Finite Group Databasebeta

← #24995741

Subgroups — #24995741

Order 11008.

650 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142896C211yesmaximal, characteristic
2#19134575C211yesmaximal, characteristic, complemented
3C2×#14582635C212yesmaximal, complemented
4C2×#14582632C212yesmaximal
5C43×#1434C211yesmaximal, characteristic, complemented
6C2×#13063313C411yescharacteristic, complemented
7C2×#13063304C2211yescharacteristic
8C2×#13063299C2211yescharacteristic
9C2×C4⋊(C43⋊C8)—21no—
10C2×C22⋊(C43⋊C8)C2212yes—
11#14582805C411yescharacteristic, complemented
12#14582801C411yescharacteristic, complemented
13#14582790—21no—
14#14582790—21no—
15#14582778—21no—
16#14582778—21no—
17#14582765C411yescharacteristic, complemented
18#14582654—21no—
19#14582635—24no—
20#14582632—24no—
21C22×C42×C43C2211yescharacteristic
22C2×#95×C43—21no—
23C2×#95×C43—21no—
24C2×#95×C43C2212yes—
25C22×Dic86C2×C411yescharacteristic
26C22×D172C2×C411yescharacteristic
27C22×C22⋊D43—21no—
28C22×C43⋊C8—22no—
29#13063313—42no—
30#13063304—22no—
31#13063304—22no—
32#13063299—22no—
33#13063299—22no—
34C2×C4⋊Dic43C2×C411yescharacteristic
35C2×C4⋊Dic43C2×C411yescharacteristic
36C2×Dic43⋊C4—21no—
37C2×C22⋊Dic43—21no—
38C2×(C2×D43)⋊C4—21no—
39C2×(C2×D43)⋊C4—21no—
40C2×(C2×D43)⋊C4—21no—
41C2×(C2×D43)⋊C4—21no—
42C2×(C2×D43)⋊C4—21no—
43C4⋊(C43⋊C8)—42no—
44C22⋊(C43⋊C8)—22no—
45C22⋊(C43⋊C8)—22no—
46C43⋊#95—21no—
47C43⋊#95—21no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C23×C4×C43—22no—
51C23×C4×C43D411yescharacteristic
52C23×C4×C43D411yescharacteristic
53C23×C4×C43C2311yescharacteristic
54C2×C42×C43—42no—
55C2×C42×C43C2×C411yescharacteristic
56C2×C42×C43C2×C411yescharacteristic
57C2×C42×C43D411yescharacteristic
58C2×C42×C43D411yescharacteristic
59#95×C43—22no—
60#95×C43—42no—
61#95×C43—42no—
62#95×C43D414yes—
63C24×C43C2×D411yescharacteristic
64C23×D43—21no—
65C22×C4×C43—22no—
66C22×C4×C43—24no—
67C22×C4×C43—22no—
68C22×C4×C43—21no—
69C22×C4×C43—21no—
70C22×C4×C43—41no—
71C22×C4×C43—41no—
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—
99C2×Dic86—22no—
100C2×Dic86—41no—
101C2×Dic86—41no—
102C42×C43—22no—
103C42×C43—22no—
104C42×C43—41no—
105C42×C43—41no—
106C22⋊Dic43—42no—
107(C2×D43)⋊C4—42no—
108(C2×D43)⋊C4—42no—
109(C2×D43)⋊C4—42no—
110(C2×D43)⋊C4—42no—
111(C2×D43)⋊C4—41no—
112(C2×D43)⋊C4—41no—
113C4⋊Dic43—22no—
114C4⋊Dic43—22no—
115Dic43⋊C4—41no—
116Dic43⋊C4—41no—
117C2×C43⋊C8—42no—
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×C43#13512yes—
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#9912yes—
164C2×C4×C43C4×D412yes—
165C2×C4×C43#12411yescharacteristic
166C2×C4×C43#12711yescharacteristic
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—
179Dic86—82no—
180C43⋊C8—82no—
181#9716—431nomaximal, Sylow
182C22×C43—22no—
183C22×C43—22no—
