Finite Group Databasebeta

← #25134353

Subgroups — #25134353

Order 11008.

1438 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583138C211yesmaximal, characteristic, complemented
2C2×#14583055C211yesmaximal, characteristic, complemented
3C2×#14583055C211yesmaximal, characteristic, complemented
4C22×#13063249C211yesmaximal, characteristic, complemented
5#19138046C211yesmaximal, characteristic
6#19135838C211yesmaximal, characteristic, complemented
7#19135795C211yesmaximal, characteristic, complemented
8#19135695C211yesmaximal, characteristic, complemented
9#19135603C211yesmaximal, characteristic, complemented
10#19134936C211yesmaximal, characteristic, complemented
11#19134903C211yesmaximal, characteristic, complemented
12#19134888C211yesmaximal, characteristic
13#19134849C211yesmaximal, characteristic, complemented
14#19134530C211yesmaximal, characteristic, complemented
15C2×D4×Q8×C43C211yesmaximal, characteristic
16C22×#10621885C2211yescharacteristic
17C22×#10621885C2211yescharacteristic
18C22×#10621885C2211yescharacteristic
19C23×C43⋊C8C2211yescharacteristic
20C2×#13063304C2211yescharacteristic
21C2×#13063304C2211yescharacteristic
22C22×C4⋊Dic43C2211yescharacteristic
23#14583138—24no—
24#14583055—24no—
25#14583055—24no—
26C2×#13063258C2211yescharacteristic
27C2×#13063249—24no—
28C2×#13063249C2211yescharacteristic
29C2×#13063249C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063249C2211yescharacteristic
33C2×#13063249C2211yescharacteristic
34C2×#13063249C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063249C2211yescharacteristic
37C2×#13063248C2211yescharacteristic
38C2×C22⋊(C43⋊C8)C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C2×C22⋊(C43⋊C8)C2211yescharacteristic
41#14582832—21no—
42#14582822—21no—
43#14582805C2211yescharacteristic
44#14582797C2211yescharacteristic
45#14582779—21no—
46#14582759C2211yescharacteristic
47#14582757—21no—
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582654C2211yescharacteristic
52C23×Q8×C43C2211yescharacteristic
53C23×Q8×C43C2211yescharacteristic
54D4×Q8×C43—24no—
55D4×Q8×C43—24no—
56C2×C4⋊Q8×C43—21no—
57C2×C4⋊Q8×C43C2211yescharacteristic
58C2×C22⋊Q8×C43—21no—
59C2×C22⋊Q8×C43—21no—
60C2×C22⋊Q8×C43C2211yescharacteristic
61C2×C22⋊Q8×C43C2211yescharacteristic
62C2×C4×Q8×C43C2211yescharacteristic
63C2×C4×D4×C43—21no—
64C2×C4×D4×C43C2211yescharacteristic
65C22×Dic86C2311yescharacteristic
66C23×Dic43—21no—
67C2×#10621885—22no—
68C2×#10621885—22no—
69C2×#10621885—22no—
70C2×#10621885—22no—
71C2×#10621885—22no—
72C2×#10621885—22no—
73C2×#10621885—41no—
74C2×#10621885—41no—
75C2×#10621885—41no—
76C22×C43⋊C8—22no—
77C22×C43⋊C8—22no—
78C22×C43⋊C8—41no—
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83#13063304—22no—
84#13063304—22no—
85#13063304—22no—
86#13063304—41no—
87C2×C4⋊Dic43—22no—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43—41no—
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×C22⋊Dic43—21no—
