Finite Group Databasebeta

← #25067102

Subgroups — #25067102

Order 11008.

590 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143744C211yesmaximal, characteristic, complemented
2#19143712C211yesmaximal, characteristic, complemented
3#19133509C211yesmaximal, characteristic, complemented
4#19133504C211yesmaximal, characteristic, complemented
5#19133486C211yesmaximal, characteristic, complemented
6#19133486C211yesmaximal, characteristic, complemented
7#19133467C211yesmaximal, characteristic, complemented
8#19133460C211yesmaximal, characteristic, complemented
9#19133439C211yesmaximal, characteristic, complemented
10#19133432C211yesmaximal, characteristic, complemented
11#19133366C211yesmaximal, characteristic, complemented
12#19133034C211yesmaximal, characteristic, complemented
13#19133008C211yesmaximal, characteristic, complemented
14#19132890C211yesmaximal, characteristic, complemented
15C43×#3102C211yesmaximal, characteristic
16#14583030C2211yescharacteristic
17#14583030C2211yescharacteristic
18#14583030C2211yescharacteristic
19Q8×C43⋊C8C2211yescharacteristic
20#14582977—21no—
21#14582977C2211yescharacteristic
22#14582977C2211yescharacteristic
23#14582977C2211yescharacteristic
24#14582971—21no—
25#14582971—21no—
26#14582971—21no—
27D4×C43⋊C8C2211yescharacteristic
28#14582960—21no—
29#14582956—21no—
30#14582952C2211yescharacteristic
31#14582926—21no—
32#14582923—21no—
33#14582923C2211yescharacteristic
34C2×C4⋊(C43⋊C8)C2211yescharacteristic
35C4×#10621877C2211yescharacteristic
36#14582650C2211yescharacteristic
37#14582650C2211yescharacteristic
38#14582650C2211yescharacteristic
39#14582650C2211yescharacteristic
40Q8⋊(C43⋊C8)C2211yescharacteristic
41Q8⋊(C43⋊C8)C2211yescharacteristic
42Q8⋊(C43⋊C8)C2211yescharacteristic
43Q8⋊(C43⋊C8)C2211yescharacteristic
44D4⋊(C43⋊C8)C2211yescharacteristic
45D4⋊(C43⋊C8)C2211yescharacteristic
46D4⋊(C43⋊C8)C2211yescharacteristic
47D4⋊(C43⋊C8)C2211yescharacteristic
48#14582621C2211yescharacteristic
49#14582621C2211yescharacteristic
50#14582620C2211yescharacteristic
51C8×C43⋊C8C2211yescharacteristic
52C43×#529C2211yescharacteristic
53C4×#41×C43C2211yescharacteristic
54C43×#485C411yescharacteristic
55C43×#482C411yescharacteristic
56C43×#479C411yescharacteristic
57C43×#478C411yescharacteristic
58C43×#464C411yescharacteristic
59C43×#463C411yescharacteristic
60C43×#452C411yescharacteristic
61C43×#449C411yescharacteristic
62C4×Q16×C43C2211yescharacteristic
63C4×SD16×C43C2211yescharacteristic
64C4×SD16×C43C2211yescharacteristic
65C4×D8×C43C2211yescharacteristic
66C43×#431C2211yescharacteristic
67C2×#10621877—21no—
68C2×#10621877—21no—
69C2×#10621877—21no—
70C2×#10621877—21no—
71C2×#10621877—21no—
72C22×C43⋊C8—21no—
73C22×C43⋊C8—21no—
74C4⋊(C43⋊C8)—21no—
75C4⋊(C43⋊C8)—21no—
76C4⋊(C43⋊C8)—21no—
77C4⋊(C43⋊C8)—21no—
78C4⋊(C43⋊C8)—21no—
79C4⋊(C43⋊C8)—21no—
80C4⋊(C43⋊C8)D411yescharacteristic
81C4⋊(C43⋊C8)D411yescharacteristic
82C4⋊(C43⋊C8)C2311yescharacteristic
83C4⋊(C43⋊C8)C2311yescharacteristic
84C4⋊(C43⋊C8)C2311yescharacteristic
85C4⋊(C43⋊C8)C2311yescharacteristic
86C22⋊(C43⋊C8)—21no—
87C22⋊(C43⋊C8)—21no—
88C22⋊(C43⋊C8)—21no—
89C22⋊(C43⋊C8)—21no—
90C22⋊(C43⋊C8)D411yescharacteristic
91C22⋊(C43⋊C8)D411yescharacteristic
92#13063236—21no—
93#13063236—21no—
94#13063236—21no—
95#13063236—21no—
96C4×C43⋊C8—21no—
97C4×C43⋊C8C2311yescharacteristic
98C4×C43⋊C8C2311yescharacteristic
99C4×C43⋊C8C2311yescharacteristic
100C4×C43⋊C8C2311yescharacteristic
101C2×#41×C43C2×C411yescharacteristic
102C2×Q16×C43C2×C411yescharacteristic
103C2×SD16×C43C2×C411yescharacteristic
