Finite Group Databasebeta

← #25019323

Subgroups — #25019323

Order 11008.

1622 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic86C211yesmaximal, characteristic
2C2×#14582766C211yesmaximal, characteristic
3C2×#14582744C211yesmaximal, characteristic
4#19132865C212yesmaximal
5#19132861C212yesmaximal
6#19132829C212yesmaximal
7#19132826C212yesmaximal
8#19132822C211yesmaximal, characteristic
9#19132819C211yesmaximal, characteristic
10#19132819C211yesmaximal, characteristic
11C43×#1434C211yesmaximal, characteristic
12C23×Dic86C2211yescharacteristic
13C2×C4×Dic86—24no—
14C2×C4×Dic86—24no—
15C2×C4×Dic86C418yescomplemented
16C22×C4⋊Dic43C2211yescharacteristic
17C22×Dic43⋊C4C2211yescharacteristic
18C22×Dic43⋊C4C2211yescharacteristic
19C22×C4×Dic43C2212yes—
20C22×C4×Dic43C2211yescharacteristic
21C22×C4×Dic43C2211yescharacteristic
22#14582766—24no—
23#14582744—24no—
24C2×C43⋊#95C2211yescharacteristic
25C2×C43⋊#95C2211yescharacteristic
26C2×C43⋊#95C2212yes—
27C2×C43⋊#95C2212yes—
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2212yes—
34C2×C43⋊#95C2212yes—
35C22×C42×C43C2211yescharacteristic
36C2×#95×C43C2211yescharacteristic
37C2×#95×C43C2211yescharacteristic
38C2×#95×C43C2212yes—
39C2×#95×C43C2212yes—
40C22×Dic86—22no—
41C22×Dic86—22no—
42C22×Dic86—22no—
43C22×Dic86—22no—
44C22×Dic86—22no—
45C22×Dic86—22no—
46C22×Dic86C2×C414yes—
47C23×Dic43C2312yes—
48C23×Dic43C2311yescharacteristic
49C23×Dic43C2312yes—
50C23×Dic43C2311yescharacteristic
51C23×Dic43C2311yescharacteristic
52C23×Dic43C2311yescharacteristic
53C4×Dic86—232no—
54C2×C4⋊Dic43—22no—
55C2×C4⋊Dic43—22no—
56C2×C4⋊Dic43C2×C414yes—
57C2×Dic43⋊C4—22no—
58C2×Dic43⋊C4—22no—
59C2×Dic43⋊C4—22no—
60C2×Dic43⋊C4—22no—
61C2×Dic43⋊C4C2×C414yes—
62C2×Dic43⋊C4C2×C414yes—
63C2×C4×Dic43—22no—
64C2×C4×Dic43—22no—
65C2×C4×Dic43—24no—
66C2×C4×Dic43—24no—
67C2×C4×Dic43—24no—
68C2×C4×Dic43C2×C414yes—
69C2×C4×Dic43C2×C414yes—
70C2×C4×Dic43D414yes—
71C2×C4×Dic43D414yes—
72C43⋊#95—22no—
73C43⋊#95—22no—
74C43⋊#95—24no—
75C43⋊#95—24no—
76C43⋊#95—24no—
77C43⋊#95—24no—
78C43⋊#95—24no—
79C43⋊#95—24no—
80C43⋊#95—24no—
81C43⋊#95—24no—
82C43⋊#95—24no—
83C23×C4×C43C2312yes—
84C23×C4×C43C2311yescharacteristic
85C23×C4×C43C2312yes—
86C23×C4×C43C2311yescharacteristic
87C23×C4×C43C2311yescharacteristic
88C2×C42×C43—22no—
89C2×C42×C43—22no—
90C2×C42×C43C2×C414yes—
91#95×C43—22no—
92#95×C43—22no—
93#95×C43—24no—
94#95×C43—24no—
95C24×C43C2411yescharacteristic
96C22×C4×C43—21no—
97C22×C4×C43—21no—
98C22×C4×C43—22no—
99C22×C4×C43—21no—
100C22×C4×C43—21no—
101C22×C4×C43—22no—
102C22×C4×C43—21no—
103C22×C4×C43—21no—
104C22×C4×C43—22no—
105C22×C4×C43—22no—
106C22×C4×C43—22no—
107C22×C4×C43—22no—
108C22×C4×C43—22no—
109C22×C4×C43—22no—
110C22×C4×C43—22no—
111C22×C4×C43—22no—
112C22×C4×C43—22no—
113C22×C4×C43—22no—
114C22×C4×C43—22no—
115C22×C4×C43—22no—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43C22×C412yes—
120C22×C4×C43C22×C412yes—
121C22×C4×C43C22×C412yes—
122C22×C4×C43C2×D412yes—
123C22×C4×C43C2×D412yes—
124C22×C4×C43#4114yes—
125C22×C4×C43#4112yes—
126C22×C4×C43#4112yes—
127C22×Dic43—21no—
128C22×Dic43—21no—
129C22×Dic43—22no—
