Finite Group Databasebeta

← #25134347

Subgroups — #25134347

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×Q8×C22⋊D43C211yesmaximal, characteristic
2C2×#14583140C211yesmaximal, characteristic, complemented
3C2×#14583056C211yesmaximal, characteristic, complemented
4C2×#14583055C211yesmaximal, characteristic, complemented
5#19138040C211yesmaximal, characteristic
6#19135840C211yesmaximal, characteristic, complemented
7#19135797C211yesmaximal, characteristic, complemented
8#19135696C211yesmaximal, characteristic, complemented
9#19135604C211yesmaximal, characteristic, complemented
10#19134934C211yesmaximal, characteristic, complemented
11#19134902C211yesmaximal, characteristic, complemented
12#19134887C211yesmaximal, characteristic
13#19134851C211yesmaximal, characteristic, complemented
14#19134528C211yesmaximal, characteristic, complemented
15C22×#103×C43C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C22×Dic172C2211yescharacteristic
18C22×#10621885C2211yescharacteristic
19C22×#10621885C2211yescharacteristic
20Q8×C22⋊D43—24no—
21Q8×C22⋊D43—24no—
22C2×#13063323—21no—
23C2×#13063323C2211yescharacteristic
24C2×#13063305C2211yescharacteristic
25C2×#13063304—21no—
26C2×#13063304C2211yescharacteristic
27C2×#13063304C2211yescharacteristic
28C2×#13063301—21no—
29C2×#13063301C2211yescharacteristic
30C2×Q8×Dic43C2211yescharacteristic
31C2×C4×C22⋊D43—21no—
32C2×C4×C22⋊D43C2211yescharacteristic
33#14583140—24no—
34#14583056—24no—
35#14583055—24no—
36C2×#13063259C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063250C2211yescharacteristic
39C2×#13063249C2211yescharacteristic
40C2×#13063249C2211yescharacteristic
41C2×#13063248C2211yescharacteristic
42C2×#13063248C2211yescharacteristic
43C2×C22⋊(C43⋊C8)C2211yescharacteristic
44C2×(C2×D43)⋊C8C2211yescharacteristic
45C2×(C2×D43)⋊C8C2211yescharacteristic
46#14582829—21no—
47#14582821—21no—
48#14582804C2211yescharacteristic
49#14582798C2211yescharacteristic
50#14582778—21no—
51#14582759—21no—
52#14582756C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582653C2211yescharacteristic
56#14582653C2211yescharacteristic
57C23×Q8×C43C2211yescharacteristic
58C23×C8×C43C2211yescharacteristic
59C22×C4⋊C4×C43C2211yescharacteristic
60C2×#103×C43—24no—
61C2×#103×C43C2211yescharacteristic
62C2×#103×C43C2211yescharacteristic
63C2×#103×C43C2211yescharacteristic
64C2×#103×C43C2211yescharacteristic
65C22×Dic86—21no—
66C22×Dic86C2311yescharacteristic
67C22×Dic86C2311yescharacteristic
68C2×Q8×D43—22no—
69C2×Q8×D43—22no—
70C2×Q8×D43—22no—
71C2×Q8×D43—22no—
72C2×Q8×D43—41no—
73C2×Q8×D43—41no—
74C22×C22⋊D43D411yescharacteristic
75C22×C4×D43—21no—
76C22×C4×D43C2311yescharacteristic
77C2×Dic172—22no—
78C2×Dic172—22no—
79C2×Dic172—41no—
80C2×#10621885—22no—
81C2×#10621885—22no—
82C2×#10621885—22no—
83C2×#10621885—22no—
84C2×#10621885—41no—
85C2×#10621885—41no—
86C22×C43⋊C8C2311yescharacteristic
87C22×C43⋊C8C2311yescharacteristic
88#13063323—28no—
