Finite Group Databasebeta

← #25117331

Subgroups — #25117331

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#19143811C211yesmaximal, characteristic
2C2×#14583018C211yesmaximal, characteristic, complemented
3#19143322C211yesmaximal, characteristic, complemented
4C22×#13063253C211yesmaximal, characteristic, complemented
5#19143045C211yesmaximal, characteristic, complemented
6#19135485C211yesmaximal, characteristic, complemented
7#19135307C211yesmaximal, characteristic, complemented
8#19135241C211yesmaximal, characteristic, complemented
9#19134920C211yesmaximal, characteristic, complemented
10#19134919C211yesmaximal, characteristic, complemented
11#19134871C211yesmaximal, characteristic, complemented
12#19134799C211yesmaximal, characteristic, complemented
13#19134436C211yesmaximal, characteristic, complemented
14#19134357C211yesmaximal, characteristic, complemented
15C43×#1896C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C2×#13063345C2211yescharacteristic
18C2×#13063345C2211yescharacteristic
19C2×#13063333C2211yescharacteristic
20C2×#13063333C2211yescharacteristic
21C2×#13063332C2211yescharacteristic, complemented
22C22×#10621877C2211yescharacteristic
23#14583059C411yescharacteristic, complemented
24#14583059C411yescharacteristic, complemented
25#14583054C411yescharacteristic, complemented
26#14583049C411yescharacteristic, complemented
27#14583042C411yescharacteristic, complemented
28#14583042C411yescharacteristic, complemented
29#14583037C411yescharacteristic, complemented
30#14583032C411yescharacteristic, complemented
31#14583018—24no—
32#14582977—21no—
33#14582971—21no—
34#14582971—21no—
35D4×C43⋊C8—21no—
36C2×#13063260C2211yescharacteristic, complemented
37C2×#13063260C2211yescharacteristic, complemented
38#14582926C2211yescharacteristic, complemented
39C2×#13063253—24no—
40C2×#13063253C2211yescharacteristic
41C2×#13063253C2211yescharacteristic
42C2×#13063253C2211yescharacteristic
43C2×#13063253C2211yescharacteristic
44#14582893C2211yescharacteristic
45#14582893C2211yescharacteristic
46#14582867C2211yescharacteristic
47#14582867C2211yescharacteristic
48#14582866C2211yescharacteristic, complemented
49#14582864—21no—
50#14582864—21no—
51#14582861—21no—
52C2×C22⋊(C43⋊C8)C2211yescharacteristic
53C2×C22⋊(C43⋊C8)C2211yescharacteristic
54C22⋊C8×D43—21no—
55#14582855C2211yescharacteristic, complemented
56C2×#13063236C2211yescharacteristic, complemented
57C2×#13063236C2211yescharacteristic, complemented
58#14582663C2211yescharacteristic, complemented
59#14582663C2211yescharacteristic, complemented
60#14582654C2211yescharacteristic, complemented
61#14582654C2211yescharacteristic, complemented
62C43×#525C2211yescharacteristic
63C22×C42×C43C2211yescharacteristic
64C2×#104×C43C2211yescharacteristic, complemented
65C2×#104×C43C2211yescharacteristic, complemented
66C43×#407C2211yescharacteristic
67C43×#339C2211yescharacteristic, complemented
