Finite Group Databasebeta

← #24991563

Subgroups — #24991563

Order 11008.

784 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 784 conjugacy classes of subgroups — too many to draw. Only its 95 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#19143622C211yesmaximal, characteristic, complemented
2#19137808C211yesmaximal, characteristic
3#19134539C211yesmaximal, characteristic, complemented
4C4×#13063239C211yesmaximal, characteristic, complemented
5#19132481C211yesmaximal, characteristic, complemented
6#19132480C211yesmaximal, characteristic, complemented
7C43×#1789C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊D43—21no—
9C2×C4×C22⋊D43C2211yescharacteristic
10#14582973—22no—
11#14582968—22no—
12#14582953—21no—
13C2×#13063252—22no—
14C2×#13063239—21no—
15#14582863C2211yescharacteristic
16C22⋊C8×D43—21no—
17#14582818C411yescharacteristic, complemented
18#14582813—21no—
19#14582813C411yescharacteristic, complemented
20#14582810C411yescharacteristic, complemented
21#14582807—21no—
22#14582807C411yescharacteristic, complemented
23C4×C22⋊Dic43—21no—
24C4×C22⋊Dic43C2211yescharacteristic
25C4×C22⋊Dic43C2211yescharacteristic
26#14582665—21no—
27C22×#41×C43C2211yescharacteristic
28C2×#104×C43—22no—
29C43×#407C2211yescharacteristic
30C4×C22⋊C4×C43C2211yescharacteristic
31C22×C22⋊D43—21no—
32C22×C22⋊D43D411yescharacteristic
33C22×C4×D43D411yescharacteristic
34C2×#10621877D412yescomplemented
35C2×C8×D43—22no—
36C4×C22⋊D43—21no—
37C4×C22⋊D43—21no—
38C4×C22⋊D43—21no—
39C4×C22⋊D43—21no—
40C4×C22⋊D43—44no—
41C2×Dic43⋊C4—21no—
42C2×Dic43⋊C4C2×C411yescharacteristic
43C2×C22⋊Dic43—21no—
44C2×C22⋊Dic43—21no—
45C2×C22⋊Dic43—21no—
46C2×C22⋊Dic43—21no—
47C2×C22⋊Dic43—21no—
48C2×C22⋊Dic43D411yescharacteristic
49C2×(C2×D43)⋊C4—21no—
50C2×(C2×D43)⋊C4C2×C411yescharacteristic
51C2×C4×Dic43—21no—
52C2×C4×Dic43—21no—
53C2×C4×Dic43D411yescharacteristic
54Dic43⋊C8—22no—
55#13063252—44no—
56#13063239—24no—
57C22⋊(C43⋊C8)—21no—
58C22⋊(C43⋊C8)—21no—
59(C2×D43)⋊C8—22no—
60#13063235—22no—
61C43⋊#95—21no—
62C43⋊#95—21no—
63C43⋊#95—21no—
64C43⋊#95C2×C411yescharacteristic
65C43⋊#95C2×C411yescharacteristic
66C2×#41×C43—21no—
67C2×#41×C43—21no—
68C2×#41×C43—21no—
69C2×#41×C43—21no—
70C2×#41×C43—44no—
71C22×Q8×C43C2×C411yescharacteristic
72C22×D4×C43—21no—
73C22×D4×C43C2×C411yescharacteristic
74C23×C4×C43—21no—
75C23×C4×C43C2311yescharacteristic
76C2×M16×C43D412yescomplemented
77C2×C22⋊C4×C43—21no—
78C2×C42×C43—21no—
79#104×C43—44no—
80C22⋊C8×C43—21no—
81C22⋊C8×C43—21no—
82#95×C43—21no—
83C24×C43—21no—
84C24×C43C2×D411yescharacteristic
85C23×D43C22⋊C411yescharacteristic
86#41×C43—24no—
87#41×C43—24no—
88#41×C43—42no—
89#41×C43—42no—
90#41×C43—42no—
91#41×C43—42no—
92#41×C43—42no—
93#41×C43—42no—
94C2×Q8×C43—21no—
95C2×Q8×C43—21no—
96C2×Q8×C43—42no—
97C2×D4×C43—21no—
98C2×D4×C43—21no—
99C2×D4×C43—42no—
100C2×D4×C43—42no—
101C2×D4×C43—42no—
102C2×D4×C43—41no—
103C2×D4×C43—41no—
104C22×C4×C43—24no—
105C22×C4×C43—21no—
106C22×C4×C43—42no—
