
585C22⋊C8C2×C4×C8911yescharacteristic
586C22⋊C8C2×C4×C8911yescharacteristic
587#97—21no—
588#97—41no—
589C4×C8—21no—
590C4×C8—41no—
591#95—21no—
592C24—21no—
593C24#41×C8911yescharacteristic
594#41—21no—
595#41—21no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—21no—
601#41—21no—
602#41—21no—
603#41—21no—
604#41—21no—
605#41—21no—
606#41—41no—
607#41—41no—
608#41—41no—
609#41—41no—
610#41—42no—
611#41—42no—
612#41—42no—
613#41—42no—
614C2×Q8—21no—
615C2×Q8—41no—
616C2×Q8—41no—
617C2×Q8C22×C4×C8911yescharacteristic
618C2×Q8C22×C4×C8911yescharacteristic
619C2×Q8C22×C4×C8911yescharacteristic
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4C22×C4×C8911yescharacteristic
633C2×D4C22×C4×C8911yescharacteristic
634C2×D4C22×C4×C8911yescharacteristic
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—42no—
648C22×C4—42no—
649C22×C4C22×C4×C8911yescharacteristic
650C22×C4C22×C4×C8911yescharacteristic
651C22×C4C2×D4×C8911yescharacteristic
652C22×C4C2×D4×C8911yescharacteristic
653C22×C4#41×C8911yescharacteristic
654C22×C4C24×C8911yescharacteristic
655Q16—41no—
656Q16—41no—
657SD16—41no—
658SD16—41no—
659SD16—41no—
660SD16—41no—
661D8—41no—
662D8—41no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—21no—
667M16—21no—
668M16—21no—
669M16—21no—
670M16—21no—
671M16—41no—
672M16—41no—
673M16—41no—
674M16—41no—
675M16—42no—
676M16—42no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—42no—
690C2×C8—42no—
691C2×C8C22×C4×C8911yescharacteristic
692C2×C8C22×C4×C8911yescharacteristic
693C2×C8C22×C4×C8911yescharacteristic
694C2×C8C22×C4×C8911yescharacteristic
695C2×C8C2×D4×C8911yescharacteristic
696C2×C8C2×D4×C8911yescharacteristic
697C2×C8C2×D4×C8911yescharacteristic
698C2×C8C2×D4×C8911yescharacteristic
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4C22×C4×C8911yescharacteristic
702C4⋊C4C22×C4×C8911yescharacteristic
703C22⋊C4—21no—
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—42no—
709C42—21no—
710C42—21no—
711C42—21no—
712C42—21no—
713C42—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—41no—
720C23—41no—
721C23—42no—
722C23—81no—
723C23—81no—
724C23C4×D4×C8911yescharacteristic
725C23C4×D4×C8911yescharacteristic
726C23C2×#41×C8911yescharacteristic
727Q8—21no—
728Q8—21no—
729Q8—21no—
730Q8—21no—
731Q8—21no—
732Q8—21no—
733Q8—42no—
734D4—21no—
735D4—21no—
736D4—21no—
737D4—21no—
738D4—21no—
739D4—21no—
740D4—42no—
741D4—42no—
742D4—42no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—81no—
750D4—81no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—41no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4C4×D4×C8911yescharacteristic
782C2×C4C4×D4×C8911yescharacteristic
783C2×C4C23×C4×C8911yescharacteristic
784C2×C4C22×D4×C8911yescharacteristic
785C2×C4H(5,𝔽2)×C8911yescharacteristic
786C2×C4H(5,𝔽2)×C8911yescharacteristic
787C2×C4H(5,𝔽2)×C8911yescharacteristic
788C2×C4H(5,𝔽2)×C8911yescharacteristic
789C8—21no—
790C8—21no—
791C8—21no—
792C8—21no—
793C8—21no—
794C8—21no—
795C8—21no—
796C8—21no—
797C8—41no—
798C8—41no—
799C8—41no—
800C8—41no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—81no—
819C22—81no—
820C22—84no—
821C22C2×C4×D4×C8911yescharacteristic
822C22#538×C8911yescharacteristic
823C22#538×C8911yescharacteristic
824C4—21no—
825C4—21no—
826C4—42no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—41no—
832C4—81no—
833C4#518×C8911yescharacteristic
834C4#518×C8911yescharacteristic
835C4#534×C8911yescharacteristic
836C4#535×C8911yescharacteristic
837C2—21no—
838C2—21no—
839C2—41no—
840C2—41no—
841C2—81no—
842C2—81no—
843C2—81no—
844C2C89×#232111yescharacteristic
845C2C89×#295611yescharacteristic
846C2C89×#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 ◁ C22×M16×C89 ◁ G

