Finite Group Databasebeta

← #25164694

Subgroups — #25164694

Order 11008.

826 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19138959C211yesmaximal, characteristic
2#19137599C211yesmaximal, characteristic, complemented
3#19135911C211yesmaximal, characteristic, complemented
4#19135794C211yesmaximal, characteristic, complemented
5#19135735C211yesmaximal, characteristic, complemented
6#19135599C211yesmaximal, characteristic
7#19135545C211yesmaximal, characteristic, complemented
8#19135225C211yesmaximal, characteristic, complemented
9#19135201C211yesmaximal, characteristic, complemented
10#19135177C211yesmaximal, characteristic, complemented
11#19134953C211yesmaximal, characteristic, complemented
12#19134909C211yesmaximal, characteristic
13#19134684C211yesmaximal, characteristic, complemented
14C4×#13063250C211yesmaximal, characteristic, complemented
15C43×#1934C211yesmaximal, characteristic, complemented
16C22×#10621883C2211yescharacteristic
17C2×#13063324C2211yescharacteristic
18C2×#13063311—21no—
19C2×#13063305C2211yescharacteristic
20C2×#13063296C2211yescharacteristic
21C2×C4×Dic86C2211yescharacteristic
22C2×C4⋊C4×D43C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×(C2×D43)⋊C8C2211yescharacteristic
30C2×(C2×D43)⋊C8C2211yescharacteristic
31#14582814—21no—
32#14582811—21no—
33#14582804C2211yescharacteristic
34#14582802C2211yescharacteristic
35#14582795—21no—
36#14582787—21no—
37#14582782—21no—
38#14582770—21no—
39#14582756C2211yescharacteristic
40C4⋊C4×Dic43C2211yescharacteristic
41C4×C4⋊Dic43C2211yescharacteristic
42C4×(C2×D43)⋊C4C2211yescharacteristic
43#14582746—21no—
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#102×C43C2211yescharacteristic
53C2×#102×C43C2211yescharacteristic
54C2×C4×C8×C43C2211yescharacteristic
55C43×#390C2211yescharacteristic
56C43×#389C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×Dic86—21no—
60C22×Dic86C2311yescharacteristic
61C22×C22⋊D43—21no—
62C22×C4×D43—21no—
63C22×C4×D43C2311yescharacteristic
64C2×#10621883—22no—
65C2×#10621883—41no—
66C2×#10621883—41no—
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69#13063324—22no—
70#13063324—41no—
71#13063311—44no—
72#13063305—22no—
73#13063305—22no—
74#13063296—22no—
75#13063296—41no—
76C4×Dic86—22no—
77C4×Dic86—41no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C4⋊C4×D43—22no—
86C4⋊C4×D43—41no—
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4D411yescharacteristic
93C2×(C2×D43)⋊C4D411yescharacteristic
94C2×C4×Dic43—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43—21no—
97C2×C4×Dic43C2311yescharacteristic
98#13063256—22no—
99Dic43⋊C8—41no—
100#13063250—22no—
101#13063250—22no—
102#13063248—41no—
103#13063246—22no—
104(C2×D43)⋊C8—41no—
105(C2×D43)⋊C8—41no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95D411yescharacteristic
112C43⋊#95D411yescharacteristic
113C22×D4×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122C2×C42×C43C2311yescharacteristic
123#102×C43—22no—
124#102×C43—41no—
125C4×C8×C43—41no—
126#95×C43—21no—
127C24×C43—21no—
128C23×D43C2×D411yescharacteristic
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2411yescharacteristic
141C2×C22⋊D43—42no—
142C2×C22⋊D43—42no—
143C2×C22⋊D43—81no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43C2×D411yescharacteristic