107C22×C4×C43—42no—
108C22×C4×C43—41no—
109C22×C4×C43—41no—
110C22×C4×C43—41no—
111C22×C4×C43C22×C411yescharacteristic
112C22×C4×C43C2×D411yescharacteristic
113C22×C4×C43C2×D411yescharacteristic
114C22×C4×C43C2×D411yescharacteristic
115C22×C4×C43#4111yescharacteristic
116C22×C4×C43#4111yescharacteristic
117C2×C22⋊D43—21no—
118C2×C22⋊D43—21no—
119C2×C22⋊D43—22no—
120C2×C22⋊D43—41no—
121C2×C22⋊D43—42no—
122C2×C22⋊D43—42no—
123C2×C22⋊D43—42no—
124C22×Dic43—21no—
125C22×Dic43—21no—
126C22×Dic43—41no—
127C22×Dic43C22⋊C411yescharacteristic
128C22×Dic43C22⋊C411yescharacteristic
129C22×Dic43C22⋊C411yescharacteristic
130C2×C4×D43—21no—
131C2×C4×D43—21no—
132C2×C4×D43—42no—
133M16×C43—42no—
134C2×C8×C43—22no—
135C22⋊C4×C43—22no—
136C22⋊C4×C43—41no—
137C42×C43—42no—
138C22⋊Dic43—22no—
139C22⋊Dic43—21no—
140C22⋊Dic43—21no—
141C22⋊Dic43—41no—
142C22⋊Dic43—42no—
143C22⋊Dic43—42no—
144C22⋊Dic43—42no—
145C22⋊Dic43—42no—
146(C2×D43)⋊C4—21no—
147(C2×D43)⋊C4—21no—
148(C2×D43)⋊C4—42no—
149Dic43⋊C4—21no—
150Dic43⋊C4—21no—
151Dic43⋊C4—42no—
152C4×Dic43—21no—
153C4×Dic43—21no—
154C4×Dic43—42no—
155C4×Dic43—42no—
156#10621877—42no—
157C2×C43⋊C8—22no—
158C8×D43—82no—
159C23×C43—21no—
160C23×C43—21no—
161C23×C43—22no—
162C23×C43—41no—
163C23×C43—41no—
164C23×C43—41no—
165C23×C43—41no—
166C23×C43—41no—
167C23×C43—41no—
168C23×C43—41no—
169C23×C43—41no—
170C23×C43C2×C22⋊C411yescharacteristic
171C23×C43#12111yescharacteristic
172C23×C43#12111yescharacteristic
173C22×D43—21no—
174C22×D43—21no—
175C22×D43—41no—
176C22×D43—41no—
177C22×D43#10412yescomplemented
178Q8×C43—22no—
179Q8×C43—22no—
180Q8×C43—41no—
181Q8×C43—41no—
182D4×C43—22no—
183D4×C43—22no—
184D4×C43—41no—
185D4×C43—41no—
186D4×C43—44no—
187D4×C43—44no—
188C2×C4×C43—22no—
189C2×C4×C43—22no—
190C2×C4×C43—22no—
191C2×C4×C43—22no—
192C2×C4×C43—41no—
193C2×C4×C43—41no—
194C2×C4×C43—41no—
195C2×C4×C43—44no—
196C2×C4×C43—41no—
197C2×C4×C43—41no—
198C2×C4×C43—44no—
199C2×C4×C43—42no—
200C2×C4×C43—81no—
201C2×C4×C43—81no—
202C2×C4×C43C4×D411yescharacteristic
203C2×C4×C43C4×D411yescharacteristic
204C2×C4×C43#12011yescharacteristic
205C2×C4×C43#12311yescharacteristic
206C22⋊D43—42no—
207C22⋊D43—42no—
208C22⋊D43—48no—
209C2×Dic43—22no—
210C2×Dic43—21no—
211C2×Dic43—21no—
212C2×Dic43—21no—
213C2×Dic43—21no—
214C2×Dic43—21no—
215C2×Dic43—41no—
216C2×Dic43—41no—
217C2×Dic43—41no—
218C2×Dic43—41no—
219C2×Dic43—41no—
220C2×Dic43—42no—
221C2×Dic43—41no—
222C2×Dic43—41no—
223C2×Dic43—81no—
224C2×Dic43—81no—
225C4×D43—42no—
226C4×D43—81no—
227C8×C43—42no—
228C43⋊C8—42no—
229#9009—431nomaximal, Sylow
230C22×C43—21no—
231C22×C43—21no—
232C22×C43—21no—
233C22×C43—21no—
234C22×C43—21no—
235C22×C43—21no—
236C22×C43—21no—
237C22×C43—21no—
238C22×C43—42no—
239C22×C43—42no—
240C22×C43—42no—
241C22×C43—81no—
242C22×C43—81no—
243C22×C43—81no—
244C22×C43—81no—
245C22×C43—81no—
246C22×C43—81no—
247C22×C43#38611yescharacteristic
248C22×C43C2×#10411yescharacteristic
249C22×C43#42111yescharacteristic
250C2×D43—22no—
