Finite Group Databasebeta

← C89×#26954 #36404802

Subgroups — C89×#26954 #36404802

Order 22784.

1026 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#482×C89C211yesmaximal, characteristic, complemented
2C2×#459×C89C211yesmaximal, characteristic, complemented
3C89×#2428C211yesmaximal, characteristic, complemented
4C89×#2363C211yesmaximal, characteristic, complemented
5C89×#2088C211yesmaximal, characteristic, complemented
6C89×#2041C211yesmaximal, characteristic, complemented
7C89×#1999C211yesmaximal, characteristic, complemented
8C89×#1999C211yesmaximal, characteristic, complemented
9C89×#1972C211yesmaximal, characteristic, complemented
10C89×#1925C211yesmaximal, characteristic, complemented
11C89×#1924C211yesmaximal, characteristic, complemented
12C89×#1879C211yesmaximal, characteristic, complemented
13C89×#1875C211yesmaximal, characteristic, complemented
14C89×#1862C211yesmaximal, characteristic, complemented
15C89×#1762C211yesmaximal, characteristic, complemented
16C22×D8×C89C2211yescharacteristic
17C22×D8×C89C2211yescharacteristic
18C2×#127×C89C2211yescharacteristic
19C2×#121×C89—21no—
20C2×#121×C89C2211yescharacteristic
21C2×#121×C89C2211yescharacteristic
22C2×#121×C89C2211yescharacteristic
23C2×C4×D4×C89C2211yescharacteristic
24C2×C4×D4×C89C2211yescharacteristic
25C2×#117×C89C2211yescharacteristic
26#482×C89—24no—
27#459×C89—24no—
28C2×#107×C89C2211yescharacteristic
29C2×#106×C89C2211yescharacteristic
30C2×C4⋊C8×C89C2211yescharacteristic
31C2×#102×C89C2211yescharacteristic
32C2×#102×C89C2211yescharacteristic
33C2×#102×C89C2211yescharacteristic
34C2×#102×C89C2211yescharacteristic
35C2×#102×C89C2211yescharacteristic
36C2×#102×C89C2211yescharacteristic
37C2×#102×C89C2211yescharacteristic
38C2×#102×C89C2211yescharacteristic
39C2×C22⋊C8×C89C2211yescharacteristic
40C2×C22⋊C8×C89C2211yescharacteristic
41C2×#97×C89C2211yescharacteristic
42#394×C89—21no—
43#392×C89—21no—
44#390×C89—21no—
45#390×C89C2211yescharacteristic
46#390×C89C2211yescharacteristic
47#389×C89C2211yescharacteristic
48#389×C89C2211yescharacteristic
49#388×C89—21no—
50#386×C89—21no—
51#386×C89—21no—
52C4×C4⋊C4×C89C2211yescharacteristic
53C4×C22⋊C4×C89—21no—
54C4×C22⋊C4×C89C2211yescharacteristic
55#340×C89C2211yescharacteristic
56#340×C89C2211yescharacteristic
57#340×C89C2211yescharacteristic
58#340×C89C2211yescharacteristic
59#336×C89C2211yescharacteristic
60#336×C89C2211yescharacteristic
61C22×D4×C89—21no—
62C22×D4×C89—21no—
63C22×D4×C89—21no—
64C22×D4×C89—21no—
65C22×D4×C89—21no—
66C22×D4×C89C2311yescharacteristic
67C22×D4×C89C2311yescharacteristic
68C22×D4×C89C2311yescharacteristic
69C23×C4×C89—21no—
70C23×C4×C89—21no—
71C23×C4×C89C2311yescharacteristic
72C2×D8×C89—22no—
73C2×D8×C89—22no—
74C2×D8×C89—22no—
75C2×D8×C89—22no—
76C2×D8×C89—41no—
77C2×D8×C89—41no—
78C22×C8×C89C2311yescharacteristic
79C22×C8×C89C2311yescharacteristic
80C22×C8×C89C2311yescharacteristic
