Finite Group Databasebeta

← #25011743

Subgroups — #25011743

Order 11008.

636 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 636 conjugacy classes of subgroups — too many to draw. Only its 113 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#19137258C211yesmaximal, characteristic
2C2×#14582687C211yesmaximal, characteristic
3C2×#14582685C211yesmaximal, characteristic
4#100×Dic43C211yesmaximal, characteristic, complemented
5#99×Dic43C211yesmaximal, characteristic, complemented
6#19132713C211yesmaximal, characteristic, complemented
7C43×#1390C211yesmaximal, characteristic, complemented
8C2×#13063293C2211yescharacteristic
9C2×D4×Dic43C2211yescharacteristic
10C22×(C2×D43)⋊C4C411yescharacteristic, complemented
11C2×#13063242C2211yescharacteristic
12C2×#13063240C2211yescharacteristic
13M16×Dic43—21no—
14#14582799—21no—
15#14582791—21no—
16#14582788—21no—
17#14582776—21no—
18#14582772C411yescharacteristic, complemented
19#14582754C411yescharacteristic, complemented
20C22⋊C4×Dic43—21no—
21C22⋊C4×Dic43C411yescharacteristic, complemented
22#14582687C414yescomplemented
23#14582685C414yescomplemented
24#14582667—21no—
25#14582665—21no—
26C2×#100×C43C2211yescharacteristic
27C2×#99×C43C2211yescharacteristic
28C43×#386C2211yescharacteristic
29C24×D43C2×C411yescharacteristic
30C22×C22⋊D43—21no—
31C23×Dic43C2×C411yescharacteristic
32C23×Dic43D411yescharacteristic
33C2×#10621877—21no—
34#13063293—21no—
35#13063293—21no—
36#13063293C2×C412yes—
37#13063293C2×C412yes—
38D4×Dic43—41no—
39D4×Dic43—41no—
40C2×C4⋊Dic43D411yescharacteristic
41C2×Dic43⋊C4—21no—
42C2×C22⋊Dic43—21no—
43C2×C22⋊Dic43C2×C411yescharacteristic
44C2×C22⋊Dic43C2×C411yescharacteristic
45C2×C22⋊Dic43D411yescharacteristic
46C2×(C2×D43)⋊C4—21no—
47C2×(C2×D43)⋊C4—21no—
48C2×(C2×D43)⋊C4—21no—
49C2×(C2×D43)⋊C4—21no—
50C2×(C2×D43)⋊C4—21no—
51C2×(C2×D43)⋊C4—41no—
52C2×(C2×D43)⋊C4—41no—
53C2×C4×Dic43—21no—
54C2×C4×Dic43—41no—
55C2×C4×Dic43D411yescharacteristic
56#13063242—21no—
57#13063242C2×C412yes—
58#13063240—21no—
59#13063240C2×C412yes—
60#13063235—41no—
61C8×Dic43—41no—
62C43⋊#95—21no—
63C43⋊#95—21no—
64C43⋊#95—41no—
65C22×D4×C43C2311yescharacteristic
66C23×C4×C43C2×C411yescharacteristic
67C2×M16×C43—21no—
68C2×C22⋊C4×C43—21no—
69C2×C22⋊C4×C43—21no—
70C2×C22⋊C4×C43C2×C411yescharacteristic
71#100×C43—21no—
72#100×C43C2×C412yes—
73#99×C43—21no—
74#99×C43C2×C412yes—
75#95×C43—21no—
76C24×C43C22×C411yescharacteristic
77C24×C43C2×D411yescharacteristic
78C23×D43—21no—
79C23×D43—21no—
80C23×D43—41no—
81C23×D43—41no—
82C23×D43—81no—
83C23×D43—81no—
84C23×D43C4212yescomplemented
85C2×D4×C43—41no—
86C2×D4×C43—41no—
87C2×D4×C43C22×C411yescharacteristic
88C2×D4×C43C22×C411yescharacteristic
89C2×D4×C43#4111yescharacteristic
90C2×D4×C43#4111yescharacteristic
91C22×C4×C43—21no—
92C22×C4×C43—21no—
93C22×C4×C43—41no—
94C22×C4×C43—41no—
95C22×C4×C43—81no—
96C22×C4×C43C2×D411yescharacteristic