89#13063323—22no—
90#13063323—22no—
91#13063305—22no—
92#13063305—41no—
93#13063304—28no—
94#13063304—22no—
95#13063304—22no—
96#13063304—22no—
97#13063304D414yes—
98#13063301—28no—
99#13063301—22no—
100#13063301—22no—
101Q8×Dic43—22no—
102Q8×Dic43—22no—
103C4×C22⋊D43—28no—
104C4×C22⋊D43—22no—
105C4×C22⋊D43—22no—
106C2×C4⋊Dic43—21no—
107C2×C4⋊Dic43—21no—
108C2×C4⋊Dic43—21no—
109C2×C4⋊Dic43C2311yescharacteristic
110C2×C4⋊Dic43C2311yescharacteristic
111C2×Dic43⋊C4—21no—
112C2×Dic43⋊C4—21no—
113C2×Dic43⋊C4—21no—
114C2×Dic43⋊C4—21no—
115C2×Dic43⋊C4—21no—
116C2×Dic43⋊C4D411yescharacteristic
117C2×C22⋊Dic43—21no—
118C2×C22⋊Dic43—21no—
119C2×C22⋊Dic43D411yescharacteristic
120C2×(C2×D43)⋊C4—21no—
121C2×(C2×D43)⋊C4—21no—
122C2×(C2×D43)⋊C4—21no—
123C2×(C2×D43)⋊C4D411yescharacteristic
124C2×C4×Dic43—21no—
125C2×C4×Dic43C2311yescharacteristic
126#13063259—22no—
127#13063250—22no—
128#13063250—22no—
129#13063249—22no—
130#13063249—22no—
131#13063248—22no—
132#13063248—41no—
133C22⋊(C43⋊C8)—22no—
134(C2×D43)⋊C8—22no—
135(C2×D43)⋊C8—41no—
136C43⋊#95—21no—
137C43⋊#95—21no—
138C43⋊#95—21no—
139C43⋊#95—21no—
140C22×Q8×C43—22no—
141C22×Q8×C43—21no—
142C22×Q8×C43—22no—
143C22×Q8×C43—22no—
144C22×Q8×C43—41no—
145C22×Q8×C43—41no—
146C22×Q8×C43D414yes—
147C22×Q8×C43C2311yescharacteristic
148C22×Q8×C43C2311yescharacteristic
149C23×C4×C43—21no—
150C23×C4×C43—21no—
151C23×C4×C43C2311yescharacteristic
152C22×C8×C43—22no—
153C22×C8×C43—22no—
154C22×C8×C43—41no—
155C22×C8×C43C2311yescharacteristic
156C22×C8×C43C2311yescharacteristic
157C2×C4⋊C4×C43—22no—
158C2×C4⋊C4×C43—21no—
159C2×C4⋊C4×C43—41no—
160C2×C4⋊C4×C43C2311yescharacteristic
161C2×C4⋊C4×C43C2311yescharacteristic
162#103×C43—22no—
163#103×C43—22no—
164#103×C43—22no—
165#103×C43D414yescomplemented
166C24×C43C2×D411yescharacteristic
167C23×D43C2×D411yescharacteristic
168C2×Q8×C43—24no—
169C2×Q8×C43—21no—
170C2×Q8×C43—21no—
171C2×Q8×C43—21no—
172C2×Q8×C43—21no—
173C2×Q8×C43—28no—
174C2×Q8×C43—21no—
175C2×Q8×C43—21no—
176C2×Q8×C43—21no—
177C2×Q8×C43—21no—
178C2×Q8×C43—42no—
179C2×Q8×C43—42no—
180C2×Q8×C43—44no—
181C2×Q8×C43—44no—
182C2×Q8×C43—44no—
183C2×Q8×C43C2×D412yes—
184C2×Q8×C43C2×D412yes—
185C2×Q8×C43C2×D412yes—
186C2×Q8×C43#4112yes—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—24no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—42no—
197C22×C4×C43—42no—
198C22×C4×C43—42no—
199C22×C4×C43—42no—
200C22×C4×C43—81no—
201C22×C4×C43C2×D412yes—
202C22×C4×C43C2×D412yes—
203C22×C4×C43C2×D411yescharacteristic
204C22×C4×C43C2411yescharacteristic
205C2×C22⋊D43—22no—
206C2×C22⋊D43—22no—
207C2×C22⋊D43Q1614yescomplemented
208C22×Dic43—21no—
209C22×Dic43—21no—
210C22×Dic43—21no—
211C22×Dic43—21no—
212C22×Dic43C2×D411yescharacteristic
213C22×Dic43C2×D411yescharacteristic
214C22×Dic43C2×D411yescharacteristic
215Q8×D43—44no—
216Q8×D43—44no—
217Q8×D43—44no—
218Q8×D43—44no—
219C2×C4×D43—24no—
220C2×C4×D43—21no—
221C2×C4×D43—21no—
222C2×C4×D43—21no—
223C2×C4×D43—21no—
