Finite Group Databasebeta

← #25113931

Subgroups — #25113931

Order 11008.

934 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137480C211yesmaximal, characteristic
2Q8×C22⋊Dic43C211yesmaximal, characteristic
3#19135287C211yesmaximal, characteristic, complemented
4#19135273C211yesmaximal, characteristic, complemented
5#19135238C211yesmaximal, characteristic, complemented
6#19135231C211yesmaximal, characteristic, complemented
7#19134865C211yesmaximal, characteristic, complemented
8#19134851C211yesmaximal, characteristic, complemented
9#19134690C211yesmaximal, characteristic
10#19134628C211yesmaximal, characteristic
11#19134530C211yesmaximal, characteristic
12#19134427C211yesmaximal, characteristic, complemented
13#103×Dic43C211yesmaximal, characteristic, complemented
14#19134376C211yesmaximal, characteristic
15C2×C43×#419C211yesmaximal, characteristic
16C2×Q8×Dic43C2211yescharacteristic
17C2×Q8×Dic43C2211yescharacteristic
18C2×#13063259C2211yescharacteristic
19C2×#13063257C2211yescharacteristic
20C2×#13063249C2211yescharacteristic
21C2×#13063249C2211yescharacteristic
22C2×#13063249C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×C22⋊(C43⋊C8)C2211yescharacteristic
25C2×#13063235C2211yescharacteristic
26C2×C8×Dic43C2211yescharacteristic
27#14582806—21no—
28#14582806—21no—
29#14582806C2211yescharacteristic
30#14582806C2211yescharacteristic
31#14582798C2211yescharacteristic
32#14582798C2211yescharacteristic
33#14582792—21no—
34#14582792—21no—
35#14582765—21no—
36#14582759—21no—
37#14582759C2211yescharacteristic
38#14582759C2211yescharacteristic
39C4⋊C4×Dic43C2211yescharacteristic
40C4⋊C4×Dic43C2211yescharacteristic
41C4×C22⋊Dic43—21no—
42C4×C22⋊Dic43C2211yescharacteristic
43#14582745—21no—
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C23×Q8×C43C2211yescharacteristic
53C22×M16×C43C2211yescharacteristic
54C2×#117×C43C2211yescharacteristic
55C43×#419C418yescomplemented
56C2×#103×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C22×C43⋊C8C2311yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62Q8×Dic43—22no—
63Q8×Dic43—22no—
64Q8×Dic43—41no—
65Q8×Dic43—41no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C22⋊Dic43—21no—
75C2×C22⋊Dic43—21no—
76C2×C22⋊Dic43D411yescharacteristic
77C2×C22⋊Dic43D411yescharacteristic
78C2×C4×Dic43—21no—
79C2×C4×Dic43—21no—
80C2×C4×Dic43—21no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43C2311yescharacteristic
83C2×C4×Dic43C2311yescharacteristic
84#13063259—41no—
85#13063257—41no—
86#13063249—22no—
87#13063249—22no—
88#13063249—41no—
89#13063249—41no—
90C22⋊(C43⋊C8)—22no—
91#13063235—41no—
92C8×Dic43—41no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95D411yescharacteristic
104C43⋊#95D411yescharacteristic
105C22×Q8×C43—21no—
106C22×Q8×C43—22no—
107C22×Q8×C43—22no—
108C22×Q8×C43—22no—
109C22×Q8×C43—41no—
110C22×Q8×C43—41no—
111C22×Q8×C43C2×C414yes—
112C22×Q8×C43C2311yescharacteristic
113C22×Q8×C43C2311yescharacteristic
114C23×C4×C43—21no—
115C23×C4×C43C2311yescharacteristic
116C2×M16×C43—41no—
117C2×M16×C43—41no—
118C2×M16×C43C2×C414yes—
119C22×C8×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121#117×C43—22no—
122#117×C43C2×C414yes—
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C22⋊C4×C43—21no—
