Finite Group Databasebeta

← #25019992

Subgroups — #25019992

Order 11008.

2474 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063287C211yesmaximal, characteristic
2C2×#14582801C211yesmaximal, characteristic
3C2×#14582800C211yesmaximal, characteristic
4C2×#14582770C212yesmaximal, complemented
5C2×C4×Dic43⋊C4C211yesmaximal, characteristic, complemented
6#19132839C212yesmaximal, complemented
7#19132837C212yesmaximal, complemented
8#19132824C211yesmaximal, characteristic, complemented
9#19132824C211yesmaximal, characteristic, complemented
10(C2×D43)⋊#95C212yesmaximal, complemented
11C2×C43×#389C211yesmaximal, characteristic, complemented
12C23×D172C2211yescharacteristic
13C23×C4×D43C2212yes—
14C2×#13063287—24no—
15C2×#13063287—24no—
16C2×#13063287—24no—
17C22×C4⋊Dic43C2211yescharacteristic
18C22×Dic43⋊C4C2211yescharacteristic
19C22×Dic43⋊C4C2211yescharacteristic
20C22×(C2×D43)⋊C4C2212yes—
21C22×(C2×D43)⋊C4C2212yes—
22C22×(C2×D43)⋊C4C2212yes—
23C22×(C2×D43)⋊C4C2212yes—
24C22×(C2×D43)⋊C4C2212yes—
25C22×C4×Dic43C2211yescharacteristic
26C22×C4×Dic43C2211yescharacteristic
27#14582801—24no—
28#14582800C418yescomplemented
29#14582770—28no—
30C4×Dic43⋊C4—24no—
31C2×C43⋊#95C2211yescharacteristic
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2212yes—
34C2×C43⋊#95C2211yescharacteristic
35C2×C43⋊#95C2212yes—
36C2×C43⋊#95C2212yes—
37C22×C4⋊C4×C43C2212yes—
38C22×C4⋊C4×C43C2211yescharacteristic
39C22×C4⋊C4×C43C2211yescharacteristic
40C22×C42×C43C2211yescharacteristic
41C43×#389—24no—
42C2×#95×C43C2212yes—
43C24×D43C2312yes—
44C22×D172—22no—
45C22×D172—22no—
46C22×D172—22no—
47C22×D172—22no—
48C22×D172C2×C414yes—
49C22×D172D414yes—
50C22×D172Q814yes—
51C23×Dic43C2312yes—
52C23×Dic43C2311yescharacteristic
53C23×Dic43C2311yescharacteristic
54C23×Dic43C2311yescharacteristic
55C23×Dic43C2311yescharacteristic
56C22×C4×D43—24no—
57C22×C4×D43—24no—
58C22×C4×D43—24no—
59C22×C4×D43—24no—
60C22×C4×D43—24no—
61C22×C4×D43—42no—
62C22×C4×D43—42no—
63#13063287—232no—
64C2×C4⋊Dic43—22no—
65C2×C4⋊Dic43—22no—
66C2×C4⋊Dic43—22no—
67C2×Dic43⋊C4—22no—
68C2×Dic43⋊C4—22no—
69C2×Dic43⋊C4—22no—
70C2×Dic43⋊C4—22no—
71C2×Dic43⋊C4—22no—
72C2×Dic43⋊C4D414yescomplemented
73C2×(C2×D43)⋊C4—24no—
74C2×(C2×D43)⋊C4—24no—
75C2×(C2×D43)⋊C4—24no—
76C2×(C2×D43)⋊C4—24no—
77C2×(C2×D43)⋊C4—24no—
78C2×(C2×D43)⋊C4—24no—
79C2×(C2×D43)⋊C4—24no—
80C2×(C2×D43)⋊C4—24no—
81C2×(C2×D43)⋊C4—24no—
82C2×(C2×D43)⋊C4—42no—
83C2×(C2×D43)⋊C4—42no—
84C2×(C2×D43)⋊C4—42no—
85C2×(C2×D43)⋊C4—42no—
86C2×(C2×D43)⋊C4C2×C418yescomplemented
87C2×(C2×D43)⋊C4C2×C418yescomplemented
88C2×C4×Dic43—22no—
89C2×C4×Dic43—22no—
90C2×C4×Dic43—22no—
91C2×C4×Dic43—22no—
92C2×C4×Dic43C2×C414yescomplemented
93C2×C4×Dic43D414yes—
94C43⋊#95—22no—
95C43⋊#95—22no—
96C43⋊#95—24no—