68C43×#339C2211yescharacteristic, complemented
69C2×#10621898—21no—
70C2×#10621898—21no—
71C2×#10621898—22no—
72C2×#10621898—22no—
73C2×#10621898—41no—
74C2×#10621898—41no—
75C2×#10621898C2×C411yescharacteristic
76C2×#10621898C2×C411yescharacteristic
77C2×#10621898C2311yescharacteristic
78C2×#10621898C2311yescharacteristic
79C22×Dic86C2×C411yescharacteristic
80C22×D172C2×C411yescharacteristic
81C22×C22⋊D43—21no—
82C22×C4×D43—21no—
83#13063345—22no—
84#13063345—22no—
85#13063345—41no—
86#13063345—41no—
87C2×#10621885C2×C411yescharacteristic, complemented
88C2×#10621885C2×C411yescharacteristic, complemented
89C2×#10621883C2×C411yescharacteristic, complemented
90C2×#10621883C2×C411yescharacteristic, complemented
91C2×#10621884C2×C411yescharacteristic, complemented
92C2×#10621884C2×C411yescharacteristic, complemented
93C2×#10621882C2×C411yescharacteristic, complemented
94C2×#10621882C2×C411yescharacteristic, complemented
95#13063333—22no—
96#13063333—22no—
97#13063333—41no—
98#13063333—41no—
99#13063332—22no—
100#13063332—41no—
101C2×#10621877—21no—
102C2×#10621877—21no—
103C2×#10621877—22no—
104C2×#10621877—41no—
105C2×#10621877C2311yescharacteristic
106C2×#10621877C2311yescharacteristic
107C2×#10621872—21no—
108C2×#10621872—21no—
109C22×C43⋊C8—21no—
110C22×C43⋊C8—21no—
111C22×C43⋊C8C2311yescharacteristic
112C22×C43⋊C8C2311yescharacteristic
113C22×C43⋊C8C2311yescharacteristic
114C22×C43⋊C8C2311yescharacteristic
115C2×C8×D43—21no—
116C2×C8×D43—21no—
117#13063260—22no—
118#13063260—41no—
119C4⋊(C43⋊C8)—21no—
120C4⋊(C43⋊C8)—21no—
121#13063253—22no—
122#13063253—22no—
123#13063253—22no—
124#13063253D414yescomplemented
125#13063248C2×C411yescharacteristic, complemented
126#13063248C2×C411yescharacteristic, complemented
127#13063248C2×C411yescharacteristic, complemented
128#13063248C2×C411yescharacteristic, complemented
129#13063245C2×C411yescharacteristic, complemented
130#13063245C2×C411yescharacteristic, complemented
131#13063245C2×C411yescharacteristic, complemented
132#13063245C2×C411yescharacteristic, complemented
133C22⋊(C43⋊C8)—21no—
134C22⋊(C43⋊C8)—21no—
135C22⋊(C43⋊C8)C2×C411yescharacteristic
136C22⋊(C43⋊C8)C2×C411yescharacteristic
137C22⋊(C43⋊C8)C2×C411yescharacteristic
138C22⋊(C43⋊C8)C2×C411yescharacteristic
139C22⋊(C43⋊C8)D411yescharacteristic
140C22⋊(C43⋊C8)D411yescharacteristic
141C22⋊(C43⋊C8)D411yescharacteristic
142C22⋊(C43⋊C8)D411yescharacteristic
143(C2×D43)⋊C8—21no—
144(C2×D43)⋊C8—21no—
145(C2×D43)⋊C8—21no—
146(C2×D43)⋊C8—21no—
147#13063236—22no—
148#13063236—21no—
149#13063236—41no—
150C4×C43⋊C8—21no—
151C2×#41×C43C2311yescharacteristic
152C23×C4×C43—21no—
153C23×C4×C43C2311yescharacteristic
154C2×M16×C43C2311yescharacteristic
155C2×M16×C43C2311yescharacteristic
156#123×C43—21no—
157C22⋊Q8×C43C2×C411yescharacteristic
158C22⋊Q8×C43C2×C411yescharacteristic
159#121×C43C2×C411yescharacteristic
160#121×C43C2×C411yescharacteristic
