Finite Group Databasebeta

← #25129354

Subgroups — #25129354

Order 11008.

1276 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583470C211yesmaximal, characteristic
2C2×#14583234C211yesmaximal, characteristic, complemented
3C2×#14583229C211yesmaximal, characteristic, complemented
4#19135798C212yesmaximal, complemented
5#19135791C212yesmaximal, complemented
6#19134907C211yesmaximal, characteristic, complemented
7#19134907C211yesmaximal, characteristic, complemented
8#19134792C212yesmaximal, complemented
9#19134529C212yesmaximal, complemented
10#19134507C211yesmaximal, characteristic
11C43×#2311C211yesmaximal, characteristic
12C23×Dic86C2211yescharacteristic
13#14583470—24no—
14#14583470—24no—
15C2×#13063323—21no—
16C2×#13063312—21no—
17C2×#13063306—21no—
18C2×#13063306—21no—
19C2×#13063304C2211yescharacteristic
20C2×#13063304C2211yescharacteristic
21C2×#13063304C2211yescharacteristic
22C2×#13063304C2211yescharacteristic
23C2×#13063284C2211yescharacteristic
24#14583234—24no—
25#14583229—24no—
26C2×#13063258C2212yes—
27C2×#13063256C2212yes—
28C2×#13063248C2212yes—
29C2×#13063248C2212yes—
30C2×#13063248C2212yes—
31C2×#13063248C2212yes—
32C2×C22⋊(C43⋊C8)C2211yescharacteristic
33C2×C22⋊(C43⋊C8)C2211yescharacteristic
34C2×C22⋊(C43⋊C8)C2212yes—
35C2×C22⋊(C43⋊C8)C2212yes—
36#14582661C2212yes—
37#14582661C2212yes—
38C22×#41×C43C2211yescharacteristic
39C2×#117×C43C2211yescharacteristic
40C22×C4⋊C4×C43C2211yescharacteristic
41C43×#391—21no—
42C43×#390—21no—
43C43×#386—21no—
44C43×#386—21no—
45C43×#380C2212yes—
46C43×#380C2212yes—
47C22×Dic86—21no—
48C22×Dic86—22no—
49C22×Dic86—22no—
50C22×Dic86—24no—
51C22×Dic86—42no—
52C22×Dic86C2311yescharacteristic
53C22×Dic86C2311yescharacteristic
54C23×Dic43—21no—
55C22×C43⋊C8C2312yes—
56C22×C43⋊C8C2312yes—
57#13063323—28no—
58#13063312—28no—
59#13063306—28no—
60#13063306—28no—
61#13063304—22no—
62#13063304—22no—
63#13063304—22no—
64#13063304—22no—
65#13063304—22no—
66#13063304—22no—
67#13063304D414yes—
68#13063304D414yes—
69#13063284—22no—
70#13063284—22no—
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C4×Dic43—21no—
83#13063258—24no—
84#13063256—24no—
85#13063248—24no—
86#13063248—24no—
87#13063248—42no—
88#13063248—42no—
89C22⋊(C43⋊C8)—22no—
90C22⋊(C43⋊C8)—22no—
91C22⋊(C43⋊C8)—24no—
92C22⋊(C43⋊C8)—42no—
93C2×#41×C43—22no—
94C2×#41×C43—22no—
95C2×#41×C43—24no—
96C2×#41×C43—42no—
97C22×Q8×C43D411yescharacteristic
98C22×D4×C43D411yescharacteristic
99C22×D4×C43D411yescharacteristic
100C22×D4×C43D411yescharacteristic
101C23×C4×C43—21no—
102C23×C4×C43C2311yescharacteristic
103C23×C4×C43C2311yescharacteristic
104C23×C4×C43C2311yescharacteristic
105#117×C43—42no—
106C2×C4⋊C4×C43—22no—
107C2×C4⋊C4×C43—22no—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43C2312yes—
110C2×C4⋊C4×C43C2312yes—
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43—22no—
113C2×C22⋊C4×C43—22no—
114C2×C42×C43—21no—
115#95×C43—22no—
116#95×C43—22no—
117C24×C43C2×D411yescharacteristic
118C24×C43C2×D411yescharacteristic
119C24×C43C2×D411yescharacteristic
120#41×C43—48no—
121#41×C43—48no—
