Finite Group Databasebeta

← #36575169

Subgroups — #36575169

Order 22784.

1058 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19151720C211yesmaximal, characteristic, complemented
2#26028979C211yesmaximal, characteristic, complemented
3C22×#15667939C211yesmaximal, characteristic, complemented
4#26028701C211yesmaximal, characteristic, complemented
5#26021146C211yesmaximal, characteristic, complemented
6#26020965C211yesmaximal, characteristic, complemented
7#26020902C211yesmaximal, characteristic, complemented
8#26020696C211yesmaximal, characteristic, complemented
9#26020581C211yesmaximal, characteristic, complemented
10#26020581C211yesmaximal, characteristic, complemented
11#26020529C211yesmaximal, characteristic, complemented
12#26020459C211yesmaximal, characteristic, complemented
13#26020099C211yesmaximal, characteristic, complemented
14#26020016C211yesmaximal, characteristic, complemented
15C89×#3002C211yesmaximal, characteristic
16C2×#15668019C2211yescharacteristic
17C2×#15668019C2211yescharacteristic
18C2×#15668019C2211yescharacteristic, complemented
19C22×#13083558C2211yescharacteristic
20C22×C4×Dic89C2211yescharacteristic
21#19151720—24no—
22#19151676—21no—
23#19151670—21no—
24#19151670—21no—
25D4×#10623494—21no—
26C2×#15667948C2211yescharacteristic, complemented
27C2×#15667948C2211yescharacteristic, complemented
28#19151625C2211yescharacteristic, complemented
29C2×#15667939—24no—
30C2×#15667939C2211yescharacteristic
31C2×#15667939C2211yescharacteristic
32C2×#15667939C2211yescharacteristic
33C2×#15667939C2211yescharacteristic
34C2×#15667939C2211yescharacteristic, complemented
35C2×#15667939C2211yescharacteristic, complemented
36#19151565—21no—
37#19151565—21no—
38#19151565C2211yescharacteristic
39#19151565C2211yescharacteristic
40#19151565C2211yescharacteristic, complemented
41#19151562—21no—
42#19151562C2211yescharacteristic
43C2×C22⋊#10623494—21no—
44C2×C22⋊#10623494C2211yescharacteristic
45#19151554C2211yescharacteristic, complemented
46C2×#15667922C2211yescharacteristic, complemented
47C2×#15667922C2211yescharacteristic, complemented
48#19151363C2211yescharacteristic, complemented
49#19151363C2211yescharacteristic, complemented
50#19151357C2211yescharacteristic, complemented
51#19151357C2211yescharacteristic, complemented
52#19151352C2211yescharacteristic, complemented
53#19151352C2211yescharacteristic, complemented
54C22×#41×C89C2211yescharacteristic
55C2×#135×C89C2211yescharacteristic
56C2×#135×C89C2211yescharacteristic
57#525×C89C2211yescharacteristic
58#452×C89C411yescharacteristic, complemented
59#452×C89C411yescharacteristic, complemented
60#451×C89C411yescharacteristic, complemented
61#450×C89C411yescharacteristic, complemented
62#449×C89C411yescharacteristic, complemented
63#449×C89C411yescharacteristic, complemented
64#448×C89C411yescharacteristic, complemented