104C2×SD16×C43C2×C411yescharacteristic
105C2×D8×C43C2×C411yescharacteristic
106#126×C43—21no—
107#125×C43C2×C411yescharacteristic
108#124×C43C2×C411yescharacteristic
109#123×C43—21no—
110C22⋊Q8×C43C2×C411yescharacteristic
111#121×C43C2×C411yescharacteristic
112C4×Q8×C43C2×C411yescharacteristic
113C4×Q8×C43C2311yescharacteristic
114C4×Q8×C43C2311yescharacteristic
115C4×D4×C43—21no—
116C4×D4×C43—21no—
117C4×D4×C43—21no—
118C4×D4×C43C2×C411yescharacteristic
119C4×D4×C43C2311yescharacteristic
120C4×D4×C43C2311yescharacteristic
121#117×C43—21no—
122#117×C43—21no—
123#117×C43C2×C411yescharacteristic
124C2×C42×C43—21no—
125C2×C42×C43C2311yescharacteristic
126#107×C43C2×C411yescharacteristic
127#107×C43C2×C411yescharacteristic
128#106×C43C2×C411yescharacteristic
129#106×C43C2×C411yescharacteristic
130C4⋊C8×C43C2×C411yescharacteristic
131C4⋊C8×C43C2×C411yescharacteristic
132#103×C43C2×C411yescharacteristic
133#103×C43C2×C411yescharacteristic
134#103×C43C2×C411yescharacteristic
135#103×C43C2×C411yescharacteristic
136#102×C43C2×C411yescharacteristic
137#102×C43C2×C411yescharacteristic
138#102×C43C2×C411yescharacteristic
139#102×C43C2×C411yescharacteristic
140C22⋊C8×C43C2×C411yescharacteristic
141C22⋊C8×C43C2×C411yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144#41×C43—41no—
145#41×C43—41no—
146C2×Q8×C43C22×C411yescharacteristic
147C2×Q8×C43C22×C411yescharacteristic
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43C22×C411yescharacteristic
151C2×D4×C43C22×C411yescharacteristic
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43C22×C411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43#4111yescharacteristic
159Q16×C43—41no—
160SD16×C43—41no—
161SD16×C43—41no—
162D8×C43—41no—
163C2×C8×C43C22×C411yescharacteristic
164C2×C8×C43C22×C411yescharacteristic
165C2×C8×C43C22×C411yescharacteristic
166C2×C8×C43C22×C411yescharacteristic
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43C22×C411yescharacteristic
174C4⋊C4×C43C22×C411yescharacteristic
175C4⋊C4×C43C22×C411yescharacteristic
176C4⋊C4×C43C22×C411yescharacteristic
177C22⋊C4×C43—21no—
178C22⋊C4×C43—21no—
179C22⋊C4×C43—21no—
180C22⋊C4×C43—21no—
181C22⋊C4×C43—21no—
182C22⋊C4×C43—21no—
183C22⋊C4×C43—21no—
184C22⋊C4×C43—21no—
185C42×C43—21no—
186C42×C43—21no—
187C42×C43—21no—
188C42×C43—21no—
189C42×C43C22×C411yescharacteristic
190C42×C43C2×D411yescharacteristic
191C42×C43#4111yescharacteristic
192C42×C43C2411yescharacteristic
193#10621877—42no—
194#10621877—81no—
195#10621877—81no—
196#10621877—81no—
197#10621877—81no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—81no—
205C2×C43⋊C8—81no—
206C2×C43⋊C8C2×D411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209C2×C43⋊C8C2×D411yescharacteristic
210C23×C43—21no—
211C23×C43—21no—
212C23×C43C4×D411yescharacteristic
213Q8×C43—21no—
214Q8×C43—21no—
215Q8×C43—21no—
216Q8×C43—21no—
217D4×C43—21no—
218D4×C43—21no—
219D4×C43—21no—
220D4×C43—21no—
221D4×C43—42no—
222D4×C43—81no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—41no—
234C2×C4×C43—42no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—81no—
240C2×C4×C43C4×D411yescharacteristic
241C2×C4×C43C4×D411yescharacteristic
242C2×C4×C43C4×D411yescharacteristic
243C2×C4×C43C23×C411yescharacteristic
244C2×C4×C43C22×D411yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C8×C43—21no—
247C8×C43—21no—
248C8×C43—21no—
249C8×C43—21no—
250C43⋊C8—22no—
251C43⋊C8—21no—
252C43⋊C8—21no—
253C43⋊C8—21no—
254C43⋊C8—21no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258C43⋊C8—41no—
259C43⋊C8—41no—
