Finite Group Databasebeta

← #25148451

Subgroups — #25148451

Order 11008.

818 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583188C211yesmaximal, characteristic
2C2×C8×Dic86C211yesmaximal, characteristic, complemented
3#19139802C211yesmaximal, characteristic, complemented
4#19139516C211yesmaximal, characteristic
5#19136096C211yesmaximal, characteristic, complemented
6#19136094C211yesmaximal, characteristic, complemented
7#19135966C211yesmaximal, characteristic
8#19135964C211yesmaximal, characteristic
9#19135554C211yesmaximal, characteristic, complemented
10#19135355C211yesmaximal, characteristic, complemented
11#19135322C211yesmaximal, characteristic, complemented
12#19135278C211yesmaximal, characteristic
13#19135276C211yesmaximal, characteristic
14#19134409C211yesmaximal, characteristic
15C43×#1941C211yesmaximal, characteristic, complemented
16C2×#13063324C2211yescharacteristic
17C2×#13063303—21no—
18C2×C4×Dic86C2211yescharacteristic
19C2×#13063287C2211yescharacteristic
20#14583188—24no—
21C8×Dic86—24no—
22C2×#13063256C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×C4⋊(C43⋊C8)C2211yescharacteristic
25C2×Dic43⋊C8C2211yescharacteristic
26C2×Dic43⋊C8C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063247C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×C8×Dic43C2211yescharacteristic
32C2×C8×Dic43C2211yescharacteristic
33#14582823—21no—
34#14582821—21no—
35#14582820—21no—
36#14582819—21no—
37#14582803—21no—
38#14582801C2211yescharacteristic
39#14582800C2211yescharacteristic
40#14582798C2211yescharacteristic
41#14582797C2211yescharacteristic
42#14582795C2211yescharacteristic
43#14582795C2211yescharacteristic
44#14582768—21no—
45#14582768C2211yescharacteristic
46#14582758—21no—
47C4⋊C4×Dic43C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54C2×#106×C43C2211yescharacteristic
55C2×#106×C43C2211yescharacteristic
56C2×C4×C8×C43C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#389C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86—21no—
62C22×Dic86D411yescharacteristic
63C22×D172C2311yescharacteristic
64C22×C4×D43—21no—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063324—22no—
68#13063324—22no—
69#13063303—44no—
70C4×Dic86—22no—
71C4×Dic86—22no—
72#13063287—22no—
73#13063287—22no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43D411yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4D411yescharacteristic
86C2×Dic43⋊C4D411yescharacteristic
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×C4×Dic43—21no—
93C2×C4×Dic43C2311yescharacteristic
94C2×C4×Dic43C2311yescharacteristic
95#13063256—22no—
96#13063256—22no—
97C4⋊(C43⋊C8)—22no—
98Dic43⋊C8—22no—
99Dic43⋊C8D414yes—
100#13063247—22no—
101#13063247Q814yescomplemented
102#13063245—22no—
103#13063245—22no—
104C8×Dic43—22no—
105C8×Dic43—22no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C22×C8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C2×C4⋊C4×C43—21no—
114C2×C4⋊C4×C43—21no—
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C42×C43C2311yescharacteristic
120#106×C43—22no—
121#106×C43—22no—
122C4×C8×C43—22no—
123#95×C43—21no—