65#447×C89C411yescharacteristic, complemented
66#416×C89C2211yescharacteristic
67#416×C89C2211yescharacteristic
68C2×C22⋊C8×C89C2211yescharacteristic
69C23×Dic89—21no—
70#15668019—22no—
71#15668019—22no—
72#15668019—22no—
73#15668019—41no—
74#15668019—41no—
75#15668019—41no—
76C2×#13083558—21no—
77C2×#13083558—21no—
78C2×#13083558—21no—
79C2×#13083558—22no—
80C2×#13083558—21no—
81C2×#13083558—41no—
82C2×#13083558C2311yescharacteristic
83C2×#13083558C2311yescharacteristic
84C2×#13083558C2311yescharacteristic
85C2×#13083558C2311yescharacteristic
86C22×#10623494—21no—
87C22×#10623494—21no—
88C22×#10623494—21no—
89C22×#10623494—21no—
90C22×#10623494C2311yescharacteristic
91C22×#10623494C2311yescharacteristic
92C2×C4×Dic89—22no—
93C2×C4×Dic89—21no—
94C2×C4×Dic89—41no—
95C2×C4×Dic89C2311yescharacteristic
96C2×C4×Dic89C2311yescharacteristic
97#15667948—22no—
98#15667948—41no—
99C4⋊#10623494—21no—
100C4⋊#10623494—21no—
101#15667939—22no—
102#15667939—22no—
103#15667939—22no—
104#15667939—22no—
105#15667939—41no—
106#15667939D414yescomplemented
107C22⋊#10623494—21no—
108C22⋊#10623494—21no—
109C22⋊#10623494—21no—
110C22⋊#10623494—21no—
111C22⋊#10623494—21no—
112C22⋊#10623494—21no—
113C22⋊#10623494—21no—
114C22⋊#10623494—21no—
115C22⋊#10623494D411yescharacteristic
116C22⋊#10623494D411yescharacteristic
117C22⋊#10623494D411yescharacteristic
118C22⋊#10623494D411yescharacteristic
119#15667923—21no—
120#15667922—22no—
121#15667922—41no—
122C4×#10623494—21no—
123C2×#41×C89—21no—
124C2×#41×C89—21no—
125C2×#41×C89—22no—
126C2×#41×C89—22no—
127C2×#41×C89—41no—
128C2×#41×C89—41no—
129C2×#41×C89C2×C411yescharacteristic
130C2×#41×C89C2×C411yescharacteristic
131C2×#41×C89C2311yescharacteristic
132C2×#41×C89C2311yescharacteristic
133C2×#41×C89C2311yescharacteristic
134C22×Q8×C89C2×C411yescharacteristic
135C22×D4×C89—21no—
136C22×D4×C89C2×C411yescharacteristic
137C23×C4×C89—21no—
138C23×C4×C89C2311yescharacteristic
139#135×C89—22no—
140#135×C89—22no—
141#135×C89—41no—
142#135×C89—41no—
143C2×Q16×C89C2×C411yescharacteristic, complemented
144C2×Q16×C89C2×C411yescharacteristic, complemented
145C2×SD16×C89C2×C411yescharacteristic, complemented
146C2×SD16×C89C2×C411yescharacteristic, complemented
147C2×SD16×C89C2×C411yescharacteristic, complemented
148C2×SD16×C89C2×C411yescharacteristic, complemented
149C2×D8×C89C2×C411yescharacteristic, complemented
150C2×D8×C89C2×C411yescharacteristic, complemented
151C22×C8×C89C2311yescharacteristic
152C22×C8×C89C2311yescharacteristic
153#123×C89—21no—
154C22⋊Q8×C89C2×C411yescharacteristic
155C22⋊Q8×C89C2×C411yescharacteristic
156#121×C89C2×C411yescharacteristic
157#121×C89C2×C411yescharacteristic
158#120×C89—21no—
159C4×D4×C89—21no—
160C4×D4×C89—21no—
161#117×C89C2311yescharacteristic
162#103×C89C2×C411yescharacteristic, complemented
163#103×C89C2×C411yescharacteristic, complemented
