Finite Group Databasebeta

← #25119000

Subgroups — #25119000

Order 11008.

1122 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583094C211yesmaximal, characteristic
2C2×#14583009C211yesmaximal, characteristic, complemented
3C2×C4×#10621882C211yesmaximal, characteristic, complemented
4#19137659C211yesmaximal, characteristic, complemented
5#19135418C211yesmaximal, characteristic, complemented
6#19135361C211yesmaximal, characteristic, complemented
7#19135291C211yesmaximal, characteristic, complemented
8#19135277C211yesmaximal, characteristic, complemented
9#19134943C211yesmaximal, characteristic, complemented
10#19134943C211yesmaximal, characteristic, complemented
11#19134855C211yesmaximal, characteristic, complemented
12#19134841C211yesmaximal, characteristic, complemented
13#19134470C211yesmaximal, characteristic, complemented
14#19134420C211yesmaximal, characteristic, complemented
15C43×#2349C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C2×#13063322C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×#13063287—21no—
22#14583094C418yescomplemented
23#14583009—24no—
24C4×#10621882—24no—
25C2×#13063258C2211yescharacteristic
26C2×#13063256C2211yescharacteristic
27C2×C4⋊(C43⋊C8)C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×#13063245C2211yescharacteristic
36C2×#13063236C2211yescharacteristic
37C2×#13063236C2211yescharacteristic
38C2×C4×C43⋊C8C2211yescharacteristic
39#14582801C2211yescharacteristic
40#14582801C2211yescharacteristic
41#14582800—21no—
42#14582777—21no—
43#14582777—21no—
44C4×C4⋊Dic43C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582654C2211yescharacteristic
51C2×C4×D4×C43C2211yescharacteristic
52C2×C4×D4×C43C2211yescharacteristic
53C2×C4×D4×C43C2211yescharacteristic
54C43×#389C2211yescharacteristic
55C43×#389C2211yescharacteristic
56C43×#385—21no—
57C43×#385—21no—
58C43×#382C2211yescharacteristic
59C43×#380—21no—
60C4×C4⋊C4×C43C2211yescharacteristic
61C2×#95×C43—21no—
62C22×D172—21no—
63C22×D172—21no—
64C22×D172C2311yescharacteristic
65C22×D172C2311yescharacteristic
66C22×C4×D43—21no—
67C22×C4×D43—21no—
68C2×#10621882—22no—
69C2×#10621882—22no—
70C2×#10621882—22no—
71C2×#10621882—22no—
72C2×#10621882C2×C414yescomplemented
73C2×#10621882C2×C414yescomplemented
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78#13063322—22no—
79#13063322C2×C414yescomplemented
80C4×D172—22no—
81C4×D172—22no—
82C4×D172—41no—
83C4×D172—41no—
84#13063287—44no—
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×C4×Dic43—21no—
94#13063258—22no—
95#13063256—22no—
96C4⋊(C43⋊C8)C2×C414yescomplemented
97#13063246—22no—
98#13063246D414yescomplemented
99#13063245—22no—
100#13063245—22no—
101#13063245—41no—
102#13063245—41no—
103#13063245C2×C414yescomplemented
104#13063245C2×C414yescomplemented
105#13063236—22no—
106#13063236—22no—
107C4×C43⋊C8—22no—
108C43⋊#95—21no—
109C22×D4×C43C2311yescharacteristic
110C23×C4×C43—21no—
111C23×C4×C43—21no—
112C23×C4×C43—21no—
113C4×D4×C43—22no—
114C4×D4×C43—22no—
115C4×D4×C43—22no—
116C4×D4×C43—41no—
117C4×D4×C43—41no—
118C4×D4×C43C2×C414yescomplemented
119C2×C4⋊C4×C43—21no—
120C2×C4⋊C4×C43—21no—
121C2×C4⋊C4×C43D411yescharacteristic
122C2×C4⋊C4×C43D411yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C42×C43C2311yescharacteristic
130C2×C42×C43C2311yescharacteristic
131C2×C42×C43C2311yescharacteristic
132#95×C43—21no—
133#95×C43—21no—
134#95×C43—21no—
135#95×C43—21no—
136#95×C43D411yescharacteristic
137#95×C43D411yescharacteristic
138C24×C43—21no—
139C23×D43—21no—
140C23×D43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43C22×C412yes—
145C2×D4×C43C2×D412yes—
146C2×D4×C43#4112yes—
