Finite Group Databasebeta

← #24992336

Subgroups — #24992336

Order 11008.

800 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142927C211yesmaximal, characteristic
2C2×#14582750C211yesmaximal, characteristic, complemented
3#19134661C211yesmaximal, characteristic, complemented
4C2×#14582634C211yesmaximal, characteristic
5C2×#14582632C211yesmaximal, characteristic
6#19132473C211yesmaximal, characteristic, complemented
7C43×#1294C211yesmaximal, characteristic, complemented
8C2×#13063309—21no—
9C2×#13063299C2211yescharacteristic
10C22×Dic43⋊C4—21no—
11C22×C4×Dic43—21no—
12C22×C4×Dic43C2211yescharacteristic
13C2×C22⋊(C43⋊C8)C2211yescharacteristic
14#14582800C412yescomplemented
15#14582798C412yescomplemented
16#14582791—22no—
17#14582776—21no—
18#14582750—22no—
19#14582750—22no—
20C2×C43⋊#95C2211yescharacteristic
21#14582653—22no—
22#14582634—22no—
23#14582632—22no—
24C2×C22⋊C8×C43C2211yescharacteristic
25C43×#380C2211yescharacteristic
26C2×#95×C43C2211yescharacteristic
27C22×D172C2×C411yescharacteristic
28C22×C22⋊D43—21no—
29C23×Dic43—21no—
30C23×Dic43D411yescharacteristic
31C23×Dic43D411yescharacteristic
32C22×C43⋊C8—21no—
33#13063309—42no—
34#13063309—42no—
35#13063299—21no—
36#13063299—21no—
37#13063299—21no—
38#13063299—21no—
39C2×C4⋊Dic43—22no—
40C2×C4⋊Dic43C2×C411yescharacteristic
41C2×Dic43⋊C4—28no—
42C2×Dic43⋊C4—24no—
43C2×(C2×D43)⋊C4—21no—
44C2×(C2×D43)⋊C4—22no—
45C2×(C2×D43)⋊C4—22no—
46C2×C4×Dic43—21no—
47C2×C4×Dic43—21no—
48C2×C4×Dic43—21no—
49C2×C4×Dic43—21no—
50C2×C4×Dic43—24no—
51C2×C4×Dic43—42no—
52C2×C4×Dic43—42no—
53C2×C4×Dic43C2×C412yes—
54C2×C4×Dic43D412yes—
55C22⋊(C43⋊C8)—21no—
56C22⋊(C43⋊C8)—21no—
57C43⋊#95—21no—
58C43⋊#95—22no—
59C43⋊#95D412yes—
60C23×C4×C43—21no—
61C23×C4×C43C2311yescharacteristic
62C22×C8×C43—21no—
63C2×C4⋊C4×C43C2×C412yes—
64C2×C22⋊C4×C43—21no—
65C22⋊C8×C43—21no—
66C22⋊C8×C43—21no—
67#95×C43—21no—
68#95×C43—21no—
69#95×C43D412yes—
70C24×C43C2×D411yescharacteristic
71C23×D43—21no—
72C22×C4×C43—24no—
73C22×C4×C43—22no—
74C22×C4×C43—22no—
75C22×C4×C43—42no—
76C22×C4×C43—42no—
77C22×C4×C43—41no—
78C22×C4×C43—41no—
79C22×C4×C43C22×C411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43C2×D411yescharacteristic
83C22×C4×C43#4111yescharacteristic
84C22×C4×C43#4111yescharacteristic
85C2×C22⋊D43—41no—
86C2×C22⋊D43—41no—
87C2×C22⋊D43—41no—
88C2×C22⋊D43—41no—
89C2×C22⋊D43—41no—
90C2×C22⋊D43—41no—
91C22×Dic43—24no—
92C22×Dic43—24no—
93C22×Dic43—21no—
94C22×Dic43—21no—
95C22×Dic43—21no—
96C22×Dic43—22no—
97C22×Dic43—21no—
98C22×Dic43—21no—
99C22×Dic43—21no—
100C22×Dic43—21no—
101C22×Dic43—42no—
102C22×Dic43—41no—
103C22×Dic43—41no—
104C22×Dic43C22⋊C412yes—
105C22×Dic43C22⋊C412yes—
106C22×Dic43D812yes—
107C22×Dic43SD1612yes—
108C2×D172—21no—
109C2×D172—21no—
110C2×D172—42no—
111C2×C8×C43—42no—
112C2×C8×C43—41no—
113C4⋊C4×C43—42no—
114C22⋊C4×C43—41no—
115C22⋊C4×C43—41no—
116(C2×D43)⋊C4—41no—
117(C2×D43)⋊C4—41no—
118(C2×D43)⋊C4—44no—
119(C2×D43)⋊C4—44no—
120C4⋊Dic43—21no—
121C4⋊Dic43—21no—
122C4⋊Dic43—44no—
123Dic43⋊C4—216no—
124C4×Dic43—22no—
125C4×Dic43—22no—
126C4×Dic43—22no—
127C4×Dic43—22no—
128C4×Dic43—48no—
129C2×C43⋊C8—42no—
130C2×C43⋊C8—41no—
131C23×C43—22no—
132C23×C43—22no—
133C23×C43C2×C22⋊C411yescharacteristic
134C23×C43#12011yescharacteristic
135C23×C43#12311yescharacteristic
136C23×C43C2×D811yescharacteristic
137C23×C43C2×SD1611yescharacteristic
138C23×C43AGL(1,ℤ/8)11yescharacteristic
139C23×C43#13711yescharacteristic
