Finite Group Databasebeta

← #25129308

Subgroups — #25129308

Order 11008.

1428 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D43C211yesmaximal, characteristic
2C2×#14583240C211yesmaximal, characteristic, complemented
3#19136974C211yesmaximal, characteristic
4#19135800C211yesmaximal, characteristic, complemented
5#19135796C211yesmaximal, characteristic, complemented
6#19135793C211yesmaximal, characteristic, complemented
7#19135789C211yesmaximal, characteristic, complemented
8#19134908C211yesmaximal, characteristic, complemented
9#19134905C211yesmaximal, characteristic, complemented
10#19134786C211yesmaximal, characteristic, complemented
11#19134781C211yesmaximal, characteristic, complemented
12#19134528C211yesmaximal, characteristic, complemented
13#19134528C211yesmaximal, characteristic, complemented
14#19134504C211yesmaximal, characteristic
15C2×C43×#485C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C2×#13063305C2211yescharacteristic
19C2×#13063304C2211yescharacteristic
20C2×#13063303—21no—
21C2×#13063302—21no—
22C2×#13063301C2211yescharacteristic
23C22⋊Q8×D43—24no—
24C22⋊Q8×D43—24no—
25C2×#13063284C2211yescharacteristic
26C2×C4⋊C4×D43—21no—
27C2×C4⋊C4×D43C2211yescharacteristic
28C2×C22⋊C4×D43—21no—
29#14583240—24no—
30C2×#13063258C2211yescharacteristic, complemented
31C2×#13063256C2211yescharacteristic, complemented
32C2×#13063250C2211yescharacteristic, complemented
33C2×#13063250C2211yescharacteristic, complemented
34C2×#13063249C2211yescharacteristic, complemented
35C2×#13063249C2211yescharacteristic, complemented
36C2×#13063248C2211yescharacteristic, complemented
37C2×#13063248C2211yescharacteristic, complemented
38C2×C22⋊(C43⋊C8)C2211yescharacteristic
39C2×(C2×D43)⋊C8C2211yescharacteristic
40C2×(C2×D43)⋊C8C2211yescharacteristic
41C2×(C2×D43)⋊C8C2211yescharacteristic
42C2×(C2×D43)⋊C8C2211yescharacteristic
43#14582760—21no—
44#14582756C2211yescharacteristic
45#14582756C2211yescharacteristic
46#14582756C2211yescharacteristic
47#14582756C2211yescharacteristic
48#14582754—21no—
49C4×(C2×D43)⋊C4—21no—
50C4×(C2×D43)⋊C4—21no—
51#14582662C2211yescharacteristic, complemented
52#14582662C2211yescharacteristic, complemented
53#14582661C2211yescharacteristic, complemented
54#14582661C2211yescharacteristic, complemented
55C2×C22⋊Q8×C43C2211yescharacteristic
56C2×#117×C43C2211yescharacteristic
57C43×#485—24no—
58C2×#107×C43C2211yescharacteristic, complemented
59C2×#106×C43C2211yescharacteristic, complemented
60C2×#103×C43C2211yescharacteristic, complemented
61C2×#103×C43C2211yescharacteristic, complemented
62C2×C22⋊C8×C43C2211yescharacteristic
63C24×D43D411yescharacteristic
64C22×Dic86—21no—
