Finite Group Databasebeta

← #25112373

Subgroups — #25112373

Order 11008.

1622 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063351C211yesmaximal, characteristic
2C2×#14582999C211yesmaximal, characteristic, complemented
3C2×C4×#10621883C211yesmaximal, characteristic, complemented
4#19137435C211yesmaximal, characteristic, complemented
5#19135470C211yesmaximal, characteristic, complemented
6#19135460C211yesmaximal, characteristic, complemented
7#19134953C211yesmaximal, characteristic, complemented
8#19134953C211yesmaximal, characteristic, complemented
9#19134943C211yesmaximal, characteristic, complemented
10#19134943C211yesmaximal, characteristic, complemented
11#19134626C211yesmaximal, characteristic, complemented
12#19134533C211yesmaximal, characteristic, complemented
13#19134526C211yesmaximal, characteristic, complemented
14#19134379C211yesmaximal, characteristic, complemented
15D4×C22⋊C4×C43C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C2×#13063351—24no—
18C2×#13063351—24no—
19C2×#13063351C418yescomplemented
20C22×#10621883C2211yescharacteristic
21C22×#10621883C2211yescharacteristic
22C22×#10621882C2211yescharacteristic
23C22×#10621882C2211yescharacteristic
24C22×#10621877C2211yescharacteristic
25C2×C4×Dic86C2211yescharacteristic, complemented
26C2×C4×Dic86C2211yescharacteristic, complemented
27#14582999—24no—
28C4×#10621883—24no—
29C2×#13063258C2211yescharacteristic, complemented
30C2×#13063256C2211yescharacteristic, complemented
31C2×#13063248C2211yescharacteristic, complemented
32C2×#13063248C2211yescharacteristic, complemented
33C2×#13063246C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×#13063246C2211yescharacteristic
37C2×#13063245C2211yescharacteristic, complemented
38C2×#13063245C2211yescharacteristic, complemented
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C2×#13063236C2211yescharacteristic, complemented
41C2×C4×C43⋊C8C2211yescharacteristic, complemented
42#14582801C2211yescharacteristic, complemented
43#14582801C2211yescharacteristic, complemented
44#14582799—21no—
45#14582799—21no—
46#14582759C2211yescharacteristic
47#14582758—21no—
48#14582746—21no—
49#14582661C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582654C2211yescharacteristic, complemented
52#14582654C2211yescharacteristic, complemented
53C23×D4×C43C2211yescharacteristic
54C2×C4×D4×C43C2211yescharacteristic
55C2×C4×D4×C43C2211yescharacteristic
56C22×C22⋊C4×C43—21no—
57C43×#390C2211yescharacteristic
58C43×#390C2211yescharacteristic
59C43×#386—21no—
60C43×#386—21no—
61C43×#380C2211yescharacteristic
62C43×#379—21no—
63C4×C22⋊C4×C43C2211yescharacteristic
64C2×#10621898—22no—
65C2×#10621898—22no—
66C2×#10621898—22no—
67C2×#10621898—41no—
68C2×#10621898—41no—
69C2×#10621898C2×C414yescomplemented
70C22×Dic86C2311yescharacteristic
71C22×D172C2311yescharacteristic