97C2×C22⋊Dic43—21no—
98C2×C22⋊Dic43—21no—
99#13063258—22no—
100#13063249—22no—
101#13063249—22no—
102#13063249—22no—
103#13063249—22no—
104#13063249—22no—
105#13063249—22no—
106#13063249—22no—
107#13063249—41no—
108#13063249D414yescomplemented
109#13063248—22no—
110C22⋊(C43⋊C8)—22no—
111C22⋊(C43⋊C8)—22no—
112C22⋊(C43⋊C8)—41no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C22×Q8×C43—22no—
118C22×Q8×C43—22no—
119C22×Q8×C43—21no—
120C22×Q8×C43—21no—
121C22×Q8×C43—22no—
122C22×Q8×C43—22no—
123C22×Q8×C43—22no—
124C22×Q8×C43—22no—
125C22×Q8×C43—22no—
126C22×Q8×C43—41no—
127C22×Q8×C43—41no—
128C22×Q8×C43—41no—
129C22×Q8×C43—41no—
130C22×Q8×C43D414yes—
131C22×Q8×C43C2311yescharacteristic
132C22×Q8×C43C2311yescharacteristic
133C22×Q8×C43C2311yescharacteristic
134C22×D4×C43D411yescharacteristic
135C23×C4×C43—21no—
136C23×C4×C43—21no—
137C23×C4×C43C2311yescharacteristic
138C23×C4×C43C2311yescharacteristic
139C4⋊Q8×C43—28no—
140C4⋊Q8×C43—22no—
141C4⋊Q8×C43—22no—
142C22⋊Q8×C43—28no—
143C22⋊Q8×C43—28no—
144C22⋊Q8×C43—22no—
145C22⋊Q8×C43—22no—
146C22⋊Q8×C43—22no—
147C22⋊Q8×C43D414yes—
148C4×Q8×C43—22no—
149C4×Q8×C43—22no—
150C4×D4×C43—28no—
151C4×D4×C43—22no—
152C4×D4×C43—22no—
153C2×C4⋊C4×C43—21no—
154C2×C4⋊C4×C43—21no—
155C2×C4⋊C4×C43—21no—
156C2×C4⋊C4×C43—21no—
157C2×C4⋊C4×C43—21no—
158C2×C4⋊C4×C43D411yescharacteristic
159C2×C4⋊C4×C43C2311yescharacteristic
160C2×C22⋊C4×C43—21no—
161C2×C22⋊C4×C43—21no—
162C2×C22⋊C4×C43D411yescharacteristic
163C2×C22⋊C4×C43D411yescharacteristic
164C2×C42×C43—21no—
165C2×C42×C43C2311yescharacteristic
166C24×C43C2×D411yescharacteristic
167C24×C43C2×D411yescharacteristic
168C2×Q8×C43—24no—
169C2×Q8×C43—24no—
170C2×Q8×C43—21no—
171C2×Q8×C43—21no—
172C2×Q8×C43—21no—
173C2×Q8×C43—21no—
174C2×Q8×C43—21no—
175C2×Q8×C43—28no—
176C2×Q8×C43—21no—
177C2×Q8×C43—21no—
178C2×Q8×C43—21no—
179C2×Q8×C43—21no—
180C2×Q8×C43—21no—
181C2×Q8×C43—21no—
182C2×Q8×C43—21no—
183C2×Q8×C43—21no—
184C2×Q8×C43—42no—
185C2×Q8×C43—42no—
186C2×Q8×C43—42no—
187C2×Q8×C43—42no—
188C2×Q8×C43—44no—
189C2×Q8×C43—44no—
190C2×Q8×C43—44no—
191C2×Q8×C43—44no—
192C2×Q8×C43—44no—
193C2×Q8×C43—44no—
194C2×Q8×C43—44no—
195C2×Q8×C43C2×D412yes—
196C2×Q8×C43C2×D412yes—
197C2×Q8×C43C2×D412yes—
198C2×Q8×C43C2×D412yes—
199C2×Q8×C43#4112yes—
200C2×D4×C43—22no—
201C2×D4×C43—22no—
202C2×D4×C43Q1614yescomplemented
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—24no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—24no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—42no—
220C22×C4×C43—42no—
221C22×C4×C43—42no—
222C22×C4×C43—42no—
223C22×C4×C43C2×D412yes—
224C22×C4×C43C2×D412yes—
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2×D411yescharacteristic
227C22×C4×C43C2×D411yescharacteristic
228C22×C4×C43C2×D411yescharacteristic
229C22×C4×C43C2411yescharacteristic
230C22×Dic43—21no—
231C22×Dic43—21no—
232C22×Dic43—21no—
233C22×Dic43—21no—
234C22×Dic43—42no—
235C22×Dic43—42no—
236C22×Dic43—81no—
237C2×Dic86—21no—