81C22×C8×C89C2311yescharacteristic
82#127×C89—22no—
83#127×C89—41no—
84#121×C89—22no—
85#121×C89—22no—
86#121×C89—22no—
87#121×C89—22no—
88#121×C89—44no—
89#121×C89—41no—
90#121×C89—41no—
91C4×D4×C89—22no—
92C4×D4×C89—22no—
93C4×D4×C89—41no—
94C4×D4×C89—41no—
95#117×C89—22no—
96#117×C89—41no—
97C2×C4⋊C4×C89—21no—
98C2×C4⋊C4×C89—21no—
99C2×C4⋊C4×C89C2311yescharacteristic
100C2×C4⋊C4×C89C2311yescharacteristic
101C2×C4⋊C4×C89C2311yescharacteristic
102C2×C4⋊C4×C89C2311yescharacteristic
103C2×C4⋊C4×C89C2311yescharacteristic
104C2×C22⋊C4×C89—21no—
105C2×C22⋊C4×C89—21no—
106C2×C22⋊C4×C89—21no—
107C2×C22⋊C4×C89—21no—
108C2×C22⋊C4×C89—21no—
109C2×C22⋊C4×C89—21no—
110C2×C22⋊C4×C89—21no—
111C2×C22⋊C4×C89—21no—
112C2×C22⋊C4×C89—21no—
113C2×C22⋊C4×C89—21no—
114C2×C22⋊C4×C89D411yescharacteristic
115C2×C22⋊C4×C89D411yescharacteristic
116C2×C42×C89—21no—
117C2×C42×C89—21no—
118C2×C42×C89C2311yescharacteristic
119C2×C42×C89C2311yescharacteristic
120#107×C89—22no—
121#106×C89—22no—
122C4⋊C8×C89—22no—
123#102×C89—22no—
124#102×C89—22no—
125#102×C89—22no—
126#102×C89—22no—
127#102×C89—22no—
128#102×C89—41no—
129#102×C89—41no—
130#102×C89D414yescomplemented
131C22⋊C8×C89—22no—
132C22⋊C8×C89—41no—
133#97×C89—41no—
134#95×C89—21no—
135#95×C89—21no—
136#95×C89—21no—
137#95×C89D411yescharacteristic
138#95×C89D411yescharacteristic
139C24×C89—21no—
140C24×C89—21no—
141C24×C89—21no—
142C24×C89C2×D411yescharacteristic
143C2×D4×C89—24no—
144C2×D4×C89—21no—
145C2×D4×C89—21no—
146C2×D4×C89—21no—
147C2×D4×C89—21no—
148C2×D4×C89—21no—
149C2×D4×C89—21no—
150C2×D4×C89—21no—
151C2×D4×C89—21no—
152C2×D4×C89—21no—
153C2×D4×C89—21no—
154C2×D4×C89—21no—
155C2×D4×C89—21no—
156C2×D4×C89—21no—
157C2×D4×C89—21no—
158C2×D4×C89—21no—
159C2×D4×C89—21no—
160C2×D4×C89—42no—
161C2×D4×C89—42no—
162C2×D4×C89—42no—
163C2×D4×C89—42no—
164C2×D4×C89—42no—
165C2×D4×C89—42no—
166C2×D4×C89—42no—
167C2×D4×C89—42no—
168C2×D4×C89—81no—
169C2×D4×C89—81no—
170C2×D4×C89—81no—
171C2×D4×C89—81no—
172C2×D4×C89—81no—
173C2×D4×C89—81no—
174C2×D4×C89C2×D412yes—
175C2×D4×C89#4112yes—
176C22×C4×C89—21no—
177C22×C4×C89—21no—
178C22×C4×C89—21no—
179C22×C4×C89—21no—
180C22×C4×C89—21no—
181C22×C4×C89—21no—
182C22×C4×C89—21no—
183C22×C4×C89—21no—
184C22×C4×C89—21no—
185C22×C4×C89—21no—
186C22×C4×C89—21no—
187C22×C4×C89—42no—
188C22×C4×C89—42no—
189C22×C4×C89—42no—
190C22×C4×C89—42no—
191C22×C4×C89—81no—
192C22×C4×C89—81no—
193C22×C4×C89C2×D411yescharacteristic
194C22×C4×C89C2×D411yescharacteristic
195C22×C4×C89C2×D411yescharacteristic
196C22×C4×C89C2×D411yescharacteristic
197C22×C4×C89C2×D411yescharacteristic
198C22×C4×C89C2411yescharacteristic
199D8×C89—44no—
200D8×C89—44no—
201C2×C8×C89—21no—
202C2×C8×C89—21no—
203C2×C8×C89—21no—
204C2×C8×C89—21no—
205C2×C8×C89—21no—
206C2×C8×C89—21no—
207C2×C8×C89—21no—
208C2×C8×C89—21no—
209C2×C8×C89—21no—
210C2×C8×C89—21no—
211C2×C8×C89—21no—
212C2×C8×C89C2×D412yes—