97C2×C22⋊D43—22no—
98C2×C22⋊D43—22no—
99C2×C22⋊D43—81no—
100C2×C22⋊D43—81no—
101C22×Dic43—21no—
102C22×Dic43—21no—
103C22×Dic43—21no—
104C22×Dic43—21no—
105C22×Dic43—21no—
106C22×Dic43—41no—
107C22×Dic43—81no—
108C22×Dic43—81no—
109C22×Dic43C22⋊C411yescharacteristic
110C22×Dic43C22⋊C411yescharacteristic
111C22×Dic43C22⋊C411yescharacteristic
112C22×Dic43C22⋊C411yescharacteristic
113M16×C43—22no—
114M16×C43—41no—
115C2×C8×C43—41no—
116C22⋊C4×C43—22no—
117C22⋊C4×C43—41no—
118C22⋊C4×C43—41no—
119C22⋊C4×C43—81no—
120C22⋊Dic43—21no—
121C22⋊Dic43—22no—
122C22⋊Dic43—41no—
123C22⋊Dic43—41no—
124C22⋊Dic43—41no—
125C22⋊Dic43C4212yescomplemented
126(C2×D43)⋊C4—22no—
127(C2×D43)⋊C4—22no—
128(C2×D43)⋊C4—42no—
129(C2×D43)⋊C4—41no—
130(C2×D43)⋊C4—41no—
131(C2×D43)⋊C4—81no—
132(C2×D43)⋊C4—81no—
133C4⋊Dic43—41no—
134Dic43⋊C4—81no—
135C4×Dic43—21no—
136C4×Dic43—21no—
137C4×Dic43—81no—
138C4×Dic43—82no—
139#10621877—22no—
140#10621877—41no—
141C2×C43⋊C8—41no—
142C23×C43—21no—
143C23×C43—21no—
144C23×C43—21no—
145C23×C43—21no—
146C23×C43—41no—
147C23×C43—41no—
148C23×C43—41no—
149C23×C43—41no—
150C23×C43C2×C4211yescharacteristic
151C23×C43C2×C22⋊C411yescharacteristic
152C23×C43#11711yescharacteristic
153C23×C43C4×D411yescharacteristic
154C23×C43C4×D411yescharacteristic
155C22×D43—22no—
156C22×D43—41no—
157C22×D43—41no—
158C22×D43—41no—
159C22×D43—41no—
160C22×D43—42no—
161C22×D43—41no—
162C22×D43—41no—
163C22×D43—42no—
164C22×D43—82no—
165C22×D43—82no—
166C22×D43—84no—
167C22×D43—82no—
168C22×D43—82no—
169D4×C43—41no—
170D4×C43—41no—
171D4×C43—41no—
172D4×C43—41no—
173C2×C4×C43—21no—
174C2×C4×C43—21no—
175C2×C4×C43—41no—
176C2×C4×C43—41no—
177C2×C4×C43—41no—
178C2×C4×C43—42no—
179C2×C4×C43—41no—
180C2×C4×C43—41no—
181C2×C4×C43—41no—
182C2×C4×C43—81no—
183C2×C4×C43—81no—
184C2×C4×C43—82no—
185C2×C4×C43C4×D411yescharacteristic
186C2×C4×C43C4×D411yescharacteristic
187C22⋊D43—82no—
188C22⋊D43—82no—
189C2×Dic43—22no—
190C2×Dic43—21no—
191C2×Dic43—21no—
192C2×Dic43—21no—
193C2×Dic43—41no—
194C2×Dic43—42no—
195C2×Dic43—41no—
196C2×Dic43—41no—
197C2×Dic43—41no—
198C2×Dic43—41no—
199C2×Dic43—41no—
200C2×Dic43—42no—
201C2×Dic43—81no—
202C2×Dic43—81no—
203C2×Dic43—81no—
204C2×Dic43—81no—
205C2×Dic43—81no—
206C2×Dic43#9911yescharacteristic
207C2×Dic43#9911yescharacteristic
208C8×C43—42no—
209C43⋊C8—42no—
210#12622—431nomaximal, Sylow
211C22×C43—21no—
212C22×C43—21no—
213C22×C43—21no—
214C22×C43—21no—
215C22×C43—21no—
216C22×C43—21no—
217C22×C43—41no—
218C22×C43—41no—
219C22×C43—41no—
220C22×C43—41no—
221C22×C43—42no—
222C22×C43—41no—
223C22×C43—41no—
224C22×C43—41no—
225C22×C43—41no—
226C22×C43—81no—
227C22×C43C4×C22⋊C411yescharacteristic
228C22×C43C2×#9911yescharacteristic
229C22×C43#41011yescharacteristic
230C2×D43—42no—
231C2×D43—42no—
232C2×D43—42no—
233C2×D43—81no—
234C2×D43—81no—
235C2×D43—84no—
236C2×D43—81no—
237C2×D43—81no—
238C2×D43—84no—