97C43⋊#95—24no—
98C43⋊#95—42no—
99C43⋊#95—42no—
100C23×C4×C43C2312yes—
101C23×C4×C43C2311yescharacteristic
102C23×C4×C43C2312yes—
103C23×C4×C43C2311yescharacteristic
104C23×C4×C43C2311yescharacteristic
105C2×C4⋊C4×C43—22no—
106C2×C4⋊C4×C43—22no—
107C2×C4⋊C4×C43—22no—
108C2×C4⋊C4×C43—22no—
109C2×C4⋊C4×C43—24no—
110C2×C4⋊C4×C43—24no—
111C2×C4⋊C4×C43—42no—
112C2×C4⋊C4×C43C2×C414yescomplemented
113C2×C4⋊C4×C43D414yes—
114C2×C42×C43—22no—
115C2×C42×C43—22no—
116C2×C42×C43—22no—
117#95×C43—24no—
118C24×C43C2411yescharacteristic
119C23×D43—22no—
120C23×D43—22no—
121C23×D43—22no—
122C23×D43—22no—
123C23×D43—22no—
124C23×D43—22no—
125C23×D43—22no—
126C23×D43—22no—
127C23×D43—22no—
128C23×D43—22no—
129C23×D43—22no—
130C23×D43—22no—
131C23×D43C22×C414yes—
132C23×D43C2×D414yes—
133C23×D43C2×Q814yes—
134C22×C4×C43—21no—
135C22×C4×C43—22no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—22no—
142C22×C4×C43—22no—
143C22×C4×C43—22no—
144C22×C4×C43—22no—
145C22×C4×C43—22no—
146C22×C4×C43—22no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—22no—
150C22×C4×C43—21no—
151C22×C4×C43—22no—
152C22×C4×C43—22no—
153C22×C4×C43—22no—
154C22×C4×C43—22no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43C22×C414yes—
159C22×C4×C43C22×C412yes—
160C22×C4×C43C2×D412yes—
161C22×C4×C43C2×D412yes—
162C22×C4×C43C2×D412yes—
163C22×C4×C43C2×D414yes—
164C22×C4×C43C2×D412yes—
165C22×C4×C43C2×Q812yes—
166C22×C4×C43#4112yes—
167C22×C4×C43#4112yes—
168C22×C4×C43#4112yes—
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43—21no—
172C22×Dic43—21no—
173C22×Dic43—21no—
174C22×Dic43—21no—
175C22×Dic43—22no—
176C22×Dic43—22no—
177C22×Dic43—21no—
178C22×Dic43—21no—
179C22×Dic43—21no—
180C22×Dic43—21no—
181C22×Dic43—21no—
182C22×Dic43—21no—
183C22×Dic43—22no—
184C22×Dic43—22no—
185C22×Dic43—22no—
186C22×Dic43—21no—
187C22×Dic43—21no—
188C22×Dic43—21no—
189C22×Dic43—21no—
190C22×Dic43—21no—
191C22×Dic43—21no—
192C22×Dic43—22no—
193C22×Dic43—22no—
194C22×Dic43—21no—
195C22×Dic43—21no—
196C22×Dic43C22×C412yes—
197C22×Dic43C22×C412yes—
198C22×Dic43C2×D412yes—
199C22×Dic43C2×D412yes—
200C22×Dic43C2×D412yes—
201C22×Dic43C2×D412yes—
202C22×Dic43#4112yes—
203C22×Dic43#4112yes—
204C2×D172—28no—
205C2×D172—28no—
206C2×D172—28no—
207C2×D172—28no—
208C2×D172—28no—
209C2×D172—28no—
210C2×D172C4⋊C4116yescomplemented
211C2×C4×D43—216no—
212C2×C4×D43—48no—
213C2×C4×D43—48no—
214C2×C4×D43—48no—
215C2×C4×D43—48no—
216C2×C4×D43—48no—
217C2×C4×D43—48no—
218C4⋊C4×C43—28no—
219C4⋊C4×C43—28no—
220C4⋊C4×C43—48no—
221C42×C43—44no—
222(C2×D43)⋊C4—216no—
223(C2×D43)⋊C4—216no—
224(C2×D43)⋊C4—48no—
225(C2×D43)⋊C4—48no—
226(C2×D43)⋊C4—48no—
227C4⋊Dic43—44no—
228Dic43⋊C4—28no—
229Dic43⋊C4—28no—
230C4×Dic43—28no—
231C4×Dic43—28no—
232C23×C43C23×C411yescharacteristic