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C2×C4×D43—21no—
152C2×C4×D43—21no—
153C2×C4×D43—21no—
154C2×C4×D43—21no—
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—42no—
158C2×C4×D43—42no—
159C2×C4×D43—81no—
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86—42no—
166C2×Dic86—42no—
167C2×Dic86—81no—
168C2×Dic86#4112yes—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×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—81no—
181C4⋊C4×C43#4112yes—
182C22⋊C4×C43—42no—
183C22⋊C4×C43—81no—
184C42×C43—21no—
185C42×C43—21no—
186C22⋊Dic43—42no—
187C22⋊Dic43—42no—
188C22⋊Dic43—42no—
189#10621883—44no—
190(C2×D43)⋊C4—24no—
191(C2×D43)⋊C4—41no—
192(C2×D43)⋊C4—42no—
193(C2×D43)⋊C4SD1614yescomplemented
194C4⋊Dic43—24no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43#4112yes—
200C4⋊Dic43#4112yes—
201Dic43⋊C4—42no—
202Dic43⋊C4—42no—
203Dic43⋊C4—42no—
204C4×Dic43—21no—
205C4×Dic43—21no—
206C4×Dic43—42no—
207C4×Dic43—42no—
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—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43C22×D411yescharacteristic
223C22×D43—21no—
224C22×D43—21no—
225C22×D43—21no—
226C22×D43—21no—
227C22×D43—21no—
228C22×D43—21no—
229C22×D43C2×SD1612yes—
230D4×C43—41no—
231D4×C43—41no—
232D4×C43—41no—
233D4×C43—41no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—22no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
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×C43C2×SD1612yes—
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43H(5,𝔽2)11yescharacteristic
254C2×C4×C43H(5,𝔽2)11yescharacteristic
255C22⋊D43—84no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—22no—
260C2×Dic43—21no—
261C2×Dic43—22no—
262C2×Dic43—21no—
263C2×Dic43—22no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
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×Dic43C2×SD1612yes—
277C4×D43—41no—
278C4×D43—41no—
279C4×D43—41no—
280C4×D43—41no—
281C4×D43—84no—
282Dic86—22no—
283Dic86—22no—
284Dic86—41no—
285Dic86—41no—
286Dic86—84no—
287C8×C43—41no—
288C8×C43—41no—
289C43⋊C8—41no—
290C43⋊C8—41no—
291#26724—431nomaximal, Sylow
292C22×C43—81no—
293C22×C43—81no—
294C22×C43—81no—
295C22×C43—81no—
296C22×C43—81no—
297C22×C43—81no—
298C22×C43—81no—
299C22×C43#52511yescharacteristic
300C22×C43#54611yescharacteristic
301C22×C43#54611yescharacteristic
302C22×C43C22×SD1611yescharacteristic
303C22×C43#57511yescharacteristic
304C22×C43#57611yescharacteristic
305C22×C43#57811yescharacteristic
306C2×D43—22no—
307C2×D43—22no—
308C2×D43—22no—
309C2×D43—41no—
310C2×D43—41no—
311C2×D43—41no—
312C2×D43—41no—
313C4×C43—22no—
314C4×C43—42no—
315C4×C43—41no—
316C4×C43—81no—
317C4×C43—81no—
318C4×C43#52911yescharacteristic
319C4×C43#53811yescharacteristic
320C4×C43#55511yescharacteristic
321C4×C43#55911yescharacteristic
322Dic43—22no—
323Dic43—42no—
324Dic43—41no—
325Dic43—42no—
326Dic43—42no—
327Dic43—41no—
328Dic43—81no—
329#2491—431no—
330#2360—431no—
331#2055—431no—
332#2035—431no—
333#2024—431no—
334#2000—431no—
335#1988—431no—
336#1934D4311yescharacteristic, complemented
337#1926—431no—
338#1923—431no—
339#1920—431no—
340#1880—431no—
341#1874—431no—
342#1824—431no—
343C4×#103—431no—
344C2×C43—161no—
345C2×C43#245911yescharacteristic