184C22×C43—21no—
185C22×C43—21no—
186C22×C43—21no—
187C22×C43—21no—
188C22×C43—22no—
189C22×C43—22no—
190C22×C43#39011yescharacteristic
191C22×C43C2×#9911yescharacteristic
192C22×C43#41011yescharacteristic
193C22×C43#41611yescharacteristic
194C22×C43#41711yescharacteristic
195C22×C43#42111yescharacteristic
196C22×C43#42111yescharacteristic
197C22×C43#46312yes—
198C22×C43#46412yes—
199C2×D43—81no—
200C2×D43—81no—
201C2×D43—81no—
202C2×D43—81no—
203C2×D43—81no—
204C2×D43—81no—
205C2×D43—81no—
206C4×C43—21no—
207C4×C43—22no—
208C4×C43—21no—
209C4×C43—22no—
210C4×C43—41no—
211C4×C43—41no—
212C4×C43—41no—
213C4×C43—84no—
214Dic43—81no—
215Dic43—81no—
216Dic43—81no—
217#2850—431no—
218#1797—431no—
219C2×#328—432no—
220C2×#327—432no—
221#1434D4311yescharacteristic, complemented
222C2×C43—22no—
223C2×C43—22no—
224C2×C43#151211yescharacteristic
225C2×C43#151311yescharacteristic
226C2×C43#151611yescharacteristic
227C2×C43#152111yescharacteristic
228C2×C43#196311yescharacteristic
229C2×C43#196411yescharacteristic
230C2×C43#198311yescharacteristic
231D43—161no—
232C2×#124—431no—
233C2×C22⋊Q8—431no—
234C2×#121—431no—
235C22×C42C2×D4311yescharacteristic
236C2×C4⋊C8—861no—
237C2×C22⋊C8—432no—
238#391—431no—
239#390—431no—
240#388—861no—
241#388—861no—
242#386—861no—
243#386—861no—
244#382—431no—
245C2×#95—21no—
246C2×#95—21no—
247C2×#95C2×D4312yes—
248#336—861no—
249#328—864no—
250#327—864no—
251C43#971611yescharacteristic, complemented, Sylow
252C22×Q8—431no—
253C22×D4—431no—
254C22×D4—861no—
255C23×C4—22no—
256C23×C4C22⋊D4311yescharacteristic
257C23×C4C22⋊D4311yescharacteristic
258C23×C4C22×D4311yescharacteristic
259C22×C8—862no—
260#124—1722no—
261C22⋊Q8—862no—
262C22⋊Q8—862no—
263#121—862no—
264#121—862no—
265C2×C4⋊C4—431no—
266C2×C4⋊C4—431no—
267C2×C4⋊C4—861no—
268C2×C22⋊C4—861no—
269C2×C22⋊C4—861no—
270C2×C22⋊C4—861no—
271C2×C22⋊C4—861no—
272C2×C22⋊C4—861no—
273C2×C22⋊C4—861no—
274C2×C42—42no—
275C2×C42C4×D4311yescharacteristic
276C2×C42C4×D4311yescharacteristic
277C2×C42D17211yescharacteristic
278C2×C42D17211yescharacteristic
279C4⋊C8—1722no—
280C22⋊C8—862no—
281C22⋊C8—862no—
282#95—22no—
283#95—42no—
284#95—42no—
285#95—861no—
286#95—861no—
287#95—861no—
288#95—861no—
289#95D17214yes—
290C24—861no—
291C24C2×C22⋊D4311yescharacteristic
292C2×Q8—862no—
293C2×Q8—1721no—
294C2×Q8—1721no—
295C2×D4—862no—
296C2×D4—1721no—
297C2×D4—1721no—
298C2×D4—1722no—
299C2×D4—1722no—
300C2×D4—1721no—
301C2×D4—1721no—
302C22×C4—22no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—22no—
306C22×C4—24no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—861no—
319C22×C4—861no—
320C22×C4—861no—
321C22×C4(C2×D43)⋊C411yescharacteristic
322C22×C4(C2×D43)⋊C411yescharacteristic
323C22×C4(C2×D43)⋊C411yescharacteristic
324C22×C4(C2×D43)⋊C411yescharacteristic
