Finite Group Databasebeta

← #25200225

Subgroups — #25200225

Order 11008.

798 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
1#19140384C211yesmaximal, characteristic, complemented
2#19137288C211yesmaximal, characteristic, complemented
3#19136018C211yesmaximal, characteristic, complemented
4#19135785C211yesmaximal, characteristic, complemented
5#19135785C211yesmaximal, characteristic, complemented
6#19135593C211yesmaximal, characteristic
7#19135461C211yesmaximal, characteristic, complemented
8#19135323C211yesmaximal, characteristic, complemented
9#19135292C211yesmaximal, characteristic, complemented
10#19135292C211yesmaximal, characteristic, complemented
11#19135223C211yesmaximal, characteristic, complemented
12#19135167C211yesmaximal, characteristic, complemented
13#19134942C211yesmaximal, characteristic, complemented
14#19134859C211yesmaximal, characteristic, complemented
15C43×#1750C211yesmaximal, characteristic, complemented
16C22×D344C2211yescharacteristic
17C2×#13063299C2211yescharacteristic
18C2×#13063299C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic
20C2×#13063259C2211yescharacteristic
21C2×#13063257C2211yescharacteristic
22C2×#13063257C2211yescharacteristic
23C2×#13063247C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063247C2211yescharacteristic
29#14582834—21no—
30#14582825—21no—
31#14582814—21no—
32#14582814—21no—
33#14582801C2211yescharacteristic
34#14582801C2211yescharacteristic
35#14582801C2211yescharacteristic
36#14582799—21no—
37#14582797C2211yescharacteristic
38#14582797C2211yescharacteristic
39#14582797C2211yescharacteristic
40#14582789—21no—
41#14582775—21no—
42#14582770—21no—
43#14582759C2211yescharacteristic
44#14582759C2211yescharacteristic
45C4×C4⋊Dic43C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52C2×#117×C43C2211yescharacteristic
53C2×C22⋊C8×C43C2211yescharacteristic
54C2×C22⋊C8×C43C2211yescharacteristic
55C2×#97×C43C2211yescharacteristic
56C2×C4×C8×C43C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×D172C2311yescharacteristic
60C22×D172C2311yescharacteristic
61C22×C22⋊D43—21no—
62C22×C22⋊D43—21no—
63C22×C4×D43—21no—
64C2×D344—22no—
65C2×D344—22no—
66C2×D344—41no—
67#13063299—22no—
68#13063299—22no—
69#13063299—41no—
70#13063299—41no—
71C4×D172—41no—
72C4×D172—41no—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×C4×Dic43—21no—
94#13063259—22no—
95#13063257—22no—
96#13063257—41no—
97#13063247—22no—
98#13063247—22no—
99#13063247—22no—
100#13063247—22no—
101#13063247—41no—
102#13063247—41no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C23×C4×C43C2311yescharacteristic
110C22×C8×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114#117×C43—41no—
115#117×C43—41no—
116C2×C4⋊C4×C43D411yescharacteristic
117C2×C4⋊C4×C43D411yescharacteristic
118C2×C22⋊C4×C43D411yescharacteristic
119C2×C22⋊C4×C43D411yescharacteristic
120C2×C42×C43C2311yescharacteristic
121C2×C42×C43C2311yescharacteristic
122C22⋊C8×C43—22no—
123C22⋊C8×C43—22no—
124#97×C43—41no—
125C4×C8×C43—41no—
126C24×C43C2×D411yescharacteristic
127C23×D43—21no—
128C23×D43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2411yescharacteristic
141C2×C22⋊D43—24no—
142C2×C22⋊D43—42no—
143C2×C22⋊D43—81no—
144C2×C22⋊D43—81no—
145C2×C22⋊D43—81no—