161#120×C43—21no—
162C4×D4×C43—21no—
163C4×D4×C43—21no—
164#117×C43C2311yescharacteristic
165C2×C42×C43—22no—
166C2×C42×C43—21no—
167C2×C42×C43—41no—
168C2×C42×C43C2311yescharacteristic
169C2×C42×C43C2311yescharacteristic
170#104×C43—22no—
171#104×C43—41no—
172C22⋊C8×C43—21no—
173C22⋊C8×C43—21no—
174C24×C43#4111yescharacteristic
175C23×D43—21no—
176#41×C43—21no—
177#41×C43—21no—
178#41×C43—21no—
179#41×C43—21no—
180C2×Q8×C43C22×C411yescharacteristic
181C2×D4×C43—21no—
182C2×D4×C43—21no—
183C2×D4×C43—21no—
184C2×D4×C43C22×C411yescharacteristic
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—42no—
193C22×C4×C43—42no—
194C22×C4×C43—42no—
195C22×C4×C43C22×C411yescharacteristic
196C22×C4×C43C22×C411yescharacteristic
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43#4111yescharacteristic
200C22×C4×C43C2411yescharacteristic
201C2×C22⋊D43—21no—
202C2×C22⋊D43—21no—
203C2×C22⋊D43—21no—
204C2×C22⋊D43—21no—
205C2×C22⋊D43—42no—
206C2×C22⋊D43—42no—
207C22×Dic43—21no—
208#10621898—21no—
209#10621898—21no—
210#10621898—21no—
211#10621898—21no—
212#10621898—21no—
213#10621898—21no—
214#10621898—22no—
215#10621898—22no—
216#10621898—41no—
217#10621898—41no—
218#10621898—42no—
219#10621898—42no—
220#10621898—42no—
221#10621898—42no—
222#10621898C2×D412yes—
223#10621898#4112yes—
224C2×D172—21no—
225C2×D172—22no—
226C2×D172—41no—
227C2×D172C22×C411yescharacteristic
228C2×D172C22×C411yescharacteristic
229C2×C4×D43—21no—
230C2×C4×D43—21no—
231C2×C4×D43—21no—
232C2×C4×D43—21no—
233C2×C4×D43—42no—
234C2×C4×D43—42no—
235C2×Dic86—22no—
236C2×Dic86—21no—
237C2×Dic86—41no—
238C2×Dic86C22×C411yescharacteristic
239C2×Dic86C22×C411yescharacteristic
240M16×C43—21no—
241M16×C43—21no—
242M16×C43—21no—
243M16×C43—21no—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43—21no—
248C4⋊C4×C43C22×C411yescharacteristic
249C4⋊C4×C43C22×C411yescharacteristic
250C22⋊C4×C43—21no—
251C22⋊C4×C43—21no—
252C22⋊C4×C43—21no—
253C22⋊C4×C43—21no—
254C22⋊C4×C43—21no—
255C42×C43—21no—
256C42×C43—21no—
257C42×C43—21no—
258C42×C43—21no—
259C42×C43—42no—
260C42×C43C2×D412yes—
261#10621885—22no—
262#10621885—41no—
263#10621884—22no—
264#10621884—41no—
265#10621883—22no—
266#10621883—41no—
267#10621882—22no—
268#10621882—41no—
269#10621877—21no—
270#10621877—21no—
271#10621877—21no—
272#10621877—42no—
273#10621877—42no—
274#10621877C2×D412yes—
275C2×C43⋊C8—21no—
276C2×C43⋊C8—21no—
277C2×C43⋊C8—21no—
278C2×C43⋊C8—21no—
279C2×C43⋊C8—21no—
280C2×C43⋊C8—21no—
281C2×C43⋊C8—21no—
282C2×C43⋊C8—21no—
283C2×C43⋊C8—21no—
284C2×C43⋊C8—21no—
285C2×C43⋊C8—42no—
286C2×C43⋊C8—42no—
287C2×C43⋊C8C22×C411yescharacteristic
288C2×C43⋊C8C22×C411yescharacteristic
289C2×C43⋊C8C22×C411yescharacteristic
290C2×C43⋊C8C22×C411yescharacteristic
291C2×C43⋊C8C2×D411yescharacteristic
292C2×C43⋊C8C2×D411yescharacteristic
293C2×C43⋊C8C2×D411yescharacteristic
294C2×C43⋊C8C2×D411yescharacteristic
