Finite Group Databasebeta

← #25117332

Subgroups — #25117332

Order 11008.

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
1#19143815C211yesmaximal, characteristic
2C2×#14583019C211yesmaximal, characteristic, complemented
3#19143319C211yesmaximal, characteristic, complemented
4C2×#104×D43C211yesmaximal, characteristic, complemented
5#19143042C211yesmaximal, characteristic, complemented
6#19135486C211yesmaximal, characteristic, complemented
7#19135305C211yesmaximal, characteristic, complemented
8#19135241C211yesmaximal, characteristic, complemented
9#19135037C211yesmaximal, characteristic, complemented
10#19134921C211yesmaximal, characteristic, complemented
11#19134920C211yesmaximal, characteristic, complemented
12#19134798C211yesmaximal, characteristic, complemented
13#19134442C211yesmaximal, characteristic, complemented
14#19134356C211yesmaximal, characteristic, complemented
15C43×#1866C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17C2×#13063347C2211yescharacteristic
18C2×#13063345C2211yescharacteristic
19C2×#13063332C2211yescharacteristic
20C2×#13063331C2211yescharacteristic, complemented
21C2×M16×D43C2211yescharacteristic
22#14583411C2211yescharacteristic
23C2×C42×D43C2211yescharacteristic
24#14583064C411yescharacteristic, complemented
25#14583062C411yescharacteristic, complemented
26#14583056C411yescharacteristic, complemented
27#14583051C411yescharacteristic, complemented
28#14583047C411yescharacteristic, complemented
29#14583045C411yescharacteristic, complemented
30#14583039C411yescharacteristic, complemented
31#14583034C411yescharacteristic, complemented
32#14583019—24no—
33#14582976—21no—
34#14582969—21no—
35#14582969—21no—
36#14582964—21no—
37C2×#13063260C2211yescharacteristic, complemented
38C2×#13063253C2211yescharacteristic
39C2×#13063253C2211yescharacteristic, complemented
40C2×#13063252C2211yescharacteristic
41C2×#13063251C2211yescharacteristic
42C2×#13063251C2211yescharacteristic, complemented
43#104×D43—24no—
44#14582893C2211yescharacteristic
45#14582867—21no—
46#14582867C2211yescharacteristic
47#14582867C2211yescharacteristic, complemented
48#14582865—21no—
49#14582865C2211yescharacteristic
50#14582862—21no—
51#14582862C2211yescharacteristic
52C2×(C2×D43)⋊C8—21no—
53C2×(C2×D43)⋊C8C2211yescharacteristic
54C2×(C2×D43)⋊C8C2211yescharacteristic
55#14582855C2211yescharacteristic, complemented
56C2×#13063235C2211yescharacteristic, complemented
57C2×#13063235C2211yescharacteristic, complemented
58#14582664C2211yescharacteristic, complemented
59#14582663C2211yescharacteristic, complemented
60#14582658C2211yescharacteristic, complemented
61#14582654C2211yescharacteristic, complemented
62C2×#131×C43C2211yescharacteristic
63C2×#108×C43C2211yescharacteristic, complemented
64C43×#424C2211yescharacteristic, complemented
65C2×#104×C43C2211yescharacteristic
66C43×#416C2211yescharacteristic
67C43×#339C2211yescharacteristic, complemented
68C43×#336C2211yescharacteristic, complemented
69C2×#10621902C2×C411yescharacteristic
70C2×#10621898—21no—
71C2×#10621898C2311yescharacteristic
