Finite Group Databasebeta

← #24989498

Subgroups — #24989498

Order 11008.

524 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582967C211yesmaximal, characteristic
2#19134622C211yesmaximal, characteristic, complemented
3#19134618C211yesmaximal, characteristic, complemented
4#19134580C211yesmaximal, characteristic
5#19134580C211yesmaximal, characteristic
6#19132463C211yesmaximal, characteristic, complemented
7C43×#1289C211yesmaximal, characteristic, complemented
8C22×#10621872C411yescharacteristic, complemented
9C23×C43⋊C8C2211yescharacteristic
10C2×C4×C22⋊D43C2211yescharacteristic
11#14582967—21no—
12#14582967—21no—
13#14582967—21no—
14#14582967—21no—
15C2×#13063258—21no—
16C2×#13063256—21no—
17C2×Dic43⋊C8C411yescharacteristic, complemented
18C2×#13063239—21no—
19C2×#13063239—21no—
20C2×(C2×D43)⋊C8C411yescharacteristic, complemented
21C2×#13063235C411yescharacteristic, complemented
22#14582759C2211yescharacteristic
23#14582759C2211yescharacteristic
24#14582665—21no—
25#14582665—21no—
26#14582661—21no—
27#14582661—21no—
28C2×C22⋊C8×C43C2211yescharacteristic
29C43×#380C2211yescharacteristic
30C43×#380C2211yescharacteristic
31C22×C22⋊D43D411yescharacteristic
32C22×C4×D43C2×C411yescharacteristic
33C2×#10621872—21no—
34C2×#10621872—21no—
35C2×#10621872—42no—
36C22×C43⋊C8—42no—
37C22×C43⋊C8C2×C411yescharacteristic
38C22×C43⋊C8C2×C411yescharacteristic
39C22×C43⋊C8D411yescharacteristic
40C22×C43⋊C8D411yescharacteristic
41C22×C43⋊C8D411yescharacteristic
42C22×C43⋊C8D411yescharacteristic
43C4×C22⋊D43—21no—
44C4×C22⋊D43—21no—
45C4×C22⋊D43—21no—
46C4×C22⋊D43—21no—
47C2×C4⋊Dic43—21no—
48C2×C4⋊Dic43—21no—
49C2×Dic43⋊C4Q811yescharacteristic
50C2×C22⋊Dic43—21no—
51C2×C22⋊Dic43—21no—
52C2×C22⋊Dic43D411yescharacteristic
53C2×(C2×D43)⋊C4Q811yescharacteristic
54C2×C4×Dic43C2×C411yescharacteristic
55#13063258—42no—
56#13063256—42no—
57Dic43⋊C8—21no—
58Dic43⋊C8—21no—
59#13063239—42no—
60#13063239—42no—
61(C2×D43)⋊C8—21no—
62(C2×D43)⋊C8—21no—
63#13063235—21no—
64#13063235—21no—
65C43⋊#95—21no—
66C43⋊#95—21no—
67C23×C4×C43C2311yescharacteristic
68C22×C8×C43C2×C411yescharacteristic
69C22×C8×C43C2×C411yescharacteristic
70C2×C4⋊C4×C43—21no—
71C2×C4⋊C4×C43—21no—
72C2×C22⋊C4×C43—21no—
73C2×C22⋊C4×C43—21no—
74C22⋊C8×C43—21no—
75C22⋊C8×C43—21no—
76#95×C43—21no—
77#95×C43—21no—
78C24×C43C2×D411yescharacteristic
79C23×D43C4⋊C411yescharacteristic
80C22×C4×C43—41no—
81C22×C4×C43—41no—
82C22×C4×C43—41no—
83C22×C4×C43—41no—
84C22×C4×C43C22×C411yescharacteristic
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×Q811yescharacteristic
88C22×C4×C43#4111yescharacteristic
89C22×C4×C43#4111yescharacteristic
90C2×C22⋊D43—21no—
91C2×C22⋊D43—21no—
92C2×C22⋊D43—21no—
93C2×C22⋊D43—21no—
94C2×C22⋊D43—21no—
95C2×C22⋊D43—21no—
96C22×Dic43—41no—
97C22×Dic43—41no—
98C22×Dic43C4⋊C411yescharacteristic