213C4⋊C4×C89—21no—
214C4⋊C4×C89—21no—
215C4⋊C4×C89—21no—
216C4⋊C4×C89—21no—
217C4⋊C4×C89—21no—
218C4⋊C4×C89—21no—
219C4⋊C4×C89—21no—
220C4⋊C4×C89—42no—
221C4⋊C4×C89—81no—
222C4⋊C4×C89C2×D412yes—
223C4⋊C4×C89#4112yes—
224C4⋊C4×C89#4112yes—
225C22⋊C4×C89—24no—
226C22⋊C4×C89—22no—
227C22⋊C4×C89—41no—
228C22⋊C4×C89—42no—
229C22⋊C4×C89—42no—
230C22⋊C4×C89—42no—
231C22⋊C4×C89—42no—
232C22⋊C4×C89—42no—
233C22⋊C4×C89—42no—
234C22⋊C4×C89—42no—
235C22⋊C4×C89—81no—
236C22⋊C4×C89—81no—
237C42×C89—21no—
238C42×C89—21no—
239C42×C89—21no—
240C42×C89—21no—
241C42×C89—42no—
242C42×C89—81no—
243C23×C89—22no—
244C23×C89—21no—
245C23×C89—21no—
246C23×C89—22no—
247C23×C89—21no—
248C23×C89—21no—
249C23×C89—21no—
250C23×C89—21no—
251C23×C89—21no—
252C23×C89—41no—
253C23×C89—41no—
254C23×C89—41no—
255C23×C89—41no—
256C23×C89—41no—
257C23×C89—41no—
258C23×C89—41no—
259C23×C89—41no—
260C23×C89—41no—
261C23×C89—41no—
262C23×C89—41no—
263C23×C89—41no—
264C23×C89—41no—
265C23×C89—41no—
266C23×C89—41no—
267C23×C89—41no—
268C23×C89—41no—
269C23×C89—41no—
270C23×C89—41no—
271C23×C89C22×D411yescharacteristic
272D4×C89—22no—
273D4×C89—22no—
274D4×C89—22no—
275D4×C89—22no—
276D4×C89—41no—
277D4×C89—41no—
278D4×C89—41no—
279D4×C89—41no—
280D4×C89—41no—
281D4×C89—41no—
282D4×C89—41no—
283D4×C89—41no—
284D4×C89—84no—
285D4×C89—84no—
286D4×C89—84no—
287D4×C89—84no—
288D4×C89—84no—
289C2×C4×C89—21no—
290C2×C4×C89—21no—
291C2×C4×C89—21no—
292C2×C4×C89—22no—
293C2×C4×C89—21no—
294C2×C4×C89—21no—
295C2×C4×C89—22no—
296C2×C4×C89—21no—
297C2×C4×C89—21no—
298C2×C4×C89—22no—
299C2×C4×C89—21no—
300C2×C4×C89—21no—
301C2×C4×C89—21no—
302C2×C4×C89—21no—
303C2×C4×C89—21no—
304C2×C4×C89—21no—
305C2×C4×C89—21no—
306C2×C4×C89—41no—
307C2×C4×C89—41no—
308C2×C4×C89—41no—
309C2×C4×C89—41no—
310C2×C4×C89—41no—
311C2×C4×C89—41no—
312C2×C4×C89—41no—
313C2×C4×C89—41no—
314C2×C4×C89—41no—
315C2×C4×C89—41no—
316C2×C4×C89—41no—
317C2×C4×C89—41no—
318C2×C4×C89—41no—
319C2×C4×C89—41no—
320C2×C4×C89—41no—
321C2×C4×C89—41no—
322C2×C4×C89—84no—
323C2×C4×C89—84no—
324C2×C4×C89AGL(1,ℤ/8)12yes—
325C2×C4×C89C22×D411yescharacteristic
326C2×C4×C89C2×#4111yescharacteristic
327C2×C4×C89C2×#4111yescharacteristic
328C2×C4×C89C2×#4111yescharacteristic
329C2×C4×C89H(5,𝔽2)11yescharacteristic
330C2×C4×C89H(5,𝔽2)11yescharacteristic
331C8×C89—22no—
332C8×C89—41no—
333C8×C89—41no—
334C8×C89—41no—
335C22×C89—41no—
336C22×C89—42no—
337C22×C89—41no—
338C22×C89—42no—
339C22×C89—41no—
340C22×C89—42no—
341C22×C89—42no—
342C22×C89—41no—
343C22×C89—42no—
344C22×C89—42no—
345C22×C89—41no—
346C22×C89—41no—
347C22×C89—41no—
348C22×C89—81no—
349C22×C89—81no—
350C22×C89—81no—
351C22×C89—81no—
352C22×C89—81no—
353C22×C89—81no—
354C22×C89—81no—
355C22×C89—81no—
356C22×C89—81no—
357C22×C89—81no—
358C22×C89—81no—
359C22×C89—81no—
360C22×C89—81no—
361C22×C89—81no—
362C22×C89—81no—
363C22×C89#52511yescharacteristic
364C22×C89D4211yescharacteristic