147C22×C4×C43—24no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—42no—
152C22×C4×C43—42no—
153C22×C4×C43—42no—
154C22×C4×C43—42no—
155C22×C4×C43—81no—
156C22×C4×C43—81no—
157C22×C4×C43—81no—
158C22×C4×C43—81no—
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43C2411yescharacteristic
166C22×Dic43—21no—
167C22×Dic43—21no—
168C2×D172—24no—
169C2×D172—21no—
170C2×D172—21no—
171C2×D172—24no—
172C2×D172—21no—
173C2×D172—21no—
174C2×D172—21no—
175C2×D172—21no—
176C2×D172—21no—
177C2×D172—21no—
178C2×D172—21no—
179C2×D172—21no—
180C2×D172—42no—
181C2×D172—42no—
182C2×D172—81no—
183C2×D172—81no—
184C2×D172C22×C412yes—
185C2×D172C22×C412yes—
186C2×C4×D43—42no—
187C2×C4×D43—42no—
188C2×C4×D43—42no—
189C2×C4×D43—42no—
190C2×C4×D43—81no—
191C2×C4×D43—81no—
192C4⋊C4×C43—22no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—41no—
199C4⋊C4×C43—81no—
200C4⋊C4×C43—81no—
201C4⋊C4×C43C22×C412yes—
202C22⋊C4×C43—24no—
203C22⋊C4×C43—42no—
204C22⋊C4×C43—42no—
205C42×C43—21no—
206C42×C43—21no—
207C42×C43—21no—
208C42×C43—21no—
209C42×C43C22×C412yes—
210C42×C43#4112yes—
211#10621882—28no—
212#10621882—28no—
213(C2×D43)⋊C4—42no—
214(C2×D43)⋊C4—42no—
215(C2×D43)⋊C4—42no—
216(C2×D43)⋊C4—42no—
217(C2×D43)⋊C4—81no—
218(C2×D43)⋊C4—81no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43C2×D412yes—
223C4×Dic43—42no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8C22×C412yes—
234C2×C43⋊C8C22×C412yes—
235C2×C43⋊C8C2×D412yes—
236C23×C43—22no—
237C23×C43—22no—
238C23×C43—22no—
239C23×C43—41no—
240C23×C43—41no—
241C23×C43—41no—
242C23×C43—41no—
243C23×C43C22×D411yescharacteristic
244C22×D43—22no—
245C22×D43—22no—
246C22×D43—41no—
247C22×D43—41no—
248C22×D43—41no—
249C22×D43—41no—
250C22×D43—41no—
251C22×D43—41no—
252C22×D43—41no—
253C22×D43—41no—
254C22×D43—41no—
255C22×D43—41no—
256C22×D43—41no—
257C22×D43—41no—
258D4×C43—22no—
259D4×C43—22no—
260D4×C43—22no—
261D4×C43C4×D414yescomplemented
262C2×C4×C43—21no—
263C2×C4×C43—21no—
264C2×C4×C43—21no—
265C2×C4×C43—21no—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—22no—
269C2×C4×C43—21no—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
275C2×C4×C43—21no—
276C2×C4×C43—21no—
277C2×C4×C43—21no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—84no—
287C2×C4×C43—84no—
288C2×C4×C43—84no—
289C2×C4×C43C4×D412yes—
290C2×C4×C43C4×D412yes—
291C2×C4×C43AGL(1,ℤ/8)12yes—
292C2×C4×C43C23×C411yescharacteristic
293C2×C4×C43C22×D411yescharacteristic
294C2×C4×C43C2×#4111yescharacteristic
295C2×C4×C43C2×#4111yescharacteristic
296C2×C4×C43H(5,𝔽2)11yescharacteristic
297C2×C4×C432−1+411yescharacteristic
298C2×Dic43—22no—
299C2×Dic43—41no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304D172—22no—
305D172—22no—
306D172—22no—
307D172—22no—
308D172—48no—
309D172—41no—
310D172—41no—
311D172—41no—
312D172—41no—
313D172—84no—
314C4×D43—84no—
315C4×D43—84no—
316C43⋊C8—22no—
317C43⋊C8—22no—
318C43⋊C8—22no—
319C43⋊C8—41no—
320#23008—431nomaximal, Sylow
321C22×C43—24no—
322C22×C43—42no—
323C22×C43—42no—
324C22×C43—42no—
325C22×C43—42no—
326C22×C43—42no—
327C22×C43—42no—
328C22×C43C2×C4×D411yescharacteristic
329C22×C43D4211yescharacteristic
330C22×C43#54811yescharacteristic
331C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
332C22×C43#57511yescharacteristic
333C22×C43#57611yescharacteristic
334C22×C43#57611yescharacteristic
335C2×D43—42no—
336C2×D43—42no—
337C2×D43—42no—
338C2×D43—42no—
339C2×D43—42no—
340C2×D43—42no—
341C2×D43—81no—
342C2×D43—81no—
343C2×D43—81no—
344C2×D43—81no—
345C2×D43—81no—
346C2×D43—81no—
347C2×D43—81no—
348C2×D43—81no—
349C4×C43—22no—
350C4×C43—22no—
351C4×C43—22no—
352C4×C43—42no—
353C4×C43—41no—
354C4×C43—41no—