140C22×D43—41no—
141C22×D43—42no—
142C22×D43—41no—
143C22×D43—41no—
144C22×D43—42no—
145C2×C4×C43—22no—
146C2×C4×C43—22no—
147C2×C4×C43—24no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—42no—
153C2×C4×C43—44no—
154C2×C4×C43—44no—
155C2×C4×C43—42no—
156C2×C4×C43—42no—
157C2×C4×C43—42no—
158C2×C4×C43—42no—
159C2×C4×C43C4×D411yescharacteristic
160C2×C4×C43C4×D411yescharacteristic
161C2×C4×C43#12111yescharacteristic
162C2×C4×C43#12111yescharacteristic
163C22⋊D43—81no—
164C22⋊D43—81no—
165C22⋊D43—81no—
166C22⋊D43—81no—
167C2×Dic43—24no—
168C2×Dic43—24no—
169C2×Dic43—22no—
170C2×Dic43—22no—
171C2×Dic43—22no—
172C2×Dic43—22no—
173C2×Dic43—22no—
174C2×Dic43—22no—
175C2×Dic43—22no—
176C2×Dic43—22no—
177C2×Dic43—24no—
178C2×Dic43—42no—
179C2×Dic43—44no—
180C2×Dic43—44no—
181C2×Dic43—42no—
182C2×Dic43—41no—
183C2×Dic43—41no—
184C2×Dic43—41no—
185C2×Dic43#10214yes—
186C2×Dic43#10414yes—
187D172—81no—
188D172—81no—
189C8×C43—81no—
190C43⋊C8—81no—
191#9148—431nomaximal, Sylow
192C22×C43—21no—
193C22×C43—21no—
194C22×C43—21no—
195C22×C43—21no—
196C22×C43—22no—
197C22×C43—22no—
198C22×C43—22no—
199C22×C43—22no—
200C22×C43#38611yescharacteristic
201C22×C43#41012yes—
202C22×C43C2×#10211yescharacteristic
203C22×C43#41711yescharacteristic
204C22×C43C2×#10412yes—
205C22×C43#44711yescharacteristic
206C22×C43#44811yescharacteristic
207C22×C43#48011yescharacteristic
208C22×C43#48111yescharacteristic
209C2×D43—81no—
210C2×D43—81no—
211C2×D43—81no—
212C2×D43—82no—
213C2×D43—82no—
214C4×C43—21no—
215C4×C43—21no—
216C4×C43—21no—
217C4×C43—21no—
218C4×C43—44no—
219C4×C43—82no—
220Dic43—24no—
221Dic43—24no—
222Dic43—44no—
223Dic43—81no—
224#2854—431no—
225C2×C4×C4⋊C4—431no—
226#1817—431no—
227C2×#327—431no—
228C2×#327—431no—
229#1294—431no—
230#1294D4311yescharacteristic, complemented
231C2×C43—21no—
232C2×C43—21no—
233C2×C43—21no—
234C2×C43—21no—
235C2×C43#150212yes—
236C2×C43#150912yes—
237C2×C43#187411yescharacteristic
238C2×C43#189611yescharacteristic
239C2×C43#189911yescharacteristic
240D43—161no—
241C2×#123—861no—
242C2×#121—431no—
243C22×C4⋊C4—861no—
244C22×C42—431no—
245C22×C42—861no—
246C2×C22⋊C8—431no—
247C2×C22⋊C8C2×D4311yescharacteristic
248#390—432no—
249#389—432no—
250#388—862no—
251#386—861no—
252#380C2×D4311yescharacteristic
253C4×C4⋊C4—862no—
254C4×C4⋊C4—862no—
255C2×#95—431no—
256C2×#95C2×D4311yescharacteristic
257#336—862no—
258#327—862no—
259#327—862no—
260C43#914811yescharacteristic, complemented, Sylow
261C22×D4—431no—
262C22×D4—861no—
263C23×C4—21no—
264C23×C4—431no—
265C23×C4—431no—
266C23×C4—861no—
267C23×C4C22×D4311yescharacteristic
268C22×C8—21no—
269C22×C8—861no—
270#123—1722no—
271#123—1722no—
272#121—861no—
273#121—861no—
274#121—861no—
275#121—861no—
276C2×C4⋊C4—431no—
277C2×C4⋊C4—868no—
278C2×C4⋊C4—864no—
279C2×C4⋊C4—862no—
280C2×C4⋊C4C4×D4312yes—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—862no—
283C2×C22⋊C4—862no—
284C2×C22⋊C4—861no—
285C2×C42—432no—
286C2×C42—432no—
287C2×C42—861no—
288C2×C42—861no—
289C2×C42—861no—
290C2×C42—861no—
291C2×C42—864no—
292C2×C42—1722no—
293C2×C42—1722no—
294C22⋊C8—21no—
295C22⋊C8—21no—
296C22⋊C8—861no—
297C22⋊C8—861no—
298#95—21no—
299#95—21no—
300#95—432no—
301#95—862no—
302#95—861no—
303#95D17212yes—
304C24—861no—
305C24D4×D4311yescharacteristic
306C2×D4—861no—
307C2×D4—861no—
308C2×D4—1722no—
309C2×D4—1721no—
310C2×D4—1721no—
311C2×D4—1721no—
312C2×D4—1721no—
313C2×D4—1721no—
