Finite Group Databasebeta

← #25140337

Subgroups — #25140337

Order 11008.

1232 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583033C211yesmaximal, characteristic
2C2×C4×#10621882C211yesmaximal, characteristic, complemented
3#19138109C211yesmaximal, characteristic, complemented
4#19136123C211yesmaximal, characteristic, complemented
5#19136021C211yesmaximal, characteristic, complemented
6#19135905C211yesmaximal, characteristic, complemented
7#19135777C211yesmaximal, characteristic, complemented
8#19135281C211yesmaximal, characteristic, complemented
9#19135203C211yesmaximal, characteristic, complemented
10#19134946C211yesmaximal, characteristic, complemented
11#19134943C211yesmaximal, characteristic, complemented
12#19134842C211yesmaximal, characteristic, complemented
13#19134595C211yesmaximal, characteristic, complemented
14#19134526C211yesmaximal, characteristic, complemented
15D4×C22⋊C4×C43C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C2×#13063307—21no—
19C2×#13063299C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic, complemented
21#14583033—24no—
22C4×#10621882—24no—
23C2×#13063258C2211yescharacteristic, complemented
24C2×#13063258C2211yescharacteristic, complemented
25C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063245C2211yescharacteristic, complemented
33C2×#13063245C2211yescharacteristic, complemented
34C2×C22⋊(C43⋊C8)C2211yescharacteristic
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36C2×C4×C43⋊C8C2211yescharacteristic, complemented
37#14582826—21no—
38#14582815—21no—
39#14582801C2211yescharacteristic, complemented
40#14582797C2211yescharacteristic, complemented
41#14582773—21no—
42#14582769C2211yescharacteristic, complemented
43#14582759C2211yescharacteristic
44#14582661C2211yescharacteristic, complemented
45#14582661C2211yescharacteristic, complemented
46#14582661C2211yescharacteristic, complemented
47#14582661C2211yescharacteristic, complemented
48#14582654C2211yescharacteristic, complemented
49#14582654C2211yescharacteristic, complemented
50C23×D4×C43C2211yescharacteristic
51C2×C4×D4×C43C2211yescharacteristic
52C2×C4×D4×C43C2211yescharacteristic
53C22×C22⋊C4×C43—21no—
54C43×#390C2211yescharacteristic
55C43×#390C2211yescharacteristic
56C43×#386—21no—
57C43×#386—21no—
58C43×#380C2211yescharacteristic
59C43×#379—21no—
60C4×C22⋊C4×C43C2211yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C22⋊D43—21no—
63C22×C4×D43—21no—
64C2×#10621882—22no—
65C2×#10621882—22no—
66C2×#10621882—22no—
67C2×#10621882—22no—
68C2×#10621882—41no—
69C2×#10621882D414yes—
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74#13063307—44no—
75#13063299—22no—
76#13063299—41no—
77C4×D172—22no—
78C4×D172—41no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×Dic43⋊C4—21no—
85C2×C22⋊Dic43—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90#13063258—22no—
91#13063258—41no—
92C4⋊(C43⋊C8)—41no—
93#13063246—22no—
94#13063246—22no—
95#13063246—22no—
96#13063246—22no—
97#13063246—22no—
98#13063246—41no—
99#13063245—22no—
100#13063245—41no—
101C22⋊(C43⋊C8)—22no—
102C22⋊(C43⋊C8)—41no—
103C4×C43⋊C8—22no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C25×C43—21no—
107C22×D4×C43—22no—
108C22×D4×C43—22no—
109C22×D4×C43—22no—
110C22×D4×C43—22no—
111C22×D4×C43—21no—