99C22×Dic43C4⋊C411yescharacteristic
100C22×Dic43C4⋊C411yescharacteristic
101C2×C4×D43—21no—
102C2×C4×D43—21no—
103C2×C4×D43—41no—
104C2×C4×D43—41no—
105C2×C8×C43—21no—
106C2×C8×C43—21no—
107C2×C8×C43—41no—
108C2×C8×C43—41no—
109C4⋊C4×C43—41no—
110C4⋊C4×C43—41no—
111C4⋊C4×C43—41no—
112C4⋊C4×C43—41no—
113C22⋊C4×C43—41no—
114C22⋊C4×C43—41no—
115C22⋊C4×C43—41no—
116C22⋊C4×C43—41no—
117C22⋊Dic43—21no—
118C22⋊Dic43—21no—
119C22⋊Dic43—41no—
120C22⋊Dic43—41no—
121C22⋊Dic43—41no—
122C22⋊Dic43—41no—
123(C2×D43)⋊C4—21no—
124(C2×D43)⋊C4—21no—
125C4⋊Dic43—41no—
126C4⋊Dic43—41no—
127C4⋊Dic43—41no—
128C4⋊Dic43—41no—
129Dic43⋊C4—21no—
130Dic43⋊C4—21no—
131C4×Dic43—21no—
132C4×Dic43—21no—
133C2×C43⋊C8—22no—
134C2×C43⋊C8—22no—
135C2×C43⋊C8—22no—
136C2×C43⋊C8—41no—
137C2×C43⋊C8—41no—
138C2×C43⋊C8—41no—
139C2×C43⋊C8C22⋊C411yescharacteristic
140C2×C43⋊C8C22⋊C411yescharacteristic
141C2×C43⋊C8C22⋊C411yescharacteristic
142C2×C43⋊C8C22⋊C411yescharacteristic
143#10621872—42no—
144#10621872—42no—
145C23×C43—41no—
146C23×C43—41no—
147C23×C43C2×C4⋊C411yescharacteristic
148C23×C43#12111yescharacteristic
149C23×C43#12111yescharacteristic
150C23×C43AGL(1,ℤ/8)11yescharacteristic
151C23×C43AGL(1,ℤ/8)11yescharacteristic
152C23×C43#13711yescharacteristic
153C23×C43#13711yescharacteristic
154C22×D43—21no—
155C22×D43—21no—
156C22×D43—21no—
157C22×D43—41no—
158C22×D43—41no—
159C2×C4×C43—21no—
160C2×C4×C43—21no—
161C2×C4×C43—21no—
162C2×C4×C43—21no—
163C2×C4×C43—21no—
164C2×C4×C43—21no—
165C2×C4×C43—41no—
166C2×C4×C43—41no—
167C2×C4×C43—41no—
168C2×C4×C43—81no—
169C2×C4×C43—81no—
170C2×C4×C43—81no—
171C2×C4×C43—81no—
172C2×C4×C43—81no—
173C2×C4×C43—81no—
174C2×C4×C43C2×C22⋊C411yescharacteristic
175C2×C4×C43#11711yescharacteristic
176C2×C4×C43C22⋊Q811yescharacteristic
177C2×C4×C43C22⋊Q811yescharacteristic
178C22⋊D43—41no—
179C22⋊D43—41no—
180C22⋊D43—41no—
181C22⋊D43—41no—
182C2×Dic43—21no—
183C2×Dic43—21no—
184C2×Dic43—21no—
185C2×Dic43—21no—
186C2×Dic43—21no—
187C2×Dic43—41no—
188C2×Dic43—41no—
189C2×Dic43—81no—
190C2×Dic43—81no—
191C2×Dic43—81no—
192C2×Dic43—81no—
193C2×Dic43—81no—
194C2×Dic43—81no—
195C4×D43—42no—
196C4×D43—41no—
197C4×D43—41no—
198C8×C43—41no—
199C8×C43—41no—
200C43⋊C8—21no—
201C43⋊C8—21no—
202C43⋊C8—21no—
203C43⋊C8#9912yescomplemented
204#8610—431nomaximal, Sylow
205C22×C43—21no—
206C22×C43—21no—
207C22×C43—21no—
208C22×C43—21no—
209C22×C43—21no—
210C22×C43—21no—
211C22×C43—41no—
212C22×C43—41no—
213C22×C43—41no—
214C22×C43—41no—
215C22×C43#38011yescharacteristic
216C22×C43#42811yescharacteristic
217C22×C43#42811yescharacteristic
218C22×C43#46811yescharacteristic
219C22×C43#46811yescharacteristic
220C22×C43#46911yescharacteristic
221C22×C43#47011yescharacteristic
222C2×D43—41no—
223C2×D43—41no—
224C2×D43—41no—
225C2×D43—81no—
226C2×D43—81no—
227C4×C43—21no—
228C4×C43—21no—
229C4×C43—21no—
230C4×C43—161no—