65C22×Dic86C2311yescharacteristic
66C2×Q8×D43—22no—
67C2×Q8×D43—22no—
68C2×Q8×D43—22no—
69C2×Q8×D43—22no—
70C2×Q8×D43—41no—
71C2×Q8×D43—41no—
72C23×Dic43D411yescharacteristic
73C22×C4×D43—21no—
74C22×C4×D43—21no—
75C22×C4×D43—22no—
76C22×C4×D43—22no—
77C22×C4×D43—22no—
78C22×C4×D43—22no—
79C22×C4×D43—41no—
80C22×C4×D43—41no—
81C22×C4×D43D411yescharacteristic
82C22×C4×D43D411yescharacteristic
83C22×C4×D43C2311yescharacteristic
84C22×C4×D43C2311yescharacteristic
85C22×C43⋊C8C2311yescharacteristic
86C22×C43⋊C8C2311yescharacteristic
87#13063305—22no—
88#13063305—22no—
89#13063304—22no—
90#13063304D414yes—
91#13063303—28no—
92#13063302—28no—
93#13063301—22no—
94#13063301—22no—
95#13063284—41no—
96#13063284—41no—
97C2×C4⋊Dic43—21no—
98C2×C4⋊Dic43C2311yescharacteristic
99C2×C4⋊Dic43C2311yescharacteristic
100C2×C4⋊Dic43C2311yescharacteristic
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C4⋊C4×D43—28no—
105C4⋊C4×D43—22no—
106C4⋊C4×D43—22no—
107C2×C22⋊Dic43—21no—
108C2×C22⋊Dic43—21no—
109C2×(C2×D43)⋊C4—21no—
110C2×(C2×D43)⋊C4—21no—
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4—21no—
115C22⋊C4×D43—28no—
116C2×C4×Dic43—21no—
117#13063258—22no—
118#13063256—22no—
119#13063250—41no—
120#13063250—41no—
121#13063249—41no—
122#13063249—41no—
123#13063248—22no—
124#13063248—22no—
125C22⋊(C43⋊C8)—22no—
126(C2×D43)⋊C8—22no—
127(C2×D43)⋊C8—22no—
128(C2×D43)⋊C8—41no—
129(C2×D43)⋊C8—41no—
130C43⋊#95—21no—
131C43⋊#95—21no—
132C43⋊#95—21no—
133C43⋊#95—21no—
134C22×Q8×C43C2311yescharacteristic
135C23×C4×C43C2311yescharacteristic
136C22×C8×C43C2311yescharacteristic
137C22×C8×C43C2311yescharacteristic
138C22⋊Q8×C43—22no—
139C22⋊Q8×C43D414yes—
140#117×C43—22no—
141#117×C43—22no—
142C2×C4⋊C4×C43—21no—
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C22⋊C4×C43—21no—
147C2×C22⋊C4×C43—21no—
148C2×C42×C43—21no—
149#107×C43—22no—
150#106×C43—22no—
151#103×C43—22no—
152#103×C43—22no—
153C22⋊C8×C43—22no—
154C24×C43C2×D411yescharacteristic
155C23×D43—22no—
156C23×D43—22no—
157C23×D43—22no—
158C23×D43—22no—
159C23×D43—22no—
160C23×D43—41no—
161C23×D43—41no—
162C23×D43C2×D411yescharacteristic
163C23×D43C2×D411yescharacteristic
164C2×Q8×C43—21no—
165C2×Q8×C43—21no—
166C2×Q8×C43—21no—
167C2×Q8×C43—21no—
168C2×Q8×C43—21no—
169C2×Q8×C43C2×D412yes—
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×C43C2×D412yes—
179C22×C4×C43C2×D412yes—
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43C2411yescharacteristic
182C22×Dic43—22no—
183C22×Dic43—22no—
184C22×Dic43—21no—
185C22×Dic43—21no—
186C22×Dic43—21no—
187C22×Dic43—21no—
188C22×Dic43—41no—
189C22×Dic43C2×D411yescharacteristic
190C22×Dic43C2×D411yescharacteristic
191Q8×D43—44no—
