Finite Group Databasebeta

← #25012846

Subgroups — #25012846

Order 11008.

628 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 628 conjugacy classes of subgroups — too many to draw. Only its 87 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#19137182C211yesmaximal, characteristic
2#19134520C211yesmaximal, characteristic
3#19134511C211yesmaximal, characteristic
4#19132714C211yesmaximal, characteristic, complemented
5#19132713C211yesmaximal, characteristic, complemented
6#19132712C211yesmaximal, characteristic, complemented
7C43×#1390C211yesmaximal, characteristic, complemented
8C22×#10621900C2211yescharacteristic
9C2×#13063281C411yescharacteristic, complemented
10C22×Dic43⋊C4C411yescharacteristic, complemented
11C2×#13063243—21no—
12C2×#13063242C2211yescharacteristic
13C2×#13063240C2211yescharacteristic
14C2×#13063239—21no—
15#14582862—21no—
16#14582803—21no—
17#14582799—21no—
18#14582779C2211yescharacteristic
19#14582778C411yescharacteristic, complemented
20#14582776C411yescharacteristic, complemented
21#14582760—21no—
22#14582758—21no—
23#14582757—21no—
24C2×#100×C43C2211yescharacteristic
25C2×#99×C43C2211yescharacteristic
26C43×#386C2211yescharacteristic
27C2×#10621900—21no—
28C2×#10621900—21no—
29C2×#10621900—21no—
30C2×#10621900—21no—
31C2×#10621900—42no—
32C2×#10621900—42no—
33C22×Dic86D411yescharacteristic
34C22×C22⋊D43C2×C411yescharacteristic
35C22×C22⋊D43D411yescharacteristic
36C23×Dic43C2×C411yescharacteristic
37C23×Dic43C2×C411yescharacteristic
38C23×Dic43D411yescharacteristic
39C22×C4×D43D411yescharacteristic
40C2×#10621877—21no—
41#13063281—42no—
42C2×Dic43⋊C4—21no—
43C2×Dic43⋊C4—21no—
44C2×Dic43⋊C4—21no—
45C2×Dic43⋊C4—42no—
46C2×C22⋊Dic43—21no—
47C2×C22⋊Dic43—21no—
48C2×C22⋊Dic43C2×C411yescharacteristic
49C2×(C2×D43)⋊C4—21no—
50C2×(C2×D43)⋊C4—21no—
51C2×C4×Dic43—21no—
52#13063243—42no—
53#13063242—21no—
54#13063242—21no—
55#13063240—21no—
56#13063240—21no—
57#13063239—42no—
58(C2×D43)⋊C8—42no—
59C43⋊#95—21no—
60C43⋊#95—21no—
61C43⋊#95—21no—
62C43⋊#95—42no—
63C22×D4×C43C2311yescharacteristic
64C23×C4×C43C2×C411yescharacteristic
65C2×M16×C43—21no—
66C2×C22⋊C4×C43—21no—
67C2×C22⋊C4×C43—21no—
68C2×C22⋊C4×C43C2×C411yescharacteristic
69#100×C43—21no—
70#100×C43—21no—
71#99×C43—21no—
72#99×C43—21no—
73#95×C43—21no—
74C24×C43C22×C411yescharacteristic
75C24×C43C2×D411yescharacteristic
76C23×D43C22⋊C411yescharacteristic
77C2×D4×C43—41no—
78C2×D4×C43—41no—
79C2×D4×C43#4111yescharacteristic
80C2×D4×C43#4111yescharacteristic
81C2×D4×C43#4111yescharacteristic
82C2×D4×C43#4111yescharacteristic
83C22×C4×C43—21no—
84C22×C4×C43—21no—
85C22×C4×C43—41no—
86C22×C4×C43—41no—
87C22×C4×C43—81no—
88C22×C4×C43C2×D411yescharacteristic
89C2×C22⋊D43—22no—
90C2×C22⋊D43—21no—
91C2×C22⋊D43—21no—
92C2×C22⋊D43—21no—
93C2×C22⋊D43—21no—
94C2×C22⋊D43—41no—
95C2×C22⋊D43—41no—