231C4×C43—161no—
232C4×C43C2×#9911yescharacteristic
233C4×C43#41011yescharacteristic
234Dic43—41no—
235Dic43—41no—
236Dic43—41no—
237Dic43—161no—
238Dic43—161no—
239C2×#435—431no—
240#1808—431no—
241#1807—431no—
242#1799—431no—
243#1799—431no—
244#1289—431no—
245#1289D4311yescharacteristic, complemented
246C2×C43—21no—
247C2×C43—21no—
248C2×C43—21no—
249C2×C43—21no—
250C2×C43—21no—
251C2×C43—21no—
252C2×C43#179911yescharacteristic
253C2×C43#180911yescharacteristic
254C2×C43#181211yescharacteristic
255D43—81no—
256C22×M16—431no—
257C23×C8—431no—
258C2×C4×D4—431no—
259#435—861no—
260#435—861no—
261#435—861no—
262#435—861no—
263C2×#107—861no—
264C2×#106—861no—
265C2×C4⋊C8—431no—
266C2×#99—861no—
267C2×#99—861no—
268C2×C22⋊C8—431no—
269C2×C22⋊C8C2×D4311yescharacteristic
270C2×#97—431no—
271#380—431no—
272#380—431no—
273#380C2×D4311yescharacteristic
274#380C2×D4311yescharacteristic
275#342—861no—
276#342—861no—
277#340—861no—
278#340—861no—
279C43#861011yescharacteristic, complemented, Sylow
280C22×D4—431no—
281C23×C4—431no—
282C23×C4C22×D4311yescharacteristic
283C2×M16—861no—
284C2×M16—861no—
285C2×M16—1722no—
286C22×C8—431no—
287C22×C8—431no—
288C22×C8—431no—
289C22×C8—431no—
290C22×C8—431no—
291C22×C8—431no—
292C22×C8—1722no—
293C22×C8C4×D4311yescharacteristic
294C22×C8C4×D4311yescharacteristic
295C4×D4—861no—
296C4×D4—861no—
297C4×D4—861no—
298C4×D4—861no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—431no—
302C2×C4⋊C4—861no—
303C2×C4⋊C4—861no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—431no—
307C2×C22⋊C4—431no—
308C2×C22⋊C4—861no—
309C2×C22⋊C4—861no—
310C2×C42—431no—
311#107—1722no—
312#106—1722no—
313C4⋊C8—861no—
314C4⋊C8—861no—
315#99—1722no—
316#99—1722no—
317C22⋊C8—21no—
318C22⋊C8—21no—
319C22⋊C8—861no—
320C22⋊C8—861no—
321#97—861no—
322#97—861no—
323#95—21no—
324#95—21no—
325#95—861no—
326#95—861no—
327C24—431no—
328C24D4×D4311yescharacteristic
329C2×D4—861no—
330C2×D4—861no—
331C2×D4—861no—
332C2×D4—861no—
333C2×D4—861no—
334C2×D4—861no—
335C22×C4—41no—
336C22×C4—41no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—431no—
340C22×C4—431no—
341C22×C4—431no—
342C22×C4—861no—
343C22×C4—861no—
344C22×C4—1721no—
345C22×C4—1721no—
346C22×C4—1721no—
347C22×C4—1721no—
348C22×C4C2×C4×D4311yescharacteristic
349C22×C4#1062189811yescharacteristic
350C22×C4#1062189811yescharacteristic
351C22×C4D4×D4311yescharacteristic
352C22×C4D4×D4311yescharacteristic
353C22×C4Q8×D4311yescharacteristic
354M16—1722no—
355M16—1722no—
356C2×C8—21no—
357C2×C8—21no—
358C2×C8—41no—
359C2×C8—41no—
360C2×C8—431no—
361C2×C8—431no—
362C2×C8—431no—
363C2×C8—431no—
364C2×C8—862no—
365C2×C8—862no—
366C2×C8—862no—
367C2×C8—1721no—
368C2×C8—1721no—
369C2×C8—1721no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—861no—
375C4⋊C4—861no—
376C4⋊C4—1721no—
377C4⋊C4—1721no—