164#103×C89C2×C411yescharacteristic, complemented
165#103×C89C2×C411yescharacteristic, complemented
166#102×C89C2×C411yescharacteristic, complemented
167#102×C89C2×C411yescharacteristic, complemented
168#102×C89C2×C411yescharacteristic, complemented
169#102×C89C2×C411yescharacteristic, complemented
170C22⋊C8×C89C2×C411yescharacteristic
171C22⋊C8×C89C2×C411yescharacteristic
172C22⋊C8×C89C2×C411yescharacteristic
173C22⋊C8×C89C2×C411yescharacteristic
174C22×Dic89—21no—
175C22×Dic89—21no—
176C22×Dic89—42no—
177C22×Dic89—42no—
178C22×Dic89—42no—
179#13083558—21no—
180#13083558—21no—
181#13083558—21no—
182#13083558—21no—
183#13083558—21no—
184#13083558—21no—
185#13083558—21no—
186#13083558—42no—
187#13083558—42no—
188#13083558—42no—
189#13083558—42no—
190#13083558C2×D412yes—
191C2×#10623494—21no—
192C2×#10623494—21no—
193C2×#10623494—21no—
194C2×#10623494—21no—
195C2×#10623494—21no—
196C2×#10623494—21no—
197C2×#10623494—21no—
198C2×#10623494—21no—
199C2×#10623494—42no—
200C2×#10623494—42no—
201C2×#10623494—42no—
202C2×#10623494—42no—
203C2×#10623494C2×D411yescharacteristic
204C2×#10623494C2×D411yescharacteristic
205C2×#10623494C2×D411yescharacteristic
206C2×#10623494C2×D411yescharacteristic
207C4×Dic89—21no—
208C4×Dic89—21no—
209C4×Dic89—21no—
210C4×Dic89—42no—
211C4×Dic89C2×D412yes—
212C24×C89—21no—
213C24×C89#4111yescharacteristic
214#41×C89—21no—
215#41×C89—21no—
216#41×C89—22no—
217#41×C89—22no—
218#41×C89—21no—
219#41×C89—21no—
220#41×C89—21no—
221#41×C89—21no—
222#41×C89—21no—
223#41×C89—21no—
224#41×C89—21no—
225#41×C89—21no—
226#41×C89—42no—
227#41×C89—42no—
228#41×C89—41no—
229#41×C89—41no—
230#41×C89—42no—
231#41×C89—42no—
232#41×C89C2×D412yes—
233#41×C89#4112yes—
234C2×Q8×C89—21no—
235C2×Q8×C89—22no—
236C2×Q8×C89—41no—
237C2×Q8×C89C22×C411yescharacteristic
238C2×Q8×C89C22×C411yescharacteristic
239C2×Q8×C89C22×C411yescharacteristic
240C2×D4×C89—21no—
241C2×D4×C89—22no—
242C2×D4×C89—21no—
243C2×D4×C89—21no—
244C2×D4×C89—21no—
245C2×D4×C89—21no—
246C2×D4×C89—21no—
247C2×D4×C89—21no—
248C2×D4×C89—21no—
249C2×D4×C89—41no—
250C2×D4×C89—42no—
251C2×D4×C89—42no—
252C2×D4×C89C22×C411yescharacteristic
253C2×D4×C89C22×C411yescharacteristic
254C2×D4×C89C22×C411yescharacteristic
255C22×C4×C89—21no—
256C22×C4×C89—21no—
257C22×C4×C89—21no—
258C22×C4×C89—21no—
259C22×C4×C89—21no—
260C22×C4×C89—21no—
261C22×C4×C89—21no—
262C22×C4×C89—21no—
263C22×C4×C89—21no—
264C22×C4×C89—21no—
265C22×C4×C89—42no—
266C22×C4×C89—42no—
267C22×C4×C89C22×C411yescharacteristic
268C22×C4×C89C22×C411yescharacteristic
269C22×C4×C89C2×D411yescharacteristic
270C22×C4×C89C2×D411yescharacteristic
271C22×C4×C89#4111yescharacteristic
272C22×C4×C89C2411yescharacteristic
273Q16×C89—22no—
274Q16×C89—41no—
275SD16×C89—22no—
276SD16×C89—22no—
277SD16×C89—41no—
278SD16×C89—41no—
279D8×C89—22no—
280D8×C89—41no—
281C2×C8×C89—21no—
282C2×C8×C89—21no—