239C4×C43—21no—
240C4×C43—21no—
241C4×C43—81no—
242C4×C43—82no—
243C4×C43—81no—
244Dic43—21no—
245Dic43—21no—
246Dic43—42no—
247Dic43—41no—
248Dic43—41no—
249Dic43—41no—
250Dic43—82no—
251#2321—431no—
252C2×AΣL(1,𝔽16)—431no—
253C2×AΣL(1,𝔽16)—431no—
254C4×#100—431no—
255C4×#99—431no—
256#1390—431no—
257#1390D4311yescharacteristic, complemented
258C2×C43—21no—
259C2×C43—21no—
260C2×C43—41no—
261C2×C43—41no—
262C2×C43—41no—
263C2×C43—41no—
264C2×C43C4×#9911yescharacteristic
265C2×C43#212111yescharacteristic
266C2×C43#212211yescharacteristic
267D43—82no—
268C2×#120—431no—
269C2×C4×D4—431no—
270C22×C22⋊C4—431no—
271C2×#100—431no—
272C2×#100C2×D4311yescharacteristic
273C2×#99—431no—
274C2×#99C2×D4311yescharacteristic
275C4×M16—861no—
276#390—861no—
277#388—861no—
278#388—861no—
279#386—861no—
280#386C2×D4311yescharacteristic
281#385—431no—
282#379—431no—
283C4×C22⋊C4—431no—
284C4×C22⋊C4—861no—
285AΣL(1,𝔽16)—434no—
286AΣL(1,𝔽16)—434no—
287#343—861no—
288#342—861no—
289C43#1262211yescharacteristic, complemented, Sylow
290C25—431no—
291C22×D4—861no—
292C22×D4C22×D4311yescharacteristic
293C23×C4—431no—
294C23×C4—431no—
295C23×C4C4×D4311yescharacteristic
296C2×M16—21no—
297C2×M16—861no—
298#120—432no—
299#120—432no—
300#120—861no—
301#120—861no—
302C4×D4—1721no—
303C4×D4—1721no—
304C2×C4⋊C4—431no—
305C2×C4⋊C4—861no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—431no—
309C2×C22⋊C4—431no—
310C2×C22⋊C4—431no—
311C2×C22⋊C4—861no—
312C2×C22⋊C4—861no—
313C2×C22⋊C4—861no—
314C2×C22⋊C4—861no—
315C2×C22⋊C4—861no—
316C2×C22⋊C4—861no—
317C2×C22⋊C4—1721no—
318C2×C22⋊C4—1721no—
319C2×C22⋊C4C4×D4311yescharacteristic
320C2×C42—431no—
321C2×C42—861no—
322C2×C42—1721no—
323#100—21no—
324#100—432no—
325#100—861no—
326#100C4×D4312yes—
327#99—21no—
328#99—432no—
329#99—861no—
330#99C4×D4312yes—
331#97—1721no—
332C4×C8—1721no—
333#95—21no—
334#95—861no—
335#95—861no—
336#95—1721no—
337C24—432no—
338C24—861no—
339C24—861no—
340C24—3441no—
341C24—3441no—
342C24—1721no—
343C24—1721no—
344C24C2×C4×D4311yescharacteristic
345C24D4×D4311yescharacteristic
346C2×D4—41no—
347C2×D4—41no—
348C2×D4—862no—
349C2×D4—862no—
350C2×D4—3441no—
351C2×D4—3441no—
352C2×D4C2×C4×D4311yescharacteristic
353C2×D4C2×C4×D4311yescharacteristic
354C2×D4#1062190011yescharacteristic
355C2×D4#1062190211yescharacteristic
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—81no—
361C22×C4—431no—
362C22×C4—431no—
363C22×C4—431no—
364C22×C4—431no—
365C22×C4—861no—
366C22×C4—861no—
367C22×C4—861no—
368C22×C4—861no—
369C22×C4—861no—
370C22×C4—3441no—
371C22×C4—3441no—
372C22×C4—1721no—
373C22×C4D4×D4311yescharacteristic
374M16—22no—
375M16—41no—
376M16—862no—
377M16—1721no—
378C2×C8—41no—
379C2×C8—1721no—
380C4⋊C4—3441no—
381C4⋊C4—1721no—
382C22⋊C4—22no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—81no—
386C22⋊C4—432no—
387C22⋊C4—861no—
388C22⋊C4—862no—
389C22⋊C4—862no—
