Finite Group Databasebeta

← #24991709

Subgroups — #24991709

Order 11008.

676 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 676 conjugacy classes of subgroups — too many to draw. Only its 93 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#19143813C211yesmaximal, characteristic
2#19143640C211yesmaximal, characteristic, complemented
3#19134539C211yesmaximal, characteristic, complemented
4#19133087C211yesmaximal, characteristic, complemented
5#19132483C211yesmaximal, characteristic, complemented
6#19132442C211yesmaximal, characteristic, complemented
7C43×#1780C211yesmaximal, characteristic, complemented
8C2×#13063345—21no—
9#14583410C2211yescharacteristic
10#14583061—21no—
11#14583055C411yescharacteristic, complemented
12#14583050C411yescharacteristic, complemented
13#14583044—21no—
14#14583038C411yescharacteristic, complemented
15#14583033C411yescharacteristic, complemented
16#14582974—21no—
17#14582973—21no—
18#14582970—21no—
19C8×C22⋊D43—21no—
20#14582957—21no—
21C2×#13063252—21no—
22C2×#13063252—21no—
23#14582895—21no—
24#14582864—21no—
25#14582863C2211yescharacteristic
26C2×C22⋊(C43⋊C8)C2211yescharacteristic
27C4×C22⋊Dic43C2211yescharacteristic
28#14582637—21no—
29#14582634—21no—
30C22×#41×C43C2211yescharacteristic
31C2×C22⋊C8×C43—21no—
32C2×C22⋊C8×C43—21no—
33C2×C22⋊C8×C43C2211yescharacteristic
34C2×C22⋊C8×C43C2211yescharacteristic
35C2×#10621898D411yescharacteristic
36#13063345—42no—
37#13063345—42no—
38C2×#10621885—21no—
39C2×#10621883—21no—
40C2×#10621884—21no—
41C2×#10621882—21no—
42C2×#10621877D411yescharacteristic
43C2×#10621877D411yescharacteristic
44C2×#10621872—21no—
45C22×C43⋊C8—21no—
46C2×C8×D43—21no—
47#13063308—21no—
48#13063304C2×C411yescharacteristic
49#13063304D411yescharacteristic
50#13063299C2×C411yescharacteristic
51#13063299D411yescharacteristic
52#13063294—21no—
53C4×C22⋊D43—21no—
54C4×C22⋊D43—21no—
55#13063284D411yescharacteristic
56C2×C22⋊Dic43—21no—
57C2×C4×Dic43—21no—
58Dic43⋊C8—21no—
59Dic43⋊C8—21no—
60#13063252—42no—
61#13063252—42no—
62#13063249—21no—
63#13063249—21no—
64#13063246—21no—
65#13063246—21no—
66C22⋊(C43⋊C8)—21no—
67C22⋊(C43⋊C8)—21no—
68C22⋊(C43⋊C8)—21no—
69C22⋊(C43⋊C8)C2×C411yescharacteristic
70C22⋊(C43⋊C8)C2×C411yescharacteristic
71(C2×D43)⋊C8—21no—
72(C2×D43)⋊C8—21no—
73#13063235—21no—
74C8×Dic43—21no—
75C43⋊#95—21no—
76C2×#41×C43—21no—
77C2×#41×C43—21no—
78C2×#41×C43—21no—
79C2×#41×C43—21no—
80C2×#41×C43—42no—
81C2×#41×C43—42no—
82C22×Q8×C43C2×C411yescharacteristic
83C22×D4×C43—21no—
84C22×D4×C43C2×C411yescharacteristic
85C23×C4×C43—21no—
86C23×C4×C43C2311yescharacteristic
87C22×C8×C43—21no—
88C22×C8×C43D411yescharacteristic
89C22×C8×C43D411yescharacteristic
90C22⋊C8×C43—21no—
91C22⋊C8×C43—21no—
92C22⋊C8×C43—21no—
93C22⋊C8×C43—21no—
94C22⋊C8×C43—42no—
95C22⋊C8×C43—42no—
96C24×C43—21no—
97C24×C43#4111yescharacteristic
98#41×C43—22no—
99#41×C43—22no—
100#41×C43—22no—
101#41×C43—22no—
102#41×C43—41no—
103#41×C43—41no—
104#41×C43—41no—
105#41×C43—41no—
106#41×C43—42no—