346C2×C43#310311yescharacteristic
347C2×C43#312411yescharacteristic
348C2×C43#329511yescharacteristic
349C2×C43#329811yescharacteristic
350C2×C43#331911yescharacteristic
351C2×C43#332711yescharacteristic
352D43—42no—
353C22×SD16—431no—
354C2×C4⋊Q8—431no—
355C2×#124—861no—
356C2×C22⋊Q8—431no—
357C2×#121—431no—
358C2×C4×Q8—431no—
359C22×C4⋊C4—431no—
360C2×#106—431no—
361C2×C4⋊C8—431no—
362C2×#103—431no—
363C2×#103—431no—
364C2×#103—431no—
365C2×#102—431no—
366C2×#102C2×D4311yescharacteristic
367C2×#102C2×D4311yescharacteristic
368C2×C22⋊C8—431no—
369C2×C22⋊C8—431no—
370C2×C4×C8C2×D4311yescharacteristic
371#394—861no—
372#393—861no—
373#391—431no—
374#390—431no—
375#390C2×D4311yescharacteristic
376#389—861no—
377#389C2×D4311yescharacteristic
378#388—861no—
379#387—861no—
380#385—861no—
381#380—431no—
382C4×C4⋊C4—431no—
383C4×C4⋊C4—431no—
384C4×C22⋊C4—431no—
385C4×C22⋊C4—861no—
386#340—431no—
387#340—431no—
388#340—431no—
389#340—431no—
390#340—431no—
391#340—431no—
392#340C2×D4311yescharacteristic
393#340C2×D4311yescharacteristic
394#336—431no—
395#336—431no—
396C43#2672411yescharacteristic, complemented, Sylow
397C22×Q8—431no—
398C22×Q8—861no—
399C22×D4—861no—
400C22×D4C22×D4311yescharacteristic
401C23×C4—431no—
402C23×C4—861no—
403C2×SD16—862no—
404C2×SD16—1721no—
405C2×SD16—1721no—
406C22×C8—431no—
407C22×C8—431no—
408C22×C8C22×D4311yescharacteristic
409C22×C8C22×D4311yescharacteristic
410C4⋊Q8—862no—
411C4⋊Q8—1721no—
412#124—1724no—
413C22⋊Q8—862no—
414C22⋊Q8—862no—
415#121—862no—
416#121—1721no—
417C4×Q8—862no—
418C4×Q8—1721no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—862no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—1721no—
429C2×C4⋊C4C22×D4311yescharacteristic
430C2×C4⋊C4C22×D4311yescharacteristic
431C2×C4⋊C4C22×D4311yescharacteristic
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—431no—
435C2×C22⋊C4—431no—
436C2×C22⋊C4—861no—
437C2×C22⋊C4—861no—
438C2×C22⋊C4—861no—
439C2×C22⋊C4—861no—
440C2×C22⋊C4—861no—
441C2×C42—431no—
442C2×C42—861no—
443C2×C42—861no—
444C2×C42—861no—
445C2×C42C22×D4311yescharacteristic
446#106—862no—
447C4⋊C8—1721no—
448#103—862no—
449#103—862no—
450#103—1721no—
451#102—22no—
452#102—41no—
453#102—862no—
454C22⋊C8—1721no—
455C22⋊C8—1721no—
456C4×C8—41no—
457#95—21no—
458#95—431no—
459#95—431no—
460#95—861no—
461#95—861no—
462#95—861no—
463#95—861no—
464#95—861no—
465C24—21no—
466C24—431no—
467C2×Q8—432no—
468C2×Q8—861no—
469C2×Q8—861no—
470C2×Q8—861no—
471C2×Q8—861no—
472C2×Q8—861no—
473C2×Q8—3441no—
474C2×Q8—1722no—
475C2×Q8—1722no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—3441no—
483C2×D4—1722no—
484C2×D4—1722no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—431no—
489C22×C4—431no—
490C22×C4—431no—
491C22×C4—861no—
492C22×C4—861no—
493C22×C4—861no—
494C22×C4—861no—
495C22×C4—861no—
496C22×C4—861no—
497C22×C4—861no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4—3441no—
502C22×C4—1722no—
503C22×C4—1722no—
504C22×C4D4×D4311yescharacteristic
505C22×C4D4×D4311yescharacteristic
506C22×C4C23×D4311yescharacteristic
507SD16—1724no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8—861no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—81no—
526C4⋊C4—432no—
527C4⋊C4—432no—
528C4⋊C4—864no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—861no—
