Finite Group Databasebeta

← C89×#26210 #36404058

Subgroups — C89×#26210 #36404058

Order 22784.

816 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#2417C211yesmaximal, characteristic
2C89×#2352C211yesmaximal, characteristic
3C89×#2101C211yesmaximal, characteristic, complemented
4C89×#2075C211yesmaximal, characteristic, complemented
5C89×#2074C211yesmaximal, characteristic, complemented
6C89×#2036C211yesmaximal, characteristic, complemented
7C89×#1928C211yesmaximal, characteristic, complemented
8C89×#1918C211yesmaximal, characteristic, complemented
9C89×#1892C211yesmaximal, characteristic, complemented
10C89×#1873C211yesmaximal, characteristic, complemented
11C89×#1872C211yesmaximal, characteristic, complemented
12C89×#1869C211yesmaximal, characteristic
13C89×#1852C211yesmaximal, characteristic, complemented
14C89×#1825C211yesmaximal, characteristic, complemented
15C2×#340×C89C211yesmaximal, characteristic, complemented
16C23×C8×C89C2211yescharacteristic
17C2×C22⋊Q8×C89C2211yescharacteristic
18C2×C22⋊Q8×C89C2211yescharacteristic
19C2×C4×D4×C89C2211yescharacteristic
20C2×#117×C89C2211yescharacteristic
21C22×C4⋊C4×C89C2211yescharacteristic
22C22×C4⋊C4×C89C2211yescharacteristic
23C2×#107×C89C2211yescharacteristic
24C2×#107×C89C2211yescharacteristic
25C2×#103×C89C2211yescharacteristic
26C2×#103×C89C2211yescharacteristic
27C2×#103×C89C2211yescharacteristic
28C2×#103×C89C2211yescharacteristic
29C2×C22⋊C8×C89C2211yescharacteristic
30C2×C22⋊C8×C89C2211yescharacteristic
31C2×C22⋊C8×C89C2211yescharacteristic
32#398×C89—21no—
33#396×C89—21no—
34#391×C89C2211yescharacteristic
35#389×C89C2211yescharacteristic
36#388×C89—21no—
37#387×C89—21no—
38#386×C89—21no—
39#386×C89—21no—
40#382×C89C2211yescharacteristic
41#380×C89—21no—
42#380×C89C2211yescharacteristic
43#380×C89C2211yescharacteristic
44#380×C89C2211yescharacteristic
45C4×C4⋊C4×C89C2211yescharacteristic
46C4×C22⋊C4×C89—21no—
47#340×C89C2211yescharacteristic
48#340×C89C2211yescharacteristic
49#340×C89C2211yescharacteristic
50#340×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×Q8×C89C2311yescharacteristic
60C22×D4×C89D411yescharacteristic
61C23×C4×C89—21no—
62C23×C4×C89—21no—
63C23×C4×C89C2311yescharacteristic
64C23×C4×C89C2311yescharacteristic
65C22×C8×C89—22no—
66C22×C8×C89—41no—
67C22×C8×C89—41no—
68C22×C8×C89C2311yescharacteristic
69C22×C8×C89C2311yescharacteristic
70C22×C8×C89C2311yescharacteristic
71C22×C8×C89C2311yescharacteristic
72C22⋊Q8×C89—22no—
73C22⋊Q8×C89—22no—
74C22⋊Q8×C89—22no—
75C22⋊Q8×C89—41no—
76C4×D4×C89—22no—
77C4×D4×C89—22no—
78#117×C89—22no—
79#117×C89—41no—
80C2×C4⋊C4×C89—22no—
81C2×C4⋊C4×C89—22no—
82C2×C4⋊C4×C89—21no—
83C2×C4⋊C4×C89—21no—
84C2×C4⋊C4×C89—21no—
85C2×C4⋊C4×C89—21no—
86C2×C4⋊C4×C89—21no—
87C2×C4⋊C4×C89—41no—
88C2×C4⋊C4×C89—41no—
89C2×C4⋊C4×C89D411yescharacteristic
90C2×C4⋊C4×C89C2311yescharacteristic
91C2×C4⋊C4×C89C2311yescharacteristic
92C2×C4⋊C4×C89C2311yescharacteristic
93C2×C4⋊C4×C89C2311yescharacteristic
94C2×C4⋊C4×C89C2311yescharacteristic
95C2×C4⋊C4×C89C2311yescharacteristic
96C2×C4⋊C4×C89C2311yescharacteristic
97C2×C22⋊C4×C89—21no—
98C2×C22⋊C4×C89—21no—
99C2×C22⋊C4×C89—21no—
100C2×C22⋊C4×C89—21no—
101C2×C22⋊C4×C89—21no—
102C2×C22⋊C4×C89—21no—
103C2×C22⋊C4×C89D411yescharacteristic
104C2×C22⋊C4×C89D411yescharacteristic
105C2×C42×C89—21no—
106C2×C42×C89—21no—
107C2×C42×C89C2311yescharacteristic
108#107×C89—22no—
109#107×C89—41no—
110#103×C89—22no—
111#103×C89—41no—
112#103×C89—41no—
113#103×C89—41no—
114C22⋊C8×C89—22no—
