Finite Group Databasebeta

← #24991975

Subgroups — #24991975

Order 11008.

964 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊C8×D43C211yesmaximal, characteristic
2C2×#14582770C211yesmaximal, characteristic
3#19134504C211yesmaximal, characteristic
4C2×#14582625C211yesmaximal, characteristic, complemented
5#19132437C211yesmaximal, characteristic, complemented
6#19132437C211yesmaximal, characteristic, complemented
7C2×C43×#324C211yesmaximal, characteristic, complemented
8C23×C4×D43C2211yescharacteristic
9C22×C8×D43—21no—
10C22×Dic43⋊C4C411yescharacteristic
11C22×(C2×D43)⋊C4C411yescharacteristic
12C22×(C2×D43)⋊C4C411yescharacteristic
13C2×C22⋊(C43⋊C8)C2211yescharacteristic
14C2×C22⋊(C43⋊C8)C2211yescharacteristic
15C2×(C2×D43)⋊C8—21no—
16C2×(C2×D43)⋊C8—21no—
17C2×(C2×D43)⋊C8—21no—
18C22⋊C8×D43—22no—
19C22⋊C8×D43—22no—
20#14582770—21no—
21#14582770—21no—
22#14582770—21no—
23#14582770—21no—
24C2×C43⋊#95C411yescharacteristic
25C2×C43⋊#95C2211yescharacteristic
26#14582625—22no—
27C22×C4⋊C4×C43C2211yescharacteristic
28C2×C22⋊C8×C43C2211yescharacteristic
29C2×C22⋊C8×C43C2211yescharacteristic
30C43×#324—22no—
31C24×D43C2×C411yescharacteristic
32C23×Dic43C2×C411yescharacteristic
33C23×Dic43C2×C411yescharacteristic
34C23×Dic43C2×C411yescharacteristic
35C22×C4×D43—21no—
36C22×C4×D43—21no—
37C22×C4×D43—21no—
38C22×C4×D43—21no—
39C22×C4×D43—42no—
40C22×C4×D43—42no—
41C22×C4×D43D411yescharacteristic
42C22×C4×D43D411yescharacteristic
43C22×C4×D43D411yescharacteristic
44C22×C4×D43D411yescharacteristic
45C22×C43⋊C8—21no—
46C22×C43⋊C8—21no—
47C2×C8×D43—24no—
48C2×C8×D43—42no—
49C2×C8×D43—42no—
50C2×Dic43⋊C4—21no—
51C2×Dic43⋊C4—21no—
52C2×Dic43⋊C4—42no—
53C2×(C2×D43)⋊C4—21no—
54C2×(C2×D43)⋊C4—21no—
55C2×(C2×D43)⋊C4—22no—
56C2×(C2×D43)⋊C4—21no—
57C2×(C2×D43)⋊C4—21no—
58C2×(C2×D43)⋊C4—42no—
59C2×(C2×D43)⋊C4C814yescomplemented
60C22⋊(C43⋊C8)—21no—
61C22⋊(C43⋊C8)—21no—
62C22⋊(C43⋊C8)—21no—
63C22⋊(C43⋊C8)D412yes—
64(C2×D43)⋊C8—24no—
65(C2×D43)⋊C8—42no—
66(C2×D43)⋊C8—42no—
67C43⋊#95—21no—
68C43⋊#95—21no—
69C43⋊#95—21no—
70C43⋊#95—21no—
71C23×C4×C43C2×C411yescharacteristic
72C23×C4×C43C2×C411yescharacteristic
73C23×C4×C43C2311yescharacteristic
74C22×C8×C43—21no—
75C22×C8×C43—21no—
76C2×C4⋊C4×C43—21no—
77C2×C4⋊C4×C43—21no—
78C2×C4⋊C4×C43—21no—
79C2×C4⋊C4×C43—21no—
80C2×C4⋊C4×C43—21no—
81C2×C4⋊C4×C43—21no—
82C22⋊C8×C43—21no—
83C22⋊C8×C43—21no—
84C22⋊C8×C43—21no—
85C22⋊C8×C43D412yes—
86C24×C43C22×C411yescharacteristic
87C23×D43—21no—
88C23×D43—21no—
89C23×D43—21no—
90C23×D43—21no—
91C23×D43—22no—
92C23×D43—22no—
93C23×D43—41no—
94C23×D43—41no—
95C23×D43C22⋊C411yescharacteristic
96C23×D43C22⋊C411yescharacteristic
97C23×D43C2×C812yes—
98C23×D43M1612yes—
99C22×C4×C43—21no—
100C22×C4×C43—21no—
