Finite Group Databasebeta

← #25154211

Subgroups — #25154211

Order 11008.

702 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137486C211yesmaximal, characteristic
2#19136162C211yesmaximal, characteristic, complemented
3#19136097C211yesmaximal, characteristic, complemented
4#19136091C211yesmaximal, characteristic, complemented
5#19135920C211yesmaximal, characteristic, complemented
6#19135548C211yesmaximal, characteristic, complemented
7#19135361C211yesmaximal, characteristic, complemented
8#19135184C211yesmaximal, characteristic, complemented
9#19135163C211yesmaximal, characteristic, complemented
10#19134794C211yesmaximal, characteristic
11#19134775C211yesmaximal, characteristic
12#19134687C211yesmaximal, characteristic
13#19134622C211yesmaximal, characteristic
14#19134311C211yesmaximal, characteristic
15C43×#2439C211yesmaximal, characteristic
16C23×C43⋊C8C2211yescharacteristic
17C2×#13063284C2211yescharacteristic
18C2×#13063258C2211yescharacteristic
19C2×#13063258C2211yescharacteristic
20C2×#13063258C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×C4⋊(C43⋊C8)C2211yescharacteristic
23C2×C4⋊(C43⋊C8)C2211yescharacteristic
24C2×C22⋊(C43⋊C8)C2211yescharacteristic
25#14582797C2211yescharacteristic
26#14582797C2211yescharacteristic
27#14582793—21no—
28#14582793—21no—
29#14582766—21no—
30#14582759C2211yescharacteristic
31C4×C4⋊Dic43C2211yescharacteristic
32C4×C4⋊Dic43C2211yescharacteristic
33#14582750—21no—
34#14582661C2211yescharacteristic
35#14582661C2211yescharacteristic
36#14582661C2211yescharacteristic
37#14582661C2211yescharacteristic
38#14582661C2211yescharacteristic
39#14582661C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C2×C4⋊Q8×C43C2211yescharacteristic
49C2×#117×C43C2211yescharacteristic
50C43×#396—21no—
51C43×#393—21no—
52C43×#391—21no—
53C43×#389C2211yescharacteristic
54C43×#389C2211yescharacteristic
55C43×#387—21no—
56C43×#382C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C4×C22⋊C4×C43C2211yescharacteristic
59C22×C43⋊C8—22no—
60C22×C43⋊C8—22no—
61C22×C43⋊C8—41no—
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66#13063284—22no—
67#13063284Q814yescomplemented
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×C22⋊Dic43—21no—
75C2×C22⋊Dic43—21no—
76C2×C4×Dic43—21no—
77C2×C4×Dic43—21no—
78C2×C4×Dic43—21no—
79#13063258—22no—
80#13063258—22no—
81#13063258—41no—
82#13063256—41no—
83C4⋊(C43⋊C8)—22no—
84C4⋊(C43⋊C8)—41no—
85C22⋊(C43⋊C8)—22no—
86C43⋊#95—21no—
87C43⋊#95—21no—
88C43⋊#95—21no—
89C43⋊#95—21no—
90C43⋊#95—21no—
91C22×Q8×C43—21no—
92C23×C4×C43C2311yescharacteristic
93C4⋊Q8×C43—22no—
94C4⋊Q8×C43—41no—
95#117×C43—22no—
96#117×C43—41no—
97C2×C4⋊C4×C43—21no—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43C2311yescharacteristic
101C2×C4⋊C4×C43C2311yescharacteristic
102C2×C4⋊C4×C43C2311yescharacteristic
103C2×C4⋊C4×C43C2311yescharacteristic
104C2×C22⋊C4×C43—21no—
105C2×C22⋊C4×C43—21no—
106C2×C22⋊C4×C43D411yescharacteristic
107C2×C22⋊C4×C43D411yescharacteristic
108C2×C42×C43—21no—
109C2×C42×C43C2311yescharacteristic
110C2×C42×C43C2311yescharacteristic
111#95×C43—21no—
112#95×C43—21no—
113#95×C43—21no—
114#95×C43—21no—
115#95×C43—21no—
116#95×C43D411yescharacteristic
117#95×C43D411yescharacteristic
118C24×C43C2×D411yescharacteristic
119C2×Q8×C43—42no—
120C2×Q8×C43—42no—
121C2×Q8×C43—81no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×Q812yes—
136C22×C4×C43#4112yes—
137C22×C4×C43C2411yescharacteristic
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C4⋊C4×C43—21no—
143C4⋊C4×C43—21no—
144C4⋊C4×C43—21no—
145C4⋊C4×C43—21no—
146C4⋊C4×C43—21no—
147C4⋊C4×C43—21no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—42no—
150C4⋊C4×C43—42no—
151C4⋊C4×C43—81no—
152C4⋊C4×C43#4112yes—
153C22⋊C4×C43—22no—
154C22⋊C4×C43—41no—
155C22⋊C4×C43—42no—
156C22⋊C4×C43—81no—
157C42×C43—21no—
158C42×C43—21no—
159C42×C43—21no—
160C42×C43—21no—
161C42×C43—42no—
162C22⋊Dic43—24no—
