Finite Group Databasebeta

← #24998917

Subgroups — #24998917

Order 11008.

644 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583101C211yesmaximal, characteristic
2#19139513C211yesmaximal, characteristic
3#19135557C211yesmaximal, characteristic, complemented
4C2×Q8⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
5C2×#14582626C211yesmaximal, characteristic
6#19132479C211yesmaximal, characteristic, complemented
7C2×C43×#475C211yesmaximal, characteristic, complemented
8C22×#10621884—21no—
9C2×#13063301—21no—
10C2×C4×D172C2211yescharacteristic
11#14583101—22no—
12#14583101—22no—
13C2×C4⋊(C43⋊C8)C2211yescharacteristic
14C2×#13063249—21no—
15C2×C4×C43⋊C8C2211yescharacteristic
16#14582821—22no—
17#14582801—21no—
18#14582797—21no—
19#14582769C2211yescharacteristic
20#14582756—21no—
21#14582661—22no—
22Q8⋊(C43⋊C8)—22no—
23#14582626—22no—
24C2×C4⋊Q8×C43C2211yescharacteristic
25C2×C4×Q8×C43C2211yescharacteristic
26C43×#475—22no—
27C43×#475—22no—
28C2×#106×C43—21no—
29C2×C4⋊C8×C43C2211yescharacteristic
30C2×#103×C43—21no—
31C22×D172D411yescharacteristic
32C22×C4×D43—21no—
33C2×#10621884—24no—
34C2×#10621884—42no—
35C2×#10621884—42no—
36C22×C43⋊C8—21no—
37C22×C43⋊C8—21no—
38#13063301—42no—
39#13063301—42no—
40C4×D172—21no—
41C4×D172—21no—
42C4×D172—21no—
43C4×D172—21no—
44C2×C4⋊Dic43—21no—
45C2×C4⋊Dic43—21no—
46C2×C4⋊Dic43D411yescharacteristic
47C2×C4⋊Dic43D412yes—
48C2×Dic43⋊C4—22no—
49C2×(C2×D43)⋊C4—22no—
50C2×(C2×D43)⋊C4—21no—
51C2×(C2×D43)⋊C4—22no—
52C4⋊(C43⋊C8)—21no—
53C4⋊(C43⋊C8)D412yes—
54#13063249—24no—
55C4×C43⋊C8—21no—
56C4×C43⋊C8—21no—
57C43⋊#95—22no—
58C22×Q8×C43—21no—
59C22×Q8×C43D411yescharacteristic
60C22×C8×C43—21no—
61C4⋊Q8×C43—21no—
62C4⋊Q8×C43—21no—
63C4⋊Q8×C43—21no—
64C4⋊Q8×C43D412yes—
65C4×Q8×C43—21no—
66C4×Q8×C43—21no—
67C4×Q8×C43—21no—
68C4×Q8×C43—21no—
69C2×C4⋊C4×C43—21no—
70C2×C4⋊C4×C43—21no—
71C2×C4⋊C4×C43—21no—
72C2×C4⋊C4×C43D411yescharacteristic
73C2×C42×C43—21no—
74C2×C42×C43C2311yescharacteristic
75#106×C43—24no—
76C4⋊C8×C43—21no—
77C4⋊C8×C43D412yes—
78#103×C43—24no—
79C23×D43—21no—
80C2×Q8×C43—21no—
81C2×Q8×C43—21no—
82C2×Q8×C43—22no—
83C2×Q8×C43—21no—
84C2×Q8×C43—21no—
85C2×Q8×C43—21no—
86C2×Q8×C43—41no—
87C2×Q8×C43—41no—
88C2×Q8×C43—41no—
89C2×Q8×C43—41no—
90C2×Q8×C43—41no—
91C2×Q8×C43SD1612yescomplemented
92C22×C4×C43—21no—
93C22×C4×C43—21no—
94C22×C4×C43—41no—
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43C2×D411yescharacteristic
98C22×Dic43—21no—
99C22×Dic43—22no—
100C2×D172—21no—
101C2×D172—21no—
102C2×D172—21no—
103C2×D172—21no—
104C2×D172—21no—
105C2×D172SD1612yes—
106C2×C4×D43—41no—
107C2×C4×D43—41no—
108C2×C4×D43—41no—
109C2×C4×D43—41no—
110C2×C4×D43—41no—
111C2×C4×D43—41no—
112C2×C8×C43—22no—
113C2×C8×C43—41no—
114C2×C8×C43—41no—
115C4⋊C4×C43—22no—
116C4⋊C4×C43—21no—
117C4⋊C4×C43—22no—
118C4⋊C4×C43—21no—