260#17955—431nomaximal, Sylow
261C22×C43—21no—
262C22×C43—21no—
263C22×C43—21no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43C2×C4×D411yescharacteristic
271C4×C43—21no—
272C4×C43—21no—
273C4×C43—21no—
274C4×C43—21no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43—41no—
278C4×C43—41no—
279C4×C43—41no—
280C4×C43—41no—
281C4×C43#56811yescharacteristic
282C4×C43#56811yescharacteristic
283C4×C43#57711yescharacteristic
284C4×C43#57711yescharacteristic
285#3102D4311yescharacteristic
286#2993—431no—
287#2989—431no—
288#1594—431no—
289#1593—431no—
290#1590—431no—
291#1590—431no—
292#1587—431no—
293#1586—431no—
294#1583—431no—
295#1582—431no—
296#1570—431no—
297#1489—431no—
298#1483—431no—
299#1453—431no—
300C2×C43—41no—
301C2×C43—81no—
302C2×C43—81no—
303C2×C43#293011yescharacteristic
304C2×C43#295211yescharacteristic
305C2×C43#295611yescharacteristic
306#529C2×D4311yescharacteristic
307C4×#41C2×D4311yescharacteristic
308#485Dic4311yescharacteristic
309#482Dic4311yescharacteristic
310#479Dic4311yescharacteristic
311#478Dic4311yescharacteristic
312#464Dic4311yescharacteristic
313#463Dic4311yescharacteristic
314#452Dic4311yescharacteristic
315#449Dic4311yescharacteristic
316#446—431no—
317#446—431no—
318#446—431no—
319C8×Q8—431no—
320C4×Q16C2×D4311yescharacteristic
321C4×SD16C2×D4311yescharacteristic
322C4×SD16C2×D4311yescharacteristic
323C4×D8C2×D4311yescharacteristic
324#436—431no—
325#436—431no—
326#436—431no—
327#436—861no—
328#435—861no—
329#435—861no—
330#435—861no—
331C8×D4—431no—
332#433—861no—
333#432—861no—
334#431—431no—
335#431C2×D4311yescharacteristic
336#424—861no—
337#423—431no—
338#423—861no—
339C2×C4⋊C8—431no—
340C4×M16—431no—
341#334—431no—
342#334—431no—
343#334—431no—
344#334—431no—
345Q8⋊C8—431no—
346Q8⋊C8—431no—
347Q8⋊C8—431no—
348Q8⋊C8—431no—
349D4⋊C8—431no—
350D4⋊C8—431no—
351D4⋊C8—431no—
352D4⋊C8—431no—
353#322—431no—
354#322—431no—
355#322—431no—
356C82—431no—
357C43#1795511yescharacteristic, complemented, Sylow
358C2×#41C2×Dic4311yescharacteristic
359C2×Q16C2×Dic4311yescharacteristic
360C2×SD16C2×Dic4311yescharacteristic
361C2×SD16C2×Dic4311yescharacteristic
362C2×D8C2×Dic4311yescharacteristic
363C2×M16—861no—
364C2×M16—861no—
365C2×M16—861no—
366C2×M16—861no—
367C2×M16—861no—
368C22×C8—861no—
369C22×C8—861no—
370#126—21no—
371#125C2×Dic4311yescharacteristic
372#124C2×Dic4311yescharacteristic
373#123—21no—
374C22⋊Q8C2×Dic4311yescharacteristic
375#121C2×Dic4311yescharacteristic
376C4×Q8C2×Dic4311yescharacteristic
377C4×Q8C22×D4311yescharacteristic
378C4×Q8C22×D4311yescharacteristic
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—21no—
382C4×D4C2×Dic4311yescharacteristic
383C4×D4C22×D4311yescharacteristic
384C4×D4C22×D4311yescharacteristic
385#117—21no—
386#117—21no—
387#117C2×Dic4311yescharacteristic
388C2×C42—21no—
389C2×C42C22×D4311yescharacteristic
390#107C2×Dic4311yescharacteristic
391#107C2×Dic4311yescharacteristic
392#106C2×Dic4311yescharacteristic
393#106C2×Dic4311yescharacteristic
394C4⋊C8—431no—
395C4⋊C8—431no—
396C4⋊C8—431no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—861no—
401C4⋊C8—861no—
402C4⋊C8—861no—
403C4⋊C8—861no—
404C4⋊C8—861no—
405C4⋊C8—861no—
406C4⋊C8C2×Dic4311yescharacteristic
407C4⋊C8C2×Dic4311yescharacteristic
408#103C2×Dic4311yescharacteristic
409#103C2×Dic4311yescharacteristic
410#103C2×Dic4311yescharacteristic
411#103C2×Dic4311yescharacteristic
412#102C2×Dic4311yescharacteristic
413#102C2×Dic4311yescharacteristic
414#102C2×Dic4311yescharacteristic
415#102C2×Dic4311yescharacteristic
416C22⋊C8—431no—
417C22⋊C8—431no—