251C2×D43—41no—
252C2×D43—41no—
253C2×D43—42no—
254C2×D43—81no—
255C4×C43—21no—
256C4×C43—21no—
257C4×C43—21no—
258C4×C43—42no—
259C4×C43—82no—
260C4×C43B(4,𝔽2)12yes—
261Dic43—42no—
262Dic43—41no—
263Dic43—41no—
264Dic43—41no—
265Dic43—81no—
266Dic43—82no—
267#2973—431no—
268#2388—431no—
269#1789—431no—
270#1789D4311yescharacteristic, complemented
271C4×#99—431no—
272#1297—431no—
273#1297—431no—
274C2×C43—21no—
275C2×C43—21no—
276C2×C43—41no—
277C2×C43—41no—
278C2×C43—82no—
279C2×C43#187111yescharacteristic
280C2×C43#188411yescharacteristic
281C2×C43#188911yescharacteristic
282D43—42no—
283C22×#41C2×D4311yescharacteristic
284C2×C4×D4—431no—
285C2×C4×D4—861no—
286#435—862no—
287#435—862no—
288#432—861no—
289C2×#104—22no—
290C2×#104—862no—
291C2×#99—861no—
292#407—431no—
293#407C2×D4311yescharacteristic
294C2×C22⋊C8—861no—
295#395—431no—
296#394—431no—
297#394—861no—
298#393—431no—
299#392—431no—
300#392—861no—
301C4×C22⋊C4—431no—
302C4×C22⋊C4—431no—
303C4×C22⋊C4—861no—
304C4×C22⋊C4C2×D4311yescharacteristic
305#342—861no—
306C43#900911yescharacteristic, complemented, Sylow
307C2×#41—21no—
308C2×#41—21no—
309C2×#41—21no—
310C2×#41—21no—
311C2×#41—44no—
312C22×Q8C4×D4311yescharacteristic
313C22×D4—21no—
314C22×D4—431no—
315C22×D4—861no—
316C22×D4C4×D4311yescharacteristic
317C23×C4—21no—
318C23×C4—431no—
319C23×C4C22×D4311yescharacteristic
320C2×M16—432no—
321C2×M16C22⋊D4312yescomplemented
322C22×C8—862no—
323C4×D4—861no—
324C4×D4—861no—
325C4×D4—861no—
326C4×D4—861no—
327C4×D4—1724no—
328C2×C4⋊C4—431no—
329C2×C4⋊C4—861no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—431no—
332C2×C22⋊C4—431no—
333C2×C22⋊C4—861no—
334C2×C22⋊C4—861no—
335C2×C22⋊C4—861no—
336C2×C22⋊C4—861no—
337C2×C22⋊C4—861no—
338C2×C22⋊C4—861no—
339C2×C42—21no—
340C2×C42—431no—
341C2×C42—861no—
342C2×C42—861no—
343C4⋊C8—862no—
344#104—44no—
345#104—1724no—
346#99—864no—
347C22⋊C8—21no—
348C22⋊C8—21no—
349C22⋊C8—862no—
350C22⋊C8—861no—
351C22⋊C8—861no—
352#97—862no—
353#95—21no—
354#95—431no—
355#95—431no—
356#95—861no—
357#95—861no—
358#95—861no—
359C24—21no—
360C24—431no—
361C24D4×D4311yescharacteristic
362#41—24no—
363#41—24no—
364#41—42no—
365#41—42no—
366#41—42no—
367#41—42no—
368#41—42no—
369#41—42no—
370C2×Q8—21no—
371C2×Q8—21no—
372C2×Q8—42no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—42no—
376C2×D4—42no—
377C2×D4—42no—
378C2×D4—41no—
379C2×D4—41no—
380C2×D4—862no—
381C2×D4—861no—
382C2×D4—861no—
383C2×D4—1721no—
384C2×D4—1722no—
385C2×D4—1722no—
386C2×D4—1722no—
387C22×C4—24no—
388C22×C4—21no—
389C22×C4—42no—
390C22×C4—42no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—431no—
395C22×C4—431no—
396C22×C4—431no—
397C22×C4—861no—
398C22×C4—861no—
399C22×C4—861no—
400C22×C4—861no—
401C22×C4—1722no—
402C22×C4—1721no—
403C22×C4C2×C4×D4311yescharacteristic
404C22×C4#1062189811yescharacteristic
405C22×C4D4×D4311yescharacteristic
406C22×C4D4×D4311yescharacteristic
407C22×C4#1062190011yescharacteristic
408C22×C4C2×C22⋊D4311yescharacteristic