283C2×C8×C89—21no—
284C2×C8×C89—21no—
285C2×C8×C89C22×C411yescharacteristic
286C2×C8×C89C22×C411yescharacteristic
287C2×C8×C89C22×C411yescharacteristic
288C2×C8×C89C22×C411yescharacteristic
289C4⋊C4×C89—21no—
290C4⋊C4×C89—21no—
291C4⋊C4×C89C22×C411yescharacteristic
292C4⋊C4×C89C22×C411yescharacteristic
293C22⋊C4×C89—21no—
294C22⋊C4×C89—21no—
295C22⋊C4×C89—21no—
296C22⋊C4×C89—21no—
297C22⋊C4×C89—21no—
298C42×C89—21no—
299C23×C89—21no—
300C23×C89—21no—
301C23×C89—21no—
302C23×C89—22no—
303C23×C89—21no—
304C23×C89—21no—
305C23×C89—41no—
306C23×C89—42no—
307C23×C89—42no—
308C23×C89—81no—
309C23×C89C4×D411yescharacteristic
310C23×C89C4×D411yescharacteristic
311C23×C89C2×#4111yescharacteristic
312Q8×C89—21no—
313Q8×C89—21no—
314Q8×C89—21no—
315Q8×C89—21no—
316Q8×C89—21no—
317Q8×C89—42no—
318Q8×C89C4×D412yes—
319D4×C89—22no—
320D4×C89—22no—
321D4×C89—21no—
322D4×C89—21no—
323D4×C89—21no—
324D4×C89—21no—
325D4×C89—21no—
326D4×C89—42no—
327D4×C89—42no—
328D4×C89—42no—
329D4×C89—41no—
330D4×C89—41no—
331D4×C89—41no—
332D4×C89—41no—
333D4×C89—42no—
334D4×C89—81no—
335D4×C89C4×D412yes—
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—21no—
343C2×C4×C89—21no—
344C2×C4×C89—21no—
345C2×C4×C89—22no—
346C2×C4×C89—21no—
347C2×C4×C89—21no—
348C2×C4×C89—22no—
349C2×C4×C89—21no—
350C2×C4×C89—21no—
351C2×C4×C89—21no—
352C2×C4×C89—21no—
353C2×C4×C89—42no—
354C2×C4×C89—42no—
355C2×C4×C89—42no—
356C2×C4×C89—41no—
357C2×C4×C89—41no—
358C2×C4×C89—41no—
359C2×C4×C89—41no—
360C2×C4×C89C4×D411yescharacteristic
361C2×C4×C89C4×D411yescharacteristic
362C2×C4×C89C23×C411yescharacteristic
363C2×C4×C89C22×D411yescharacteristic
364C2×C4×C89C22×D411yescharacteristic
365C2×C4×C89C2×#4111yescharacteristic
366C2×C4×C89H(5,𝔽2)11yescharacteristic
367C2×C4×C89H(5,𝔽2)11yescharacteristic
368C2×Dic89—22no—
369C2×Dic89—22no—
370C2×Dic89—41no—
371C2×Dic89—41no—
372C2×Dic89—41no—
373C2×Dic89—48no—
374C2×Dic89—41no—
375C8×C89—21no—
376C8×C89—21no—
377C8×C89—21no—
378C8×C89—21no—
379#10623494—21no—
380#10623494—21no—
381#10623494—22no—
382#10623494—21no—
383#10623494—21no—
384#10623494—41no—
385#10623494—41no—
386#10623494—41no—
387C22×C89—21no—
388C22×C89—21no—
389C22×C89—21no—
390C22×C89—21no—
391C22×C89—21no—
392C22×C89—22no—
393C22×C89—21no—
394C22×C89—21no—
395C22×C89—42no—
396C22×C89—42no—
397C22×C89—41no—
398C22×C89—41no—
399C22×C89—41no—
400C22×C89—41no—
401C22×C89—41no—
402C22×C89—41no—
403C22×C89—41no—
404C22×C89—41no—
405C22×C89—84no—
406C22×C89#44412yescomplemented
407C22×C89C2×C4×D411yescharacteristic
408C22×C89#54611yescharacteristic
409C22×C89#55111yescharacteristic
410C4×C89—21no—
411C4×C89—21no—
412C4×C89—22no—
413C4×C89—41no—
414C4×C89—41no—
415C4×C89—41no—
416C4×C89—41no—
417C4×C89C2×C4×D411yescharacteristic
418C4×C89#51811yescharacteristic
419C4×C89D4211yescharacteristic
420C4×C89#54611yescharacteristic