96C2×C22⋊D43—41no—
97C22×Dic43—22no—
98C22×Dic43—22no—
99C22×Dic43—22no—
100C22×Dic43—21no—
101C22×Dic43—21no—
102C22×Dic43—21no—
103C22×Dic43—21no—
104C22×Dic43—21no—
105C22×Dic43—21no—
106C22×Dic43—41no—
107C22×Dic43—41no—
108C22×Dic43—41no—
109C22×Dic43—81no—
110C22×Dic43C22⋊C411yescharacteristic
111C22×Dic43C22⋊C411yescharacteristic
112C22×Dic43C22⋊C411yescharacteristic
113#10621900—44no—
114#10621900—44no—
115#10621900—44no—
116#10621900—44no—
117C2×C4×D43—21no—
118C2×C4×D43—21no—
119C2×C4×D43—22no—
120C2×C4×D43—41no—
121C2×Dic86—21no—
122C2×Dic86—21no—
123C2×Dic86—22no—
124C2×Dic86—41no—
125M16×C43—41no—
126M16×C43—41no—
127C2×C8×C43—41no—
128C22⋊C4×C43—41no—
129C22⋊C4×C43—41no—
130C22⋊C4×C43—41no—
131C22⋊C4×C43—81no—
132C22⋊Dic43—41no—
133C22⋊Dic43—41no—
134C22⋊Dic43—41no—
135C22⋊Dic43—81no—
136(C2×D43)⋊C4—81no—
137(C2×D43)⋊C4—81no—
138Dic43⋊C4—42no—
139Dic43⋊C4—42no—
140Dic43⋊C4—42no—
141C4×Dic43—42no—
142#10621877—41no—
143#10621877—41no—
144C2×C43⋊C8—41no—
145C23×C43—21no—
146C23×C43—21no—
147C23×C43—21no—
148C23×C43—21no—
149C23×C43—41no—
150C23×C43—41no—
151C23×C43—41no—
152C23×C43—41no—
153C23×C43C2×C22⋊C411yescharacteristic
154C23×C43#11711yescharacteristic
155C23×C43#11711yescharacteristic
156C23×C43#12311yescharacteristic
157C23×C43#12311yescharacteristic
158C22×D43—21no—
159C22×D43—21no—
160C22×D43—21no—
161C22×D43—41no—
162C22×D43—41no—
163D4×C43—41no—
164D4×C43—41no—
165D4×C43—41no—
166D4×C43—41no—
167C2×C4×C43—21no—
168C2×C4×C43—21no—
169C2×C4×C43—41no—
170C2×C4×C43—41no—
171C2×C4×C43—41no—
172C2×C4×C43—41no—
173C2×C4×C43—41no—
174C2×C4×C43—41no—
175C2×C4×C43—82no—
176C2×C4×C43—81no—
177C2×C4×C43—81no—
178C2×C4×C43—81no—
179C2×C4×C43#12311yescharacteristic
180C2×C4×C43#12311yescharacteristic
181C22⋊D43—42no—
182C22⋊D43—42no—
183C22⋊D43—42no—
184C22⋊D43—42no—
185C2×Dic43—24no—
186C2×Dic43—24no—
187C2×Dic43—21no—
188C2×Dic43—21no—
189C2×Dic43—21no—
190C2×Dic43—21no—
191C2×Dic43—21no—
192C2×Dic43—21no—
193C2×Dic43—21no—
194C2×Dic43—42no—
195C2×Dic43—42no—
196C2×Dic43—41no—
197C2×Dic43—41no—
198C2×Dic43—41no—
199C2×Dic43—41no—
200C2×Dic43—41no—
201C2×Dic43—41no—
202C2×Dic43—82no—
203C2×Dic43—81no—
204C2×Dic43—81no—
205C2×Dic43—81no—
206C2×Dic43#9912yes—
207C2×Dic43#9912yes—
208C4×D43—42no—
209C4×D43—42no—
210Dic86—42no—
211Dic86—42no—
212C8×C43—81no—
213C43⋊C8—81no—
214#12855—431nomaximal, Sylow
215C22×C43—21no—
216C22×C43—21no—
217C22×C43—21no—
218C22×C43—21no—
219C22×C43—21no—
220C22×C43—21no—
221C22×C43—41no—
222C22×C43—41no—
223C22×C43—41no—
224C22×C43—41no—
225C22×C43—42no—
226C22×C43—41no—
227C22×C43—41no—
228C22×C43—41no—
229C22×C43—41no—
230C22×C43—81no—
231C22×C43#38111yescharacteristic
232C22×C43C2×#9911yescharacteristic
233C22×C43C2×#9911yescharacteristic
234C2×D43—42no—
235C2×D43—41no—
236C2×D43—41no—
237C2×D43—41no—
238C2×D43—81no—
239C4×C43—21no—