233C23×C43C22×D411yescharacteristic
234C23×C43C22×D411yescharacteristic
235C23×C43C22×D411yescharacteristic
236C23×C43C22×D411yescharacteristic
237C23×C43C22×Q811yescharacteristic
238C23×C43C2×#4111yescharacteristic
239C23×C43C2×#4111yescharacteristic
240C23×C43C2×#4111yescharacteristic
241C23×C43C2×#4111yescharacteristic
242C23×C43C2×#4111yescharacteristic
243C23×C43H(5,𝔽2)11yescharacteristic
244C23×C43H(5,𝔽2)11yescharacteristic
245C23×C43H(5,𝔽2)11yescharacteristic
246C23×C432−1+411yescharacteristic
247C22×D43—24no—
248C22×D43—24no—
249C22×D43—24no—
250C22×D43—24no—
251C22×D43—24no—
252C22×D43—24no—
253C22×D43—24no—
254C22×D43—24no—
255C22×D43—24no—
256C22×D43—24no—
257C22×D43—24no—
258C22×D43—24no—
259C22×D43—24no—
260C22×D43—24no—
261C22×D43—24no—
262C22×D43—24no—
263C22×D43—24no—
264C22×D43—24no—
265C22×D43—42no—
266C22×D43—42no—
267C22×D43—42no—
268C22×D43—42no—
269C22×D43—42no—
270C22×D43—42no—
271C22×D43—42no—
272C22×D43—42no—
273C22×D43—42no—
274C22×D43—42no—
275C22×D43—42no—
276C22×D43—42no—
277C22×D43—42no—
278C22×D43—42no—
279C22×D43—42no—
280C22×D43—42no—
281C22×D43C2×C4⋊C418yes—
282C2×C4×C43—24no—
283C2×C4×C43—24no—
284C2×C4×C43—24no—
285C2×C4×C43—24no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—24no—
291C2×C4×C43—22no—
292C2×C4×C43—24no—
293C2×C4×C43—22no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—42no—
297C2×C4×C43—42no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—42no—
301C2×C4×C43—42no—
302C2×C4×C43—42no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43—42no—
307C2×C4×C43—41no—
308C2×C4×C43—42no—
309C2×C4×C43—42no—
310C2×C4×C43C2×C4⋊C414yes—
311C2×C4×C43C4×D414yes—
312C2×C4×C43C4×D414yes—
313C2×C4×C43#12014yes—
314C2×C4×C43C22⋊Q814yes—
315C2×C4×C43C22⋊Q814yes—
316C2×C4×C43#12314yes—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—22no—
321C2×Dic43—22no—
322C2×Dic43—22no—
323C2×Dic43—22no—
324C2×Dic43—22no—
325C2×Dic43—22no—
326C2×Dic43—22no—
327C2×Dic43—22no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—22no—
332C2×Dic43—22no—
333C2×Dic43—22no—
334C2×Dic43—22no—
335C2×Dic43—41no—
336C2×Dic43—41no—
337C2×Dic43—41no—
338C2×Dic43—41no—
339C2×Dic43—41no—
340C2×Dic43—41no—
341C2×Dic43—41no—
342C2×Dic43—41no—
343C2×Dic43—42no—
344C2×Dic43—42no—
345C2×Dic43—42no—
346C2×Dic43—42no—
347C2×Dic43—42no—
348C2×Dic43—42no—
349C2×Dic43—42no—
350C2×Dic43C4×D414yescomplemented
351C2×Dic43#12114yes—
352D172—232no—
353C4×D43—432no—
354#14018—431nomaximal, Sylow
355C22×C43C22×C4⋊C411yescharacteristic
356C22×C43C2×C4×D411yescharacteristic
357C22×C43C2×C4×D411yescharacteristic
358C22×C43C2×C4×D411yescharacteristic
359C22×C43C4×#4111yescharacteristic
360C22×C43#51811yescharacteristic
361C22×C43#52011yescharacteristic
362C22×C43C2×#12011yescharacteristic