115C22⋊C8×C89—41no—
116C22⋊C8×C89—41no—
117#95×C89—21no—
118#95×C89—21no—
119#95×C89—21no—
120#95×C89—21no—
121#95×C89—21no—
122#95×C89—21no—
123#95×C89—21no—
124#95×C89—21no—
125#95×C89—21no—
126C24×C89C2×D411yescharacteristic
127C24×C89C2×D411yescharacteristic
128C2×Q8×C89—21no—
129C2×Q8×C89—21no—
130C2×Q8×C89—21no—
131C2×Q8×C89—21no—
132C2×Q8×C89—21no—
133C2×Q8×C89—21no—
134C2×D4×C89—22no—
135C2×D4×C89—22no—
136C2×D4×C89—22no—
137C22×C4×C89—21no—
138C22×C4×C89—21no—
139C22×C4×C89—21no—
140C22×C4×C89—21no—
141C22×C4×C89—21no—
142C22×C4×C89—21no—
143C22×C4×C89—21no—
144C22×C4×C89—21no—
145C22×C4×C89—21no—
146C22×C4×C89—21no—
147C22×C4×C89—21no—
148C22×C4×C89—21no—
149C22×C4×C89—21no—
150C22×C4×C89—21no—
151C22×C4×C89—21no—
152C22×C4×C89—21no—
153C22×C4×C89—21no—
154C22×C4×C89—21no—
155C22×C4×C89—42no—
156C22×C4×C89—42no—
157C22×C4×C89—42no—
158C22×C4×C89—42no—
159C22×C4×C89—81no—
160C22×C4×C89—81no—
161C22×C4×C89C2×D411yescharacteristic
162C22×C4×C89C2×D411yescharacteristic
163C22×C4×C89C2×D411yescharacteristic
164C22×C4×C89C2×D411yescharacteristic
165C22×C4×C89#4112yes—
166C22×C4×C89#4112yes—
167C22×C4×C89C2411yescharacteristic
168C2×C8×C89—21no—
169C2×C8×C89—21no—
170C2×C8×C89—21no—
171C2×C8×C89—21no—
172C2×C8×C89—21no—
173C2×C8×C89—21no—
174C2×C8×C89—21no—
175C2×C8×C89—21no—
176C2×C8×C89—21no—
177C2×C8×C89—21no—
178C2×C8×C89—21no—
179C2×C8×C89—21no—
180C2×C8×C89—44no—
181C4⋊C4×C89—22no—
182C4⋊C4×C89—21no—
183C4⋊C4×C89—21no—
184C4⋊C4×C89—21no—
185C4⋊C4×C89—21no—
186C4⋊C4×C89—21no—
187C4⋊C4×C89—21no—
188C4⋊C4×C89—21no—
189C4⋊C4×C89—21no—
190C4⋊C4×C89—21no—
191C4⋊C4×C89—21no—
192C4⋊C4×C89—21no—
193C4⋊C4×C89—21no—
194C4⋊C4×C89—42no—
195C4⋊C4×C89—42no—
196C4⋊C4×C89—42no—
197C4⋊C4×C89—42no—
198C4⋊C4×C89—81no—
199C4⋊C4×C89#4112yes—
200C4⋊C4×C89#4112yes—
201C22⋊C4×C89—22no—
202C22⋊C4×C89—22no—
203C22⋊C4×C89—42no—
204C22⋊C4×C89—42no—
205C22⋊C4×C89—42no—
206C22⋊C4×C89—42no—
207C22⋊C4×C89—81no—
208C22⋊C4×C89—81no—
209C42×C89—21no—
210C42×C89—21no—
211C42×C89—42no—
212C42×C89—81no—
213C23×C89—21no—
214C23×C89—21no—
215C23×C89—21no—
216C23×C89—21no—
217C23×C89—21no—
218C23×C89—21no—
219C23×C89—21no—
220C23×C89—21no—
221C23×C89—21no—
222C23×C89—21no—
223C23×C89—21no—
224C23×C89#12312yes—
225C23×C89#13512yes—
226C23×C89#13712yes—
227C23×C89C22×D411yescharacteristic
228Q8×C89—41no—
229Q8×C89—41no—
230Q8×C89—41no—
231Q8×C89—41no—
232D4×C89—44no—
233C2×C4×C89—21no—
234C2×C4×C89—21no—
235C2×C4×C89—22no—
236C2×C4×C89—22no—
237C2×C4×C89—22no—
238C2×C4×C89—22no—
239C2×C4×C89—21no—
240C2×C4×C89—21no—
241C2×C4×C89—21no—
242C2×C4×C89—21no—
243C2×C4×C89—22no—
244C2×C4×C89—22no—
245C2×C4×C89—21no—
246C2×C4×C89—21no—
247C2×C4×C89—21no—
248C2×C4×C89—21no—
249C2×C4×C89—21no—
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—41no—
258C2×C4×C89—41no—
259C2×C4×C89—41no—
260C2×C4×C89—41no—
261C2×C4×C89—41no—
262C2×C4×C89—41no—
263C2×C4×C89—41no—
264C2×C4×C89—41no—
265C2×C4×C89—41no—
266C2×C4×C89—41no—
267C2×C4×C89—41no—
268C2×C4×C89—41no—
269C2×C4×C89—41no—
270C2×C4×C89—41no—
271C2×C4×C89—41no—
272C2×C4×C89—41no—
273C2×C4×C89—41no—
274C2×C4×C89—41no—
275C2×C4×C89—41no—
276C2×C4×C89—84no—
277C2×C4×C89—84no—
278C2×C4×C89#12312yes—
279C2×C4×C89C2×#4111yescharacteristic
280C2×C4×C89C2×#4111yescharacteristic
281C2×C4×C89C2×#4111yescharacteristic
282C2×C4×C89C2×#4111yescharacteristic
283C2×C4×C89H(5,𝔽2)11yescharacteristic
284C2×C4×C89H(5,𝔽2)11yescharacteristic
285C8×C89—41no—
286C8×C89—41no—
287C8×C89—41no—
288C8×C89—41no—
289C22×C89—22no—
290C22×C89—22no—
