Finite Group Databasebeta

← #25013350

Subgroups — #25013350

Order 11008.

728 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 728 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582686C211yesmaximal, characteristic
2#19135004C211yesmaximal, characteristic
3#19134875C211yesmaximal, characteristic, complemented
4#19134804C211yesmaximal, characteristic, complemented
5#19132720C211yesmaximal, characteristic, complemented
6#19132713C211yesmaximal, characteristic, complemented
7C43×#2358C211yesmaximal, characteristic
8#14583374C2211yescharacteristic
9#14582939—21no—
10C2×#13063242C2211yescharacteristic
11C2×#13063240C2211yescharacteristic
12C2×#13063240C2211yescharacteristic
13#14582772—21no—
14#14582755—21no—
15#14582686C414yescomplemented
16#14582665—21no—
17#14582665—21no—
18#14582659—21no—
19C2×#120×C43C2211yescharacteristic
20C2×C4×D4×C43—21no—
21C22×C22⋊C4×C43—21no—
22C43×#390C2211yescharacteristic
23C43×#388—21no—
24C43×#386—21no—
25C43×#386C2211yescharacteristic
26C43×#385—21no—
27C4×C22⋊C4×C43—21no—
28C2×#10621877—21no—
29D4×Dic43—41no—
30D4×Dic43—41no—
31#13063284—21no—
32C2×Dic43⋊C4—41no—
33C2×C22⋊Dic43—21no—
34C2×C22⋊Dic43—21no—
35C2×C22⋊Dic43—21no—
36C2×C22⋊Dic43—21no—
37C2×C22⋊Dic43—41no—
38C2×C22⋊Dic43—41no—
39#13063258—41no—
40#13063256—41no—
41#13063242—21no—
42#13063242C2×C412yescomplemented
43#13063240—21no—
44#13063240—21no—
45#13063240—21no—
46#13063240C2×C412yescomplemented
47C43⋊#95—41no—
48C25×C43D411yescharacteristic
49C22×D4×C43—21no—
50C22×D4×C43C2311yescharacteristic
51C23×C4×C43—21no—
52C23×C4×C43—21no—
53C23×C4×C43D411yescharacteristic
54#120×C43—21no—
55#120×C43—21no—
56#120×C43C2×C412yes—
57#120×C43Q812yes—
58C4×D4×C43—44no—
59C2×C4⋊C4×C43—21no—
60C2×C4⋊C4×C43D411yescharacteristic
61C2×C22⋊C4×C43—21no—
62C2×C22⋊C4×C43—21no—
63C2×C22⋊C4×C43—21no—
64C2×C22⋊C4×C43—21no—
65C2×C22⋊C4×C43—21no—
66C2×C22⋊C4×C43—21no—
67C2×C22⋊C4×C43—44no—
68C2×C22⋊C4×C43D411yescharacteristic
69C2×C22⋊C4×C43D411yescharacteristic
70C2×C42×C43—21no—
71C2×C42×C43D411yescharacteristic
72#95×C43—21no—
73#95×C43—21no—
74#95×C43—21no—
75C24×C43—21no—
76C24×C43—21no—
77C24×C43—42no—
78C24×C43—42no—
79C24×C43—41no—
80C24×C43—41no—
81C24×C43C4⋊C412yescomplemented
82C24×C43C2×D411yescharacteristic
83C24×C43C2×D411yescharacteristic
84C2×D4×C43—22no—
85C2×D4×C43—22no—
86C2×D4×C43—41no—
87C2×D4×C43—41no—
88C2×D4×C43—42no—
89C2×D4×C43—42no—
90C2×D4×C43C22×C411yescharacteristic
91C2×D4×C43C2×Q811yescharacteristic
92C2×D4×C43#4111yescharacteristic
93C2×D4×C43#4111yescharacteristic
94C22×C4×C43—21no—
95C22×C4×C43—21no—
96C22×C4×C43—21no—
97C22×C4×C43—21no—
98C22×C4×C43—21no—
99C22×C4×C43—41no—
100C22×C4×C43—42no—
101C22×C4×C43—42no—
102C22×C4×C43—42no—
103C22×C4×C43—42no—
104C22×C4×C43—42no—
105C22×C4×C43—81no—
106C22×C4×C43—81no—