295#10621872—42no—
296#10621872—42no—
297C8×D43—42no—
298C8×D43—42no—
299C23×C43—21no—
300C23×C43—21no—
301C23×C43—22no—
302C23×C43—21no—
303C23×C43—41no—
304C23×C43C4×D411yescharacteristic
305C23×C43C4×D411yescharacteristic
306C23×C43C2×#4111yescharacteristic
307C22×D43—21no—
308C22×D43—21no—
309C22×D43—42no—
310C22×D43—42no—
311C22×D43—81no—
312Q8×C43—21no—
313Q8×C43—21no—
314D4×C43—21no—
315D4×C43—21no—
316D4×C43—41no—
317D4×C43—41no—
318D4×C43—42no—
319D4×C43—81no—
320C2×C4×C43—21no—
321C2×C4×C43—21no—
322C2×C4×C43—21no—
323C2×C4×C43—21no—
324C2×C4×C43—21no—
325C2×C4×C43—21no—
326C2×C4×C43—21no—
327C2×C4×C43—21no—
328C2×C4×C43—21no—
329C2×C4×C43—21no—
330C2×C4×C43—22no—
331C2×C4×C43—21no—
332C2×C4×C43—21no—
333C2×C4×C43—21no—
334C2×C4×C43—22no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43—48no—
339C2×C4×C43—41no—
340C2×C4×C43—41no—
341C2×C4×C43—41no—
342C2×C4×C43C4×D411yescharacteristic
343C2×C4×C43C4×D411yescharacteristic
344C2×C4×C43C23×C411yescharacteristic
345C2×C4×C43C22×D411yescharacteristic
346C2×C4×C43C22×D411yescharacteristic
347C2×C4×C43C2×#4111yescharacteristic
348C2×C4×C43H(5,𝔽2)11yescharacteristic
349C2×C4×C43H(5,𝔽2)11yescharacteristic
350C22⋊D43—22no—
351C22⋊D43—22no—
352C22⋊D43—42no—
353C22⋊D43—42no—
354C22⋊D43—41no—
355C22⋊D43—41no—
356C2×Dic43—21no—
357C2×Dic43—21no—
358C2×Dic43—42no—
359D172—21no—
360D172—21no—
361D172—21no—
362D172—42no—
363D172C4×D412yes—
364C4×D43—22no—
365C4×D43—22no—
366C4×D43—42no—
367C4×D43—42no—
368C4×D43—41no—
369C4×D43—41no—
370Dic86—21no—
371Dic86—21no—
372Dic86—21no—
373Dic86—42no—
374Dic86C4×D412yes—
375C8×C43—41no—
376C8×C43—41no—
377C43⋊C8—21no—
378C43⋊C8—21no—
379C43⋊C8—21no—
380C43⋊C8—21no—
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—21no—
391C22×C43—21no—
392C22×C43—21no—
393C22×C43—21no—
394C22×C43—21no—
395C22×C43—42no—
396C22×C43—42no—
397C22×C43—41no—
398C22×C43—41no—
399C22×C43—41no—
400C22×C43#44412yescomplemented
401C22×C43C2×C4×D411yescharacteristic
402C22×C43#54611yescharacteristic
403C22×C43#55111yescharacteristic
404C2×D43—22no—
405C2×D43—41no—
406C2×D43—41no—
407C2×D43—41no—
408C2×D43—41no—
409C2×D43—41no—
410C2×D43—84no—
411C4×C43—21no—
412C4×C43—21no—
413C4×C43—42no—
414C4×C43—42no—
415C4×C43—41no—
416C4×C43—41no—
417C4×C43—41no—
418C4×C43C2×C4×D411yescharacteristic
419C4×C43#51811yescharacteristic
420C4×C43D4211yescharacteristic
421C4×C43#54611yescharacteristic
422Dic43—22no—
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#1896D4311yescharacteristic, complemented
433#1876—431no—
434#1876—431no—
435#1866—431no—
436#1855—431no—
437#1765—431no—
438#1749—431no—
439C2×C43—21no—
440C2×C43—22no—
441C2×C43—21no—
442C2×C43—41no—
443C2×C43—81no—
444C2×C43#235811yescharacteristic
445C2×C43C2×#44411yescharacteristic
446C2×C43#295611yescharacteristic
447D43—42no—
448D43—81no—
449C22×#41—431no—
450C2×#135—431no—
451C2×#135—431no—
452C2×#131—431no—
453C2×#131—431no—