421Dic89—42no—
422Dic89—42no—
423#22886—891nomaximal, Sylow
424C2×C89—21no—
425C2×C89—22no—
426C2×C89—21no—
427C2×C89—41no—
428C2×C89—42no—
429C2×C89—81no—
430C2×C89—81no—
431C2×C89#235811yescharacteristic
432C2×C89C2×#44411yescharacteristic
433C2×C89#295611yescharacteristic
434#3002D8911yescharacteristic
435C2×#444—891no—
436#2933—891no—
437C22×#104—891no—
438#2880—891no—
439#1975—891no—
440#1938—891no—
441#1929—891no—
442#1896—891no—
443#1876—891no—
444#1876—891no—
445#1866—891no—
446#1855—891no—
447#1765—891no—
448#1749—891no—
449C89#2288611yescharacteristic, complemented, Sylow
450C22×#41C2×D8911yescharacteristic
451C2×#135C2×D8911yescharacteristic
452C2×#135C2×D8911yescharacteristic
453C2×#131—891no—
454C2×#131—891no—
455C2×#131—891no—
456C22×M16—891no—
457#525C2×D8911yescharacteristic
458C22×C42—891no—
459#452Dic8911yescharacteristic, complemented
460#452Dic8911yescharacteristic, complemented
461#451Dic8911yescharacteristic, complemented
462#450Dic8911yescharacteristic, complemented
463#449Dic8911yescharacteristic, complemented
464#449Dic8911yescharacteristic, complemented
465#448Dic8911yescharacteristic, complemented
466#447Dic8911yescharacteristic, complemented
467#444—1784no—
468#436—1781no—
469#435—1781no—
470#435—1781no—
471C8×D4—1781no—
472C2×#108—891no—
473C2×#108—891no—
474#424—891no—
475C2×#104—891no—
476C2×#104—891no—
477C2×#104—891no—
478C2×#104—891no—
479C2×#104—891no—
480C2×#104—891no—
481C2×#104—1784no—
482#416C2×D8911yescharacteristic
483#416C2×D8911yescharacteristic
484#408—891no—
485#408—891no—
486#408—891no—
487#408—1781no—
488#408—1781no—
489#407—891no—
490#407—1781no—
491C2×C22⋊C8—891no—
492C2×C22⋊C8—1781no—
493C2×C22⋊C8C2×D8911yescharacteristic
494#405—891no—
495C2×#97—891no—
496C2×#97—891no—
497#341—891no—
498#341—891no—
499#339—891no—
500#339—891no—
501#336—891no—
502#336—891no—
503C2×#41—21no—
504C2×#41—21no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41C2×Dic8911yescharacteristic
510C2×#41C2×Dic8911yescharacteristic
511C2×#41C22×D8911yescharacteristic
512C2×#41C22×D8911yescharacteristic
513C2×#41C22×D8911yescharacteristic
514C22×Q8C2×Dic8911yescharacteristic
515C22×D4—21no—
516C22×D4C2×Dic8911yescharacteristic
517C23×C4—21no—
518C23×C4—1781no—
519C23×C4C22×D8911yescharacteristic
520#135—22no—
521#135—22no—
522#135—41no—
523#135—41no—
524C2×Q16C2×Dic8911yescharacteristic, complemented
525C2×Q16C2×Dic8911yescharacteristic, complemented
526C2×SD16C2×Dic8911yescharacteristic, complemented
527C2×SD16C2×Dic8911yescharacteristic, complemented
528C2×SD16C2×Dic8911yescharacteristic, complemented
529C2×SD16C2×Dic8911yescharacteristic, complemented
530C2×D8C2×Dic8911yescharacteristic, complemented
531C2×D8C2×Dic8911yescharacteristic, complemented
532#131—3561no—
533#131—3561no—
534#131—3561no—
535#131—1782no—
536#131—1782no—
537#131—1782no—
538C2×M16—891no—
539C2×M16—891no—