101C22×C4×C43—21no—
102C22×C4×C43—21no—
103C22×C4×C43—21no—
104C22×C4×C43—21no—
105C22×C4×C43—21no—
106C22×C4×C43—21no—
107C22×C4×C43—21no—
108C22×C4×C43—41no—
109C22×C4×C43—41no—
110C22×C4×C43—41no—
111C22×C4×C43—41no—
112C22×C4×C43C2×C812yescomplemented
113C22×C4×C43C2×D411yescharacteristic
114C22×C4×C43C2×D411yescharacteristic
115C22×C4×C43C2×D411yescharacteristic
116C22×C4×C43C2×D411yescharacteristic
117C22×C4×C43#4111yescharacteristic
118C22×C4×C43#4111yescharacteristic
119C22×Dic43—22no—
120C22×Dic43—21no—
121C22×Dic43—21no—
122C22×Dic43—21no—
123C22×Dic43—21no—
124C22×Dic43—21no—
125C22×Dic43—21no—
126C22×Dic43—21no—
127C22×Dic43—41no—
128C22×Dic43—41no—
129C22×Dic43—41no—
130C22×Dic43—41no—
131C22×Dic43—41no—
132C22×Dic43C22⋊C411yescharacteristic
133C22×Dic43C22⋊C411yescharacteristic
134C22×Dic43C2×C812yescomplemented
135C2×C4×D43—21no—
136C2×C4×D43—21no—
137C2×C4×D43—22no—
138C2×C4×D43—21no—
139C2×C4×D43—21no—
140C2×C4×D43—21no—
141C2×C4×D43—21no—
142C2×C4×D43—21no—
143C2×C4×D43—21no—
144C2×C4×D43—22no—
145C2×C4×D43—22no—
146C2×C4×D43—22no—
147C2×C4×D43—41no—
148C2×C4×D43—41no—
149C2×C4×D43—41no—
150C2×C4×D43—41no—
151C2×C4×D43—44no—
152C2×C4×D43—44no—
153C2×C4×D43—44no—
154C2×C4×D43—44no—
155C2×C8×C43—22no—
156C2×C8×C43—41no—
157C2×C8×C43—41no—
158C2×C8×C43—41no—
159C2×C8×C43—41no—
160C2×C8×C43—41no—
161C4⋊C4×C43—41no—
162C4⋊C4×C43—41no—
163C4⋊C4×C43—41no—
164C4⋊C4×C43—41no—
165(C2×D43)⋊C4—24no—
166(C2×D43)⋊C4—24no—
167(C2×D43)⋊C4—42no—
168(C2×D43)⋊C4—42no—
169Dic43⋊C4—42no—
170Dic43⋊C4—42no—
171C2×C43⋊C8—22no—
172C2×C43⋊C8—41no—
173C2×C43⋊C8—41no—
174C2×C43⋊C8—41no—
175C2×C43⋊C8—41no—
176C2×C43⋊C8—41no—
177C8×D43—48no—
178C23×C43—21no—
179C23×C43—21no—
180C23×C43—21no—
181C23×C43—21no—
182C23×C43C2×C22⋊C411yescharacteristic
183C23×C43C4×D411yescharacteristic
184C23×C43C4×D411yescharacteristic
185C23×C43C22×C811yescharacteristic
186C23×C43C2×M1611yescharacteristic
187C23×C43#13111yescharacteristic
188C23×C43#13111yescharacteristic
189C22×D43—21no—
190C22×D43—21no—
191C22×D43—21no—
192C22×D43—21no—
193C22×D43—21no—
194C22×D43—21no—
195C22×D43—21no—
196C22×D43—21no—
197C22×D43—21no—
198C22×D43—21no—
199C22×D43—22no—
200C22×D43—22no—
201C22×D43—22no—
202C22×D43—22no—
203C22×D43—24no—
204C22×D43—24no—
205C22×D43—42no—
206C22×D43—42no—
207C22×D43—42no—
208C22×D43—42no—
209C22×D43—42no—
210C22×D43—42no—
211C22×D43—42no—
212C22×D43—42no—
213C22×D43—42no—
214C22×D43—42no—
215C22×D43C22⋊C812yes—
216C22×D43C22⋊C812yes—
217C22×D43#9912yes—
218C22×D43#10112yes—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—22no—
224C2×C4×C43—22no—
225C2×C4×C43—22no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—81no—
238C2×C4×C43—81no—
239C2×C4×C43#12011yescharacteristic
240C2×C4×C43#12111yescharacteristic