122C2×Q8×C43—22no—
123C2×Q8×C43—22no—
124C2×Q8×C43—41no—
125C2×D4×C43—22no—
126C2×D4×C43—22no—
127C2×D4×C43—22no—
128C2×D4×C43—22no—
129C2×D4×C43—22no—
130C2×D4×C43—22no—
131C2×D4×C43—41no—
132C2×D4×C43—41no—
133C2×D4×C43—41no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—22no—
137C22×C4×C43—22no—
138C22×C4×C43—22no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—22no—
142C22×C4×C43—22no—
143C22×C4×C43—22no—
144C22×C4×C43—22no—
145C22×C4×C43—42no—
146C22×C4×C43—82no—
147C22×C4×C43C2×D412yes—
148C22×C4×C43C2×D412yes—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43#4114yes—
153C22×C4×C43C2411yescharacteristic
154C22×Dic43—24no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—42no—
160C22×Dic43—42no—
161C2×Dic86—22no—
162C2×Dic86—22no—
163C2×Dic86—22no—
164C2×Dic86—22no—
165C2×Dic86—24no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—48no—
169C2×Dic86—48no—
170C2×Dic86—42no—
171C2×Dic86—42no—
172C2×Dic86C2×D412yes—
173C2×Dic86C2×D412yes—
174C4⋊C4×C43—22no—
175C4⋊C4×C43—22no—
176C4⋊C4×C43—22no—
177C4⋊C4×C43—22no—
178C4⋊C4×C43—42no—
179C22⋊C4×C43—42no—
180C22⋊C4×C43—82no—
181C22⋊C4×C43—82no—
182C42×C43—42no—
183C22⋊Dic43—24no—
184C22⋊Dic43—24no—
185C22⋊Dic43—24no—
186C22⋊Dic43—24no—
187C22⋊Dic43—24no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43C2×D412yes—
191C4⋊Dic43C2×D412yes—
192Dic43⋊C4—24no—
193Dic43⋊C4—24no—
194Dic43⋊C4—24no—
195Dic43⋊C4—24no—
196C4×Dic43—24no—
197C2×C43⋊C8—22no—
198C2×C43⋊C8—22no—
199C2×C43⋊C8—22no—
200C2×C43⋊C8—22no—
201C2×C43⋊C8—22no—
202C2×C43⋊C8—22no—
203C23×C43—21no—
204C23×C43—21no—
205C23×C43—21no—
206C23×C43—21no—
207C23×C43—22no—
208C23×C43—22no—
209C23×C43—22no—
210C23×C43—22no—
211C23×C43—21no—
212C23×C43—21no—
213C23×C43—21no—
214C23×C43—22no—
215C23×C43—22no—
216C23×C43#12012yes—
217C23×C43#12312yes—
218C23×C43C22×D411yescharacteristic
219Q8×C43—44no—
220D4×C43—44no—
221D4×C43—44no—
222D4×C43—44no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—24no—
228C2×C4×C43—24no—
229C2×C4×C43—24no—
230C2×C4×C43—24no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43—42no—
237C2×C4×C43—42no—
238C2×C4×C43—42no—
239C2×C4×C43—42no—
240C2×C4×C43—42no—
241C2×C4×C43—42no—
242C2×C4×C43—84no—
243C2×C4×C43#12012yes—
244C2×C4×C43#12312yes—
245C2×C4×C43C22×D411yescharacteristic
246C2×C4×C43C22×D411yescharacteristic
247C2×C4×C43C2×#4112yes—
248C2×C4×C43H(5,𝔽2)12yes—
249C2×Dic43—22no—
250C2×Dic43—22no—
251C2×Dic43—22no—
252C2×Dic43—22no—
253C2×Dic43—48no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—42no—
259C2×Dic43—42no—
260Dic86—24no—
261Dic86—24no—
262Dic86—48no—
263Dic86—42no—
264Dic86—42no—
265C43⋊C8—42no—
266C43⋊C8—42no—
267#24014—431nomaximal, Sylow
268C22×C43—24no—
269C22×C43—22no—
270C22×C43—22no—
271C22×C43—22no—
272C22×C43—22no—
273C22×C43—42no—
274C22×C43—42no—
275C22×C43—42no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—42no—
279C22×C43—41no—
280C22×C43—42no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43C2×#12011yescharacteristic
284C22×C43C2×#12311yescharacteristic
285C22×C43#53411yescharacteristic