72C22×C22⋊D43—21no—
73C22×C4×D43—21no—
74#13063351—232no—
75C2×#10621883—22no—
76C2×#10621883—22no—
77C2×#10621883C2×C414yes—
78C2×#10621883C2×C414yescomplemented
79C2×#10621883D414yes—
80C2×#10621883D414yes—
81C2×#10621882—22no—
82C2×#10621882—22no—
83C2×#10621882—22no—
84C2×#10621882—22no—
85C2×#10621882C2×C414yes—
86C2×#10621882C2×C414yescomplemented
87C2×#10621877—22no—
88C2×#10621877—22no—
89C2×#10621877C2×C414yescomplemented
90C22×C43⋊C8C2311yescharacteristic
91C22×C43⋊C8C2311yescharacteristic
92C22×C43⋊C8C2311yescharacteristic
93C22×C43⋊C8C2311yescharacteristic
94C4×Dic86—22no—
95C4×Dic86—22no—
96C4×Dic86—41no—
97C4×Dic86—41no—
98C2×C4⋊Dic43C2311yescharacteristic
99C2×C4⋊Dic43C2311yescharacteristic
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×C22⋊Dic43—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×C4×Dic43—21no—
108C2×C4×Dic43—21no—
109#13063258—22no—
110#13063256—22no—
111#13063248—22no—
112#13063248—22no—
113#13063246—22no—
114#13063246—22no—
115#13063246—41no—
116#13063246—41no—
117#13063245—41no—
118#13063245—41no—
119C22⋊(C43⋊C8)—22no—
120#13063236—22no—
121C4×C43⋊C8—22no—
122C43⋊#95—21no—
123C25×C43—21no—
124C22×D4×C43—22no—
125C22×D4×C43—22no—
126C22×D4×C43—21no—
127C22×D4×C43—22no—
128C22×D4×C43—41no—
129C22×D4×C43—41no—
130C22×D4×C43C2×C414yes—
131C22×D4×C43C2311yescharacteristic
132C22×D4×C43C2311yescharacteristic
133C23×C4×C43—21no—
134C23×C4×C43—21no—
135C23×C4×C43C2311yescharacteristic
136C4×D4×C43—22no—
137C4×D4×C43—22no—
138C4×D4×C43—41no—
139C4×D4×C43—41no—
140C2×C4⋊C4×C43C2311yescharacteristic
141C2×C4⋊C4×C43C2311yescharacteristic
142C2×C22⋊C4×C43—21no—
143C2×C22⋊C4×C43—21no—
144C2×C22⋊C4×C43—21no—
145C2×C22⋊C4×C43—21no—
146C2×C22⋊C4×C43—21no—
147C2×C22⋊C4×C43—21no—
148C2×C22⋊C4×C43—21no—
149C2×C22⋊C4×C43—44no—
150C2×C22⋊C4×C43D411yescharacteristic
151C2×C22⋊C4×C43D411yescharacteristic
152C2×C42×C43C2311yescharacteristic
153C2×C42×C43C2311yescharacteristic
154#95×C43—21no—
155#95×C43D411yescharacteristic
156#95×C43D411yescharacteristic
157C24×C43—21no—
158C24×C43—21no—
159C24×C43—24no—
160C24×C43—42no—
161C24×C43—42no—
162C24×C43—42no—
163C24×C43—42no—
164C24×C43—81no—
165C24×C43—81no—
166C24×C43C2×D411yescharacteristic
167C23×D43—21no—
168C2×D4×C43—24no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43—28no—
174C2×D4×C43—21no—
175C2×D4×C43—21no—
176C2×D4×C43—21no—
177C2×D4×C43—21no—
178C2×D4×C43—42no—
179C2×D4×C43—42no—
180C2×D4×C43—44no—
181C2×D4×C43—44no—
182C2×D4×C43—44no—
183C2×D4×C43C22×C412yes—
184C2×D4×C43C22×C412yes—
185C2×D4×C43C2×D412yes—
186C2×D4×C43C2×D412yes—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—42no—
194C22×C4×C43—42no—
195C22×C4×C43—42no—
196C22×C4×C43—42no—
197C22×C4×C43—81no—
198C22×C4×C43—81no—
199C22×C4×C43C22×C412yes—
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2×D411yescharacteristic