241C2×C4×C43#12111yescharacteristic
242C2×C4×C43#12311yescharacteristic
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—22no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—42no—
250C2×Dic43—42no—
251C2×Dic43—42no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—42no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—81no—
259C2×Dic43—81no—
260C2×Dic43#9912yes—
261C4×D43—24no—
262C4×D43—24no—
263C4×D43—42no—
264C4×D43—42no—
265C4×D43—42no—
266C4×D43—42no—
267C4×D43—42no—
268C4×D43—42no—
269C8×C43—42no—
270C8×C43—81no—
271C43⋊C8—42no—
272C43⋊C8—81no—
273#9081—431nomaximal, Sylow
274C22×C43—21no—
275C22×C43—21no—
276C22×C43—21no—
277C22×C43—21no—
278C22×C43—21no—
279C22×C43—21no—
280C22×C43—21no—
281C22×C43—21no—
282C22×C43—21no—
283C22×C43—21no—
284C22×C43—21no—
285C22×C43—21no—
286C22×C43#38611yescharacteristic
287C22×C43C2×C22⋊C811yescharacteristic
288C22×C43#40811yescharacteristic
289C22×C43C2×#9911yescharacteristic
290C22×C43C2×#9911yescharacteristic
291C22×C43C2×#10111yescharacteristic
292C22×C43#41311yescharacteristic
293C22×C43C8×D411yescharacteristic
294C22×C43C8×D411yescharacteristic
295C22×C43#43511yescharacteristic
296C22×C43#43511yescharacteristic
297C2×D43—22no—
298C2×D43—22no—
299C2×D43—22no—
300C2×D43—22no—
301C2×D43—22no—
302C2×D43—22no—
303C2×D43—22no—
304C2×D43—22no—
305C2×D43—22no—
306C2×D43—44no—
307C2×D43—44no—
308C2×D43—44no—
309C2×D43—44no—
310C2×D43—41no—
311C2×D43—41no—
312C2×D43—41no—
313C2×D43—41no—
314C2×D43#32414yescomplemented
315C4×C43—21no—
316C4×C43—21no—
317C4×C43—21no—
318C4×C43—21no—
319C4×C43—42no—
320C4×C43—81no—
321Dic43—22no—
322Dic43—41no—
323Dic43—42no—
324Dic43—81no—
325C22×C22⋊C8—431no—
326C2×#385—431no—
327#1779—431no—
328C2×#324—431no—
329C2×#324D4311yescharacteristic, complemented
330#1280—431no—
331#1280—431no—
332C2×C43—21no—
333C2×C43—21no—
334C2×C43—21no—
335C2×C43—21no—
336C2×C43C2×#32411yescharacteristic
337C2×C43#145911yescharacteristic
338C2×C43#146811yescharacteristic
339C2×C43#147211yescharacteristic
340C2×C43#186911yescharacteristic
341C2×C43#189811yescharacteristic
342C2×C43#190111yescharacteristic
343D43—24no—
344D43—42no—
345C24×C4—431no—
346C23×C8—861no—
347C22×C4⋊C4—431no—
348C22×C4⋊C4C2×D4311yescharacteristic
349C22×C22⋊C4—431no—
350C22×C22⋊C4—431no—
351C2×C22⋊C8—431no—
352C2×C22⋊C8—431no—
353C2×C22⋊C8—862no—
354C2×C22⋊C8—861no—
355C2×C22⋊C8—862no—
356C2×C22⋊C8—861no—
357C2×C22⋊C8—861no—
358C2×C22⋊C8C2×D4311yescharacteristic
359C2×C22⋊C8C2×D4311yescharacteristic
360#385—861no—
361#385—861no—
362#385—861no—
363#385—861no—
364C2×#95—431no—
365C2×#95—431no—
366#324—22no—
367#324—862no—
368C43#908111yescharacteristic, complemented, Sylow
369C25—431no—
370C23×C4—431no—
371C23×C4—431no—
