Finite Group Databasebeta

← #25012558

Subgroups — #25012558

Order 11008.

808 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 808 conjugacy classes of subgroups — too many to draw. Only its 103 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
1#120×Dic43C211yesmaximal, characteristic
2C2×#14582686C211yesmaximal, characteristic
3#19134585C211yesmaximal, characteristic, complemented
4#19134581C211yesmaximal, characteristic, complemented
5#19132714C211yesmaximal, characteristic, complemented
6#19132712C211yesmaximal, characteristic, complemented
7C2×C43×AΣL(1,𝔽16)C211yesmaximal, characteristic
8C24×Dic43C411yescharacteristic, complemented
9C2×D4×Dic43—21no—
10C2×D4×Dic43C2211yescharacteristic
11#14582922—21no—
12C2×#13063242C2211yescharacteristic
13C2×#13063240C2211yescharacteristic
14#14582779—21no—
15#14582779C2211yescharacteristic
16#14582774—21no—
17#14582774C411yescharacteristic, complemented
18#14582757—21no—
19#14582755C411yescharacteristic, complemented
20C22⋊C4×Dic43—21no—
21C22⋊C4×Dic43C411yescharacteristic, complemented
22#14582686—22no—
23#14582667—21no—
24#14582665—21no—
25C2×#120×C43C2211yescharacteristic
26C2×#100×C43C2211yescharacteristic
27C2×#99×C43C2211yescharacteristic
28C43×AΣL(1,𝔽16)—22no—
29C23×Dic43—21no—
30C23×Dic43—21no—
31C23×Dic43—44no—
32C23×Dic43—41no—
33C23×Dic43—41no—
34C23×Dic43C2×C411yescharacteristic
35C23×Dic43C2×C411yescharacteristic
36C23×Dic43D411yescharacteristic
37C2×#10621877—21no—
38D4×Dic43—41no—
39D4×Dic43—41no—
40D4×Dic43—44no—
41C2×C4⋊Dic43—21no—
42C2×C4⋊Dic43D411yescharacteristic
43C2×Dic43⋊C4—41no—
44C2×C22⋊Dic43—21no—
45C2×C22⋊Dic43—21no—
46C2×C22⋊Dic43—21no—
47C2×C22⋊Dic43—21no—
48C2×C22⋊Dic43C2×C411yescharacteristic
49C2×C22⋊Dic43C2×C411yescharacteristic
50C2×C22⋊Dic43D411yescharacteristic
51C2×C4×Dic43—21no—
52C2×C4×Dic43D411yescharacteristic
53Dic43⋊C8—41no—
54Dic43⋊C8—41no—
55#13063242—21no—
56#13063242—21no—
57#13063240—21no—
58#13063240—21no—
59C43⋊#95—21no—
60C43⋊#95—21no—
61C43⋊#95—21no—
62C43⋊#95—41no—
63C25×C43C2×C411yescharacteristic
64C22×D4×C43—21no—
65C22×D4×C43C2311yescharacteristic
66C2×M16×C43—21no—
67#120×C43—21no—
68#120×C43—21no—
69#120×C43D412yes—
70#120×C43Q812yes—
71C2×C22⋊C4×C43—21no—
72C2×C22⋊C4×C43—21no—
73C2×C22⋊C4×C43C2×C411yescharacteristic
74#100×C43—21no—
75#100×C43—21no—
76#99×C43—21no—
77#99×C43—21no—
78C24×C43—21no—
79C24×C43—21no—
80C24×C43—42no—
81C24×C43—41no—
82C24×C43—42no—
83C24×C43—41no—
84C24×C43C4⋊C412yescomplemented
85C24×C43C22×C411yescharacteristic
86C24×C43C2×D411yescharacteristic
87C2×D4×C43—22no—
88C2×D4×C43—22no—
89C2×D4×C43—41no—
90C2×D4×C43—41no—
91C2×D4×C43—42no—
92C2×D4×C43—42no—
93C2×D4×C43C2×D411yescharacteristic
94C2×D4×C43C2×Q811yescharacteristic
95C2×D4×C43#4111yescharacteristic
96C2×D4×C43#4111yescharacteristic
97C22×C4×C43—21no—
98C22×C4×C43—41no—
99C22×C4×C43C2×D411yescharacteristic
100C22×Dic43—24no—
101C22×Dic43—21no—
102C22×Dic43—21no—
103C22×Dic43—21no—
104C22×Dic43—21no—
105C22×Dic43—21no—
106C22×Dic43—21no—
107C22×Dic43—41no—
108C22×Dic43—42no—
109C22×Dic43—41no—
110C22×Dic43—42no—