286C22×C43#57712yes—
287C22×C43#57812yes—
288C4×C43—22no—
289C4×C43—22no—
290C4×C43—41no—
291C4×C43—82no—
292C4×C43—82no—
293C4×C43#54612yes—
294C4×C43#54612yes—
295Dic43—42no—
296Dic43—42no—
297Dic43—42no—
298Dic43—42no—
299C2×#536—431no—
300C2×#484—431no—
301C2×#483—431no—
302#2311D4311yescharacteristic
303#2036—432no—
304#2035—432no—
305#1873—431no—
306#1873—431no—
307#1854—432no—
308#1787—432no—
309#1780—431no—
310C2×C43—42no—
311C2×C43—42no—
312C2×C43—81no—
313C2×C43#240511yescharacteristic
314C2×C43#301011yescharacteristic
315C2×C43#301111yescharacteristic
316C2×C43#309712yes—
317C2×C43#320112yes—
318C22×#41C2×D4311yescharacteristic
319C23×Q8—431no—
320#536—864no—
321#536—864no—
322C2×C4⋊Q8—861no—
323C2×#124—861no—
324C2×#123—861no—
325C2×#123—861no—
326C2×C22⋊Q8—431no—
327C2×C22⋊Q8—431no—
328C2×C22⋊Q8—431no—
329C2×C22⋊Q8—431no—
330C2×#117—431no—
331C2×#117C2×D4311yescharacteristic
332C22×C4⋊C4C2×D4311yescharacteristic
333#484—864no—
334#483—864no—
335C2×#107—432no—
336C2×#106—432no—
337C2×#103—432no—
338C2×#103—432no—
339C2×#103—432no—
340C2×#103—432no—
341C2×C22⋊C8—431no—
342C2×C22⋊C8—431no—
343C2×C22⋊C8—432no—
344C2×C22⋊C8—432no—
345#391—21no—
346#390—21no—
347#386—21no—
348#386—21no—
349#380C2×D4312yes—
350#380C2×D4312yes—
351#340—432no—
352#340—432no—
353C43#2401411yescharacteristic, complemented, Sylow
354C2×#41—24no—
355C2×#41—22no—
356C2×#41—22no—
357C2×#41—42no—
358C22×Q8—431no—
359C22×Q8—431no—
360C22×Q8—862no—
361C22×Q8—862no—
362C22×Q8—861no—
363C22×Q8—864no—
364C22×Q8—1722no—
365C22×Q8C22⋊D4311yescharacteristic
366C22×D4C22⋊D4311yescharacteristic
367C22×D4C22⋊D4311yescharacteristic
368C22×D4C22⋊D4311yescharacteristic
369C23×C4—21no—
370C23×C4—861no—
371C23×C4C22×D4311yescharacteristic
372C23×C4C22×D4311yescharacteristic
373C23×C4C22×D4311yescharacteristic
374C22×C8—432no—
375C22×C8—432no—
376C4⋊Q8—868no—
377#124—868no—
378#123—868no—
379#123—868no—
380C22⋊Q8—434no—
381C22⋊Q8—434no—
382C22⋊Q8—862no—
383C22⋊Q8—862no—
384C22⋊Q8—862no—
385C22⋊Q8—862no—
386C22⋊Q8—862no—
387C22⋊Q8—862no—
388#117—42no—
389#117—862no—
390#117—862no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4C22×D4312yes—
401C2×C4⋊C4C22×D4312yes—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—861no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C22⋊C4—861no—
409C2×C22⋊C4—861no—
410C2×C42—21no—
411C2×C42—861no—
412#107—864no—
413#106—864no—
414#103—864no—
415#103—864no—
416#103—1722no—
417#103—1722no—
418C22⋊C8—864no—
419C22⋊C8—862no—
420C22⋊C8—862no—
421C22⋊C8—1722no—
422#95—22no—
423#95—22no—
424C24C2×C22⋊D4311yescharacteristic
425C24C2×C22⋊D4311yescharacteristic
426C24C2×C22⋊D4311yescharacteristic
427#41—48no—
428#41—48no—
429C2×Q8—22no—
430C2×Q8—22no—
431C2×Q8—41no—
432C2×Q8—432no—
433C2×Q8—432no—
434C2×Q8—864no—
435C2×Q8—861no—
436C2×Q8—861no—
437C2×Q8—862no—
438C2×Q8—862no—
439C2×Q8—862no—
440C2×Q8—862no—
441C2×Q8—1728no—
442C2×Q8—1728no—
443C2×Q8—1722no—
444C2×Q8—1722no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—41no—
452C2×D4—41no—
453C2×D4—41no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—42no—