224C2×C4×D43—21no—
225C2×C4×D43—21no—
226C2×C4×D43—42no—
227C2×C4×D43—42no—
228C2×Dic86—21no—
229C2×Dic86—21no—
230C2×Dic86—21no—
231C2×Dic86—21no—
232C2×Dic86—24no—
233C2×Dic86—21no—
234C2×Dic86—21no—
235C2×Dic86—21no—
236C2×Dic86—21no—
237C2×Dic86—21no—
238C2×Dic86—21no—
239C2×Dic86—21no—
240C2×Dic86—42no—
241C2×Dic86—42no—
242C2×Dic86C2×D412yes—
243C2×C8×C43—21no—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C2×C8×C43—44no—
249C2×C8×C43C2×D412yes—
250C4⋊C4×C43—21no—
251C4⋊C4×C43—21no—
252C4⋊C4×C43—21no—
253C4⋊C4×C43—42no—
254C4⋊C4×C43C2×D412yes—
255C22⋊Dic43—24no—
256C22⋊Dic43—22no—
257C22⋊Dic43—42no—
258#10621885—44no—
259#10621885—44no—
260(C2×D43)⋊C4—24no—
261(C2×D43)⋊C4—22no—
262(C2×D43)⋊C4—42no—
263(C2×D43)⋊C4—81no—
264C4⋊Dic43—24no—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43—21no—
268C4⋊Dic43—42no—
269C4⋊Dic43—81no—
270C4⋊Dic43C2×D412yes—
271Dic43⋊C4—24no—
272Dic43⋊C4—24no—
273Dic43⋊C4—24no—
274Dic43⋊C4—24no—
275Dic43⋊C4—22no—
276Dic43⋊C4—42no—
277C4×Dic43—24no—
278C4×Dic43—21no—
279C4×Dic43—21no—
280C2×C43⋊C8—21no—
281C2×C43⋊C8—21no—
282C2×C43⋊C8—21no—
283C2×C43⋊C8—21no—
284C2×C43⋊C8—21no—
285C2×C43⋊C8—21no—
286Dic172—44no—
287C23×C43—21no—
288C23×C43—21no—
289C23×C43—21no—
290C23×C43—21no—
291C23×C43#12012yes—
292C23×C43C2×Q1612yes—
293C23×C43#13712yes—
294C23×C43C22×D411yescharacteristic
295C22×D43—21no—
296C22×D43—21no—
297C22×D43—21no—
298C22×D43—21no—
299C22×D43—21no—
300C22×D43—21no—
301C22×D43C2×Q1612yes—
302Q8×C43—22no—
303Q8×C43—22no—
304Q8×C43—22no—
305Q8×C43—22no—
306Q8×C43—22no—
307Q8×C43—48no—
308Q8×C43—41no—
309Q8×C43—41no—
310Q8×C43#12114yes—
311C2×C4×C43—22no—
312C2×C4×C43—21no—
313C2×C4×C43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—21no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—48no—
323C2×C4×C43—41no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
326C2×C4×C43—41no—
327C2×C4×C43—41no—
328C2×C4×C43—41no—
329C2×C4×C43—41no—
330C2×C4×C43—84no—
331C2×C4×C43#12012yes—
332C2×C4×C43C22×D411yescharacteristic
333C2×C4×C43C22×D411yescharacteristic
334C2×C4×C43C22×D411yescharacteristic
335C2×C4×C43C2×#4111yescharacteristic
336C2×C4×C43H(5,𝔽2)11yescharacteristic
337C2×C4×C43H(5,𝔽2)11yescharacteristic
338C22⋊D43—28no—
339C2×Dic43—21no—
340C2×Dic43—21no—
341C2×Dic43—21no—
342C2×Dic43—22no—
343C2×Dic43—21no—
344C2×Dic43—22no—
345C2×Dic43—21no—
346C2×Dic43—21no—
347C2×Dic43—21no—
348C2×Dic43—21no—
349C2×Dic43—41no—
350C2×Dic43—41no—
351C2×Dic43—41no—
352C2×Dic43—41no—
353C2×Dic43—41no—
354C2×Dic43—41no—
355C2×Dic43—41no—
356C2×Dic43—41no—
357C2×Dic43—41no—
358C2×Dic43—41no—
359C2×Dic43C2×Q1612yes—
360C4×D43—48no—
361C4×D43—41no—
362C4×D43—41no—
363C4×D43—41no—
364C4×D43—41no—
365Dic86—22no—
366Dic86—22no—
367Dic86—48no—
368Dic86—41no—
369Dic86—41no—
370Dic86—41no—
371Dic86—41no—
372Dic86—41no—
373Dic86—41no—
374C8×C43—22no—
375C8×C43—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#45114yescomplemented