146C2×C22⋊D43—81no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172#4112yes—
165C2×C4×D43—42no—
166C2×C4×D43—81no—
167C2×C4×D43—81no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43#4112yes—
179C2×C8×C43#4112yes—
180C4⋊C4×C43—41no—
181C4⋊C4×C43—41no—
182C22⋊C4×C43—41no—
183C22⋊C4×C43—41no—
184C42×C43—21no—
185C42×C43—21no—
186C42×C43—21no—
187C42×C43—21no—
188C22⋊Dic43—81no—
189C22⋊Dic43—81no—
190(C2×D43)⋊C4—24no—
191(C2×D43)⋊C4—42no—
192(C2×D43)⋊C4—42no—
193(C2×D43)⋊C4—81no—
194(C2×D43)⋊C4—81no—
195(C2×D43)⋊C4—81no—
196(C2×D43)⋊C4—81no—
197(C2×D43)⋊C4—81no—
198(C2×D43)⋊C4—81no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43#4112yes—
211Dic43⋊C4—81no—
212Dic43⋊C4—81no—
213Dic43⋊C4—81no—
214C4×Dic43—81no—
215D344—44no—
216C23×C43—21no—
217C23×C43—21no—
218C23×C43—21no—
219C23×C43—21no—
220C23×C43—21no—
221C23×C43—21no—
222C23×C43—21no—
223C23×C43C22×D411yescharacteristic
224C22×D43—22no—
225C22×D43—41no—
226C22×D43—41no—
227C22×D43—41no—
228C22×D43—41no—
229C22×D43—41no—
230C22×D43—41no—
231C22×D43—41no—
232C22×D43—41no—
233C22×D43—41no—
234C22×D43—41no—
235C22×D43—41no—
236C22×D43—41no—
237C22×D43—41no—
238C2×C4×C43—21no—
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—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×C4×C43C2×#4111yescharacteristic
261C2×C4×C43H(5,𝔽2)11yescharacteristic
262C2×C4×C43H(5,𝔽2)11yescharacteristic
263C22⋊D43—84no—
264C22⋊D43—84no—
265C2×Dic43—22no—
266C2×Dic43—41no—
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—
283D172—22no—
284D172—22no—
285D172—41no—
286D172—41no—
287D172—41no—
288D172—41no—
289D172—41no—
290D172—41no—
291C4×D43—84no—
292C8×C43—22no—
293C8×C43—22no—
294C8×C43—41no—
295C8×C43—41no—
296#29469—431nomaximal, Sylow
297C22×C43—41no—
298C22×C43—41no—
299C22×C43—41no—
300C22×C43—41no—
301C22×C43—41no—
302C22×C43—41no—
303C22×C43—41no—
304C22×C43#52511yescharacteristic
305C22×C43#53211yescharacteristic
306C22×C43#53411yescharacteristic
307C22×C43#57611yescharacteristic
308C22×C43#57611yescharacteristic
309C22×C43#57711yescharacteristic
310C22×C43#57711yescharacteristic
311C2×D43—42no—
312C2×D43—42no—
313C2×D43—42no—
314C2×D43—81no—
315C2×D43—81no—
316C2×D43—81no—
317C2×D43—81no—
318C2×D43—81no—
319C2×D43—81no—
320C2×D43—81no—
321C2×D43—81no—
322C2×D43—81no—
323C2×D43—81no—
324C2×D43—81no—
325C4×C43—41no—
326C4×C43—41no—
327C4×C43—41no—
328C4×C43—41no—
329C4×C43—41no—
330C4×C43#55111yescharacteristic
331C4×C43#55311yescharacteristic
332C4×C43#55311yescharacteristic
333C4×C43#55911yescharacteristic
334Dic43—42no—
335Dic43—81no—
336Dic43—81no—
337Dic43—81no—
338Dic43—81no—
339Dic43—81no—
340#2624—431no—
341#2324—431no—
342#2075—431no—
343#2034—431no—
344#2034—431no—
345#1999—431no—
346#1970—431no—
347#1941—431no—
348#1936—431no—
349#1936—431no—
350#1926—431no—
351#1918—431no—
352#1879—431no—
353#1864—431no—
354#1750D4311yescharacteristic, complemented
355C2×C43—81no—
356C2×C43#260211yescharacteristic
357C2×C43#311811yescharacteristic
358C2×C43#311911yescharacteristic
359C2×C43#317311yescharacteristic
360C2×C43#317611yescharacteristic
361C2×C43#319811yescharacteristic
362C2×C43#319811yescharacteristic
363D43—82no—
364D43—161no—
365C22×D8—431no—
366C2×#121—431no—
367C2×#121—431no—
368C2×C4×D4—431no—
