Finite Group Databasebeta

← #24995739

Subgroups — #24995739

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
2C2×#14582637C212yesmaximal, complemented
3C2×#14582634C212yesmaximal
4#19132822C211yesmaximal, characteristic, complemented
5C43×#1797C211yesmaximal, characteristic, complemented
6C2×#13063313C411yescharacteristic, complemented
7C2×#13063304C2211yescharacteristic
8C2×#13063299C2211yescharacteristic
9#14582805C411yescharacteristic, complemented
10#14582801C411yescharacteristic, complemented
11#14582790—21no—
12#14582790—21no—
13#14582778—21no—
14#14582778—21no—
15#14582765C411yescharacteristic, complemented
16C2×C43⋊#95—21no—
17C2×C43⋊#95—21no—
18C2×C43⋊#95C2212yes—
19#14582637—24no—
20#14582634—24no—
21C22×C42×C43C2211yescharacteristic
22C2×C4⋊C8×C43—21no—
23C2×C22⋊C8×C43C2212yes—
24C43×#336—21no—
25C22×Dic86C2×C411yescharacteristic
26C22×D172C2×C411yescharacteristic
27C22×C22⋊D43—21no—
28C23×Dic43—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—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C43⋊#95—21no—
47C43⋊#95—22no—
48C43⋊#95—42no—
49C43⋊#95—42no—
50C43⋊#95D414yes—
51C23×C4×C43D411yescharacteristic
52C23×C4×C43D411yescharacteristic
53C23×C4×C43C2311yescharacteristic
54C22×C8×C43—22no—
55C2×C42×C43—42no—
56C2×C42×C43C2×C411yescharacteristic
57C2×C42×C43C2×C411yescharacteristic
58C2×C42×C43D411yescharacteristic
59C2×C42×C43D411yescharacteristic
60C4⋊C8×C43—42no—
61C22⋊C8×C43—22no—
62C22⋊C8×C43—22no—
63C24×C43C2×D411yescharacteristic
64C23×D43—21no—
65C22×C4×C43—22no—
66C22×C4×C43—22no—
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43—41no—
70C22×C4×C43—41no—
71C22×C4×C43—41no—
72C22×C4×C43—41no—
73C22×C4×C43—41no—
74C22×C4×C43C22⋊C411yescharacteristic
75C22×C4×C43C22⋊C411yescharacteristic
76C22×C4×C43C22⋊C411yescharacteristic
77C22×C4×C43C22⋊C411yescharacteristic
78C22×C4×C43C22×C411yescharacteristic
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D412yes—
81C22×C4×C43#4112yes—
82C2×C22⋊D43—42no—
83C2×C22⋊D43—42no—
84C2×C22⋊D43—41no—
85C2×C22⋊D43—41no—
86C22×Dic43—21no—
87C22×Dic43—21no—
88C22×Dic43—21no—
89C22×Dic43—24no—
90C22×Dic43—42no—
91C22×Dic43—42no—
92C22×Dic43—42no—
93C22×Dic43—42no—
94C22×Dic43—42no—
95C22×Dic43—42no—
96C2×D172—22no—
97C2×D172—41no—
98C2×D172—41no—
99C2×Dic86—22no—
100C2×Dic86—41no—
101C2×Dic86—41no—
102C2×C8×C43—42no—
103C2×C8×C43—42no—
104C2×C8×C43—42no—
105C42×C43—22no—
106C42×C43—22no—
107C42×C43—41no—
108C42×C43—41no—
109C22⋊Dic43—42no—
110(C2×D43)⋊C4—42no—
111(C2×D43)⋊C4—42no—
112(C2×D43)⋊C4—42no—
113(C2×D43)⋊C4—42no—
114(C2×D43)⋊C4—41no—
115(C2×D43)⋊C4—41no—
116C4⋊Dic43—22no—
117C4⋊Dic43—22no—
118Dic43⋊C4—41no—
119Dic43⋊C4—41no—
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#9912yes—
157C2×C4×C43C4×D412yes—
158C2×C4×C43#12411yescharacteristic
159C2×C4×C43#12711yescharacteristic
160C22⋊D43—82no—
161C22⋊D43—82no—
162C2×Dic43—44no—
163C2×Dic43—44no—
164C2×Dic43—41no—
165C2×Dic43—41no—
166C2×Dic43—41no—
167C2×Dic43—41no—
168C2×Dic43—41no—
169C2×Dic43—41no—
170C2×Dic43—41no—
171C2×Dic43—41no—
172C2×Dic43—41no—
173C2×Dic43—44no—
174C2×Dic43—82no—
175C2×Dic43—82no—
176C2×Dic43—82no—
177C2×Dic43—82no—
178D172—82no—
179Dic86—82no—
180C8×C43—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—
213Dic43—84no—
214Dic43—81no—
215Dic43—81no—
216Dic43—81no—
217#2850—431no—
218#1797D4311yescharacteristic, complemented
219C2×#328—432no—