363C22×C43C2×#12111yescharacteristic
364C22×C43C2×C22⋊Q811yescharacteristic
365C22×C43C2×C22⋊Q811yescharacteristic
366C22×C43C2×#12311yescharacteristic
367C22×C43#52511yescharacteristic
368C22×C43#52911yescharacteristic
369C22×C43#53211yescharacteristic
370C22×C43#53511yescharacteristic
371C22×C43#53711yescharacteristic
372C22×C43#54011yescharacteristic
373C22×C43#54211yescharacteristic
374C22×C43D4211yescharacteristic
375C22×C43D4211yescharacteristic
376C22×C43#54611yescharacteristic
377C22×C43#54611yescharacteristic
378C22×C43#54611yescharacteristic
379C22×C43#54711yescharacteristic
380C22×C43#54811yescharacteristic
381C22×C43D4×Q811yescharacteristic
382C22×C43#55011yescharacteristic
383C22×C43#55011yescharacteristic
384C22×C43#55411yescharacteristic
385C22×C43#55411yescharacteristic
386C22×C43#55411yescharacteristic
387C22×C43#55611yescharacteristic
388C22×C43#55911yescharacteristic
389C22×C43#55911yescharacteristic
390C2×D43—28no—
391C2×D43—28no—
392C2×D43—28no—
393C2×D43—44no—
394C2×D43—44no—
395C2×D43—44no—
396C2×D43—44no—
397C2×D43—44no—
398C2×D43—44no—
399C2×D43—44no—
400C2×D43—44no—
401C2×D43—44no—
402C2×D43—44no—
403C2×D43—44no—
404C2×D43—44no—
405C4×C43—44no—
406C4×C43—42no—
407C4×C43—44no—
408C4×C43—42no—
409C4×C43#38518yescomplemented
410Dic43—24no—
411Dic43—24no—
412Dic43—42no—
413Dic43—42no—
414Dic43—82no—
415C22×C4×D4—431no—
416C2×#390—431no—
417C2×#390—431no—
418C2×#389D4311yescharacteristic, complemented
419C2×#385—432no—
420C2×C4×C4⋊C4—431no—
421#1439—432no—
422#1439—432no—
423C4⋊#95—431no—
424C4⋊#95—431no—
425C22⋊#95—432no—
426C2×C43C2×#38511yescharacteristic
427C2×C43C4×#12111yescharacteristic
428C2×C43#232411yescharacteristic
429C2×C43D4×C4⋊C411yescharacteristic
430C2×C43#234911yescharacteristic
431C2×C43#236611yescharacteristic
432C2×C43#236711yescharacteristic
433C2×C43#240711yescharacteristic
434C2×C43#240811yescharacteristic
435C2×C43#244511yescharacteristic
436C2×C43#244711yescharacteristic
437C2×C43#245211yescharacteristic
438C2×C43#245411yescharacteristic
439C2×C43#253811yescharacteristic
440C2×C43#258011yescharacteristic
441D43—48no—
442C23×D4—431no—
443C24×C4—432no—
444C2×C4×D4—864no—
445C2×C4×D4—864no—
446C2×C4×D4—864no—
447C22×C4⋊C4—431no—
448C22×C4⋊C4—431no—
449C22×C4⋊C4—431no—
450C22×C4⋊C4C2×D4312yes—
451C22×C4⋊C4C2×D4311yescharacteristic
452C22×C4⋊C4C2×D4311yescharacteristic
453C22×C22⋊C4—432no—
454C22×C22⋊C4—432no—
455C22×C22⋊C4—432no—
456C22×C22⋊C4—432no—
457C22×C22⋊C4—432no—
458C22×C42—431no—
459C22×C42—431no—
460C22×C42C2×D4311yescharacteristic
461#390—438no—
462#390—864no—
463#389—24no—
464#385—868no—
465C4×C4⋊C4—864no—
466C2×#95—431no—
467C2×#95—432no—
468C2×#95—432no—
469C2×#95—431no—
470C2×#95—432no—
471C2×#95—432no—
472C2×#95C2×D4312yes—
473C43#1401811yescharacteristic, complemented, Sylow