163C22⋊Dic43—81no—
164C4⋊Dic43—21no—
165C4⋊Dic43—21no—
166C4⋊Dic43—21no—
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C4⋊Dic43C2×Q812yes—
171C4⋊Dic43C2×Q812yes—
172Dic43⋊C4—42no—
173Dic43⋊C4—42no—
174C4×Dic43—24no—
175C4×Dic43—81no—
176C4×Dic43—81no—
177C2×C43⋊C8—21no—
178C2×C43⋊C8—21no—
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—44no—
189C2×C43⋊C8#4112yes—
190C23×C43—21no—
191C23×C43—21no—
192C23×C43—21no—
193C23×C43—21no—
194C23×C43—21no—
195C23×C43—21no—
196C23×C43C22⋊Q812yes—
197C23×C43C22×D411yescharacteristic
198Q8×C43—84no—
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—22no—
206C2×C4×C43—22no—
207C2×C4×C43—21no—
208C2×C4×C43—22no—
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×C43—41no—
228C2×C4×C43C22⋊Q812yes—
229C2×C4×C43#13512yes—
230C2×C4×C43C22×Q811yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C43H(5,𝔽2)11yescharacteristic
235C2×C4×C432−1+411yescharacteristic
236C2×Dic43—22no—
237C2×Dic43—22no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C43⋊C8—22no—
249C43⋊C8—41no—
250C43⋊C8—41no—
251C43⋊C8—41no—
252#25989—431nomaximal, Sylow
253C22×C43—22no—
254C22×C43—22no—
255C22×C43—22no—
256C22×C43—41no—
257C22×C43—41no—
258C22×C43—41no—
259C22×C43—41no—
260C22×C43C2×C22⋊Q811yescharacteristic
261C22×C43#54611yescharacteristic
262C22×C43#54711yescharacteristic
263C22×C43C2×#13511yescharacteristic
264C22×C43#57511yescharacteristic
265C22×C43#57611yescharacteristic
266C22×C43#57811yescharacteristic
267C4×C43—22no—
268C4×C43—22no—
269C4×C43—41no—
270C4×C43—41no—
271C4×C43—42no—
272C4×C43—41no—
273C4×C43—81no—
274C4×C43—81no—
275C4×C43—81no—
276C4×C43#53311yescharacteristic
277C4×C43#54411yescharacteristic
278C4×C43#55111yescharacteristic
279C4×C43#55211yescharacteristic
280Dic43—42no—
281Dic43—42no—
282Dic43—81no—
283Dic43—81no—
284#2439D4311yescharacteristic
285#2347—431no—
286#2101—431no—
287#2088—431no—
288#2087—431no—
289#2057—431no—
290#1988—431no—
291#1949—431no—
292#1921—431no—
293#1918—431no—
294#1854—431no—
295#1850—431no—
296#1825—431no—
297#1808—431no—
298#1735—431no—
299C2×C43—42no—
300C2×C43#243811yescharacteristic
301C2×C43#307611yescharacteristic
302C2×C43#308311yescharacteristic
303C2×C43#329711yescharacteristic
304C2×C43#331311yescharacteristic
305C2×C43#334211yescharacteristic
306C2×C43#334711yescharacteristic
307C23×C8—431no—
308C2×C4⋊Q8C2×D4311yescharacteristic
309C2×#117—431no—
310C2×#117C2×D4311yescharacteristic
311C2×#107—431no—
312C2×#107—431no—
313C2×#107—431no—
314C2×#106—431no—
315C2×C4⋊C8—431no—
316C2×C4⋊C8—431no—
317C2×C22⋊C8—431no—
318#396—21no—
319#393—21no—
320#391—21no—
321#389—431no—
322#389—431no—
323#389C2×D4311yescharacteristic
324#389C2×D4311yescharacteristic
325#388—861no—
326#388—861no—
327#387—21no—
328#383—861no—
329#382C2×D4311yescharacteristic
330#380—431no—
331#380C2×D4311yescharacteristic
332C4×C4⋊C4—431no—
333C4×C4⋊C4—431no—
334C4×C4⋊C4—861no—
335C4×C22⋊C4C2×D4311yescharacteristic
336#340—431no—
337#340—431no—
338#340—431no—
339#340—431no—
340#340—431no—
341#340—431no—
342#340—431no—
343#340—431no—
344#340—431no—
345#340—431no—
346#340—431no—
347#340—431no—
348#336—431no—
349#336—431no—
350C43#2598911yescharacteristic, complemented, Sylow
351C22×Q8—21no—
352C23×C4C22×D4311yescharacteristic
353C22×C8—431no—
354C22×C8—431no—
355C22×C8—431no—
356C22×C8—431no—
357C22×C8—862no—
358C22×C8—862no—
359C22×C8—1721no—
360C4⋊Q8—22no—
361C4⋊Q8—41no—
362#117—22no—
363#117—41no—
364#117—434no—
365#117—862no—
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—431no—
373C2×C4⋊C4—861no—
374C2×C4⋊C4—861no—
375C2×C4⋊C4C22×D4311yescharacteristic
376C2×C4⋊C4C22×D4311yescharacteristic
377C2×C4⋊C4C22×D4311yescharacteristic
378C2×C4⋊C4C22×D4311yescharacteristic
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—861no—
382C2×C22⋊C4—861no—
383C2×C22⋊C4C22⋊D4311yescharacteristic
384C2×C22⋊C4C22⋊D4311yescharacteristic
