Finite Group Databasebeta

← #25133255

Subgroups — #25133255

Order 11008.

1072 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583609C211yesmaximal, characteristic
2C2×#14583207C211yesmaximal, characteristic, complemented
3C2×#14583001C211yesmaximal, characteristic
4#19139965C211yesmaximal, characteristic, complemented
5#19135934C211yesmaximal, characteristic, complemented
6#19135924C211yesmaximal, characteristic, complemented
7#19135747C211yesmaximal, characteristic, complemented
8#19135737C211yesmaximal, characteristic, complemented
9#19135564C211yesmaximal, characteristic, complemented
10#19134928C211yesmaximal, characteristic
11#19134928C211yesmaximal, characteristic
12#19134859C211yesmaximal, characteristic
13#19134845C211yesmaximal, characteristic
14#19134596C211yesmaximal, characteristic
15C43×#1985C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17#14583609—24no—
18#14583609—24no—
19C2×#13063325C2211yescharacteristic
20C2×#13063317C2211yescharacteristic
21C2×#13063317C2211yescharacteristic
22C2×#13063303—21no—
23C2×#13063303—21no—
24C2×#13063301—21no—
25C2×C4×Dic86C2211yescharacteristic
26C2×C4×D172C2211yescharacteristic
27C2×C4×D172C2211yescharacteristic
28C2×C4×D172C2211yescharacteristic
29C2×C4⋊C4×D43—21no—
30#14583207—24no—
31#14583001—24no—
32C2×#13063259C2211yescharacteristic
33C2×#13063259C2211yescharacteristic
34C2×#13063257C2211yescharacteristic
35C2×#13063250C2211yescharacteristic
36C2×#13063250C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063247C2211yescharacteristic
39C2×#13063247C2211yescharacteristic
40C2×#13063247C2211yescharacteristic
41#14582832—21no—
42#14582832—21no—
43#14582806—21no—
44#14582805C2211yescharacteristic
45#14582805C2211yescharacteristic
46#14582797C2211yescharacteristic
47#14582797C2211yescharacteristic
48#14582795—21no—
49#14582769C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582662C2211yescharacteristic
54#14582662C2211yescharacteristic
55#14582662C2211yescharacteristic
56C2×C4×Q8×C43C2211yescharacteristic
57C2×C4⋊C8×C43C2211yescharacteristic
58C2×#97×C43C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86C2311yescharacteristic
65C22×D172C2311yescharacteristic
66C22×C4×D43—21no—
67C22×C4×D43—21no—
68C22×C4×D43—21no—
69C2×#10621873—22no—
70C2×#10621873—22no—
71C2×#10621873Q814yescomplemented
72#13063325—22no—
73#13063325—22no—
74#13063317—22no—
75#13063317—22no—
76#13063317—22no—
77#13063317D414yes—
78#13063303—28no—
79#13063303—28no—
80#13063301—28no—
81C4×Dic86—22no—
82C4×Dic86—22no—
83C4×D172—22no—
84C4×D172—22no—
85C4×D172—22no—
86C4×D172—22no—
87C4×D172—22no—
88C4×D172D414yes—
89C2×C4⋊Dic43—21no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4—21no—
105C4⋊C4×D43—28no—
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4—21no—
109C2×C4×Dic43—21no—
110#13063259—22no—
111#13063259—22no—
112#13063257—22no—
113#13063250—22no—
114#13063250—22no—
115#13063250—22no—
116#13063247—22no—
117#13063247—22no—
118#13063247—22no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C22×Q8×C43D411yescharacteristic
126C22×C8×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129C22×C8×C43C2311yescharacteristic
130C4×Q8×C43—22no—
131C4×Q8×C43—22no—
132C2×C4⋊C4×C43D411yescharacteristic
133C2×C4⋊C4×C43D411yescharacteristic
134C2×C4⋊C4×C43D411yescharacteristic
135C2×C42×C43C2311yescharacteristic
136C2×C42×C43C2311yescharacteristic
137C2×C42×C43C2311yescharacteristic