238C2×Dic86—21no—
239C2×Dic86—21no—
240C2×Dic86—21no—
241C2×Dic86—21no—
242C2×Dic86—21no—
243C4⋊C4×C43—24no—
244C4⋊C4×C43—24no—
245C4⋊C4×C43—24no—
246C4⋊C4×C43—24no—
247C4⋊C4×C43—24no—
248C4⋊C4×C43—22no—
249C4⋊C4×C43—21no—
250C4⋊C4×C43C2×D412yes—
251C22⋊C4×C43—24no—
252C22⋊C4×C43—22no—
253C22⋊C4×C43—24no—
254C22⋊C4×C43—22no—
255C42×C43—24no—
256C42×C43—21no—
257C42×C43—21no—
258C22⋊Dic43—42no—
259C22⋊Dic43—42no—
260C22⋊Dic43—81no—
261#10621885—44no—
262#10621885—44no—
263#10621885—44no—
264C4⋊Dic43—21no—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43—21no—
268C4⋊Dic43—21no—
269C4⋊Dic43—42no—
270C4⋊Dic43C2×D412yes—
271Dic43⋊C4—42no—
272Dic43⋊C4—42no—
273Dic43⋊C4—81no—
274C2×C43⋊C8—21no—
275C2×C43⋊C8—21no—
276C2×C43⋊C8—21no—
277C2×C43⋊C8—21no—
278C2×C43⋊C8—21no—
279C2×C43⋊C8—21no—
280C2×C43⋊C8—21no—
281C2×C43⋊C8—21no—
282C2×C43⋊C8—21no—
283C2×C43⋊C8—21no—
284C2×C43⋊C8—21no—
285C2×C43⋊C8—44no—
286C2×C43⋊C8C2×D412yes—
287C23×C43—21no—
288C23×C43—21no—
289C23×C43—21no—
290C23×C43—21no—
291C23×C43—21no—
292C23×C43—21no—
293C23×C43—21no—
294C23×C43—21no—
295C23×C43—21no—
296C23×C43—21no—
297C23×C43#12012yes—
298C23×C43C2×Q1612yes—
299C23×C43C2×Q1612yes—
300C23×C43#13712yes—
301C23×C43C22×D411yescharacteristic
302Q8×C43—22no—
303Q8×C43—22no—
304Q8×C43—22no—
305Q8×C43—22no—
306Q8×C43—22no—
307Q8×C43—22no—
308Q8×C43—22no—
309Q8×C43—48no—
310Q8×C43—48no—
311Q8×C43—41no—
312Q8×C43—41no—
313Q8×C43—41no—
314Q8×C43—41no—
315Q8×C43#12114yes—
316D4×C43—28no—
317C2×C4×C43—21no—
318C2×C4×C43—22no—
319C2×C4×C43—21no—
320C2×C4×C43—22no—
321C2×C4×C43—21no—
322C2×C4×C43—22no—
323C2×C4×C43—21no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—21no—
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—48no—
338C2×C4×C43—48no—
339C2×C4×C43—41no—
340C2×C4×C43—41no—
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—41no—
348C2×C4×C43—41no—
349C2×C4×C43#12012yes—
350C2×C4×C43C2×Q1612yes—
351C2×C4×C43C22×D411yescharacteristic
352C2×C4×C43C22×D411yescharacteristic
353C2×C4×C43C22×D411yescharacteristic
354C2×C4×C43C2×#4111yescharacteristic
355C2×C4×C43H(5,𝔽2)11yescharacteristic
356C2×C4×C43H(5,𝔽2)11yescharacteristic
357C2×Dic43—22no—
358C2×Dic43—41no—
359C2×Dic43—41no—
360C2×Dic43—41no—
361C2×Dic43—41no—
362C2×Dic43—41no—
363C2×Dic43—41no—
364C2×Dic43—41no—
365C2×Dic43—41no—
366C2×Dic43—41no—
367C2×Dic43—41no—
368C2×Dic43—41no—
369C2×Dic43—84no—
370Dic86—41no—
371Dic86—41no—
372Dic86—41no—
373Dic86—41no—
374C43⋊C8—22no—
375C43⋊C8—41no—
376C43⋊C8—41no—
377C43⋊C8—41no—
378#24437—431nomaximal, Sylow
379C22×C43—22no—
380C22×C43—22no—
381C22×C43—22no—
382C22×C43—22no—
383C22×C43—22no—
384C22×C43—22no—
385C22×C43—22no—
386C22×C43—22no—
387C22×C43—22no—
388C22×C43—41no—
389C22×C43—41no—
390C22×C43—41no—
391C22×C43—41no—
392C22×C43#45114yescomplemented
393C22×C43C2×#12011yescharacteristic
394C22×C43D4211yescharacteristic
395C22×C43#54611yescharacteristic
396C22×C43C22×Q1611yescharacteristic