385C2×C42—21no—
386C2×C42—861no—
387C2×C42—861no—
388C2×C42—861no—
389C2×C42C22×D4311yescharacteristic
390C2×C42C22×D4311yescharacteristic
391#107—862no—
392#107—862no—
393#107—1721no—
394#106—1721no—
395C4⋊C8—862no—
396C4⋊C8—1721no—
397C22⋊C8—862no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—861no—
404#95—861no—
405#95—861no—
406#95—861no—
407#95—861no—
408#95C22⋊D4311yescharacteristic
409#95C22⋊D4311yescharacteristic
410C24C2×C22⋊D4311yescharacteristic
411C2×Q8—42no—
412C2×Q8—42no—
413C2×Q8—81no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—861no—
423C22×C4—861no—
424C22×C4—861no—
425C22×C4—861no—
426C22×C4Q8×D4312yes—
427C22×C4#1062190212yes—
428C22×C4C2×C22⋊D4311yescharacteristic
429C22×C4C2×C22⋊D4311yescharacteristic
430C22×C4C2×C22⋊D4311yescharacteristic
431C22×C4C2×C22⋊D4311yescharacteristic
432C22×C4C2×C22⋊D4311yescharacteristic
433C22×C4C23×D4311yescharacteristic
434C2×C8—432no—
435C2×C8—861no—
436C2×C8—861no—
437C2×C8—861no—
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—1724no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—42no—
455C4⋊C4—42no—
456C4⋊C4—81no—
457C4⋊C4—432no—
458C4⋊C4—432no—
459C4⋊C4—861no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—1722no—
466C4⋊C4—1722no—
467C4⋊C4#1062190012yes—
468C22⋊C4—22no—
469C22⋊C4—41no—
470C22⋊C4—42no—
471C22⋊C4—81no—
472C22⋊C4—864no—
473C22⋊C4—3441no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—42no—
479C42—864no—
480C42—3441no—
481C42—3441no—
482C23—21no—
483C23—21no—
484C23—21no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23#1306330112yes—
489C23C22×C22⋊D4311yescharacteristic
490Q8—84no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—862no—
521C2×C4—862no—
522C2×C4—1721no—
523C2×C4—1721no—
524C2×C4—1721no—
525C2×C4—1721no—
526C2×C4—1721no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4—1721no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4#1306330112yes—
533C2×C4#1306334512yes—
534C2×C4C2×Q8×D4311yescharacteristic
535C2×C4#41×D4311yescharacteristic
536C2×C4C2×#1062190011yescharacteristic
537C2×C4C2×#1062190211yescharacteristic
538C2×C4#1306337011yescharacteristic
539C2×C4#1306337211yescharacteristic
540C8—862no—
541C8—1721no—
542C8—1721no—
543C8—1721no—
544C22—22no—
545C22—22no—
546C22—22no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22C2×#1306330111yescharacteristic
552C22#1458354311yescharacteristic
553C22#1458354811yescharacteristic
554C22C2×#1306334511yescharacteristic
555C22#1458369711yescharacteristic
556C22#1458370211yescharacteristic
557C22#1458371411yescharacteristic
558C4—22no—
559C4—22no—
560C4—41no—
561C4—41no—
562C4—41no—
563C4—42no—
564C4—81no—
565C4—81no—
566C4—81no—
567C4—3441no—
568C4—3441no—
569C4—1722no—
570C4—1722no—
571C4#1458345111yescharacteristic
572C4#1458352811yescharacteristic
573C4#1458357611yescharacteristic
574C4#1458359111yescharacteristic
575C2—42no—
576C2#1913826711yescharacteristic
577C2#1914437711yescharacteristic
578C2#1914444211yescharacteristic
579C2#1914644511yescharacteristic
580C2#1914666111yescharacteristic
581C2#1914702111yescharacteristic
582C2#1914709511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2439C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#2439D43
hypocenterC43#25989
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2439

Complements

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

NH ≅ G/Ntype
2. #19136162C2semidirect
3. #19136097C2semidirect
4. #19136091C2semidirect
5. #19135920C2semidirect
6. #19135548C2semidirect
7. #19135361C2semidirect
8. #19135184C2semidirect
9. #19135163C2semidirect
67. #13063284Q8semidirect
350. C43#25989semidirect

Maximal subgroups

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

subgroupindex
#191374862
#191361622
#191360972
#191360912
#191359202
#191355482
#191353612
#191351842
#191351632
#191347942
#191347752
#191346872
#191346222
#191343112
C43×#24392
#2598943