Finite Group Databasebeta

← #24992376

Subgroups — #24992376

Order 11008.

692 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142927C211yesmaximal, characteristic
2C2×#14582763C211yesmaximal, 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×Dic43C2211yescharacteristic
12C2×C22⋊(C43⋊C8)C2211yescharacteristic
13#14582800C412yescomplemented
14#14582798C412yescomplemented
15#14582791—22no—
16#14582776—21no—
17#14582763—22no—
18#14582763—22no—
19C2×C43⋊#95—21no—
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—24no—
42C2×Dic43⋊C4—42no—
43C2×Dic43⋊C4—42no—
44C2×(C2×D43)⋊C4—21no—
45C2×(C2×D43)⋊C4—22no—
46C2×(C2×D43)⋊C4—22no—
47C2×C4×Dic43—21no—
48C2×C4×Dic43—21no—
49C2×C4×Dic43—21no—
50C2×C4×Dic43—21no—
51C2×C4×Dic43C2×C412yes—
52C2×C4×Dic43D412yes—
53C22⋊(C43⋊C8)—21no—
54C22⋊(C43⋊C8)—21no—
55C43⋊#95—24no—
56C43⋊#95—21no—
57C43⋊#95—22no—
58C43⋊#95D412yes—
59C23×C4×C43—21no—
60C23×C4×C43C2311yescharacteristic
61C22×C8×C43—21no—
62C2×C4⋊C4×C43C2×C412yes—
63C2×C22⋊C4×C43—21no—
64C22⋊C8×C43—21no—
65C22⋊C8×C43—21no—
66#95×C43—21no—
67#95×C43—21no—
68#95×C43D412yes—
69C24×C43C2×D411yescharacteristic
70C23×D43—21no—
71C22×C4×C43—22no—
72C22×C4×C43—22no—
73C22×C4×C43—42no—
74C22×C4×C43—42no—
75C22×C4×C43—42no—
76C22×C4×C43—41no—
77C22×C4×C43—41no—
78C22×C4×C43C22×C411yescharacteristic
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43#4111yescharacteristic
83C22×C4×C43#4111yescharacteristic
84C2×C22⋊D43—41no—
85C2×C22⋊D43—41no—
86C2×C22⋊D43—41no—
87C2×C22⋊D43—41no—
88C2×C22⋊D43—41no—
89C2×C22⋊D43—41no—
90C22×Dic43—21no—
91C22×Dic43—21no—
92C22×Dic43—21no—
93C22×Dic43—22no—
94C22×Dic43—21no—
95C22×Dic43—21no—
96C22×Dic43—21no—
97C22×Dic43—21no—
98C22×Dic43—42no—
99C22×Dic43—42no—
100C22×Dic43—42no—
101C22×Dic43—41no—
102C22×Dic43—41no—
103C22×Dic43C22⋊C412yes—
104C22×Dic43C22⋊C412yes—
105C22×Dic43D812yes—
106C22×Dic43SD1612yes—
107C2×D172—21no—
108C2×D172—21no—
109C2×D172—42no—
110C2×C8×C43—42no—
111C2×C8×C43—41no—
112C4⋊C4×C43—42no—
113C22⋊C4×C43—41no—
114C22⋊C4×C43—41no—
115(C2×D43)⋊C4—44no—
116(C2×D43)⋊C4—41no—
117(C2×D43)⋊C4—41no—
118(C2×D43)⋊C4—44no—
119C4⋊Dic43—21no—
120C4⋊Dic43—21no—
121C4⋊Dic43—44no—
122Dic43⋊C4—48no—
123C4×Dic43—22no—
124C4×Dic43—22no—
125C4×Dic43—22no—
126C4×Dic43—22no—
127C2×C43⋊C8—42no—
128C2×C43⋊C8—41no—
129C23×C43—22no—
130C23×C43—22no—
131C23×C43C2×C22⋊C411yescharacteristic
132C23×C43#12011yescharacteristic
133C23×C43#12311yescharacteristic
134C23×C43C2×D811yescharacteristic
135C23×C43C2×SD1611yescharacteristic
136C23×C43AGL(1,ℤ/8)11yescharacteristic
137C23×C43#13711yescharacteristic
138C22×D43—41no—
139C22×D43—42no—
140C22×D43—41no—
141C22×D43—41no—
142C22×D43—42no—
143C2×C4×C43—22no—
144C2×C4×C43—22no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—42no—
150C2×C4×C43—42no—
151C2×C4×C43—42no—
152C2×C4×C43—42no—
153C2×C4×C43—42no—
154C2×C4×C43—42no—
155C2×C4×C43—82no—
156C2×C4×C43—82no—
157C2×C4×C43C4×D411yescharacteristic
158C2×C4×C43C4×D411yescharacteristic
159C2×C4×C43#12111yescharacteristic
160C2×C4×C43#12111yescharacteristic
