Finite Group Databasebeta

← #25117333

Subgroups — #25117333

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#19143809C211yesmaximal, characteristic
2C2×#14583018C211yesmaximal, characteristic, complemented
3#19143325C211yesmaximal, characteristic, complemented
4C2×#104×D43C211yesmaximal, characteristic, complemented
5#19143043C211yesmaximal, characteristic, complemented
6#19135303C211yesmaximal, characteristic, complemented
7#19135240C211yesmaximal, characteristic, complemented
8#19135035C211yesmaximal, characteristic, complemented
9#19134925C211yesmaximal, characteristic, complemented
10#19134924C211yesmaximal, characteristic, complemented
11#19134867C211yesmaximal, characteristic, complemented
12#19134798C211yesmaximal, characteristic, complemented
13#19134439C211yesmaximal, characteristic, complemented
14#19134358C211yesmaximal, characteristic, complemented
15C43×#1975C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17C2×#13063345C2211yescharacteristic
18C2×#13063333C2211yescharacteristic
19C2×#13063332C2211yescharacteristic, complemented
20C2×#13063331C2211yescharacteristic
21C2×M16×D43C2211yescharacteristic
22#14583406C2211yescharacteristic
23C2×C42×D43C2211yescharacteristic
24#14583060C411yescharacteristic, complemented
25#14583058C411yescharacteristic, complemented
26#14583053C411yescharacteristic, complemented
27#14583048C411yescharacteristic, complemented
28#14583043C411yescharacteristic, complemented
29#14583041C411yescharacteristic, complemented
30#14583036C411yescharacteristic, complemented
31#14583031C411yescharacteristic, complemented
32#14583018—24no—
33#14582974—21no—
34#14582973—21no—
35#14582967—21no—
36(C22⋊D43)⋊C8—21no—
37C2×#13063260C2211yescharacteristic, complemented
38#14582927C2211yescharacteristic, complemented
39C2×#13063253C2211yescharacteristic
40C2×#13063252C2211yescharacteristic
41C2×#13063252C2211yescharacteristic, complemented
42C2×#13063251C2211yescharacteristic
43#104×D43—24no—
44#14582896C2211yescharacteristic
45#14582895C2211yescharacteristic
46#14582866C2211yescharacteristic
47#14582864—21no—
48#14582864—21no—
49#14582862C2211yescharacteristic
50#14582861—21no—
51C2×(C2×D43)⋊C8C2211yescharacteristic
52C2×(C2×D43)⋊C8C2211yescharacteristic
53C22⋊C8×D43—21no—
54#14582854C2211yescharacteristic, complemented
55C2×#13063236C2211yescharacteristic, complemented
56#14582664C2211yescharacteristic, complemented
57#14582663C2211yescharacteristic, complemented
58#14582660C2211yescharacteristic, complemented
59#14582659C2211yescharacteristic, complemented
60#14582653C2211yescharacteristic, complemented
61#14582653C2211yescharacteristic, complemented
62C2×#135×C43C2211yescharacteristic
63C2×#108×C43C2211yescharacteristic, complemented
64C2×#104×C43C2211yescharacteristic
65C2×#104×C43C2211yescharacteristic, complemented
66C43×#408C2211yescharacteristic
67C43×#408C2211yescharacteristic, complemented
68C2×#97×C43C2211yescharacteristic, complemented
69C2×#10621902C2×C411yescharacteristic
70C2×#10621898—21no—
71C2×#10621898C2311yescharacteristic
72C2×#10621900—21no—
73C2×#10621900C2×C411yescharacteristic
74#41×D43—22no—
75#41×D43—22no—
76#41×D43—41no—
77#41×D43—41no—
78C2×Q8×D43C2×C411yescharacteristic
79C2×D4×D43—21no—