386C22×C43C2×#12011yescharacteristic
387C22×C43D4211yescharacteristic
388C22×C43#54611yescharacteristic
389C22×C43C22×Q1611yescharacteristic
390C22×C43C2×#13711yescharacteristic
391C22×C43#57711yescharacteristic
392C22×C43#57811yescharacteristic
393C2×D43—22no—
394C2×D43—22no—
395C2×D43—22no—
396C2×D43—41no—
397C2×D43—41no—
398C2×D43—41no—
399C2×D43—41no—
400C4×C43—24no—
401C4×C43—22no—
402C4×C43—42no—
403C4×C43—42no—
404C4×C43—81no—
405C4×C43C2×#12111yescharacteristic
406C4×C43#53411yescharacteristic
407C4×C43D4211yescharacteristic
408C4×C43#54611yescharacteristic
409Dic43—22no—
410Dic43—42no—
411Dic43—41no—
412Dic43—41no—
413Dic43—42no—
414Dic43—81no—
415Dic43—81no—
416C2×D4×Q8—431no—
417C2×#467—431no—
418C2×#451—431no—
419C2×#451—431no—
420C22×#103D4311yescharacteristic, complemented
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#241011yescharacteristic
433C2×C43C2×#45111yescharacteristic
434C2×C43#301311yescharacteristic
435C2×C43#326611yescharacteristic
436C2×C43D4×Q1611yescharacteristic
437C2×C43#329911yescharacteristic
438C2×C43#331211yescharacteristic
439D43—42no—
440C23×Q8—431no—
441C23×Q8C2×D4311yescharacteristic
442C22×Q16—431no—
443C22×Q16—431no—
444C22×Q16—431no—
445C23×C8C2×D4311yescharacteristic
446D4×Q8—864no—
447D4×Q8—864no—
448C2×C4⋊Q8—431no—
449C2×C4⋊Q8—861no—
450C2×C22⋊Q8—431no—
451C2×C22⋊Q8—431no—
452C2×C22⋊Q8—431no—
453C2×C22⋊Q8—431no—
454C2×C22⋊Q8—861no—
455C2×C22⋊Q8—861no—
456C2×C4×Q8—431no—
457C2×C4×D4—431no—
458C2×C4×D4—861no—
459C22×C4⋊C4C2×D4311yescharacteristic
460#467—864no—
461#451—864no—
462#451—864no—
463C2×#107—431no—
464C2×#103—24no—
465C2×#103—431no—
466C2×#103—431no—
467C2×#103—431no—
468C2×#103—431no—
469C2×#103—431no—
470C2×#103—431no—
471C2×#103C2×D4311yescharacteristic
472C2×#103C2×D4311yescharacteristic
473C2×#103C2×D4311yescharacteristic
474C2×#103C2×D4311yescharacteristic
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—21no—
491C22×Q8—22no—
492C22×Q8—22no—
493C22×Q8—22no—
494C22×Q8—41no—
495C22×Q8—41no—
496C22×Q8—431no—
497C22×Q8—431no—
498C22×Q8—861no—
499C22×Q8—862no—
500C22×Q8—862no—
501C22×Q8—862no—
502C22×Q8—862no—
503C22×Q8—1721no—
504C22×Q8—1721no—
505C22×Q8D17214yes—
506C22×Q8C22×D4311yescharacteristic
507C22×Q8C22×D4311yescharacteristic
508C22×D4—431no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—431no—
512C23×C4—861no—
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—22no—
524C22×C8—22no—
525C22×C8—41no—
526C22×C8—431no—
527C22×C8—431no—
528C22×C8C22×D4311yescharacteristic
529C22×C8C22×D4311yescharacteristic
530C4⋊Q8—862no—
531C4⋊Q8—868no—
532C4⋊Q8—862no—
533C22⋊Q8—434no—
534C22⋊Q8—862no—
535C22⋊Q8—868no—
536C22⋊Q8—868no—
537C22⋊Q8—862no—
538C22⋊Q8—862no—
539C22⋊Q8—862no—
540C22⋊Q8—862no—
541C22⋊Q8—862no—
542C22⋊Q8—1721no—
543C4×Q8—862no—
544C4×Q8—862no—
545C4×D4—868no—
546C4×D4—862no—
547C4×D4—862no—
548C2×C4⋊C4—22no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—41no—
551C2×C4⋊C4—431no—
552C2×C4⋊C4—431no—