203C22×C4×C43C2×D411yescharacteristic
204C22×C4×C43C2×D411yescharacteristic
205C22×C4×C43#4112yes—
206C22×C4×C43C2411yescharacteristic
207C2×C22⋊D43—24no—
208C2×C22⋊D43—42no—
209C2×C22⋊D43—42no—
210C22×Dic43—21no—
211C22×Dic43—21no—
212C22×Dic43—21no—
213#10621898—28no—
214#10621898—44no—
215#10621898—44no—
216#10621898—44no—
217C2×D172—21no—
218C2×D172—21no—
219C2×D172—21no—
220C2×D172—21no—
221C2×D172—21no—
222C2×D172C22×C412yes—
223C2×C4×D43—24no—
224C2×C4×D43—42no—
225C2×C4×D43—42no—
226C2×Dic86—21no—
227C2×Dic86—21no—
228C2×Dic86—21no—
229C2×Dic86C22×C412yes—
230C2×Dic86C2×D412yes—
231C2×Dic86C2×D412yes—
232C4⋊C4×C43—21no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43—21no—
236C22⋊C4×C43—22no—
237C22⋊C4×C43—41no—
238C22⋊C4×C43—42no—
239C22⋊C4×C43—42no—
240C22⋊C4×C43—42no—
241C22⋊C4×C43—42no—
242C22⋊C4×C43—42no—
243C22⋊C4×C43—81no—
244C22⋊C4×C43—81no—
245C42×C43—21no—
246C42×C43—21no—
247C42×C43—21no—
248C42×C43—21no—
249C22⋊Dic43—81no—
250#10621883—28no—
251#10621883C22⋊C4116yescomplemented
252#10621882—28no—
253#10621882—28no—
254(C2×D43)⋊C4—42no—
255(C2×D43)⋊C4—42no—
256(C2×D43)⋊C4—81no—
257(C2×D43)⋊C4—81no—
258C4⋊Dic43—21no—
259C4⋊Dic43—21no—
260C4⋊Dic43—21no—
261C4⋊Dic43—21no—
262Dic43⋊C4—42no—
263Dic43⋊C4—42no—
264C4×Dic43—42no—
265C4×Dic43—42no—
266#10621877—28no—
267C2×C43⋊C8—21no—
268C2×C43⋊C8—21no—
269C2×C43⋊C8—21no—
270C2×C43⋊C8—21no—
271C2×C43⋊C8—21no—
272C2×C43⋊C8—21no—
273C2×C43⋊C8—21no—
274C2×C43⋊C8—21no—
275C2×C43⋊C8C22×C412yes—
276C2×C43⋊C8C22×C412yes—
277C2×C43⋊C8C2×D412yes—
278C2×C43⋊C8C2×D412yes—
279C23×C43—22no—
280C23×C43—22no—
281C23×C43—22no—
282C23×C43—21no—
283C23×C43—21no—
284C23×C43—21no—
285C23×C43—21no—
286C23×C43—21no—
287C23×C43—21no—
288C23×C43—22no—
289C23×C43—48no—
290C23×C43—48no—
291C23×C43—41no—
292C23×C43—41no—
293C23×C43—41no—
294C23×C43—41no—
295C23×C43—41no—
296C23×C43—41no—
297C23×C43—41no—
298C23×C43—41no—
299C23×C43—41no—
300C23×C43—41no—
301C23×C43—84no—
302C23×C43—84no—
303C23×C43—84no—
304C23×C43—84no—
305C23×C43—84no—
306C23×C43C4×D412yes—
307C23×C43C22×D411yescharacteristic
308C22×D43—22no—
309C22×D43—41no—
310C22×D43—41no—
311C22×D43—41no—
312C22×D43—41no—
313C22×D43—41no—
314C22×D43—41no—
315D4×C43—22no—
316D4×C43—22no—
317D4×C43—22no—
318D4×C43—22no—
319D4×C43—22no—
320D4×C43—48no—
321D4×C43—41no—
322D4×C43—41no—
323D4×C43C2×C22⋊C414yes—
324C2×C4×C43—21no—
325C2×C4×C43—21no—
326C2×C4×C43—21no—
327C2×C4×C43—21no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—21no—
333C2×C4×C43—21no—
334C2×C4×C43—21no—
335C2×C4×C43—21no—
336C2×C4×C43—21no—
337C2×C4×C43—21no—
338C2×C4×C43—21no—
339C2×C4×C43—21no—
340C2×C4×C43—21no—
341C2×C4×C43—41no—
342C2×C4×C43—41no—
343C2×C4×C43—41no—
344C2×C4×C43—41no—
345C2×C4×C43—41no—
346C2×C4×C43—41no—
347C2×C4×C43—84no—
