Finite Group Databasebeta

← #25117335

Subgroups — #25117335

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×#14583019C211yesmaximal, characteristic, complemented
3C22×#13063251C211yesmaximal, characteristic, complemented
4#19143041C211yesmaximal, characteristic, complemented
5#19135487C211yesmaximal, characteristic, complemented
6#19135305C211yesmaximal, characteristic, complemented
7#19135243C211yesmaximal, characteristic, complemented
8#19135039C211yesmaximal, characteristic, complemented
9#19134925C211yesmaximal, characteristic, complemented
10#19134922C211yesmaximal, characteristic, complemented
11#19134869C211yesmaximal, characteristic, complemented
12#19134800C211yesmaximal, characteristic, complemented
13#19134441C211yesmaximal, characteristic, complemented
14#19134359C211yesmaximal, characteristic, complemented
15C43×#2933C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C2×#13063345C2211yescharacteristic
18C2×#13063345C2211yescharacteristic
19C2×#13063331C2211yescharacteristic
20C2×#13063331C2211yescharacteristic
21C22×C4×Dic43C2211yescharacteristic
22#14583059C411yescharacteristic, complemented
23#14583059C411yescharacteristic, complemented
24#14583054C411yescharacteristic, complemented
25#14583049C411yescharacteristic, complemented
26#14583042C411yescharacteristic, complemented
27#14583042C411yescharacteristic, complemented
28#14583037C411yescharacteristic, complemented
29#14583032C411yescharacteristic, complemented
30#14583019—24no—
31C2×#13063260C2211yescharacteristic, complemented
32C2×#13063260C2211yescharacteristic, complemented
33C2×#13063252C2211yescharacteristic, complemented
34C2×#13063252C2211yescharacteristic, complemented
35C2×#13063251—24no—
36C2×#13063251C2211yescharacteristic
37C2×#13063251C2211yescharacteristic
38C2×#13063251C2211yescharacteristic
39C2×#13063251C2211yescharacteristic
40#14582893C2211yescharacteristic
41#14582893C2211yescharacteristic
42#14582865C2211yescharacteristic
43#14582865C2211yescharacteristic
44#14582864—21no—
45#14582864—21no—
46#14582863C2211yescharacteristic
47#14582861—21no—
48C2×C22⋊(C43⋊C8)C2211yescharacteristic
49C22⋊C8×D43—21no—
50C2×#13063235C2211yescharacteristic, complemented
51C2×#13063235C2211yescharacteristic, complemented
52#14582663C2211yescharacteristic, complemented
53#14582663C2211yescharacteristic, complemented
54#14582658C2211yescharacteristic, complemented
55#14582658C2211yescharacteristic, complemented
56#14582653C2211yescharacteristic, complemented
57#14582653C2211yescharacteristic, complemented
58C2×#131×C43C2211yescharacteristic, complemented
59C22×M16×C43C2211yescharacteristic
60C43×#525C2211yescharacteristic
61C43×#436—21no—
62C43×#435—21no—
63C43×#435—21no—
64C8×D4×C43—21no—
65C43×#424C2211yescharacteristic, complemented
66C43×#408C2211yescharacteristic, complemented
67C2×C22⋊C8×C43C2211yescharacteristic
68C43×#405C2211yescharacteristic, 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—
82C23×Dic43—21no—
83C22×C4×D43—21no—
84#13063345—22no—
85#13063345—22no—
86#13063345—41no—
87#13063345—41no—
88C2×#10621885C2×C411yescharacteristic, complemented
89C2×#10621885C2×C411yescharacteristic, complemented
90C2×#10621883C2×C411yescharacteristic, complemented
91C2×#10621883C2×C411yescharacteristic, complemented
92C2×#10621884C2×C411yescharacteristic, complemented
93C2×#10621884C2×C411yescharacteristic, complemented
94C2×#10621882C2×C411yescharacteristic, complemented
95C2×#10621882C2×C411yescharacteristic, complemented
