Finite Group Databasebeta

← #25108838

Subgroups — #25108838

Order 11008.

732 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583196C211yesmaximal, characteristic
2#19137239C211yesmaximal, characteristic
3#19135553C211yesmaximal, characteristic, complemented
4#19135351C211yesmaximal, characteristic, complemented
5#19135335C211yesmaximal, characteristic, complemented
6#19135325C211yesmaximal, characteristic, complemented
7#19135291C211yesmaximal, characteristic
8#19135277C211yesmaximal, characteristic
9#19135215C211yesmaximal, characteristic
10#19135215C211yesmaximal, characteristic
11#19135187C211yesmaximal, characteristic, complemented
12#19135173C211yesmaximal, characteristic, complemented
13#19134592C211yesmaximal, characteristic
14#19134452C211yesmaximal, characteristic, complemented
15C43×#2330C211yesmaximal, characteristic, complemented
16C2×C4×D172C2211yescharacteristic
17#14583196C418yescomplemented
18C2×#13063258C2211yescharacteristic
19C2×#13063258C2211yescharacteristic
20C2×#13063258C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×C4⋊(C43⋊C8)C2211yescharacteristic
23C2×C4⋊(C43⋊C8)C2211yescharacteristic
24C2×#13063245C2211yescharacteristic
25C2×#13063245C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063236C2211yescharacteristic
29C2×C4×C43⋊C8C2211yescharacteristic
30#14582801C2211yescharacteristic
31#14582801C2211yescharacteristic
32#14582797C2211yescharacteristic
33#14582797C2211yescharacteristic
34#14582788—21no—
35#14582788—21no—
36#14582761—21no—
37#14582758—21no—
38C4×C4⋊Dic43C2211yescharacteristic
39#14582661C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582654C2211yescharacteristic
48#14582654C2211yescharacteristic
49C2×#125×C43C2211yescharacteristic
50C43×#389—21no—
51C43×#389—21no—
52C43×#389C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C43×#387—21no—
55C43×#387—21no—
56C43×#384C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C4×C4⋊C4×C43C2211yescharacteristic
59C43×#376C2211yescharacteristic
60C22×D172C2311yescharacteristic
61C22×C4×D43—21no—
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C4×D172—22no—
67C4×D172C2×C414yes—
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×Dic43⋊C4—21no—
72C2×Dic43⋊C4—21no—
73C2×(C2×D43)⋊C4—21no—
74C2×(C2×D43)⋊C4—21no—
75C2×(C2×D43)⋊C4—21no—
76C2×(C2×D43)⋊C4—21no—
77C2×(C2×D43)⋊C4—21no—
78C2×C4×Dic43—21no—
79#13063258—41no—
80#13063258—41no—
81#13063258C2×C414yes—
82#13063256C2×C414yes—
83C4⋊(C43⋊C8)—22no—
84C4⋊(C43⋊C8)C2×C414yes—
85#13063245—41no—
86#13063245—41no—
87#13063245C2×C414yes—
88#13063245C2×C414yes—
89#13063236—41no—
90C4×C43⋊C8—41no—
91C43⋊#95—21no—
92C43⋊#95—21no—
93C43⋊#95—21no—
94#125×C43—22no—
95#125×C43C2×C414yes—
96C2×C4⋊C4×C43—21no—
97C2×C4⋊C4×C43—21no—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43C2311yescharacteristic
103C2×C4⋊C4×C43C2311yescharacteristic
104C2×C4⋊C4×C43C2311yescharacteristic
105C2×C4⋊C4×C43C2311yescharacteristic
106C2×C42×C43—21no—
107C2×C42×C43—21no—
108C2×C42×C43C2311yescharacteristic
109C2×C42×C43C2311yescharacteristic
110C2×C42×C43C2311yescharacteristic