348C2×C4×C43—84no—
349C2×C4×C43C4×D412yes—
350C2×C4×C43AGL(1,ℤ/8)12yescomplemented
351C2×C4×C43C23×C411yescharacteristic
352C2×C4×C43C22×D411yescharacteristic
353C2×C4×C43C22×D411yescharacteristic
354C2×C4×C43C2×#4111yescharacteristic
355C2×C4×C43H(5,𝔽2)11yescharacteristic
356C2×C4×C43H(5,𝔽2)11yescharacteristic
357C22⋊D43—48no—
358C2×Dic43—22no—
359C2×Dic43—22no—
360C2×Dic43—22no—
361C2×Dic43—41no—
362C2×Dic43—41no—
363C2×Dic43—41no—
364C2×Dic43—41no—
365C2×Dic43—41no—
366C2×Dic43—41no—
367D172—22no—
368D172—22no—
369D172—41no—
370D172—41no—
371C4×D43—48no—
372Dic86—22no—
373Dic86—22no—
374Dic86—22no—
375Dic86C2×C22⋊C414yescomplemented
376C43⋊C8—22no—
377C43⋊C8—41no—
378C43⋊C8—41no—
379C43⋊C8C2×C22⋊C414yescomplemented
380#22443—431nomaximal, Sylow
381C22×C43—24no—
382C22×C43—22no—
383C22×C43—22no—
384C22×C43—22no—
385C22×C43—42no—
386C22×C43—42no—
387C22×C43—41no—
388C22×C43—42no—
389C22×C43—41no—
390C22×C43—42no—
391C22×C43—41no—
392C22×C43—42no—
393C22×C43—41no—
394C22×C43—42no—
395C22×C43—42no—
396C22×C43—42no—
397C22×C43—42no—
398C22×C43—816no—
399C22×C43—81no—
400C22×C43—81no—
401C22×C43—81no—
402C22×C43—81no—
403C22×C43C2×C4×D411yescharacteristic
404C22×C43D4211yescharacteristic
405C22×C43D4211yescharacteristic
406C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
407C22×C43#57511yescharacteristic
408C22×C43#57611yescharacteristic
409C22×C43#57711yescharacteristic
410C2×D43—42no—
411C2×D43—42no—
412C2×D43—42no—
413C2×D43—81no—
414C2×D43—81no—
415C2×D43—81no—
416C2×D43—81no—
417C4×C43—22no—
418C4×C43—22no—
419C4×C43—41no—
420C4×C43—41no—
421C4×C43—41no—
422C4×C43—81no—
423C4×C43—81no—
424C4×C43C22×C22⋊C411yescharacteristic
425C4×C43#51811yescharacteristic
426C4×C43#54611yescharacteristic
427C4×C43#54611yescharacteristic
428Dic43—24no—
429Dic43—81no—
430Dic43—81no—
431C22×AGL(1,ℤ/8)—431no—
432C2×#440—431no—
433C2×C4×SD16—431no—
434#2341—431no—
435D4×C22⋊C4D4311yescharacteristic, complemented
436#1972—431no—
437#1970—431no—
438#1880—431no—
439#1880—431no—
440#1879—431no—
441#1879—431no—
442#1809—431no—
443#1788—431no—
444#1786—431no—
445#1753—431no—
446C2×C43—42no—
447C2×C43—44no—
448C2×C43—82no—
449C2×C43D4×C22⋊C411yescharacteristic
450C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
451C2×C43#294611yescharacteristic
452C2×C43#326511yescharacteristic
453C2×C43#326811yescharacteristic
454C2×C43#327411yescharacteristic
455C2×C43#327511yescharacteristic
456D43—82no—
457C22×#41—431no—
458C23×D4C2×D4311yescharacteristic
459C2×AGL(1,ℤ/8)—438no—
460C2×AGL(1,ℤ/8)—864no—
461C2×AGL(1,ℤ/8)—864no—
462C22×SD16—431no—
463C22×SD16—431no—
464C22×D8—431no—
465C22×D8—431no—
466C22×M16—431no—
467C2×C4×Q8—431no—
468C2×C4×Q8—431no—
469C2×C4×D4C2×D4311yescharacteristic
470C2×C4×D4C2×D4311yescharacteristic
471C22×C22⋊C4—21no—
472#440—864no—
473C4×SD16—864no—