72C2×#10621898C2311yescharacteristic
73C2×#10621900—21no—
74C2×#10621900C2×C411yescharacteristic
75#41×D43—22no—
76#41×D43—22no—
77#41×D43—41no—
78#41×D43—41no—
79C2×Q8×D43C2×C411yescharacteristic
80C2×D4×D43—21no—
81C2×D4×D43C2×C411yescharacteristic
82C22×C4×D43—21no—
83C22×C4×D43—21no—
84C22×C4×D43C2311yescharacteristic
85#13063347—41no—
86#13063347—41no—
87#13063345—22no—
88#13063345—22no—
89C2×Dic172C2×C411yescharacteristic, complemented
90C2×#10621885C2×C411yescharacteristic, complemented
91C2×#10621873C2×C411yescharacteristic, complemented
92C2×#10621873C2×C411yescharacteristic, complemented
93C2×#10621883C2×C411yescharacteristic, complemented
94C2×#10621884C2×C411yescharacteristic, complemented
95C2×D344C2×C411yescharacteristic, complemented
96C2×#10621882C2×C411yescharacteristic, complemented
97#13063332—22no—
98#13063332—41no—
99#13063331—22no—
100#13063331—41no—
101C2×#10621877—21no—
102C2×#10621877C2311yescharacteristic
103C2×#10621877C2311yescharacteristic
104C2×#10621872—21no—
105C2×#10621872—21no—
106M16×D43—22no—
107M16×D43—41no—
108C22×C43⋊C8—21no—
109C22×C43⋊C8C2311yescharacteristic
110C22×C43⋊C8C2311yescharacteristic
111C2×C8×D43—21no—
112C2×C8×D43—21no—
113#13063309—21no—
114#13063305C2×C411yescharacteristic
115#13063305C2×C411yescharacteristic
116#13063300C2×C411yescharacteristic
117#13063300C2×C411yescharacteristic
118#13063295—21no—
119C4×D172—21no—
120C4×D172—21no—
121C2×C4×Dic43—21no—
122C2×C4×Dic43C2311yescharacteristic
123C42×D43—22no—
124C42×D43—41no—
125#13063260—22no—
126#13063253—22no—
127#13063253—41no—
128#13063252D414yescomplemented
129#13063251—22no—
130#13063251—22no—
131#13063248C2×C411yescharacteristic, complemented
132#13063248C2×C411yescharacteristic, complemented
133#13063245C2×C411yescharacteristic, complemented
134#13063245C2×C411yescharacteristic, complemented
135(C2×D43)⋊C8—21no—
136(C2×D43)⋊C8—21no—
137(C2×D43)⋊C8—21no—
138(C2×D43)⋊C8—21no—
139(C2×D43)⋊C8—21no—
140(C2×D43)⋊C8—21no—
141(C2×D43)⋊C8—21no—
142(C2×D43)⋊C8—21no—
143(C2×D43)⋊C8C2×C411yescharacteristic
144(C2×D43)⋊C8C2×C411yescharacteristic
145(C2×D43)⋊C8C2×C411yescharacteristic
146(C2×D43)⋊C8C2×C411yescharacteristic
147(C2×D43)⋊C8D411yescharacteristic
148(C2×D43)⋊C8D411yescharacteristic
149(C2×D43)⋊C8D411yescharacteristic
150(C2×D43)⋊C8D411yescharacteristic
151#13063236—21no—
152#13063235—22no—
153#13063235—41no—
154C4×C43⋊C8—21no—
155C2×#41×C43C2311yescharacteristic
156#131×C43—22no—
157#131×C43—41no—
158C2×M16×C43—21no—
159C2×M16×C43C2311yescharacteristic
160C2×M16×C43C2311yescharacteristic
161C22×C8×C43—21no—
162C22×C8×C43C2311yescharacteristic
163C22×C8×C43C2311yescharacteristic
164#117×C43C2311yescharacteristic
165C2×C42×C43C2311yescharacteristic
166#108×C43—41no—
167C4⋊C8×C43—21no—
168C4⋊C8×C43—21no—
169#104×C43—22no—
170#103×C43C2×C411yescharacteristic, complemented
171#103×C43C2×C411yescharacteristic, complemented
172#102×C43C2×C411yescharacteristic, complemented
173#102×C43C2×C411yescharacteristic, complemented
174C23×D43—21no—
175C23×D43#4111yescharacteristic
176#41×C43—21no—
177#41×C43—21no—