80C2×D4×D43C2×C411yescharacteristic
81C22×C4×D43—21no—
82C22×C4×D43—21no—
83C22×C4×D43C2311yescharacteristic
84#13063345—22no—
85#13063345—22no—
86C2×#10621885C2×C411yescharacteristic, complemented
87C2×#10621883C2×C411yescharacteristic, complemented
88C2×#10621884C2×C411yescharacteristic, complemented
89C2×#10621882C2×C411yescharacteristic, complemented
90#13063333—22no—
91#13063333—41no—
92#13063332—22no—
93#13063332—41no—
94#13063331—22no—
95#13063331—41no—
96C2×#10621877—21no—
97C2×#10621877C2311yescharacteristic
98C2×#10621877C2311yescharacteristic
99C2×#10621872—21no—
100C2×#10621872—21no—
101C2×#10621872—21no—
102M16×D43—22no—
103M16×D43—41no—
104C22×C43⋊C8—21no—
105C22×C43⋊C8C2311yescharacteristic
106C22×C43⋊C8C2311yescharacteristic
107C2×C8×D43—21no—
108C2×C8×D43—21no—
109C2×C8×D43—21no—
110#13063306—21no—
111#13063301C2×C411yescharacteristic
112#13063301C2×C411yescharacteristic
113#13063296C2×C411yescharacteristic
114#13063296C2×C411yescharacteristic
115#13063293—21no—
116C4×C22⋊D43—21no—
117C4×C22⋊D43—21no—
118#13063284C2311yescharacteristic
119C2×C4×Dic43—21no—
120C2×C4×Dic43C2311yescharacteristic
121C42×D43—22no—
122C42×D43—41no—
123#13063260—22no—
124Dic43⋊C8—21no—
125Dic43⋊C8—21no—
126#13063253D414yescomplemented
127#13063252—22no—
128#13063252—41no—
129#13063251—22no—
130#13063250C2×C411yescharacteristic, complemented
131#13063250C2×C411yescharacteristic, complemented
132#13063249C2×C411yescharacteristic, complemented
133#13063249C2×C411yescharacteristic, complemented
134#13063247C2×C411yescharacteristic, complemented
135#13063247C2×C411yescharacteristic, complemented
136#13063246C2×C411yescharacteristic, complemented
137#13063246C2×C411yescharacteristic, complemented
138C22⋊(C43⋊C8)—21no—
139C22⋊(C43⋊C8)—21no—
140(C2×D43)⋊C8—21no—
141(C2×D43)⋊C8—21no—
142(C2×D43)⋊C8C2×C411yescharacteristic
143(C2×D43)⋊C8C2×C411yescharacteristic
144(C2×D43)⋊C8C2×C411yescharacteristic
145(C2×D43)⋊C8C2×C411yescharacteristic
146(C2×D43)⋊C8D411yescharacteristic
147(C2×D43)⋊C8D411yescharacteristic
148(C2×D43)⋊C8D411yescharacteristic
149(C2×D43)⋊C8D411yescharacteristic
150#13063236—22no—
151#13063235—21no—
152C8×Dic43—21no—
153C2×#41×C43C2311yescharacteristic
154C2×#41×C43C2311yescharacteristic
155#135×C43—41no—
156#135×C43—41no—
157C2×Q16×C43C2×C411yescharacteristic, complemented
158C2×SD16×C43C2×C411yescharacteristic, complemented
159C2×SD16×C43C2×C411yescharacteristic, complemented
160C2×D8×C43C2×C411yescharacteristic, complemented
161C2×M16×C43C2311yescharacteristic
162C2×M16×C43C2311yescharacteristic
163C22×C8×C43C2311yescharacteristic
164C22×C8×C43C2311yescharacteristic
165C2×C42×C43C2311yescharacteristic
166#108×C43—41no—
167#104×C43—22no—
168#104×C43—22no—
169C22⋊C8×C43—21no—
170C22⋊C8×C43—21no—
171C22⋊C8×C43—21no—
172C22⋊C8×C43—21no—
173#97×C43—41no—
174C23×D43—21no—
175C23×D43#4111yescharacteristic
176#41×C43—21no—
177#41×C43—21no—
178#41×C43—21no—
179#41×C43—21no—
180#41×C43—21no—
181#41×C43—21no—
182#41×C43—21no—
183#41×C43—21no—
184C2×Q8×C43C22×C411yescharacteristic
185C2×Q8×C43C22×C411yescharacteristic
186C2×D4×C43—21no—
187C2×D4×C43—21no—
188C2×D4×C43C22×C411yescharacteristic
189C2×D4×C43C22×C411yescharacteristic
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43C2411yescharacteristic