325C22×C4C2×C4×D4311yescharacteristic
326C22×C4C2×D17211yescharacteristic
327C22×C4C2×D17212yes—
328C22×C4#1062189812yes—
329C2×C8—1722no—
330C2×C8—1722no—
331C2×C8—1722no—
332C4⋊C4—862no—
333C4⋊C4—862no—
334C4⋊C4—1721no—
335C4⋊C4—1721no—
336C22⋊C4—1722no—
337C22⋊C4—1722no—
338C22⋊C4—1722no—
339C22⋊C4—1722no—
340C22⋊C4—1722no—
341C22⋊C4—1721no—
342C22⋊C4—1721no—
343C42—22no—
344C42—22no—
345C42—41no—
346C42—41no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—1721no—
352C23—1721no—
353C23—1721no—
354C23—1721no—
355C23—1721no—
356C23—1721no—
357C23—1721no—
358C23C2×(C2×D43)⋊C411yescharacteristic
359C23#1306329912yes—
360C23#1306334512yes—
361C23#1306335111yescharacteristic
362C23#1306335611yescharacteristic
363Q8—3442no—
364D4—3442no—
365D4—3442no—
366D4—3442no—
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—21no—
381C2×C4—21no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—44no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—44no—
388C2×C4—44no—
389C2×C4—44no—
390C2×C4—82no—
391C2×C4—82no—
392C2×C4—82no—
393C2×C4—82no—
394C2×C4—1721no—
395C2×C4—1721no—
396C2×C4—1721no—
397C2×C4—1721no—
398C2×C4—1721no—
399C2×C4—1721no—
400C2×C4—1721no—
401C2×C4—1721no—
402C2×C4—1721no—
403C2×C4#1306323912yes—
404C2×C4C4×D17212yes—
405C2×C4#1306331311yescharacteristic
406C2×C4#1306332211yescharacteristic
407C8—3442no—
408C22—22no—
409C22—22no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—22no—
415C22—22no—
416C22—3441no—
417C22—3441no—
418C22—3441no—
419C22—3441no—
420C22—3441no—
421C22—3441no—
422C22—3441no—
423C22#1458280111yescharacteristic
424C22C2×#1306323911yescharacteristic
425C22#1458287211yescharacteristic
426C22#1458289311yescharacteristic
427C22#1458289811yescharacteristic
428C22#1458291711yescharacteristic
429C22#1458291711yescharacteristic
430C22#1458311412yes—
431C22#1458312112yes—
432C4—21no—
433C4—22no—
434C4—21no—
435C4—22no—
436C4—41no—
437C4—41no—
438C4—41no—
439C4—84no—
440C4—3441no—
441C4—3441no—
442C4—3441no—
443C2—22no—
444C2—22no—
445C2—6881no—
446C2#1913313111yescharacteristic
447C2#1913313611yescharacteristic
448C2#1913314911yescharacteristic
449C2#1913317011yescharacteristic
450C2#1913542711yescharacteristic
451C2#1913543111yescharacteristic
452C2#1913552711yescharacteristic
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#9716
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
2. #19134575C2semidirect
3. C2×#14582635C2semidirect
5. C43×#1434C2semidirect
6. C2×#13063313C4semidirect
11. #14582805C4semidirect
12. #14582801C4semidirect
17. #14582765C4semidirect
221. #1434D43semidirect
251. C43#9716semidirect

Maximal subgroups

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

subgroupindex
#191428962
#191345752
C2×#145826352
C2×#145826322
C43×#14342
#971643