397C22×C43C2×#13711yescharacteristic
398C22×C43#57711yescharacteristic
399C22×C43#57811yescharacteristic
400C4×C43—22no—
401C4×C43—24no—
402C4×C43—22no—
403C4×C43—41no—
404C4×C43—42no—
405C4×C43—42no—
406C4×C43—41no—
407C4×C43—42no—
408C4×C43C2×#12111yescharacteristic
409C4×C43#53411yescharacteristic
410C4×C43D4211yescharacteristic
411C4×C43#54611yescharacteristic
412Dic43—42no—
413Dic43—81no—
414Dic43—81no—
415Dic43—81no—
416C2×D4×Q8D4311yescharacteristic
417C2×#467—431no—
418C2×#451—431no—
419C2×#451—431no—
420C22×#103—431no—
421#2417—431no—
422#2043—431no—
423#2036—431no—
424#2016—431no—
425#2001—431no—
426#1878—431no—
427#1872—431no—
428#1869—431no—
429#1863—431no—
430#1787—431no—
431C2×C43—24no—
432C2×C43—42no—
433C2×C43#241011yescharacteristic
434C2×C43C2×#45111yescharacteristic
435C2×C43#301311yescharacteristic
436C2×C43#326611yescharacteristic
437C2×C43D4×Q1611yescharacteristic
438C2×C43#329911yescharacteristic
439C2×C43#331211yescharacteristic
440C23×Q8C2×D4311yescharacteristic
441C23×Q8C2×D4311yescharacteristic
442C22×Q16—431no—
443C22×Q16—431no—
444C22×Q16—431no—
445C23×C8—431no—
446D4×Q8—24no—
447D4×Q8—24no—
448C2×C4⋊Q8—21no—
449C2×C4⋊Q8C2×D4311yescharacteristic
450C2×C22⋊Q8—21no—
451C2×C22⋊Q8—21no—
452C2×C22⋊Q8—431no—
453C2×C22⋊Q8—431no—
454C2×C22⋊Q8C2×D4311yescharacteristic
455C2×C22⋊Q8C2×D4311yescharacteristic
456C2×C4×Q8C2×D4311yescharacteristic
457C2×C4×D4—21no—
458C2×C4×D4C2×D4311yescharacteristic
459C22×C4⋊C4—431no—
460#467—864no—
461#451—864no—
462#451—864no—
463C2×#107—431no—
464C2×#103—431no—
465C2×#103—431no—
466C2×#103—431no—
467C2×#103—431no—
468C2×#103—431no—
469C2×#103—431no—
470C2×#103—431no—
471C2×#103—431no—
472C2×#103—431no—
473C2×#103—431no—
474C2×#103—864no—
475C2×C22⋊C8—431no—
476C2×C22⋊C8—431no—
477C2×C22⋊C8—431no—
478#398—861no—
479#396—861no—
480#391—431no—
481#389—431no—
482#386—861no—
483#380—431no—
484#380—861no—
485#340—431no—
486#340—431no—
487#336—431no—
488#336—431no—
489C43#2443711yescharacteristic, complemented, Sylow
490C22×Q8—22no—
491C22×Q8—22no—
492C22×Q8—21no—
493C22×Q8—21no—
494C22×Q8—22no—
495C22×Q8—22no—
496C22×Q8—22no—
497C22×Q8—22no—
498C22×Q8—22no—
499C22×Q8—41no—
500C22×Q8—41no—
501C22×Q8—41no—
502C22×Q8—41no—
503C22×Q8—431no—
504C22×Q8C22⋊D4314yes—
505C22×Q8C22×D4311yescharacteristic
506C22×Q8C22×D4311yescharacteristic
507C22×Q8C22×D4311yescharacteristic
508C22×D4C22⋊D4311yescharacteristic
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—861no—
512C23×C4C22×D4311yescharacteristic
513C23×C4C22×D4311yescharacteristic
514C2×Q16—862no—
515C2×Q16—862no—
516C2×Q16—862no—
517C2×Q16—862no—
518C2×Q16—862no—
519C2×Q16—862no—
520C2×Q16—1721no—
521C2×Q16—1721no—
522C2×Q16—1721no—
523C22×C8—431no—
524C22×C8—431no—
525C22×C8—431no—
526C22×C8—431no—
527C22×C8—862no—
528C22×C8—862no—
529C22×C8—1721no—
530C4⋊Q8—28no—
531C4⋊Q8—22no—
532C4⋊Q8—22no—
533C22⋊Q8—28no—
534C22⋊Q8—28no—
535C22⋊Q8—22no—
536C22⋊Q8—22no—
537C22⋊Q8—22no—
538C22⋊Q8—862no—
539C22⋊Q8—862no—