192Q8×D43—44no—
193Q8×D43—44no—
194Q8×D43—44no—
195C2×C4×D43—21no—
196C2×C4×D43—21no—
197C2×C4×D43—21no—
198C2×C4×D43—21no—
199C2×C4×D43—24no—
200C2×C4×D43—24no—
201C2×C4×D43—22no—
202C2×C4×D43—22no—
203C2×C4×D43—21no—
204C2×C4×D43—21no—
205C2×C4×D43—21no—
206C2×C4×D43—21no—
207C2×C4×D43—21no—
208C2×C4×D43—21no—
209C2×C4×D43—22no—
210C2×C4×D43—22no—
211C2×C4×D43—41no—
212C2×C4×D43—41no—
213C2×C4×D43—42no—
214C2×C4×D43—42no—
215C2×C4×D43—44no—
216C2×C4×D43—44no—
217C2×C4×D43—44no—
218C2×C4×D43—44no—
219C2×C4×D43—42no—
220C2×C4×D43—42no—
221C2×C4×D43#4112yes—
222C2×C4×D43#4112yes—
223C2×Dic86—21no—
224C2×Dic86—21no—
225C2×Dic86—21no—
226C2×Dic86—21no—
227C2×Dic86—24no—
228C2×Dic86—21no—
229C2×Dic86—42no—
230C2×Dic86—42no—
231C2×Dic86C2×D412yes—
232C2×C8×C43—21no—
233C2×C8×C43—21no—
234C2×C8×C43—21no—
235C2×C8×C43—21no—
236C2×C8×C43—21no—
237C2×C8×C43—21no—
238C4⋊C4×C43—24no—
239C4⋊C4×C43—21no—
240C4⋊C4×C43—21no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43—21no—
243C4⋊C4×C43—21no—
244C4⋊C4×C43C2×D412yes—
245C22⋊C4×C43—24no—
246C22⋊C4×C43—42no—
247C42×C43—42no—
248C22⋊Dic43—24no—
249C22⋊Dic43—42no—
250(C2×D43)⋊C4—24no—
251(C2×D43)⋊C4—24no—
252(C2×D43)⋊C4—42no—
253(C2×D43)⋊C4—42no—
254(C2×D43)⋊C4—42no—
255(C2×D43)⋊C4—42no—
256C4⋊Dic43—24no—
257C4⋊Dic43—21no—
258C4⋊Dic43—21no—
259C4⋊Dic43—21no—
260C4⋊Dic43—21no—
261C4⋊Dic43—21no—
262C4⋊Dic43C2×D412yes—
263Dic43⋊C4—24no—
264Dic43⋊C4—24no—
265Dic43⋊C4—24no—
266C4×Dic43—42no—
267C2×C43⋊C8—21no—
268C2×C43⋊C8—21no—
269C2×C43⋊C8—21no—
270C2×C43⋊C8—21no—
271C2×C43⋊C8—21no—
272C2×C43⋊C8—21no—
273C23×C43—21no—
274C23×C43—21no—
275C23×C43—21no—
276C23×C43—21no—
277C23×C43—21no—
278C23×C43—21no—
279C23×C43#12012yes—
280C23×C43C22×D411yescharacteristic
281C22×D43—21no—
282C22×D43—21no—
283C22×D43—21no—
284C22×D43—21no—
285C22×D43—28no—
286C22×D43—21no—
287C22×D43—21no—
288C22×D43—21no—
289C22×D43—21no—
290C22×D43—21no—
291C22×D43—21no—
292C22×D43—44no—
293C22×D43—44no—
294C22×D43—44no—
295C22×D43—44no—
296C22×D43—44no—
297C22×D43—44no—
298C22×D43#12312yes—
299C22×D43#13512yes—
300C22×D43#13712yes—
301C22×D43#13712yes—
302Q8×C43—22no—
303Q8×C43—22no—
304Q8×C43—41no—
305Q8×C43—41no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
308C2×C4×C43—22no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—41no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43—41no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43—41no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
324C2×C4×C43#12012yes—
325C2×C4×C43C22×D411yescharacteristic
326C2×C4×C43C22×D411yescharacteristic
327C2×C4×C43C2×#4111yescharacteristic
328C2×C4×C43C2×#4111yescharacteristic