96#13063331—22no—
97#13063331—22no—
98#13063331—41no—
99#13063331—41no—
100C2×#10621877C2311yescharacteristic
101C2×#10621877C2311yescharacteristic
102C2×#10621872—21no—
103C2×#10621872—21no—
104C22×C43⋊C8C2311yescharacteristic
105C22×C43⋊C8C2311yescharacteristic
106C2×C8×D43—21no—
107C2×C8×D43—21no—
108C2×C4×Dic43—22no—
109C2×C4×Dic43—21no—
110C2×C4×Dic43—41no—
111C2×C4×Dic43C2311yescharacteristic
112C2×C4×Dic43C2311yescharacteristic
113#13063260—22no—
114#13063260—41no—
115#13063252—22no—
116#13063252—41no—
117#13063251—22no—
118#13063251—22no—
119#13063251—22no—
120#13063251D414yescomplemented
121#13063248C2×C411yescharacteristic, complemented
122#13063248C2×C411yescharacteristic, complemented
123#13063248C2×C411yescharacteristic, complemented
124#13063248C2×C411yescharacteristic, complemented
125#13063245C2×C411yescharacteristic, complemented
126#13063245C2×C411yescharacteristic, complemented
127#13063245C2×C411yescharacteristic, complemented
128#13063245C2×C411yescharacteristic, complemented
129C22⋊(C43⋊C8)—21no—
130C22⋊(C43⋊C8)—21no—
131C22⋊(C43⋊C8)C2×C411yescharacteristic
132C22⋊(C43⋊C8)C2×C411yescharacteristic
133C22⋊(C43⋊C8)C2×C411yescharacteristic
134C22⋊(C43⋊C8)C2×C411yescharacteristic
135(C2×D43)⋊C8—21no—
136(C2×D43)⋊C8—21no—
137(C2×D43)⋊C8—21no—
138(C2×D43)⋊C8—21no—
139#13063235—22no—
140#13063235—41no—
141C2×#41×C43C2311yescharacteristic
142C23×C4×C43C2311yescharacteristic
143#131×C43—22no—
144#131×C43—41no—
145C2×M16×C43—21no—
146C2×M16×C43—21no—
147C2×M16×C43—22no—
148C2×M16×C43—41no—
149C2×M16×C43C2311yescharacteristic
150C2×M16×C43C2311yescharacteristic
151C22×C8×C43—21no—
152C22×C8×C43—21no—
153C22×C8×C43C2311yescharacteristic
154C22×C8×C43C2311yescharacteristic
155#123×C43—21no—
156C22⋊Q8×C43C2×C411yescharacteristic
157C22⋊Q8×C43C2×C411yescharacteristic
158#121×C43C2×C411yescharacteristic
159#121×C43C2×C411yescharacteristic
160#120×C43—21no—
161C4×D4×C43—21no—
162C4×D4×C43—21no—
163#117×C43C2311yescharacteristic
164C4⋊C8×C43—21no—
165C4⋊C8×C43—21no—
166C22⋊C8×C43—21no—
167C22⋊C8×C43—21no—
168C22⋊C8×C43D411yescharacteristic
169C22⋊C8×C43D411yescharacteristic
170C22⋊C8×C43D411yescharacteristic
171C22⋊C8×C43D411yescharacteristic
172#97×C43—21no—
173C4×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×C43C22×C411yescharacteristic
191C22×C4×C43C22×C411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43#4111yescharacteristic
195C22×C4×C43C2411yescharacteristic
196C2×C22⋊D43—21no—
197C2×C22⋊D43—21no—
198C2×C22⋊D43—21no—
199C2×C22⋊D43—21no—
200C2×C22⋊D43—42no—
201C2×C22⋊D43—42no—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43—21no—
205C22×Dic43—42no—
206C22×Dic43—42no—
207C22×Dic43—42no—
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—42no—
244M16×C43—42no—
245M16×C43C2×D412yes—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C2×C8×C43—21no—
249C2×C8×C43—21no—
250C2×C8×C43—21no—
251C2×C8×C43—21no—
252C2×C8×C43—42no—
253C2×C8×C43—42no—
254C2×C8×C43C2×D411yescharacteristic
255C2×C8×C43C2×D411yescharacteristic
256C2×C8×C43C2×D411yescharacteristic
257C2×C8×C43C2×D411yescharacteristic
258C4⋊C4×C43—21no—
259C4⋊C4×C43—21no—
260C4⋊C4×C43C22×C411yescharacteristic
261C4⋊C4×C43C22×C411yescharacteristic
262C22⋊C4×C43—21no—
263C22⋊C4×C43—21no—
264C22⋊C4×C43—21no—
265C22⋊C4×C43—21no—
266C22⋊C4×C43—21no—
267C42×C43—21no—
268#10621885—22no—
269#10621885—41no—
270#10621884—22no—
271#10621884—41no—
272#10621883—22no—
273#10621883—41no—
274#10621882—22no—
275#10621882—41no—
276C4×Dic43—21no—