194C2×C22⋊D43—21no—
195C2×C22⋊D43—21no—
196C2×C22⋊D43—21no—
197C2×C22⋊D43—21no—
198C2×C22⋊D43—21no—
199C22×Dic43—21no—
200C22×Dic43—21no—
201C22×Dic43#4111yescharacteristic
202#10621902—22no—
203#10621902—41no—
204Q8×D43—22no—
205Q8×D43—41no—
206#10621900—22no—
207#10621900—41no—
208#10621900—42no—
209#10621900—42no—
210D4×D43—22no—
211D4×D43—42no—
212D4×D43—42no—
213D4×D43—41no—
214#10621898—21no—
215#10621898—21no—
216#10621898—42no—
217#10621898—42no—
218#10621898C2×D412yes—
219#10621898#4112yes—
220C2×D172—21no—
221C2×D172C22×C411yescharacteristic
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—21no—
229C2×C4×D43—42no—
230C2×C4×D43—42no—
231C2×C4×D43—42no—
232C2×C4×D43—42no—
233C2×C4×D43—42no—
234C2×C4×D43C22×C411yescharacteristic
235C2×C4×D43C22×C411yescharacteristic
236C2×C4×D43C2×D411yescharacteristic
237C2×C4×D43C2×D411yescharacteristic
238C2×Dic86—21no—
239C2×Dic86C22×C411yescharacteristic
240Q16×C43—41no—
241SD16×C43—41no—
242SD16×C43—41no—
243D8×C43—41no—
244M16×C43—21no—
245M16×C43—21no—
246M16×C43—21no—
247M16×C43—21no—
248C2×C8×C43—21no—
249C2×C8×C43—21no—
250C2×C8×C43—21no—
251C2×C8×C43—21no—
252C2×C8×C43—21no—
253C2×C8×C43—21no—
254C2×C8×C43C22×C411yescharacteristic
255C2×C8×C43C22×C411yescharacteristic
256C2×C8×C43C2×D411yescharacteristic
257C2×C8×C43C2×D411yescharacteristic
258C42×C43—21no—
259C42×C43C2×D412yes—
260C22⋊Dic43—21no—
261C22⋊Dic43—21no—
262C22⋊Dic43—21no—
263#10621885—22no—
264#10621884—22no—
265#10621883—22no—
266#10621882—22no—
267(C2×D43)⋊C4—21no—
268(C2×D43)⋊C4—21no—
269C4⋊Dic43C22×C411yescharacteristic
270C4⋊Dic43C22×C411yescharacteristic
271Dic43⋊C4—21no—
272Dic43⋊C4—21no—
273C4×Dic43—21no—
274C4×Dic43—21no—
275C4×Dic43—21no—
276C4×Dic43—42no—
277#10621877—21no—
278#10621877—21no—
279#10621877—21no—
280#10621877—42no—
281#10621877C2×D412yes—
282C2×C43⋊C8—21no—
283C2×C43⋊C8—21no—
284C2×C43⋊C8—21no—
285C2×C43⋊C8—21no—
286C2×C43⋊C8—21no—
287C2×C43⋊C8—21no—
288C2×C43⋊C8—42no—
289C2×C43⋊C8C22×C411yescharacteristic
290C2×C43⋊C8C22×C411yescharacteristic
291C2×C43⋊C8C2×D411yescharacteristic
292C2×C43⋊C8C2×D411yescharacteristic
293#10621872—42no—
294#10621872—42no—
295#10621872—42no—
296C8×D43—42no—
297C8×D43—42no—
298C8×D43—42no—
299C23×C43—21no—
300C23×C43—21no—
301C23×C43C2×#4111yescharacteristic
302C22×D43—21no—
303C22×D43—21no—
304C22×D43—21no—
305C22×D43—22no—
306C22×D43—41no—
307C22×D43—42no—
308C22×D43—42no—
309C22×D43—81no—
310C22×D43C4×D411yescharacteristic
311C22×D43C4×D411yescharacteristic
312Q8×C43—21no—
313Q8×C43—21no—
314Q8×C43—21no—
315Q8×C43—21no—
316D4×C43—21no—
317D4×C43—21no—
318D4×C43—21no—
319D4×C43—21no—
320D4×C43—41no—
321D4×C43—41no—
322D4×C43—41no—
323D4×C43—41no—
324C2×C4×C43—21no—
325C2×C4×C43—21no—
326C2×C4×C43—22no—
327C2×C4×C43—41no—
328C2×C4×C43—41no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43C23×C411yescharacteristic
334C2×C4×C43C22×D411yescharacteristic
335C2×C4×C43C22×D411yescharacteristic
336C2×C4×C43C2×#4111yescharacteristic
337C2×C4×C43H(5,𝔽2)11yescharacteristic
338C2×C4×C43H(5,𝔽2)11yescharacteristic
339C22⋊D43—22no—
340C22⋊D43—22no—
341C22⋊D43—42no—
342C22⋊D43—42no—
343C22⋊D43—42no—
344C22⋊D43—81no—
345C2×Dic43—21no—
346C2×Dic43—21no—
347C2×Dic43—21no—
