Finite Group Databasebeta

← #25151017

Subgroups — #25151017

Order 11008.

1096 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583504C211yesmaximal, characteristic
2C2×#14583305C211yesmaximal, characteristic, complemented
3C2×#14583247C211yesmaximal, characteristic, complemented
4#19135784C212yesmaximal, complemented
5#19135777C212yesmaximal, complemented
6#19135559C211yesmaximal, characteristic, complemented
7#19135418C211yesmaximal, characteristic, complemented
8#19134855C212yesmaximal, complemented
9#19134841C212yesmaximal, complemented
10#19134361C211yesmaximal, characteristic, complemented
11C43×#2628C211yesmaximal, characteristic, complemented
12#14583504—24no—
13#14583504—24no—
14C2×#13063322C2211yescharacteristic
15C2×#13063317C2211yescharacteristic
16C2×#13063310—21no—
17C2×#13063310—21no—
18C2×#13063299C2211yescharacteristic
19C2×#13063299C2211yescharacteristic
20C2×#13063298—21no—
21C2×#13063298—21no—
22C2×C4×D172C2211yescharacteristic
23C2×C4×D172C2211yescharacteristic
24#14583305—24no—
25#14583247—24no—
26C2×#13063258C2212yes—
27C2×#13063256C2212yes—
28C2×#13063245C2212yes—
29C2×#13063245C2212yes—
30C2×#13063245C2212yes—
31C2×#13063245C2212yes—
32C2×C22⋊(C43⋊C8)C2212yes—
33C2×#13063236C2211yescharacteristic
34C2×C4×C43⋊C8C2211yescharacteristic
35#14582661C2212yes—
36#14582661C2212yes—
37#14582654C2212yes—
38C2×C4⋊Q8×C43C2211yescharacteristic
39C2×#117×C43C2211yescharacteristic
40C43×#400—21no—
41C43×#399—21no—
42C43×#395—21no—
43C43×#393—21no—
44C43×#389C2212yes—
45C43×#382C2211yescharacteristic
46C43×#380C2212yes—
47C22×D172—21no—
48C22×D172—21no—
49C22×D172C2311yescharacteristic
50C22×D172C2311yescharacteristic
51C22×C22⋊D43—21no—
52C22×C22⋊D43—21no—
53C22×C4×D43—21no—
54C22×C4×D43—21no—
55C22×C43⋊C8C2312yes—
56C22×C43⋊C8C2312yes—
57#13063322—22no—
58#13063322D414yes—
59#13063317—22no—
60#13063317D414yes—
61#13063310—28no—
62#13063310—28no—
63#13063299—22no—
64#13063299—22no—
65#13063299—22no—
66#13063299—22no—
67#13063298—28no—
68#13063298—28no—
69C4×D172—22no—
70C4×D172—22no—
71C4×D172—22no—
72C4×D172—22no—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81#13063258—24no—
82#13063256—24no—
83#13063245—24no—
84#13063245—24no—
85#13063245—24no—
86#13063245—24no—
87C22⋊(C43⋊C8)—24no—
88#13063236—22no—
89C4×C43⋊C8—22no—
90C22×Q8×C43—21no—
91C23×C4×C43C2311yescharacteristic
92C4⋊Q8×C43—22no—
93C4⋊Q8×C43—22no—
94#117×C43—22no—
95#117×C43—22no—
96C2×C4⋊C4×C43—21no—
97C2×C4⋊C4×C43—22no—
98C2×C4⋊C4×C43D411yescharacteristic
99C2×C4⋊C4×C43D411yescharacteristic
100C2×C4⋊C4×C43C2312yes—
101C2×C4⋊C4×C43C2312yes—
102C2×C22⋊C4×C43—22no—
103C2×C22⋊C4×C43D411yescharacteristic
104C2×C22⋊C4×C43D411yescharacteristic
105C2×C42×C43C2311yescharacteristic
106C2×C42×C43C2311yescharacteristic
107#95×C43—22no—
108#95×C43—21no—
109#95×C43—21no—
110#95×C43—22no—
111C24×C43C2×D411yescharacteristic