138C4⋊C8×C43—22no—
139#97×C43—22no—
140C23×D43—21no—
141C2×Q8×C43—22no—
142C2×Q8×C43—22no—
143C2×Q8×C43—41no—
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2411yescharacteristic
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172C2×D412yes—
162C2×D172C2×Q812yes—
163C2×D172#4112yes—
164C2×C4×D43—24no—
165C2×C4×D43—24no—
166C2×C4×D43—24no—
167C2×C4×D43—42no—
168C2×C4×D43—42no—
169C2×C4×D43—81no—
170C2×C4×D43—81no—
171C2×C4×D43—81no—
172C2×C4×D43—81no—
173C2×Dic86—21no—
174C2×Dic86—21no—
175C2×Dic86—21no—
176C2×Dic86—21no—
177C2×Dic86—21no—
178C2×Dic86—24no—
179C2×Dic86—81no—
180C2×Dic86—81no—
181C2×Dic86C2×Q812yes—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43C2×Q812yes—
194C4⋊C4×C43—22no—
195C4⋊C4×C43—22no—
196C4⋊C4×C43—22no—
197C42×C43—21no—
198C42×C43—21no—
199C42×C43—21no—
200C42×C43—21no—
201C42×C43C2×D412yes—
202C42×C43C2×D412yes—
203(C2×D43)⋊C4—24no—
204(C2×D43)⋊C4—24no—
205(C2×D43)⋊C4—24no—
206C4⋊Dic43—24no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—21no—
212C4⋊Dic43—21no—
213C4⋊Dic43—21no—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—42no—
217C4⋊Dic43—81no—
218C4⋊Dic43C2×D412yes—
219C4⋊Dic43C2×D412yes—
220C4⋊Dic43C2×D412yes—
221Dic43⋊C4—24no—
222Dic43⋊C4—24no—
223Dic43⋊C4—24no—
224Dic43⋊C4—24no—
225Dic43⋊C4—42no—
226Dic43⋊C4—81no—
227Dic43⋊C4—81no—
228C4×Dic43—42no—
229#10621873—28no—
230C23×C43C22×D411yescharacteristic
231C22×D43—22no—
232C22×D43—22no—
233C22×D43—22no—
234C22×D43—41no—
235C22×D43—41no—
236C22×D43—41no—
237C22×D43—41no—
238Q8×C43—44no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43#12012yes—
255C2×C4×C43#12012yes—
256C2×C4×C43#13712yes—
257C2×C4×C43C22×D411yescharacteristic
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43C22×Q811yescharacteristic
260C2×C4×C43C2×#4111yescharacteristic
261C2×C4×C432−1+411yescharacteristic
262C2×C4×C432−1+411yescharacteristic
263C2×Dic43—22no—
264C2×Dic43—22no—
265C2×Dic43—22no—
266C2×Dic43—22no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284D172—22no—
285D172—22no—
286D172—22no—
287D172C22⋊Q814yes—
288C4×D43—48no—
289C4×D43—84no—
290C4×D43—84no—
291Dic86—22no—
292Dic86—22no—
293Dic86—41no—
294Dic86—41no—
295Dic86—84no—
296C8×C43—22no—
297C8×C43—41no—
298C8×C43—41no—
299C8×C43—41no—
300#24349—431nomaximal, Sylow
301C22×C43C2×#12011yescharacteristic
302C22×C43#54811yescharacteristic
303C22×C43D4×Q811yescharacteristic
304C22×C43C2×#13711yescharacteristic
305C22×C43#57511yescharacteristic
306C22×C43#57611yescharacteristic
307C22×C43#57711yescharacteristic
308C2×D43—24no—
309C2×D43—42no—
310C2×D43—42no—
311C2×D43—42no—
312C2×D43—42no—
313C2×D43—42no—
314C2×D43—42no—
315C4×C43—22no—
316C4×C43—22no—
317C4×C43—22no—
318C4×C43—41no—
319C4×C43—41no—
320C4×C43—41no—
321C4×C43C2×C22⋊Q811yescharacteristic
322C4×C43#53611yescharacteristic
323C4×C43#54811yescharacteristic
324C4×C43D4×Q811yescharacteristic
325Dic43—42no—
326Dic43—42no—
327Dic43—42no—
328Dic43—42no—
329Dic43—81no—
330Dic43—81no—
331Dic43—81no—
332C2×#554—431no—
333C2×#479—431no—
334C2×#440—431no—
335#2582—431no—
336#2059—431no—
337#2057—431no—
338#2026—431no—
339#2024—431no—
340#1992—431no—
341#1985D4311yescharacteristic, complemented
342#1877—431no—
343#1877—431no—
344#1864—431no—
345#1862—431no—
346#1802—431no—
347C2×C43#240911yescharacteristic
348C2×C43#300711yescharacteristic
349C2×C43#301211yescharacteristic
350C2×C43#337011yescharacteristic