291C22×C89—22no—
292C22×C89—22no—
293C22×C89—22no—
294C22×C89—22no—
295C22×C89—41no—
296C22×C89—41no—
297C22×C89—41no—
298C22×C89—41no—
299C22×C89—41no—
300C22×C89—41no—
301C22×C89—41no—
302C22×C89#48514yes—
303C22×C89C2×#12311yescharacteristic
304C22×C89#54611yescharacteristic
305C22×C89#54611yescharacteristic
306C22×C89C2×#13511yescharacteristic
307C22×C89C2×#13711yescharacteristic
308C22×C89#57611yescharacteristic
309C22×C89#57811yescharacteristic
310C4×C89—22no—
311C4×C89—41no—
312C4×C89—41no—
313C4×C89—41no—
314C4×C89—42no—
315C4×C89—42no—
316C4×C89—81no—
317C4×C89—81no—
318C4×C89—81no—
319C4×C89—81no—
320C4×C89—81no—
321C4×C89—81no—
322C4×C89#52911yescharacteristic
323C4×C89#53811yescharacteristic
324C4×C89#55311yescharacteristic
325C4×C89#55311yescharacteristic
326#26210C8911yesmaximal, characteristic, direct product factor, Sylow
327C2×C89—24no—
328C2×C89—81no—
329C2×C89#244411yescharacteristic
330C2×C89C2×#48511yescharacteristic
331C2×C89#309811yescharacteristic
332C2×C89#329711yescharacteristic
333C2×C89#330011yescharacteristic
334C2×C89#331211yescharacteristic
335C2×C89#331411yescharacteristic
336#2417C2×C8911yescharacteristic
337#2352C2×C8911yescharacteristic
338#2101C2×C8911yescharacteristic, complemented
339#2075C2×C8911yescharacteristic, complemented
340#2074C2×C8911yescharacteristic, complemented
341#2036C2×C8911yescharacteristic, complemented
342#1928C2×C8911yescharacteristic, complemented
343#1918C2×C8911yescharacteristic, complemented
344#1892C2×C8911yescharacteristic, complemented
345#1873C2×C8911yescharacteristic, complemented
346#1872C2×C8911yescharacteristic, complemented
347#1869C2×C8911yescharacteristic
348#1852C2×C8911yescharacteristic, complemented
349#1825C2×C8911yescharacteristic, complemented
350C2×#340C2×C8911yescharacteristic, complemented
351C89#2621011yescharacteristic, direct product factor, Sylow
352C23×C8C22×C8911yescharacteristic
353C2×C22⋊Q8C22×C8911yescharacteristic
354C2×C22⋊Q8C22×C8911yescharacteristic
355C2×C4×D4C22×C8911yescharacteristic
356C2×#117C22×C8911yescharacteristic
357C22×C4⋊C4C22×C8911yescharacteristic
358C22×C4⋊C4C22×C8911yescharacteristic
359C2×#107C22×C8911yescharacteristic
360C2×#107C22×C8911yescharacteristic
361C2×#103C22×C8911yescharacteristic
362C2×#103C22×C8911yescharacteristic
363C2×#103C22×C8911yescharacteristic
364C2×#103C22×C8911yescharacteristic
365C2×C22⋊C8C22×C8911yescharacteristic
366C2×C22⋊C8C22×C8911yescharacteristic
367C2×C22⋊C8C22×C8911yescharacteristic
368#398—21no—
369#396—21no—
370#391C22×C8911yescharacteristic
371#389C22×C8911yescharacteristic
372#388—21no—
373#387—21no—
374#386—21no—
375#386—21no—
376#382C22×C8911yescharacteristic
377#380—21no—
378#380C22×C8911yescharacteristic
379#380C22×C8911yescharacteristic
380#380C22×C8911yescharacteristic
381C4×C4⋊C4C22×C8911yescharacteristic
382C4×C22⋊C4—21no—
383#340C22×C8911yescharacteristic
384#340C22×C8911yescharacteristic
385#340C22×C8911yescharacteristic
386#340C22×C8911yescharacteristic
387#340C22×C8911yescharacteristic
388#340C22×C8911yescharacteristic
389#340C22×C8911yescharacteristic
390#340C22×C8911yescharacteristic
391#340C22×C8911yescharacteristic
392#340C22×C8911yescharacteristic
393#336C22×C8911yescharacteristic
394#336C22×C8911yescharacteristic
395C22×Q8C23×C8911yescharacteristic
396C22×D4D4×C8911yescharacteristic
397C23×C4—21no—
398C23×C4—21no—
399C23×C4C23×C8911yescharacteristic
400C23×C4C23×C8911yescharacteristic
401C22×C8—22no—
402C22×C8—41no—
403C22×C8—41no—
404C22×C8C23×C8911yescharacteristic