119C4⋊C4×C43—41no—
120C4⋊C4×C43—41no—
121C4⋊C4×C43—41no—
122C4⋊C4×C43—41no—
123C42×C43—41no—
124C42×C43—41no—
125C42×C43C2×D411yescharacteristic
126C42×C43C2×D411yescharacteristic
127C42×C43C2×D411yescharacteristic
128C42×C43#4111yescharacteristic
129#10621884—48no—
130(C2×D43)⋊C4—44no—
131(C2×D43)⋊C4—41no—
132(C2×D43)⋊C4—41no—
133(C2×D43)⋊C4—82no—
134C4⋊Dic43—21no—
135C4⋊Dic43—21no—
136C4⋊Dic43—41no—
137C4⋊Dic43—41no—
138C4⋊Dic43—41no—
139C4⋊Dic43—41no—
140C4⋊Dic43—42no—
141Dic43⋊C4—44no—
142C2×C43⋊C8—22no—
143C2×C43⋊C8—22no—
144C2×C43⋊C8—41no—
145C2×C43⋊C8—41no—
146C2×C43⋊C8—41no—
147C2×C43⋊C8—41no—
148C23×C43#12011yescharacteristic
149C22×D43—22no—
150C22×D43—41no—
151C22×D43—41no—
152C22×D43—41no—
153C22×D43—41no—
154C22×D43—41no—
155C22×D43—41no—
156Q8×C43—22no—
157Q8×C43—22no—
158Q8×C43—41no—
159Q8×C43—41no—
160Q8×C43—42no—
161Q8×C43—42no—
162Q8×C43—81no—
163Q8×C43—81no—
164C2×C4×C43—21no—
165C2×C4×C43—21no—
166C2×C4×C43—22no—
167C2×C4×C43—41no—
168C2×C4×C43—41no—
169C2×C4×C43—41no—
170C2×C4×C43—42no—
171C2×C4×C43—41no—
172C2×C4×C43—41no—
173C2×C4×C43—81no—
174C2×C4×C43—81no—
175C2×C4×C43#12011yescharacteristic
176C2×C4×C43#12011yescharacteristic
177C2×C4×C43#12111yescharacteristic
178C2×C4×C43#12111yescharacteristic
179C2×C4×C43#12111yescharacteristic
180C2×C4×C43#12711yescharacteristic
181C2×C4×C43C2×SD1611yescharacteristic
182C2×C4×C43C2×SD1611yescharacteristic
183C2×C4×C43#13511yescharacteristic
184C2×C4×C43#13511yescharacteristic
185C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
186C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
187C2×C4×C43#13711yescharacteristic
188C2×C4×C43#13711yescharacteristic
189C2×Dic43—41no—
190C2×Dic43—42no—
191C2×Dic43—41no—
192C2×Dic43—42no—
193C2×Dic43—41no—
194C2×Dic43—42no—
195D172—22no—
196D172—22no—
197D172—41no—
198D172—41no—
199C4×D43—81no—
200C4×D43—81no—
201C4×D43—81no—
202C4×D43—81no—
203C8×C43—42no—
204C43⋊C8—42no—
205C43⋊C8—42no—
206#10232—431nomaximal, Sylow
207C22×C43#39211yescharacteristic
208C22×C43#44811yescharacteristic
209C22×C43#44911yescharacteristic
210C22×C43#45011yescharacteristic
211C22×C43#45211yescharacteristic
212C22×C43#45511yescharacteristic
213C22×C43#45611yescharacteristic
214C2×D43—42no—
215C2×D43—42no—
216C2×D43—42no—
217C2×D43—81no—
218C2×D43—81no—
219C2×D43—81no—
220C2×D43—81no—
221C4×C43—21no—
222C4×C43—21no—
223C4×C43—42no—
224C4×C43—82no—
225C4×C43—81no—
226C4×C43#44811yescharacteristic
227C4×C43#44911yescharacteristic
228C4×C43#45011yescharacteristic
229C4×C43#45211yescharacteristic
230C4×C43#46511yescharacteristic
231C4×C43#46511yescharacteristic
232C4×C43#46811yescharacteristic
233C4×C43#46811yescharacteristic
234Dic43—82no—
235Dic43—81no—
236C2×#475D4311yescharacteristic, complemented
237C2×#461—431no—
238#2538—431no—
239#1990—431no—
240C2×Q8⋊C8—431no—
241C2×D4⋊C8—431no—