369C2×#117C2×D4311yescharacteristic
370C2×#107—431no—
371C2×#106—431no—
372C2×#106—431no—
373C2×#102—431no—
374C2×#102—431no—
375C2×#102—431no—
376C2×#102—431no—
377C2×#102—431no—
378C2×#102—431no—
379C2×C22⋊C8C2×D4311yescharacteristic
380C2×C22⋊C8C2×D4311yescharacteristic
381C2×#97C2×D4311yescharacteristic
382C2×C4×C8C2×D4311yescharacteristic
383#399—861no—
384#397—861no—
385#394—861no—
386#394—861no—
387#390—431no—
388#390—431no—
389#390—431no—
390#390—861no—
391#389—431no—
392#389—431no—
393#389—431no—
394#388—861no—
395#386—861no—
396#385—861no—
397#380—431no—
398#380—431no—
399C4×C4⋊C4—431no—
400#340—431no—
401#340—431no—
402#340—431no—
403#340—431no—
404#340—431no—
405#340—431no—
406#336C2×D4311yescharacteristic
407#336C2×D4311yescharacteristic
408C43#2946911yescharacteristic, complemented, Sylow
409C22×D4—431no—
410C22×D4—431no—
411C22×D4—861no—
412C22×D4—861no—
413C23×C4—861no—
414C23×C4C22×D4311yescharacteristic
415C2×D8—862no—
416C2×D8—862no—
417C2×D8—1721no—
418C22×C8C22×D4311yescharacteristic
419C22×C8C22×D4311yescharacteristic
420C22×C8C22×D4311yescharacteristic
421C22×C8C22×D4311yescharacteristic
422#121—862no—
423#121—862no—
424#121—1721no—
425#121—1721no—
426C4×D4—1721no—
427C4×D4—1721no—
428#117—41no—
429#117—41no—
430C2×C4⋊C4—431no—
431C2×C4⋊C4—431no—
432C2×C4⋊C4—431no—
433C2×C4⋊C4—431no—
434C2×C4⋊C4—431no—
435C2×C4⋊C4—431no—
436C2×C4⋊C4—861no—
437C2×C4⋊C4—861no—
438C2×C4⋊C4—861no—
439C2×C4⋊C4D17211yescharacteristic
440C2×C4⋊C4D17211yescharacteristic
441C2×C22⋊C4—861no—
442C2×C22⋊C4—861no—
443C2×C22⋊C4—861no—
444C2×C22⋊C4—861no—
445C2×C22⋊C4—861no—
446C2×C22⋊C4—861no—
447C2×C22⋊C4—861no—
448C2×C22⋊C4—861no—
449C2×C22⋊C4—861no—
450C2×C22⋊C4—861no—
451C2×C22⋊C4—861no—
452C2×C22⋊C4D17211yescharacteristic
453C2×C22⋊C4D17211yescharacteristic
454C2×C42—861no—
455C2×C42C22×D4311yescharacteristic
456C2×C42C22×D4311yescharacteristic
457#107—862no—
458#106—862no—
459#106—1721no—
460#102—862no—
461#102—862no—
462#102—862no—
463#102—862no—
464#102—1721no—
465#102—1721no—
466C22⋊C8—22no—
467C22⋊C8—22no—
468#97—41no—
469C4×C8—41no—
470#95—861no—
471#95—861no—
472#95—861no—
473#95—861no—
474#95—861no—
475#95—861no—
476C24—861no—
477C24—861no—
478C24C2×D17211yescharacteristic
479C2×D4—432no—
480C2×D4—864no—
481C2×D4—861no—
482C2×D4—861no—
483C2×D4—861no—
484C2×D4—861no—
485C2×D4—861no—
486C2×D4—861no—
487C2×D4—861no—
488C2×D4—861no—
489C2×D4—861no—
490C2×D4—861no—
491C2×D4—861no—
492C2×D4—3441no—
493C2×D4—3441no—
494C2×D4—3441no—
495C2×D4—3441no—
496C2×D4—1722no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—861no—
504C22×C4—861no—
505C22×C4—861no—
506C22×C4—861no—
507C22×C4—861no—
508C22×C4—861no—
509C22×C4—3441no—
510C22×C4—3441no—
511C22×C4—1722no—
512C22×C4C2×D17211yescharacteristic
513C22×C4C2×D17211yescharacteristic
514C22×C4C2×D17211yescharacteristic
515C22×C4C2×D17211yescharacteristic
516C22×C4C2×D17211yescharacteristic
517C22×C4C23×D4311yescharacteristic
518D8—1724no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8#1062189812yes—
530C2×C8#1062189812yes—
531C4⋊C4—41no—
532C4⋊C4—41no—
533C4⋊C4—432no—
534C4⋊C4—861no—
535C4⋊C4—861no—
536C4⋊C4—861no—
537C4⋊C4—861no—
538C4⋊C4—861no—
539C4⋊C4—861no—
540C4⋊C4—861no—
541C4⋊C4—861no—
542C4⋊C4—861no—