112C22×D4×C43—41no—
113C22×D4×C43—41no—
114C22×D4×C43C2311yescharacteristic
115C22×D4×C43C2311yescharacteristic
116C23×C4×C43—21no—
117C23×C4×C43—21no—
118C23×C4×C43C2311yescharacteristic
119C4×D4×C43—22no—
120C4×D4×C43—22no—
121C4×D4×C43—41no—
122C4×D4×C43—41no—
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43—21no—
132C2×C22⋊C4×C43—44no—
133C2×C22⋊C4×C43D411yescharacteristic
134C2×C22⋊C4×C43D411yescharacteristic
135C2×C42×C43C2311yescharacteristic
136C2×C42×C43C2311yescharacteristic
137#95×C43—21no—
138#95×C43D411yescharacteristic
139#95×C43D411yescharacteristic
140C24×C43—21no—
141C24×C43—24no—
142C24×C43—21no—
143C24×C43—42no—
144C24×C43—42no—
145C24×C43—42no—
146C24×C43—42no—
147C24×C43—81no—
148C24×C43—81no—
149C24×C43C2×D411yescharacteristic
150C23×D43—21no—
151C2×D4×C43—24no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—42no—
161C2×D4×C43—42no—
162C2×D4×C43—44no—
163C2×D4×C43—44no—
164C2×D4×C43—44no—
165C2×D4×C43—44no—
166C2×D4×C43C2×D412yes—
167C2×D4×C43#4112yes—
168C2×D4×C43#4112yes—
169C2×D4×C43#4112yes—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—42no—
179C22×C4×C43—42no—
180C22×C4×C43—42no—
181C22×C4×C43—42no—
182C22×C4×C43—81no—
183C22×C4×C43—81no—
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2411yescharacteristic
190C2×C22⋊D43—42no—
191C2×C22⋊D43—42no—
192C2×C22⋊D43—81no—
193C22×Dic43—21no—
194C22×Dic43—21no—
195C22×Dic43—21no—
196C2×D172—21no—
197C2×D172—21no—
198C2×D172—21no—
199C2×D172—21no—
200C2×D172—21no—
201C2×D172C2×D412yes—
202C2×C4×D43—42no—
203C2×C4×D43—42no—
204C2×C4×D43—81no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—21no—
209C22⋊C4×C43—41no—
210C22⋊C4×C43—42no—
211C22⋊C4×C43—42no—
212C22⋊C4×C43—42no—
213C22⋊C4×C43—42no—
214C22⋊C4×C43—42no—
215C22⋊C4×C43—81no—
216C22⋊C4×C43—81no—
217C22⋊C4×C43D814yescomplemented
218C42×C43—21no—
219C42×C43—21no—
220C42×C43—21no—
221C42×C43—21no—
222C22⋊Dic43—42no—
223#10621882—28no—
224#10621882—44no—
225(C2×D43)⋊C4—42no—
226(C2×D43)⋊C4—42no—
227(C2×D43)⋊C4—42no—
228(C2×D43)⋊C4—42no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43—21no—
234C4⋊Dic43—21no—
235C4⋊Dic43—42no—
236C4⋊Dic43—81no—
237Dic43⋊C4—42no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8C2×D412yes—
250C23×C43—21no—
251C23×C43—22no—
252C23×C43—22no—
253C23×C43—21no—
254C23×C43—22no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—22no—
260C23×C43—48no—
261C23×C43—48no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43—84no—
273C23×C43—84no—
274C23×C43—84no—
275C23×C43—84no—
276C23×C43—84no—
277C23×C43C2×D812yes—
278C23×C43C22×D411yescharacteristic
279C22×D43—22no—
280C22×D43—41no—
281C22×D43—41no—
282C22×D43—41no—
283C22×D43—41no—
284C22×D43—41no—
285C22×D43—41no—
286D4×C43—22no—
287D4×C43—22no—
288D4×C43—22no—
289D4×C43—22no—
290D4×C43—22no—
291D4×C43—48no—
292D4×C43—41no—
293D4×C43—41no—
294D4×C43#12314yescomplemented
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43—41no—
318C2×C4×C43—84no—
319C2×C4×C43—84no—
320C2×C4×C43C2×D812yes—
321C2×C4×C43C2×D812yes—
322C2×C4×C43C22×D411yescharacteristic
323C2×C4×C43C2×#4111yescharacteristic
324C2×C4×C43C2×#4111yescharacteristic
325C2×C4×C43C2×#4111yescharacteristic
326C2×C4×C43H(5,𝔽2)11yescharacteristic
327C2×C4×C43H(5,𝔽2)11yescharacteristic
