Finite Group Databasebeta

← #25153704

Subgroups — #25153704

Order 11008.

958 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583207C211yesmaximal, characteristic, complemented
2C2×#14582896C211yesmaximal, characteristic
3#19138308C211yesmaximal, characteristic, complemented
4#19137435C211yesmaximal, characteristic
5#19136127C211yesmaximal, characteristic, complemented
6#19135982C211yesmaximal, characteristic, complemented
7#19135968C211yesmaximal, characteristic, complemented
8#19135742C211yesmaximal, characteristic, complemented
9#19134866C211yesmaximal, characteristic, complemented
10#19134866C211yesmaximal, characteristic, complemented
11#19134796C211yesmaximal, characteristic, complemented
12#19134620C211yesmaximal, characteristic, complemented
13#19134601C211yesmaximal, characteristic, complemented
14#19134536C211yesmaximal, characteristic
15C43×#1850C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C2×#13063317C2211yescharacteristic
18C2×C4×Dic86C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20C2×#13063284C2211yescharacteristic
21#14583207—24no—
22C2×#13063259C2211yescharacteristic
23C2×#13063257C2211yescharacteristic
24C2×#13063257C2211yescharacteristic
25C2×#13063257C2211yescharacteristic
26#14582896—24no—
27C2×#13063250C2211yescharacteristic
28C2×#13063250C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063247C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34C2×#13063247C2211yescharacteristic
35#14582835—21no—
36#14582822—21no—
37#14582801C2211yescharacteristic
38#14582801C2211yescharacteristic
39#14582799—21no—
40#14582799—21no—
41#14582797C2211yescharacteristic
42#14582797C2211yescharacteristic
43#14582796—21no—
44#14582782—21no—
45#14582769C2211yescharacteristic
46#14582759C2211yescharacteristic
47#14582759C2211yescharacteristic
48#14582758—21no—
49#14582746—21no—
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582662C2211yescharacteristic
54C23×C8×C43C2211yescharacteristic
55C2×C4⋊C8×C43C2211yescharacteristic
56C2×C4⋊C8×C43C2211yescharacteristic
57C2×C22⋊C8×C43C2211yescharacteristic
58C4×C22⋊C4×C43C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C2×#10621898—22no—
62C2×#10621898—22no—
63C2×#10621898—22no—
64C2×#10621898—41no—
65C2×#10621898—41no—
66C2×#10621898Q814yes—
67C22×Dic86C2311yescharacteristic
68C22×D172C2311yescharacteristic
69C22×C22⋊D43—21no—
70C22×C4×D43—21no—
71#13063317—22no—
72#13063317—41no—
73C4×Dic86—22no—
74C4×Dic86—22no—
75C4×Dic86—41no—
76C4×Dic86—41no—
77#13063284—22no—
78#13063284—41no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×C22⋊Dic43—21no—
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43—21no—
102C2×C4×Dic43—21no—
103#13063259—22no—
104#13063257—22no—
105#13063257—41no—
106#13063257—41no—
107#13063250—22no—
108#13063250—22no—
109#13063250—22no—
110#13063250D414yes—
111#13063247—22no—
112#13063247—22no—
113#13063247—41no—
114#13063247—41no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C23×C4×C43C2311yescharacteristic
120C22×C8×C43—22no—
121C22×C8×C43—22no—
122C22×C8×C43—41no—
123C22×C8×C43C2311yescharacteristic
124C22×C8×C43C2311yescharacteristic
125C22×C8×C43C2311yescharacteristic
126C22×C8×C43C2311yescharacteristic
127C2×C22⋊C4×C43D411yescharacteristic
128C2×C22⋊C4×C43D411yescharacteristic
129C2×C42×C43C2311yescharacteristic
130C2×C42×C43C2311yescharacteristic
131C4⋊C8×C43—22no—
132C4⋊C8×C43—41no—
133C22⋊C8×C43—22no—
134#95×C43D411yescharacteristic
135#95×C43D411yescharacteristic
136C24×C43C2×D411yescharacteristic