124#95×C43—21no—
125C23×D43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2411yescharacteristic
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43C2×D411yescharacteristic
137C22×Dic43C2×D411yescharacteristic
138C22×Dic43C2×D411yescharacteristic
139C22×Dic43C2×D411yescharacteristic
140C2×D172—21no—
141C2×D172—21no—
142C2×D172—21no—
143C2×D172—21no—
144C2×D172—21no—
145C2×D172C2×Q812yes—
146C2×C4×D43—42no—
147C2×C4×D43—42no—
148C2×C4×D43—42no—
149C2×Dic86—22no—
150C2×Dic86—22no—
151C2×Dic86—42no—
152C2×Dic86—81no—
153C2×Dic86—81no—
154C2×Dic86SD1614yes—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43C2×D412yes—
160C2×C8×C43C2×Q812yes—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—42no—
169C4⋊C4×C43—81no—
170C4⋊C4×C43#4112yes—
171C42×C43—21no—
172C42×C43—21no—
173(C2×D43)⋊C4—42no—
174(C2×D43)⋊C4—42no—
175(C2×D43)⋊C4—42no—
176(C2×D43)⋊C4—81no—
177(C2×D43)⋊C4—81no—
178C4⋊Dic43—21no—
179C4⋊Dic43—22no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—81no—
185C4⋊Dic43C2×Q812yes—
186Dic43⋊C4—22no—
187Dic43⋊C4—22no—
188Dic43⋊C4—42no—
189Dic43⋊C4—42no—
190Dic43⋊C4—42no—
191Dic43⋊C4—81no—
192Dic43⋊C4—81no—
193Dic43⋊C4—81no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—42no—
197C4×Dic43C2×D412yes—
198C4×Dic43#4112yes—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8C2×D412yes—
205C23×C43C22×D411yescharacteristic
206C22×D43—22no—
207C22×D43—41no—
208C22×D43—41no—
209C22×D43—41no—
210C22×D43—41no—
211C22×D43—41no—
212C22×D43—41no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—22no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43C2×SD1612yes—
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43C22×Q811yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C432−1+411yescharacteristic
236C2×C4×C432−1+411yescharacteristic
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—22no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43#12112yes—
254C2×Dic43#12112yes—
255C2×Dic43C2×SD1612yes—
256C2×Dic43C2×SD1612yes—
257C2×Dic43#13512yes—
258D172—22no—
259D172—22no—
260D172—41no—
261D172—41no—
262C4×D43—84no—
263Dic86—28no—
264Dic86—84no—
265C8×C43—22no—
266C8×C43—22no—
267C43⋊C8—22no—
268C43⋊C8—41no—
269#25470—431nomaximal, Sylow
270C22×C43C2×#12111yescharacteristic
271C22×C43#54811yescharacteristic
272C22×C43D4×Q811yescharacteristic
273C22×C43C22×SD1611yescharacteristic
274C22×C43C2×#13511yescharacteristic
275C22×C43#57611yescharacteristic
276C22×C43#57711yescharacteristic
277C2×D43—42no—
278C2×D43—42no—
279C2×D43—42no—
280C2×D43—81no—
281C2×D43—81no—
282C2×D43—81no—
283C2×D43—81no—
284C4×C43—22no—
285C4×C43—42no—
286C4×C43—41no—
287C4×C43—81no—
288C4×C43—81no—
289C4×C43—81no—
290C4×C43#53311yescharacteristic
291C4×C43#54111yescharacteristic
292C4×C43#54711yescharacteristic
293C4×C43D4×Q811yescharacteristic
294Dic43—22no—
295Dic43—22no—
296Dic43—42no—
297Dic43—41no—
298Dic43—81no—
299Dic43—81no—
300Dic43#46514yes—
301C2×#476—431no—
302C2×C8×Q8—431no—
303#2567—431no—
304#2538—431no—
305#2088—431no—
306#2088—431no—
307#2065—431no—
308#2065—431no—
309#1990—431no—
310#1948—431no—
311#1941—431no—
312#1941D4311yescharacteristic, complemented