533C4⋊C4—1722no—
534C4⋊C4—1722no—
535C4⋊C4—1722no—
536C4⋊C4#1062189812yes—
537C22⋊C4—42no—
538C22⋊C4—81no—
539C22⋊C4—434no—
540C22⋊C4—864no—
541C22⋊C4—1721no—
542C22⋊C4—1722no—
543C22⋊C4—1722no—
544C22⋊C4—1722no—
545C22⋊C4—1722no—
546C42—21no—
547C42—21no—
548C42—861no—
549C42—861no—
550C42—3441no—
551C42—1722no—
552C42—1722no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—432no—
561C23—861no—
562C23—861no—
563C23—861no—
564C23—861no—
565C23—861no—
566C23—861no—
567C23C2×D4×D4311yescharacteristic
568Q8—862no—
569Q8—862no—
570Q8—3444no—
571Q8—1721no—
572Q8—1721no—
573D4—41no—
574D4—41no—
575D4—41no—
576D4—41no—
577D4—3444no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—432no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—862no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—862no—
600C2×C4—861no—
601C2×C4—861no—
602C2×C4—861no—
603C2×C4—862no—
604C2×C4—3444no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
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×C4SD16×D4312yes—
619C2×C4#41×D4311yescharacteristic
620C2×C4#41×D4311yescharacteristic
621C2×C4#41×D4311yescharacteristic
622C2×C4C2×#1062189811yescharacteristic
623C2×C4#1306337011yescharacteristic
624C2×C4#1306337111yescharacteristic
625C8—41no—
626C8—41no—
627C8—1721no—
628C8—1721no—
629C22—81no—
630C22—81no—
631C22—81no—
632C22—81no—
633C22—81no—
634C22—81no—
635C22—81no—
636C22—862no—
637C22—862no—
638C22—862no—
639C22—1721no—
640C22—1721no—
641C22—1721no—
642C22—1721no—
643C22#1458340811yescharacteristic
644C22#1458353811yescharacteristic
645C22#1458354211yescharacteristic
646C22C2×SD16×D4311yescharacteristic
647C22#1458369611yescharacteristic
648C22#1458370011yescharacteristic
649C22#1458371311yescharacteristic
650C4—22no—
651C4—41no—
652C4—42no—
653C4—81no—
654C4—81no—
655C4—862no—
656C4—3441no—
657C4—1722no—
658C4—1721no—
659C4—1722no—
660C4—1721no—
661C4—1722no—
662C4#1458343211yescharacteristic
663C4#1458348511yescharacteristic
664C4#1458361211yescharacteristic
665C4#1458363211yescharacteristic
666C2—161no—
667C2—1722no—
668C2#1913853811yescharacteristic
669C2#1914462411yescharacteristic
670C2#1914485311yescharacteristic
671C2#1914641811yescharacteristic
672C2#1914645511yescharacteristic
673C2#1914675711yescharacteristic
674C2#1914686211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1934C2
socleC23×C43C22×D4
prime radicalC2×#13063296C22
hypercenter#1934D43
hypocenterC43#26724
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1934

Complements

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

NH ≅ G/Ntype
2. #19137599C2semidirect
3. #19135911C2semidirect
4. #19135794C2semidirect
5. #19135735C2semidirect
7. #19135545C2semidirect
8. #19135225C2semidirect
9. #19135201C2semidirect
10. #19135177C2semidirect
11. #19134953C2semidirect
13. #19134684C2semidirect
14. C4×#13063250C2semidirect
15. C43×#1934C2semidirect
193. (C2×D43)⋊C4SD16semidirect
336. #1934D43semidirect
396. C43#26724semidirect

Maximal subgroups

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

subgroupindex
#191389592
#191375992
#191359112
#191357942
#191357352
#191355992
#191355452
#191352252
#191352012
#191351772
#191349532
#191349092
#191346842
C4×#130632502
C43×#19342
#2672443