130C22×Dic43—21no—
131C22×Dic43—21no—
132C22×Dic43—22no—
133C22×Dic43—22no—
134C22×Dic43—22no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—22no—
142C22×Dic43—22no—
143C22×Dic43—22no—
144C22×Dic43—22no—
145C22×Dic43—22no—
146C22×Dic43—22no—
147C22×Dic43—22no—
148C22×Dic43—22no—
149C22×Dic43—22no—
150C22×Dic43—22no—
151C22×Dic43—22no—
152C22×Dic43—22no—
153C22×Dic43—22no—
154C22×Dic43C22×C412yes—
155C22×Dic43C22×C412yes—
156C22×Dic43C22×C412yes—
157C22×Dic43C22×C412yes—
158C22×Dic43C2×D412yes—
159C22×Dic43C2×D412yes—
160C22×Dic43C2×D412yes—
161C22×Dic43C2×D412yes—
162C22×Dic43#4114yes—
163C22×Dic43#4112yes—
164C22×Dic43#4112yes—
165C2×Dic86—28no—
166C2×Dic86—28no—
167C2×Dic86—28no—
168C2×Dic86—28no—
169C2×Dic86—28no—
170C2×Dic86—28no—
171C2×Dic86—28no—
172C42×C43—28no—
173C4⋊Dic43—28no—
174Dic43⋊C4—28no—
175Dic43⋊C4—28no—
176C4×Dic43—216no—
177C4×Dic43—28no—
178C4×Dic43C22⋊C4116yes—
179C23×C43C23×C411yescharacteristic
180C23×C43C22×D411yescharacteristic
181C23×C43C22×D411yescharacteristic
182C23×C43C2×#4111yescharacteristic
183C23×C43C2×#4111yescharacteristic
184C23×C43C2×#4112yes—
185C23×C43C2×#4111yescharacteristic
186C23×C43C2×#4112yes—
187C23×C43C2×#4111yescharacteristic
188C23×C432−1+412yes—
189C23×C432−1+412yes—
190C2×C4×C43—22no—
191C2×C4×C43—22no—
192C2×C4×C43—22no—
193C2×C4×C43—22no—
194C2×C4×C43—22no—
195C2×C4×C43—22no—
196C2×C4×C43—22no—
197C2×C4×C43—22no—
198C2×C4×C43—24no—
199C2×C4×C43—24no—
200C2×C4×C43—22no—
201C2×C4×C43—22no—
202C2×C4×C43—22no—
203C2×C4×C43—24no—
204C2×C4×C43—24no—
205C2×C4×C43—24no—
206C2×C4×C43—42no—
207C2×C4×C43—42no—
208C2×C4×C43—42no—
209C2×C4×C43—42no—
210C2×C4×C43—42no—
211C2×C4×C43—42no—
212C2×C4×C43—42no—
213C2×C4×C43—42no—
214C2×C4×C43—42no—
215C2×C4×C43—42no—
216C2×C4×C43—42no—
217C2×C4×C43—42no—
218C2×C4×C43—42no—
219C2×C4×C43C2×C22⋊C414yes—
220C2×C4×C43#11714yes—
221C2×Dic43—22no—
222C2×Dic43—22no—
223C2×Dic43—22no—
224C2×Dic43—22no—
225C2×Dic43—22no—
226C2×Dic43—22no—
227C2×Dic43—24no—
228C2×Dic43—22no—
229C2×Dic43—22no—
230C2×Dic43—22no—
231C2×Dic43—22no—
232C2×Dic43—22no—
233C2×Dic43—22no—
234C2×Dic43—22no—
235C2×Dic43—22no—
236C2×Dic43—24no—
237C2×Dic43—22no—
238C2×Dic43—22no—
239C2×Dic43—22no—
240C2×Dic43—24no—
241C2×Dic43—24no—
242C2×Dic43—24no—
243C2×Dic43—42no—
244C2×Dic43—42no—
245C2×Dic43—42no—
246C2×Dic43—42no—
247C2×Dic43—42no—
248C2×Dic43—42no—
249C2×Dic43—42no—
250C2×Dic43—42no—
251C2×Dic43—42no—
252C2×Dic43—42no—
253C2×Dic43—42no—
254C2×Dic43—42no—
255C2×Dic43—42no—
256C2×Dic43C2×C22⋊C414yes—
257C2×Dic43C2×C22⋊C414yes—
258C2×Dic43#11714yes—
259Dic86—232no—
260#13961—431nomaximal, Sylow
261C22×C43C22×C22⋊C411yescharacteristic
262C22×C43C2×#11711yescharacteristic
263C22×C43C2×#11711yescharacteristic
264C22×C43C4×#4111yescharacteristic
265C22×C43C4×#4111yescharacteristic
266C22×C43#51911yescharacteristic
267C22×C43#51911yescharacteristic
268C22×C43#52512yes—
269C22×C43#52511yescharacteristic
270C22×C43#52511yescharacteristic
271C22×C43#52511yescharacteristic
272C22×C43#52511yescharacteristic
273C22×C43#53212yes—
274C22×C43#53612yes—
275C22×C43#53612yes—
276C22×C43#55212yes—
277C22×C43#55212yes—