112C23×D43—21no—
113C23×D43—21no—
114C2×Q8×C43—42no—
115C2×Q8×C43—82no—
116C22×C4×C43—21no—
117C22×C4×C43—21no—
118C22×C4×C43—22no—
119C22×C4×C43—22no—
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2411yescharacteristic
128C2×C22⋊D43—24no—
129C2×C22⋊D43—24no—
130C2×C22⋊D43—82no—
131C2×C22⋊D43—82no—
132C22×Dic43—21no—
133C22×Dic43—21no—
134C2×D172—21no—
135C2×D172—21no—
136C2×D172—24no—
137C2×D172—24no—
138C2×D172—22no—
139C2×D172—22no—
140C2×D172—22no—
141C2×D172—22no—
142C2×D172—82no—
143C2×D172—82no—
144C2×D172C2×D412yes—
145C2×D172C2×D412yes—
146C2×C4×D43—24no—
147C2×C4×D43—24no—
148C2×C4×D43—82no—
149C2×C4×D43—82no—
150C4⋊C4×C43—22no—
151C4⋊C4×C43—22no—
152C4⋊C4×C43—22no—
153C4⋊C4×C43—22no—
154C4⋊C4×C43—22no—
155C4⋊C4×C43—22no—
156C4⋊C4×C43—42no—
157C4⋊C4×C43—82no—
158C22⋊C4×C43—22no—
159C22⋊C4×C43—22no—
160C22⋊C4×C43—82no—
161C42×C43—21no—
162C42×C43—21no—
163C42×C43C2×D412yes—
164C42×C43C2×D412yes—
165(C2×D43)⋊C4—24no—
166(C2×D43)⋊C4—24no—
167(C2×D43)⋊C4—24no—
168(C2×D43)⋊C4—24no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43C2×D412yes—
172C4⋊Dic43C2×D412yes—
173Dic43⋊C4—24no—
174Dic43⋊C4—24no—
175C2×C43⋊C8—22no—
176C2×C43⋊C8—22no—
177C2×C43⋊C8—22no—
178C2×C43⋊C8—22no—
179C2×C43⋊C8—22no—
180C2×C43⋊C8#4114yes—
181C23×C43—21no—
182C23×C43—21no—
183C23×C43—21no—
184C23×C43—22no—
185C23×C43—22no—
186C23×C43C22×D411yescharacteristic
187C22×D43—22no—
188C22×D43—22no—
189C22×D43—41no—
190C22×D43—41no—
191C22×D43—41no—
192C22×D43—41no—
193C22×D43—42no—
194C22×D43—42no—
195C22×D43—42no—
196C22×D43—42no—
197Q8×C43—84no—
198C2×C4×C43—22no—
199C2×C4×C43—22no—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—21no—
205C2×C4×C43—22no—
206C2×C4×C43—22no—
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#12012yes—
216C2×C4×C43#12012yes—
217C2×C4×C43C22×D411yescharacteristic
218C2×C4×C43C22×D411yescharacteristic
219C2×C4×C43C2×#4112yes—
220C2×C4×C432−1+412yes—
221C22⋊D43—84no—
222C22⋊D43—84no—
223C2×Dic43—22no—
224C2×Dic43—22no—
225C2×Dic43—42no—
226C2×Dic43—42no—
227D172—24no—
228D172—24no—
229D172—42no—
230D172—42no—
231D172—84no—
232D172—84no—
233C4×D43—84no—
234C4×D43—84no—
235C43⋊C8—24no—
236C43⋊C8—42no—
237#25685—431nomaximal, Sylow
238C22×C43—42no—
239C22×C43—41no—
240C22×C43—42no—
241C22×C43—41no—
242C22×C43—41no—
243C22×C43C2×#12011yescharacteristic
244C22×C43#53211yescharacteristic
245C22×C43#53611yescharacteristic
246C22×C43#57612yes—
247C22×C43#57712yes—
248C2×D43—42no—
249C2×D43—42no—
250C2×D43—42no—
251C2×D43—42no—
252C2×D43—42no—
253C2×D43—42no—
254C2×D43—82no—
255C2×D43—82no—
256C2×D43—82no—
257C2×D43—82no—
258C4×C43—22no—
259C4×C43—22no—
260C4×C43—41no—
261C4×C43—41no—
262C4×C43—41no—
263C4×C43—82no—
264C4×C43—82no—
265C4×C43#54712yes—
266C4×C43#54812yes—
267Dic43—42no—
268Dic43—42no—
269C2×#540—431no—
270C2×#501—431no—
271C2×#486—431no—
272#2628D4311yescharacteristic, complemented