107#41×C43—42no—
108#41×C43—42no—
109#41×C43—42no—
110C2×Q8×C43—21no—
111C2×Q8×C43—21no—
112C2×Q8×C43—42no—
113C2×D4×C43—21no—
114C2×D4×C43—21no—
115C2×D4×C43—42no—
116C2×D4×C43—42no—
117C2×D4×C43—42no—
118C2×D4×C43—41no—
119C2×D4×C43—41no—
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—21no—
123C22×C4×C43—41no—
124C22×C4×C43—41no—
125C22×C4×C43—41no—
126C22×C4×C43—41no—
127C22×C4×C43—41no—
128C22×C4×C43—41no—
129C22×C4×C43C22×C411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43#4111yescharacteristic
135C2×C22⋊D43—21no—
136C2×C22⋊D43—21no—
137C2×C22⋊D43—21no—
138C22×Dic43—41no—
139#10621898—41no—
140#10621898—41no—
141C2×D172C22⋊C411yescharacteristic
142C2×C4×D43—21no—
143C2×Dic86C22⋊C411yescharacteristic
144C2×C8×C43—21no—
145C2×C8×C43—21no—
146C2×C8×C43—41no—
147C2×C8×C43—41no—
148C2×C8×C43—41no—
149C2×C8×C43—41no—
150C2×C8×C43—41no—
151C22⋊Dic43—22no—
152C22⋊Dic43—21no—
153C22⋊Dic43—21no—
154C22⋊Dic43—21no—
155C22⋊Dic43—41no—
156#10621885—42no—
157#10621884—42no—
158#10621883—42no—
159#10621882—42no—
160(C2×D43)⋊C4—21no—
161(C2×D43)⋊C4—21no—
162C4⋊Dic43C22⋊C411yescharacteristic
163C4⋊Dic43C22⋊C411yescharacteristic
164Dic43⋊C4—21no—
165Dic43⋊C4—21no—
166C4×Dic43—21no—
167C4×Dic43—41no—
168C4×Dic43—41no—
169#10621877—41no—
170#10621877—41no—
171C2×C43⋊C8—21no—
172C2×C43⋊C8—21no—
173C2×C43⋊C8—21no—
174C2×C43⋊C8—21no—
175C2×C43⋊C8—41no—
176C2×C43⋊C8—41no—
177#10621872—81no—
178C8×D43—81no—
179C23×C43—21no—
180C23×C43—21no—
181C23×C43—22no—
182C23×C43—41no—
183C23×C43—41no—
184C23×C43—41no—
185C23×C43—41no—
186C23×C43—41no—
187C23×C43—41no—
188C23×C43—41no—
189C23×C43—41no—
190C23×C43C4×D411yescharacteristic
191C23×C43#12111yescharacteristic
192C23×C43#12311yescharacteristic
193C22×D43—21no—
194Q8×C43—22no—
195Q8×C43—22no—
196Q8×C43—41no—
197Q8×C43—41no—
198D4×C43—22no—
199D4×C43—22no—
200D4×C43—41no—
201D4×C43—41no—
202D4×C43—42no—
203D4×C43—42no—
204D4×C43—42no—
205D4×C43—42no—
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—22no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—42no—
217C2×C4×C43—42no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—42no—
221C2×C4×C43—42no—
222C2×C4×C43C2×C22⋊C411yescharacteristic
223C2×C4×C43C4×D411yescharacteristic
224C2×C4×C43#12011yescharacteristic
225C2×C4×C43#12111yescharacteristic
226C22⋊D43—41no—
227C22⋊D43—41no—
228C22⋊D43—81no—
229C22⋊D43—81no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—42no—
234C2×Dic43—81no—
235C2×Dic43—81no—
236D172—41no—
237C4×D43—41no—
238C4×D43—41no—
239Dic86—41no—
240C8×C43—41no—
241C8×C43—41no—
242C8×C43—81no—
243C43⋊C8—41no—
244C43⋊C8—41no—
245C43⋊C8—41no—
246C43⋊C8—41no—
247#9037—431nomaximal, Sylow
248C22×C43—21no—
249C22×C43—21no—
250C22×C43—21no—
251C22×C43—21no—
252C22×C43—21no—
253C22×C43—21no—
254C22×C43—21no—
255C22×C43—21no—
256C22×C43—42no—
257C22×C43—42no—
258C22×C43—42no—
259C22×C43—81no—
260C22×C43—81no—
261C22×C43—81no—
262C22×C43—81no—
263C22×C43—81no—
264C22×C43—81no—
265C22×C43#38611yescharacteristic