474C25—432no—
475C22×D4—434no—
476C22×D4—434no—
477C22×D4—434no—
478C22×D4—862no—
479C22×D4—862no—
480C22×D4—862no—
481C22×D4—862no—
482C23×C4—431no—
483C23×C4—431no—
484C23×C4—431no—
485C23×C4—431no—
486C23×C4—432no—
487C23×C4—864no—
488C23×C4—864no—
489C23×C4—864no—
490C23×C4—864no—
491C23×C4—864no—
492C23×C4—1722no—
493C23×C4—1722no—
494C23×C4C22×D4312yes—
495C23×C4C22×D4311yescharacteristic
496C23×C4C22×D4311yescharacteristic
497C23×C4C22×D4312yes—
498C23×C4C22×D4311yescharacteristic
499C4×D4—8632no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—22no—
504C2×C4⋊C4—24no—
505C2×C4⋊C4—24no—
506C2×C4⋊C4—42no—
507C2×C4⋊C4—434no—
508C2×C4⋊C4—862no—
509C2×C4⋊C4—862no—
510C2×C4⋊C4—862no—
511C2×C4⋊C4—862no—
512C2×C4⋊C4—862no—
513C2×C4⋊C4—862no—
514C2×C4⋊C4—862no—
515C2×C4⋊C4—862no—
516C2×C4⋊C4C4×D4314yescomplemented
517C2×C4⋊C4C22⋊D4314yes—
518C2×C22⋊C4—438no—
519C2×C22⋊C4—438no—
520C2×C22⋊C4—864no—
521C2×C22⋊C4—864no—
522C2×C22⋊C4—864no—
523C2×C22⋊C4—864no—
524C2×C22⋊C4—864no—
525C2×C22⋊C4—864no—
526C2×C22⋊C4—864no—
527C2×C22⋊C4—864no—
528C2×C22⋊C4—864no—
529C2×C22⋊C4—1722no—
530C2×C22⋊C4—1722no—
531C2×C22⋊C4—1722no—
532C2×C22⋊C4—1722no—
533C2×C42—22no—
534C2×C42—22no—
535C2×C42—22no—
536C2×C42—434no—
537C2×C42—434no—
538C2×C42—862no—
539C2×C42—862no—
540C2×C42—862no—
541C2×C42—862no—
542#95—24no—
543#95—862no—
544#95—862no—
545#95—864no—
546#95—864no—
547#95—1722no—
548#95—1722no—
549C24—434no—
550C24—434no—
551C24—434no—
552C24—862no—
553C24—862no—
554C24—862no—
555C24—862no—
556C24—862no—
557C24—862no—
558C24—862no—
559C24—862no—
560C24—862no—
561C24—862no—
562C24—862no—
563C24—862no—
564C24C23×D4311yescharacteristic
565C2×D4—4316no—
566C2×D4—868no—
567C2×D4—868no—
568C2×D4—868no—
569C2×D4—868no—
570C2×D4—868no—
571C2×D4—868no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—21no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—432no—
597C22×C4—432no—
598C22×C4—432no—
599C22×C4—432no—
600C22×C4—432no—
601C22×C4—432no—
602C22×C4—432no—
603C22×C4—432no—
604C22×C4—8616no—
605C22×C4—861no—
606C22×C4—861no—
607C22×C4—861no—
608C22×C4—861no—
609C22×C4—861no—
610C22×C4—861no—
611C22×C4—861no—
612C22×C4—861no—
613C22×C4—861no—
614C22×C4—861no—
615C22×C4—861no—
616C22×C4—861no—
617C22×C4—861no—
618C22×C4—861no—
619C22×C4—861no—
620C22×C4—861no—
621C22×C4—861no—
622C22×C4—861no—
623C22×C4—861no—
624C22×C4—861no—
625C22×C4—862no—
626C22×C4—862no—
627C22×C4—862no—
628C22×C4—862no—
629C22×C4—862no—
630C22×C4—862no—
631C22×C4—862no—
632C22×C4—1728no—
633C22×C4—1728no—
634C22×C4—1728no—
635C22×C4—1728no—
636C22×C4—1728no—
637C22×C4—1728no—
638C22×C4C2×C4×D4314yes—
639C22×C4C2×C4×D4312yes—
640C22×C4#1062189812yes—
641C22×C4D4×D4312yes—
642C22×C4D4×D4312yes—
643C22×C4D4×D4312yes—
