Finite Group Databasebeta

← #24992185

Subgroups — #24992185

Order 11008.

674 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582956C211yesmaximal, characteristic, complemented
2#19142926C211yesmaximal, characteristic
3C2×#14582632C212yesmaximal
4#19132474C212yesmaximal, complemented
5C43×#1434C211yesmaximal, characteristic, complemented
6C2×#13063308—21no—
7C2×#13063299C2211yescharacteristic
8#14582956—24no—
9C2×C4⋊(C43⋊C8)—21no—
10C2×C22⋊(C43⋊C8)C2212yes—
11C2×#13063236—21no—
12#14582801C411yescharacteristic, complemented
13#14582801C411yescharacteristic, complemented
14#14582797C411yescharacteristic, complemented
15#14582797C411yescharacteristic, complemented
16#14582790—21no—
17#14582790—21no—
18#14582778—21no—
19#14582759C2211yescharacteristic
20#14582632—24no—
21C22×C42×C43C2211yescharacteristic
22C2×#95×C43—21no—
23C2×#95×C43—21no—
24C2×#95×C43C2212yes—
25C22×D172C2×C411yescharacteristic
26C22×C22⋊D43—21no—
27C22×C43⋊C8—22no—
28#13063308—44no—
29#13063299—22no—
30#13063299—22no—
31C2×C4⋊Dic43C2×C411yescharacteristic
32C2×C4⋊Dic43C2×C411yescharacteristic
33C2×C4⋊Dic43C2×C411yescharacteristic
34C2×Dic43⋊C4—21no—
35C2×Dic43⋊C4—21no—
36C2×C22⋊Dic43—21no—
37C2×(C2×D43)⋊C4—21no—
38C2×(C2×D43)⋊C4—21no—
39C2×(C2×D43)⋊C4—21no—
40C2×(C2×D43)⋊C4—21no—
41C2×(C2×D43)⋊C4—21no—
42C4⋊(C43⋊C8)—24no—
43C22⋊(C43⋊C8)—22no—
44C22⋊(C43⋊C8)D414yes—
45#13063236—24no—
46C43⋊#95—21no—
47C43⋊#95—21no—
48C43⋊#95—21no—
49C23×C4×C43—22no—
50C23×C4×C43D411yescharacteristic
51C23×C4×C43D411yescharacteristic
52C23×C4×C43C2311yescharacteristic
53C2×C42×C43—22no—
54C2×C42×C43—22no—
55C2×C42×C43C2×C411yescharacteristic
56C2×C42×C43C2×C411yescharacteristic
57C2×C42×C43D411yescharacteristic
58C2×C42×C43D411yescharacteristic
59#95×C43—24no—
60#95×C43—22no—
61#95×C43—22no—
62#95×C43—42no—
63C24×C43C2×D411yescharacteristic
64C23×D43—21no—
65C22×C4×C43—22no—
66C22×C4×C43—24no—
67C22×C4×C43—22no—
68C22×C4×C43—22no—
69C22×C4×C43—21no—
70C22×C4×C43—22no—
71C22×C4×C43—21no—
72C22×C4×C43—41no—
73C22×C4×C43—41no—
74C22×C4×C43—41no—
75C22×C4×C43—42no—
76C22×C4×C43—42no—
77C22×C4×C43—42no—
78C22×C4×C43—42no—
79C22×C4×C43—42no—
80C22×C4×C43—42no—
81C22×C4×C43C22⋊C411yescharacteristic
82C22×C4×C43C22⋊C411yescharacteristic
83C22×C4×C43C22⋊C411yescharacteristic
84C22×C4×C43C22⋊C411yescharacteristic
85C22×C4×C43C22×C411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D412yes—
88C22×C4×C43#4112yes—
89C2×C22⋊D43—42no—
90C2×C22⋊D43—42no—
91C2×C22⋊D43—41no—
92C2×C22⋊D43—41no—
93C22×Dic43—21no—
94C22×Dic43—21no—
95C22×Dic43—21no—
96C2×D172—22no—
97C2×D172—41no—
98C2×D172—41no—
99C42×C43—22no—
100C42×C43—22no—
101C42×C43—21no—
102C42×C43—21no—
103C42×C43—21no—
104C42×C43—21no—
105C22⋊Dic43—42no—
106(C2×D43)⋊C4—42no—
107(C2×D43)⋊C4—42no—
108(C2×D43)⋊C4—42no—
109(C2×D43)⋊C4—42no—
110(C2×D43)⋊C4—41no—
111(C2×D43)⋊C4—41no—
112C4⋊Dic43—22no—
113C4⋊Dic43—41no—
114C4⋊Dic43—41no—
115Dic43⋊C4—42no—
116Dic43⋊C4—42no—
117C2×C43⋊C8—24no—
118C2×C43⋊C8—42no—
119C2×C43⋊C8—42no—
120C23×C43—21no—
121C23×C43—21no—
122C23×C43—21no—
123C23×C43—21no—
124C23×C43C2×C22⋊C411yescharacteristic
125C23×C43#12112yes—
126C23×C43AGL(1,ℤ/8)12yes—
127C23×C43AGL(1,ℤ/8)11yescharacteristic
128C23×C43#13711yescharacteristic
129C22×D43—41no—
130C22×D43—41no—
131C22×D43—41no—