111#95×C43—21no—
112#95×C43—21no—
113#95×C43—21no—
114#95×C43—21no—
115#95×C43D411yescharacteristic
116#95×C43D411yescharacteristic
117#95×C43D411yescharacteristic
118#95×C43D411yescharacteristic
119C23×D43—21no—
120C22×C4×C43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2411yescharacteristic
131C22×Dic43—21no—
132C22×Dic43—21no—
133C22×Dic43—21no—
134C2×D172—21no—
135C2×D172—21no—
136C2×D172—21no—
137C2×D172—21no—
138C2×D172—21no—
139C2×D172C22×C412yes—
140C2×C4×D43—24no—
141C2×C4×D43—81no—
142C2×C4×D43—81no—
143C4⋊C4×C43—24no—
144C4⋊C4×C43—24no—
145C4⋊C4×C43—21no—
146C4⋊C4×C43—21no—
147C4⋊C4×C43—21no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—21no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—81no—
152C4⋊C4×C43—81no—
153C4⋊C4×C43—81no—
154C4⋊C4×C43—81no—
155C4⋊C4×C43C22×C412yes—
156C4⋊C4×C43C22×C412yes—
157C42×C43—21no—
158C42×C43—21no—
159C42×C43—21no—
160C42×C43—21no—
161C42×C43—81no—
162C42×C43—81no—
163C42×C43C22×C412yes—
164C42×C43#4112yes—
165(C2×D43)⋊C4—24no—
166(C2×D43)⋊C4—81no—
167(C2×D43)⋊C4—81no—
168(C2×D43)⋊C4—81no—
169(C2×D43)⋊C4—81no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43C22×C412yes—
176Dic43⋊C4—81no—
177Dic43⋊C4—81no—
178C4×Dic43—81no—
179C2×C43⋊C8—21no—
180C2×C43⋊C8—21no—
181C2×C43⋊C8—21no—
182C2×C43⋊C8—21no—
183C2×C43⋊C8—21no—
184C2×C43⋊C8—21no—
185C2×C43⋊C8—21no—
186C2×C43⋊C8—21no—
187C2×C43⋊C8—21no—
188C2×C43⋊C8—21no—
189C2×C43⋊C8C22×C412yes—
190C2×C43⋊C8C22×C412yes—
191C23×C43C22×D411yescharacteristic
192C22×D43—22no—
193C22×D43—41no—
194C22×D43—41no—
195C22×D43—41no—
196C22×D43—41no—
197C22×D43—41no—
198C22×D43—41no—
199C2×C4×C43—21no—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—22no—
204C2×C4×C43—22no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43C4×D412yes—
228C2×C4×C43C4×D412yes—
229C2×C4×C43C23×C411yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C2×C4×C43H(5,𝔽2)11yescharacteristic
232C2×C4×C432−1+411yescharacteristic
233C2×C4×C432−1+411yescharacteristic
234C2×C4×C432−1+411yescharacteristic
235C2×Dic43—22no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244D172—22no—
245D172—22no—
246D172—41no—
247D172—41no—
248C4×D43—84no—
249C43⋊C8—22no—
250C43⋊C8—22no—
251C43⋊C8—41no—
252C43⋊C8—41no—
253#22126—431nomaximal, Sylow
254C22×C43C2×C4×D411yescharacteristic
255C22×C43#53611yescharacteristic
256C22×C43#53711yescharacteristic
257C22×C43#57611yescharacteristic
258C22×C43#57611yescharacteristic
259C22×C43#57711yescharacteristic
260C22×C43#57811yescharacteristic
261C2×D43—42no—
262C2×D43—42no—
263C2×D43—42no—
264C2×D43—81no—
265C2×D43—81no—
266C2×D43—81no—
267C2×D43—81no—
268C4×C43—22no—
269C4×C43—22no—
270C4×C43—42no—
271C4×C43—42no—
272C4×C43—41no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43—41no—
276C4×C43—81no—
277C4×C43—81no—
278C4×C43#51911yescharacteristic
279C4×C43#52011yescharacteristic
280C4×C43#54111yescharacteristic
281C4×C43#54211yescharacteristic
282Dic43—42no—
283Dic43—81no—
284Dic43—81no—
285C2×#478—431no—
286#2330D4311yescharacteristic, complemented
287#2319—431no—
288#1989—431no—