543C4⋊C4—861no—
544C4⋊C4—861no—
545C4⋊C4—3441no—
546C4⋊C4—3441no—
547C4⋊C4—3441no—
548C22⋊C4—41no—
549C22⋊C4—41no—
550C22⋊C4—864no—
551C22⋊C4—3441no—
552C22⋊C4—3441no—
553C22⋊C4—3441no—
554C22⋊C4—3441no—
555C22⋊C4—3441no—
556C22⋊C4—3441no—
557C22⋊C4—3441no—
558C22⋊C4—3441no—
559C22⋊C4—1722no—
560C22⋊C4—1722no—
561C42—21no—
562C42—21no—
563C42—21no—
564C42—21no—
565C42—3441no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—862no—
574C23—1721no—
575C23—1721no—
576C23—1721no—
577C23—1721no—
578C23—1721no—
579C23—1721no—
580C23—1721no—
581C23—1721no—
582C23—1721no—
583C23—1721no—
584C23—1721no—
585C23—1721no—
586C23—1721no—
587C23C22×D17211yescharacteristic
588D4—862no—
589D4—862no—
590D4—3444no—
591D4—3444no—
592D4—1721no—
593D4—1721no—
594D4—1721no—
595D4—1721no—
596D4—1721no—
597D4—1721no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—862no—
618C2×C4—3444no—
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—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#41×D4311yescharacteristic
637C2×C4#41×D4311yescharacteristic
638C2×C4C2×#1062189811yescharacteristic
639C2×C4C2×#1062189811yescharacteristic
640C2×C4#1306337011yescharacteristic
641C2×C4#1306337011yescharacteristic
642C8—22no—
643C8—22no—
644C8—41no—
645C8—41no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—3441no—
654C22—3441no—
655C22—3441no—
656C22—3441no—
657C22—3441no—
658C22—3441no—
659C22—3441no—
660C22—3441no—
661C22—3441no—
662C22—3441no—
663C22—3441no—
664C22—1722no—
665C22—1722no—
666C22—1722no—
667C22#1458341111yescharacteristic
668C22#1458344911yescharacteristic
669C22#1458346111yescharacteristic
670C22#1458370411yescharacteristic
671C22#1458370411yescharacteristic
672C22#1458371111yescharacteristic
673C22#1458371111yescharacteristic
674C4—41no—
675C4—41no—
676C4—41no—
677C4—41no—
678C4—41no—
679C4—3441no—
680C4—3441no—
681C4—3441no—
682C4—3441no—
683C4—3441no—
684C4—1722no—
685C4#1458357811yescharacteristic
686C4#1458359811yescharacteristic
687C4#1458359911yescharacteristic
688C4#1458363211yescharacteristic
689C2—81no—
690C2—3442no—
691C2—6881no—
692C2#1914020111yescharacteristic
693C2#1914478111yescharacteristic
694C2#1914479611yescharacteristic
695C2#1914521211yescharacteristic
696C2#1914524511yescharacteristic
697C2#1914544911yescharacteristic
698C2#1914544911yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1750C2
socleC23×C43C22×D4
prime radical#19135593C2
hypercenter#1750D43
hypocenterC43#29469
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #1750

Complements

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

NH ≅ G/Ntype
1. #19140384C2semidirect
2. #19137288C2semidirect
3. #19136018C2semidirect
4. #19135785C2semidirect
5. #19135785C2semidirect
7. #19135461C2semidirect
8. #19135323C2semidirect
9. #19135292C2semidirect
10. #19135292C2semidirect
11. #19135223C2semidirect
12. #19135167C2semidirect
13. #19134942C2semidirect
14. #19134859C2semidirect
15. C43×#1750C2semidirect
354. #1750D43semidirect
408. C43#29469semidirect

Maximal subgroups

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

subgroupindex
#191403842
#191372882
#191360182
#191357852
#191355932
#191354612
#191353232
#191352922
#191352232
#191351672
#191349422
#191348592
C43×#17502
#2946943