240C4×C43—21no—
241C4×C43—81no—
242C4×C43—81no—
243C4×C43—161no—
244Dic43—22no—
245Dic43—22no—
246Dic43—41no—
247Dic43—81no—
248Dic43—81no—
249Dic43—161no—
250#2311—431no—
251#1785—431no—
252#1782—431no—
253#1390—431no—
254#1390—431no—
255#1390—431no—
256#1390D4311yescharacteristic, complemented
257C2×C43—21no—
258C2×C43—21no—
259C2×C43—41no—
260C2×C43—41no—
261C2×C43—41no—
262C2×C43—41no—
263C2×C43#181911yescharacteristic
264C2×C43#212211yescharacteristic
265C2×C43#212311yescharacteristic
266D43—81no—
267C22×#41—431no—
268C2×#117—431no—
269C22×C4⋊C4—431no—
270C2×#101—861no—
271C2×#100—431no—
272C2×#100C2×D4311yescharacteristic
273C2×#99—431no—
274C2×#99—861no—
275C2×#99C2×D4311yescharacteristic
276#407—861no—
277#391—861no—
278#390—861no—
279#386—431no—
280#386—431no—
281#386—431no—
282#386C2×D4311yescharacteristic
283#381—861no—
284#380—861no—
285#380—861no—
286C43#1285511yescharacteristic, complemented, Sylow
287C2×#41—861no—
288C2×#41—861no—
289C2×#41—861no—
290C2×#41—861no—
291C2×#41—1722no—
292C2×#41—1722no—
293C22×Q8—431no—
294C22×D4—431no—
295C22×D4—431no—
296C22×D4C22×D4311yescharacteristic
297C23×C4—431no—
298C23×C4—431no—
299C23×C4—431no—
300C23×C4—431no—
301C23×C4C4×D4311yescharacteristic
302C2×M16—21no—
303C2×M16—861no—
304#117—1722no—
305C2×C4⋊C4—861no—
306C2×C4⋊C4—861no—
307C2×C4⋊C4—861no—
308C2×C4⋊C4—1722no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—431no—
312C2×C22⋊C4—861no—
313C2×C22⋊C4—861no—
314C2×C22⋊C4—861no—
315C2×C22⋊C4—861no—
316C2×C22⋊C4C4×D4311yescharacteristic
317C2×C42—861no—
318#101—1722no—
319#100—21no—
320#100—21no—
321#100—861no—
322#100—861no—
323#99—21no—
324#99—21no—
325#99—861no—
326#99—861no—
327#99—1722no—
328C22⋊C8—1722no—
329#95—21no—
330#95—861no—
331#95—861no—
332#95—861no—
333#95—1722no—
334C24—431no—
335C24C2×C4×D4311yescharacteristic
336C24D4×D4311yescharacteristic
337#41—1724no—
338#41—1724no—
339#41—1724no—
340#41—1724no—
341C2×Q8—862no—
342C2×Q8—861no—
343C2×Q8—861no—
344C2×Q8—1721no—
345C2×D4—41no—
346C2×D4—41no—
347C2×D4—862no—
348C2×D4—861no—
349C2×D4—861no—
350C2×D4—861no—
351C2×D4—861no—
352C2×D4—1721no—
353C2×D4—1721no—
354C2×D4—1721no—
355C2×D4#1062189811yescharacteristic
356C2×D4#1062189811yescharacteristic
357C2×D4#1062190011yescharacteristic
358C2×D4#1062190211yescharacteristic
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—41no—
362C22×C4—41no—
363C22×C4—81no—
364C22×C4—431no—
365C22×C4—431no—
366C22×C4—431no—
367C22×C4—862no—
368C22×C4—862no—
369C22×C4—862no—
370C22×C4—862no—
371C22×C4—861no—
372C22×C4—861no—
373C22×C4—861no—
374C22×C4—861no—
375C22×C4—861no—
376C22×C4—861no—
377C22×C4—861no—
378C22×C4—861no—
379C22×C4—3441no—
380C22×C4—1721no—
381C22×C4—1721no—
382C22×C4—1721no—
383C22×C4—1721no—
384C22×C4D4×D4311yescharacteristic
385M16—41no—
386M16—41no—
387M16—1721no—
388M16—1721no—