365C22×C89#54611yescharacteristic
366C22×C89C2×AGL(1,ℤ/8)11yescharacteristic
367C22×C89#57511yescharacteristic
368C22×C89#57611yescharacteristic
369C22×C89#57611yescharacteristic
370C4×C89—22no—
371C4×C89—42no—
372C4×C89—41no—
373C4×C89—42no—
374C4×C89—41no—
375C4×C89—41no—
376C4×C89—41no—
377C4×C89—42no—
378C4×C89—81no—
379C4×C89—81no—
380C4×C89#53211yescharacteristic
381C4×C89#54011yescharacteristic
382C4×C89#54611yescharacteristic
383C4×C89#55311yescharacteristic
384#26954C8911yesmaximal, characteristic, direct product factor, Sylow
385C2×C89—81no—
386C2×C89—82no—
387C2×C89—82no—
388C2×C89—161no—
389C2×C89#246411yescharacteristic
390C2×C89#311511yescharacteristic
391C2×C89#312211yescharacteristic
392C2×C89#326411yescharacteristic
393C2×C89#326811yescharacteristic
394C2×C89#330911yescharacteristic
395C2×C89#332511yescharacteristic
396C2×#482C2×C8911yescharacteristic, complemented
397C2×#459C2×C8911yescharacteristic, complemented
398#2428C2×C8911yescharacteristic, complemented
399#2363C2×C8911yescharacteristic, complemented
400#2088C2×C8911yescharacteristic, complemented
401#2041C2×C8911yescharacteristic, complemented
402#1999C2×C8911yescharacteristic, complemented
403#1999C2×C8911yescharacteristic, complemented
404#1972C2×C8911yescharacteristic, complemented
405#1925C2×C8911yescharacteristic, complemented
406#1924C2×C8911yescharacteristic, complemented
407#1879C2×C8911yescharacteristic, complemented
408#1875C2×C8911yescharacteristic, complemented
409#1862C2×C8911yescharacteristic, complemented
410#1762C2×C8911yescharacteristic, complemented
411C89#2695411yescharacteristic, direct product factor, Sylow
412C22×D8C22×C8911yescharacteristic
413C22×D8C22×C8911yescharacteristic
414C2×#127C22×C8911yescharacteristic
415C2×#121—21no—
416C2×#121C22×C8911yescharacteristic
417C2×#121C22×C8911yescharacteristic
418C2×#121C22×C8911yescharacteristic
419C2×C4×D4C22×C8911yescharacteristic
420C2×C4×D4C22×C8911yescharacteristic
421C2×#117C22×C8911yescharacteristic
422#482—24no—
423#459—24no—
424C2×#107C22×C8911yescharacteristic
425C2×#106C22×C8911yescharacteristic
426C2×C4⋊C8C22×C8911yescharacteristic
427C2×#102C22×C8911yescharacteristic
428C2×#102C22×C8911yescharacteristic
429C2×#102C22×C8911yescharacteristic
430C2×#102C22×C8911yescharacteristic
431C2×#102C22×C8911yescharacteristic
432C2×#102C22×C8911yescharacteristic
433C2×#102C22×C8911yescharacteristic
434C2×#102C22×C8911yescharacteristic
435C2×C22⋊C8C22×C8911yescharacteristic
436C2×C22⋊C8C22×C8911yescharacteristic
437C2×#97C22×C8911yescharacteristic
438#394—21no—
439#392—21no—
440#390—21no—
441#390C22×C8911yescharacteristic
442#390C22×C8911yescharacteristic
443#389C22×C8911yescharacteristic
444#389C22×C8911yescharacteristic
445#388—21no—
446#386—21no—
447#386—21no—
448C4×C4⋊C4C22×C8911yescharacteristic
449C4×C22⋊C4—21no—
450C4×C22⋊C4C22×C8911yescharacteristic
451#340C22×C8911yescharacteristic