111C22×Dic43—42no—
112C22×Dic43—42no—
113C22×Dic43—42no—
114C22×Dic43—42no—
115C22×Dic43—42no—
116C22×Dic43—44no—
117C22×Dic43—44no—
118C22×Dic43—44no—
119C22×Dic43—44no—
120C22×Dic43—41no—
121C22×Dic43—41no—
122C22×Dic43C22⋊C411yescharacteristic
123C22×Dic43C22⋊C411yescharacteristic
124C22×Dic43C22⋊C411yescharacteristic
125C22×Dic43C22⋊C411yescharacteristic
126M16×C43—41no—
127M16×C43—41no—
128C2×C8×C43—41no—
129C22⋊C4×C43—22no—
130C22⋊C4×C43—22no—
131C22⋊C4×C43—21no—
132C22⋊C4×C43—41no—
133C22⋊C4×C43—41no—
134C22⋊C4×C43C4⋊C412yescomplemented
135C22⋊Dic43—41no—
136C22⋊Dic43—41no—
137C22⋊Dic43—41no—
138C22⋊Dic43—42no—
139C22⋊Dic43—42no—
140C22⋊Dic43—41no—
141C22⋊Dic43—42no—
142C22⋊Dic43—41no—
143C4⋊Dic43—41no—
144C4⋊Dic43—42no—
145Dic43⋊C4—82no—
146C4×Dic43—21no—
147C4×Dic43—21no—
148C4×Dic43—42no—
149#10621877—41no—
150#10621877—41no—
151C2×C43⋊C8—41no—
152C23×C43—22no—
153C23×C43—22no—
154C23×C43—22no—
155C23×C43—21no—
156C23×C43—21no—
157C23×C43—21no—
158C23×C43—21no—
159C23×C43—41no—
160C23×C43—44no—
161C23×C43—42no—
162C23×C43—41no—
163C23×C43—41no—
164C23×C43—41no—
165C23×C43—44no—
166C23×C43—42no—
167C23×C43—41no—
168C23×C43—41no—
169C23×C43—42no—
170C23×C43—42no—
171C23×C43—42no—
172C23×C43—48no—
173C23×C43—42no—
174C23×C43—41no—
175C23×C43—41no—
176C23×C43C2×C22⋊C411yescharacteristic
177C23×C43C2×C4⋊C411yescharacteristic
178C23×C43#11711yescharacteristic
179C23×C43#12111yescharacteristic
180C23×C43C22⋊Q811yescharacteristic
181D4×C43—41no—
182D4×C43—41no—
183D4×C43—41no—
184D4×C43—41no—
185D4×C43—44no—
186D4×C43—44no—
187C2×C4×C43—21no—
188C2×C4×C43—21no—
189C2×C4×C43—22no—
190C2×C4×C43—41no—
191C2×C4×C43—41no—
192C2×C4×C43—81no—
193C2×C4×C43—81no—
194C2×C4×C43—81no—
195C2×C4×C43#12111yescharacteristic
196C2×C4×C43C22⋊Q811yescharacteristic
197C2×Dic43—22no—
198C2×Dic43—22no—
199C2×Dic43—21no—
200C2×Dic43—21no—
201C2×Dic43—21no—
202C2×Dic43—44no—
203C2×Dic43—42no—
204C2×Dic43—41no—
205C2×Dic43—42no—
206C2×Dic43—48no—
207C2×Dic43—41no—
208C2×Dic43—42no—
209C2×Dic43—44no—
210C2×Dic43—42no—
211C2×Dic43—41no—
212C2×Dic43—41no—
213C2×Dic43—41no—
214C2×Dic43—42no—
215C2×Dic43—41no—
216C2×Dic43—41no—
217C2×Dic43—41no—
218C2×Dic43—81no—
219C2×Dic43—81no—
220C2×Dic43—81no—
221C2×Dic43—81no—
222C2×Dic43#9911yescharacteristic
223C2×Dic43#9911yescharacteristic
224C8×C43—81no—
225C43⋊C8—81no—
226#12793—431nomaximal, Sylow
227C22×C43—21no—
228C22×C43—21no—
229C22×C43—24no—
230C22×C43—21no—
231C22×C43—21no—
232C22×C43—21no—
233C22×C43—21no—
234C22×C43—41no—
235C22×C43—41no—
236C22×C43—41no—
237C22×C43—41no—
238C22×C43—42no—
239C22×C43—42no—
240C22×C43—42no—
241C22×C43—42no—
242C22×C43—44no—
243C22×C43—44no—
244C22×C43—44no—
245C22×C43—44no—
246C22×C43—42no—
247C22×C43—42no—
248C22×C43—41no—
249C22×C43—41no—
250C22×C43—42no—
251C22×C43—41no—
252C22×C43—41no—
253C22×C43—81no—
254C22×C43#38011yescharacteristic
255C22×C43C2×#9911yescharacteristic
256C22×C43#41011yescharacteristic
257C4×C43—21no—
258C4×C43—21no—
259C4×C43—42no—
260C4×C43—161no—
261Dic43—21no—
262Dic43—42no—
263Dic43—41no—
264Dic43—41no—
265Dic43—41no—
266Dic43—81no—