474C2×#107—431no—
475C2×#106—431no—
476C2×#103—431no—
477C2×#103—431no—
478C2×#102—431no—
479C2×#102—431no—
480C2×#102—431no—
481C2×#102—431no—
482C2×#102—431no—
483C2×#102—431no—
484C2×C22⋊C8—431no—
485C2×#97—431no—
486C2×C4×C8—431no—
487#390—431no—
488#390—431no—
489#390—861no—
490#390—861no—
491#390C2×D4311yescharacteristic
492#390C2×D4311yescharacteristic
493#386—21no—
494#386—21no—
495#380—431no—
496#380—861no—
497#380C2×D4311yescharacteristic
498#379—21no—
499C4×C22⋊C4—861no—
500C4×C22⋊C4C2×D4311yescharacteristic
501#340—431no—
502#340—431no—
503#336—431no—
504#336—431no—
505C43#2244311yescharacteristic, complemented, Sylow
506C25—21no—
507C2×#41—434no—
508C2×#41—862no—
509C2×#41—862no—
510C2×#41—862no—
511C2×#41—1721no—
512C2×#41—1721no—
513C22×Q8—431no—
514C22×D4—22no—
515C22×D4—22no—
516C22×D4—22no—
517C22×D4—21no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4—431no—
521C22×D4—861no—
522C22×D4C4×D4314yes—
523C22×D4C22×D4311yescharacteristic
524C22×D4C22×D4311yescharacteristic
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—861no—
528C23×C4C22×D4311yescharacteristic
529AGL(1,ℤ/8)—8632no—
530C2×SD16—434no—
531C2×SD16—434no—
532C2×SD16—434no—
533C2×SD16—434no—
534C2×SD16—862no—
535C2×SD16—862no—
536C2×D8—434no—
537C2×D8—434no—
538C2×D8—862no—
539C2×D8—862no—
540C2×D8—862no—
541C2×D8—862no—
542C2×M16—434no—
543C2×M16—862no—
544C2×M16—862no—
545C22×C8—431no—
546C22×C8—431no—
547C22×C8—431no—
548C22×C8—431no—
549C4×Q8—862no—
550C4×Q8—862no—
551C4×Q8—1721no—
552C4×Q8—1721no—
553C4×D4—22no—
554C4×D4—22no—
555C4×D4—41no—
556C4×D4—41no—
557C2×C4⋊C4—431no—
558C2×C4⋊C4—431no—
559C2×C4⋊C4—861no—
560C2×C4⋊C4—861no—
561C2×C4⋊C4C22×D4311yescharacteristic
562C2×C4⋊C4C22×D4311yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—44no—
571C2×C22⋊C4—861no—
572C2×C22⋊C4—861no—
573C2×C22⋊C4—861no—
574C2×C22⋊C4—861no—
575C2×C22⋊C4—861no—
576C2×C22⋊C4C22⋊D4311yescharacteristic
577C2×C22⋊C4C22⋊D4311yescharacteristic
578C2×C42—861no—
579C2×C42—861no—
580C2×C42C22×D4311yescharacteristic
581C2×C42C22×D4311yescharacteristic
582#107—862no—
583#106—862no—
584#103—862no—
585#103—862no—
586#102—862no—
587#102—862no—
588#102—1721no—
589#102—1721no—
590#102—1721no—
591#102—1721no—
592C22⋊C8—862no—
593#97—862no—
594C4×C8—862no—
595#95—21no—
596#95—861no—
597#95C22⋊D4311yescharacteristic
598#95C22⋊D4311yescharacteristic
599C24—21no—
600C24—21no—
601C24—24no—
602C24—42no—
603C24—42no—
604C24—42no—
605C24—42no—
606C24—81no—
607C24—81no—
608C24—861no—
609C24C2×C22⋊D4311yescharacteristic
610#41—868no—
611#41—1724no—
612#41—1724no—
613#41—1724no—
614C2×Q8—432no—
615C2×Q8—432no—
616C2×Q8—432no—
617C2×Q8—861no—
618C2×Q8—861no—
619C2×Q8—861no—
620C2×D4—28no—
621C2×D4—24no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—44no—
631C2×D4—44no—
632C2×D4—44no—
633C2×D4—42no—
634C2×D4—42no—