107C22×C4×C43C2×D411yescharacteristic
108C22×Dic43—21no—
109C22×Dic43—21no—
110C22×Dic43—21no—
111C22×Dic43—21no—
112C22×Dic43—41no—
113C22×Dic43—41no—
114C4⋊C4×C43—41no—
115C4⋊C4×C43—42no—
116C22⋊C4×C43—24no—
117C22⋊C4×C43—22no—
118C22⋊C4×C43—22no—
119C22⋊C4×C43—21no—
120C22⋊C4×C43—41no—
121C22⋊C4×C43—42no—
122C22⋊C4×C43—42no—
123C22⋊C4×C43—42no—
124C22⋊C4×C43—42no—
125C22⋊C4×C43C4⋊C412yescomplemented
126C42×C43—41no—
127C42×C43—42no—
128C22⋊Dic43—22no—
129C22⋊Dic43—41no—
130C22⋊Dic43—41no—
131C22⋊Dic43—41no—
132C22⋊Dic43—41no—
133C22⋊Dic43—41no—
134C22⋊Dic43—41no—
135C22⋊Dic43—82no—
136C22⋊Dic43—82no—
137C4⋊Dic43—21no—
138C4⋊Dic43—21no—
139Dic43⋊C4—82no—
140C4×Dic43—41no—
141#10621877—22no—
142#10621877—41no—
143C2×C43⋊C8—41no—
144C23×C43—22no—
145C23×C43—22no—
146C23×C43—22no—
147C23×C43—21no—
148C23×C43—21no—
149C23×C43—21no—
150C23×C43—21no—
151C23×C43—41no—
152C23×C43—41no—
153C23×C43—41no—
154C23×C43—41no—
155C23×C43—41no—
156C23×C43—44no—
157C23×C43—42no—
158C23×C43—41no—
159C23×C43—44no—
160C23×C43—41no—
161C23×C43—41no—
162C23×C43—42no—
163C23×C43—42no—
164C23×C43—81no—
165C23×C43—84no—
166C23×C43—81no—
167C23×C43—81no—
168C23×C43C2×C4⋊C411yescharacteristic
169C23×C43C4×D411yescharacteristic
170C23×C43#12011yescharacteristic
171C23×C43C22⋊Q811yescharacteristic
172C23×C43#12311yescharacteristic
173D4×C43—41no—
174D4×C43—41no—
175D4×C43—41no—
176D4×C43—41no—
177D4×C43—44no—
178D4×C43—44no—
179C2×C4×C43—21no—
180C2×C4×C43—21no—
181C2×C4×C43—22no—
182C2×C4×C43—22no—
183C2×C4×C43—22no—
184C2×C4×C43—41no—
185C2×C4×C43—41no—
186C2×C4×C43—41no—
187C2×C4×C43—41no—
188C2×C4×C43—41no—
189C2×C4×C43—41no—
190C2×C4×C43—42no—
191C2×C4×C43—41no—
192C2×C4×C43—41no—
193C2×C4×C43—41no—
194C2×C4×C43—41no—
195C2×C4×C43—41no—
196C2×C4×C43—41no—
197C2×C4×C43—81no—
198C2×C4×C43—84no—
199C2×C4×C43—84no—
200C2×C4×C43C4×D411yescharacteristic
201C2×C4×C43C22⋊Q811yescharacteristic
202C2×Dic43—42no—
203C2×Dic43—41no—
204C2×Dic43—41no—
205C2×Dic43—81no—
206C2×Dic43—81no—
207C2×Dic43—81no—
208C2×Dic43—81no—
209C2×Dic43—81no—
210C2×Dic43—81no—
211C2×Dic43—81no—
212C2×Dic43—81no—
213C2×Dic43—81no—
214C43⋊C8—42no—
215#12958—431nomaximal, Sylow
216C22×C43—21no—
217C22×C43—21no—
218C22×C43—24no—
219C22×C43—21no—
220C22×C43—21no—
221C22×C43—21no—
222C22×C43—21no—
223C22×C43—41no—
224C22×C43—41no—
225C22×C43—41no—
226C22×C43—41no—
227C22×C43—42no—
228C22×C43—42no—
229C22×C43—42no—
230C22×C43—44no—
231C22×C43—42no—
232C22×C43—41no—
233C22×C43—42no—
234C22×C43—41no—
235C22×C43—42no—
236C22×C43—41no—
237C22×C43—41no—
238C22×C43—81no—
239C22×C43—81no—
240C22×C43—82no—
241C22×C43—82no—
242C22×C43—82no—
243C22×C43#38511yescharacteristic
244C22×C43B(4,𝔽2)11yescharacteristic
245C22×C43#45811yescharacteristic
246C4×C43—21no—
247C4×C43—21no—
248C4×C43—42no—
249C4×C43—42no—
250C4×C43—42no—