454C2×#131—431no—
455C22×M16—431no—
456#525C2×D4311yescharacteristic
457C22×C42C2×D4311yescharacteristic
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×#108—431no—
473#424—431no—
474C2×#104—431no—
475C2×#104—431no—
476C2×#104—431no—
477C2×#104—431no—
478C2×#104—864no—
479C2×#104C2×D4311yescharacteristic, complemented
480C2×#104C2×D4311yescharacteristic, complemented
481#416—431no—
482#416—431no—
483#408—431no—
484#408—431no—
485#408—431no—
486#408—861no—
487#408—861no—
488#407—861no—
489#407C2×D4311yescharacteristic
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#339C2×D4311yescharacteristic, complemented
499#339C2×D4311yescharacteristic, complemented
500#336—431no—
501#336—431no—
502C43#2288611yescharacteristic, complemented, Sylow
503C2×#41—431no—
504C2×#41—431no—
505C2×#41—431no—
506C2×#41—431no—
507C2×#41—862no—
508C2×#41—862no—
509C2×#41—861no—
510C2×#41—861no—
511C2×#41—1721no—
512C2×#41—1721no—
513C2×#41C22×D4311yescharacteristic
514C22×Q8—431no—
515C22×D4—431no—
516C22×D4—861no—
517C23×C4—21no—
518C23×C4—861no—
519C23×C4C22×D4311yescharacteristic
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—862no—
533#131—862no—
534#131—862no—
535#131—1721no—
536#131—1721no—
537#131—1721no—
538C2×M16—431no—
539C2×M16—431no—
540C2×M16—861no—
541C2×M16—861no—
542C2×M16—861no—
543C2×M16—861no—
544C2×M16—862no—
545C2×M16—1721no—
546C2×M16C22×D4311yescharacteristic
547C2×M16C22×D4311yescharacteristic
548C22×C8—431no—
549C22×C8—431no—
550C22×C8—431no—
551C22×C8—431no—
552C22×C8—861no—
553C22×C8—861no—
554C22×C8—861no—
555C22×C8—861no—
556#123—21no—
557C22⋊Q8C4×D4311yescharacteristic
558C22⋊Q8C4×D4311yescharacteristic
559#121C4×D4311yescharacteristic
560#121C4×D4311yescharacteristic
561#120—21no—
562C4×D4—21no—
563C4×D4—21no—
564#117C22×D4311yescharacteristic
565C2×C42—22no—
566C2×C42—21no—
567C2×C42—41no—
568C2×C42C22×D4311yescharacteristic
569C2×C42C22×D4311yescharacteristic
570#108—862no—
571#108—1721no—
572C4⋊C8—861no—
573C4⋊C8—861no—
574#104—22no—
575#104—41no—
576#104—434no—
577#104—862no—
578#104—862no—
579#104—862no—
580#103—431no—
581#103—431no—
582#103—431no—
583#103—431no—
584#102—431no—
585#102—431no—
586#102—431no—
587#102—431no—
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8—431no—
591C22⋊C8—431no—
592C22⋊C8—431no—
593C22⋊C8—431no—
594C22⋊C8—431no—
595C22⋊C8—431no—
596C22⋊C8—431no—
597C22⋊C8—431no—
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—861no—
609C24#1062190011yescharacteristic
610#41—21no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—432no—
615#41—432no—
616#41—862no—
617#41—862no—
618#41—861no—
619#41—861no—
620#41—861no—
621#41—861no—
622#41—861no—
623#41—861no—
624#41—1722no—
625#41—1722no—
626#41—1721no—
627#41—1721no—
628#41—1722no—
629#41—1722no—
630C2×Q8—431no—
631C2×Q8—431no—
632C2×Q8—862no—
633C2×Q8—861no—
634C2×Q8—1721no—
635C2×Q8C2×C4×D4311yescharacteristic