635C2×D4—432no—
636C2×D4—864no—
637C2×D4—861no—
638C2×D4—861no—
639C2×D4—861no—
640C2×D4—861no—
641C2×D4—861no—
642C2×D4—1722no—
643C2×D4—1722no—
644C2×D4C2×C4×D4312yes—
645C2×D4C2×C4×D4312yes—
646C2×D4D4×D4312yes—
647C2×D4D4×D4312yes—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—42no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—81no—
659C22×C4—81no—
660C22×C4—861no—
661C22×C4—864no—
662C22×C4—861no—
663C22×C4—861no—
664C22×C4—1722no—
665C22×C4—1722no—
666C22×C4C2×C4×D4312yes—
667C22×C4#1062189812yes—
668C22×C4C2×C22⋊D4311yescharacteristic
669C22×C4C2×C22⋊D4311yescharacteristic
670C22×C4C2×C22⋊D4311yescharacteristic
671C22×C4C2×C22⋊D4311yescharacteristic
672C22×C4C2×C22⋊D4311yescharacteristic
673C22×C4C23×D4311yescharacteristic
674SD16—4316no—
675SD16—868no—
676D8—868no—
677D8—868no—
678M16—868no—
679C2×C8—432no—
680C2×C8—432no—
681C2×C8—432no—
682C2×C8—432no—
683C2×C8—861no—
684C2×C8—861no—
685C2×C8—861no—
686C2×C8—861no—
687C2×C8—861no—
688C2×C8—861no—
689C2×C8—861no—
690C2×C8—861no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—861no—
696C4⋊C4—861no—
697C4⋊C4—861no—
698C4⋊C4—861no—
699C4⋊C4—1722no—
700C4⋊C4—1722no—
701C22⋊C4—22no—
702C22⋊C4—41no—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C22⋊C4—42no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—81no—
709C22⋊C4—81no—
710C22⋊C4—3441no—
711C22⋊C4—3441no—
712C22⋊C4—3441no—
713C22⋊C4—1722no—
714C22⋊C4—1722no—
715C42—21no—
716C42—21no—
717C42—21no—
718C42—21no—
719C42—1722no—
720C42—1722no—
721C23—22no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—22no—
727C23—22no—
728C23—21no—
729C23—21no—
730C23—22no—
731C23—48no—
732C23—48no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—84no—
744C23—84no—
745C23—84no—
746C23—84no—
747C23—84no—
748C23—862no—
749C23—1721no—
750C23—1721no—
751C23—1721no—
752C23—1721no—
753C23—1721no—
754C23—1721no—
755C23C4×C22⋊D4312yes—
756C23C22×C22⋊D4311yescharacteristic
757Q8—434no—
758Q8—862no—
759Q8—862no—
760Q8—862no—
761D4—22no—
762D4—22no—
763D4—22no—
764D4—22no—
765D4—22no—
766D4—48no—
767D4—41no—
768D4—41no—
769D4—862no—
770D4—862no—
771D4—1728no—
772D4—1721no—
773D4—1721no—
774D4C22⋊C4×D4314yes—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—84no—
799C2×C4—84no—
800C2×C4—862no—
801C2×C4—862no—
802C2×C4—862no—
803C2×C4—1728no—
804C2×C4—1721no—
805C2×C4—1721no—
806C2×C4—1721no—
807C2×C4—1721no—
808C2×C4—1721no—
809C2×C4—1721no—
810C2×C4C4×C22⋊D4312yes—
811C2×C4#1306335112yescomplemented
812C2×C4C22×C4×D4311yescharacteristic
813C2×C4C2×D4×D4311yescharacteristic
814C2×C4C2×D4×D4311yescharacteristic
815C2×C4C2×#1062189811yescharacteristic
816C2×C4#1306337011yescharacteristic
817C2×C4#1306337011yescharacteristic
818C8—434no—
819C8—862no—
820C8—1721no—
821C8—1721no—
822C22—22no—
823C22—22no—
824C22—24no—
825C22—22no—