329C2×C4×C43H(5,𝔽2)11yescharacteristic
330C2×C4×C43H(5,𝔽2)11yescharacteristic
331C2×Dic43—21no—
332C2×Dic43—21no—
333C2×Dic43—22no—
334C2×Dic43—21no—
335C2×Dic43—22no—
336C2×Dic43—21no—
337C2×Dic43—21no—
338C2×Dic43—44no—
339C2×Dic43—41no—
340C2×Dic43—41no—
341C2×Dic43—41no—
342C2×Dic43—41no—
343C2×Dic43—41no—
344C2×Dic43—41no—
345C2×Dic43—41no—
346C2×Dic43—41no—
347C2×Dic43—41no—
348C2×Dic43—41no—
349C2×Dic43#12312yes—
350C4×D43—22no—
351C4×D43—22no—
352C4×D43—22no—
353C4×D43—22no—
354C4×D43—44no—
355C4×D43—44no—
356C4×D43—48no—
357C4×D43—48no—
358C4×D43—41no—
359C4×D43—41no—
360C4×D43—41no—
361C4×D43—41no—
362Dic86—22no—
363Dic86—22no—
364Dic86—48no—
365Dic86—41no—
366Dic86—41no—
367C8×C43—41no—
368C8×C43—41no—
369C43⋊C8—41no—
370C43⋊C8—41no—
371#24010—431nomaximal, Sylow
372C22×C43—22no—
373C22×C43—22no—
374C22×C43—22no—
375C22×C43—41no—
376C22×C43—41no—
377C22×C43—41no—
378C22×C43—41no—
379C22×C43C2×#12011yescharacteristic
380C22×C43C2×#12311yescharacteristic
381C22×C43#53411yescharacteristic
382C22×C43C2×#13511yescharacteristic
383C22×C43C2×#13711yescharacteristic
384C22×C43C2×#13711yescharacteristic
385C22×C43#57511yescharacteristic
386C2×D43—22no—
387C2×D43—22no—
388C2×D43—22no—
389C2×D43—22no—
390C2×D43—22no—
391C2×D43—22no—
392C2×D43—22no—
393C2×D43—22no—
394C2×D43—22no—
395C2×D43—416no—
396C2×D43—41no—
397C2×D43—41no—
398C2×D43—41no—
399C2×D43—41no—
400C2×D43#48514yescomplemented
401C4×C43—22no—
402C4×C43—42no—
403C4×C43—42no—
404C4×C43—81no—
405C4×C43—81no—
406C4×C43#54611yescharacteristic
407C4×C43#54611yescharacteristic
408C4×C43#54611yescharacteristic
409C4×C43#54611yescharacteristic
410Dic43—22no—
411Dic43—42no—
412Dic43—41no—
413Dic43—42no—
414Dic43—81no—
415Dic43—81no—
416C22×C22⋊Q8—431no—
417C2×#485—431no—
418C2×#485D4311yescharacteristic, complemented
419#2280—431no—
420#2036—431no—
421#2036—431no—
422#2035—431no—
423#2035—431no—
424#1873—431no—
425#1873—431no—
426#1853—431no—
427#1852—431no—
428#1787—431no—
429#1787—431no—
430#1779—431no—
431C2×C43—42no—
432C2×C43#240511yescharacteristic
433C2×C43#300211yescharacteristic
434C2×C43#300411yescharacteristic
435C2×C43C2×#48511yescharacteristic
436C2×C43#309511yescharacteristic
437C2×C43#319011yescharacteristic
438C2×C43#319611yescharacteristic
439D43—24no—
440D43—42no—
441C23×Q8—431no—
442C24×C4—431no—
443C2×C22⋊Q8—431no—
444C2×C22⋊Q8—431no—
445C2×C22⋊Q8—431no—
446C2×C22⋊Q8—861no—
447C2×C22⋊Q8—861no—
448C2×C22⋊Q8—864no—
449C2×C22⋊Q8—864no—
450C2×C22⋊Q8C2×D4311yescharacteristic
451C2×#117—431no—
452C2×#117C2×D4311yescharacteristic
453C22×C4⋊C4—431no—
454C22×C4⋊C4—861no—
455C22×C22⋊C4—861no—
456#485—24no—
457#485—864no—
458C2×#107—431no—
