Finite Group Databasebeta

← #24991363

Subgroups — #24991363

Order 11008.

616 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583099C211yesmaximal, characteristic
2#19137552C211yesmaximal, characteristic, complemented
3#19135521C211yesmaximal, characteristic
4#19135401C211yesmaximal, characteristic
5#19132479C211yesmaximal, characteristic, complemented
6#19132435C211yesmaximal, characteristic, complemented
7C2×C43×Q8⋊C8C211yesmaximal, characteristic, complemented
8C22×#10621884—21no—
9C2×#13063322C2211yescharacteristic
10#14583099—22no—
11#14583099C414yescomplemented
12C2×C4⋊(C43⋊C8)C2211yescharacteristic
13C2×#13063247—21no—
14C2×#13063247—21no—
15C2×#13063247—22no—
16C2×#13063245—21no—
17#14582806—21no—
18#14582785—22no—
19#14582769C2211yescharacteristic
20#14582765—21no—
21C4⋊C4×Dic43—21no—
22C4×C4⋊Dic43—21no—
23C4×C4⋊Dic43C2211yescharacteristic
24C2×C4×Q8×C43C2211yescharacteristic
25C2×C4⋊C8×C43C2211yescharacteristic
26C2×C4×C8×C43C2211yescharacteristic
27C43×Q8⋊C8—22no—
28C22×D172—21no—
29C22×D172—21no—
30C22×D172—21no—
31C2×#10621884—24no—
32C2×#10621884—42no—
33C2×#10621884—42no—
34C22×C43⋊C8—21no—
35#13063322—21no—
36#13063322—21no—
37#13063322—21no—
38#13063322C2×C412yes—
39C2×C4⋊Dic43—21no—
40C2×C4⋊Dic43—21no—
41C2×C4⋊Dic43D411yescharacteristic
42C2×C4⋊Dic43D411yescharacteristic
43C2×C4⋊Dic43D412yes—
44C2×C4×Dic43—21no—
45C2×C4×Dic43—22no—
46C4⋊(C43⋊C8)—21no—
47C4⋊(C43⋊C8)C2×C412yes—
48#13063247—42no—
49#13063247—44no—
50#13063247—42no—
51#13063245—24no—
52C43⋊#95—22no—
53C43⋊#95—22no—
54C43⋊#95—22no—
55C43⋊#95—21no—
56C22×Q8×C43D411yescharacteristic
57C22×C8×C43—21no—
58C22×C8×C43—21no—
59C4×Q8×C43—21no—
60C4×Q8×C43—21no—
61C4×Q8×C43C2×C412yes—
62C4×Q8×C43D412yes—
63C2×C4⋊C4×C43—21no—
64C2×C4⋊C4×C43D411yescharacteristic
65C2×C42×C43—21no—
66C2×C42×C43C2311yescharacteristic
67C4⋊C8×C43—21no—
68C4⋊C8×C43—21no—
69C4×C8×C43—21no—
70C4×C8×C43—21no—
71C23×D43—41no—
72C2×Q8×C43—21no—
73C2×Q8×C43—21no—
74C2×Q8×C43—21no—
75C2×Q8×C43—21no—
76C2×Q8×C43—21no—
77C2×Q8×C43C22⋊C412yes—
78C22×C4×C43—21no—
79C22×C4×C43—21no—
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43C2×D411yescharacteristic
83C22×Dic43—21no—
84C22×Dic43—21no—
85C22×Dic43—22no—
86C2×D172—22no—
87C2×D172—22no—
88C2×D172—22no—
89C2×D172—41no—
90C2×D172—41no—
91C2×D172—41no—
92C2×D172—42no—
93C2×D172—42no—
94C2×D172—41no—
95C2×D172—41no—
96C2×D172—41no—
97C2×D172—41no—
98C2×D172—41no—
99C2×D172—41no—
100C2×D172—41no—
101C2×D172—41no—
102C2×C8×C43—22no—
103C2×C8×C43—41no—
104C2×C8×C43—41no—
105C2×C8×C43—41no—
106C2×C8×C43—41no—
107C2×C8×C43—41no—
108C4⋊C4×C43—22no—
109C4⋊C4×C43—22no—
110C4⋊C4×C43—21no—
111C4⋊C4×C43C22⋊C412yes—