220C2×#327—432no—
221#1434—431no—
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—21no—
237C2×C22⋊C8C2×D4312yes—
238#391—431no—
239#390—431no—
240#388—861no—
241#388—861no—
242#386—861no—
243#386—861no—
244#382—431no—
245C2×#95—432no—
246C2×#95—861no—
247C2×#95—861no—
248#336—21no—
249#328—864no—
250#327—864no—
251C43#971611yescharacteristic, complemented, Sylow
252C22×Q8—431no—
253C22×D4—431no—
254C22×D4—861no—
255C23×C4—862no—
256C23×C4D17211yescharacteristic
257C23×C4D17211yescharacteristic
258C23×C4C22×D4311yescharacteristic
259C22×C8—22no—
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×C42C22⋊D4311yescharacteristic
278C2×C42C22⋊D4311yescharacteristic
279C4⋊C8—42no—
280C22⋊C8—22no—
281C22⋊C8—22no—
282#95—434no—
283#95—861no—
284#95—861no—
285#95—861no—
286#95—861no—
287#95—862no—
288#95—1722no—
289#95—1722no—
290C24—861no—
291C24C2×D17211yescharacteristic
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—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—861no—
312C22×C4—861no—
313C22×C4—861no—
314C22×C4—864no—
315C22×C4—1722no—
316C22×C4—1722no—
317C22×C4—1722no—
318C22×C4—1722no—
319C22×C4—1722no—
320C22×C4—1722no—
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×C4D4×D4312yes—
327C22×C4#1062190212yes—
328C22×C4C2×C22⋊D4311yescharacteristic
329C2×C8—42no—
330C2×C8—42no—
331C2×C8—42no—
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#1306330012yes—
360C23#1306334712yes—
361C23#1306335311yescharacteristic
362C23#1306335811yescharacteristic
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—3442no—
388C2×C4—3442no—
389C2×C4—3442no—
390C2×C4—3442no—
391C2×C4—1724no—
392C2×C4—1724no—
393C2×C4—1721no—
394C2×C4—1721no—
395C2×C4—1721no—
396C2×C4—1724no—
397C2×C4—1721no—
398C2×C4—1721no—
399C2×C4—1721no—
400C2×C4—1721no—
401C2×C4—1721no—
402C2×C4—1721no—
403C2×C4#1306323912yes—
404C2×C4#1306328712yes—
405C2×C4#1306331411yescharacteristic
406C2×C4#1306332111yescharacteristic
407C8—82no—
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#1458280011yescharacteristic
424C22C2×#1306323911yescharacteristic
425C22#1458287211yescharacteristic
426C22#1458289611yescharacteristic
427C22#1458290111yescharacteristic
428C22#1458291511yescharacteristic
429C22#1458291511yescharacteristic
430C22#1458311512yes—
431C22#1458312212yes—
432C4—21no—
433C4—22no—
434C4—21no—
435C4—22no—
436C4—41no—
437C4—41no—
438C4—41no—
439C4—3444no—
440C4—3441no—
441C4—3441no—
442C4—3441no—
443C2—22no—
444C2—22no—
445C2—6881no—
446C2#1913313411yescharacteristic
447C2#1913313911yescharacteristic
448C2#1913315211yescharacteristic
449C2#1913317311yescharacteristic
450C2#1913542611yescharacteristic
451C2#1913543011yescharacteristic
452C2#1913552511yescharacteristic
subgroupG/H
centerC23C2×(C2×D43)⋊C4
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1797C2
socleC23×C43C2×C22⋊C4
prime radicalC2×#13063299C22
cosocleC23×C4×C43C23
hypercenter#1797D43
hypocenterC43#9716
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
2. C2×#14582637C2semidirect
4. #19132822C2semidirect
5. C43×#1797C2semidirect
6. C2×#13063313C4semidirect
9. #14582805C4semidirect
10. #14582801C4semidirect
15. #14582765C4semidirect
218. #1797D43semidirect
251. C43#9716semidirect

Maximal subgroups

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

subgroupindex
#191428962
C2×#145826372
C2×#145826342
#191328222
C43×#17972
#971643