328C22⋊D43—84no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331C2×Dic43—41no—
332C2×Dic43—41no—
333C2×Dic43—41no—
334C2×Dic43—41no—
335C2×Dic43—41no—
336C2×Dic43—41no—
337C2×Dic43—41no—
338D172—22no—
339D172—22no—
340D172—41no—
341D172—41no—
342C4×D43—84no—
343C43⋊C8—22no—
344C43⋊C8—41no—
345C43⋊C8—41no—
346C43⋊C8—41no—
347#24893—431nomaximal, Sylow
348C22×C43—22no—
349C22×C43—24no—
350C22×C43—22no—
351C22×C43—22no—
352C22×C43—42no—
353C22×C43—41no—
354C22×C43—42no—
355C22×C43—41no—
356C22×C43—41no—
357C22×C43—42no—
358C22×C43—42no—
359C22×C43—42no—
360C22×C43—41no—
361C22×C43—42no—
362C22×C43—42no—
363C22×C43—42no—
364C22×C43—42no—
365C22×C43—816no—
366C22×C43—81no—
367C22×C43—81no—
368C22×C43—81no—
369C22×C43—81no—
370C22×C43#52511yescharacteristic
371C22×C43D4211yescharacteristic
372C22×C43#54611yescharacteristic
373C22×C43C22×D811yescharacteristic
374C22×C43#57511yescharacteristic
375C22×C43#57611yescharacteristic
376C22×C43#57711yescharacteristic
377C2×D43—42no—
378C2×D43—42no—
379C2×D43—42no—
380C2×D43—81no—
381C2×D43—81no—
382C2×D43—81no—
383C2×D43—81no—
384C4×C43—22no—
385C4×C43—22no—
386C4×C43—41no—
387C4×C43—41no—
388C4×C43—41no—
389C4×C43—81no—
390C4×C43—81no—
391C4×C43C2×#12311yescharacteristic
392C4×C43#53811yescharacteristic
393C4×C43#54611yescharacteristic
394C4×C43#55111yescharacteristic
395Dic43—81no—
396Dic43—81no—
397Dic43—81no—
398C2×#447—431no—
399C2×C4×D8—431no—
400#2422—431no—
401D4×C22⋊C4D4311yescharacteristic, complemented
402#2093—431no—
403#2075—431no—
404#2054—431no—
405#2033—431no—
406#1934—431no—
407#1923—431no—
408#1879—431no—
409#1879—431no—
410#1862—431no—
411#1802—431no—
412#1786—431no—
413C2×C43—42no—
414C2×C43—44no—
415C2×C43—82no—
416C2×C43#241811yescharacteristic
417C2×C43#310011yescharacteristic
418C2×C43#311811yescharacteristic
419C2×C43#326711yescharacteristic
420C2×C43D4×D811yescharacteristic
421C2×C43#329411yescharacteristic
422C2×C43#332211yescharacteristic
423D43—82no—
424C23×D4C2×D4311yescharacteristic
425C22×D8—431no—
426C22×D8—431no—
427C2×#123—861no—
428C2×#121—431no—
429C2×C4×D4—431no—
430C2×C4×D4C2×D4311yescharacteristic
431C2×C4×D4C2×D4311yescharacteristic
432C22×C22⋊C4—21no—
433#447—864no—
434C4×D8—864no—
435C2×#107—431no—
436C2×#107—431no—
437C2×C4⋊C8—431no—
438C2×#102—431no—
439C2×#102—431no—
440C2×#102—431no—
441C2×#102—431no—
442C2×#102—431no—
443C2×#102—431no—
444C2×#102—431no—
445C2×#102—431no—
446C2×C22⋊C8—431no—
447C2×C22⋊C8—431no—
448C2×C4×C8—431no—
449#397—861no—
450#394—861no—
451#390—431no—
452#390C2×D4311yescharacteristic
453#390C2×D4311yescharacteristic
454#389—431no—
455#386—21no—
456#386—21no—
457#385—861no—
458#384—431no—
459#380—431no—
460#380C2×D4311yescharacteristic
461#379—21no—
462C4×C22⋊C4C2×D4311yescharacteristic
463#340—431no—
464#340—431no—
465#340—431no—
466#340—431no—
467#336—431no—
468#336—431no—
469C43#2489311yescharacteristic, complemented, Sylow
470C25—21no—
471C22×D4—22no—
472C22×D4—22no—
473C22×D4—22no—
474C22×D4—22no—
475C22×D4—21no—
476C22×D4—41no—
477C22×D4—41no—
478C22×D4—431no—
479C22×D4—861no—
480C22×D4C22×D4311yescharacteristic
481C22×D4C22×D4311yescharacteristic
482C23×C4—21no—
483C23×C4—21no—
484C23×C4—861no—
485C23×C4C22×D4311yescharacteristic
486C2×D8—434no—
487C2×D8—862no—
488C2×D8—862no—
489C2×D8—862no—