277C4×Dic43—21no—
278C4×Dic43—21no—
279C4×Dic43—42no—
280C4×Dic43C2×D412yes—
281#10621877—21no—
282#10621877—21no—
283#10621877—21no—
284#10621877—21no—
285C2×C43⋊C8—21no—
286C2×C43⋊C8—21no—
287C2×C43⋊C8—21no—
288C2×C43⋊C8—21no—
289C2×C43⋊C8—21no—
290C2×C43⋊C8—21no—
291C2×C43⋊C8C22×C411yescharacteristic
292C2×C43⋊C8C22×C411yescharacteristic
293C2×C43⋊C8C22×C411yescharacteristic
294C2×C43⋊C8C22×C411yescharacteristic
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—21no—
331C2×C4×C43—21no—
332C2×C4×C43—21no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43C4×D411yescharacteristic
336C2×C4×C43C4×D411yescharacteristic
337C2×C4×C43C23×C411yescharacteristic
338C2×C4×C43C22×D411yescharacteristic
339C2×C4×C43C22×D411yescharacteristic
340C2×C4×C43C2×#4111yescharacteristic
341C2×C4×C43H(5,𝔽2)11yescharacteristic
342C2×C4×C43H(5,𝔽2)11yescharacteristic
343C22⋊D43—22no—
344C22⋊D43—22no—
345C22⋊D43—42no—
346C22⋊D43—42no—
347C22⋊D43—41no—
348C22⋊D43—41no—
349C2×Dic43—21no—
350C2×Dic43—22no—
351C2×Dic43—21no—
352C2×Dic43—22no—
353C2×Dic43—42no—
354C2×Dic43—41no—
355C2×Dic43—41no—
356C2×Dic43—41no—
357C2×Dic43—48no—
358C2×Dic43—41no—
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—21no—
376C8×C43—21no—
377C8×C43—22no—
378C8×C43—21no—
379C8×C43—21no—
380C8×C43—41no—
381C43⋊C8—21no—
382C43⋊C8—21no—
383C43⋊C8—21no—
384C43⋊C8—21no—
385C43⋊C8—41no—
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—41no—
414C4×C43—41no—
415C4×C43—41no—
416C4×C43C2×C4×D411yescharacteristic
417C4×C43#51811yescharacteristic
418C4×C43D4211yescharacteristic
419C4×C43#54611yescharacteristic
420Dic43—22no—
421Dic43—42no—
422Dic43—42no—
423Dic43—41no—
424#3002—431no—
425C2×#444—431no—
426#2933D4311yescharacteristic, complemented
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#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×#131C2×D4311yescharacteristic, complemented
455C22×M16C2×D4311yescharacteristic
456#525C2×D4311yescharacteristic
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—21no—
468#435—21no—
469#435—21no—
470C8×D4—21no—
471C2×#108—431no—
472C2×#108—431no—
473#424C2×D4311yescharacteristic, complemented
474C2×#104—431no—
475C2×#104—431no—
476C2×#104—431no—
477C2×#104—431no—
478C2×#104—431no—
479C2×#104—431no—
480C2×#104—864no—
481#416—431no—
482#416—431no—
483#408—431no—
484#408—431no—
485#408—861no—
486#408—861no—
487#408C2×D4311yescharacteristic, complemented
488#407—431no—
489#407—861no—
490C2×C22⋊C8—431no—
491C2×C22⋊C8—861no—
492C2×C22⋊C8C2×D4311yescharacteristic
493#405C2×D4311yescharacteristic, complemented
494C2×#97—431no—
495C2×#97—431no—
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—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—861no—
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—22no—
533#131—41no—
534#131—862no—
535#131—862no—
536#131—1721no—
537#131—1721no—
538C2×M16—21no—
539C2×M16—21no—
540C2×M16—22no—
541C2×M16—41no—
542C2×M16—431no—
543C2×M16—431no—
544C2×M16—861no—
545C2×M16—861no—
546C2×M16C22×D4311yescharacteristic
547C2×M16C22×D4311yescharacteristic
548C22×C8—21no—
549C22×C8—21no—
550C22×C8—431no—
551C22×C8—431no—
552C22×C8—861no—
553C22×C8—861no—
554C22×C8C22×D4311yescharacteristic
555C22×C8C22×D4311yescharacteristic
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—431no—
566C2×C42—431no—
567C2×C42—862no—
568C2×C42—861no—
569C2×C42—1721no—
570#108—862no—
571#108—1721no—
572C4⋊C8—21no—
573C4⋊C8—21no—
574#104—434no—
575#104—862no—
576#104—862no—