348C2×Dic43—22no—
349C2×Dic43—21no—
350C2×Dic43—21no—
351C2×Dic43—42no—
352C2×Dic43—41no—
353C2×Dic43—41no—
354C2×Dic43C4×D411yescharacteristic
355C2×Dic43C4×D411yescharacteristic
356D172—21no—
357D172—42no—
358D172C4×D412yes—
359C4×D43—21no—
360C4×D43—21no—
361C4×D43—21no—
362C4×D43—21no—
363C4×D43—21no—
364C4×D43—22no—
365C4×D43—21no—
366C4×D43—22no—
367C4×D43—21no—
368C4×D43—21no—
369C4×D43—42no—
370C4×D43—42no—
371C4×D43—48no—
372Dic86—21no—
373Dic86—42no—
374Dic86C4×D412yes—
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—21no—
384C43⋊C8—22no—
385C43⋊C8—21no—
386C43⋊C8—41no—
387#22886—431nomaximal, Sylow
388C22×C43—21no—
389C22×C43—21no—
390C22×C43—41no—
391C22×C43—41no—
392C22×C43—41no—
393C22×C43—41no—
394C22×C43—41no—
395C22×C43—41no—
396C22×C43C2×C4×D411yescharacteristic
397C22×C43#54611yescharacteristic
398C22×C43#55111yescharacteristic
399C2×D43—21no—
400C2×D43—21no—
401C2×D43—21no—
402C2×D43—22no—
403C2×D43—21no—
404C2×D43—21no—
405C2×D43—42no—
406C2×D43—42no—
407C2×D43—41no—
408C2×D43—41no—
409C2×D43—84no—
410C2×D43#44412yescomplemented
411C4×C43—42no—
412C4×C43—41no—
413C4×C43—41no—
414C4×C43C2×C4×D411yescharacteristic
415C4×C43#51811yescharacteristic
416C4×C43D4211yescharacteristic
417C4×C43#54611yescharacteristic
418Dic43—22no—
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#1975D4311yescharacteristic, complemented
430#1938—431no—
431#1929—431no—
432#1896—431no—
433#1876—431no—
434#1876—431no—
435#1866—431no—
436#1855—431no—
437#1765—431no—
438#1749—431no—
439C2×C43—21no—
440C2×C43—21no—
441C2×C43—81no—
442C2×C43—81no—
443C2×C43#235811yescharacteristic
444C2×C43C2×#44411yescharacteristic
445C2×C43#295611yescharacteristic
446D43—22no—
447D43—41no—
448D43—42no—
449C22×#41—431no—
450C2×#135—431no—
451C2×#135C2×D4311yescharacteristic
452C2×#131—431no—
453C2×#131—431no—
454C2×#131—431no—
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#424—431no—
474C2×#104—431no—
475C2×#104—431no—
476C2×#104—431no—
477C2×#104—431no—
478C2×#104—864no—
479C2×#104C2×D4311yescharacteristic
480C2×#104C2×D4311yescharacteristic, complemented
481#416—431no—
482#416—431no—
483#408—431no—
484#408—861no—
485#408—861no—
486#408C2×D4311yescharacteristic
487#408C2×D4311yescharacteristic, complemented
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×#97C2×D4311yescharacteristic, complemented
496#341—431no—
497#341—431no—
498#339—431no—
499#339—431no—
500#336—431no—
501#336—431no—
502C43#2288611yescharacteristic, complemented, Sylow
503C2×#41—431no—
504C2×#41—431no—
505C2×#41—431no—
506C2×#41—861no—
507C2×#41—861no—
508C2×#41—862no—
509C2×#41—862no—
510C2×#41—1721no—
511C2×#41—1721no—
512C2×#41C22×D4311yescharacteristic
513C2×#41C22×D4311yescharacteristic
514C22×Q8—431no—
515C22×D4—431no—
516C22×D4—861no—
517C23×C4—431no—
518C23×C4—861no—
519C23×C4—861no—
520#135—41no—
521#135—41no—
522#135—862no—
523#135—862no—
524C2×Q16—431no—
525C2×Q16C4×D4311yescharacteristic, complemented
526C2×SD16—431no—
527C2×SD16—431no—
528C2×SD16C4×D4311yescharacteristic, complemented
529C2×SD16C4×D4311yescharacteristic, complemented
530C2×D8—431no—
531C2×D8C4×D4311yescharacteristic, complemented
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—861no—