278C22×C43#55212yes—
279C22×C43#55212yes—
280C22×C43#55612yes—
281C22×C43#55612yes—
282C22×C43#55612yes—
283C22×C43#55612yes—
284C4×C43—24no—
285C4×C43—24no—
286C4×C43—44no—
287C4×C43—42no—
288C4×C43—82no—
289Dic43—24no—
290Dic43—24no—
291Dic43—24no—
292Dic43—44no—
293Dic43—42no—
294Dic43—82no—
295C22×C4×Q8—431no—
296C2×#383—431no—
297C2×#376—431no—
298#1446—432no—
299#1445—432no—
300#1436—432no—
301#1436—432no—
302#1434—431no—
303#1434—431no—
304#1434—431no—
305#1434D4311yescharacteristic
306C2×C43#228011yescharacteristic
307C2×C43#229711yescharacteristic
308C2×C43#231011yescharacteristic
309C2×C43#235611yescharacteristic
310C2×C43#235611yescharacteristic
311C2×C43#235611yescharacteristic
312C2×C43#235611yescharacteristic
313C2×C43#259912yes—
314C2×C43#259912yes—
315C2×C43#260412yes—
316C2×C43#260412yes—
317C23×Q8—431no—
318C2×C4×Q8—438no—
319C2×C4×Q8—864no—
320C2×C4×Q8—864no—
321C22×C4⋊C4—431no—
322C22×C4⋊C4—431no—
323C22×C4⋊C4—431no—
324C22×C42—431no—
325C22×C42—431no—
326C22×C42—432no—
327C22×C42C2×D4311yescharacteristic
328#383—864no—
329#376—864no—
330C2×#95—431no—
331C2×#95—431no—
332C2×#95—432no—
333C2×#95—432no—
334C2×#95—432no—
335C2×#95—432no—
336C2×#95—432no—
337C2×#95—432no—
338C2×#95—432no—
339C2×#95—432no—
340C2×#95—432no—
341C2×#95C2×D4311yescharacteristic
342C2×#95C2×D4311yescharacteristic
343C2×#95C2×D4312yes—
344C2×#95C2×D4312yes—
345C43#1396111yescharacteristic, complemented, Sylow
346C22×Q8—434no—
347C22×Q8—862no—
348C22×Q8—862no—
349C22×Q8—862no—
350C22×Q8—862no—
351C22×Q8—862no—
352C22×Q8—862no—
353C23×C4—431no—
354C23×C4—431no—
355C23×C4—431no—
356C23×C4—431no—
357C23×C4—432no—
358C23×C4—432no—
359C23×C4C22×D4312yes—
360C23×C4C22×D4311yescharacteristic
361C23×C4C22×D4312yes—
362C23×C4C22×D4311yescharacteristic
363C23×C4C22×D4311yescharacteristic
364C4×Q8—8632no—
365C2×C4⋊C4—434no—
366C2×C4⋊C4—434no—
367C2×C4⋊C4—434no—
368C2×C4⋊C4—862no—
369C2×C4⋊C4—862no—
370C2×C4⋊C4—862no—
371C2×C4⋊C4—862no—
372C2×C4⋊C4—862no—
373C2×C4⋊C4—862no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—434no—
377C2×C42—434no—
378C2×C42—434no—
379C2×C42—434no—
380C2×C42—864no—
381C2×C42—864no—
382C2×C42—864no—
383C2×C42—862no—
384C2×C42—862no—
385C2×C42C4×D4314yes—
386#95—24no—
387#95—22no—
388#95—22no—
389#95—24no—
390#95—864no—
391#95—864no—
392#95—864no—
393#95—864no—
394#95—864no—
395#95—864no—
396#95—864no—
397#95—864no—
398#95—862no—
399#95—862no—
400#95—864no—
401C24C23×D4311yescharacteristic
402C2×Q8—868no—
403C2×Q8—868no—
404C2×Q8—868no—
405C2×Q8—868no—
406C2×Q8—868no—
407C2×Q8—868no—
408C2×Q8—868no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—432no—
433C22×C4—432no—
434C22×C4—432no—
435C22×C4—432no—
436C22×C4—432no—
437C22×C4—432no—
438C22×C4—432no—
439C22×C4—432no—
440C22×C4—432no—
441C22×C4—432no—
442C22×C4—434no—
443C22×C4—861no—
444C22×C4—861no—
445C22×C4—862no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4—861no—
449C22×C4—861no—
450C22×C4—862no—
451C22×C4—861no—
452C22×C4—861no—
453C22×C4—862no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4—862no—
457C22×C4—862no—
458C22×C4—862no—
459C22×C4—862no—
460C22×C4—862no—