540C22⋊Q8—862no—
541C22⋊Q8—1721no—
542C22⋊Q8C22⋊D4314yes—
543C4×Q8—22no—
544C4×Q8—22no—
545C4×D4—28no—
546C4×D4—22no—
547C4×D4—22no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—431no—
554C2×C4⋊C4—431no—
555C2×C4⋊C4—431no—
556C2×C4⋊C4—862no—
557C2×C4⋊C4—861no—
558C2×C4⋊C4—861no—
559C2×C4⋊C4—861no—
560C2×C4⋊C4—861no—
561C2×C4⋊C4—1721no—
562C2×C4⋊C4C22⋊D4311yescharacteristic
563C2×C4⋊C4C22×D4311yescharacteristic
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—861no—
567C2×C22⋊C4—861no—
568C2×C22⋊C4—861no—
569C2×C22⋊C4C22⋊D4311yescharacteristic
570C2×C22⋊C4C22⋊D4311yescharacteristic
571C2×C42—21no—
572C2×C42C22×D4311yescharacteristic
573#107—862no—
574#103—434no—
575#103—862no—
576#103—862no—
577#103—862no—
578#103—862no—
579#103—862no—
580#103—862no—
581#103—862no—
582#103—862no—
583#103—1721no—
584C22⋊C8—862no—
585C22⋊C8—862no—
586C22⋊C8—1721no—
587#95—861no—
588#95—861no—
589#95—861no—
590#95—861no—
591C24C2×C22⋊D4311yescharacteristic
592C24C2×C22⋊D4311yescharacteristic
593C2×Q8—24no—
594C2×Q8—24no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—28no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—42no—
610C2×Q8—42no—
611C2×Q8—42no—
612C2×Q8—42no—
613C2×Q8—44no—
614C2×Q8—44no—
615C2×Q8—44no—
616C2×Q8—44no—
617C2×Q8—44no—
618C2×Q8—44no—
619C2×Q8—44no—
620C2×Q8—861no—
621C2×Q8—861no—
622C2×Q8—861no—
623C2×Q8—861no—
624C2×Q8—861no—
625C2×Q8—861no—
626C2×Q8D4×D4312yes—
627C2×Q8#1062190012yes—
628C2×Q8C2×C22⋊D4312yes—
629C2×Q8C2×C22⋊D4312yes—
630C2×Q8C2×C22⋊D4312yes—
631C2×D4—22no—
632C2×D4—22no—
633C2×D4#1062188514yescomplemented
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—24no—
640C22×C4—24no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—42no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—42no—
654C22×C4—861no—
655C22×C4—861no—
656C22×C4—861no—
657C22×C4—861no—
658C22×C4—3441no—
659C22×C4—1722no—
660C22×C4—1722no—
661C22×C4C2×C22⋊D4311yescharacteristic
662C22×C4C2×C22⋊D4311yescharacteristic
663C22×C4C2×C22⋊D4311yescharacteristic
664C22×C4C2×C22⋊D4312yes—
665C22×C4C2×C22⋊D4312yes—
666C22×C4C2×C22⋊D4311yescharacteristic
667C22×C4C23×D4311yescharacteristic
668Q16—1724no—
669Q16—1724no—
670Q16—1724no—
671C2×C8—432no—
672C2×C8—861no—
673C2×C8—861no—
674C2×C8—861no—
675C2×C8—861no—
676C2×C8—861no—
677C2×C8—861no—
678C2×C8—861no—
679C2×C8—861no—
680C2×C8—861no—
681C2×C8—861no—
682C2×C8—861no—
683C2×C8—1724no—
684C4⋊C4—24no—
685C4⋊C4—24no—
686C4⋊C4—24no—
687C4⋊C4—24no—
688C4⋊C4—24no—
689C4⋊C4—22no—
690C4⋊C4—21no—
691C4⋊C4—432no—
692C4⋊C4—861no—
693C4⋊C4—861no—
694C4⋊C4—861no—
695C4⋊C4—861no—
696C4⋊C4—861no—
697C4⋊C4—3441no—
698C4⋊C4—1722no—
699C4⋊C4—1722no—
700C4⋊C4—1722no—
701C4⋊C4C2×C22⋊D4312yes—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—22no—
705C22⋊C4—22no—
706C22⋊C4—3441no—
707C22⋊C4—1722no—
708C22⋊C4—1722no—
709C42—24no—
710C42—21no—
711C42—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23#1306329412yes—
723C23C2×#1062188512yes—