378C4⋊C4—1721no—
379C4⋊C4—1721no—
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—41no—
384C22⋊C4—861no—
385C22⋊C4—861no—
386C22⋊C4—861no—
387C22⋊C4—861no—
388C22⋊C4—1721no—
389C22⋊C4—1721no—
390C22⋊C4—1721no—
391C22⋊C4—1721no—
392C42—861no—
393C42—861no—
394C23—41no—
395C23—41no—
396C23—861no—
397C23—861no—
398C23—861no—
399C23—1721no—
400C23—1721no—
401C23C4⋊C4×D4311yescharacteristic
402C23#1306329811yescharacteristic
403C23#1306329811yescharacteristic
404C23#1306334911yescharacteristic
405C23#1306335211yescharacteristic
406C23#1306335411yescharacteristic
407C23#1306335711yescharacteristic
408D4—1721no—
409D4—1721no—
410D4—1721no—
411D4—1721no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—81no—
422C2×C4—81no—
423C2×C4—81no—
424C2×C4—81no—
425C2×C4—81no—
426C2×C4—81no—
427C2×C4—861no—
428C2×C4—861no—
429C2×C4—861no—
430C2×C4—861no—
431C2×C4—861no—
432C2×C4—3441no—
433C2×C4—3441no—
434C2×C4—3441no—
435C2×C4—3441no—
436C2×C4—3441no—
437C2×C4—3441no—
438C2×C4—1722no—
439C2×C4—1721no—
440C2×C4—1721no—
441C2×C4—1721no—
442C2×C4—1721no—
443C2×C4C22⋊C4×D4311yescharacteristic
444C2×C4#1306328211yescharacteristic
445C2×C4#1306330311yescharacteristic
446C2×C4#1306330311yescharacteristic
447C8—41no—
448C8—41no—
449C8—432no—
450C8—861no—
451C8—861no—
452C8—861no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—3441no—
464C22—3441no—
465C22—1721no—
466C22—1721no—
467C22—1721no—
468C22#1458275811yescharacteristic
469C22#1458293811yescharacteristic
470C22#1458294011yescharacteristic
471C22#1458314411yescharacteristic
472C22#1458314811yescharacteristic
473C22#1458315111yescharacteristic
474C22#1458315611yescharacteristic
475C4—21no—
476C4—21no—
477C4—21no—
478C4—161no—
479C4—161no—
480C4—1721no—
481C4—1721no—
482C4—1721no—
483C4—6881no—
484C4—6881no—
485C4#99×D4311yescharacteristic
486C4#1458287111yescharacteristic
487C2—21no—
488C2—21no—
489C2—21no—
490C2—21no—
491C2—21no—
492C2—21no—
493C2—3441no—
494C2#1913458211yescharacteristic
495C2#1913462711yescharacteristic
496C2#1913464011yescharacteristic
subgroupG/H
centerC22#14582758
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1289C2
socleC22×C43#380
prime radicalC22×C22⋊D43D4
cosocleC23×C4×C43C23
hypercenter#1289D43
hypocenterC43#8610
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1289

Complements

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

NH ≅ G/Ntype
2. #19134622C2semidirect
3. #19134618C2semidirect
6. #19132463C2semidirect
7. C43×#1289C2semidirect
8. C22×#10621872C4semidirect
17. C2×Dic43⋊C8C4semidirect
20. C2×(C2×D43)⋊C8C4semidirect
21. C2×#13063235C4semidirect
203. C43⋊C8#99semidirect
245. #1289D43semidirect
279. C43#8610semidirect

Maximal subgroups

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

subgroupindex
C2×#145829672
#191346222
#191346182
#191345802
#191324632
C43×#12892
#861043