251C4×C43—81no—
252C4×C43—81no—
253Dic43—82no—
254Dic43—81no—
255Dic43—81no—
256Dic43—161no—
257#2358D4311yescharacteristic
258C2×AΣL(1,𝔽16)—431no—
259#1889—431no—
260#1867—431no—
261#1856—431no—
262#1393—431no—
263#1390—431no—
264C2×C43—21no—
265C2×C43—21no—
266C2×C43—41no—
267C2×C43—41no—
268C2×C43—44no—
269C2×C43—41no—
270C2×C43—41no—
271C2×C43#186711yescharacteristic
272C2×C43#219611yescharacteristic
273C2×C43#219711yescharacteristic
274C2×#120C2×D4311yescharacteristic
275#518—431no—
276C2×C4×D4—21no—
277C22×C22⋊C4—21no—
278#428—861no—
279C2×#100—431no—
280C2×#99—431no—
281C2×#99—431no—
282#390C2×D4311yescharacteristic
283#388—21no—
284#386—21no—
285#386C2×D4311yescharacteristic
286#385—21no—
287#385—861no—
288#379—861no—
289C4×C22⋊C4—21no—
290AΣL(1,𝔽16)—434no—
291#342—861no—
292#342—861no—
293#339—861no—
294C43#1295811yescharacteristic, complemented, Sylow
295C25C22⋊D4311yescharacteristic
296C22×D4—21no—
297C22×D4C22×D4311yescharacteristic
298C23×C4—21no—
299C23×C4—21no—
300C23×C4C22⋊D4311yescharacteristic
301C2×M16—861no—
302#120—21no—
303#120—21no—
304#120Dic8612yes—
305#120C4×D4312yes—
306C4×D4—44no—
307C4×D4—1721no—
308C4×D4—1721no—
309#117—861no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—1721no—
312C2×C4⋊C4C22⋊D4311yescharacteristic
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—44no—
320C2×C22⋊C4—861no—
321C2×C22⋊C4—861no—
322C2×C22⋊C4—861no—
323C2×C22⋊C4—861no—
324C2×C22⋊C4—1721no—
325C2×C22⋊C4—1721no—
326C2×C22⋊C4C22⋊D4311yescharacteristic
327C2×C22⋊C4C22⋊D4311yescharacteristic
328C2×C42—21no—
329C2×C42C22⋊D4311yescharacteristic
330#107—1721no—
331#106—1721no—
332#100—432no—
333#100—861no—
334#99—432no—
335#99—861no—
336#99—861no—
337#99—861no—
338#95—21no—
339#95—21no—
340#95—21no—
341#95—1721no—
342C24—21no—
343C24—21no—
344C24—42no—
345C24—41no—
346C24—42no—
347C24—41no—
348C24Dic43⋊C412yescomplemented
349C24C2×C22⋊D4311yescharacteristic
350C24C2×C22⋊D4311yescharacteristic
351C2×D4—22no—
352C2×D4—22no—
353C2×D4—41no—
354C2×D4—41no—
355C2×D4—42no—
356C2×D4—42no—
357C2×D4C2×Dic8611yescharacteristic
358C2×D4C2×C4×D4311yescharacteristic
359C2×D4#1062189811yescharacteristic
360C2×D4#1062189811yescharacteristic
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—42no—
367C22×C4—42no—
368C22×C4—42no—
369C22×C4—41no—
370C22×C4—42no—
371C22×C4—42no—
372C22×C4—81no—
373C22×C4—81no—
374C22×C4—861no—
375C22×C4—861no—
376C22×C4—861no—
377C22×C4—861no—
378C22×C4—1721no—
379C22×C4—1721no—
380C22×C4C2×C22⋊D4311yescharacteristic
381M16—862no—
382M16—1721no—
383C2×C8—1721no—
384C4⋊C4—41no—
385C4⋊C4—42no—
386C4⋊C4—861no—
387C4⋊C4—861no—
388C4⋊C4—3442no—
389C22⋊C4—24no—
390C22⋊C4—21no—
391C22⋊C4—22no—
392C22⋊C4—22no—
393C22⋊C4—42no—
394C22⋊C4—42no—
395C22⋊C4—42no—
396C22⋊C4—42no—
397C22⋊C4—41no—
398C22⋊C4—862no—
399C22⋊C4—3442no—