Complements

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

NH ≅ G/Ntype
2. C89×#2930C2semidirect
3. C89×#2879C2semidirect
4. C89×#1975C2semidirect
5. C89×#1974C2semidirect
6. C89×#1938C2semidirect
7. C89×#1937C2semidirect
8. C89×#1929C2semidirect
9. C89×#1929C2semidirect
10. C89×#1876C2semidirect
11. C89×#1876C2semidirect
12. C89×#1871C2semidirect
13. C89×#1855C2semidirect
14. C89×#1789C2semidirect
15. C89×#1753C2semidirect
19. C2×#131×C89C22semidirect
23. #452×C89C4semidirect
24. #452×C89C4semidirect
25. #451×C89C4semidirect
26. #450×C89C4semidirect
27. #449×C89C4semidirect
28. #449×C89C4semidirect
29. #448×C89C4semidirect
30. #447×C89C4semidirect
35. C2×#108×C89C22semidirect
36. C2×#108×C89C22semidirect
37. #424×C89C22semidirect
42. C2×#104×C89C22semidirect
43. C2×#104×C89C22semidirect
52. #408×C89C22semidirect
57. #405×C89C22semidirect
58. C2×#97×C89C22semidirect
59. C2×C4×C8×C89C22semidirect
61. #341×C89C22semidirect
62. #341×C89C22semidirect
63. #339×C89C22semidirect
64. #339×C89C22semidirect
65. #336×C89C22semidirect
66. #336×C89C22semidirect
413. #22062C89direct (N × H)
425. #2930C2×C89semidirect
426. #2879C2×C89semidirect
427. #1975C2×C89semidirect
428. #1974C2×C89semidirect
429. #1938C2×C89semidirect
430. #1937C2×C89semidirect
431. #1929C2×C89semidirect
432. #1929C2×C89semidirect
433. #1876C2×C89semidirect
434. #1876C2×C89semidirect
435. #1871C2×C89semidirect
436. #1855C2×C89semidirect
437. #1789C2×C89semidirect
438. #1753C2×C89semidirect
439. C89#22062direct (N × H)
443. C2×#131C22×C89semidirect
447. #452C4×C89semidirect
448. #452C4×C89semidirect
449. #451C4×C89semidirect
450. #450C4×C89semidirect
451. #449C4×C89semidirect
452. #449C4×C89semidirect
453. #448C4×C89semidirect
454. #447C4×C89semidirect
459. C2×#108C22×C89semidirect
460. C2×#108C22×C89semidirect
461. #424C22×C89semidirect
466. C2×#104C22×C89semidirect
467. C2×#104C22×C89semidirect
476. #408C22×C89semidirect
481. #405C22×C89semidirect
482. C2×#97C22×C89semidirect
483. C2×C4×C8C22×C89semidirect
485. #341C22×C89semidirect
486. #341C22×C89semidirect
487. #339C22×C89semidirect
488. #339C22×C89semidirect
489. #336C22×C89semidirect
490. #336C22×C89semidirect

Maximal subgroups

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

subgroupindex
C89×#30022
C89×#29302
C89×#28792
C89×#19752
C89×#19742
C89×#19382
C89×#19372
C89×#19292
C89×#18762
C89×#18712
C89×#18552
C89×#17892
C89×#17532
#2206289