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—431no—
591C22⋊C8—431no—
592C22⋊C8—431no—
593C22⋊C8—431no—
594C22⋊C8—861no—
595C22⋊C8—861no—
596C22⋊C8—861no—
597C22⋊C8—861no—
598C22⋊C8—861no—
599C22⋊C8—861no—
600C22⋊C8C22⋊D4311yescharacteristic
601C22⋊C8C22⋊D4311yescharacteristic
602C22⋊C8C22⋊D4311yescharacteristic
603C22⋊C8C22⋊D4311yescharacteristic
604#97—21no—
605#97—862no—
606#97—1721no—
607C4×C8—21no—
608C24—861no—
609C24#1062189811yescharacteristic
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—861no—
657C22×C4—861no—
658C22×C4—861no—
659C22×C4—861no—
660C22×C4—861no—
661C22×C4—861no—
662C22×C4—861no—
663C22×C4—1722no—
664C22×C4—1722no—
665C22×C4—1722no—
666C22×C4—1722no—
667C22×C4—1722no—
668C22×C4C2×C4×D4311yescharacteristic
669C22×C4C2×C4×D4311yescharacteristic
670C22×C4#1062189811yescharacteristic
671C22×C4C2×C22⋊D4311yescharacteristic
672C22×C4C2×C22⋊D4311yescharacteristic
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—42no—
686M16—42no—
687M16—861no—
688M16—861no—
689M16—861no—
690M16—861no—
691M16—1722no—
692M16—1722no—
693M16D4×D4312yes—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—42no—
701C2×C8—42no—
702C2×C8—431no—
703C2×C8—431no—
704C2×C8—431no—
705C2×C8—431no—
706C2×C8—861no—
707C2×C8—861no—
708C2×C8—861no—
709C2×C8—861no—
710C2×C8—861no—
711C2×C8—861no—
712C2×C8—1722no—
713C2×C8—1722no—
714C2×C8C2×C22⋊D4311yescharacteristic
715C2×C8C2×C22⋊D4311yescharacteristic
716C2×C8C2×C22⋊D4311yescharacteristic
717C2×C8C2×C22⋊D4311yescharacteristic
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—432no—
729C42—861no—
730C42—861no—
731C42—861no—
732C42—1722no—
733C23—21no—
734C23—22no—
735C23—21no—
736C23—21no—
737C23—41no—
738C23—861no—
739C23—861no—
740C23—3441no—
741C23—1722no—
742C23—1722no—
743C23C4×C22⋊D4311yescharacteristic
744C23C4×C22⋊D4311yescharacteristic
745C23C2×#1062189811yescharacteristic
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—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—861no—
786C2×C4—862no—
787C2×C4—862no—
788C2×C4—862no—
789C2×C4—861no—
790C2×C4—862no—
791C2×C4—1722no—
792C2×C4—1722no—
793C2×C4—1722no—
794C2×C4—1721no—
795C2×C4—1721no—
796C2×C4—1721no—
797C2×C4—1728no—
798C2×C4—1721no—
799C2×C4—1721no—
800C2×C4—1721no—
801C2×C4C4×C22⋊D4311yescharacteristic
802C2×C4C4×C22⋊D4311yescharacteristic
803C2×C4C22×C4×D4311yescharacteristic
804C2×C4C2×D4×D4311yescharacteristic
805C2×C4C22×C22⋊D4311yescharacteristic
806C2×C4#41×D4311yescharacteristic
807C2×C4#1306337011yescharacteristic
808C2×C4#1306337111yescharacteristic
809C8—21no—
810C8—21no—
811C8—22no—
812C8—21no—
813C8—21no—
814C8—41no—
815C8—861no—
816C8—861no—
817C8—861no—
818C8—861no—
819C8—1721no—
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#1458301912yescomplemented
841C22C2×C4×C22⋊D4311yescharacteristic
842C22#1458354511yescharacteristic
843C22#1458357811yescharacteristic
844C4—21no—
845C4—21no—
846C4—41no—
847C4—41no—
848C4—41no—
849C4—862no—
850C4—1722no—
851C4—1722no—
852C4—1721no—
853C4C4×D4×D4311yescharacteristic
854C4#1458337111yescharacteristic
855C4D4×C22⋊D4311yescharacteristic
856C4#1458353711yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—81no—
862C2—3441no—
863C2—1722no—
864C2#1913757211yescharacteristic
865C2C2×#1458301911yescharacteristic
866C2#1914350211yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2933C2
socleC22×C43C2×C4×D4
prime radical#19143811C2
cosocleC22×C4×C43C24
hypercenter#2933D43
hypocenterC43#22886
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2933