405C22×C8C23×C8911yescharacteristic
406C22×C8C23×C8911yescharacteristic
407C22×C8C23×C8911yescharacteristic
408C22⋊Q8—22no—
409C22⋊Q8—22no—
410C22⋊Q8—22no—
411C22⋊Q8—41no—
412C4×D4—22no—
413C4×D4—22no—
414#117—22no—
415#117—41no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—41no—
424C2×C4⋊C4—41no—
425C2×C4⋊C4D4×C8911yescharacteristic
426C2×C4⋊C4C23×C8911yescharacteristic
427C2×C4⋊C4C23×C8911yescharacteristic
428C2×C4⋊C4C23×C8911yescharacteristic
429C2×C4⋊C4C23×C8911yescharacteristic
430C2×C4⋊C4C23×C8911yescharacteristic
431C2×C4⋊C4C23×C8911yescharacteristic
432C2×C4⋊C4C23×C8911yescharacteristic
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4D4×C8911yescharacteristic
440C2×C22⋊C4D4×C8911yescharacteristic
441C2×C42—21no—
442C2×C42—21no—
443C2×C42C23×C8911yescharacteristic
444#107—22no—
445#107—41no—
446#103—22no—
447#103—41no—
448#103—41no—
449#103—41no—
450C22⋊C8—22no—
451C22⋊C8—41no—
452C22⋊C8—41no—
453#95—21no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462C24C2×D4×C8911yescharacteristic
463C24C2×D4×C8911yescharacteristic
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—22no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—81no—
496C22×C4—81no—
497C22×C4C2×D4×C8911yescharacteristic
498C22×C4C2×D4×C8911yescharacteristic
499C22×C4C2×D4×C8911yescharacteristic
500C22×C4C2×D4×C8911yescharacteristic
501C22×C4#41×C8912yes—
502C22×C4#41×C8912yes—
503C22×C4C24×C8911yescharacteristic
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—44no—
517C4⋊C4—22no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—42no—
531C4⋊C4—42no—
532C4⋊C4—42no—
533C4⋊C4—42no—
534C4⋊C4—81no—
535C4⋊C4#41×C8912yes—
536C4⋊C4#41×C8912yes—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—42no—
540C22⋊C4—42no—
541C22⋊C4—42no—
542C22⋊C4—42no—
543C22⋊C4—81no—
544C22⋊C4—81no—
545C42—21no—
546C42—21no—
547C42—42no—
548C42—81no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23#123×C8912yes—
561C23#135×C8912yes—
562C23#137×C8912yes—
563C23C22×D4×C8911yescharacteristic
564Q8—41no—
565Q8—41no—
566Q8—41no—
567Q8—41no—
568D4—44no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—84no—
613C2×C4—84no—
614C2×C4#123×C8912yes—
615C2×C4C2×#41×C8911yescharacteristic
616C2×C4C2×#41×C8911yescharacteristic
617C2×C4C2×#41×C8911yescharacteristic
618C2×C4C2×#41×C8911yescharacteristic
619C2×C4H(5,𝔽2)×C8911yescharacteristic
620C2×C4H(5,𝔽2)×C8911yescharacteristic
621C8—41no—
622C8—41no—
623C8—41no—
624C8—41no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22#485×C8914yes—
639C22C2×#123×C8911yescharacteristic
640C22#546×C8911yescharacteristic
641C22#546×C8911yescharacteristic
642C22C2×#135×C8911yescharacteristic
643C22C2×#137×C8911yescharacteristic
644C22#576×C8911yescharacteristic
645C22#578×C8911yescharacteristic
646C4—22no—
647C4—41no—
648C4—41no—
649C4—41no—
650C4—42no—
651C4—42no—
652C4—81no—
653C4—81no—
654C4—81no—
655C4—81no—
656C4—81no—
657C4—81no—
658C4#529×C8911yescharacteristic
659C4#538×C8911yescharacteristic
660C4#553×C8911yescharacteristic
661C4#553×C8911yescharacteristic
662C2—24no—
663C2—81no—
664C2C89×#244411yescharacteristic
665C2C2×#485×C8911yescharacteristic
666C2C89×#309811yescharacteristic
667C2C89×#329711yescharacteristic
668C2C89×#330011yescharacteristic
669C2C89×#331211yescharacteristic
670C2C89×#331411yescharacteristic
subgroupG/H
center, socleC23×C89C22×D4
commutator, Frattini, cosocleC22×C4C24×C89
prime radicalC22×D4×C89D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C89 ◁ C2×C4×D4×C89 ◁ G