355C4×C43—41no—
356C4×C43—81no—
357C4×C43—81no—
358C4×C43C2×C4×D411yescharacteristic
359C4×C43#52011yescharacteristic
360C4×C43#54711yescharacteristic
361C4×C43#55311yescharacteristic
362Dic43—42no—
363Dic43—81no—
364C2×#459—431no—
365C2×#442—431no—
366C2×C4×D8—431no—
367#2366—431no—
368#2349D4311yescharacteristic, complemented
369#1961—431no—
370#1949—431no—
371#1936—431no—
372#1934—431no—
373#1879—431no—
374#1879—431no—
375#1864—431no—
376#1862—431no—
377#1771—431no—
378#1762—431no—
379C2×C43—44no—
380C2×C43#236111yescharacteristic
381C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
382C2×C43#294811yescharacteristic
383C2×C43#326411yescharacteristic
384C2×C43#326811yescharacteristic
385C2×C43#336611yescharacteristic
386C2×C43#337011yescharacteristic
387D43—82no—
388D43—82no—
389C22×D8—431no—
390C22×D8—431no—
391C2×#127—431no—
392C2×C4×D4—431no—
393C2×C4×D4—431no—
394C2×C4×D4—861no—
395C2×C4×D4C2×D4311yescharacteristic
396C2×C4×D4C2×D4311yescharacteristic
397C2×C4×D4C2×D4311yescharacteristic
398#459—438no—
399#442—864no—
400C4×D8—864no—
401C2×#107—431no—
402C2×#106—431no—
403C2×C4⋊C8—431no—
404C2×#102—431no—
405C2×#102—431no—
406C2×#102—431no—
407C2×#102—431no—
408C2×#102—431no—
409C2×#102—431no—
410C2×#102—431no—
411C2×#102—431no—
412C2×#97—431no—
413C2×#97—431no—
414C2×C4×C8—431no—
415#390—431no—
416#390—431no—
417#390—861no—
418#389C2×D4311yescharacteristic
419#389C2×D4311yescharacteristic
420#386—861no—
421#386—861no—
422#385—21no—
423#385—21no—
424#382C2×D4311yescharacteristic
425#380—21no—
426C4×C4⋊C4—431no—
427C4×C4⋊C4C2×D4311yescharacteristic
428C2×#95—21no—
429#340—431no—
430#340—431no—
431#340—431no—
432#340—431no—
433#336—431no—
434#336—431no—
435C43#2300811yescharacteristic, complemented, Sylow
436C22×D4—431no—
437C22×D4—431no—
438C22×D4—861no—
439C22×D4—861no—
440C22×D4C22×D4311yescharacteristic
441C23×C4—21no—
442C23×C4—21no—
443C23×C4—21no—
444C23×C4—861no—
445C23×C4—861no—
446C2×D8—434no—
447C2×D8—434no—
448C2×D8—862no—
449C2×D8—862no—
450C2×D8—862no—
451C2×D8—862no—
452C22×C8—431no—
453C22×C8—431no—
454C22×C8—431no—
455C22×C8—431no—
456#127—434no—
457#127—862no—
458C4×D4—22no—
459C4×D4—22no—
460C4×D4—22no—
461C4×D4—41no—
462C4×D4—41no—
463C4×D4—862no—
464C4×D4—862no—
465C4×D4—1721no—
466C4×D4—1721no—
467C4×D4—1724no—
468C4×D4C4×D4314yescomplemented
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—431no—
472C2×C4⋊C4—431no—
473C2×C4⋊C4C22⋊D4311yescharacteristic
474C2×C4⋊C4C22⋊D4311yescharacteristic
475C2×C4⋊C4C22×D4311yescharacteristic
476C2×C4⋊C4C22×D4311yescharacteristic
477C2×C4⋊C4C22×D4311yescharacteristic
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—861no—
482C2×C22⋊C4—861no—
483C2×C22⋊C4—861no—
484C2×C22⋊C4—861no—
485C2×C22⋊C4—861no—
486C2×C22⋊C4—861no—
487C2×C42—861no—
488C2×C42C22×D4311yescharacteristic
489C2×C42C22×D4311yescharacteristic
490C2×C42C22×D4311yescharacteristic
491#107—862no—
492#106—862no—
493C4⋊C8—434no—
494#102—434no—
495#102—434no—
496#102—434no—
497#102—862no—
498#102—862no—
499#102—862no—
500#102—1721no—
501#102—1721no—
502#97—862no—
503#97—862no—
504C4×C8—862no—
505#95—21no—
506#95—21no—
507#95—21no—
508#95—21no—
509#95—861no—
510#95C22⋊D4311yescharacteristic
511#95C22⋊D4311yescharacteristic
512C24—21no—
513C24—861no—
514C24—861no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—432no—
519C2×D4—432no—
520C2×D4—864no—
521C2×D4—864no—
522C2×D4—861no—
523C2×D4—861no—
524C2×D4—861no—
525C2×D4—861no—
526C2×D4—861no—
527C2×D4—861no—
528C2×D4—861no—
529C2×D4—861no—
530C2×D4—861no—
531C2×D4—861no—
532C2×D4—3441no—
533C2×D4—3441no—
534C2×D4—1722no—
535C2×D4—1722no—
536C2×D4C2×C4×D4312yes—