289#1947—431no—
290#1944—431no—
291#1942—431no—
292#1936—431no—
293#1934—431no—
294#1925—431no—
295#1925—431no—
296#1921—431no—
297#1919—431no—
298#1802—431no—
299#1768—431no—
300C2×C43#232311yescharacteristic
301C2×C43#294611yescharacteristic
302C2×C43#295111yescharacteristic
303C2×C43#324111yescharacteristic
304C2×C43#324311yescharacteristic
305C2×C43#325811yescharacteristic
306C2×C43#325911yescharacteristic
307D43—82no—
308C2×#125C2×D4311yescharacteristic
309C2×C4×D4—431no—
310#478—438no—
311C2×#107—431no—
312C2×#107—431no—
313C2×#107—431no—
314C2×#106—431no—
315C2×C4⋊C8—431no—
316C2×C4⋊C8—431no—
317C2×#102—431no—
318C2×#102—431no—
319C2×#102—431no—
320C2×#102—431no—
321C2×#97—431no—
322C2×C4×C8—431no—
323#390—431no—
324#390—431no—
325#389—21no—
326#389—21no—
327#389—431no—
328#389—431no—
329#389C2×D4311yescharacteristic
330#389C2×D4311yescharacteristic
331#388—861no—
332#388—861no—
333#387—21no—
334#387—21no—
335#384C2×D4311yescharacteristic
336#381—861no—
337#380—861no—
338C4×C4⋊C4—431no—
339C4×C4⋊C4C2×D4311yescharacteristic
340C4×C4⋊C4C2×D4311yescharacteristic
341#376C2×D4311yescharacteristic
342#340—431no—
343#340—431no—
344#340—431no—
345#340—431no—
346#340—431no—
347#340—431no—
348#340—431no—
349#340—431no—
350#336—431no—
351#336—431no—
352C43#2212611yescharacteristic, complemented, Sylow
353C22×D4—431no—
354C23×C4—861no—
355C22×C8—431no—
356C22×C8—431no—
357C22×C8—431no—
358C22×C8—431no—
359#125—22no—
360#125C4×D4314yes—
361C4×D4—434no—
362C4×D4—862no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—431no—
370C2×C4⋊C4—431no—
371C2×C4⋊C4—431no—
372C2×C4⋊C4—861no—
373C2×C4⋊C4—861no—
374C2×C4⋊C4C22×D4311yescharacteristic
375C2×C4⋊C4C22×D4311yescharacteristic
376C2×C4⋊C4C22×D4311yescharacteristic
377C2×C4⋊C4C22×D4311yescharacteristic
378C2×C22⋊C4—861no—
379C2×C22⋊C4—861no—
380C2×C22⋊C4—861no—
381C2×C22⋊C4—861no—
382C2×C22⋊C4—861no—
383C2×C42—21no—
384C2×C42—21no—
385C2×C42—861no—
386C2×C42C22×D4311yescharacteristic
387C2×C42C22×D4311yescharacteristic
388C2×C42C22×D4311yescharacteristic
389#107—434no—
390#107—1721no—
391#107—1721no—
392#106—434no—
393C4⋊C8—434no—
394C4⋊C8—862no—
395#102—434no—
396#102—434no—
397#102—1721no—
398#102—1721no—
399#97—1721no—
400C4×C8—1721no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—861no—
406#95—861no—
407#95—861no—
408#95C22⋊D4311yescharacteristic
409#95C22⋊D4311yescharacteristic
410#95C22⋊D4311yescharacteristic
411#95C22⋊D4311yescharacteristic
412C24—861no—
413C2×D4—432no—
414C2×D4—861no—
415C2×D4—861no—
416C2×D4—861no—
417C2×D4—861no—
418C2×D4—861no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—861no—
424C22×C4—864no—
425C22×C4—861no—
426C22×C4—861no—
427C22×C4—3441no—
428C22×C4—3441no—
429C22×C4C2×C22⋊D4311yescharacteristic
430C22×C4C2×C22⋊D4311yescharacteristic
431C22×C4C2×C22⋊D4311yescharacteristic
432C22×C4C2×C22⋊D4311yescharacteristic
433C22×C4C2×C22⋊D4311yescharacteristic
434C22×C4C2×C22⋊D4311yescharacteristic
435C22×C4C23×D4311yescharacteristic
436C2×C8—432no—
437C2×C8—432no—
438C2×C8—861no—
439C2×C8—861no—
440C2×C8—861no—