112C42×C43—22no—
113C42×C43—22no—
114C42×C43C22×C411yescharacteristic
115C42×C43C2×D411yescharacteristic
116C42×C43#4111yescharacteristic
117C42×C43#4111yescharacteristic
118#10621884—48no—
119C4⋊Dic43—21no—
120C4⋊Dic43—21no—
121C4⋊Dic43—21no—
122C4⋊Dic43—41no—
123C4⋊Dic43—41no—
124C4⋊Dic43—41no—
125C4⋊Dic43—41no—
126C4⋊Dic43—42no—
127C4⋊Dic43SD1612yescomplemented
128C4×Dic43—41no—
129C4×Dic43—41no—
130C4×Dic43—82no—
131C2×C43⋊C8—22no—
132C2×C43⋊C8—41no—
133C2×C43⋊C8—41no—
134C23×C43#12011yescharacteristic
135C22×D43—42no—
136C22×D43—81no—
137C22×D43—81no—
138C22×D43—81no—
139C22×D43—81no—
140C22×D43—81no—
141C22×D43—81no—
142Q8×C43—22no—
143Q8×C43—22no—
144Q8×C43—41no—
145Q8×C43—41no—
146C2×C4×C43—21no—
147C2×C4×C43—21no—
148C2×C4×C43—22no—
149C2×C4×C43—22no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—41no—
154C2×C4×C43C2×C22⋊C411yescharacteristic
155C2×C4×C43C4×D411yescharacteristic
156C2×C4×C43C4×D411yescharacteristic
157C2×C4×C43#12111yescharacteristic
158C2×C4×C43#12111yescharacteristic
159C2×C4×C43#12311yescharacteristic
160C2×C4×C43C2×SD1611yescharacteristic
161C2×C4×C43#13511yescharacteristic
162C2×C4×C43#13511yescharacteristic
163C2×C4×C43#13511yescharacteristic
164C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C43#13711yescharacteristic
168C2×Dic43—22no—
169C2×Dic43—41no—
170C2×Dic43—41no—
171C2×Dic43—41no—
172C2×Dic43—41no—
173C2×Dic43—42no—
174C2×Dic43—42no—
175C2×Dic43—42no—
176C2×Dic43—41no—
177D172—44no—
178D172—42no—
179D172—42no—
180D172—42no—
181D172—42no—
182D172—82no—
183D172—81no—
184D172—81no—
185D172—81no—
186D172—81no—
187C8×C43—42no—
188C8×C43—81no—
189C43⋊C8—42no—
190#8978—431nomaximal, Sylow
191C22×C43#38611yescharacteristic
192C22×C43#44811yescharacteristic
193C22×C43#44911yescharacteristic
194C22×C43#44911yescharacteristic
195C22×C43#44911yescharacteristic
196C22×C43#45311yescharacteristic
197C22×C43#45411yescharacteristic
198C2×D43—82no—
199C2×D43—82no—
200C2×D43—82no—
201C2×D43—161no—
202C2×D43—161no—
203C2×D43—161no—
204C2×D43—161no—
205C4×C43—21no—
206C4×C43—21no—
207C4×C43—42no—
208C4×C43—42no—
209C4×C43#41611yescharacteristic
210C4×C43#41811yescharacteristic
211C4×C43C4×SD1611yescharacteristic
212C4×C43#44011yescharacteristic
213C4×C43#46011yescharacteristic
214C4×C43#46411yescharacteristic
215C4×C43#48211yescharacteristic
216C4×C43#48211yescharacteristic
217Dic43—42no—
218Dic43—82no—
219Dic43—81no—
220C2×#460—431no—
221#2355—431no—
222#1982—431no—
223#1957—431no—
224C2×Q8⋊C8D4311yescharacteristic, complemented
225#1296—431no—
226#1279—431no—
227C2×C43#162011yescharacteristic
228C2×C43#162211yescharacteristic
229C2×C43#162611yescharacteristic