418C22⋊C8—861no—
419C22⋊C8—861no—
420C22⋊C8—861no—
421C22⋊C8—861no—
422C22⋊C8C2×Dic4311yescharacteristic
423C22⋊C8C2×Dic4311yescharacteristic
424#97—861no—
425#97—861no—
426#97—861no—
427#97—861no—
428C4×C8—431no—
429C4×C8—431no—
430C4×C8—431no—
431C4×C8—431no—
432C4×C8—861no—
433C4×C8C22×D4311yescharacteristic
434C4×C8C22×D4311yescharacteristic
435#41—41no—
436#41—41no—
437C2×Q8C22×Dic4311yescharacteristic
438C2×Q8C22×Dic4311yescharacteristic
439C2×D4—21no—
440C2×D4—21no—
441C2×D4C22×Dic4311yescharacteristic
442C2×D4C22×Dic4311yescharacteristic
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4D4×D4311yescharacteristic
448C22×C4#1062190011yescharacteristic
449C22×C4C22×Dic4311yescharacteristic
450Q16—41no—
451SD16—41no—
452SD16—41no—
453D8—41no—
454M16—3441no—
455M16—3441no—
456M16—3441no—
457M16—3441no—
458M16—1722no—
459C2×C8—431no—
460C2×C8—431no—
461C2×C8—431no—
462C2×C8—431no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—861no—
469C2×C8—3441no—
470C2×C8—3441no—
471C2×C8C22×Dic4311yescharacteristic
472C2×C8C22×Dic4311yescharacteristic
473C2×C8C22×Dic4311yescharacteristic
474C2×C8C22×Dic4311yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4C22×Dic4311yescharacteristic
482C4⋊C4C22×Dic4311yescharacteristic
483C4⋊C4C22×Dic4311yescharacteristic
484C4⋊C4C22×Dic4311yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—21no—
491C22⋊C4—21no—
492C22⋊C4—21no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42D4×D4311yescharacteristic
498C42#1062190011yescharacteristic
499C42C22×Dic4311yescharacteristic
500C42C23×D4311yescharacteristic
501C23—21no—
502C23—21no—
503C23D4×Dic4311yescharacteristic
504Q8—21no—
505Q8—21no—
506Q8—21no—
507Q8—21no—
508D4—21no—
509D4—21no—
510D4—21no—
511D4—21no—
512D4—42no—
513D4—81no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—81no—
531C2×C4D4×Dic4311yescharacteristic
532C2×C4D4×Dic4311yescharacteristic
533C2×C4D4×Dic4311yescharacteristic
534C2×C4C23×Dic4311yescharacteristic
535C2×C4C2×D4×D4311yescharacteristic
536C2×C4C2×#1062190011yescharacteristic
537C8—21no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—862no—
542C8—861no—
543C8—861no—
544C8—861no—
545C8—861no—
546C8—1721no—
547C8—1721no—
548C8—1721no—
549C8—1721no—
550C8—1721no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22C2×D4×Dic4311yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4#1458366611yescharacteristic
572C4#1458366611yescharacteristic
573C4#1458370611yescharacteristic
574C4#1458370611yescharacteristic
575C2—41no—
576C2—81no—
577C2—81no—
578C2#1914329911yescharacteristic
579C2#1914347911yescharacteristic
580C2#1914350511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#3102C2
socleC22×C43C2×C4×D4
prime radicalC43×#449C4
cosocleC42×C43C24
hypercenter#3102D43
hypocenterC43#17955
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3102

Complements

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

NH ≅ G/Ntype
1. #19143744C2semidirect
2. #19143712C2semidirect
3. #19133509C2semidirect
4. #19133504C2semidirect
5. #19133486C2semidirect
6. #19133486C2semidirect
7. #19133467C2semidirect
8. #19133460C2semidirect
9. #19133439C2semidirect
10. #19133432C2semidirect
11. #19133366C2semidirect
12. #19133034C2semidirect
13. #19133008C2semidirect
14. #19132890C2semidirect
357. C43#17955semidirect

Maximal subgroups

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

subgroupindex
#191437442
#191437122
#191335092
#191335042
#191334862
#191334672
#191334602
#191334392
#191334322
#191333662
#191330342
#191330082
#191328902
C43×#31022
#1795543