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—431no—
640C2×D4—431no—
641C2×D4—862no—
642C2×D4—861no—
643C2×D4—861no—
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—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—861no—
662C22×C4—861no—
663C22×C4—861no—
664C22×C4—861no—
665C22×C4—861no—
666C22×C4—1722no—
667C22×C4—1722no—
668C22×C4C2×C4×D4311yescharacteristic
669C22×C4C2×C4×D4311yescharacteristic
670C22×C4D4×D4311yescharacteristic
671C22×C4D4×D4311yescharacteristic
672C22×C4#1062190011yescharacteristic
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—432no—
687M16—861no—
688M16—861no—
689M16—861no—
690M16—1722no—
691M16—1722no—
692M16—1722no—
693M16—1722no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—431no—
697C2×C8—431no—
698C2×C8—431no—
699C2×C8—431no—
700C2×C8—431no—
701C2×C8—431no—
702C2×C8—431no—
703C2×C8—431no—
704C2×C8—861no—
705C2×C8—861no—
706C2×C8—861no—
707C2×C8—861no—
708C2×C8—861no—
709C2×C8—861no—
710C2×C8—861no—
711C2×C8—861no—
712C2×C8—861no—
713C2×C8—861no—
714C2×C8—1722no—
715C2×C8—1722no—
716C2×C8—1722no—
717C2×C8—1722no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4C2×C4×D4311yescharacteristic
721C4⋊C4C2×C4×D4311yescharacteristic
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—21no—
727C42—21no—
728C42—21no—
729C42—21no—
730C42—21no—
731C42—42no—
732C42D4×D4312yes—
733C23—21no—
734C23—22no—
735C23—21no—
736C23—21no—
737C23—41no—
738C23—861no—
739C23—861no—
740C23—3441no—
741C23—1722no—
742C23—1722no—
743C23(C22⋊D43)⋊C411yescharacteristic
744C23(C22⋊D43)⋊C411yescharacteristic
745C23C2×#1062190011yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—432no—
749Q8—861no—
750Q8—861no—
751Q8—861no—
752Q8—1722no—
753D4—21no—
754D4—21no—
755D4—41no—
756D4—42no—
757D4—41no—
758D4—81no—
759D4—432no—
760D4—862no—
761D4—862no—
762D4—861no—
763D4—861no—
764D4—861no—
765D4—1722no—
766D4—1722no—
767D4—1722no—
768D4—1721no—
769D4—1721no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—22no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—48no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—861no—
793C2×C4—862no—
794C2×C4—862no—
795C2×C4—861no—
796C2×C4—1722no—
797C2×C4—1722no—
798C2×C4—1722no—
799C2×C4—1721no—
800C2×C4—1721no—
801C2×C4(C22⋊D43)⋊C411yescharacteristic
802C2×C4(C22⋊D43)⋊C411yescharacteristic
803C2×C4C22×C4×D4311yescharacteristic
804C2×C4C2×D4×D4311yescharacteristic
805C2×C4C2×D4×D4311yescharacteristic
806C2×C4#41×D4311yescharacteristic
807C2×C4#1306337011yescharacteristic
808C2×C4#1306337111yescharacteristic
809C8—41no—
810C8—41no—
811C8—861no—
812C8—861no—
813C8—861no—
814C8—861no—
815C8—861no—
816C8—861no—
817C8—862no—
818C8—861no—
819C8—861no—
820C8—1721no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—42no—
829C22—42no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—862no—
834C22—3444no—
835C22—1721no—
836C22—1721no—
837C22—1721no—
838C22—1721no—
839C22—1721no—