230C2×C43#162811yescharacteristic
231C2×C43#187511yescharacteristic
232C2×C43#188011yescharacteristic
233C2×C43#188311yescharacteristic
234D43—162no—
235C22×SD16—861no—
236C2×#127—431no—
237C2×C4×Q8C2×D4311yescharacteristic
238#460—434no—
239#460—862no—
240C2×C4⋊C8—431no—
241C2×C4⋊C8C2×D4311yescharacteristic
242C2×#102—861no—
243C2×#102—862no—
244C2×#102—861no—
245C2×#102—861no—
246C2×C4×C8C2×D4311yescharacteristic
247#391—861no—
248#387—862no—
249#384—431no—
250#382—861no—
251C4×C4⋊C4—431no—
252C4×C4⋊C4—861no—
253C4×C4⋊C4—861no—
254Q8⋊C8—22no—
255C43#897811yescharacteristic, complemented, Sylow
256C22×Q8D17211yescharacteristic
257C22×D4—861no—
258C22×D4—861no—
259C22×D4—861no—
260C2×SD16—864no—
261C2×SD16—1722no—
262C2×SD16—1722no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—861no—
266#127—432no—
267#127—861no—
268#127—861no—
269#127—861no—
270C4×Q8—21no—
271C4×Q8—21no—
272C4×Q8C4×D4312yes—
273C4×Q8C22⋊D4312yes—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—431no—
276C2×C4⋊C4—431no—
277C2×C4⋊C4—432no—
278C2×C4⋊C4—861no—
279C2×C4⋊C4—861no—
280C2×C4⋊C4D17211yescharacteristic
281C2×C42—21no—
282C2×C42—862no—
283C2×C42—861no—
284C2×C42C22×D4311yescharacteristic
285C4⋊C8—21no—
286C4⋊C8—21no—
287C4⋊C8—432no—
288C4⋊C8—861no—
289#102—864no—
290#102—1722no—
291#102—1722no—
292#102—1724no—
293C4×C8—21no—
294C4×C8—21no—
295#95—862no—
296#95—862no—
297#95—862no—
298#95—861no—
299C24—1721no—
300C2×Q8—21no—
301C2×Q8—21no—
302C2×Q8—21no—
303C2×Q8—21no—
304C2×Q8—21no—
305C2×Q8(C2×D43)⋊C412yes—
306C2×D4—862no—
307C2×D4—862no—
308C2×D4—862no—
309C2×D4—1722no—
310C2×D4—1722no—
311C2×D4—1721no—
312C2×D4—1721no—
313C2×D4—1721no—
314C2×D4—1721no—
315C2×D4—1721no—
316C2×D4—1721no—
317C2×D4—1721no—
318C2×D4—1721no—
319C2×D4—1721no—
320C2×D4—1721no—
321C2×D4—1721no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—861no—
325C22×C4—861no—
326C22×C4—862no—
327C22×C4C2×D17211yescharacteristic
328C22×C4D4×D4311yescharacteristic
329C22×C4D4×D4311yescharacteristic
330SD16—1728no—
331C2×C8—22no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—41no—
336C2×C8—41no—
337C2×C8—862no—
338C2×C8—1721no—
339C2×C8—1721no—
340C4⋊C4—22no—
341C4⋊C4—22no—
342C4⋊C4—21no—
343C4⋊C4—432no—
344C4⋊C4—861no—
345C4⋊C4—861no—
346C4⋊C4—861no—
347C4⋊C4—1722no—
348C4⋊C4—1721no—
349C4⋊C4—1721no—
350C4⋊C4—1721no—
351C4⋊C4—1721no—
352C4⋊C4(C2×D43)⋊C412yes—
353C42—22no—
354C42—22no—
355C42—3442no—
356C42—1721no—
357C42—1721no—
358C42C2×C4×D4311yescharacteristic
359C42#1062190011yescharacteristic
360C42#1062190011yescharacteristic
361C42C2×C22⋊D4311yescharacteristic
362C23—3441no—
363C23—3441no—
364C23—3441no—
365C23—3441no—