459C2×#107C2×D4311yescharacteristic, complemented
460C2×#106—431no—
461C2×#106C2×D4311yescharacteristic, complemented
462C2×#103—431no—
463C2×#103—431no—
464C2×#103—431no—
465C2×#103—431no—
466C2×#103—431no—
467C2×#103—431no—
468C2×#103C2×D4311yescharacteristic, complemented
469C2×#103C2×D4311yescharacteristic, complemented
470C2×C22⋊C8—431no—
471C2×C22⋊C8—431no—
472C2×C22⋊C8—431no—
473C2×C22⋊C8—431no—
474C2×C22⋊C8—431no—
475C2×C22⋊C8C2×D4311yescharacteristic
476#381—861no—
477#380—431no—
478#380—431no—
479#380—431no—
480#380—431no—
481#379—861no—
482C4×C22⋊C4—861no—
483C4×C22⋊C4—861no—
484#340—431no—
485#340—431no—
486#340—431no—
487#340—431no—
488C43#2401011yescharacteristic, complemented, Sylow
489C25—431no—
490C22×Q8—431no—
491C22×Q8—861no—
492C22×Q8—862no—
493C22×Q8—862no—
494C22×Q8—862no—
495C22×Q8—862no—
496C22×Q8—1721no—
497C22×Q8—1721no—
498C22×Q8C22×D4311yescharacteristic
499C23×C4—431no—
500C23×C4—431no—
501C23×C4—431no—
502C23×C4—431no—
503C23×C4—431no—
504C23×C4—862no—
505C23×C4—862no—
506C23×C4—861no—
507C23×C4—861no—
508C23×C4—862no—
509C23×C4—862no—
510C23×C4—1721no—
511C23×C4—1721no—
512C23×C4C22×D4311yescharacteristic
513C22×C8—431no—
514C22×C8—431no—
515C22×C8C22×D4311yescharacteristic
516C22×C8C22×D4311yescharacteristic
517C22⋊Q8—22no—
518C22⋊Q8—434no—
519C22⋊Q8—868no—
520C22⋊Q8—862no—
521C22⋊Q8—868no—
522C22⋊Q8—862no—
523C22⋊Q8—862no—
524C22⋊Q8—862no—
525C22⋊Q8—862no—
526C22⋊Q8C22⋊D4314yes—
527#117—22no—
528#117—22no—
529#117—1721no—
530#117—1721no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—431no—
533C2×C4⋊C4—431no—
534C2×C4⋊C4—431no—
535C2×C4⋊C4—862no—
536C2×C4⋊C4—868no—
537C2×C4⋊C4—861no—
538C2×C4⋊C4—861no—
539C2×C4⋊C4—861no—
540C2×C4⋊C4—861no—
541C2×C4⋊C4—862no—
542C2×C4⋊C4C22×D4311yescharacteristic
543C2×C4⋊C4C22×D4311yescharacteristic
544C2×C4⋊C4C22×D4311yescharacteristic
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—868no—
548C2×C22⋊C4—861no—
549C2×C22⋊C4—861no—
550C2×C22⋊C4—861no—
551C2×C22⋊C4—861no—
552C2×C22⋊C4—861no—
553C2×C22⋊C4—861no—
554C2×C22⋊C4—861no—
555C2×C22⋊C4—861no—
556C2×C42—21no—
557C2×C42—861no—
558#107—22no—
559#107—862no—
560#106—22no—
561#106—862no—
562#103—22no—
563#103—22no—
564#103—862no—
565#103—862no—
566#103—1721no—
567#103—1721no—
568#103—1721no—
569#103—1721no—
570C22⋊C8—22no—
571C22⋊C8—862no—
572C22⋊C8—862no—
573C22⋊C8—862no—
574C22⋊C8—1721no—
575C22⋊C8—1721no—
576#95—861no—
577#95—861no—
578#95—861no—
579#95—861no—
580C24—431no—
581C24—431no—
582C24—862no—
583C24—862no—
584C24—862no—
585C24—862no—
586C24—862no—
587C24—1721no—
588C24—1721no—
589C24D4×D4311yescharacteristic
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—432no—