137C23×D43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×Q812yes—
148C22×C4×C43#4112yes—
149C22×C4×C43C2411yescharacteristic
150C2×C22⋊D43—24no—
151C2×C22⋊D43—42no—
152C2×C22⋊D43—42no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160#10621898—28no—
161#10621898—44no—
162#10621898—44no—
163#10621898—44no—
164C2×D172—21no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—21no—
169C2×D172C2×Q812yes—
170C2×C4×D43—24no—
171C2×C4×D43—42no—
172C2×C4×D43—42no—
173C2×Dic86—21no—
174C2×Dic86—21no—
175C2×Dic86—21no—
176C2×Dic86C2×D412yes—
177C2×Dic86C2×Q812yes—
178C2×Dic86#4112yes—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
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—44no—
191C2×C8×C43C2×D412yes—
192C22⋊C4×C43—22no—
193C22⋊C4×C43—41no—
194C42×C43—21no—
195C42×C43—21no—
196C42×C43—21no—
197C42×C43—21no—
198C22⋊Dic43—42no—
199C22⋊Dic43—81no—
200C22⋊Dic43—81no—
201(C2×D43)⋊C4—42no—
202(C2×D43)⋊C4—42no—
203(C2×D43)⋊C4—81no—
204(C2×D43)⋊C4—81no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
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—
219Dic43⋊C4—42no—
220Dic43⋊C4—42no—
221Dic43⋊C4—42no—
222Dic43⋊C4—42no—
223Dic43⋊C4—42no—
224Dic43⋊C4—81no—
225C4×Dic43—42no—
226C4×Dic43—42no—
227C4×Dic43—42no—
228C23×C43—21no—
229C23×C43—21no—
230C23×C43—21no—
231C23×C43—21no—
232C23×C43—21no—
233C23×C43—21no—
234C23×C43C22⋊Q812yes—
235C23×C43C22×D411yescharacteristic
236C22×D43—22no—
237C22×D43—41no—
238C22×D43—41no—
239C22×D43—41no—
240C22×D43—41no—
241C22×D43—41no—
242C22×D43—41no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—22no—
248C2×C4×C43—22no—
249C2×C4×C43—22no—
250C2×C4×C43—22no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—21no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—21no—
260C2×C4×C43C22⋊Q812yes—
261C2×C4×C43#13512yes—
262C2×C4×C43C22×D411yescharacteristic
263C2×C4×C43C22×Q811yescharacteristic
264C2×C4×C43C2×#4111yescharacteristic
265C2×C4×C43C2×#4111yescharacteristic
266C2×C4×C43H(5,𝔽2)11yescharacteristic
267C2×C4×C43H(5,𝔽2)11yescharacteristic
268C22⋊D43—48no—
269C2×Dic43—22no—
270C2×Dic43—22no—
271C2×Dic43—22no—
272C2×Dic43—22no—
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—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43—41no—
289C2×Dic43—41no—
290D172—22no—
291D172—22no—
292D172—41no—
293D172—41no—
294C4×D43—48no—
295Dic86—22no—
296Dic86—22no—
297Dic86—22no—
298Dic86C22⋊Q814yes—
299C8×C43—22no—
300C8×C43—41no—
301C8×C43—41no—
302C8×C43—41no—
303#25953—431nomaximal, Sylow
304C22×C43—22no—
305C22×C43—22no—
306C22×C43—22no—
307C22×C43—41no—
308C22×C43—41no—
309C22×C43—41no—
310C22×C43—41no—
311C22×C43C2×C22⋊Q811yescharacteristic
312C22×C43D4211yescharacteristic
313C22×C43#54611yescharacteristic
314C22×C43C2×#13511yescharacteristic
315C22×C43#57511yescharacteristic
316C22×C43#57711yescharacteristic
317C22×C43#57711yescharacteristic
318C2×D43—42no—
319C2×D43—42no—
320C2×D43—42no—
321C2×D43—81no—
322C2×D43—81no—
323C2×D43—81no—
324C2×D43—81no—
325C4×C43—22no—
326C4×C43—22no—
327C4×C43—41no—
328C4×C43—41no—
329C4×C43—41no—
330C4×C43C2×C22⋊Q811yescharacteristic
331C4×C43#54311yescharacteristic
332C4×C43#54611yescharacteristic
333C4×C43#55111yescharacteristic
334Dic43—24no—
335Dic43—42no—
336Dic43—81no—
337Dic43—81no—
338Dic43—81no—
339Dic43—81no—
340Dic43—81no—
341C2×#479—431no—
342C2×#416—431no—
343#2441—431no—
344#2341—431no—
345#2094—431no—
346#2067—431no—
347#2065—431no—
348#2025—431no—
349#1865—431no—
350#1865—431no—