126C2×C42×C43—21no—
127#103×C43C2×C414yes—
128#103×C43C2×C414yes—
129#103×C43C2×C414yes—
130#103×C43C2×C414yes—
131C24×C43C2×D411yescharacteristic
132C2×Q8×C43—24no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—28no—
138C2×Q8×C43—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—42no—
143C2×Q8×C43—42no—
144C2×Q8×C43—44no—
145C2×Q8×C43—44no—
146C2×Q8×C43—44no—
147C2×Q8×C43C22×C412yes—
148C2×Q8×C43C22×C412yes—
149C2×Q8×C43#4112yes—
150C2×Q8×C43#4112yes—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—24no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—42no—
161C22×C4×C43—42no—
162C22×C4×C43C22×C412yes—
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43#4112yes—
165C22×C4×C43C2411yescharacteristic
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43C2×D411yescharacteristic
171C22×Dic43C2×D411yescharacteristic
172C22×Dic43C2×D411yescharacteristic
173C22×Dic43C2×D411yescharacteristic
174M16×C43—44no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43C22×C412yes—
180C2×C8×C43C22×C412yes—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43C22×C412yes—
184C4⋊C4×C43C22×C412yes—
185C22⋊C4×C43—24no—
186C42×C43—24no—
187C22⋊Dic43—22no—
188C22⋊Dic43—41no—
189C22⋊Dic43—42no—
190C22⋊Dic43—81no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—42no—
200C4⋊Dic43—42no—
201C4⋊Dic43—81no—
202C4⋊Dic43—81no—
203C4×Dic43—21no—
204C4×Dic43—21no—
205C4×Dic43—21no—
206C4×Dic43—21no—
207C4×Dic43—42no—
208C4×Dic43—42no—
209C4×Dic43—42no—
210C4×Dic43—42no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C23×C43—21no—
218C23×C43—21no—
219C23×C43—21no—
220C23×C43—21no—
221C23×C43—21no—
222C23×C43—21no—
223C23×C43C4×D412yes—
224C23×C43C22×D411yescharacteristic
225Q8×C43—22no—
226Q8×C43—22no—
227Q8×C43—22no—
228Q8×C43—22no—
229Q8×C43—22no—
230Q8×C43—48no—
231Q8×C43—41no—
232Q8×C43—41no—
233Q8×C43#11714yes—
234C2×C4×C43—22no—
235C2×C4×C43—22no—
236C2×C4×C43—22no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—22no—
243C2×C4×C43—22no—
244C2×C4×C43—22no—
245C2×C4×C43—22no—
246C2×C4×C43—48no—
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×C43C4×D412yes—
254C2×C4×C43C23×C411yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43H(5,𝔽2)11yescharacteristic
259C2×C4×C43H(5,𝔽2)11yescharacteristic
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—21no—
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—
283C2×Dic43#13712yes—
284C8×C43—22no—
285C8×C43—22no—
286C43⋊C8—41no—
287C43⋊C8—41no—
288#22585—431nomaximal, Sylow
289C22×C43—22no—
290C22×C43—22no—
291C22×C43—22no—
292C22×C43—41no—
293C22×C43—41no—
294C22×C43—41no—
295C22×C43—41no—
296C22×C43C2×C4×D411yescharacteristic
297C22×C43#54611yescharacteristic
298C22×C43#54611yescharacteristic
299C22×C43C2×#13711yescharacteristic
300C22×C43#57511yescharacteristic
301C22×C43#57711yescharacteristic
302C22×C43#57811yescharacteristic
303C4×C43—22no—
304C4×C43—24no—
305C4×C43—42no—
306C4×C43—42no—
307C4×C43—42no—
308C4×C43C2×#11711yescharacteristic
309C4×C43#51811yescharacteristic
310C4×C43#55111yescharacteristic
311C4×C43#55111yescharacteristic
312Dic43—22no—
313Dic43—41no—
314Dic43—41no—
315Dic43—41no—
316Dic43—81no—
317Dic43—81no—
318Dic43—81no—
319Dic43—81no—