372C23×C4—431no—
373C23×C4—431no—
374C23×C4—431no—
375C23×C4—431no—
376C23×C4—431no—
377C23×C4—861no—
378C23×C4—861no—
379C23×C4—861no—
380C23×C4—861no—
381C23×C4—1722no—
382C23×C4—1722no—
383C23×C4C4×D4311yescharacteristic
384C23×C4C4×D4311yescharacteristic
385C23×C4C22×D4311yescharacteristic
386C22×C8—21no—
387C22×C8—21no—
388C22×C8—864no—
389C22×C8—861no—
390C22×C8—861no—
391C22×C8—1722no—
392C22×C8—1722no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—1722no—
402C2×C22⋊C4—434no—
403C2×C22⋊C4—862no—
404C2×C22⋊C4—861no—
405C2×C22⋊C4—861no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C22⋊C4—1722no—
409C22⋊C8—21no—
410C22⋊C8—21no—
411C22⋊C8—21no—
412C22⋊C8—432no—
413C22⋊C8—864no—
414C22⋊C8—861no—
415C22⋊C8—861no—
416C22⋊C8—861no—
417C22⋊C8—1722no—
418C22⋊C8—1722no—
419C22⋊C8C22⋊D4312yes—
420#95—861no—
421#95—861no—
422#95—861no—
423#95—861no—
424C24—431no—
425C24—431no—
426C24—432no—
427C24—432no—
428C24—862no—
429C24—862no—
430C24—861no—
431C24—861no—
432C24—861no—
433C24—861no—
434C24—1721no—
435C24—1721no—
436C24C2×C4×D4311yescharacteristic
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—431no—
451C22×C4—431no—
452C22×C4—432no—
453C22×C4—862no—
454C22×C4—862no—
455C22×C4—862no—
456C22×C4—862no—
457C22×C4—862no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4—1721no—
474C22×C4—1721no—
475C22×C4—1721no—
476C22×C4—1721no—
477C22×C4—1724no—
478C22×C4—1724no—
479C22×C4—1724no—
480C22×C4—1724no—
481C22×C4—1721no—
482C22×C4—1721no—
483C22×C4—1721no—
484C22×C4—1721no—
485C22×C4—1721no—
486C22×C4C8×D4312yescomplemented
487C22×C4#1062189811yescharacteristic
488C22×C4D4×D4311yescharacteristic
489C22×C4D4×D4311yescharacteristic
490C22×C4D4×D4311yescharacteristic
491C22×C4#1062190011yescharacteristic
492C22×C4C2×C22⋊D4311yescharacteristic
493C2×C8—22no—
494C2×C8—41no—
495C2×C8—41no—
496C2×C8—41no—
497C2×C8—41no—
498C2×C8—41no—
499C2×C8—862no—
500C2×C8—1728no—
501C2×C8—1721no—
502C2×C8—1721no—
503C2×C8—1721no—
504C2×C8—1721no—
505C2×C8—1721no—
506C4⋊C4—41no—
507C4⋊C4—41no—
508C4⋊C4—41no—
509C4⋊C4—41no—
510C4⋊C4—1722no—
511C4⋊C4—1722no—
512C22⋊C4—864no—
513C22⋊C4—864no—
514C22⋊C4—1722no—
515C22⋊C4—1722no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—432no—
521C23—432no—
522C23—432no—
523C23—432no—
524C23—864no—
525C23—864no—
526C23—861no—
527C23—861no—
528C23—861no—
529C23—861no—
530C23—861no—
531C23—861no—
532C23—861no—
533C23—861no—
534C23—861no—
535C23—862no—
536C23—862no—
537C23—862no—
538C23—862no—
539C23—861no—
540C23—1722no—
541C23—1722no—
542C23—1722no—
543C23—1722no—
544C23—1722no—
545C23—1722no—
546C23—1722no—
547C23—1722no—
548C23—1722no—
549C23—1722no—
550C23C22⋊C4×D4311yescharacteristic
551C23(C22⋊D43)⋊C411yescharacteristic
552C23C4×C22⋊D4311yescharacteristic