461C22×C4—862no—
462C22×C4—862no—
463C22×C4—862no—
464C22×C4—862no—
465C22×C4—862no—
466C22×C4—862no—
467C22×C4—862no—
468C22×C4—862no—
469C22×C4—862no—
470C22×C4C2×C4×D4312yes—
471C22×C4C2×C4×D4312yes—
472C22×C4C2×C4×D4312yes—
473C22×C4#1062189814yes—
474C22×C4D4×D4312yes—
475C22×C4D4×D4312yes—
476C22×C4#1062190012yes—
477C22×C4#1062190212yes—
478C4⋊C4—868no—
479C4⋊C4—868no—
480C4⋊C4—868no—
481C42—28no—
482C42—4316no—
483C42—8616no—
484C42—868no—
485C23C22×C4×D4311yescharacteristic
486C23C2×D4×D4311yescharacteristic
487C23C2×D4×D4311yescharacteristic
488C23#41×D4311yescharacteristic
489C23#41×D4311yescharacteristic
490C23#41×D4312yes—
491C23C2×#1062190011yescharacteristic
492C23C2×#1062189812yes—
493C23C2×#1062190211yescharacteristic
494C23#1306337212yes—
495C23#1306337212yes—
496Q8—8632no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—24no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—434no—
527C2×C4—434no—
528C2×C4—434no—
529C2×C4—862no—
530C2×C4—862no—
531C2×C4—862no—
532C2×C4—862no—
533C2×C4—862no—
534C2×C4—862no—
535C2×C4—864no—
536C2×C4—862no—
537C2×C4—862no—
538C2×C4—862no—
539C2×C4—862no—
540C2×C4—862no—
541C2×C4—862no—
542C2×C4—862no—
543C2×C4—862no—
544C2×C4—864no—
545C2×C4—864no—
546C2×C4—864no—
547C2×C4—862no—
548C2×C4—862no—
549C2×C4—862no—
550C2×C4—864no—
551C2×C4—1722no—
552C2×C4—1722no—
553C2×C4—1722no—
554C2×C4—1722no—
555C2×C4—1722no—
556C2×C4—1722no—
557C2×C4—1722no—
558C2×C4—1722no—
559C2×C4—1722no—
560C2×C4—1722no—
561C2×C4—1722no—
562C2×C4—1722no—
563C2×C4—1722no—
564C2×C4C22⋊C4×D4314yes—
565C2×C4#1306328314yes—
566C22C2×C22⋊C4×D4311yescharacteristic
567C22#117×D4311yescharacteristic
568C22C2×#1306328311yescharacteristic
569C22#1458336711yescharacteristic
570C22C4×#1062189811yescharacteristic
571C22#1458337611yescharacteristic
572C22#1458337611yescharacteristic
573C22#1458340812yes—
574C22#1458340911yescharacteristic
575C22#1458340911yescharacteristic
576C22#1458341211yescharacteristic
577C22#1458341211yescharacteristic
578C22#1458344612yes—
579C22#1458347112yes—
580C22#1458347112yes—
581C22#1458358212yes—
582C22#1458358512yes—
583C22#1458358712yes—
584C22#1458358912yes—
585C22#1458361612yes—
586C22#1458361712yes—
587C22#1458361812yes—
588C22#1458362212yes—
589C4—24no—
590C4—24no—
591C4—42no—
592C4—44no—
593C4—82no—
594C4—864no—
595C4—864no—
596C4—864no—
597C4—3442no—
598C4—1722no—
599C4—1724no—
600C2#1913697711yescharacteristic
601C2#1913708111yescharacteristic
602C2#1913718011yescharacteristic
603C2#1913755511yescharacteristic
604C2#1913755811yescharacteristic
605C2#1913756111yescharacteristic
606C2#1913756211yescharacteristic
607C2#1914016912yes—
608C2#1914017112yes—
609C2#1914023012yes—
610C2#1914023212yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1434C2
socle, prime radical, cosocleC24×C43C24
hypercenter#1434D43
hypocenterC43#13961
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
15. C2×C4×Dic86C4semidirect
345. C43#13961semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic862
C2×#145827662
C2×#145827442
#191328652
#191328612
#191328292
#191328262
#191328222
#191328192
C43×#14342
#1396143