267Dic43—161no—
268Dic43AΣL(1,𝔽16)12yescomplemented
269C4×#120—431no—
270C2×AΣL(1,𝔽16)—431no—
271C2×AΣL(1,𝔽16)D4311yescharacteristic
272#1800—431no—
273#1799—431no—
274#1390—431no—
275#1390—431no—
276C2×C43—21no—
277C2×C43—21no—
278C2×C43—41no—
279C2×C43—44no—
280C2×C43—41no—
281C2×C43—41no—
282C2×C43—41no—
283C2×C43#179911yescharacteristic
284C2×C43C2×AΣL(1,𝔽16)11yescharacteristic
285C2×C43#212011yescharacteristic
286C24×C4—431no—
287C2×#120C2×D4311yescharacteristic
288C2×C4×D4—431no—
289C2×C4×D4—861no—
290#423—861no—
291C2×#100—431no—
292C2×#100C2×D4311yescharacteristic
293C2×#99—431no—
294C2×#99C2×D4311yescharacteristic
295#386—431no—
296#386—861no—
297#385—431no—
298#385—861no—
299#380—861no—
300#379—431no—
301C4×C22⋊C4—431no—
302C4×C22⋊C4—861no—
303AΣL(1,𝔽16)—22no—
304AΣL(1,𝔽16)—862no—
305#343—861no—
306#342—861no—
307C43#1279311yescharacteristic, complemented, Sylow
308C25C4×D4311yescharacteristic
309C22×D4—21no—
310C22×D4C22×D4311yescharacteristic
311C23×C4—431no—
312C23×C4—431no—
313C23×C4—431no—
314C23×C4—861no—
315C23×C4—861no—
316C23×C4—1721no—
317C23×C4—1721no—
318C23×C4—1724no—
319C2×M16—21no—
320C2×M16—861no—
321#120—21no—
322#120—21no—
323#120Dic8612yes—
324#120C22⋊D4312yes—
325C4×D4—1721no—
326C4×D4—1721no—
327C4×D4—1724no—
328C2×C4⋊C4—431no—
329C2×C4⋊C4—861no—
330C2×C4⋊C4—1721no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—431no—
334C2×C22⋊C4—431no—
335C2×C22⋊C4—431no—
336C2×C22⋊C4—861no—
337C2×C22⋊C4—861no—
338C2×C22⋊C4—861no—
339C2×C22⋊C4—861no—
340C2×C22⋊C4C4×D4311yescharacteristic
341C2×C42—431no—
342C2×C42—861no—
343C4⋊C8—1721no—
344C4⋊C8—1721no—
345#100—21no—
346#100—21no—
347#100—861no—
348#100—861no—
349#99—21no—
350#99—21no—
351#99—861no—
352#99—861no—
353#95—861no—
354#95—861no—
355#95—861no—
356#95—1721no—
357C24—21no—
358C24—21no—
359C24—42no—
360C24—41no—
361C24—42no—
362C24—41no—
363C24Dic43⋊C412yescomplemented
364C24C2×C4×D4311yescharacteristic
365C24D4×D4311yescharacteristic
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—42no—
371C2×D4—42no—
372C2×D4C2×Dic8611yescharacteristic
373C2×D4#1062190011yescharacteristic
374C2×D4#1062190011yescharacteristic
375C2×D4C2×C22⋊D4311yescharacteristic
376C22×C4—21no—
377C22×C4—41no—
378C22×C4—431no—
379C22×C4—431no—
380C22×C4—431no—
381C22×C4—431no—
382C22×C4—861no—
383C22×C4—861no—
384C22×C4—861no—
385C22×C4—861no—
386C22×C4—864no—
387C22×C4—861no—
388C22×C4—861no—
389C22×C4—1721no—
390C22×C4—1721no—
391C22×C4—1722no—
392C22×C4—1722no—
393C22×C4—1722no—
394C22×C4—1722no—
395C22×C4—1722no—
396C22×C4—1722no—
397C22×C4—1721no—
398C22×C4—1722no—
399C22×C4—1724no—
400C22×C4—1724no—
401C22×C4—1724no—
402C22×C4—1721no—
403C22×C4—1724no—
404C22×C4D4×D4311yescharacteristic
405M16—41no—
406M16—41no—
407M16—1721no—
408M16—1721no—
409C2×C8—41no—
410C2×C8—1721no—
411C4⋊C4—3442no—
412C4⋊C4—1721no—
413C4⋊C4—1722no—
414C22⋊C4—21no—
415C22⋊C4—22no—
416C22⋊C4—22no—
417C22⋊C4—41no—
418C22⋊C4—41no—
419C22⋊C4—1721no—
420C22⋊C4—1721no—
421C22⋊C4—1722no—
422C22⋊C4—1721no—
423C22⋊C4—1721no—
424C22⋊C4—1722no—
425C22⋊C4—1722no—
426C22⋊C4—1721no—