178#41×C43C2×D412yes—
179#41×C43#4112yes—
180C2×Q8×C43C22×C411yescharacteristic
181C2×D4×C43—21no—
182C2×D4×C43C22×C411yescharacteristic
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43C2411yescharacteristic
186C2×C22⋊D43—21no—
187C2×C22⋊D43—21no—
188C2×C22⋊D43—21no—
189C2×C22⋊D43—21no—
190C22×Dic43—21no—
191C22×Dic43—21no—
192C22×Dic43#4111yescharacteristic
193#10621902—22no—
194#10621902—41no—
195Q8×D43—22no—
196Q8×D43—41no—
197#10621900—22no—
198#10621900—41no—
199#10621900—42no—
200#10621900—42no—
201D4×D43—22no—
202D4×D43—42no—
203D4×D43—42no—
204D4×D43—41no—
205#10621898—21no—
206#10621898—21no—
207#10621898—21no—
208#10621898—21no—
209#10621898—21no—
210#10621898—21no—
211#10621898—21no—
212#10621898—21no—
213#10621898—42no—
214#10621898—42no—
215C2×D172—21no—
216C2×D172—21no—
217C2×D172—21no—
218C2×D172C22×C411yescharacteristic
219C2×D172C22×C411yescharacteristic
220C2×C4×D43—21no—
221C2×C4×D43—21no—
222C2×C4×D43—21no—
223C2×C4×D43—21no—
224C2×C4×D43—21no—
225C2×C4×D43—21no—
226C2×C4×D43—21no—
227C2×C4×D43—21no—
228C2×C4×D43—42no—
229C2×C4×D43—42no—
230C2×C4×D43—42no—
231C2×C4×D43—42no—
232C2×C4×D43—42no—
233C2×C4×D43C22×C411yescharacteristic
234C2×C4×D43C22×C411yescharacteristic
235C2×C4×D43C2×D411yescharacteristic
236C2×C4×D43C2×D411yescharacteristic
237C2×Dic86—21no—
238C2×Dic86C22×C411yescharacteristic
239C2×Dic86C22×C411yescharacteristic
240M16×C43—21no—
241M16×C43—21no—
242M16×C43—21no—
243M16×C43—21no—
244M16×C43—42no—
245C2×C8×C43—21no—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C2×C8×C43—21no—
249C2×C8×C43—21no—
250C2×C8×C43—21no—
251C2×C8×C43—42no—
252C2×C8×C43C22×C411yescharacteristic
253C2×C8×C43C22×C411yescharacteristic
254C2×C8×C43C2×D411yescharacteristic
255C2×C8×C43C2×D411yescharacteristic
256C4⋊C4×C43C22×C411yescharacteristic
257C4⋊C4×C43C22×C411yescharacteristic
258C22⋊C4×C43—21no—
259C42×C43—21no—
260C42×C43—21no—
261C42×C43—21no—
262#10621885—22no—
263#10621884—22no—
264#10621883—22no—
265#10621882—22no—
266(C2×D43)⋊C4—21no—
267(C2×D43)⋊C4—21no—
268(C2×D43)⋊C4—21no—
269(C2×D43)⋊C4—21no—
270C4⋊Dic43—21no—
271C4⋊Dic43—21no—
272C4×Dic43—21no—
273C4×Dic43—42no—
274C4×Dic43C2×D412yes—
275#10621877—21no—
276#10621877—21no—
277#10621877—21no—
278#10621877—42no—
279#10621877C2×D412yes—
280C2×C43⋊C8—21no—
281C2×C43⋊C8—21no—
282C2×C43⋊C8—21no—
283C2×C43⋊C8—21no—
284C2×C43⋊C8—21no—
285C2×C43⋊C8—21no—
286C2×C43⋊C8—42no—
287C2×C43⋊C8C22×C411yescharacteristic
288C2×C43⋊C8C22×C411yescharacteristic
289C2×C43⋊C8C2×D411yescharacteristic
290C2×C43⋊C8C2×D411yescharacteristic
291Dic172—41no—
292D344—41no—
293#10621873—41no—
294#10621873—41no—
295#10621872—42no—
296#10621872—42no—
297C8×D43—42no—
298C8×D43—42no—
299C23×C43—21no—
300C23×C43C2×#4111yescharacteristic
301C22×D43—21no—
302C22×D43—21no—
303C22×D43—22no—
304C22×D43—21no—
305C22×D43—21no—
306C22×D43—41no—
307C22×D43—42no—
308C22×D43—42no—
309C22×D43—81no—
310C22×D43C4×D411yescharacteristic
311C22×D43C4×D411yescharacteristic
312Q8×C43—21no—
313Q8×C43C4×D412yes—
314D4×C43—22no—
315D4×C43—22no—
316D4×C43—21no—
317D4×C43C4×D412yes—