644C22×C4Q8×D4312yes—
645C22×C4#1062190212yes—
646C22×C4#1062190212yes—
647C22×C4C2×C22⋊D4314yes—
648C22×C4C2×C22⋊D4312yes—
649C4⋊C4—28no—
650C4⋊C4—28no—
651C4⋊C4—48no—
652C4⋊C4—868no—
653C4⋊C4—868no—
654C4⋊C4—1724no—
655C22⋊C4—8616no—
656C22⋊C4—8616no—
657C22⋊C4—1728no—
658C22⋊C4—1728no—
659C22⋊C4—1728no—
660C42—44no—
661C42—868no—
662C42—868no—
663C23—438no—
664C23—864no—
665C23—864no—
666C23—864no—
667C23—864no—
668C23—864no—
669C23—864no—
670C23—864no—
671C23—864no—
672C23—864no—
673C23—864no—
674C23—864no—
675C23—864no—
676C23—864no—
677C23—864no—
678C23—864no—
679C23—864no—
680C23—864no—
681C23—864no—
682C23—1722no—
683C23—1722no—
684C23—1722no—
685C23—1722no—
686C23—1722no—
687C23—1722no—
688C23—1722no—
689C23—1722no—
690C23—1722no—
691C23—1722no—
692C23—1722no—
693C23—1722no—
694C23—1722no—
695C23—1722no—
696C23—1722no—
697C23—1722no—
698C23C22×C4×D4311yescharacteristic
699C23C2×D4×D4311yescharacteristic
700C23C2×D4×D4311yescharacteristic
701C23C2×D4×D4311yescharacteristic
702C23C22×C22⋊D4311yescharacteristic
703C23C2×Q8×D4311yescharacteristic
704C23#41×D4311yescharacteristic
705C23#41×D4311yescharacteristic
706C23C2×#1062189811yescharacteristic
707C23C2×#1062190211yescharacteristic
708C23C2×#1062190211yescharacteristic
709C23#1306337011yescharacteristic
710C23#1306337111yescharacteristic
711C23#1306337111yescharacteristic
712C23#1306337311yescharacteristic
713D4—8632no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—42no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—41no—
739C2×C4—42no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—434no—
743C2×C4—434no—
744C2×C4—862no—
745C2×C4—862no—
746C2×C4—862no—
747C2×C4—862no—
748C2×C4—862no—
749C2×C4—862no—
750C2×C4—862no—
751C2×C4—862no—
752C2×C4—862no—
753C2×C4—862no—
754C2×C4—862no—
755C2×C4—862no—
756C2×C4—862no—
757C2×C4—862no—
758C2×C4—862no—
759C2×C4—862no—
760C2×C4—862no—
761C2×C4—862no—
762C2×C4—17232no—
763C2×C4—1722no—
764C2×C4—1722no—
765C2×C4—1722no—
766C2×C4—1722no—
767C2×C4—1722no—
768C2×C4—1722no—
769C2×C4—1722no—
770C2×C4—1721no—
771C2×C4—1721no—
772C2×C4—1721no—
773C2×C4—1721no—
774C2×C4—1721no—
775C2×C4—1721no—
776C2×C4—1721no—
777C2×C4—1721no—
778C2×C4C4⋊C4×D4314yes—
779C2×C4C4×C22⋊D4314yes—
780C2×C4#1306328714yes—
781C2×C4#1306329314yes—
782C2×C4#1306330114yes—
783C2×C4#1306330314yes—
784C2×C4#1306331014yes—
785C22—868no—
786C22—868no—
787C22—868no—
788C22—1724no—
789C22—1724no—
790C22—1724no—
791C22—1724no—
792C22—1724no—
793C22—1724no—
794C22—1724no—
795C22—1724no—
796C22—1724no—
797C22—1724no—
798C22—1724no—
799C22—1724no—
800C22C2×C4⋊C4×D4311yescharacteristic
801C22C4×D4×D4311yescharacteristic
802C22C2×C4×C22⋊D4311yescharacteristic
803C22C2×#1306328711yescharacteristic
804C22C4×#1062190211yescharacteristic