389C2×C8—41no—
390C2×C8—1721no—
391C4⋊C4—1722no—
392C4⋊C4—1722no—
393C4⋊C4—1722no—
394C22⋊C4—41no—
395C22⋊C4—41no—
396C22⋊C4—41no—
397C22⋊C4—81no—
398C22⋊C4—3441no—
399C22⋊C4—3441no—
400C22⋊C4—3441no—
401C22⋊C4—1721no—
402C22⋊C4—1721no—
403C22⋊C4—1721no—
404C42—1722no—
405C23—21no—
406C23—21no—
407C23—21no—
408C23—21no—
409C23—41no—
410C23—41no—
411C23—41no—
412C23—41no—
413C23—861no—
414C23—861no—
415C23—861no—
416C23—1721no—
417C23—1721no—
418C23C22⋊C4×D4311yescharacteristic
419C23#1306328211yescharacteristic
420C23#1306328311yescharacteristic
421C23#1306330711yescharacteristic
422C23#1306331011yescharacteristic
423Q8—1722no—
424Q8—1722no—
425D4—41no—
426D4—41no—
427D4—41no—
428D4—41no—
429D4—1722no—
430D4—1722no—
431D4—1722no—
432D4—1722no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—82no—
442C2×C4—81no—
443C2×C4—81no—
444C2×C4—81no—
445C2×C4—432no—
446C2×C4—432no—
447C2×C4—864no—
448C2×C4—864no—
449C2×C4—861no—
450C2×C4—861no—
451C2×C4—861no—
452C2×C4—861no—
453C2×C4—861no—
454C2×C4—861no—
455C2×C4—861no—
456C2×C4—3442no—
457C2×C4—3441no—
458C2×C4—3441no—
459C2×C4—3441no—
460C2×C4—1722no—
461C2×C4—1722no—
462C2×C4—1722no—
463C2×C4—1722no—
464C2×C4—1721no—
465C2×C4—1721no—
466C2×C4—1721no—
467C2×C4—1721no—
468C2×C4—1721no—
469C2×C4—1721no—
470C2×C4#1306330711yescharacteristic
471C2×C4#1306331011yescharacteristic
472C8—81no—
473C8—3441no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—41no—
481C22—41no—
482C22—41no—
483C22—41no—
484C22—42no—
485C22—41no—
486C22—41no—
487C22—41no—
488C22—41no—
489C22—81no—
490C22—3441no—
491C22—1722no—
492C22—1721no—
493C22—1721no—
494C22—1721no—
495C22#1458276111yescharacteristic
496C22#99×D4311yescharacteristic
497C22#99×D4311yescharacteristic
498C4—21no—
499C4—21no—
500C4—81no—
501C4—81no—
502C4—161no—
503C4—862no—
504C4—862no—
505C4—3441no—
506C4—3441no—
507C4—1721no—
508C4—6881no—
509C2—21no—
510C2—21no—
511C2—41no—
512C2—41no—
513C2—41no—
514C2—41no—
515C2—3441no—
516C2#1913466811yescharacteristic
517C2#1913624311yescharacteristic
518C2#1913624711yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC24×C43C22×C4
FrattiniC22×D4C22×D43
FittingC43×#1390C2
socleC22×C43C2×#99
prime radicalC22×#10621900C22
cosocleC22×D4×C43C23
hypercenter#1390D43
hypocenterC43#12855
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1390

Complements

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

NH ≅ G/Ntype
4. #19132714C2semidirect
5. #19132713C2semidirect
6. #19132712C2semidirect
7. C43×#1390C2semidirect
9. C2×#13063281C4semidirect
10. C22×Dic43⋊C4C4semidirect
19. #14582778C4semidirect
20. #14582776C4semidirect
256. #1390D43semidirect
286. C43#12855semidirect

Maximal subgroups

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

subgroupindex
#191371822
#191345202
#191345112
#191327142
#191327132
#191327122
C43×#13902
#1285543