Finite Group Databasebeta

← #25164775

Subgroups — #25164775

Order 11008.

824 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#19138943C211yesmaximal, characteristic, complemented
2#19137633C211yesmaximal, characteristic, complemented
3#19135907C211yesmaximal, characteristic, complemented
4#19135777C211yesmaximal, characteristic, complemented
5#19135740C211yesmaximal, characteristic, complemented
6#19135593C211yesmaximal, characteristic
7#19135551C211yesmaximal, characteristic, complemented
8#19135276C211yesmaximal, characteristic, complemented
9#19135213C211yesmaximal, characteristic, complemented
10#19135198C211yesmaximal, characteristic, complemented
11#19135185C211yesmaximal, characteristic, complemented
12#19134944C211yesmaximal, characteristic, complemented
13#19134917C211yesmaximal, characteristic, complemented
14#19134409C211yesmaximal, characteristic, complemented
15C43×#1825C211yesmaximal, characteristic, complemented
16C22×D344C2211yescharacteristic
17C2×#13063316C2211yescharacteristic
18C2×#13063299C2211yescharacteristic
19C2×#13063299C2211yescharacteristic
20C2×#13063287C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×Dic43⋊C8C2211yescharacteristic
23C2×#13063247C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063245C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×C22⋊(C43⋊C8)C2211yescharacteristic
30C2×C8×Dic43C2211yescharacteristic
31#14582828—21no—
32#14582815—21no—
33#14582800C2211yescharacteristic
34#14582800C2211yescharacteristic
35#14582800C2211yescharacteristic
36#14582799—21no—
37#14582799—21no—
38#14582795C2211yescharacteristic
39#14582791—21no—
40#14582790—21no—
41#14582775—21no—
42C4⋊C4×Dic43C2211yescharacteristic
43C4⋊C4×Dic43C2211yescharacteristic
44C4×(C2×D43)⋊C4—21no—
45C4×C22⋊Dic43C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#117×C43C2211yescharacteristic
53C2×C22⋊C8×C43C2211yescharacteristic
54C43×#380C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×D172C2311yescharacteristic
60C22×D172C2311yescharacteristic
61C22×C22⋊D43—21no—
62C22×C22⋊D43—21no—
63C22×C4×D43—21no—
64C2×D344—22no—
65C2×D344—41no—
66C2×D344—41no—
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69#13063316—22no—
70#13063316—41no—
71#13063299—22no—
72#13063299—22no—
73#13063299—22no—
74#13063299—41no—
75#13063287—22no—
76#13063287—41no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×C22⋊Dic43D411yescharacteristic
83C2×C22⋊Dic43D411yescharacteristic
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—
94C2×C4×Dic43—21no—
95C2×C4×Dic43C2311yescharacteristic
96C2×C4×Dic43C2311yescharacteristic
97#13063258—22no—
98Dic43⋊C8—41no—
99#13063247—22no—
100#13063247—22no—
101#13063245—22no—
102#13063245—22no—
103#13063245—41no—
104#13063245—41no—
105C22⋊(C43⋊C8)—41no—
106C8×Dic43—41no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95D411yescharacteristic
111C43⋊#95D411yescharacteristic
112C23×C4×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115#117×C43—22no—
116#117×C43—41no—
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C22⋊C4×C43—21no—
122C2×C22⋊C4×C43—21no—
123C2×C42×C43—21no—
124C22⋊C8×C43—41no—
125#95×C43—21no—
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×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2411yescharacteristic
141C2×C22⋊D43—24no—
142C2×C22⋊D43—42no—
143C2×C22⋊D43—42no—
144C2×C22⋊D43—81no—
145C2×C22⋊D43—81no—
146C2×C22⋊D43—81no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
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—42no—
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—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43#4112yes—
182C22⋊C4×C43—42no—
183C22⋊C4×C43—81no—
184C42×C43—42no—
185C22⋊Dic43—22no—
186C22⋊Dic43—41no—
187(C2×D43)⋊C4—24no—
188(C2×D43)⋊C4—42no—
189(C2×D43)⋊C4—42no—
190(C2×D43)⋊C4—42no—
191(C2×D43)⋊C4—42no—
192(C2×D43)⋊C4—81no—