314C2×D4—1721no—
315C22×C4—24no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—432no—
323C22×C4—432no—
324C22×C4—432no—
325C22×C4—432no—
326C22×C4—864no—
327C22×C4—861no—
328C22×C4—861no—
329C22×C4—861no—
330C22×C4—861no—
331C22×C4—861no—
332C22×C4—861no—
333C22×C4—864no—
334C22×C4—862no—
335C22×C4—861no—
336C22×C4—1722no—
337C22×C4—1721no—
338C22×C4—1721no—
339C22×C4C2×C4×D4311yescharacteristic
340C22×C4C2×D17211yescharacteristic
341C22×C4#1062189811yescharacteristic
342C22×C4D4×D4311yescharacteristic
343C22×C4D4×D4311yescharacteristic
344C22×C4#1062190211yescharacteristic
345C2×C8—42no—
346C2×C8—41no—
347C2×C8—1722no—
348C2×C8—1721no—
349C4⋊C4—42no—
350C4⋊C4—8616no—
351C4⋊C4—861no—
352C4⋊C4—861no—
353C4⋊C4—1724no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—1724no—
357C22⋊C4—1724no—
358C22⋊C4—1721no—
359C22⋊C4—1721no—
360C42—862no—
361C42—862no—
362C42—862no—
363C42—862no—
364C42—1728no—
365C23—22no—
366C23—22no—
367C23—1722no—
368C23—1721no—
369C23—1721no—
370C23—1722no—
371C23—1721no—
372C23C22⋊C4×D4311yescharacteristic
373C23#1306329511yescharacteristic
374C23#1306331011yescharacteristic
375C23D8×D4311yescharacteristic
376C23SD16×D4311yescharacteristic
377C23#1306335211yescharacteristic
378C23#1306335711yescharacteristic
379D4—3441no—
380D4—3441no—
381D4—3441no—
382D4—3441no—
383D4—3441no—
384D4—3441no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—24no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—42no—
393C2×C4—44no—
394C2×C4—44no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—434no—
400C2×C4—434no—
401C2×C4—864no—
402C2×C4—864no—
403C2×C4—862no—
404C2×C4—862no—
405C2×C4—862no—
406C2×C4—862no—
407C2×C4—862no—
408C2×C4—862no—
409C2×C4—862no—
410C2×C4—862no—
411C2×C4—864no—
412C2×C4—1721no—
413C2×C4—1721no—
414C2×C4—1721no—
415C2×C4—1722no—
416C2×C4—1724no—
417C2×C4—1724no—
418C2×C4—1722no—
419C2×C4#1306328711yescharacteristic
420C2×C4C4×D17211yescharacteristic
421C2×C4#1306329811yescharacteristic
422C2×C4#1306330011yescharacteristic
423C8—81no—
424C8—3441no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—22no—
430C22—22no—
431C22—22no—
432C22—22no—
433C22—3441no—
434C22—3441no—
435C22—3442no—
436C22—3442no—
437C22—3441no—
438C22#1458277711yescharacteristic
439C22#1458287112yes—
440C22#102×D4311yescharacteristic
441C22#1458289911yescharacteristic
442C22#104×D4312yes—
443C22#1458303411yescharacteristic
444C22#1458303911yescharacteristic
445C22#1458321411yescharacteristic
446C22#1458321911yescharacteristic
447C4—21no—
448C4—21no—
449C4—21no—
450C4—21no—
451C4—44no—
452C4—82no—
453C4—864no—
454C4—864no—
455C4—3441no—
456C4—1724no—
457C2—21no—
458C2—21no—
459C2—21no—
460C2—21no—
461C2—6881no—
462C2#1913308812yes—
463C2#1913311912yes—
464C2#1913491111yescharacteristic
465C2#1913503711yescharacteristic
466C2#1913505211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1294C2
socleC23×C43C2×C22⋊C4
prime radicalC2×#13063299C22
cosocleC23×C4×C43C23
hypercenter#1294D43
hypocenterC43#9148
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
2. C2×#14582750C2semidirect
3. #19134661C2semidirect
6. #19132473C2semidirect
7. C43×#1294C2semidirect
14. #14582800C4semidirect
15. #14582798C4semidirect
230. #1294D43semidirect
260. C43#9148semidirect

Maximal subgroups

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

subgroupindex
#191429272
C2×#145827502
#191346612
C2×#145826342
C2×#145826322
#191324732
C43×#12942
#914843