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#117—431no—
565C2×C42—431no—
566C2×C42—862no—
567C2×C42—861no—
568C2×C42—1721no—
569C2×C42C22×D4311yescharacteristic
570#108—41no—
571#108—862no—
572C4⋊C8—861no—
573C4⋊C8—861no—
574#104—22no—
575#104—22no—
576#104—434no—
577#104—862no—
578#104—862no—
579#104—1721no—
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—21no—
591C22⋊C8—21no—
592C22⋊C8—431no—
593C22⋊C8—431no—
594C22⋊C8—431no—
595C22⋊C8—431no—
596C22⋊C8—431no—
597C22⋊C8—431no—
598C22⋊C8—431no—
599C22⋊C8—431no—
600C22⋊C8—861no—
601C22⋊C8—861no—
602C22⋊C8—861no—
603C22⋊C8—861no—
604#97—41no—
605#97—861no—
606#97—862no—
607C4×C8—861no—
608C24—431no—
609C24—861no—
610#41—21no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—432no—
619#41—432no—
620#41—861no—
621#41—861no—
622#41—862no—
623#41—862no—
624#41—1722no—
625#41—1722no—
626#41—1721no—
627#41—1722no—
628#41—1722no—
629#41—1721no—
630C2×Q8—431no—
631C2×Q8—861no—
632C2×Q8—862no—
633C2×Q8—1721no—
634C2×Q8C2×C4×D4311yescharacteristic
635C2×Q8C2×C4×D4311yescharacteristic
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—431no—
639C2×D4—861no—
640C2×D4—861no—
641C2×D4—862no—
642C2×D4—861no—
643C2×D4—861no—
644C2×D4—861no—
645C2×D4—861no—
646C2×D4—1721no—
647C2×D4—1722no—
648C2×D4—1722no—
649C2×D4C2×C4×D4311yescharacteristic
650C2×D4C2×C4×D4311yescharacteristic
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—431no—
655C22×C4—431no—
656C22×C4—431no—
657C22×C4—431no—
658C22×C4—431no—
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—41no—
675Q16—862no—
676SD16—41no—
677SD16—41no—
678SD16—862no—
679SD16—862no—
680D8—41no—
681D8—862no—
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—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
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—1722no—
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—431no—
719C4⋊C4—431no—
720C4⋊C4—861no—
721C4⋊C4—861no—
722C22⋊C4—861no—
723C22⋊C4—861no—
724C22⋊C4—861no—
725C22⋊C4—861no—
726C22⋊C4—861no—
727C42—21no—
728C42—861no—
729C42—861no—
730C42—861no—
731C42—1722no—
732C42D4×D4312yes—
733C23—21no—
734C23—21no—
735C23—431no—
736C23—431no—
737C23—862no—
738C23—861no—
739C23—861no—
740C23—861no—
741C23—3441no—
742C23—1721no—
743C23—1722no—
744C23—1722no—
745C23#41×D4311yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—21no—
749Q8—21no—
750Q8—432no—
751Q8—861no—
752Q8—1722no—
753D4—21no—
754D4—21no—
755D4—21no—
756D4—21no—
757D4—41no—
758D4—41no—
759D4—41no—
760D4—41no—
761D4—432no—
762D4—862no—
763D4—862no—
764D4—861no—
765D4—3441no—
766D4—1722no—
767D4—1722no—
768D4—1722no—
769D4—1722no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—431no—
780C2×C4—431no—
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—862no—
790C2×C4—861no—
791C2×C4—862no—
792C2×C4—861no—
793C2×C4—861no—
794C2×C4—862no—
795C2×C4—861no—
796C2×C4—861no—
797C2×C4—1722no—
798C2×C4—1722no—
799C2×C4—1728no—
800C2×C4—1722no—
801C2×C4—1721no—
802C2×C4—1721no—
803C2×C4C22×C4×D4311yescharacteristic
804C2×C4C2×D4×D4311yescharacteristic
805C2×C4C2×D4×D4311yescharacteristic
806C2×C4#41×D4311yescharacteristic
807C2×C4#1306337011yescharacteristic
808C2×C4#1306337011yescharacteristic
809C8—21no—
810C8—21no—
811C8—21no—
812C8—21no—
813C8—41no—