313#1934—431no—
314#1934—431no—
315C4×#102—431no—
316C2×C43#242911yescharacteristic
317C2×C43C2×#46511yescharacteristic
318C2×C43#306211yescharacteristic
319C2×C43#336011yescharacteristic
320C2×C43#336211yescharacteristic
321C2×C43Q8×SD1611yescharacteristic
322C2×C43#338011yescharacteristic
323D43—82no—
324C2×C4⋊Q8—431no—
325C2×C22⋊Q8—861no—
326C2×C4×Q8—431no—
327C2×C4×D4—431no—
328#476—864no—
329C8×Q8—864no—
330C2×#106—431no—
331C2×#106—431no—
332C2×#106C2×D4311yescharacteristic
333C2×#106C2×D4311yescharacteristic
334C2×C4⋊C8—431no—
335C2×C4⋊C8—431no—
336C2×C4⋊C8—431no—
337C2×#102—431no—
338C2×#102—431no—
339C2×#102—431no—
340C2×#102—431no—
341C2×C4×C8—431no—
342C2×C4×C8—431no—
343C2×C4×C8C2×D4311yescharacteristic
344#396—861no—
345#396—861no—
346#395—861no—
347#395—861no—
348#391—861no—
349#390—431no—
350#390—431no—
351#389—431no—
352#389—431no—
353#389—431no—
354#389—431no—
355#389C2×D4311yescharacteristic
356#389C2×D4311yescharacteristic
357#384—431no—
358#384—861no—
359#380—861no—
360C4×C4⋊C4—431no—
361#340—431no—
362#340—431no—
363#340—431no—
364#340—431no—
365#340—431no—
366#340—431no—
367#340C2×D4311yescharacteristic
368#340C2×D4311yescharacteristic
369C43#2547011yescharacteristic, complemented, Sylow
370C22×Q8—431no—
371C22×Q8—861no—
372C22×D4—431no—
373C23×C4—861no—
374C22×C8—431no—
375C22×C8—431no—
376C22×C8C22×D4311yescharacteristic
377C22×C8C22×D4311yescharacteristic
378C4⋊Q8—862no—
379C4⋊Q8—862no—
380C22⋊Q8—1724no—
381C4×Q8—862no—
382C4×Q8—862no—
383C4×D4—862no—
384C4×D4—862no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—431no—
388C2×C4⋊C4—431no—
389C2×C4⋊C4—431no—
390C2×C4⋊C4—431no—
391C2×C4⋊C4—431no—
392C2×C4⋊C4—431no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4—861no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4C22×D4311yescharacteristic
401C2×C4⋊C4C22×D4311yescharacteristic
402C2×C4⋊C4C22×D4311yescharacteristic
403C2×C4⋊C4C22×D4311yescharacteristic
404C2×C22⋊C4—861no—
405C2×C22⋊C4—861no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C22⋊C4—861no—
409C2×C42—431no—
410C2×C42—431no—
411C2×C42—861no—
412C2×C42C22×D4311yescharacteristic
413#106—22no—
414#106—22no—
415#106—862no—
416#106—862no—
417C4⋊C8—434no—
418C4⋊C8—862no—
419C4⋊C8—862no—
420#102—434no—
421#102—862no—
422#102—862no—
423#102—862no—
424C4×C8—22no—
425C4×C8—862no—
426C4×C8—862no—
427#95—21no—
428#95—21no—
429#95—861no—
430#95—861no—
431#95—861no—
432#95—861no—
433#95—861no—
434C24—861no—
435C2×Q8—434no—
436C2×Q8—862no—
437C2×Q8—862no—
438C2×Q8—3441no—
439C2×Q8—3441no—
440C2×Q8—1722no—
441C2×D4—432no—
442C2×D4—861no—
443C2×D4—861no—
444C2×D4—861no—
445C2×D4—861no—
446C2×D4—861no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—431no—
452C22×C4—431no—
453C22×C4—431no—
454C22×C4—431no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—1722no—
459C22×C4—1722no—
460C22×C4—1722no—
461C22×C4D4×D4311yescharacteristic
462C22×C4D4×D4311yescharacteristic
463C22×C4C23×D4311yescharacteristic
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—432no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8—861no—
473C2×C8—861no—