490C2×D8—862no—
491C2×D8—1721no—
492C22×C8—431no—
493C22×C8—431no—
494C22×C8—431no—
495C22×C8—431no—
496#123—1724no—
497#121—862no—
498#121—1721no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—41no—
502C4×D4—41no—
503C4×D4—862no—
504C4×D4—1721no—
505C2×C4⋊C4—431no—
506C2×C4⋊C4—431no—
507C2×C4⋊C4—431no—
508C2×C4⋊C4—861no—
509C2×C4⋊C4—861no—
510C2×C4⋊C4—861no—
511C2×C4⋊C4C22×D4311yescharacteristic
512C2×C4⋊C4C22×D4311yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—44no—
521C2×C22⋊C4—861no—
522C2×C22⋊C4—861no—
523C2×C22⋊C4—861no—
524C2×C22⋊C4—861no—
525C2×C22⋊C4—861no—
526C2×C22⋊C4C22⋊D4311yescharacteristic
527C2×C22⋊C4C22⋊D4311yescharacteristic
528C2×C42C22×D4311yescharacteristic
529C2×C42C22×D4311yescharacteristic
530#107—862no—
531#107—1721no—
532C4⋊C8—1721no—
533#102—862no—
534#102—862no—
535#102—862no—
536#102—862no—
537#102—862no—
538#102—862no—
539#102—1721no—
540#102—1721no—
541C22⋊C8—862no—
542C22⋊C8—1721no—
543C4×C8—862no—
544#95—21no—
545#95—861no—
546#95—861no—
547#95C22⋊D4311yescharacteristic
548#95C22⋊D4311yescharacteristic
549C24—21no—
550C24—24no—
551C24—21no—
552C24—42no—
553C24—42no—
554C24—42no—
555C24—42no—
556C24—81no—
557C24—81no—
558C24—861no—
559C24C2×C22⋊D4311yescharacteristic
560C2×D4—24no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—44no—
572C2×D4—44no—
573C2×D4—44no—
574C2×D4—44no—
575C2×D4—432no—
576C2×D4—861no—
577C2×D4—861no—
578C2×D4—861no—
579C2×D4—861no—
580C2×D4—861no—
581C2×D4—3441no—
582C2×D4—1722no—
583C2×D4—1722no—
584C2×D4#1062189812yes—
585C2×D4#1062189812yes—
586C2×D4D4×D4312yes—
587C2×D4#1062190012yes—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—81no—
601C22×C4—81no—
602C22×C4—861no—
603C22×C4—861no—
604C22×C4—861no—
605C22×C4—3441no—
606C22×C4—1722no—
607C22×C4—1722no—
608C22×C4C2×C22⋊D4311yescharacteristic
609C22×C4C2×C22⋊D4311yescharacteristic
610C22×C4C2×C22⋊D4311yescharacteristic
611C22×C4C2×C22⋊D4311yescharacteristic
612C22×C4C2×C22⋊D4311yescharacteristic
613C22×C4C23×D4311yescharacteristic
614D8—868no—
615D8—1724no—
616C2×C8—432no—
617C2×C8—861no—
618C2×C8—861no—
619C2×C8—861no—
620C2×C8—861no—
621C2×C8—861no—
622C2×C8—861no—
623C2×C8—861no—
624C2×C8—861no—
625C2×C8—861no—
626C2×C8—861no—
627C2×C8—861no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—861no—
633C4⋊C4—861no—
634C4⋊C4—861no—
635C4⋊C4—861no—
636C4⋊C4—861no—
637C4⋊C4—861no—
638C4⋊C4—3441no—
639C4⋊C4—1722no—
640C4⋊C4—1722no—
641C22⋊C4—41no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—42no—
647C22⋊C4—81no—
648C22⋊C4—81no—
649C22⋊C4—1722no—
650C22⋊C4—1722no—
651C22⋊C4—1722no—
652C22⋊C4—1722no—
653C22⋊C4—1722no—
654C22⋊C4#1062188214yescomplemented
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C23—21no—
660C23—22no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—22no—
665C23—21no—
666C23—22no—
667C23—21no—
668C23—22no—
669C23—48no—
670C23—48no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—84no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23—862no—
687C23—1721no—
688C23—1721no—
689C23—1721no—
690C23—1721no—
691C23—1721no—
692C23—1721no—
693C23C2×#1062188212yes—
694C23C22×C22⋊D4311yescharacteristic
695D4—22no—
696D4—22no—
697D4—22no—
698D4—22no—
699D4—22no—
700D4—48no—
701D4—41no—
702D4—41no—
703D4—862no—
704D4—862no—