390C22⋊C4—862no—
391C22⋊C4—3441no—
392C22⋊C4—3441no—
393C22⋊C4—1721no—
394C22⋊C4—1721no—
395C22⋊C4—1722no—
396C22⋊C4—1721no—
397C22⋊C4—1721no—
398C22⋊C4—1721no—
399C42—861no—
400C42—861no—
401C42—3441no—
402C42—3442no—
403C23—21no—
404C23—21no—
405C23—21no—
406C23—21no—
407C23—41no—
408C23—41no—
409C23—41no—
410C23—41no—
411C23—862no—
412C23—3442no—
413C23—3442no—
414C23—3444no—
415C23—3442no—
416C23—3442no—
417C23—1722no—
418C23—1721no—
419C23—1721no—
420C23—1721no—
421C23—1721no—
422C23—1722no—
423C23—1721no—
424C23—1721no—
425C23C42×D4311yescharacteristic
426C23C22⋊C4×D4311yescharacteristic
427C23#1306328311yescharacteristic
428C23(C22⋊D43)⋊C411yescharacteristic
429C23#1306328711yescharacteristic
430D4—41no—
431D4—41no—
432D4—41no—
433D4—41no—
434D4—3442no—
435D4—3442no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—81no—
446C2×C4—81no—
447C2×C4—82no—
448C2×C4—431no—
449C2×C4—431no—
450C2×C4—861no—
451C2×C4—861no—
452C2×C4—861no—
453C2×C4—862no—
454C2×C4—3441no—
455C2×C4—3441no—
456C2×C4—3441no—
457C2×C4—3441no—
458C2×C4—3441no—
459C2×C4—1721no—
460C2×C4—1722no—
461C2×C4—1722no—
462C2×C4—1721no—
463C2×C4—1721no—
464C2×C4—1721no—
465C2×C4—1721no—
466C2×C4—1721no—
467C2×C4(C22⋊D43)⋊C411yescharacteristic
468C2×C4#1306328711yescharacteristic
469C8—42no—
470C8—1722no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—41no—
478C22—41no—
479C22—41no—
480C22—41no—
481C22—42no—
482C22—41no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—81no—
487C22—3441no—
488C22—3441no—
489C22—3444no—
490C22—3444no—
491C22—3441no—
492C22—3441no—
493C22—1722no—
494C22—1722no—
495C22—1722no—
496C22#1458274611yescharacteristic
497C22#99×D4311yescharacteristic
498C22#1458287111yescharacteristic
499C4—21no—
500C4—21no—
501C4—81no—
502C4—82no—
503C4—81no—
504C4—861no—
505C4—861no—
506C4—3442no—
507C4—1722no—
508C4—1721no—
509C4—1721no—
510C4—1721no—
511C2—21no—
512C2—21no—
513C2—41no—
514C2—41no—
515C2—41no—
516C2—41no—
517C2—3442no—
518C2#1913438211yescharacteristic
519C2#1913624011yescharacteristic
520C2#1913624311yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC23×C43C2×C42
FrattiniC22×D4C22×D43
FittingC43×#1390C2
socleC22×C43C2×#99
prime radicalC2×#13063293C22
cosocleC22×D4×C43C23
hypercenter#1390D43
hypocenterC43#12622
LCSG ▷ C23×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. #100×Dic43C2semidirect
5. #99×Dic43C2semidirect
6. #19132713C2semidirect
7. C43×#1390C2semidirect
10. C22×(C2×D43)⋊C4C4semidirect
18. #14582772C4semidirect
19. #14582754C4semidirect
21. C22⋊C4×Dic43C4semidirect
22. #14582687C4semidirect
23. #14582685C4semidirect
84. C23×D43C42semidirect
125. C22⋊Dic43C42semidirect
257. #1390D43semidirect
289. C43#12622semidirect

Maximal subgroups

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

subgroupindex
#191372582
C2×#145826872
C2×#145826852
#100×Dic432
#99×Dic432
#191327132
C43×#13902
#1262243