161C22⋊D43—81no—
162C22⋊D43—81no—
163C22⋊D43—81no—
164C22⋊D43—81no—
165C2×Dic43—22no—
166C2×Dic43—22no—
167C2×Dic43—22no—
168C2×Dic43—22no—
169C2×Dic43—22no—
170C2×Dic43—22no—
171C2×Dic43—22no—
172C2×Dic43—22no—
173C2×Dic43—22no—
174C2×Dic43—42no—
175C2×Dic43—42no—
176C2×Dic43—42no—
177C2×Dic43—42no—
178C2×Dic43—41no—
179C2×Dic43—41no—
180C2×Dic43—41no—
181C2×Dic43—42no—
182C2×Dic43—82no—
183C2×Dic43—82no—
184C2×Dic43#10214yes—
185D172—81no—
186D172—81no—
187C8×C43—81no—
188C43⋊C8—81no—
189#9156—431nomaximal, Sylow
190C22×C43—21no—
191C22×C43—21no—
192C22×C43—21no—
193C22×C43—21no—
194C22×C43—22no—
195C22×C43—22no—
196C22×C43—22no—
197C22×C43—22no—
198C22×C43#38611yescharacteristic
199C22×C43#41012yes—
200C22×C43C2×#10211yescharacteristic
201C22×C43#41711yescharacteristic
202C22×C43#42112yes—
203C22×C43#44711yescharacteristic
204C22×C43#44811yescharacteristic
205C22×C43#48011yescharacteristic
206C22×C43#48111yescharacteristic
207C2×D43—81no—
208C2×D43—81no—
209C2×D43—81no—
210C2×D43—82no—
211C2×D43—82no—
212C4×C43—21no—
213C4×C43—21no—
214C4×C43—21no—
215C4×C43—21no—
216C4×C43—82no—
217C4×C43—82no—
218Dic43—24no—
219Dic43—42no—
220Dic43—82no—
221Dic43—81no—
222#2854—431no—
223C2×#382—431no—
224#1817—431no—
225C2×#327—431no—
226C2×#327—431no—
227#1294—431no—
228#1294D4311yescharacteristic, complemented
229C2×C43—21no—
230C2×C43—21no—
231C2×C43—21no—
232C2×C43—21no—
233C2×C43#151212yes—
234C2×C43#151712yes—
235C2×C43#187411yescharacteristic
236C2×C43#189711yescharacteristic
237C2×C43#189911yescharacteristic
238D43—161no—
239C2×#123—861no—
240C2×#121—431no—
241C22×C4⋊C4—861no—
242C22×C42—431no—
243C2×C22⋊C8—431no—
244C2×C22⋊C8C2×D4311yescharacteristic
245#390—432no—
246#389—432no—
247#388—862no—
248#386—861no—
249#382—862no—
250#382—862no—
251#380C2×D4311yescharacteristic
252C2×#95—431no—
253C2×#95—861no—
254C2×#95C2×D4311yescharacteristic
255#336—862no—
256#327—862no—
257#327—862no—
258C43#915611yescharacteristic, complemented, Sylow
259C22×D4—431no—
260C22×D4—861no—
261C23×C4—21no—
262C23×C4—431no—
263C23×C4—431no—
264C23×C4—861no—
265C23×C4C22×D4311yescharacteristic
266C22×C8—21no—
267C22×C8—861no—
268#123—1722no—
269#123—1722no—
270#121—861no—
271#121—861no—
272#121—861no—
273#121—861no—
274C2×C4⋊C4—431no—
275C2×C4⋊C4—862no—
276C2×C4⋊C4—864no—
277C2×C4⋊C4—1722no—
278C2×C4⋊C4—1722no—
279C2×C4⋊C4C4×D4312yes—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—862no—
282C2×C22⋊C4—862no—
283C2×C22⋊C4—861no—
284C2×C42—432no—
285C2×C42—432no—
286C2×C42—861no—
287C2×C42—861no—
288C2×C42—861no—
289C2×C42—861no—
290C22⋊C8—21no—
291C22⋊C8—21no—
292C22⋊C8—861no—
293C22⋊C8—861no—
294#95—21no—
295#95—21no—
296#95—432no—
297#95—862no—
298#95—864no—
299#95—861no—
300#95D17212yes—
301C24—861no—
302C24D4×D4311yescharacteristic
303C2×D4—861no—
304C2×D4—861no—
305C2×D4—1722no—
306C2×D4—1721no—
307C2×D4—1721no—
308C2×D4—1721no—
309C2×D4—1721no—
310C2×D4—1721no—
311C2×D4—1721no—
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—432no—
320C22×C4—432no—
321C22×C4—432no—
322C22×C4—432no—