318C2×C4×C43—21no—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—21no—
323C2×C4×C43—21no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
326C2×C4×C43C23×C411yescharacteristic
327C2×C4×C43C22×D411yescharacteristic
328C2×C4×C43C22×D411yescharacteristic
329C2×C4×C43C2×#4111yescharacteristic
330C2×C4×C43H(5,𝔽2)11yescharacteristic
331C2×C4×C43H(5,𝔽2)11yescharacteristic
332C22⋊D43—42no—
333C22⋊D43—42no—
334C22⋊D43—41no—
335C22⋊D43—41no—
336C22⋊D43—41no—
337C22⋊D43—41no—
338C2×Dic43—21no—
339C2×Dic43—21no—
340C2×Dic43—21no—
341C2×Dic43—21no—
342C2×Dic43—22no—
343C2×Dic43—42no—
344C2×Dic43—41no—
345C2×Dic43—41no—
346C2×Dic43C4×D411yescharacteristic
347C2×Dic43C4×D411yescharacteristic
348D172—21no—
349D172—21no—
350D172—21no—
351D172—21no—
352D172—42no—
353D172—42no—
354D172—81no—
355C4×D43—21no—
356C4×D43—21no—
357C4×D43—21no—
358C4×D43—21no—
359C4×D43—21no—
360C4×D43—21no—
361C4×D43—21no—
362C4×D43—21no—
363C4×D43—42no—
364C4×D43—42no—
365C4×D43—48no—
366C4×D43—41no—
367C4×D43—41no—
368C4×D43—41no—
369C4×D43—41no—
370Dic86—21no—
371Dic86—21no—
372Dic86—21no—
373Dic86—21no—
374Dic86—42no—
375C8×C43—21no—
376C8×C43—21no—
377C8×C43—21no—
378C8×C43—21no—
379C8×C43—41no—
380C8×C43—41no—
381C43⋊C8—21no—
382C43⋊C8—21no—
383C43⋊C8—22no—
384C43⋊C8—21no—
385C43⋊C8—21no—
386C43⋊C8—41no—
387#22886—431nomaximal, Sylow
388C22×C43—21no—
389C22×C43—21no—
390C22×C43—22no—
391C22×C43—41no—
392C22×C43—41no—
393C22×C43C2×C4×D411yescharacteristic
394C22×C43#54611yescharacteristic
395C22×C43#55111yescharacteristic
396C2×D43—21no—
397C2×D43—21no—
398C2×D43—21no—
399C2×D43—21no—
400C2×D43—21no—
401C2×D43—42no—
402C2×D43—42no—
403C2×D43—41no—
404C2×D43—41no—
405C2×D43—41no—
406C2×D43—41no—
407C2×D43—41no—
408C2×D43—41no—
409C2×D43—84no—
410C2×D43#44412yescomplemented
411C4×C43—22no—
412C4×C43—42no—
413C4×C43—41no—
414C4×C43—41no—
415C4×C43C2×C4×D411yescharacteristic
416C4×C43#51811yescharacteristic
417C4×C43D4211yescharacteristic
418C4×C43#54611yescharacteristic
419Dic43—21no—
420Dic43—21no—
421Dic43—42no—
422Dic43—41no—
423Dic43—41no—
424#3002—431no—
425C2×#444—431no—
426#2933—431no—
427C22×#104—431no—
428#2880—431no—
429#1975—431no—
430#1938—431no—
431#1929—431no—
432#1896—431no—
433#1876—431no—
434#1876—431no—
435#1866D4311yescharacteristic, complemented
436#1855—431no—
437#1765—431no—
438#1749—431no—
439C2×C43—21no—
440C2×C43—21no—
441C2×C43—42no—
442C2×C43#235811yescharacteristic
443C2×C43C2×#44411yescharacteristic
444C2×C43#295611yescharacteristic
445D43—22no—
446D43—41no—
447D43—81no—
448D43—81no—
449C22×#41—431no—
450C2×#135—431no—
451C2×#135—431no—
452C2×#131—431no—
453C2×#131—431no—
454C2×#131C2×D4311yescharacteristic
455C22×M16—431no—
456#525—431no—
457C22×C42—431no—
458#452—431no—
459#452—431no—
460#451—431no—
461#450—431no—
462#449—431no—
463#449—431no—
464#448—431no—
465#447—431no—
466#444—864no—
467#436—861no—
468#435—861no—
469#435—861no—
470C8×D4—861no—
471C2×#108—431no—
472C2×#108C2×D4311yescharacteristic, complemented
473#424C2×D4311yescharacteristic, complemented
474C2×#104—431no—
475C2×#104—431no—