427C22⋊C4Dic43⋊C412yescomplemented
428C42—861no—
429C42—861no—
430C42—1722no—
431C23—22no—
432C23—22no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23—22no—
437C23—21no—
438C23—41no—
439C23—44no—
440C23—42no—
441C23—41no—
442C23—41no—
443C23—41no—
444C23—44no—
445C23—42no—
446C23—41no—
447C23—41no—
448C23—42no—
449C23—42no—
450C23—42no—
451C23—48no—
452C23—42no—
453C23—41no—
454C23—41no—
455C23C22⋊C4×D4311yescharacteristic
456C23C2×Dic43⋊C411yescharacteristic
457C23#1306328111yescharacteristic
458C23#1306329711yescharacteristic
459C23#1306330211yescharacteristic
460D4—41no—
461D4—41no—
462D4—41no—
463D4—41no—
464D4—44no—
465D4—44no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—22no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—81no—
472C2×C4—81no—
473C2×C4—81no—
474C2×C4—431no—
475C2×C4—431no—
476C2×C4—862no—
477C2×C4—862no—
478C2×C4—861no—
479C2×C4—861no—
480C2×C4—861no—
481C2×C4—3441no—
482C2×C4—3441no—
483C2×C4—3441no—
484C2×C4—3441no—
485C2×C4—1722no—
486C2×C4—1722no—
487C2×C4—1724no—
488C2×C4—1722no—
489C2×C4—1724no—
490C2×C4—1721no—
491C2×C4—1721no—
492C2×C4—1721no—
493C2×C4—1721no—
494C2×C4—1728no—
495C2×C4—1722no—
496C2×C4—1721no—
497C2×C4—1721no—
498C2×C4—1721no—
499C2×C4—1721no—
500C2×C4—1722no—
501C2×C4#1306329711yescharacteristic
502C2×C4#1306330211yescharacteristic
503C8—81no—
504C8—3441no—
505C22—21no—
506C22—21no—
507C22—24no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—41no—
513C22—41no—
514C22—41no—
515C22—41no—
516C22—42no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22—44no—
521C22—44no—
522C22—44no—
523C22—44no—
524C22—42no—
525C22—41no—
526C22—42no—
527C22—41no—
528C22—41no—
529C22—42no—
530C22—41no—
531C22—81no—
532C22#1458275711yescharacteristic
533C22#99×D4311yescharacteristic
534C22#1458287111yescharacteristic
535C4—21no—
536C4—21no—
537C4—42no—
538C4—161no—
539C4—432no—
540C4—861no—
541C4—3441no—
542C4—1721no—
543C4—1722no—
544C4—1721no—
545C4—1721no—
546C4—6881no—
547C2—21no—
548C2—21no—
549C2—41no—
550C2—44no—
551C2—41no—
552C2—41no—
553C2—41no—
554C2#1913458111yescharacteristic
555C2AΣL(1,𝔽16)×D4311yescharacteristic
556C2#1913623311yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC24×C43C22×C4
FrattiniC22×D4C22×D43
FittingC2×C43×AΣL(1,𝔽16)C2
socleC22×C43C2×#99
prime radicalC2×#120×C43C22
cosocleC22×D4×C43C23
hypercenterC2×AΣL(1,𝔽16)D43
hypocenterC43#12793
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×AΣL(1,𝔽16)

Complements

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

NH ≅ G/Ntype
3. #19134585C2semidirect
4. #19134581C2semidirect
5. #19132714C2semidirect
6. #19132712C2semidirect
8. C24×Dic43C4semidirect
17. #14582774C4semidirect
19. #14582755C4semidirect
21. C22⋊C4×Dic43C4semidirect
84. C24×C43C4⋊C4semidirect
134. C22⋊C4×C43C4⋊C4semidirect
268. Dic43AΣL(1,𝔽16)semidirect
307. C43#12793semidirect
363. C24Dic43⋊C4semidirect
427. C22⋊C4Dic43⋊C4semidirect

Maximal subgroups

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

subgroupindex
#120×Dic432
C2×#145826862
#191345852
#191345812
#191327142
#191327122
C2×C43×AΣL(1,𝔽16)2
#1279343