553C23C2×C8×D4311yescharacteristic
554C23M16×D4311yescharacteristic
555C23#1306333111yescharacteristic
556C23#1306333311yescharacteristic
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—81no—
576C2×C4—81no—
577C2×C4—432no—
578C2×C4—864no—
579C2×C4—864no—
580C2×C4—861no—
581C2×C4—861no—
582C2×C4—862no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—3441no—
587C2×C4—3441no—
588C2×C4—1722no—
589C2×C4—1722no—
590C2×C4—1722no—
591C2×C4—1722no—
592C2×C4—1722no—
593C2×C4—1722no—
594C2×C4—1722no—
595C2×C4—1722no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1722no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1722no—
603C2×C4#1306329311yescharacteristic
604C2×C4#1306329611yescharacteristic
605C2×C4#1306329811yescharacteristic
606C2×C4#1306330711yescharacteristic
607C8—42no—
608C8—81no—
609C8—3441no—
610C8—1722no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—21no—
619C22—21no—
620C22—21no—
621C22—21no—
622C22—21no—
623C22—434no—
624C22—862no—
625C22—862no—
626C22—862no—
627C22—862no—
628C22—862no—
629C22—862no—
630C22—862no—
631C22—862no—
632C22—862no—
633C22—1724no—
634C22—1724no—
635C22—1724no—
636C22—1724no—
637C22—1721no—
638C22—1721no—
639C22—1721no—
640C22—1721no—
641C22#1458277511yescharacteristic
642C22C22⋊C8×D4311yescharacteristic
643C22#1458286411yescharacteristic
644C22#99×D4311yescharacteristic
645C22#99×D4311yescharacteristic
646C22#101×D4311yescharacteristic
647C22#1458288211yescharacteristic
648C22(C22⋊D43)⋊C811yescharacteristic
649C22C8×C22⋊D4311yescharacteristic
650C22#1458296811yescharacteristic
651C22#1458297311yescharacteristic
652C4—21no—
653C4—21no—
654C4—21no—
655C4—21no—
656C4—42no—
657C4—81no—
658C4—862no—
659C4—3441no—
660C4—1721no—
661C4—1722no—
662C2—21no—
663C2—21no—
664C2—21no—
665C2—21no—
666C2—864no—
667C2—1722no—
668C2#324×D4311yescharacteristic
669C2#1913291211yescharacteristic
670C2#1913294211yescharacteristic
671C2#1913295711yescharacteristic
672C2#1913488411yescharacteristic
673C2#1913504511yescharacteristic
674C2#1913506011yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC23×C43C22×C8
FrattiniC23×C4C22×D43
FittingC2×C43×#324C2
socleC23×C43C2×C22⋊C4
prime radicalC24×D43C2×C4
cosocleC23×C4×C43C23
hypercenterC2×#324D43
hypocenterC43#9081
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
4. C2×#14582625C2semidirect
5. #19132437C2semidirect
6. #19132437C2semidirect
7. C2×C43×#324C2semidirect
59. C2×(C2×D43)⋊C4C8semidirect
112. C22×C4×C43C2×C8semidirect
134. C22×Dic43C2×C8semidirect
314. C2×D43#324semidirect
329. C2×#324D43semidirect
368. C43#9081semidirect
486. C22×C4C8×D43semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C8×D432
C2×#145827702
#191345042
C2×#145826252
#191324372
C2×C43×#3242
#908143