351C2×C43#337211yescharacteristic
352C2×C43#338511yescharacteristic
353C2×C43#338811yescharacteristic
354D43—44no—
355C22×SD16—431no—
356#554—864no—
357#554—864no—
358C2×C4⋊Q8—431no—
359C2×#125—431no—
360C2×#125—431no—
361C2×C22⋊Q8—861no—
362C2×C22⋊Q8—861no—
363C2×C22⋊Q8—861no—
364C2×C4×Q8—431no—
365C2×C4×Q8C2×D4311yescharacteristic
366C2×C4×D4—431no—
367C2×C4×D4—431no—
368C2×C4×D4—431no—
369C22×C4⋊C4—861no—
370#479—864no—
371#440—864no—
372C2×#107—431no—
373C2×#107—431no—
374C2×#106—431no—
375C2×C4⋊C8C2×D4311yescharacteristic
376C2×#103—431no—
377C2×#103—431no—
378C2×#103—431no—
379C2×#102—431no—
380C2×#102—431no—
381C2×#102—431no—
382C2×#97C2×D4311yescharacteristic
383#398—861no—
384#398—861no—
385#391—431no—
386#391—431no—
387#391—861no—
388#389—431no—
389#389—431no—
390#389—861no—
391#384—431no—
392#340—431no—
393#340—431no—
394#340—431no—
395#340—431no—
396#340—431no—
397#340—431no—
398#336C2×D4311yescharacteristic
399#336C2×D4311yescharacteristic
400#336C2×D4311yescharacteristic
401#336C2×D4311yescharacteristic
402C43#2434911yescharacteristic, complemented, Sylow
403C22×Q8—431no—
404C22×Q8—861no—
405C22×Q8D17211yescharacteristic
406C22×D4—431no—
407C23×C4—861no—
408C23×C4—861no—
409C23×C4—861no—
410C2×SD16—434no—
411C2×SD16—862no—
412C2×SD16—862no—
413C22×C8C22×D4311yescharacteristic
414C22×C8C22×D4311yescharacteristic
415C22×C8C22×D4311yescharacteristic
416C22×C8C22×D4311yescharacteristic
417C4⋊Q8—862no—
418C4⋊Q8—862no—
419#125—434no—
420#125—862no—
421#125—862no—
422#125—862no—
423C22⋊Q8—868no—
424C22⋊Q8—868no—
425C22⋊Q8—868no—
426C4×Q8—22no—
427C4×Q8—22no—
428C4×Q8—862no—
429C4×Q8—862no—
430C4×D4—434no—
431C4×D4—862no—
432C4×D4—862no—
433C4×D4—862no—
434C4×D4—862no—
435C4×D4—862no—
436C2×C4⋊C4—431no—
437C2×C4⋊C4—431no—
438C2×C4⋊C4—431no—
439C2×C4⋊C4—431no—
440C2×C4⋊C4—431no—
441C2×C4⋊C4—431no—
442C2×C4⋊C4—868no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4—861no—
445C2×C4⋊C4—861no—
446C2×C4⋊C4—861no—
447C2×C4⋊C4—861no—
448C2×C4⋊C4—861no—
449C2×C4⋊C4—861no—
450C2×C4⋊C4—861no—
451C2×C4⋊C4—861no—
452C2×C4⋊C4—861no—
453C2×C4⋊C4D17211yescharacteristic
454C2×C4⋊C4D17211yescharacteristic
455C2×C4⋊C4D17211yescharacteristic
456C2×C22⋊C4—861no—
457C2×C22⋊C4—861no—
458C2×C22⋊C4—861no—
459C2×C42—861no—
460C2×C42C22×D4311yescharacteristic
461C2×C42C22×D4311yescharacteristic
462C2×C42C22×D4311yescharacteristic
463#107—862no—
464#107—862no—
465#106—862no—
466C4⋊C8—22no—
467#103—862no—
468#103—862no—
469#103—862no—
470#102—862no—
471#102—862no—
472#102—862no—
473#97—22no—
474#95—861no—
475#95—861no—
476#95—861no—
477#95—861no—
478#95—861no—
479#95—861no—
480C24—861no—
481C2×Q8—22no—
482C2×Q8—22no—
483C2×Q8—41no—
484C2×Q8—432no—
485C2×Q8—864no—
486C2×Q8—861no—
487C2×Q8—861no—
488C2×Q8—861no—
489C2×Q8—861no—
490C2×Q8—861no—
491C2×Q8—3441no—
492C2×Q8—3441no—
493C2×D4—432no—
494C2×D4—432no—
495C2×D4—432no—
496C2×D4—861no—
497C2×D4—861no—
498C2×D4—861no—
499C22×C4—864no—
500C22×C4—864no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4—861no—
504C22×C4—861no—
505C22×C4—864no—
506C22×C4—861no—
507C22×C4—861no—
508C22×C4—861no—
509C22×C4—3441no—
510C22×C4—3441no—
511C22×C4—3441no—
512C22×C4—3441no—
513C22×C4—1722no—
514C22×C4—1722no—
515C22×C4C2×D17211yescharacteristic
516C22×C4C2×D17211yescharacteristic
517C22×C4C2×D17211yescharacteristic
518C22×C4C2×D17211yescharacteristic
519C22×C4C2×D17211yescharacteristic