540C2×M16—891no—
541C2×M16—891no—
542C2×M16—3561no—
543C2×M16—1781no—
544C2×M16—1781no—
545C2×M16—1781no—
546C2×M16—1782no—
547C2×M16—1781no—
548C22×C8—891no—
549C22×C8—891no—
550C22×C8—1781no—
551C22×C8—1781no—
552C22×C8—1781no—
553C22×C8—1781no—
554C22×C8C22×D8911yescharacteristic
555C22×C8C22×D8911yescharacteristic
556#123—21no—
557C22⋊Q8C2×Dic8911yescharacteristic
558C22⋊Q8C2×Dic8911yescharacteristic
559#121C2×Dic8911yescharacteristic
560#121C2×Dic8911yescharacteristic
561#120—21no—
562C4×D4—21no—
563C4×D4—21no—
564#117C22×D8911yescharacteristic
565C2×C42—891no—
566C2×C42—891no—
567C2×C42—3561no—
568C2×C42—1782no—
569C2×C42—1781no—
570#108—3561no—
571#108—1782no—
572C4⋊C8—1781no—
573C4⋊C8—1781no—
574#104—894no—
575#104—3561no—
576#104—1782no—
577#104—1782no—
578#104—1782no—
579#104—1782no—
580#103C2×Dic8911yescharacteristic, complemented
581#103C2×Dic8911yescharacteristic, complemented
582#103C2×Dic8911yescharacteristic, complemented
583#103C2×Dic8911yescharacteristic, complemented
584#102C2×Dic8911yescharacteristic, complemented
585#102C2×Dic8911yescharacteristic, complemented
586#102C2×Dic8911yescharacteristic, complemented
587#102C2×Dic8911yescharacteristic, complemented
588C22⋊C8—891no—
589C22⋊C8—891no—
590C22⋊C8—891no—
591C22⋊C8—891no—
592C22⋊C8—1781no—
593C22⋊C8—1781no—
594C22⋊C8—1781no—
595C22⋊C8—1781no—
596C22⋊C8—1781no—
597C22⋊C8—1781no—
598C22⋊C8—1781no—
599C22⋊C8—1781no—
600C22⋊C8C2×Dic8911yescharacteristic
601C22⋊C8C2×Dic8911yescharacteristic
602C22⋊C8C2×Dic8911yescharacteristic
603C22⋊C8C2×Dic8911yescharacteristic
604#97—3561no—
605#97—1781no—
606#97—1782no—
607C4×C8—1781no—
608C24—21no—
609C24#1308357311yescharacteristic
610#41—21no—
611#41—21no—
612#41—22no—
613#41—22no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—21no—
619#41—21no—
620#41—21no—
621#41—21no—
622#41—42no—
623#41—42no—
624#41—41no—
625#41—41no—
626#41—42no—
627#41—42no—
628#41D4×D8912yes—
629#41#1308357312yes—
630C2×Q8—21no—
631C2×Q8—22no—
632C2×Q8—41no—
633C2×Q8C22×Dic8911yescharacteristic
634C2×Q8C22×Dic8911yescharacteristic
635C2×Q8C22×Dic8911yescharacteristic
636C2×D4—21no—
637C2×D4—22no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—41no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4C22×Dic8911yescharacteristic
649C2×D4C22×Dic8911yescharacteristic
650C2×D4C22×Dic8911yescharacteristic
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—21no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—3562no—
664C22×C4—3562no—
665C22×C4—3562no—
666C22×C4—1781no—
667C22×C4—1781no—
668C22×C4C22×Dic8911yescharacteristic
669C22×C4C22×Dic8911yescharacteristic
670C22×C4D4×D8911yescharacteristic
671C22×C4D4×D8911yescharacteristic
672C22×C4#1308357311yescharacteristic
673C22×C4C23×D8911yescharacteristic
674Q16—22no—
675Q16—41no—
676SD16—22no—
677SD16—22no—
678SD16—41no—
679SD16—41no—