266C22×C43#44311yescharacteristic
267C22×C43#44411yescharacteristic
268C2×D43—41no—
269C2×D43—41no—
270C2×D43—41no—
271C4×C43—21no—
272C4×C43—21no—
273C4×C43—21no—
274C4×C43—42no—
275C4×C43B(4,𝔽2)11yescharacteristic
276C4×C43B(4,𝔽2)11yescharacteristic
277Dic43—41no—
278Dic43—41no—
279Dic43—41no—
280Dic43—82no—
281#3002—431no—
282#2976—431no—
283#1789—431no—
284#1780D4311yescharacteristic, complemented
285#1501—431no—
286#1298—431no—
287#1282—431no—
288C2×C43—21no—
289C2×C43—21no—
290C2×C43—41no—
291C2×C43—41no—
292C2×C43—82no—
293C2×C43#187611yescharacteristic
294C2×C43#188111yescharacteristic
295C2×C43#188911yescharacteristic
296D43—81no—
297C22×#41C2×D4311yescharacteristic
298C2×#135—861no—
299#525—431no—
300#452—861no—
301#451—431no—
302#450—431no—
303#449—861no—
304#448—431no—
305#447—431no—
306#436—861no—
307#435—861no—
308#435—861no—
309C8×D4—861no—
310#433—861no—
311C2×#104—861no—
312C2×#104—861no—
313#416—861no—
314#408—861no—
315#407—431no—
316C2×C22⋊C8—21no—
317C2×C22⋊C8—21no—
318C2×C22⋊C8—431no—
319C2×C22⋊C8C2×D4311yescharacteristic
320C2×C22⋊C8C2×D4311yescharacteristic
321C4×C22⋊C4—431no—
322#328—861no—
323#327—861no—
324C43#903711yescharacteristic, complemented, Sylow
325C2×#41—21no—
326C2×#41—21no—
327C2×#41—21no—
328C2×#41—21no—
329C2×#41—42no—
330C2×#41—42no—
331C2×#41—431no—
332C22×Q8C4×D4311yescharacteristic
333C22×D4—21no—
334C22×D4C4×D4311yescharacteristic
335C23×C4—21no—
336C23×C4C22×D4311yescharacteristic
337#135—1722no—
338#135—1722no—
339C2×Q16—861no—
340C2×SD16—861no—
341C2×SD16—861no—
342C2×D8—861no—
343C2×M16—431no—
344C2×M16—431no—
345C2×M16—861no—
346C22×C8—21no—
347C22×C8—861no—
348C22×C8—861no—
349C22×C8C22⋊D4311yescharacteristic
350C22×C8C22⋊D4311yescharacteristic
351#123—861no—
352C22⋊Q8—431no—
353C22⋊Q8—431no—
354#121—431no—
355#121—431no—
356#120—861no—
357C4×D4—861no—
358C4×D4—861no—
359#117—431no—
360C2×C22⋊C4—861no—
361C2×C42—861no—
362C4⋊C8—861no—
363C4⋊C8—861no—
364#104—1722no—
365#104—1722no—
366#103—861no—
367#103—861no—
368#102—861no—
369#102—861no—
370C22⋊C8—21no—
371C22⋊C8—21no—
372C22⋊C8—21no—
373C22⋊C8—21no—
374C22⋊C8—42no—
375C22⋊C8—42no—
376C22⋊C8—431no—
377C22⋊C8—431no—
378C22⋊C8—861no—
379C22⋊C8—861no—
380C22⋊C8—861no—
381C22⋊C8—861no—
382C22⋊C8—861no—
383#97—861no—
384C4×C8—861no—
385#95—861no—
386C24—21no—
387C24#1062189811yescharacteristic
388#41—22no—
389#41—22no—
390#41—22no—
391#41—22no—
392#41—41no—
393#41—41no—
394#41—41no—
395#41—41no—
396#41—42no—
397#41—42no—
398#41—42no—
399#41—42no—
400#41—1721no—
401#41—1721no—
402C2×Q8—21no—
403C2×Q8—21no—
404C2×Q8—42no—
405C2×Q8—431no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—42no—
409C2×D4—42no—
410C2×D4—42no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4—431no—
414C2×D4—861no—
415C2×D4—861no—
416C2×D4—861no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—861no—
427C22×C4—1721no—
428C22×C4C2×C4×D4311yescharacteristic
429C22×C4D4×D4311yescharacteristic
430C22×C4D4×D4311yescharacteristic
431C22×C4D4×D4311yescharacteristic