476C2×#104—431no—
477C2×#104—431no—
478C2×#104—431no—
479C2×#104—864no—
480C2×#104C2×D4311yescharacteristic
481#416—431no—
482#416C2×D4311yescharacteristic
483#408—431no—
484#408—431no—
485#408—431no—
486#408—861no—
487#408—861no—
488#407—431no—
489#407—861no—
490C2×C22⋊C8—431no—
491C2×C22⋊C8—431no—
492C2×C22⋊C8—861no—
493#405—431no—
494C2×#97—431no—
495C2×#97—431no—
496#341—431no—
497#341—431no—
498#339—431no—
499#339C2×D4311yescharacteristic, complemented
500#336—431no—
501#336C2×D4311yescharacteristic, complemented
502C43#2288611yescharacteristic, complemented, Sylow
503C2×#41—431no—
504C2×#41—431no—
505C2×#41—431no—
506C2×#41—431no—
507C2×#41—861no—
508C2×#41—861no—
509C2×#41—862no—
510C2×#41—862no—
511C2×#41—1721no—
512C2×#41—1721no—
513C2×#41C22×D4311yescharacteristic
514C22×Q8—431no—
515C22×D4—431no—
516C22×D4—861no—
517C23×C4—431no—
518C23×C4—861no—
519C23×C4—861no—
520#135—862no—
521#135—862no—
522#135—1721no—
523#135—1721no—
524C2×Q16—431no—
525C2×Q16—431no—
526C2×SD16—431no—
527C2×SD16—431no—
528C2×SD16—431no—
529C2×SD16—431no—
530C2×D8—431no—
531C2×D8—431no—
532#131—22no—
533#131—41no—
534#131—862no—
535#131—862no—
536#131—1721no—
537#131—1721no—
538C2×M16—21no—
539C2×M16—431no—
540C2×M16—431no—
541C2×M16—861no—
542C2×M16—861no—
543C2×M16—861no—
544C2×M16—862no—
545C2×M16—1721no—
546C2×M16C22×D4311yescharacteristic
547C2×M16C22×D4311yescharacteristic
548C22×C8—21no—
549C22×C8—431no—
550C22×C8—431no—
551C22×C8—861no—
552C22×C8—861no—
553C22×C8—861no—
554C22×C8C22×D4311yescharacteristic
555C22×C8C22×D4311yescharacteristic
556#123—861no—
557C22⋊Q8—431no—
558C22⋊Q8—431no—
559#121—431no—
560#121—431no—
561#120—861no—
562C4×D4—861no—
563C4×D4—861no—
564#117C22×D4311yescharacteristic
565C2×C42—431no—
566C2×C42—862no—
567C2×C42—861no—
568C2×C42—1721no—
569C2×C42C22×D4311yescharacteristic
570#108—41no—
571#108—862no—
572C4⋊C8—21no—
573C4⋊C8—21no—
574#104—22no—
575#104—434no—
576#104—862no—
577#104—862no—
578#104—862no—
579#104—1721no—
580#103—431no—
581#103—431no—
582#103C4×D4311yescharacteristic, complemented
583#103C4×D4311yescharacteristic, complemented
584#102—431no—
585#102—431no—
586#102C4×D4311yescharacteristic, complemented
587#102C4×D4311yescharacteristic, complemented
588C22⋊C8—431no—
589C22⋊C8—431no—
590C22⋊C8—431no—
591C22⋊C8—431no—
592C22⋊C8—431no—
593C22⋊C8—431no—
594C22⋊C8—431no—
595C22⋊C8—431no—
596C22⋊C8—861no—
597C22⋊C8—861no—
598C22⋊C8—861no—
599C22⋊C8—861no—
600C22⋊C8—861no—
601C22⋊C8—861no—
602C22⋊C8—861no—
603C22⋊C8—861no—
604#97—861no—
605#97—862no—
606#97—1721no—
607C4×C8—861no—
608C24—431no—
609C24—861no—
610#41—21no—
611#41—21no—
612#41—862no—
613#41—862no—
614#41—861no—
615#41—861no—
616#41—861no—
617#41—861no—
618#41—861no—
619#41—861no—
620#41—861no—
621#41—861no—
622#41—1722no—
623#41—1722no—
624#41—1721no—
625#41—1722no—
626#41—1722no—
627#41—1721no—
628#41D4×D4312yes—
629#41#1062190212yes—
630C2×Q8—431no—
631C2×Q8—431no—
632C2×Q8—861no—
633C2×Q8—862no—
634C2×Q8—1721no—
635C2×Q8C2×C4×D4311yescharacteristic
636C2×D4—21no—
637C2×D4—431no—
638C2×D4—431no—
639C2×D4—861no—