409M16—42no—
410M16—1722no—
411C2×C8—22no—
412C2×C8—862no—
413C2×C8—3442no—
414C4⋊C4—861no—
415C4⋊C4—861no—
416C4⋊C4—1722no—
417C22⋊C4—22no—
418C22⋊C4—41no—
419C22⋊C4—861no—
420C22⋊C4—861no—
421C22⋊C4—861no—
422C22⋊C4—861no—
423C22⋊C4—862no—
424C22⋊C4—1722no—
425C22⋊C4—1722no—
426C22⋊C4—1722no—
427C22⋊C4—1722no—
428C22⋊C4—1722no—
429C22⋊C4—1721no—
430C42—42no—
431C42—861no—
432C42—861no—
433C42—1722no—
434C42—1722no—
435C23—21no—
436C23—21no—
437C23—22no—
438C23—41no—
439C23—41no—
440C23—41no—
441C23—41no—
442C23—41no—
443C23—41no—
444C23—41no—
445C23—41no—
446C23—432no—
447C23—861no—
448C23—861no—
449C23—1721no—
450C23—1721no—
451C23C22⋊C4×D4311yescharacteristic
452C23#1306329611yescharacteristic
453C23#1306329811yescharacteristic
454Q8—22no—
455Q8—22no—
456Q8—41no—
457Q8—41no—
458D4—22no—
459D4—22no—
460D4—41no—
461D4—41no—
462D4—44no—
463D4—44no—
464D4—1722no—
465D4—1722no—
466D4—1728no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—44no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—44no—
478C2×C4—42no—
479C2×C4—81no—
480C2×C4—81no—
481C2×C4—862no—
482C2×C4—861no—
483C2×C4—861no—
484C2×C4—861no—
485C2×C4—861no—
486C2×C4—861no—
487C2×C4—3441no—
488C2×C4—3441no—
489C2×C4—3441no—
490C2×C4—1721no—
491C2×C4—1722no—
492C2×C4—1721no—
493C2×C4—1721no—
494C2×C4—1721no—
495C2×C4—1721no—
496C2×C4—1722no—
497C2×C4—1721no—
498C2×C4—1721no—
499C2×C4(C22⋊D43)⋊C411yescharacteristic
500C2×C4C4×C22⋊D4311yescharacteristic
501C2×C4#1306329311yescharacteristic
502C2×C4#1306330711yescharacteristic
503C8—42no—
504C8—1722no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—42no—
514C22—42no—
515C22—42no—
516C22—81no—
517C22—81no—
518C22—81no—
519C22—81no—
520C22—81no—
521C22—81no—
522C22—862no—
523C22—3441no—
524C22—1722no—
525C22—1721no—
526C22—1721no—
527C22#1458277511yescharacteristic
528C22#104×D4311yescharacteristic
529C22#1458291411yescharacteristic
530C4—21no—
531C4—21no—
532C4—21no—
533C4—42no—
534C4—82no—
535C4—3441no—
536C4—3442no—
537C4—1722no—
538C4—1721no—
539C4—1721no—
540C4—1721no—
541C4#1458308512yes—
542C2—21no—
543C2—21no—
544C2—41no—
545C2—41no—
546C2—82no—
547C2—1722no—
548C2#1913489411yescharacteristic
549C2#1913497511yescharacteristic
550C2#1913500011yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1789C2
socleC22×C43#386
prime radical#19137808C2
cosocleC23×C4×C43C23
hypercenter#1789D43
hypocenterC43#9009
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
1. #19143622C2semidirect
3. #19134539C2semidirect
4. C4×#13063239C2semidirect
5. #19132481C2semidirect
6. #19132480C2semidirect
7. C43×#1789C2semidirect
17. #14582818C4semidirect
19. #14582813C4semidirect
20. #14582810C4semidirect
22. #14582807C4semidirect
34. C2×#10621877D4semidirect
76. C2×M16×C43D4semidirect
177. C22×D43#104semidirect
270. #1789D43semidirect
306. C43#9009semidirect
321. C2×M16C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
#191436222
#191378082
#191345392
C4×#130632392
#191324812
#191324802
C43×#17892
#900943