273#2034—432no—
274#2033—432no—
275#1991—431no—
276#1961—431no—
277#1864—432no—
278#1862—432no—
279#1750—431no—
280C2×C43—81no—
281C2×C43#243211yescharacteristic
282C2×C43#300811yescharacteristic
283C2×C43#300911yescharacteristic
284C2×C43#317912yes—
285C2×C43#324112yes—
286D43—82no—
287D43—82no—
288#540—864no—
289#540—864no—
290C2×C4⋊Q8C2×D4311yescharacteristic
291C2×#127—431no—
292C2×#125—431no—
293C2×#123—861no—
294C2×#123—861no—
295C2×#121—431no—
296C2×#121—431no—
297C2×#121—861no—
298C2×#121—861no—
299C2×C4×D4—431no—
300C2×C4×D4—431no—
301C2×#117C2×D4311yescharacteristic
302#501—864no—
303#486—864no—
304C2×#107—432no—
305C2×#106—432no—
306C2×#102—432no—
307C2×#102—432no—
308C2×#102—432no—
309C2×#102—432no—
310C2×C22⋊C8—432no—
311C2×#97—431no—
312C2×C4×C8—431no—
313#400—21no—
314#399—21no—
315#395—21no—
316#393—21no—
317#389C2×D4312yes—
318#382C2×D4311yescharacteristic
319#380C2×D4312yes—
320#340—432no—
321#340—432no—
322#336—432no—
323C43#2568511yescharacteristic, complemented, Sylow
324C22×Q8—21no—
325C22×D4—431no—
326C22×D4—431no—
327C22×D4—861no—
328C22×D4—861no—
329C22×D4—861no—
330C22×D4—861no—
331C23×C4—861no—
332C23×C4—861no—
333C23×C4C22×D4311yescharacteristic
334C22×C8—432no—
335C22×C8—432no—
336C4⋊Q8—22no—
337C4⋊Q8—22no—
338#127—434no—
339#127—862no—
340#125—434no—
341#125—862no—
342#123—868no—
343#123—868no—
344#121—868no—
345#121—868no—
346#121—862no—
347#121—862no—
348#121—862no—
349#121—862no—
350C4×D4—862no—
351C4×D4—862no—
352C4×D4—862no—
353C4×D4—862no—
354#117—22no—
355#117—22no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—431no—
359C2×C4⋊C4—431no—
360C2×C4⋊C4—861no—
361C2×C4⋊C4—861no—
362C2×C4⋊C4C22⋊D4311yescharacteristic
363C2×C4⋊C4C22⋊D4311yescharacteristic
364C2×C4⋊C4C22×D4312yes—
365C2×C4⋊C4C22×D4312yes—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—861no—
368C2×C22⋊C4—861no—
369C2×C22⋊C4—861no—
370C2×C22⋊C4—861no—
371C2×C22⋊C4C22⋊D4311yescharacteristic
372C2×C22⋊C4C22⋊D4311yescharacteristic
373C2×C42C22×D4311yescharacteristic
374C2×C42C22×D4311yescharacteristic
375#107—864no—
376#106—864no—
377#102—864no—
378#102—864no—
379#102—864no—
380#102—864no—
381C22⋊C8—864no—
382#97—862no—
383C4×C8—862no—
384#95—22no—
385#95—21no—
386#95—21no—
387#95—22no—
388C24—861no—
389C24—861no—
390C24C2×C22⋊D4311yescharacteristic
391C2×Q8—42no—
392C2×Q8—82no—
393C2×D4—432no—
394C2×D4—432no—
395C2×D4—864no—
396C2×D4—864no—
397C2×D4—864no—
398C2×D4—864no—
399C2×D4—861no—
400C2×D4—861no—
401C2×D4—862no—
402C2×D4—862no—
403C2×D4—862no—
404C2×D4—862no—
405C2×D4—3442no—
406C2×D4—3442no—
407C2×D4—3442no—
408C2×D4—3442no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—864no—
416C22×C4—864no—
417C22×C4—861no—
418C22×C4—861no—
419C22×C4—3442no—
420C22×C4—3442no—
421C22×C4C2×C22⋊D4311yescharacteristic
422C22×C4C2×C22⋊D4311yescharacteristic
423C22×C4C2×C22⋊D4311yescharacteristic