640C2×D4—861no—
641C2×D4—861no—
642C2×D4—861no—
643C2×D4—862no—
644C2×D4—861no—
645C2×D4—861no—
646C2×D4—861no—
647C2×D4—1721no—
648C2×D4—1722no—
649C2×D4—1722no—
650C2×D4C2×C4×D4311yescharacteristic
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—431no—
654C22×C4—431no—
655C22×C4—431no—
656C22×C4—431no—
657C22×C4—431no—
658C22×C4—861no—
659C22×C4—861no—
660C22×C4—861no—
661C22×C4—861no—
662C22×C4—861no—
663C22×C4—861no—
664C22×C4—861no—
665C22×C4—861no—
666C22×C4—861no—
667C22×C4—861no—
668C22×C4—1722no—
669C22×C4—1722no—
670C22×C4—1722no—
671C22×C4—1722no—
672C22×C4—1722no—
673C22×C4C23×D4311yescharacteristic
674Q16—862no—
675Q16—1721no—
676SD16—862no—
677SD16—862no—
678SD16—1721no—
679SD16—1721no—
680D8—862no—
681D8—1721no—
682M16—21no—
683M16—21no—
684M16—21no—
685M16—21no—
686M16—42no—
687M16—432no—
688M16—861no—
689M16—861no—
690M16—861no—
691M16—1722no—
692M16—1722no—
693M16—1722no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—42no—
701C2×C8—431no—
702C2×C8—431no—
703C2×C8—431no—
704C2×C8—431no—
705C2×C8—861no—
706C2×C8—861no—
707C2×C8—861no—
708C2×C8—861no—
709C2×C8—861no—
710C2×C8—861no—
711C2×C8—1722no—
712C2×C8—1722no—
713C2×C8—1722no—
714C2×C8C2×C4×D4311yescharacteristic
715C2×C8C2×C4×D4311yescharacteristic
716C2×C8D4×D4311yescharacteristic
717C2×C8D4×D4311yescharacteristic
718C4⋊C4—861no—
719C4⋊C4—861no—
720C4⋊C4C2×C4×D4311yescharacteristic
721C4⋊C4C2×C4×D4311yescharacteristic
722C22⋊C4—21no—
723C22⋊C4—861no—
724C22⋊C4—861no—
725C22⋊C4—861no—
726C22⋊C4—861no—
727C42—21no—
728C42—21no—
729C42—21no—
730C42—432no—
731C42—861no—
732C42—1722no—
733C23—21no—
734C23—431no—
735C23—431no—
736C23—862no—
737C23—861no—
738C23—861no—
739C23—861no—
740C23—861no—
741C23—3441no—
742C23—1721no—
743C23—1722no—
744C23—1722no—
745C23#41×D4311yescharacteristic
746Q8—21no—
747Q8—861no—
748Q8—861no—
749Q8—861no—
750Q8—861no—
751Q8—1722no—
752Q8#1306328712yes—
753D4—22no—
754D4—22no—
755D4—21no—
756D4—861no—
757D4—861no—
758D4—861no—
759D4—861no—
760D4—3441no—
761D4—1722no—
762D4—1722no—
763D4—1722no—
764D4—1722no—
765D4—1721no—
766D4—1721no—
767D4—1721no—
768D4—1721no—
769D4#1306328712yes—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—431no—
779C2×C4—431no—
780C2×C4—861no—
781C2×C4—861no—
782C2×C4—861no—
783C2×C4—861no—
784C2×C4—861no—
785C2×C4—861no—
786C2×C4—861no—
787C2×C4—861no—
788C2×C4—861no—
789C2×C4—861no—
790C2×C4—861no—
791C2×C4—861no—
792C2×C4—862no—
793C2×C4—1722no—
794C2×C4—1722no—
795C2×C4—1728no—
796C2×C4—1722no—
797C2×C4—1721no—
798C2×C4—1721no—
799C2×C4—1721no—
800C2×C4—1721no—
801C2×C4—1721no—
802C2×C4—1721no—
803C2×C4C22×C4×D4311yescharacteristic
804C2×C4C2×D4×D4311yescharacteristic
805C2×C4C2×D4×D4311yescharacteristic
806C2×C4C2×#1062190211yescharacteristic
807C2×C4#1306337011yescharacteristic
808C2×C4#1306337111yescharacteristic
809C8—21no—
810C8—21no—
811C8—21no—
812C8—21no—
813C8—41no—
814C8—41no—
815C8—861no—
816C8—861no—
817C8—862no—
818C8—861no—
819C8—861no—
820C8—1721no—
821C22—21no—
822C22—21no—
823C22—22no—
824C22—41no—
825C22—41no—
826C22—432no—
827C22—861no—