400C22⋊C4—3442no—
401C22⋊C4—1721no—
402C22⋊C4—1721no—
403C22⋊C4—1721no—
404C22⋊C4—1721no—
405C22⋊C4—1721no—
406C22⋊C4—1721no—
407C22⋊C4Dic43⋊C412yescomplemented
408C42—41no—
409C42—42no—
410C42—1721no—
411C23—22no—
412C23—22no—
413C23—21no—
414C23—21no—
415C23—22no—
416C23—21no—
417C23—21no—
418C23—41no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23—44no—
424C23—42no—
425C23—41no—
426C23—44no—
427C23—41no—
428C23—41no—
429C23—42no—
430C23—42no—
431C23—81no—
432C23—84no—
433C23—81no—
434C23—81no—
435C23C2×Dic43⋊C411yescharacteristic
436C23C4×C22⋊D4311yescharacteristic
437C23#1306329411yescharacteristic
438C23#1306330411yescharacteristic
439C23#1306330811yescharacteristic
440D4—41no—
441D4—41no—
442D4—41no—
443D4—41no—
444D4—44no—
445D4—44no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—42no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—81no—
465C2×C4—84no—
466C2×C4—84no—
467C2×C4—3441no—
468C2×C4—3441no—
469C2×C4—3441no—
470C2×C4—3441no—
471C2×C4—3441no—
472C2×C4—3441no—
473C2×C4—3441no—
474C2×C4—3441no—
475C2×C4—3441no—
476C2×C4—1722no—
477C2×C4—1721no—
478C2×C4—1721no—
479C2×C4C4×C22⋊D4311yescharacteristic
480C2×C4#1306330411yescharacteristic
481C8—1722no—
482C22—21no—
483C22—21no—
484C22—24no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22—41no—
490C22—41no—
491C22—41no—
492C22—41no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—44no—
497C22—41no—
498C22—42no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—42no—
503C22—42no—
504C22—81no—
505C22—81no—
506C22—82no—
507C22—82no—
508C22—82no—
509C22#1458277211yescharacteristic
510C22#1458308611yescharacteristic
511C22#1458308911yescharacteristic
512C4—21no—
513C4—21no—
514C4—42no—
515C4—42no—
516C4—42no—
517C4—81no—
518C4—81no—
519C4—3442no—
520C4—3441no—
521C4—3441no—
522C4—6881no—
523C2—21no—
524C2—21no—
525C2—41no—
526C2—41no—
527C2—44no—
528C2—41no—
529C2—41no—
530C2#1913487611yescharacteristic
531C2#1913657911yescharacteristic
532C2#1913658511yescharacteristic
subgroupG/H
centerC22#14583086
commutatorC2×D4×C43C22×C4
FrattiniC22×D4C22×D43
FittingC43×#2358C2
socleC22×C43B(4,𝔽2)
prime radicalC2×#120×C43C22
cosocleC22×D4×C43C23
hypercenter#2358D43
hypocenterC43#12958
LCSG ▷ C2×D4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #2358

Complements

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

NH ≅ G/Ntype
3. #19134875C2semidirect
4. #19134804C2semidirect
5. #19132720C2semidirect
6. #19132713C2semidirect
15. #14582686C4semidirect
42. #13063242C2×C4semidirect
46. #13063240C2×C4semidirect
81. C24×C43C4⋊C4semidirect
125. C22⋊C4×C43C4⋊C4semidirect
294. C43#12958semidirect
348. C24Dic43⋊C4semidirect
407. C22⋊C4Dic43⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#145826862
#191350042
#191348752
#191348042
#191327202
#191327132
C43×#23582
#1295843