193(C2×D43)⋊C4—81no—
194(C2×D43)⋊C4—81no—
195(C2×D43)⋊C4—81no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—42no—
199C4⋊Dic43#4112yes—
200C4⋊Dic43#4112yes—
201Dic43⋊C4—42no—
202Dic43⋊C4—81no—
203C4×Dic43—21no—
204C4×Dic43—21no—
205C4×Dic43—21no—
206C4×Dic43—21no—
207C4×Dic43—81no—
208C4×Dic43—81no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
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—22no—
241C2×C4×C43—21no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
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—21no—
266C2×Dic43—21no—
267C2×Dic43—22no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—22no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—21no—
277C2×Dic43—21no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43#13512yes—
283D172—22no—
284D172—22no—
285D172—41no—
286D172—41no—
287D172—41no—
288D172—41no—
289D172—41no—
290D172—41no—
291C4×D43—84no—
292C8×C43—41no—
293C8×C43—41no—
294C43⋊C8—41no—
295C43⋊C8—41no—
296#26730—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#54611yescharacteristic
306C22×C43#54611yescharacteristic
307C22×C43C2×#13511yescharacteristic
308C22×C43#57511yescharacteristic
309C22×C43#57611yescharacteristic
310C22×C43#57611yescharacteristic
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—42no—
327C4×C43—81no—
328C4×C43—81no—
329C4×C43—81no—
330C4×C43#52911yescharacteristic
331C4×C43#53811yescharacteristic
332C4×C43#55511yescharacteristic
333C4×C43#55911yescharacteristic
334Dic43—22no—
335Dic43—42no—
336Dic43—41no—
337Dic43—41no—
338Dic43—41no—
339Dic43—42no—
340#2490—431no—
341#2363—431no—
342#2054—431no—
343#2033—431no—
344#2025—431no—
345#1999—431no—
346#1989—431no—
347#1934—431no—
348#1925—431no—
349#1923—431no—
350#1921—431no—
351#1879—431no—
352#1875—431no—
353#1825D4311yescharacteristic, complemented
354C4×#102—431no—
355C2×C43—81no—
356C2×C43#245911yescharacteristic
357C2×C43#310211yescharacteristic
358C2×C43#312211yescharacteristic
359C2×C43#329711yescharacteristic
360C2×C43#330511yescharacteristic
361C2×C43#330911yescharacteristic
362C2×C43#332211yescharacteristic
363D43—82no—
364D43—161no—
365C22×D8—431no—
366C2×#125—431no—
367C2×#121—431no—
368C2×#121—431no—
369C2×C4×D4—431no—
370C2×#117C2×D4311yescharacteristic
371C2×#107—431no—
372C2×C4⋊C8—431no—
373C2×#102—431no—
374C2×#102—431no—
375C2×#102—431no—
376C2×#102—431no—
377C2×#102—431no—
378C2×#102—431no—
379C2×C22⋊C8—431no—
380C2×C22⋊C8C2×D4311yescharacteristic
381C2×C4×C8—431no—
382#397—861no—
383#394—861no—
384#390—431no—
385#390—431no—
386#390—431no—
387#390—861no—
388#390—861no—
389#389—431no—
390#388—861no—
391#388—861no—
392#386—861no—
393#380C2×D4311yescharacteristic
394C4×C4⋊C4—431no—
395C4×C4⋊C4—431no—
396C4×C22⋊C4—431no—
397C4×C22⋊C4—861no—
398#340—431no—
399#340—431no—
400#340—431no—
401#340—431no—
402#340C2×D4311yescharacteristic
403#340C2×D4311yescharacteristic
404#340C2×D4311yescharacteristic
405#340C2×D4311yescharacteristic
406#336—431no—
407#336—431no—
408C43#2673011yescharacteristic, 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—1721no—
417C2×D8—1721no—
418C22×C8—431no—
419C22×C8—431no—
420C22×C8C22×D4311yescharacteristic
421C22×C8C22×D4311yescharacteristic
422#125—862no—
423#125—1721no—
424#121—862no—
425#121—862no—
426#121—862no—
427#121—1721no—
428C4×D4—862no—
429C4×D4—1721no—
430#117—22no—
431#117—41no—
432C2×C4⋊C4—431no—
433C2×C4⋊C4—431no—
434C2×C4⋊C4—861no—
435C2×C4⋊C4—861no—
436C2×C4⋊C4—861no—
437C2×C4⋊C4C22×D4311yescharacteristic
438C2×C4⋊C4C22×D4311yescharacteristic
439C2×C4⋊C4C22×D4311yescharacteristic
440C2×C4⋊C4C22×D4311yescharacteristic
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—431no—
444C2×C22⋊C4—431no—
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⋊C4—861no—
453C2×C22⋊C4—861no—
454C2×C42—21no—
455C2×C42—431no—
456C2×C42—431no—
457C2×C42—861no—
458C2×C42—861no—