724C23C2×#1062188512yes—
725C23#1306335612yes—
726C23C22×C22⋊D4311yescharacteristic
727Q8—22no—
728Q8—22no—
729Q8—22no—
730Q8—22no—
731Q8—22no—
732Q8—22no—
733Q8—22no—
734Q8—48no—
735Q8—48no—
736Q8—41no—
737Q8—41no—
738Q8—41no—
739Q8—41no—
740Q8—1721no—
741Q8—1721no—
742Q8—1721no—
743Q8—1721no—
744Q8#1306329714yes—
745D4—28no—
746C2×C4—21no—
747C2×C4—22no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—22no—
751C2×C4—21no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—48no—
767C2×C4—48no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—862no—
779C2×C4—3444no—
780C2×C4—1721no—
781C2×C4—1721no—
782C2×C4—1721no—
783C2×C4—1721no—
784C2×C4—1721no—
785C2×C4—1721no—
786C2×C4—1721no—
787C2×C4—1721no—
788C2×C4—1721no—
789C2×C4—1721no—
790C2×C4—1721no—
791C2×C4#1306329412yes—
792C2×C4C2×#1062188512yes—
793C2×C4C2×D4×D4311yescharacteristic
794C2×C4C22×C22⋊D4311yescharacteristic
795C2×C4C22×C22⋊D4311yescharacteristic
796C2×C4C2×#1062190011yescharacteristic
797C2×C4#1306337011yescharacteristic
798C2×C4#1306337011yescharacteristic
799C8—862no—
800C8—1721no—
801C8—1721no—
802C8—1721no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22#1458305514yescomplemented
817C22C2×#1306329411yescharacteristic
818C22D4×C22⋊D4311yescharacteristic
819C22#1458354311yescharacteristic
820C22C22×#1062188511yescharacteristic
821C22C2×#1306335611yescharacteristic
822C22#1458370711yescharacteristic
823C22#1458371411yescharacteristic
824C4—22no—
825C4—22no—
826C4—24no—
827C4—41no—
828C4—42no—
829C4—42no—
830C4—41no—
831C4—42no—
832C4—3441no—
833C4—3441no—
834C4—3441no—
835C4—1722no—
836C4C2×#1306329711yescharacteristic
837C4#1458345811yescharacteristic
838C4D4×C22⋊D4311yescharacteristic
839C4#1458354311yescharacteristic
840C2—24no—
841C2—42no—
842C2#1913796911yescharacteristic
843C2C2×#1458305511yescharacteristic
844C2#1914391011yescharacteristic
845C2#1914610611yescharacteristic
846C2D4×#1062188511yescharacteristic
847C2#1914647111yescharacteristic
848C2#1914664611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×D4×Q8×C43C2
socleC23×C43C22×D4
prime radicalC22×D4×C43D4
hypercenterC2×D4×Q8D43
hypocenterC43#24437
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#14583138C2semidirect
2. C2×#14583055C2semidirect
3. C2×#14583055C2semidirect
4. C22×#13063249C2semidirect
6. #19135838C2semidirect
7. #19135795C2semidirect
8. #19135695C2semidirect
9. #19135603C2semidirect
10. #19134936C2semidirect
11. #19134903C2semidirect
13. #19134849C2semidirect
14. #19134530C2semidirect
108. #13063249D4semidirect
202. C2×D4×C43Q16semidirect
392. C22×C43#451semidirect
489. C43#24437semidirect
633. C2×D4#10621885semidirect
816. C22#14583055semidirect

Maximal subgroups

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

subgroupindex
C2×#145831382
C2×#145830552
C22×#130632492
#191380462
#191358382
#191357952
#191356952
#191356032
#191349362
#191349032
#191348882
#191348492
#191345302
C2×D4×Q8×C432
#2443743