553C2×C4⋊C4—431no—
554C2×C4⋊C4—861no—
555C2×C4⋊C4—861no—
556C2×C4⋊C4—861no—
557C2×C4⋊C4—861no—
558C2×C4⋊C4—861no—
559C2×C4⋊C4—861no—
560C2×C4⋊C4—861no—
561C2×C4⋊C4—861no—
562C2×C4⋊C4C22×D4311yescharacteristic
563C2×C4⋊C4C22×D4311yescharacteristic
564C2×C22⋊C4—431no—
565C2×C22⋊C4—431no—
566C2×C22⋊C4—861no—
567C2×C22⋊C4—861no—
568C2×C22⋊C4—861no—
569C2×C22⋊C4—861no—
570C2×C22⋊C4—861no—
571C2×C42—431no—
572C2×C42—861no—
573#107—862no—
574#103—22no—
575#103—22no—
576#103—22no—
577#103—862no—
578#103—862no—
579#103—862no—
580#103—862no—
581#103—862no—
582#103—1721no—
583#103C22⋊D4314yescomplemented
584C22⋊C8—862no—
585C22⋊C8—862no—
586C22⋊C8—1721no—
587#95—861no—
588#95—861no—
589#95—861no—
590#95—861no—
591C24—431no—
592C24D4×D4311yescharacteristic
593C2×Q8—24no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—28no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—42no—
604C2×Q8—42no—
605C2×Q8—44no—
606C2×Q8—44no—
607C2×Q8—44no—
608C2×Q8—432no—
609C2×Q8—864no—
610C2×Q8—861no—
611C2×Q8—861no—
612C2×Q8—861no—
613C2×Q8—861no—
614C2×Q8—861no—
615C2×Q8—861no—
616C2×Q8—861no—
617C2×Q8—861no—
618C2×Q8—861no—
619C2×Q8—861no—
620C2×Q8—861no—
621C2×Q8—1722no—
622C2×Q8—1722no—
623C2×Q8—1724no—
624C2×Q8—1724no—
625C2×Q8—1724no—
626C2×Q8—1724no—
627C2×Q8C2×D17212yes—
628C2×Q8C2×D17212yes—
629C2×Q8#1062189812yes—
630C2×Q8C2×C22⋊D4312yes—
631C2×D4—434no—
632C2×D4—862no—
633C2×D4—862no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—24no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—42no—
644C22×C4—42no—
645C22×C4—42no—
646C22×C4—42no—
647C22×C4—81no—
648C22×C4—431no—
649C22×C4—431no—
650C22×C4—431no—
651C22×C4—864no—
652C22×C4—861no—
653C22×C4—861no—
654C22×C4—861no—
655C22×C4—861no—
656C22×C4—861no—
657C22×C4—861no—
658C22×C4—861no—
659C22×C4—861no—
660C22×C4—861no—
661C22×C4—861no—
662C22×C4—1722no—
663C22×C4—1722no—
664C22×C4C2×D17212yes—
665C22×C4D4×D4311yescharacteristic
666C22×C4D4×D4312yes—
667C22×C4C23×D4311yescharacteristic
668Q16—1724no—
669Q16—1724no—
670Q16—1724no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—44no—
677C2×C8—861no—
678C2×C8—861no—
679C2×C8—861no—
680C2×C8—861no—
681C2×C8—861no—
682C2×C8—861no—
683C2×C8C2×C22⋊D4312yes—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—42no—
688C4⋊C4—432no—
689C4⋊C4—864no—
690C4⋊C4—864no—
691C4⋊C4—864no—
692C4⋊C4—864no—
693C4⋊C4—862no—
694C4⋊C4—864no—
695C4⋊C4—861no—
696C4⋊C4—861no—
697C4⋊C4—861no—
698C4⋊C4—3441no—
699C4⋊C4—1722no—
700C4⋊C4—1722no—
701C4⋊C4C2×C22⋊D4312yes—
702C22⋊C4—864no—
703C22⋊C4—862no—
704C22⋊C4—864no—
705C22⋊C4—862no—
706C22⋊C4—3441no—
707C22⋊C4—1722no—
708C22⋊C4—1722no—
709C42—864no—
710C42—861no—
711C42—861no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—432no—
717C23—861no—
718C23—861no—
719C23—861no—
720C23—861no—
721C23—861no—
722C23—861no—
723C23#1306329512yes—
724C23Q16×D4312yes—
725C23#1306335412yes—
726C23C2×D4×D4311yescharacteristic
727Q8—22no—
728Q8—22no—
729Q8—22no—