Complements

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

NH ≅ G/Ntype
2. C2×#14583019C2semidirect
3. C22×#13063251C2semidirect
4. #19143041C2semidirect
5. #19135487C2semidirect
6. #19135305C2semidirect
7. #19135243C2semidirect
8. #19135039C2semidirect
9. #19134925C2semidirect
10. #19134922C2semidirect
11. #19134869C2semidirect
12. #19134800C2semidirect
13. #19134441C2semidirect
14. #19134359C2semidirect
15. C43×#2933C2semidirect
22. #14583059C4semidirect
23. #14583059C4semidirect
24. #14583054C4semidirect
25. #14583049C4semidirect
26. #14583042C4semidirect
27. #14583042C4semidirect
28. #14583037C4semidirect
29. #14583032C4semidirect
31. C2×#13063260C22semidirect
32. C2×#13063260C22semidirect
33. C2×#13063252C22semidirect
34. C2×#13063252C22semidirect
50. C2×#13063235C22semidirect
51. C2×#13063235C22semidirect
52. #14582663C22semidirect
53. #14582663C22semidirect
54. #14582658C22semidirect
55. #14582658C22semidirect
56. #14582653C22semidirect
57. #14582653C22semidirect
58. C2×#131×C43C22semidirect
65. C43×#424C22semidirect
66. C43×#408C22semidirect
68. C43×#405C22semidirect
88. C2×#10621885C2×C4semidirect
89. C2×#10621885C2×C4semidirect
90. C2×#10621883C2×C4semidirect
91. C2×#10621883C2×C4semidirect
92. C2×#10621884C2×C4semidirect
93. C2×#10621884C2×C4semidirect
94. C2×#10621882C2×C4semidirect
95. C2×#10621882C2×C4semidirect
120. #13063251D4semidirect
121. #13063248C2×C4semidirect
122. #13063248C2×C4semidirect
123. #13063248C2×C4semidirect
124. #13063248C2×C4semidirect
125. #13063245C2×C4semidirect
126. #13063245C2×C4semidirect
127. #13063245C2×C4semidirect
128. #13063245C2×C4semidirect
400. C22×C43#444semidirect
426. #2933D43semidirect
454. C2×#131C2×D43semidirect
473. #424C2×D43semidirect
487. #408C2×D43semidirect
493. #405C2×D43semidirect
502. C43#22886semidirect
840. C22#14583019semidirect

Maximal subgroups

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

subgroupindex
#191438112
C2×#145830192
C22×#130632512
#191430412
#191354872
#191353052
#191352432
#191350392
#191349252
#191349222
#191348692
#191348002
#191344412
#191343592
C43×#29332
#2288643