828C22—861no—
829C22—861no—
830C22—861no—
831C22—861no—
832C22—3444no—
833C22—1722no—
834C22—1722no—
835C22—1721no—
836C22—1721no—
837C22—1721no—
838C22—1721no—
839C22—1721no—
840C22—1721no—
841C22C4×D4×D4311yescharacteristic
842C22#1458354111yescharacteristic
843C22#1458357611yescharacteristic
844C4—22no—
845C4—42no—
846C4—41no—
847C4—41no—
848C4—861no—
849C4—861no—
850C4—1722no—
851C4—1721no—
852C4—1721no—
853C4C2×#1306328711yescharacteristic
854C4#1458337111yescharacteristic
855C4#1458353111yescharacteristic
856C4#1458354011yescharacteristic
857C2—21no—
858C2—21no—
859C2—42no—
860C2—862no—
861C2—3441no—
862C2—3441no—
863C2—1721no—
864C2#1913757111yescharacteristic
865C2#444×D4311yescharacteristic
866C2#1914350011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1866C2
socleC22×C43C2×C4×D4
prime radical#19143815C2
cosocleC22×C4×C43C24
hypercenter#1866D43
hypocenterC43#22886
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1866

Complements

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

NH ≅ G/Ntype
2. C2×#14583019C2semidirect
3. #19143319C2semidirect
4. C2×#104×D43C2semidirect
5. #19143042C2semidirect
6. #19135486C2semidirect
7. #19135305C2semidirect
8. #19135241C2semidirect
9. #19135037C2semidirect
10. #19134921C2semidirect
11. #19134920C2semidirect
12. #19134798C2semidirect
13. #19134442C2semidirect
14. #19134356C2semidirect
15. C43×#1866C2semidirect
20. C2×#13063331C22semidirect
24. #14583064C4semidirect
25. #14583062C4semidirect
26. #14583056C4semidirect
27. #14583051C4semidirect
28. #14583047C4semidirect
29. #14583045C4semidirect
30. #14583039C4semidirect
31. #14583034C4semidirect
37. C2×#13063260C22semidirect
39. C2×#13063253C22semidirect
42. C2×#13063251C22semidirect
47. #14582867C22semidirect
55. #14582855C22semidirect
56. C2×#13063235C22semidirect
57. C2×#13063235C22semidirect
58. #14582664C22semidirect
59. #14582663C22semidirect
60. #14582658C22semidirect
61. #14582654C22semidirect
63. C2×#108×C43C22semidirect
64. C43×#424C22semidirect
67. C43×#339C22semidirect
68. C43×#336C22semidirect
89. C2×Dic172C2×C4semidirect
90. C2×#10621885C2×C4semidirect
91. C2×#10621873C2×C4semidirect
92. C2×#10621873C2×C4semidirect
93. C2×#10621883C2×C4semidirect
94. C2×#10621884C2×C4semidirect
95. C2×D344C2×C4semidirect
96. C2×#10621882C2×C4semidirect
128. #13063252D4semidirect
131. #13063248C2×C4semidirect
132. #13063248C2×C4semidirect
133. #13063245C2×C4semidirect
134. #13063245C2×C4semidirect
170. #103×C43C2×C4semidirect
171. #103×C43C2×C4semidirect
172. #102×C43C2×C4semidirect
173. #102×C43C2×C4semidirect
410. C2×D43#444semidirect
435. #1866D43semidirect
472. C2×#108C2×D43semidirect
473. #424C2×D43semidirect
499. #339C2×D43semidirect
501. #336C2×D43semidirect
502. C43#22886semidirect
582. #103C4×D43semidirect
583. #103C4×D43semidirect
586. #102C4×D43semidirect
587. #102C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191438152
C2×#145830192
#191433192
C2×#104×D432
#191430422
#191354862
#191353052
#191352412
#191350372
#191349212
#191349202
#191347982
#191344422
#191343562
C43×#18662
#2288643