730Q8—22no—
731Q8—22no—
732Q8—48no—
733Q8—41no—
734Q8—41no—
735Q8—862no—
736Q8—862no—
737Q8—1728no—
738Q8—1721no—
739Q8—1721no—
740Q8—1721no—
741Q8—1721no—
742Q8—1721no—
743Q8—1721no—
744Q8#1306329914yes—
745D4—868no—
746C2×C4—22no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—21no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—48no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—84no—
766C2×C4—432no—
767C2×C4—861no—
768C2×C4—861no—
769C2×C4—862no—
770C2×C4—861no—
771C2×C4—861no—
772C2×C4—862no—
773C2×C4—861no—
774C2×C4—861no—
775C2×C4—861no—
776C2×C4—861no—
777C2×C4—1728no—
778C2×C4—1721no—
779C2×C4—1721no—
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—1721no—
792C2×C4#1306329512yes—
793C2×C4C2×D4×D4311yescharacteristic
794C2×C4C22×C22⋊D4311yescharacteristic
795C2×C4C22×D17211yescharacteristic
796C2×C4C2×#1062189811yescharacteristic
797C2×C4#1306337011yescharacteristic
798C2×C4#1306337011yescharacteristic
799C8—22no—
800C8—41no—
801C8—1721no—
802C8—1721no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—862no—
810C22—862no—
811C22—862no—
812C22—1721no—
813C22—1721no—
814C22—1721no—
815C22—1721no—
816C22#1458305614yescomplemented
817C22C2×#1306329511yescharacteristic
818C22D4×C22⋊D4311yescharacteristic
819C22#1458353911yescharacteristic
820C22C2×Q16×D4311yescharacteristic
821C22C2×#1306335411yescharacteristic
822C22#1458370511yescharacteristic
823C22#1458371211yescharacteristic
824C4—22no—
825C4—24no—
826C4—42no—
827C4—42no—
828C4—81no—
829C4—862no—
830C4—3441no—
831C4—3441no—
832C4—1721no—
833C4—1722no—
834C4—1721no—
835C4—1722no—
836C4C2×#1306329911yescharacteristic
837C4#1458346111yescharacteristic
838C4D4×C22⋊D4311yescharacteristic
839C4#1458353911yescharacteristic
840C2—24no—
841C2—1722no—
842C2#1913796311yescharacteristic
843C2C2×#1458305611yescharacteristic
844C2#1914391511yescharacteristic
845C2#1914610511yescharacteristic
846C2Q16×C22⋊D4311yescharacteristic
847C2#1914646711yescharacteristic
848C2#1914664211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC22×#103×C43C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
hypercenterC22×#103D43
hypocenterC43#24437
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
2. C2×#14583140C2semidirect
3. C2×#14583056C2semidirect
4. C2×#14583055C2semidirect
6. #19135840C2semidirect
7. #19135797C2semidirect
8. #19135696C2semidirect
9. #19135604C2semidirect
10. #19134934C2semidirect
11. #19134902C2semidirect
13. #19134851C2semidirect
14. #19134528C2semidirect
15. C22×#103×C43C2semidirect
165. #103×C43D4semidirect
207. C2×C22⋊D43Q16semidirect
385. C22×C43#451semidirect
420. C22×#103D43semidirect
489. C43#24437semidirect
583. #103C22⋊D43semidirect
816. C22#14583056semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C22⋊D432
C2×#145831402
C2×#145830562
C2×#145830552
#191380402
#191358402
#191357972
#191356962
#191356042
#191349342
#191349022
#191348872
#191348512
#191345282
C22×#103×C432
#2443743