132C22×D43—41no—
133C22×D43—41no—
134C22×D43—41no—
135C22×D43—41no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—21no—
145C2×C4×C43—21no—
146C2×C4×C43—21no—
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43—21no—
150C2×C4×C43—21no—
151C2×C4×C43—42no—
152C2×C4×C43—42no—
153C2×C4×C43—44no—
154C2×C4×C43—42no—
155C2×C4×C43—42no—
156C2×C4×C43—44no—
157C2×C4×C43—44no—
158C2×C4×C43—44no—
159C2×C4×C43—82no—
160C2×C4×C43—82no—
161C2×C4×C43—82no—
162C2×C4×C43—82no—
163C2×C4×C43#10412yes—
164C2×C4×C43C4×D412yes—
165C2×C4×C43#12011yescharacteristic
166C2×C4×C43#12311yescharacteristic
167C22⋊D43—82no—
168C22⋊D43—82no—
169C2×Dic43—41no—
170C2×Dic43—41no—
171C2×Dic43—41no—
172C2×Dic43—41no—
173C2×Dic43—41no—
174C2×Dic43—41no—
175C2×Dic43—41no—
176C2×Dic43—41no—
177C2×Dic43—41no—
178D172—82no—
179C43⋊C8—44no—
180#9118—431nomaximal, Sylow
181C22×C43—22no—
182C22×C43—22no—
183C22×C43—22no—
184C22×C43—21no—
185C22×C43—21no—
186C22×C43—21no—
187C22×C43—21no—
188C22×C43—22no—
189C22×C43#38611yescharacteristic
190C22×C43#41011yescharacteristic
191C22×C43#41011yescharacteristic
192C22×C43#41711yescharacteristic
193C22×C43#41811yescharacteristic
194C22×C43C2×#10411yescharacteristic
195C22×C43#42111yescharacteristic
196C22×C43#46812yes—
197C22×C43#46912yes—
198C2×D43—81no—
199C2×D43—81no—
200C2×D43—81no—
201C2×D43—81no—
202C2×D43—81no—
203C2×D43—81no—
204C2×D43—81no—
205C4×C43—22no—
206C4×C43—21no—
207C4×C43—22no—
208C4×C43—21no—
209C4×C43—41no—
210C4×C43—41no—
211C4×C43—41no—
212C4×C43—84no—
213Dic43—81no—
214Dic43—81no—
215Dic43—81no—
216C2×#432—431no—
217#2854—431no—
218C2×#327—432no—
219#1434D4311yescharacteristic, complemented
220#1294—432no—
221C2×C43—22no—
222C2×C43—22no—
223C2×C43#150511yescharacteristic
224C2×C43#150911yescharacteristic
225C2×C43#151211yescharacteristic
226C2×C43#151411yescharacteristic
227C2×C43#187111yescharacteristic
228C2×C43#189511yescharacteristic
229C2×C43#189911yescharacteristic
230D43—161no—
231C2×#123—861no—
232C2×#121—431no—
233C22×C42C2×D4311yescharacteristic
234#432—864no—
235C2×C4⋊C8—861no—
236C2×C22⋊C8—432no—
237C2×#97—861no—
238#390—431no—
239#390—431no—
240#389—431no—
241#389—431no—
242#388—861no—
243#388—861no—
244#386—861no—
245#380—431no—
246C2×#95—21no—
247C2×#95—21no—
248C2×#95C2×D4312yes—
249#327—864no—
250C43#911811yescharacteristic, complemented, Sylow
251C22×D4—431no—
252C22×D4—861no—
253C23×C4—22no—
254C23×C4C22⋊D4311yescharacteristic
255C23×C4C22⋊D4311yescharacteristic
256C23×C4C22×D4311yescharacteristic
257C22×C8—862no—
258#123—1724no—
259#121—862no—
260#121—862no—
261C2×C4⋊C4—431no—
262C2×C4⋊C4—431no—
263C2×C4⋊C4—431no—
264C2×C4⋊C4—861no—
265C2×C4⋊C4—861no—
266C2×C22⋊C4—861no—
267C2×C22⋊C4—861no—
268C2×C22⋊C4—861no—
269C2×C22⋊C4—861no—
270C2×C22⋊C4—861no—
271C2×C22⋊C4—861no—
272C2×C42—22no—
273C2×C42—22no—
274C2×C42C4×D4311yescharacteristic
275C2×C42C4×D4311yescharacteristic
276C2×C42D17211yescharacteristic
277C2×C42D17211yescharacteristic
278C4⋊C8—864no—
279C22⋊C8—434no—
280C22⋊C8—862no—
281#97—864no—
282#95—24no—
283#95—22no—
284#95—22no—
285#95—42no—
286#95—861no—
287#95—861no—
288#95—861no—
289C24—861no—
290C24C2×C22⋊D4311yescharacteristic
291C2×D4—862no—
292C2×D4—1721no—
293C2×D4—1721no—
294C2×D4—1722no—
295C2×D4—1722no—
296C2×D4—1721no—