424C22×C4C2×C22⋊D4311yescharacteristic
425C22×C4C2×C22⋊D4311yescharacteristic
426C22×C4C23×D4311yescharacteristic
427C2×C8—434no—
428C2×C8—862no—
429C2×C8—862no—
430C2×C8—862no—
431C2×C8—862no—
432C2×C8—862no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—42no—
440C4⋊C4—82no—
441C4⋊C4—432no—
442C4⋊C4—432no—
443C4⋊C4—864no—
444C4⋊C4—864no—
445C4⋊C4—861no—
446C4⋊C4—861no—
447C22⋊C4—22no—
448C22⋊C4—22no—
449C22⋊C4—82no—
450C22⋊C4—864no—
451C22⋊C4—864no—
452C22⋊C4—864no—
453C22⋊C4—864no—
454C42—21no—
455C42—21no—
456C42D4×D4312yes—
457C42D4×D4312yes—
458C23—21no—
459C23—21no—
460C23—22no—
461C23—22no—
462C23—21no—
463C23—862no—
464C23—862no—
465C23—1721no—
466C23—1721no—
467C23—1722no—
468C23—1722no—
469C23—1722no—
470C23—1722no—
471C23—1721no—
472C23—1721no—
473C23C22×C22⋊D4311yescharacteristic
474Q8—84no—
475D4—864no—
476D4—864no—
477D4—3444no—
478D4—3444no—
479D4—3444no—
480D4—3444no—
481D4—1722no—
482D4—1722no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—21no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—862no—
501C2×C4—862no—
502C2×C4—3444no—
503C2×C4—3444no—
504C2×C4—1722no—
505C2×C4—1722no—
506C2×C4#1306329312yes—
507C2×C4#1306329312yes—
508C2×C4C2×D4×D4311yescharacteristic
509C2×C4C2×D4×D4311yescharacteristic
510C2×C4#41×D4312yes—
511C2×C4#1306337312yes—
512C8—864no—
513C8—1722no—
514C22—42no—
515C22—42no—
516C22—41no—
517C22—41no—
518C22—41no—
519C22—3442no—
520C22—3442no—
521C22—3442no—
522C22—3442no—
523C22—1722no—
524C22—1722no—
525C22—1722no—
526C22—1722no—
527C22—1722no—
528C22—1722no—
529C22C2×#1306329311yescharacteristic
530C22#1458344511yescharacteristic
531C22#1458347311yescharacteristic
532C22#1458370212yes—
533C22#1458370712yes—
534C4—22no—
535C4—22no—
536C4—41no—
537C4—41no—
538C4—41no—
539C4—82no—
540C4—82no—
541C4—1722no—
542C4—1722no—
543C4#1458355112yes—
544C4#1458355912yes—
545C2—81no—
546C2—3442no—
547C2—3442no—
548C2#1913822411yescharacteristic
549C2#1914386111yescharacteristic
550C2#1914387011yescharacteristic
551C2#1914527212yes—
552C2#1914584812yes—
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2628C2
socleC23×C43C22×D4
prime radicalC2×#14583504C2
hypercenter#2628D43
hypocenterC43#25685
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2628

Complements

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

NH ≅ G/Ntype
2. C2×#14583305C2semidirect
3. C2×#14583247C2semidirect
4. #19135784C2semidirect
5. #19135777C2semidirect
6. #19135559C2semidirect
7. #19135418C2semidirect
8. #19134855C2semidirect
9. #19134841C2semidirect
10. #19134361C2semidirect
11. C43×#2628C2semidirect
272. #2628D43semidirect
323. C43#25685semidirect

Maximal subgroups

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

subgroupindex
C2×#145835042
C2×#145833052
C2×#145832472
#191357842
#191357772
#191355592
#191354182
#191348552
#191348412
#191343612
C43×#26282
#2568543