351#1854—431no—
352#1850D4311yescharacteristic, complemented
353#1807—431no—
354#1803—431no—
355#1788—431no—
356C2×C43—42no—
357C2×C43#243711yescharacteristic
358C2×C43#307611yescharacteristic
359C2×C43#308411yescharacteristic
360C2×C43#327111yescharacteristic
361C2×C43#328411yescharacteristic
362C2×C43#330111yescharacteristic
363C2×C43#331711yescharacteristic
364D43—82no—
365C22×#41—431no—
366C23×C8C2×D4311yescharacteristic
367C2×#125—431no—
368C2×C4×Q8—431no—
369C2×C4×Q8—431no—
370C2×#117—431no—
371#479—864no—
372C2×#107—431no—
373C2×#106—431no—
374C2×#106—431no—
375C2×#106—431no—
376C2×C4⋊C8C2×D4311yescharacteristic
377C2×C4⋊C8C2×D4311yescharacteristic
378#416—864no—
379C2×#103—431no—
380C2×#103—431no—
381C2×#103—431no—
382C2×#103—431no—
383C2×#102—431no—
384C2×#102—431no—
385C2×#102—431no—
386C2×#102—431no—
387C2×C22⋊C8C2×D4311yescharacteristic
388#399—861no—
389#396—861no—
390#390—431no—
391#390—431no—
392#390—861no—
393#390—861no—
394#389—431no—
395#389—431no—
396#389—861no—
397#387—861no—
398#384—431no—
399#380—431no—
400#380—431no—
401#380—861no—
402C4×C22⋊C4—861no—
403C4×C22⋊C4C2×D4311yescharacteristic
404#340—431no—
405#340—431no—
406#340—431no—
407#340—431no—
408#336C2×D4311yescharacteristic
409#336C2×D4311yescharacteristic
410C43#2595311yescharacteristic, complemented, Sylow
411C2×#41—434no—
412C2×#41—862no—
413C2×#41—862no—
414C2×#41—862no—
415C2×#41—1721no—
416C2×#41—1721no—
417C22×Q8—431no—
418C22×D4—431no—
419C22×D4—861no—
420C23×C4—861no—
421C23×C4C22×D4311yescharacteristic
422C22×C8—22no—
423C22×C8—22no—
424C22×C8—41no—
425C22×C8C22×D4311yescharacteristic
426C22×C8C22×D4311yescharacteristic
427C22×C8C22×D4311yescharacteristic
428C22×C8C22×D4311yescharacteristic
429#125—862no—
430#125—1721no—
431C4×Q8—862no—
432C4×Q8—862no—
433C4×Q8—1721no—
434C4×Q8—1721no—
435#117—862no—
436#117—1721no—
437C2×C4⋊C4—431no—
438C2×C4⋊C4—431no—
439C2×C4⋊C4—431no—
440C2×C4⋊C4—431no—
441C2×C4⋊C4—431no—
442C2×C4⋊C4—431no—
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×C22⋊C4—861no—
452C2×C22⋊C4—861no—
453C2×C22⋊C4—861no—
454C2×C22⋊C4—861no—
455C2×C22⋊C4—861no—
456C2×C22⋊C4—861no—
457C2×C22⋊C4—861no—
458C2×C22⋊C4D17211yescharacteristic
459C2×C22⋊C4D17211yescharacteristic
460C2×C42—861no—
461C2×C42—861no—
462C2×C42—861no—
463C2×C42C22×D4311yescharacteristic
464C2×C42C22×D4311yescharacteristic
465#107—862no—
466#106—862no—
467#106—1721no—
468#106—1721no—
469C4⋊C8—22no—
470C4⋊C8—41no—
471#103—434no—
472#103—862no—
473#103—862no—
474#103—862no—
475#102—862no—
476#102—862no—
477#102—1721no—
478#102—1721no—
479C22⋊C8—22no—
480#95—861no—
481#95—861no—
482#95—861no—
483#95—861no—
484#95D17211yescharacteristic
485#95D17211yescharacteristic
486C24—861no—
487C24C2×D17211yescharacteristic
488#41—868no—
489#41—1724no—
490#41—1724no—
491#41—1724no—
492C2×Q8—432no—
493C2×Q8—432no—
494C2×Q8—432no—
495C2×Q8—861no—
496C2×Q8—861no—
497C2×Q8—861no—
498C2×D4—432no—
499C2×D4—864no—
500C2×D4—861no—
501C2×D4—861no—
502C2×D4—861no—
503C2×D4—861no—
504C2×D4—861no—
505C2×D4—1722no—
506C2×D4—1722no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—861no—
512C22×C4—861no—
513C22×C4—864no—
514C22×C4—861no—
515C22×C4—861no—
516C22×C4—861no—
517C22×C4—861no—
518C22×C4—861no—
519C22×C4—1722no—
520C22×C4—1722no—
521C22×C4C2×D17211yescharacteristic
522C22×C4C2×D17211yescharacteristic
523C22×C4C2×D17211yescharacteristic
524C22×C4C2×D17211yescharacteristic
525C22×C4C2×D17211yescharacteristic
526C22×C4#1062190012yes—
527C22×C4Q8×D4312yes—