297C2×D4—1721no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—22no—
304C22×C4—24no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—861no—
315C22×C4—861no—
316C22×C4—861no—
317C22×C4(C2×D43)⋊C411yescharacteristic
318C22×C4(C2×D43)⋊C411yescharacteristic
319C22×C4(C2×D43)⋊C411yescharacteristic
320C22×C4(C2×D43)⋊C411yescharacteristic
321C22×C4C2×C4×D4311yescharacteristic
322C22×C4C2×D17211yescharacteristic
323C22×C4D4×D4312yes—
324C22×C4#1062190012yes—
325C2×C8—864no—
326C2×C8—1722no—
327C2×C8—1722no—
328C4⋊C4—862no—
329C4⋊C4—1721no—
330C4⋊C4—1721no—
331C4⋊C4—1722no—
332C4⋊C4—1722no—
333C22⋊C4—1722no—
334C22⋊C4—1722no—
335C22⋊C4—1722no—
336C22⋊C4—1722no—
337C22⋊C4—1722no—
338C22⋊C4—1721no—
339C22⋊C4—1721no—
340C42—22no—
341C42—22no—
342C42—21no—
343C42—21no—
344C42—21no—
345C42—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—1721no—
351C23—1721no—
352C23—1721no—
353C23—1721no—
354C23—1721no—
355C23—1721no—
356C23—1721no—
357C23C2×(C2×D43)⋊C411yescharacteristic
358C23#1306329712yes—
359C23#1306335012yes—
360C23#1306335111yescharacteristic
361C23#1306335611yescharacteristic
362D4—3442no—
363D4—3442no—
364D4—3442no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—44no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—44no—
386C2×C4—44no—
387C2×C4—44no—
388C2×C4—82no—
389C2×C4—82no—
390C2×C4—82no—
391C2×C4—82no—
392C2×C4—1721no—
393C2×C4—1721no—
394C2×C4—1721no—
395C2×C4—1721no—
396C2×C4—1721no—
397C2×C4—1721no—
398C2×C4—1721no—
399C2×C4—1721no—
400C2×C4—1721no—
401C2×C4#1306325312yes—
402C2×C4(C22⋊D43)⋊C412yes—
403C2×C4#1306329511yescharacteristic
404C2×C4#1306330911yescharacteristic
405C8—1724no—
406C22—22no—
407C22—22no—
408C22—22no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—22no—
414C22—3441no—
415C22—3441no—
416C22—3441no—
417C22—3441no—
418C22—3441no—
419C22—3441no—
420C22—3441no—
421C22#1458277611yescharacteristic
422C22#1458287211yescharacteristic
423C22#1458287211yescharacteristic
424C22#1458289811yescharacteristic
425C22#1458290311yescharacteristic
426C22C2×#1306325311yescharacteristic
427C22#1458291711yescharacteristic
428C22#1458314712yes—
429C22#1458315012yes—
430C4—21no—
431C4—22no—
432C4—21no—
433C4—22no—
434C4—41no—
435C4—41no—
436C4—41no—
437C4—84no—
438C4—3441no—
439C4—3441no—
440C4—3441no—
441C2—22no—
442C2—22no—
443C2—6881no—
444C2#1913310211yescharacteristic
445C2#1913311811yescharacteristic
446C2#1913313111yescharacteristic
447C2#1913314111yescharacteristic
448C2#1913489511yescharacteristic
449C2#1913503111yescharacteristic
450C2#1913505111yescharacteristic
subgroupG/H
centerC23C2×(C2×D43)⋊C4
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1434C2
socleC23×C43C2×C22⋊C4
prime radicalC2×#13063299C22
cosocleC23×C4×C43C23
hypercenter#1434D43
hypocenterC43#9118
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1434

Complements

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

NH ≅ G/Ntype
1. C2×#14582956C2semidirect
4. #19132474C2semidirect
5. C43×#1434C2semidirect
12. #14582801C4semidirect
13. #14582801C4semidirect
14. #14582797C4semidirect
15. #14582797C4semidirect
219. #1434D43semidirect
250. C43#9118semidirect

Maximal subgroups

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

subgroupindex
C2×#145829562
#191429262
C2×#145826322
#191324742
C43×#14342
#911843