441C2×C8—861no—
442C2×C8—861no—
443C2×C8—861no—
444C2×C8—861no—
445C2×C8—861no—
446C2×C8—861no—
447C2×C8—861no—
448C4⋊C4—24no—
449C4⋊C4—24no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—81no—
457C4⋊C4—81no—
458C4⋊C4—81no—
459C4⋊C4—81no—
460C4⋊C4—432no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—3441no—
467C4⋊C4—3441no—
468C4⋊C4C2×C4×D4312yes—
469C4⋊C4C2×C4×D4312yes—
470C22⋊C4—864no—
471C22⋊C4—3441no—
472C22⋊C4—3441no—
473C22⋊C4—3441no—
474C22⋊C4—3441no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—81no—
480C42—81no—
481C42—3441no—
482C42C2×C4×D4312yes—
483C42#1062189812yes—
484C23—862no—
485C23—1721no—
486C23—1721no—
487C23—1721no—
488C23—1721no—
489C23—1721no—
490C23—1721no—
491C23C22×C22⋊D4311yescharacteristic
492D4—862no—
493D4—862no—
494D4—1721no—
495D4—1721no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—862no—
525C2×C4—3444no—
526C2×C4—1721no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4—1721no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4C4×C22⋊D4312yes—
535C2×C4C4×C22⋊D4312yes—
536C2×C4C22×C4×D4311yescharacteristic
537C2×C4C2×#1062189811yescharacteristic
538C2×C4#1306337111yescharacteristic
539C2×C4#1306337211yescharacteristic
540C2×C4#1306337311yescharacteristic
541C2×C4#1306337311yescharacteristic
542C8—862no—
543C8—862no—
544C8—1721no—
545C8—1721no—
546C22—3441no—
547C22—3441no—
548C22—3441no—
549C22—3441no—
550C22—1722no—
551C22—1722no—
552C22—1722no—
553C22C2×C4×C22⋊D4311yescharacteristic
554C22#1458347311yescharacteristic
555C22#1458347711yescharacteristic
556C22#1458370211yescharacteristic
557C22#1458370211yescharacteristic
558C22#1458370711yescharacteristic
559C22#1458371411yescharacteristic
560C4—22no—
561C4—22no—
562C4—41no—
563C4—42no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—42no—
568C4—81no—
569C4—81no—
570C4—3441no—
571C4—3441no—
572C4—1722no—
573C4#1458337511yescharacteristic
574C4#1458338111yescharacteristic
575C4#1458350711yescharacteristic
576C4#1458352111yescharacteristic
577C2—3442no—
578C2#1913727111yescharacteristic
579C2#1914342311yescharacteristic
580C2#1914346811yescharacteristic
581C2#1914584811yescharacteristic
582C2#1914587811yescharacteristic
583C2#1914601511yescharacteristic
584C2#1914603011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2330C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenter#2330D43
hypocenterC43#22126
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ #376 ◁ #2330

Complements

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

NH ≅ G/Ntype
3. #19135553C2semidirect
4. #19135351C2semidirect
5. #19135335C2semidirect
6. #19135325C2semidirect
11. #19135187C2semidirect
12. #19135173C2semidirect
14. #19134452C2semidirect
15. C43×#2330C2semidirect
17. #14583196C4semidirect
286. #2330D43semidirect
352. C43#22126semidirect

Maximal subgroups

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

subgroupindex
C2×#145831962
#191372392
#191355532
#191353512
#191353352
#191353252
#191352912
#191352772
#191352152
#191351872
#191351732
#191345922
#191344522
C43×#23302
#2212643