320C2×#419D4311yescharacteristic
321#2346—431no—
322Q8×C22⋊C4—431no—
323#1935—431no—
324#1933—431no—
325#1928—431no—
326#1927—431no—
327#1865—431no—
328#1863—431no—
329#1825—431no—
330#1809—431no—
331#1787—431no—
332#1763—431no—
333C4×#103—431no—
334#1753—431no—
335C2×C43—42no—
336C2×C43#234211yescharacteristic
337C2×C43C4×#13711yescharacteristic
338C2×C43#294711yescharacteristic
339C2×C43#331211yescharacteristic
340C2×C43#332111yescharacteristic
341C2×C43#332711yescharacteristic
342C2×C43#332911yescharacteristic
343C23×Q8C2×D4311yescharacteristic
344C22×M16C2×D4311yescharacteristic
345C2×C4×Q8—431no—
346C2×C4×Q8—431no—
347C2×#117C2×D4311yescharacteristic
348C2×#107—431no—
349C2×#106—431no—
350#419Dic4318yescomplemented
351C2×#103—431no—
352C2×#103—431no—
353C2×#103—431no—
354C2×#103—431no—
355C2×#103C2×D4311yescharacteristic
356C2×#103C2×D4311yescharacteristic
357C2×#103C2×D4311yescharacteristic
358C2×#103C2×D4311yescharacteristic
359C2×C22⋊C8—431no—
360C2×#97—431no—
361C2×C4×C8—431no—
362#391—431no—
363#391—431no—
364#391—861no—
365#391—861no—
366#389—431no—
367#389—431no—
368#388—861no—
369#388—861no—
370#382—861no—
371#380—431no—
372#380—431no—
373#380—861no—
374C4×C4⋊C4—431no—
375C4×C4⋊C4—431no—
376C4×C22⋊C4—431no—
377C4×C22⋊C4—861no—
378#376—861no—
379#340—431no—
380#340—431no—
381#340—431no—
382#340—431no—
383#340—431no—
384#340—431no—
385#336—431no—
386#336—431no—
387C43#2258511yescharacteristic, complemented, Sylow
388C22×Q8—21no—
389C22×Q8—22no—
390C22×Q8—22no—
391C22×Q8—22no—
392C22×Q8—41no—
393C22×Q8—41no—
394C22×Q8C2×Dic4314yes—
395C22×Q8C22×D4311yescharacteristic
396C22×Q8C22×D4311yescharacteristic
397C23×C4—21no—
398C23×C4C22×D4311yescharacteristic
399C2×M16—41no—
400C2×M16—41no—
401C2×M16C2×Dic4314yes—
402C22×C8—431no—
403C22×C8—431no—
404C22×C8C22×D4311yescharacteristic
405C22×C8C22×D4311yescharacteristic
406C4×Q8—862no—
407C4×Q8—862no—
408C4×Q8—1721no—
409C4×Q8—1721no—
410#117—22no—
411#117C2×Dic4314yes—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4C22×D4311yescharacteristic
421C2×C4⋊C4C22×D4311yescharacteristic
422C2×C22⋊C4—21no—
423C2×C22⋊C4—431no—
424C2×C22⋊C4—431no—
425C2×C22⋊C4—861no—
426C2×C22⋊C4—861no—
427C2×C42—21no—
428C2×C42—431no—
429C2×C42—431no—
430C2×C42—861no—
431C2×C42—861no—
432C2×C42—861no—
433C2×C42—861no—
434#107—1721no—
435#106—1721no—
436#103—862no—
437#103—862no—
438#103—1721no—
439#103—1721no—
440#103C2×Dic4314yes—
441#103C2×Dic4314yes—
442#103C2×Dic4314yes—
443#103C2×Dic4314yes—
444C22⋊C8—862no—
445#97—1721no—
446C4×C8—1721no—
447#95—431no—
448#95—431no—
449#95—861no—
450#95—861no—
451#95—861no—
452#95—861no—
453#95—861no—
454#95—861no—
455#95—861no—
456#95—861no—
457#95—861no—
458#95—861no—
459C24D4×D4311yescharacteristic
460C2×Q8—24no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—28no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—42no—
471C2×Q8—42no—
472C2×Q8—44no—
473C2×Q8—44no—
474C2×Q8—44no—
475C2×Q8#1062189812yes—
476C2×Q8#1062189812yes—
477C2×Q8C22×Dic4312yes—
478C2×Q8C22×Dic4312yes—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—24no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—431no—
491C22×C4—431no—
492C22×C4—431no—
493C22×C4—431no—
494C22×C4—861no—