680D8—22no—
681D8—41no—
682M16—892no—
683M16—3562no—
684M16—3562no—
685M16—3562no—
686M16—3562no—
687M16—1781no—
688M16—1781no—
689M16—1781no—
690M16—1781no—
691M16—1781no—
692M16—1781no—
693M16—1781no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—891no—
699C2×C8—891no—
700C2×C8—891no—
701C2×C8—891no—
702C2×C8—3562no—
703C2×C8—3562no—
704C2×C8—3562no—
705C2×C8—3562no—
706C2×C8—1781no—
707C2×C8—1781no—
708C2×C8—1781no—
709C2×C8—1781no—
710C2×C8—1781no—
711C2×C8—1781no—
712C2×C8—1781no—
713C2×C8—1781no—
714C2×C8C22×Dic8911yescharacteristic
715C2×C8C22×Dic8911yescharacteristic
716C2×C8C22×Dic8911yescharacteristic
717C2×C8C22×Dic8911yescharacteristic
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4C22×Dic8911yescharacteristic
721C4⋊C4C22×Dic8911yescharacteristic
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—21no—
727C42—21no—
728C42—892no—
729C42—3562no—
730C42—1781no—
731C42—1781no—
732C42—1781no—
733C23—22no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—41no—
740C23—42no—
741C23—42no—
742C23—81no—
743C23D4×Dic8911yescharacteristic
744C23D4×Dic8911yescharacteristic
745C23C2×#1308357311yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—21no—
749Q8—21no—
750Q8—21no—
751Q8—42no—
752Q8D4×Dic8912yes—
753D4—22no—
754D4—22no—
755D4—21no—
756D4—21no—
757D4—21no—
758D4—21no—
759D4—21no—
760D4—42no—
761D4—42no—
762D4—42no—
763D4—42no—
764D4—41no—
765D4—41no—
766D4—41no—
767D4—41no—
768D4—81no—
769D4D4×Dic8912yes—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—3561no—
795C2×C4—3561no—
796C2×C4—3561no—
797C2×C4—3568no—
798C2×C4—3561no—
799C2×C4—1782no—
800C2×C4—1782no—
801C2×C4D4×Dic8911yescharacteristic
802C2×C4D4×Dic8911yescharacteristic
803C2×C4C23×Dic8911yescharacteristic
804C2×C4C2×D4×D8911yescharacteristic
805C2×C4C2×D4×D8911yescharacteristic
806C2×C4C2×#1308357311yescharacteristic
807C2×C4#1566805711yescharacteristic
808C2×C4#1566805711yescharacteristic
809C8—21no—
810C8—21no—
811C8—21no—
812C8—21no—
813C8—3561no—
814C8—3561no—
815C8—3561no—
816C8—1781no—
817C8—1781no—
818C8—1782no—
819C8—1781no—
820C8—1781no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—22no—
827C22—21no—
828C22—21no—
829C22—42no—
830C22—42no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—84no—
840C22#1915172012yescomplemented
841C22C2×D4×Dic8911yescharacteristic
842C22#1915223511yescharacteristic
843C22#1915227911yescharacteristic
844C4—21no—
845C4—21no—
846C4—22no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—41no—
851C4—3562no—
852C4—3562no—
853C4C2×D4×Dic8911yescharacteristic
854C4#1915207311yescharacteristic
855C4#1915223011yescharacteristic
856C4#1915223511yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—42no—
862C2—81no—
863C2—81no—
864C2#2602323611yescharacteristic
865C2C2×#1915172011yescharacteristic
866C2#2602916211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D89