452#340C22×C8911yescharacteristic
453#340C22×C8911yescharacteristic
454#340C22×C8911yescharacteristic
455#336C22×C8911yescharacteristic
456#336C22×C8911yescharacteristic
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—21no—
461C22×D4—21no—
462C22×D4C23×C8911yescharacteristic
463C22×D4C23×C8911yescharacteristic
464C22×D4C23×C8911yescharacteristic
465C23×C4—21no—
466C23×C4—21no—
467C23×C4C23×C8911yescharacteristic
468C2×D8—22no—
469C2×D8—22no—
470C2×D8—22no—
471C2×D8—22no—
472C2×D8—41no—
473C2×D8—41no—
474C22×C8C23×C8911yescharacteristic
475C22×C8C23×C8911yescharacteristic
476C22×C8C23×C8911yescharacteristic
477C22×C8C23×C8911yescharacteristic
478#127—22no—
479#127—41no—
480#121—22no—
481#121—22no—
482#121—22no—
483#121—22no—
484#121—44no—
485#121—41no—
486#121—41no—
487C4×D4—22no—
488C4×D4—22no—
489C4×D4—41no—
490C4×D4—41no—
491#117—22no—
492#117—41no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4C23×C8911yescharacteristic
496C2×C4⋊C4C23×C8911yescharacteristic
497C2×C4⋊C4C23×C8911yescharacteristic
498C2×C4⋊C4C23×C8911yescharacteristic
499C2×C4⋊C4C23×C8911yescharacteristic
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4D4×C8911yescharacteristic
511C2×C22⋊C4D4×C8911yescharacteristic
512C2×C42—21no—
513C2×C42—21no—
514C2×C42C23×C8911yescharacteristic
515C2×C42C23×C8911yescharacteristic
516#107—22no—
517#106—22no—
518C4⋊C8—22no—
519#102—22no—
520#102—22no—
521#102—22no—
522#102—22no—
523#102—22no—
524#102—41no—
525#102—41no—
526#102D4×C8914yescomplemented
527C22⋊C8—22no—
528C22⋊C8—41no—
529#97—41no—
530#95—21no—
531#95—21no—
532#95—21no—
533#95D4×C8911yescharacteristic
534#95D4×C8911yescharacteristic
535C24—21no—
536C24—21no—
537C24—21no—
538C24C2×D4×C8911yescharacteristic
539C2×D4—24no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—81no—
565C2×D4—81no—
566C2×D4—81no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4—81no—
570C2×D4C2×D4×C8912yes—
571C2×D4#41×C8912yes—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—81no—
588C22×C4—81no—
589C22×C4C2×D4×C8911yescharacteristic
590C22×C4C2×D4×C8911yescharacteristic
591C22×C4C2×D4×C8911yescharacteristic
592C22×C4C2×D4×C8911yescharacteristic
593C22×C4C2×D4×C8911yescharacteristic
594C22×C4C24×C8911yescharacteristic
595D8—44no—
596D8—44no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8C2×D4×C8912yes—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—42no—
617C4⋊C4—81no—
618C4⋊C4C2×D4×C8912yes—
619C4⋊C4#41×C8912yes—
620C4⋊C4#41×C8912yes—
621C22⋊C4—24no—
622C22⋊C4—22no—
623C22⋊C4—41no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—42no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—81no—
632C22⋊C4—81no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42—21no—
637C42—42no—
638C42—81no—
639C23—22no—
640C23—21no—
641C23—21no—
642C23—22no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23C22×D4×C8911yescharacteristic
668D4—22no—