520C22×C4C2×D17211yescharacteristic
521C22×C4C23×D4311yescharacteristic
522SD16—868no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8Q8×D4312yes—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—432no—
539C4⋊C4—432no—
540C4⋊C4—432no—
541C4⋊C4—864no—
542C4⋊C4—864no—
543C4⋊C4—864no—
544C4⋊C4—864no—
545C4⋊C4—864no—
546C4⋊C4—861no—
547C4⋊C4—861no—
548C4⋊C4—861no—
549C4⋊C4—861no—
550C4⋊C4—861no—
551C4⋊C4—861no—
552C4⋊C4—861no—
553C4⋊C4—861no—
554C4⋊C4—861no—
555C4⋊C4—3441no—
556C4⋊C4—3441no—
557C4⋊C4—3441no—
558C4⋊C4—1722no—
559C4⋊C4—1722no—
560C22⋊C4—864no—
561C22⋊C4—864no—
562C22⋊C4—864no—
563C42—21no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—1722no—
568C42D4×D4312yes—
569C42D4×D4312yes—
570C23—862no—
571C23—862no—
572C23—862no—
573C23—1721no—
574C23—1721no—
575C23—1721no—
576C23—1721no—
577C23C22×D17211yescharacteristic
578Q8—44no—
579Q8—862no—
580Q8—862no—
581Q8—3444no—
582Q8—1721no—
583Q8—1721no—
584D4—434no—
585D4—862no—
586D4—862no—
587D4—862no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—862no—
604C2×C4—862no—
605C2×C4—862no—
606C2×C4—862no—
607C2×C4—3444no—
608C2×C4—3444no—
609C2×C4—1728no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4—1721no—
620C2×C4—1721no—
621C2×C4—1721no—
622C2×C4—1721no—
623C2×C4—1721no—
624C2×C4—1721no—
625C2×C4—1721no—
626C2×C4—1721no—
627C2×C4#1306329512yes—
628C2×C4#1306329512yes—
629C2×C4#1306335812yes—
630C2×C4C2×D4×D4311yescharacteristic
631C2×C4C2×D4×D4311yescharacteristic
632C2×C4C2×Q8×D4311yescharacteristic
633C2×C4#41×D4311yescharacteristic
634C2×C4#1306337211yescharacteristic
635C2×C4#1306337311yescharacteristic
636C8—22no—
637C8—41no—
638C8—41no—
639C8—41no—
640C22—864no—
641C22—1722no—
642C22—1722no—
643C22—1722no—
644C22—1722no—
645C22—1722no—
646C22—1722no—
647C22C2×#1306329511yescharacteristic
648C22#1458356111yescharacteristic
649C22Q8×D17211yescharacteristic
650C22C2×#1306335811yescharacteristic
651C22#1458369911yescharacteristic
652C22#1458370411yescharacteristic
653C22#1458371111yescharacteristic
654C4—22no—
655C4—22no—
656C4—22no—
657C4—41no—
658C4—41no—
659C4—41no—
660C4—3441no—
661C4—3441no—
662C4—3441no—
663C4—1722no—
664C4—1722no—
665C4—1722no—
666C4—1722no—
667C4C22⋊Q8×D4311yescharacteristic
668C4#1458347211yescharacteristic
669C4#1458355711yescharacteristic
670C4#1458356411yescharacteristic
671C2—1724no—
672C2#1913795811yescharacteristic
673C2#1914385711yescharacteristic
674C2#1914390211yescharacteristic
675C2#1914735011yescharacteristic
676C2#1914737811yescharacteristic
677C2#1914750711yescharacteristic
678C2#1914754211yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1985C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#1985D43
hypocenterC43#24349
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #1985

Complements

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

NH ≅ G/Ntype
2. C2×#14583207C2semidirect
4. #19139965C2semidirect
5. #19135934C2semidirect
6. #19135924C2semidirect
7. #19135747C2semidirect
8. #19135737C2semidirect
9. #19135564C2semidirect
15. C43×#1985C2semidirect
71. C2×#10621873Q8semidirect
341. #1985D43semidirect
402. C43#24349semidirect

Maximal subgroups

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

subgroupindex
C2×#145836092
C2×#145832072
C2×#145830012
#191399652
#191359342
#191359242
#191357472
#191357372
#191355642
#191349282
#191348592
#191348452
#191345962
C43×#19852
#2434943