323C22×C4—861no—
324C22×C4—861no—
325C22×C4—861no—
326C22×C4—861no—
327C22×C4—861no—
328C22×C4—861no—
329C22×C4—861no—
330C22×C4—862no—
331C22×C4—1722no—
332C22×C4—1722no—
333C22×C4—1722no—
334C22×C4—1721no—
335C22×C4—1721no—
336C22×C4C2×C4×D4311yescharacteristic
337C22×C4C2×D17211yescharacteristic
338C22×C4#1062189811yescharacteristic
339C22×C4D4×D4311yescharacteristic
340C22×C4D4×D4311yescharacteristic
341C22×C4#1062190211yescharacteristic
342C2×C8—42no—
343C2×C8—41no—
344C2×C8—1722no—
345C2×C8—1721no—
346C4⋊C4—42no—
347C4⋊C4—861no—
348C4⋊C4—861no—
349C4⋊C4—1724no—
350C4⋊C4—1728no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—1724no—
354C22⋊C4—1724no—
355C22⋊C4—1721no—
356C22⋊C4—1721no—
357C42—862no—
358C42—862no—
359C42—862no—
360C42—862no—
361C23—22no—
362C23—22no—
363C23—1722no—
364C23—1721no—
365C23—1721no—
366C23—1722no—
367C23—1721no—
368C23C22⋊C4×D4311yescharacteristic
369C23#1306329511yescharacteristic
370C23#1306331011yescharacteristic
371C23D8×D4311yescharacteristic
372C23SD16×D4311yescharacteristic
373C23#1306335211yescharacteristic
374C23#1306335711yescharacteristic
375D4—3441no—
376D4—3441no—
377D4—3441no—
378D4—3441no—
379D4—3441no—
380D4—3441no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—82no—
394C2×C4—82no—
395C2×C4—434no—
396C2×C4—862no—
397C2×C4—862no—
398C2×C4—862no—
399C2×C4—862no—
400C2×C4—862no—
401C2×C4—862no—
402C2×C4—862no—
403C2×C4—862no—
404C2×C4—862no—
405C2×C4—3442no—
406C2×C4—3442no—
407C2×C4—1722no—
408C2×C4—1722no—
409C2×C4—1721no—
410C2×C4—1721no—
411C2×C4—1721no—
412C2×C4—1722no—
413C2×C4—1722no—
414C2×C4—1722no—
415C2×C4#1306328711yescharacteristic
416C2×C4C4×D17211yescharacteristic
417C2×C4#1306329811yescharacteristic
418C2×C4#1306330011yescharacteristic
419C8—81no—
420C8—3441no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—22no—
426C22—22no—
427C22—22no—
428C22—22no—
429C22—3441no—
430C22—3441no—
431C22—3441no—
432C22—3442no—
433C22—3442no—
434C22#1458277711yescharacteristic
435C22#1458287112yes—
436C22#102×D4311yescharacteristic
437C22#1458289911yescharacteristic
438C22#1458291412yes—
439C22#1458303411yescharacteristic
440C22#1458303911yescharacteristic
441C22#1458321411yescharacteristic
442C22#1458321911yescharacteristic
443C4—21no—
444C4—21no—
445C4—21no—
446C4—21no—
447C4—82no—
448C4—82no—
449C4—864no—
450C4—3442no—
451C4—3441no—
452C4—1722no—
453C2—21no—
454C2—21no—
455C2—21no—
456C2—21no—
457C2—6881no—
458C2#1913313212yes—
459C2#1913315312yes—
460C2#1913491111yescharacteristic
461C2#1913504211yescharacteristic
462C2#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#9156
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×#14582763C2semidirect
3. #19134661C2semidirect
6. #19132473C2semidirect
7. C43×#1294C2semidirect
13. #14582800C4semidirect
14. #14582798C4semidirect
228. #1294D43semidirect
258. C43#9156semidirect

Maximal subgroups

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

subgroupindex
#191429272
C2×#145827632
#191346612
C2×#145826342
C2×#145826322
#191324732
C43×#12942
#915643