Complements

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

NH ≅ G/Ntype
3. C89×#2101C2semidirect
4. C89×#2075C2semidirect
5. C89×#2074C2semidirect
6. C89×#2036C2semidirect
7. C89×#1928C2semidirect
8. C89×#1918C2semidirect
9. C89×#1892C2semidirect
10. C89×#1873C2semidirect
11. C89×#1872C2semidirect
13. C89×#1852C2semidirect
14. C89×#1825C2semidirect
15. C2×#340×C89C2semidirect
326. #26210C89direct (N × H)
338. #2101C2×C89semidirect
339. #2075C2×C89semidirect
340. #2074C2×C89semidirect
341. #2036C2×C89semidirect
342. #1928C2×C89semidirect
343. #1918C2×C89semidirect
344. #1892C2×C89semidirect
345. #1873C2×C89semidirect
346. #1872C2×C89semidirect
348. #1852C2×C89semidirect
349. #1825C2×C89semidirect
350. C2×#340C2×C89semidirect
351. C89#26210direct (N × H)

Maximal subgroups

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

subgroupindex
C89×#24172
C89×#23522
C89×#21012
C89×#20752
C89×#20742
C89×#20362
C89×#19282
C89×#19182
C89×#18922
C89×#18732
C89×#18722
C89×#18692
C89×#18522
C89×#18252
C2×#340×C892
#2621089