669D4—22no—
670D4—22no—
671D4—22no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—84no—
681D4—84no—
682D4—84no—
683D4—84no—
684D4—84no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—84no—
719C2×C4—84no—
720C2×C4AGL(1,ℤ/8)×C8912yes—
721C2×C4C22×D4×C8911yescharacteristic
722C2×C4C2×#41×C8911yescharacteristic
723C2×C4C2×#41×C8911yescharacteristic
724C2×C4C2×#41×C8911yescharacteristic
725C2×C4H(5,𝔽2)×C8911yescharacteristic
726C2×C4H(5,𝔽2)×C8911yescharacteristic
727C8—22no—
728C8—41no—
729C8—41no—
730C8—41no—
731C22—41no—
732C22—41no—
733C22—42no—
734C22—41no—
735C22—42no—
736C22—41no—
737C22—42no—
738C22—42no—
739C22—41no—
740C22—42no—
741C22—42no—
742C22—41no—
743C22—41no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22#525×C8911yescharacteristic
760C22D42×C8911yescharacteristic
761C22#546×C8911yescharacteristic
762C22C2×AGL(1,ℤ/8)×C8911yescharacteristic
763C22#575×C8911yescharacteristic
764C22#576×C8911yescharacteristic
765C22#576×C8911yescharacteristic
766C4—22no—
767C4—41no—
768C4—42no—
769C4—42no—
770C4—41no—
771C4—42no—
772C4—41no—
773C4—41no—
774C4—81no—
775C4—81no—
776C4#532×C8911yescharacteristic
777C4#540×C8911yescharacteristic
778C4#546×C8911yescharacteristic
779C4#553×C8911yescharacteristic
780C2—81no—
781C2—82no—
782C2—82no—
783C2—161no—
784C2C89×#246411yescharacteristic
785C2C89×#311511yescharacteristic
786C2C89×#312211yescharacteristic
787C2C89×#326411yescharacteristic
788C2C89×#326811yescharacteristic
789C2C89×#330911yescharacteristic
790C2C89×#332511yescharacteristic
subgroupG/H
center, socleC23×C89C22×D4
commutator, Frattini, cosocleC22×C4C24×C89
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C89 ◁ C4×C22⋊C4×C89 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#482×C89C2semidirect
2. C2×#459×C89C2semidirect
3. C89×#2428C2semidirect
4. C89×#2363C2semidirect
5. C89×#2088C2semidirect
6. C89×#2041C2semidirect
7. C89×#1999C2semidirect
8. C89×#1999C2semidirect
9. C89×#1972C2semidirect
10. C89×#1925C2semidirect
11. C89×#1924C2semidirect
12. C89×#1879C2semidirect
13. C89×#1875C2semidirect
14. C89×#1862C2semidirect
15. C89×#1762C2semidirect
130. #102×C89D4semidirect
384. #26954C89direct (N × H)
396. C2×#482C2×C89semidirect
397. C2×#459C2×C89semidirect
398. #2428C2×C89semidirect
399. #2363C2×C89semidirect
400. #2088C2×C89semidirect
401. #2041C2×C89semidirect
402. #1999C2×C89semidirect
403. #1999C2×C89semidirect
404. #1972C2×C89semidirect
405. #1925C2×C89semidirect
406. #1924C2×C89semidirect
407. #1879C2×C89semidirect
408. #1875C2×C89semidirect
409. #1862C2×C89semidirect
410. #1762C2×C89semidirect
411. C89#26954direct (N × H)
526. #102D4×C89semidirect

Maximal subgroups

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

subgroupindex
C2×#482×C892
C2×#459×C892
C89×#24282
C89×#23632
C89×#20882
C89×#20412
C89×#19992
C89×#19722
C89×#19252
C89×#19242
C89×#18792
C89×#18752
C89×#18622
C89×#17622
#2695489