537C2×D4D4×D4312yes—
538C2×D4#1062190212yes—
539C22×C4—21no—
540C22×C4—24no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—81no—
548C22×C4—81no—
549C22×C4—81no—
550C22×C4—81no—
551C22×C4—861no—
552C22×C4—861no—
553C22×C4—3441no—
554C22×C4—3441no—
555C22×C4—1722no—
556C22×C4—1722no—
557C22×C4—1722no—
558C22×C4—1722no—
559C22×C4C2×C22⋊D4311yescharacteristic
560C22×C4C2×C22⋊D4311yescharacteristic
561C22×C4C2×C22⋊D4311yescharacteristic
562C22×C4C2×C22⋊D4311yescharacteristic
563C22×C4C2×C22⋊D4311yescharacteristic
564C22×C4C2×C22⋊D4311yescharacteristic
565C22×C4C23×D4311yescharacteristic
566D8—868no—
567D8—868no—
568C2×C8—432no—
569C2×C8—432no—
570C2×C8—432no—
571C2×C8—861no—
572C2×C8—861no—
573C2×C8—861no—
574C2×C8—861no—
575C2×C8—861no—
576C2×C8—861no—
577C2×C8—861no—
578C2×C8—861no—
579C2×C8—861no—
580C4⋊C4—22no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—41no—
587C4⋊C4—81no—
588C4⋊C4—81no—
589C4⋊C4—432no—
590C4⋊C4—861no—
591C4⋊C4—861no—
592C4⋊C4—861no—
593C4⋊C4C2×C4×D4312yes—
594C22⋊C4—24no—
595C22⋊C4—42no—
596C22⋊C4—42no—
597C22⋊C4—3441no—
598C22⋊C4—3441no—
599C22⋊C4—1722no—
600C22⋊C4—1722no—
601C22⋊C4—1722no—
602C22⋊C4—1722no—
603C42—21no—
604C42—21no—
605C42—21no—
606C42—21no—
607C42—1722no—
608C42C2×C4×D4312yes—
609C42#1062189812yes—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—862no—
618C23—862no—
619C23—1721no—
620C23—1721no—
621C23—1721no—
622C23—1721no—
623C23—1721no—
624C23—1721no—
625C23—1721no—
626C23—1721no—
627C23—1721no—
628C23—1721no—
629C23—1721no—
630C23—1721no—
631C23C22×C22⋊D4311yescharacteristic
632D4—22no—
633D4—22no—
634D4—22no—
635D4—862no—
636D4—862no—
637D4—862no—
638D4—862no—
639D4—3444no—
640D4—1728no—
641D4—1721no—
642D4—1721no—
643D4—1721no—
644D4—1721no—
645D4#1306328714yescomplemented
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—84no—
671C2×C4—84no—
672C2×C4—84no—
673C2×C4—862no—
674C2×C4—3444no—
675C2×C4—3444no—
676C2×C4—1721no—
677C2×C4—1721no—
678C2×C4—1721no—
679C2×C4—1721no—
680C2×C4—1721no—
681C2×C4C4×C22⋊D4312yes—
682C2×C4C4×C22⋊D4312yes—
683C2×C4#1306335012yes—
684C2×C4C22×C4×D4311yescharacteristic
685C2×C4C2×D4×D4311yescharacteristic
686C2×C4C2×#1062189811yescharacteristic
687C2×C4C2×#1062190211yescharacteristic
688C2×C4#1306337011yescharacteristic
689C2×C4#1306337311yescharacteristic
690C8—862no—
691C8—862no—
692C8—862no—
693C8—1721no—
694C22—24no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—3441no—
702C22—3441no—
703C22—3441no—
704C22—3441no—
705C22—3441no—
706C22—3441no—
707C22—3441no—
708C22—3441no—
709C22—1722no—
710C22—1722no—
711C22—1722no—
712C22—1722no—
713C22—1722no—
714C22—1722no—
715C22C2×C4×C22⋊D4311yescharacteristic
716C22D4×C22⋊D4311yescharacteristic
717C22#1458356011yescharacteristic
718C22C2×#1306335011yescharacteristic
719C22#1458369711yescharacteristic
720C22#1458370211yescharacteristic
721C22#1458370211yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—42no—
726C4—41no—
727C4—41no—
728C4—41no—
729C4—81no—
730C4—81no—
731C4—3441no—
732C4—1722no—
733C4C2×#1306328711yescharacteristic
734C4#1458338011yescharacteristic
735C4#1458355011yescharacteristic
736C4#1458359711yescharacteristic
737C2—44no—
738C2—3442no—
739C2—3442no—
740C2#1913761111yescharacteristic
741C2C4×#1306335011yescharacteristic
742C2#1914344511yescharacteristic
743C2#1914607611yescharacteristic
744C2#1914613111yescharacteristic
745C2#1914730211yescharacteristic
746C2#1914734811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2349C2
socleC23×C43C22×D4
prime radicalC2×#14583094C2
cosocleC22×C4×C43C24
hypercenter#2349D43
hypocenterC43#23008
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2349