826C22—42no—
827C22—42no—
828C22—41no—
829C22—41no—
830C22—42no—
831C22—42no—
832C22—41no—
833C22—42no—
834C22—41no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—816no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—3441no—
845C22—3441no—
846C22—3441no—
847C22—3441no—
848C22—1722no—
849C22—1722no—
850C22—1722no—
851C22C2×C4×C22⋊D4311yescharacteristic
852C22D4×C22⋊D4311yescharacteristic
853C22D4×C22⋊D4311yescharacteristic
854C22C2×#1306335111yescharacteristic
855C22#1458369711yescharacteristic
856C22#1458370211yescharacteristic
857C22#1458371011yescharacteristic
858C4—22no—
859C4—22no—
860C4—41no—
861C4—41no—
862C4—41no—
863C4—81no—
864C4—81no—
865C4—864no—
866C4—3441no—
867C4—3441no—
868C4C2×C22⋊C4×D4311yescharacteristic
869C4#1458337211yescharacteristic
870C4#1458353911yescharacteristic
871C4#1458353911yescharacteristic
872C2—42no—
873C2—44no—
874C2—82no—
875C2—3442no—
876C2C22⋊C4×C22⋊D4311yescharacteristic
877C2C4×#1306335111yescharacteristic
878C2#1914342711yescharacteristic
879C2#1914608611yescharacteristic
880C2#1914613111yescharacteristic
881C2#1914621111yescharacteristic
882C2#1914622211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingD4×C22⋊C4×C43C2
socleC23×C43C22×D4
prime radicalC22×#13063351C2
cosocleC22×C4×C43C24
hypercenterD4×C22⋊C4D43
hypocenterC43#22443
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#14582999C2semidirect
3. C2×C4×#10621883C2semidirect
4. #19137435C2semidirect
5. #19135470C2semidirect
6. #19135460C2semidirect
7. #19134953C2semidirect
8. #19134953C2semidirect
9. #19134943C2semidirect
10. #19134943C2semidirect
11. #19134626C2semidirect
12. #19134533C2semidirect
13. #19134526C2semidirect
14. #19134379C2semidirect
15. D4×C22⋊C4×C43C2semidirect
19. C2×#13063351C4semidirect
25. C2×C4×Dic86C22semidirect
26. C2×C4×Dic86C22semidirect
29. C2×#13063258C22semidirect
30. C2×#13063256C22semidirect
31. C2×#13063248C22semidirect
32. C2×#13063248C22semidirect
37. C2×#13063245C22semidirect
38. C2×#13063245C22semidirect
40. C2×#13063236C22semidirect
41. C2×C4×C43⋊C8C22semidirect
42. #14582801C22semidirect
43. #14582801C22semidirect
49. #14582661C22semidirect
50. #14582661C22semidirect
51. #14582654C22semidirect
52. #14582654C22semidirect
69. C2×#10621898C2×C4semidirect
78. C2×#10621883C2×C4semidirect
86. C2×#10621882C2×C4semidirect
89. C2×#10621877C2×C4semidirect
251. #10621883C22⋊C4semidirect
350. C2×C4×C43AGL(1,ℤ/8)semidirect
375. Dic86C2×C22⋊C4semidirect
379. C43⋊C8C2×C22⋊C4semidirect
435. D4×C22⋊C4D43semidirect
505. C43#22443semidirect
811. C2×C4#13063351semidirect

Maximal subgroups

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

subgroupindex
C22×#130633512
C2×#145829992
C2×C4×#106218832
#191374352
#191354702
#191354602
#191349532
#191349432
#191346262
#191345332
#191345262
#191343792
D4×C22⋊C4×C432
#2244343