242#1296—431no—
243C2×C43#164211yescharacteristic
244C2×C43#164311yescharacteristic
245C2×C43#165011yescharacteristic
246C2×C43#165111yescharacteristic
247C2×C43#200011yescharacteristic
248C2×C43#200011yescharacteristic
249C2×C43#200711yescharacteristic
250D43—82no—
251C22×SD16—861no—
252C2×C4⋊Q8C2×D4311yescharacteristic
253C2×C22⋊Q8—861no—
254C2×C4×Q8C2×D4311yescharacteristic
255C2×C4×D4—431no—
256#475—22no—
257#475—22no—
258#461—862no—
259#461—862no—
260C2×#106—21no—
261C2×C4⋊C8—431no—
262C2×C4⋊C8C2×D4311yescharacteristic
263C2×#103—21no—
264C2×#103—861no—
265C2×C4×C8—431no—
266#396—862no—
267#390—861no—
268#389—861no—
269#384—431no—
270#380—861no—
271#340—862no—
272Q8⋊C8—862no—
273D4⋊C8—862no—
274C43#1023211yescharacteristic, complemented, Sylow
275C22×Q8—21no—
276C22×Q8C22⋊D4311yescharacteristic
277C22×D4—431no—
278C23×C4—861no—
279C2×SD16—864no—
280C2×SD16—1722no—
281C2×SD16—1722no—
282C22×C8—21no—
283C22×C8—861no—
284C22×C8—861no—
285C4⋊Q8—21no—
286C4⋊Q8—21no—
287C4⋊Q8—21no—
288C4⋊Q8C22⋊D4312yes—
289C22⋊Q8—1722no—
290C22⋊Q8—1722no—
291C4×Q8—21no—
292C4×Q8—21no—
293C4×Q8—21no—
294C4×Q8—21no—
295C4×D4—861no—
296C4×D4—861no—
297C4×D4—861no—
298C4×D4—861no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—431no—
303C2×C4⋊C4—432no—
304C2×C4⋊C4—862no—
305C2×C4⋊C4—861no—
306C2×C4⋊C4—861no—
307C2×C4⋊C4C22⋊D4311yescharacteristic
308C2×C22⋊C4—862no—
309C2×C22⋊C4—862no—
310C2×C22⋊C4—861no—
311C2×C42—21no—
312C2×C42C22×D4311yescharacteristic
313#106—24no—
314C4⋊C8—21no—
315C4⋊C8—432no—
316C4⋊C8—861no—
317C4⋊C8C22⋊D4312yes—
318#103—24no—
319#103—864no—
320C4×C8—861no—
321C4×C8—861no—
322#95—862no—
323C24—861no—
324C2×Q8—21no—
325C2×Q8—22no—
326C2×Q8—21no—
327C2×Q8—21no—
328C2×Q8—21no—
329C2×Q8—21no—
330C2×Q8—41no—
331C2×Q8—41no—
332C2×Q8—41no—
333C2×Q8—41no—
334C2×Q8—41no—
335C2×Q8#1062188412yescomplemented
336C2×D4—432no—
337C2×D4—861no—
338C2×D4—861no—
339C2×D4—861no—
340C2×D4—861no—
341C2×D4—861no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—41no—
345C22×C4—861no—
346C22×C4—862no—
347C22×C4—1721no—
348C22×C4—1721no—
349C22×C4—1721no—
350C22×C4—1721no—
351C22×C4—1721no—
352C22×C4—1721no—
353C22×C4D4×D4311yescharacteristic
354C22×C4D4×D4311yescharacteristic
355C22×C4C2×C22⋊D4311yescharacteristic
356SD16—1728no—
357C2×C8—22no—
358C2×C8—41no—
359C2×C8—41no—
360C2×C8—862no—
361C2×C8—862no—
362C2×C8—1721no—
363C2×C8—1721no—
364C2×C8—1721no—
365C2×C8—1721no—
366C4⋊C4—22no—
367C4⋊C4—21no—
368C4⋊C4—22no—
369C4⋊C4—21no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—861no—
375C4⋊C4—861no—
376C4⋊C4—1722no—
377C4⋊C4—1724no—
378C4⋊C4—1721no—
379C4⋊C4—1721no—
380C4⋊C4—1721no—
381C4⋊C4—1721no—
382C22⋊C4—3442no—
383C22⋊C4—1724no—
384C22⋊C4—1721no—
385C22⋊C4—1721no—
386C42—41no—
387C42—41no—
388C42D4×D4311yescharacteristic
389C42#1062190011yescharacteristic