432C22×C4#1062190011yescharacteristic
433C22×C4C2×C22⋊D4311yescharacteristic
434Q16—1722no—
435SD16—1722no—
436SD16—1722no—
437D8—1722no—
438M16—3441no—
439M16—1721no—
440M16—1721no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—41no—
444C2×C8—41no—
445C2×C8—41no—
446C2×C8—41no—
447C2×C8—41no—
448C2×C8—861no—
449C2×C8—861no—
450C2×C8—861no—
451C2×C8—861no—
452C2×C8—3441no—
453C2×C8—1721no—
454C2×C8—1721no—
455C4⋊C4—431no—
456C4⋊C4—431no—
457C4⋊C4—861no—
458C4⋊C4—861no—
459C22⋊C4—861no—
460C22⋊C4—861no—
461C22⋊C4—861no—
462C22⋊C4—861no—
463C22⋊C4—861no—
464C22⋊C4—862no—
465C22⋊C4—1721no—
466C42—861no—
467C42—1721no—
468C42—1721no—
469C23—21no—
470C23—21no—
471C23—22no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23—861no—
481C23C4×C22⋊D4311yescharacteristic
482C23#1306329811yescharacteristic
483C23#1306330711yescharacteristic
484Q8—22no—
485Q8—22no—
486Q8—41no—
487Q8—41no—
488Q8—1721no—
489D4—22no—
490D4—22no—
491D4—41no—
492D4—41no—
493D4—42no—
494D4—42no—
495D4—42no—
496D4—42no—
497D4—3441no—
498D4—3441no—
499D4—1721no—
500D4—1721no—
501D4—1721no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—22no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—861no—
519C2×C4—861no—
520C2×C4—861no—
521C2×C4—3441no—
522C2×C4—3441no—
523C2×C4—1722no—
524C2×C4—1721no—
525C2×C4—1721no—
526C2×C4C22⋊C4×D4311yescharacteristic
527C2×C4(C22⋊D43)⋊C411yescharacteristic
528C2×C4#1306329311yescharacteristic
529C2×C4#1306329611yescharacteristic
530C8—41no—
531C8—41no—
532C8—81no—
533C8—1721no—
534C8—1721no—
535C8—1721no—
536C8—1721no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—42no—
546C22—42no—
547C22—42no—
548C22—81no—
549C22—81no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—1721no—
555C22—1721no—
556C22—1721no—
557C22#1458277511yescharacteristic
558C22#1458301411yescharacteristic
559C22#1458301911yescharacteristic
560C4—21no—
561C4—21no—
562C4—21no—
563C4—42no—
564C4—3442no—
565C4—1721no—
566C4—1721no—
567C4—1721no—
568C4#1458308511yescharacteristic
569C4#1458308511yescharacteristic
570C2—21no—
571C2—21no—
572C2—41no—
573C2—41no—
574C2—82no—
575C2—3441no—
576C2#1913492511yescharacteristic
577C2#1913496011yescharacteristic
578C2#1913500011yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1780C2
socleC22×C43#386
prime radical#19143813C2
cosocleC23×C4×C43C23
hypercenter#1780D43
hypocenterC43#9037
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1780

Complements

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

NH ≅ G/Ntype
2. #19143640C2semidirect
3. #19134539C2semidirect
4. #19133087C2semidirect
5. #19132483C2semidirect
6. #19132442C2semidirect
7. C43×#1780C2semidirect
11. #14583055C4semidirect
12. #14583050C4semidirect
14. #14583038C4semidirect
15. #14583033C4semidirect
284. #1780D43semidirect
324. C43#9037semidirect

Maximal subgroups

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

subgroupindex
#191438132
#191436402
#191345392
#191330872
#191324832
#191324422
C43×#17802
#903743