495C22×C4—861no—
496C22×C4—861no—
497C22×C4—861no—
498C22×C4D4×D4311yescharacteristic
499C22×C4#1062190012yes—
500C22×C4C22×Dic4312yes—
501C22×C4C23×D4311yescharacteristic
502M16—44no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8—861no—
510C2×C8—861no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8C22×Dic4312yes—
514C2×C8C22×Dic4312yes—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—3441no—
526C4⋊C4—3441no—
527C4⋊C4—1722no—
528C4⋊C4—1722no—
529C4⋊C4C22×Dic4312yes—
530C4⋊C4C22×Dic4312yes—
531C22⋊C4—24no—
532C22⋊C4—862no—
533C22⋊C4—3441no—
534C22⋊C4—1721no—
535C22⋊C4—1722no—
536C42—24no—
537C42—861no—
538C42—861no—
539C42—861no—
540C42—861no—
541C42—1722no—
542C42—1722no—
543C42—1722no—
544C42—1722no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23D4×Dic4312yes—
552C23C2×D4×D4311yescharacteristic
553Q8—22no—
554Q8—22no—
555Q8—22no—
556Q8—22no—
557Q8—22no—
558Q8—48no—
559Q8—41no—
560Q8—41no—
561Q8#1306328414yes—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—48no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—432no—
582C2×C4—861no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—861no—
592C2×C4—861no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4D4×Dic4312yes—
606C2×C4C23×Dic4311yescharacteristic
607C2×C4C2×#1062190011yescharacteristic
608C2×C4C2×#1062189811yescharacteristic
609C2×C4C2×#1062189811yescharacteristic
610C2×C4#1306337011yescharacteristic
611C2×C4#1306337011yescharacteristic
612C8—22no—
613C8—22no—
614C8—1721no—
615C8—1721no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22C2×D4×Dic4311yescharacteristic
624C22#1458353911yescharacteristic
625C22#1458353911yescharacteristic
626C22#137×D4311yescharacteristic
627C22#1458369811yescharacteristic
628C22#1458370811yescharacteristic
629C22#1458371511yescharacteristic
630C4—22no—
631C4—24no—
632C4—42no—
633C4—42no—
634C4—42no—
635C4—862no—
636C4—3441no—
637C4—3441no—
638C4—3441no—
639C4—3441no—
640C4—1721no—
641C4—1721no—
642C4—1721no—
643C4C2×#1306328411yescharacteristic
644C4#1458337411yescharacteristic
645C4#1458357511yescharacteristic
646C4#1458357511yescharacteristic
647C2—42no—
648C2#1913744411yescharacteristic
649C2#137×Dic4311yescharacteristic
650C2#1914343911yescharacteristic
651C2#1914664711yescharacteristic
652C2#1914678211yescharacteristic
653C2#1914685911yescharacteristic
654C2#1914688511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#419C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
cosocleC22×C4×C43C24
hypercenterC2×#419D43
hypocenterC43#22585
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#419

Complements

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

NH ≅ G/Ntype
3. #19135287C2semidirect
4. #19135273C2semidirect
5. #19135238C2semidirect
6. #19135231C2semidirect
7. #19134865C2semidirect
8. #19134851C2semidirect
12. #19134427C2semidirect
13. #103×Dic43C2semidirect
55. C43×#419C4semidirect
350. #419Dic43semidirect
387. C43#22585semidirect

Maximal subgroups

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

subgroupindex
#191374802
Q8×C22⋊Dic432
#191352872
#191352732
#191352382
#191352312
#191348652
#191348512
#191346902
#191346282
#191345302
#191344272
#103×Dic432
#191343762
C2×C43×#4192
#2258543