390C42C2×C22⋊D4311yescharacteristic
391C42C2×C22⋊D4311yescharacteristic
392C23—862no—
393C23—1721no—
394C23—1721no—
395C23—1721no—
396C23—1721no—
397C23—1721no—
398C23—1721no—
399C23#1306329311yescharacteristic
400Q8—22no—
401Q8—22no—
402Q8—41no—
403Q8—41no—
404Q8—42no—
405Q8—42no—
406Q8—81no—
407Q8—81no—
408D4—862no—
409D4—862no—
410D4—1721no—
411D4—1721no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—22no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—42no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—81no—
422C2×C4—81no—
423C2×C4—3441no—
424C2×C4—3441no—
425C2×C4—3441no—
426C2×C4—3441no—
427C2×C4—1722no—
428C2×C4—1722no—
429C2×C4—1721no—
430C2×C4—1721no—
431C2×C4—1721no—
432C2×C4—1722no—
433C2×C4#1306329311yescharacteristic
434C2×C4#1306329411yescharacteristic
435C2×C4#1306329611yescharacteristic
436C2×C4#1306329711yescharacteristic
437C2×C4#1306329711yescharacteristic
438C2×C4#1306332111yescharacteristic
439C2×C4SD16×D4311yescharacteristic
440C2×C4C2×#1062188411yescharacteristic
441C2×C4#1306334511yescharacteristic
442C2×C4#1306334611yescharacteristic
443C2×C4#1306335011yescharacteristic
444C2×C4#1306335211yescharacteristic
445C2×C4#1306335411yescharacteristic
446C2×C4#1306335611yescharacteristic
447C8—42no—
448C8—1722no—
449C8—1722no—
450C22—3441no—
451C22—3441no—
452C22—3441no—
453C22—3441no—
454C22—1722no—
455C22—1722no—
456C22—1722no—
457C22#1458280711yescharacteristic
458C22#1458303611yescharacteristic
459C22#1458304311yescharacteristic
460C22#1458304911yescharacteristic
461C22#1458305911yescharacteristic
462C22#1458307511yescharacteristic
463C22#1458308011yescharacteristic
464C4—21no—
465C4—21no—
466C4—42no—
467C4—82no—
468C4—81no—
469C4—3442no—
470C4—3441no—
471C4#1458303811yescharacteristic
472C4#1458304411yescharacteristic
473C4#1458304811yescharacteristic
474C4#1458305811yescharacteristic
475C4#1458312511yescharacteristic
476C4#1458313011yescharacteristic
477C4#1458314211yescharacteristic
478C4#1458314711yescharacteristic
479C2—3442no—
480C2#1913379411yescharacteristic
481C2#1913380111yescharacteristic
482C2#1913385011yescharacteristic
483C2#1913385711yescharacteristic
484C2#1913559511yescharacteristic
485C2#1913559611yescharacteristic
486C2#1913564011yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC2×C43×#475C2
socleC23×C43#120
prime radicalC22×D172D4
hypercenterC2×#475D43
hypocenterC43#10232
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
3. #19135557C2semidirect
4. C2×Q8⋊(C43⋊C8)C2semidirect
6. #19132479C2semidirect
7. C2×C43×#475C2semidirect
91. C2×Q8×C43SD16semidirect
236. C2×#475D43semidirect
274. C43#10232semidirect
335. C2×Q8#10621884semidirect

Maximal subgroups

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

subgroupindex
C2×#145831012
#191395132
#191355572
C2×Q8⋊(C43⋊C8)2
C2×#145826262
#191324792
C2×C43×#4752
#1023243