840C22#1458301812yescomplemented
841C22C2×(C22⋊D43)⋊C411yescharacteristic
842C22#1458353611yescharacteristic
843C22#1458357211yescharacteristic
844C4—21no—
845C4—21no—
846C4—42no—
847C4—42no—
848C4—41no—
849C4—41no—
850C4—41no—
851C4—862no—
852C4—1721no—
853C4C4×D4×D4311yescharacteristic
854C4#1458337111yescharacteristic
855C4#1458353311yescharacteristic
856C4#1458353811yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—81no—
862C2—3441no—
863C2—1722no—
864C2#1913757511yescharacteristic
865C2C2×#1458301811yescharacteristic
866C2#1914350111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1896C2
socleC22×C43C2×C4×D4
prime radical#19143811C2
cosocleC22×C4×C43C24
hypercenter#1896D43
hypocenterC43#22886
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1896

Complements

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

NH ≅ G/Ntype
2. C2×#14583018C2semidirect
3. #19143322C2semidirect
4. C22×#13063253C2semidirect
5. #19143045C2semidirect
6. #19135485C2semidirect
7. #19135307C2semidirect
8. #19135241C2semidirect
9. #19134920C2semidirect
10. #19134919C2semidirect
11. #19134871C2semidirect
12. #19134799C2semidirect
13. #19134436C2semidirect
14. #19134357C2semidirect
15. C43×#1896C2semidirect
21. C2×#13063332C22semidirect
23. #14583059C4semidirect
24. #14583059C4semidirect
25. #14583054C4semidirect
26. #14583049C4semidirect
27. #14583042C4semidirect
28. #14583042C4semidirect
29. #14583037C4semidirect
30. #14583032C4semidirect
36. C2×#13063260C22semidirect
37. C2×#13063260C22semidirect
38. #14582926C22semidirect
48. #14582866C22semidirect
55. #14582855C22semidirect
56. C2×#13063236C22semidirect
57. C2×#13063236C22semidirect
58. #14582663C22semidirect
59. #14582663C22semidirect
60. #14582654C22semidirect
61. #14582654C22semidirect
64. C2×#104×C43C22semidirect
65. C2×#104×C43C22semidirect
67. C43×#339C22semidirect
68. C43×#339C22semidirect
87. C2×#10621885C2×C4semidirect
88. C2×#10621885C2×C4semidirect
89. C2×#10621883C2×C4semidirect
90. C2×#10621883C2×C4semidirect
91. C2×#10621884C2×C4semidirect
92. C2×#10621884C2×C4semidirect
93. C2×#10621882C2×C4semidirect
94. C2×#10621882C2×C4semidirect
124. #13063253D4semidirect
125. #13063248C2×C4semidirect
126. #13063248C2×C4semidirect
127. #13063248C2×C4semidirect
128. #13063248C2×C4semidirect
129. #13063245C2×C4semidirect
130. #13063245C2×C4semidirect
131. #13063245C2×C4semidirect
132. #13063245C2×C4semidirect
400. C22×C43#444semidirect
432. #1896D43semidirect
479. C2×#104C2×D43semidirect
480. C2×#104C2×D43semidirect
498. #339C2×D43semidirect
499. #339C2×D43semidirect
502. C43#22886semidirect
840. C22#14583018semidirect

Maximal subgroups

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

subgroupindex
#191438112
C2×#145830182
#191433222
C22×#130632532
#191430452
#191354852
#191353072
#191352412
#191349202
#191349192
#191348712
#191347992
#191344362
#191343572
C43×#18962
#2288643