705D4—3444no—
706D4—1721no—
707D4—1721no—
708D4#1306330714yescomplemented
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—84no—
733C2×C4—84no—
734C2×C4—3444no—
735C2×C4—1721no—
736C2×C4—1721no—
737C2×C4—1721no—
738C2×C4—1721no—
739C2×C4—1721no—
740C2×C4—1721no—
741C2×C4—1721no—
742C2×C4—1721no—
743C2×C4—1721no—
744C2×C4C2×#1062188212yes—
745C2×C4C2×#1062188212yes—
746C2×C4C2×D4×D4311yescharacteristic
747C2×C4C2×#1062190011yescharacteristic
748C2×C4C2×#1062189811yescharacteristic
749C2×C4C2×#1062189811yescharacteristic
750C2×C4#1306337011yescharacteristic
751C2×C4#1306337011yescharacteristic
752C8—862no—
753C8—1721no—
754C8—1721no—
755C8—1721no—
756C22—24no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—42no—
764C22—41no—
765C22—42no—
766C22—41no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—816no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—3441no—
779C22—3441no—
780C22—3441no—
781C22—3441no—
782C22—1722no—
783C22—1722no—
784C22—1722no—
785C22#1458341011yescharacteristic
786C22D4×C22⋊D4311yescharacteristic
787C22#1458354311yescharacteristic
788C22C22×#1062188211yescharacteristic
789C22#1458369711yescharacteristic
790C22#1458370211yescharacteristic
791C22#1458371011yescharacteristic
792C4—22no—
793C4—22no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—81no—
798C4—81no—
799C4—3441no—
800C4—3441no—
801C4—3441no—
802C4C2×#1306330711yescharacteristic
803C4#1458348711yescharacteristic
804C4#1458353911yescharacteristic
805C4#1458357511yescharacteristic
806C2—42no—
807C2—44no—
808C2—82no—
809C2—3442no—
810C2#1913805711yescharacteristic
811C2#1914459511yescharacteristic
812C2#1914477911yescharacteristic
813C2#1914611611yescharacteristic
814C2D4×#1062188211yescharacteristic
815C2#1914640811yescharacteristic
816C2#1914679611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingD4×C22⋊C4×C43C2
socleC23×C43C22×D4
prime radicalC2×#14583033C2
hypercenterD4×C22⋊C4D43
hypocenterC43#24893
LCSG ▷ C22×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×C4×#10621882C2semidirect
3. #19138109C2semidirect
4. #19136123C2semidirect
5. #19136021C2semidirect
6. #19135905C2semidirect
7. #19135777C2semidirect
8. #19135281C2semidirect
9. #19135203C2semidirect
10. #19134946C2semidirect
11. #19134943C2semidirect
12. #19134842C2semidirect
13. #19134595C2semidirect
14. #19134526C2semidirect
15. D4×C22⋊C4×C43C2semidirect
20. C2×C4×D172C22semidirect
23. C2×#13063258C22semidirect
24. C2×#13063258C22semidirect
25. C2×C4⋊(C43⋊C8)C22semidirect
32. C2×#13063245C22semidirect
33. C2×#13063245C22semidirect
36. C2×C4×C43⋊C8C22semidirect
39. #14582801C22semidirect
40. #14582797C22semidirect
42. #14582769C22semidirect
44. #14582661C22semidirect
45. #14582661C22semidirect
46. #14582661C22semidirect
47. #14582661C22semidirect
48. #14582654C22semidirect
49. #14582654C22semidirect
217. C22⋊C4×C43D8semidirect
294. D4×C43#123semidirect
401. D4×C22⋊C4D43semidirect
469. C43#24893semidirect
654. C22⋊C4#10621882semidirect
708. D4#13063307semidirect

Maximal subgroups

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

subgroupindex
C2×#145830332
C2×C4×#106218822
#191381092
#191361232
#191360212
#191359052
#191357772
#191352812
#191352032
#191349462
#191349432
#191348422
#191345952
#191345262
D4×C22⋊C4×C432
#2489343