Complements

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

NH ≅ G/Ntype
2. C2×#14583009C2semidirect
3. C2×C4×#10621882C2semidirect
4. #19137659C2semidirect
5. #19135418C2semidirect
6. #19135361C2semidirect
7. #19135291C2semidirect
8. #19135277C2semidirect
9. #19134943C2semidirect
10. #19134943C2semidirect
11. #19134855C2semidirect
12. #19134841C2semidirect
13. #19134470C2semidirect
14. #19134420C2semidirect
15. C43×#2349C2semidirect
22. #14583094C4semidirect
72. C2×#10621882C2×C4semidirect
73. C2×#10621882C2×C4semidirect
79. #13063322C2×C4semidirect
96. C4⋊(C43⋊C8)C2×C4semidirect
98. #13063246D4semidirect
103. #13063245C2×C4semidirect
104. #13063245C2×C4semidirect
118. C4×D4×C43C2×C4semidirect
261. D4×C43C4×D4semidirect
368. #2349D43semidirect
435. C43#23008semidirect
468. C4×D4C4×D43semidirect
645. D4#13063287semidirect

Maximal subgroups

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

subgroupindex
C2×#145830942
C2×#145830092
C2×C4×#106218822
#191376592
#191354182
#191353612
#191352912
#191352772
#191349432
#191348552
#191348412
#191344702
#191344202
C43×#23492
#2300843