459#107—862no—
460C4⋊C8—1721no—
461#102—862no—
462#102—862no—
463#102—862no—
464#102—862no—
465#102—1721no—
466#102—1721no—
467C22⋊C8—41no—
468C22⋊C8—1721no—
469C4×C8—1721no—
470#95—21no—
471#95—431no—
472#95—431no—
473#95—861no—
474#95—861no—
475#95—861no—
476C24—861no—
477C24—861no—
478C24D4×D4311yescharacteristic
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—1722no—
496C2×D4—1722no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—431no—
508C22×C4—431no—
509C22×C4—431no—
510C22×C4—431no—
511C22×C4—861no—
512C22×C4—861no—
513C22×C4—3441no—
514C22×C4—1722no—
515C22×C4—1722no—
516C22×C4D4×D4311yescharacteristic
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—861no—
526C2×C8—861no—
527C2×C8—861no—
528C2×C8—861no—
529C2×C8—861no—
530C2×C8—861no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—432no—
539C4⋊C4—432no—
540C4⋊C4—861no—
541C4⋊C4—861no—
542C4⋊C4—3441no—
543C4⋊C4—1722no—
544C4⋊C4—1722no—
545C4⋊C4#1062189812yes—
546C22⋊C4—42no—
547C22⋊C4—81no—
548C22⋊C4—864no—
549C22⋊C4—862no—
550C22⋊C4—3441no—
551C22⋊C4—3441no—
552C22⋊C4—3441no—
553C22⋊C4—3441no—
554C22⋊C4—1722no—
555C22⋊C4—1722no—
556C22⋊C4—1722no—
557C22⋊C4—1722no—
558C22⋊C4—1721no—
559C42—42no—
560C42—861no—
561C42—861no—
562C42—861no—
563C42—861no—
564C42—3441no—
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—
587C23C2×D4×D4311yescharacteristic
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—22no—
601C2×C4—21no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—432no—
618C2×C4—861no—
619C2×C4—861no—
620C2×C4—862no—
621C2×C4—861no—
622C2×C4—861no—
623C2×C4—861no—
624C2×C4—861no—
625C2×C4—861no—
626C2×C4—861no—
627C2×C4—861no—
628C2×C4—861no—
629C2×C4—861no—
630C2×C4—862no—
631C2×C4—3444no—
632C2×C4—1721no—
633C2×C4—1721no—
634C2×C4—1721no—
635C2×C4—1721no—
636C2×C4#41×D4311yescharacteristic
637C2×C4#41×D4311yescharacteristic
638C2×C4#41×D4311yescharacteristic
639C2×C4C2×#1062189811yescharacteristic
640C2×C4#1306337011yescharacteristic
641C2×C4#1306337111yescharacteristic
642C8—41no—
643C8—41no—
644C8—1721no—
645C8—1721no—
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#1458340711yescharacteristic
668C22#1458353911yescharacteristic
669C22#1458354111yescharacteristic
670C22#135×D4311yescharacteristic
671C22#1458369811yescharacteristic
672C22#1458370111yescharacteristic
673C22#1458370311yescharacteristic
674C4—42no—
675C4—41no—
676C4—81no—
677C4—81no—
678C4—81no—
679C4—862no—
680C4—1721no—
681C4—1722no—
682C4—1721no—
683C4—1721no—
684C4—1722no—
685C4#1458342711yescharacteristic
686C4#1458348511yescharacteristic
687C4#1458361211yescharacteristic
688C4#1458363311yescharacteristic
689C2—81no—
690C2—3442no—
691C2—6881no—
692C2#1913852911yescharacteristic
693C2#1914461611yescharacteristic
694C2#1914483411yescharacteristic
695C2#1914644611yescharacteristic
696C2#1914654311yescharacteristic
697C2#1914660211yescharacteristic
698C2#1914679411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1825C2
socleC23×C43C22×D4
prime radical#19135593C2
hypercenter#1825D43
hypocenterC43#26730
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1825

Complements

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

NH ≅ G/Ntype
1. #19138943C2semidirect
2. #19137633C2semidirect
3. #19135907C2semidirect
4. #19135777C2semidirect
5. #19135740C2semidirect
7. #19135551C2semidirect
8. #19135276C2semidirect
9. #19135213C2semidirect
10. #19135198C2semidirect
11. #19135185C2semidirect
12. #19134944C2semidirect
13. #19134917C2semidirect
14. #19134409C2semidirect
15. C43×#1825C2semidirect
353. #1825D43semidirect
408. C43#26730semidirect

Maximal subgroups

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

subgroupindex
#191389432
#191376332
#191359072
#191357772
#191357402
#191355932
#191355512
#191352762
#191352132
#191351982
#191351852
#191349442
#191349172
#191344092
C43×#18252
#2673043