366C23—3441no—
367C23—3441no—
368C23—1722no—
369C23#1306329511yescharacteristic
370Q8—22no—
371Q8—22no—
372Q8—41no—
373Q8—41no—
374D4—3442no—
375D4—3441no—
376D4—3441no—
377D4—3441no—
378D4—3441no—
379D4—1724no—
380D4—1722no—
381D4—1722no—
382D4—1722no—
383D4—1722no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—862no—
393C2×C4—1721no—
394C2×C4—1722no—
395C2×C4—1721no—
396C2×C4—1722no—
397C2×C4—1722no—
398C2×C4—1721no—
399C2×C4—1721no—
400C2×C4—1721no—
401C2×C4C2×(C2×D43)⋊C411yescharacteristic
402C2×C4(C22⋊D43)⋊C411yescharacteristic
403C2×C4(C22⋊D43)⋊C411yescharacteristic
404C2×C4#1306329711yescharacteristic
405C2×C4#1306329711yescharacteristic
406C2×C4#1306330911yescharacteristic
407C2×C4SD16×D4311yescharacteristic
408C2×C4#1306334711yescharacteristic
409C2×C4#1306334711yescharacteristic
410C2×C4#1306334811yescharacteristic
411C2×C4#1306335211yescharacteristic
412C2×C4#1306335311yescharacteristic
413C2×C4#1306335311yescharacteristic
414C2×C4#1306335711yescharacteristic
415C8—42no—
416C8—81no—
417C8—1722no—
418C22—3442no—
419C22—3442no—
420C22—3442no—
421C22—6881no—
422C22—6881no—
423C22—6881no—
424C22—6881no—
425C22#1458277611yescharacteristic
426C22#1458303911yescharacteristic
427C22#1458304611yescharacteristic
428C22#1458304611yescharacteristic
429C22#1458304711yescharacteristic
430C22#1458306811yescharacteristic
431C22#1458307311yescharacteristic
432C4—21no—
433C4—21no—
434C4—42no—
435C4—42no—
436C4—3441no—
437C4—3442no—
438C4—1722no—
439C4#1458289611yescharacteristic
440C4#1458290511yescharacteristic
441C4#1458298411yescharacteristic
442C4#1458300211yescharacteristic
443C4#1458309711yescharacteristic
444C4#1458312311yescharacteristic
445C4#1458322411yescharacteristic
446C4#1458322411yescharacteristic
447C2—6882no—
448C2#1913365611yescharacteristic
449C2#1913367011yescharacteristic
450C2#1913369311yescharacteristic
451C2#1913370811yescharacteristic
452C2#1913491511yescharacteristic
453C2#1913494811yescharacteristic
454C2#1913496911yescharacteristic
subgroupG/H
centerC23#13063295
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC2×C43×Q8⋊C8C2
socleC23×C43#120
prime radicalC2×#13063322C22
cosocleC2×C42×C43C23
hypercenterC2×Q8⋊C8D43
hypocenterC43#8978
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #19137552C2semidirect
5. #19132479C2semidirect
6. #19132435C2semidirect
7. C2×C43×Q8⋊C8C2semidirect
11. #14583099C4semidirect
127. C4⋊Dic43SD16semidirect
224. C2×Q8⋊C8D43semidirect
255. C43#8978semidirect

Maximal subgroups

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

subgroupindex
C2×#145830992
#191375522
#191355212
#191354012
#191324792
#191324352
C2×C43×Q8⋊C82
#897843