596C2×Q8—864no—
597C2×Q8—861no—
598C2×Q8—861no—
599C2×Q8—861no—
600C2×Q8—861no—
601C2×Q8—861no—
602C2×Q8—1722no—
603C2×Q8—1722no—
604C2×Q8—1724no—
605C2×Q8—1724no—
606C2×Q8—1724no—
607C2×Q8—1724no—
608C2×Q8C2×C22⋊D4312yes—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—431no—
618C22×C4—432no—
619C22×C4—432no—
620C22×C4—431no—
621C22×C4—862no—
622C22×C4—862no—
623C22×C4—864no—
624C22×C4—864no—
625C22×C4—862no—
626C22×C4—861no—
627C22×C4—861no—
628C22×C4—861no—
629C22×C4—861no—
630C22×C4—862no—
631C22×C4—861no—
632C22×C4—861no—
633C22×C4—862no—
634C22×C4—862no—
635C22×C4—861no—
636C22×C4—861no—
637C22×C4—861no—
638C22×C4—861no—
639C22×C4—861no—
640C22×C4—861no—
641C22×C4—861no—
642C22×C4—861no—
643C22×C4—1721no—
644C22×C4—1721no—
645C22×C4—1724no—
646C22×C4—1724no—
647C22×C4—1724no—
648C22×C4—1724no—
649C22×C4—1722no—
650C22×C4—1722no—
651C22×C4—1722no—
652C22×C4—1722no—
653C22×C4—1721no—
654C22×C4D4×D4311yescharacteristic
655C22×C4D4×D4312yes—
656C22×C4C2×C22⋊D4312yes—
657C22×C4C23×D4311yescharacteristic
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—861no—
665C2×C8—861no—
666C2×C8—861no—
667C2×C8—861no—
668C2×C8—861no—
669C2×C8—861no—
670C4⋊C4—24no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—432no—
677C4⋊C4—864no—
678C4⋊C4—864no—
679C4⋊C4—864no—
680C4⋊C4—864no—
681C4⋊C4—861no—
682C4⋊C4—861no—
683C4⋊C4—861no—
684C4⋊C4—861no—
685C4⋊C4—861no—
686C4⋊C4C2×C22⋊D4312yes—
687C22⋊C4—24no—
688C22⋊C4—42no—
689C22⋊C4—864no—
690C22⋊C4—864no—
691C22⋊C4—864no—
692C22⋊C4—1722no—
693C22⋊C4—1722no—
694C22⋊C4—1722no—
695C22⋊C4—1722no—
696C22⋊C4—1722no—
697C42—42no—
698C42—1722no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—432no—
706C23—432no—
707C23—432no—
708C23—432no—
709C23—868no—
710C23—861no—
711C23—861no—
712C23—861no—
713C23—861no—
714C23—861no—
715C23—861no—
716C23—861no—
717C23—861no—
718C23—861no—
719C23—861no—
720C23—1724no—
721C23—1724no—
722C23—1724no—
723C23—1724no—
724C23—1724no—
725C23—1724no—
726C23#1306329312yes—
727C23C2×D4×D4311yescharacteristic
728Q8—22no—
729Q8—22no—
730Q8—41no—
731Q8—41no—
732Q8—862no—
733Q8—862no—
734Q8—1728no—
735Q8—1721no—
736Q8—1721no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—432no—
756C2×C4—861no—
757C2×C4—861no—
758C2×C4—862no—
759C2×C4—862no—
760C2×C4—862no—
761C2×C4—862no—
762C2×C4—862no—
763C2×C4—862no—
764C2×C4—861no—
765C2×C4—861no—
766C2×C4—861no—
767C2×C4—1724no—
768C2×C4—1724no—
769C2×C4—1728no—
770C2×C4—1728no—
771C2×C4—1724no—
772C2×C4—1721no—
773C2×C4—1721no—
774C2×C4—1721no—
775C2×C4—1721no—
776C2×C4—1721no—
777C2×C4—1721no—
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#1306329312yes—
787C2×C4C2×D4×D4311yescharacteristic