commutatorC2×C4×C89C23×C4
FrattiniC22×C4C23×D89
Fitting, prime radicalC89×#3002C2
socleC22×C89C2×C4×D4
cosocleC22×C4×C89C24
hypercenter#3002D89
hypocenterC89#22886
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #3002

Complements

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

NH ≅ G/Ntype
1. C2×#19151720C2semidirect
2. #26028979C2semidirect
3. C22×#15667939C2semidirect
4. #26028701C2semidirect
5. #26021146C2semidirect
6. #26020965C2semidirect
7. #26020902C2semidirect
8. #26020696C2semidirect
9. #26020581C2semidirect
10. #26020581C2semidirect
11. #26020529C2semidirect
12. #26020459C2semidirect
13. #26020099C2semidirect
14. #26020016C2semidirect
18. C2×#15668019C22semidirect
26. C2×#15667948C22semidirect
27. C2×#15667948C22semidirect
28. #19151625C22semidirect
34. C2×#15667939C22semidirect
35. C2×#15667939C22semidirect
40. #19151565C22semidirect
45. #19151554C22semidirect
46. C2×#15667922C22semidirect
47. C2×#15667922C22semidirect
48. #19151363C22semidirect
49. #19151363C22semidirect
50. #19151357C22semidirect
51. #19151357C22semidirect
52. #19151352C22semidirect
53. #19151352C22semidirect
58. #452×C89C4semidirect
59. #452×C89C4semidirect
60. #451×C89C4semidirect
61. #450×C89C4semidirect
62. #449×C89C4semidirect
63. #449×C89C4semidirect
64. #448×C89C4semidirect
65. #447×C89C4semidirect
106. #15667939D4semidirect
143. C2×Q16×C89C2×C4semidirect
144. C2×Q16×C89C2×C4semidirect
145. C2×SD16×C89C2×C4semidirect
146. C2×SD16×C89C2×C4semidirect
147. C2×SD16×C89C2×C4semidirect
148. C2×SD16×C89C2×C4semidirect
149. C2×D8×C89C2×C4semidirect
150. C2×D8×C89C2×C4semidirect
162. #103×C89C2×C4semidirect
163. #103×C89C2×C4semidirect
164. #103×C89C2×C4semidirect
165. #103×C89C2×C4semidirect
166. #102×C89C2×C4semidirect
167. #102×C89C2×C4semidirect
168. #102×C89C2×C4semidirect
169. #102×C89C2×C4semidirect
406. C22×C89#444semidirect
449. C89#22886semidirect
459. #452Dic89semidirect
460. #452Dic89semidirect
461. #451Dic89semidirect
462. #450Dic89semidirect
463. #449Dic89semidirect
464. #449Dic89semidirect
465. #448Dic89semidirect
466. #447Dic89semidirect
524. C2×Q16C2×Dic89semidirect
525. C2×Q16C2×Dic89semidirect
526. C2×SD16C2×Dic89semidirect
527. C2×SD16C2×Dic89semidirect
528. C2×SD16C2×Dic89semidirect
529. C2×SD16C2×Dic89semidirect
530. C2×D8C2×Dic89semidirect
531. C2×D8C2×Dic89semidirect
580. #103C2×Dic89semidirect
581. #103C2×Dic89semidirect
582. #103C2×Dic89semidirect
583. #103C2×Dic89semidirect
584. #102C2×Dic89semidirect
585. #102C2×Dic89semidirect
586. #102C2×Dic89semidirect
587. #102C2×Dic89semidirect
840. C22#19151720semidirect

Maximal subgroups

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

subgroupindex
C2×#191517202
#260289792
C22×#156679392
#260287012
#260211462
#260209652
#260209022
#260206962
#260205812
#260205292
#260204592
#260200992
#260200162
C89×#30022
#2288689