805C22#1458337111yescharacteristic
806C22#1458338111yescharacteristic
807C22C2×#1306329311yescharacteristic
808C22#121×D4311yescharacteristic
809C22C2×#1306330111yescharacteristic
810C22C2×#1306330311yescharacteristic
811C22C2×#1306331011yescharacteristic
812C22#1458341211yescharacteristic
813C22#1458343411yescharacteristic
814C22#1458345011yescharacteristic
815C22#1458346511yescharacteristic
816C22#1458347911yescharacteristic
817C22#1458350511yescharacteristic
818C22#1458352311yescharacteristic
819C22D4×C22⋊D4311yescharacteristic
820C22#1458353311yescharacteristic
821C22#1458353711yescharacteristic
822C22#1458354011yescharacteristic
823C22#1458354611yescharacteristic
824C22#1458355111yescharacteristic
825C22#1458356011yescharacteristic
826C22#1458356411yescharacteristic
827C22#1458356811yescharacteristic
828C22#1458357011yescharacteristic
829C22#1458360511yescharacteristic
830C22#1458360511yescharacteristic
831C22#1458361011yescharacteristic
832C22#1458362111yescharacteristic
833C22#1458363211yescharacteristic
834C22#1458363411yescharacteristic
835C4—44no—
836C4—42no—
837C4—44no—
838C4—42no—
839C4—864no—
840C4—864no—
841C4—3442no—
842C4—1722no—
843C4—1722no—
844C4#1458277018yescomplemented
845C2—1728no—
846C2C2×#1458277011yescharacteristic
847C2#1913710311yescharacteristic
848C2#1913728611yescharacteristic
849C2#1913749611yescharacteristic
850C2#1913750411yescharacteristic
851C2#1913765711yescharacteristic
852C2#1913766211yescharacteristic
853C2#1913794211yescharacteristic
854C2#1913794711yescharacteristic
855C2#1913836211yescharacteristic
856C2#1913838411yescharacteristic
857C2#1913844111yescharacteristic
858C2#1913846311yescharacteristic
859C2#1913951611yescharacteristic
860C2#1913995511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#389C2
socle, cosocleC24×C43C24
prime radicalC23×D172C22
hypercenterC2×#389D43
hypocenterC43#14018
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
4. C2×#14582770C2semidirect
5. C2×C4×Dic43⋊C4C2semidirect
6. #19132839C2semidirect
7. #19132837C2semidirect
8. #19132824C2semidirect
9. #19132824C2semidirect
10. (C2×D43)⋊#95C2semidirect
11. C2×C43×#389C2semidirect
28. #14582800C4semidirect
72. C2×Dic43⋊C4D4semidirect
86. C2×(C2×D43)⋊C4C2×C4semidirect
87. C2×(C2×D43)⋊C4C2×C4semidirect
92. C2×C4×Dic43C2×C4semidirect
112. C2×C4⋊C4×C43C2×C4semidirect
210. C2×D172C4⋊C4semidirect
350. C2×Dic43C4×D4semidirect
409. C4×C43#385semidirect
418. C2×#389D43semidirect
473. C43#14018semidirect
516. C2×C4⋊C4C4×D43semidirect
844. C4#14582770semidirect

Maximal subgroups

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

subgroupindex
C22×#130632872
C2×#145828012
C2×#145828002
C2×#145827702
C2×C4×Dic43⋊C42
#191328392
#191328372
#191328242
(C2×D43)⋊#952
C2×C43×#3892
#1401843