528C22×C4C23×D4311yescharacteristic
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—44no—
541C2×C8D4×D4312yes—
542C4⋊C4—432no—
543C4⋊C4—861no—
544C4⋊C4—861no—
545C4⋊C4—861no—
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—3441no—
555C4⋊C4—3441no—
556C4⋊C4—1722no—
557C4⋊C4—1722no—
558C4⋊C4—1722no—
559C4⋊C4—1722no—
560C4⋊C4—1722no—
561C4⋊C4—1722no—
562C22⋊C4—22no—
563C22⋊C4—41no—
564C22⋊C4—3441no—
565C22⋊C4—3441no—
566C22⋊C4—3441no—
567C22⋊C4—3441no—
568C22⋊C4—1722no—
569C22⋊C4—1722no—
570C22⋊C4—1722no—
571C42—21no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—1722no—
576C42—1722no—
577C42—1722no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—862no—
585C23—1721no—
586C23—1721no—
587C23—1721no—
588C23—1721no—
589C23—1721no—
590C23—1721no—
591C23#1306330512yes—
592C23C22×D17211yescharacteristic
593Q8—434no—
594Q8—862no—
595Q8—862no—
596Q8—862no—
597D4—862no—
598D4—862no—
599D4—1728no—
600D4—1721no—
601D4—1721no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—862no—
620C2×C4—862no—
621C2×C4—862no—
622C2×C4—862no—
623C2×C4—1728no—
624C2×C4—1721no—
625C2×C4—1721no—
626C2×C4—1721no—
627C2×C4—1721no—
628C2×C4—1721no—
629C2×C4—1721no—
630C2×C4—1721no—
631C2×C4—1721no—
632C2×C4—1721no—
633C2×C4—1721no—
634C2×C4—1721no—
635C2×C4—1721no—
636C2×C4—1721no—
637C2×C4—1721no—
638C2×C4—1721no—
639C2×C4—1721no—
640C2×C4—1721no—
641C2×C4#1306330512yes—
642C2×C4#1306334712yes—
643C2×C4C2×D4×D4311yescharacteristic
644C2×C4C2×Q8×D4311yescharacteristic
645C2×C4#41×D4311yescharacteristic
646C2×C4C2×#1062190011yescharacteristic
647C2×C4#1306337011yescharacteristic
648C2×C4#1306337111yescharacteristic
649C8—22no—
650C8—41no—
651C8—41no—
652C8—41no—
653C22—22no—
654C22—22no—
655C22—22no—
656C22—41no—
657C22—41no—
658C22—41no—
659C22—41no—
660C22—3441no—
661C22—3441no—
662C22—3441no—
663C22—3441no—
664C22—1722no—
665C22—1722no—
666C22—1722no—
667C22C2×#1306330511yescharacteristic
668C22D4×D17211yescharacteristic
669C22#1458354411yescharacteristic
670C22C2×#1306334711yescharacteristic
671C22#1458369911yescharacteristic
672C22#1458371111yescharacteristic
673C22#1458371111yescharacteristic
674C4—22no—
675C4—22no—
676C4—41no—
677C4—41no—
678C4—41no—
679C4—864no—
680C4—3441no—
681C4—3441no—
682C4—3441no—
683C4—3441no—
684C4—3441no—
685C4—1722no—
686C4C22⋊Q8×D4311yescharacteristic
687C4#1458352411yescharacteristic
688C4#1458353611yescharacteristic
689C4#1458357211yescharacteristic
690C2—42no—
691C2—3442no—
692C2#1913825911yescharacteristic
693C2#1914438511yescharacteristic
694C2#1914445911yescharacteristic
695C2#1914618511yescharacteristic
696C2#1914632711yescharacteristic
697C2#1914649911yescharacteristic
698C2#1914672311yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1850C2
socleC23×C43C22×D4
prime radicalC22×#10621898C22
hypercenter#1850D43
hypocenterC43#25953
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
1. C2×#14583207C2semidirect
3. #19138308C2semidirect
5. #19136127C2semidirect
6. #19135982C2semidirect
7. #19135968C2semidirect
8. #19135742C2semidirect
9. #19134866C2semidirect
10. #19134866C2semidirect
11. #19134796C2semidirect
12. #19134620C2semidirect
13. #19134601C2semidirect
15. C43×#1850C2semidirect
352. #1850D43semidirect
410. C43#25953semidirect

Maximal subgroups

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

subgroupindex
C2×#145832072
C2×#145828962
#191383082
#191374352
#191361272
#191359822
#191359682
#191357422
#191348662
#191347962
#191346202
#191346012
#191345362
C43×#18502
#2595343