474C2×C8D4×D4312yes—
475C2×C8Q8×D4312yes—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—42no—
484C4⋊C4—81no—
485C4⋊C4—432no—
486C4⋊C4—862no—
487C4⋊C4—862no—
488C4⋊C4—862no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—3441no—
495C4⋊C4—3441no—
496C4⋊C4—3441no—
497C4⋊C4—3441no—
498C4⋊C4—1722no—
499C4⋊C4—1722no—
500C4⋊C4—1722no—
501C4⋊C4#1062189812yes—
502C22⋊C4—3441no—
503C22⋊C4—3441no—
504C22⋊C4—1722no—
505C22⋊C4—1722no—
506C22⋊C4—1722no—
507C42—21no—
508C42—21no—
509C42—432no—
510C42—432no—
511C42—861no—
512C42—861no—
513C42—1722no—
514C23—862no—
515C23—1721no—
516C23—1721no—
517C23—1721no—
518C23—1721no—
519C23—1721no—
520C23—1721no—
521C23C2×D4×D4311yescharacteristic
522Q8—868no—
523Q8—3444no—
524D4—862no—
525D4—862no—
526D4—1721no—
527D4—1721no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—432no—
546C2×C4—432no—
547C2×C4—432no—
548C2×C4—432no—
549C2×C4—432no—
550C2×C4—861no—
551C2×C4—861no—
552C2×C4—861no—
553C2×C4—861no—
554C2×C4—862no—
555C2×C4—861no—
556C2×C4—861no—
557C2×C4—861no—
558C2×C4—3444no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4SD16×D4312yes—
568C2×C4C2×D4×D4311yescharacteristic
569C2×C4C2×Q8×D4311yescharacteristic
570C2×C4#41×D4311yescharacteristic
571C2×C4C2×#1062189811yescharacteristic
572C2×C4#1306337211yescharacteristic
573C2×C4#1306337311yescharacteristic
574C8—22no—
575C8—22no—
576C8—862no—
577C8—1721no—
578C22—3441no—
579C22—3441no—
580C22—3441no—
581C22—3441no—
582C22—1722no—
583C22—1722no—
584C22—1722no—
585C22#121×D4311yescharacteristic
586C22#1458355811yescharacteristic
587C22#1458356411yescharacteristic
588C22C2×SD16×D4311yescharacteristic
589C22#135×D4311yescharacteristic
590C22#1458370111yescharacteristic
591C22#1458370511yescharacteristic
592C4—22no—
593C4—41no—
594C4—42no—
595C4—81no—
596C4—81no—
597C4—81no—
598C4—434no—
599C4—862no—
600C4—862no—
601C4—3441no—
602C4—3441no—
603C4—1721no—
604C4—1722no—
605C4#1458345311yescharacteristic
606C4#1458350811yescharacteristic
607C4#1458355011yescharacteristic
608C4#1458356211yescharacteristic
609C2—3442no—
610C2#1913819311yescharacteristic
611C2#465×D4311yescharacteristic
612C2#1914426811yescharacteristic
613C2#1914724511yescharacteristic
614C2#1914726411yescharacteristic
615C2#1914745211yescharacteristic
616C2#1914745911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1941C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#1941D43
hypocenterC43#25470
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1941

Complements

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

NH ≅ G/Ntype
2. C2×C8×Dic86C2semidirect
3. #19139802C2semidirect
5. #19136096C2semidirect
6. #19136094C2semidirect
9. #19135554C2semidirect
10. #19135355C2semidirect
11. #19135322C2semidirect
15. C43×#1941C2semidirect
101. #13063247Q8semidirect
312. #1941D43semidirect
369. C43#25470semidirect

Maximal subgroups

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

subgroupindex
C2×#145831882
C2×C8×Dic862
#191398022
#191395162
#191360962
#191360942
#191359662
#191359642
#191355542
#191353552
#191353222
#191352782
#191352762
#191344092
C43×#19412
#2547043