788C2×C4C22×C22⋊D4311yescharacteristic
789C2×C4#41×D4311yescharacteristic
790C2×C4#41×D4311yescharacteristic
791C2×C4#1306337111yescharacteristic
792C2×C4#1306337111yescharacteristic
793C8—41no—
794C8—41no—
795C8—1721no—
796C8—1721no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—434no—
805C22—862no—
806C22—862no—
807C22—862no—
808C22—862no—
809C22—862no—
810C22—862no—
811C22—862no—
812C22—862no—
813C22—862no—
814C22—17216no—
815C22—1721no—
816C22—1721no—
817C22—1721no—
818C22—1721no—
819C22C2×#1306329311yescharacteristic
820C22#123×D4311yescharacteristic
821C22#1458346011yescharacteristic
822C22#135×D4311yescharacteristic
823C22#137×D4311yescharacteristic
824C22#137×D4311yescharacteristic
825C22#1458369611yescharacteristic
826C4—22no—
827C4—42no—
828C4—42no—
829C4—81no—
830C4—81no—
831C4—862no—
832C4—3441no—
833C4—3441no—
834C4—1721no—
835C4—1722no—
836C4—1722no—
837C4#1458353711yescharacteristic
838C4#1458353711yescharacteristic
839C4#1458354111yescharacteristic
840C4#1458354111yescharacteristic
841C2—42no—
842C2—864no—
843C2—1722no—
844C2#1913791911yescharacteristic
845C2#1914380911yescharacteristic
846C2#1914382711yescharacteristic
847C2#485×D4311yescharacteristic
848C2#1914454211yescharacteristic
849C2#1914538011yescharacteristic
850C2#1914542911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#485C2
socleC23×C43C22×D4
prime radicalC24×D43D4
hypercenterC2×#485D43
hypocenterC43#24010
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
2. C2×#14583240C2semidirect
4. #19135800C2semidirect
5. #19135796C2semidirect
6. #19135793C2semidirect
7. #19135789C2semidirect
8. #19134908C2semidirect
9. #19134905C2semidirect
10. #19134786C2semidirect
11. #19134781C2semidirect
12. #19134528C2semidirect
13. #19134528C2semidirect
15. C2×C43×#485C2semidirect
30. C2×#13063258C22semidirect
31. C2×#13063256C22semidirect
32. C2×#13063250C22semidirect
33. C2×#13063250C22semidirect
34. C2×#13063249C22semidirect
35. C2×#13063249C22semidirect
36. C2×#13063248C22semidirect
37. C2×#13063248C22semidirect
51. #14582662C22semidirect
52. #14582662C22semidirect
53. #14582661C22semidirect
54. #14582661C22semidirect
58. C2×#107×C43C22semidirect
59. C2×#106×C43C22semidirect
60. C2×#103×C43C22semidirect
61. C2×#103×C43C22semidirect
400. C2×D43#485semidirect
418. C2×#485D43semidirect
459. C2×#107C2×D43semidirect
461. C2×#106C2×D43semidirect
468. C2×#103C2×D43semidirect
469. C2×#103C2×D43semidirect
488. C43#24010semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D432
C2×#145832402
#191369742
#191358002
#191357962
#191357932
#191357892
#191349082
#191349052
#191347862
#191347812
#191345282
#191345042
C2×C43×#4852
#2401043