814C8—41no—
815C8—861no—
816C8—861no—
817C8—861no—
818C8—861no—
819C8—862no—
820C8—1721no—
821C22—21no—
822C22—21no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—432no—
830C22—861no—
831C22—861no—
832C22—861no—
833C22—862no—
834C22—861no—
835C22—861no—
836C22—3444no—
837C22—1722no—
838C22—1722no—
839C22—1721no—
840C22—1721no—
841C22C4×D4×D4311yescharacteristic
842C22#1458353811yescharacteristic
843C22#1458357911yescharacteristic
844C4—42no—
845C4—41no—
846C4—41no—
847C4—861no—
848C4—861no—
849C4—862no—
850C4—1722no—
851C4—1721no—
852C4—1721no—
853C4C4×D4×D4311yescharacteristic
854C4#1458337211yescharacteristic
855C4#1458353411yescharacteristic
856C4#1458353811yescharacteristic
857C2—21no—
858C2—21no—
859C2—81no—
860C2—81no—
861C2—862no—
862C2—1721no—
863C2—1722no—
864C2#1913757611yescharacteristic
865C2#444×D4311yescharacteristic
866C2#1914350311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1975C2
socleC22×C43C2×C4×D4
prime radical#19143809C2
cosocleC22×C4×C43C24
hypercenter#1975D43
hypocenterC43#22886
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1975

Complements

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

NH ≅ G/Ntype
2. C2×#14583018C2semidirect
3. #19143325C2semidirect
4. C2×#104×D43C2semidirect
5. #19143043C2semidirect
6. #19135303C2semidirect
7. #19135240C2semidirect
8. #19135035C2semidirect
9. #19134925C2semidirect
10. #19134924C2semidirect
11. #19134867C2semidirect
12. #19134798C2semidirect
13. #19134439C2semidirect
14. #19134358C2semidirect
15. C43×#1975C2semidirect
19. C2×#13063332C22semidirect
24. #14583060C4semidirect
25. #14583058C4semidirect
26. #14583053C4semidirect
27. #14583048C4semidirect
28. #14583043C4semidirect
29. #14583041C4semidirect
30. #14583036C4semidirect
31. #14583031C4semidirect
37. C2×#13063260C22semidirect
38. #14582927C22semidirect
41. C2×#13063252C22semidirect
54. #14582854C22semidirect
55. C2×#13063236C22semidirect
56. #14582664C22semidirect
57. #14582663C22semidirect
58. #14582660C22semidirect
59. #14582659C22semidirect
60. #14582653C22semidirect
61. #14582653C22semidirect
63. C2×#108×C43C22semidirect
65. C2×#104×C43C22semidirect
67. C43×#408C22semidirect
68. C2×#97×C43C22semidirect
86. C2×#10621885C2×C4semidirect
87. C2×#10621883C2×C4semidirect
88. C2×#10621884C2×C4semidirect
89. C2×#10621882C2×C4semidirect
126. #13063253D4semidirect
130. #13063250C2×C4semidirect
131. #13063250C2×C4semidirect
132. #13063249C2×C4semidirect
133. #13063249C2×C4semidirect
134. #13063247C2×C4semidirect
135. #13063247C2×C4semidirect
136. #13063246C2×C4semidirect
137. #13063246C2×C4semidirect
157. C2×Q16×C43C2×C4semidirect
158. C2×SD16×C43C2×C4semidirect
159. C2×SD16×C43C2×C4semidirect
160. C2×D8×C43C2×C4semidirect
410. C2×D43#444semidirect
429. #1975D43semidirect
472. C2×#108C2×D43semidirect
480. C2×#104C2×D43semidirect
487. #408C2×D43semidirect
495. C2×#97C2×D43semidirect
502. C43#22886semidirect
525. C2×Q16C4×D43semidirect
528. C2×SD16C4×D43semidirect
529. C2×SD16C4×D43semidirect
531. C2×D8C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191438092
C2×#145830182
#191433252
C2×#104×D432
#191430432
#191353032
#191352402
#191350352
#191349252
#191349242
#191348672
#191347982
#191344392
#191343582
C43×#19752
#2288643