466C22×C4—82no—
467C22×C4—864no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4—1722no—
473C22×C4—1722no—
474C22×C4#1062189814yes—
475C22×C4D4×D4312yes—
476C22×C4D4×D4312yes—
477C22×C4C2×C22⋊D4311yescharacteristic
478C22×C4C2×C22⋊D4311yescharacteristic
479C22×C4C2×C22⋊D4311yescharacteristic
480C22×C4C23×D4311yescharacteristic
481C2×C8—862no—
482C2×C8—862no—
483C2×C8—862no—
484C2×C8—862no—
485C2×C8—862no—
486C2×C8—862no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—42no—
492C4⋊C4—432no—
493C4⋊C4—432no—
494C4⋊C4—864no—
495C4⋊C4—864no—
496C4⋊C4—864no—
497C4⋊C4—864no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C22⋊C4—42no—
501C22⋊C4—82no—
502C22⋊C4—82no—
503C22⋊C4—864no—
504C22⋊C4—864no—
505C22⋊C4—864no—
506C22⋊C4—864no—
507C22⋊C4—864no—
508C42—42no—
509C42—864no—
510C23—21no—
511C23—21no—
512C23—22no—
513C23—22no—
514C23—21no—
515C23—21no—
516C23—22no—
517C23—22no—
518C23—21no—
519C23—21no—
520C23—22no—
521C23—21no—
522C23—22no—
523C23#1306329312yes—
524C23#1306330812yes—
525C23C22×C22⋊D4311yescharacteristic
526Q8—44no—
527Q8—864no—
528Q8—864no—
529Q8—1728no—
530Q8—1722no—
531Q8—1722no—
532D4—44no—
533D4—44no—
534D4—44no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—84no—
555C2×C4—862no—
556C2×C4—862no—
557C2×C4—862no—
558C2×C4—862no—
559C2×C4—1728no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4—1722no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1722no—
566C2×C4#1306329312yes—
567C2×C4#1306330812yes—
568C2×C4C2×D4×D4311yescharacteristic
569C2×C4C2×D4×D4311yescharacteristic
570C2×C4C2×#1062189812yes—
571C2×C4#1306337012yes—
572C8—1722no—
573C8—1722no—
574C22—24no—
575C22—22no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—42no—
580C22—41no—
581C22—41no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—42no—
589C22C2×#1306329311yescharacteristic
590C22C2×#1306330811yescharacteristic
591C22#1458345811yescharacteristic
592C22#1458371012yes—
593C22#1458371412yes—
594C4—22no—
595C4—22no—
596C4—41no—
597C4—82no—
598C4—82no—
599C4—1722no—
600C4—1722no—
601C4—1722no—
602C4—1722no—
603C4#1458353912yes—
604C4#1458353912yes—
605C2—42no—
606C2—42no—
607C2—81no—
608C2#1913792211yescharacteristic
609C2#1914387911yescharacteristic
610C2#1914388811yescharacteristic
611C2#1914456412yes—
612C2#1914547112yes—
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2311C2
socleC23×C43C22×D4
prime radicalC22×#41×C43C22
hypercenter#2311D43
hypocenterC43#24014
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×#41 ◁ #2311

Complements

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

NH ≅ G/Ntype
2. C2×#14583234C2semidirect
3. C2×#14583229C2semidirect
4. #19135798C2semidirect
5. #19135791C2semidirect
6. #19134907C2semidirect
7. #19134907C2semidirect
8. #19134792C2semidirect
9. #19134529C2semidirect
353. C43#24014semidirect

Maximal subgroups

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

subgroupindex
C2×#145834702
C2×#145832342
C2×#145832292
#191357982
#191357912
#191349072
#191347922
#191345292
#191345072
C43×#23112
#2401443