Finite Group Databasebeta

← #25000037

Subgroups — #25000037

Order 11008.

556 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139549C211yesmaximal, characteristic
2#19135356C211yesmaximal, characteristic, complemented
3#19134592C211yesmaximal, characteristic
4C2×#14582645C211yesmaximal, characteristic, complemented
5C2×#14582628C211yesmaximal, characteristic
6#19132435C211yesmaximal, characteristic, complemented
7C43×#1990C211yesmaximal, characteristic, complemented
8C2×#13063301—21no—
9C2×#13063301—21no—
10C2×C4×D172C2211yescharacteristic
11C2×#13063256—21no—
12C2×C4⋊(C43⋊C8)C2211yescharacteristic
13C2×C4⋊(C43⋊C8)C2211yescharacteristic
14C2×#13063245—21no—
15#14582834—22no—
16#14582800—21no—
17#14582768—21no—
18C4×C4⋊Dic43C2211yescharacteristic
19#14582661—21no—
20#14582661—21no—
21#14582645—22no—
22#14582628—22no—
23C2×C4⋊Q8×C43C2211yescharacteristic
24C2×C4×C8×C43C2211yescharacteristic
25C43×#384C2211yescharacteristic
26C43×#340—22no—
27C22×D172D411yescharacteristic
28C22×C4×D43—21no—
29C22×C43⋊C8—21no—
30C22×C43⋊C8—21no—
31#13063301—42no—
32#13063301—42no—
33#13063301—42no—
34#13063301—42no—
35C4×D172—21no—
36C4×D172—21no—
37C4×D172—21no—
38C4×D172—21no—
39C2×C4⋊Dic43D411yescharacteristic
40C2×C4⋊Dic43D411yescharacteristic
41C2×C4⋊Dic43D411yescharacteristic
42C2×Dic43⋊C4—22no—
43C2×Dic43⋊C4—22no—
44C2×(C2×D43)⋊C4—22no—
45C2×(C2×D43)⋊C4—22no—
46C2×(C2×D43)⋊C4—21no—
47C2×C4×Dic43—21no—
48#13063256—42no—
49C4⋊(C43⋊C8)—21no—
50C4⋊(C43⋊C8)—21no—
51C4⋊(C43⋊C8)—21no—
52C4⋊(C43⋊C8)D412yes—
53#13063245—42no—
54C43⋊#95—21no—
55C22×Q8×C43—21no—
56C22×C8×C43—21no—
57C4⋊Q8×C43—21no—
58C4⋊Q8×C43—21no—
59C4⋊Q8×C43—21no—
60C4⋊Q8×C43—21no—
61C2×C4⋊C4×C43—21no—
62C2×C4⋊C4×C43—21no—
63C2×C4⋊C4×C43—21no—
64C2×C4⋊C4×C43—21no—
65C2×C4⋊C4×C43D412yes—
66C2×C42×C43C2311yescharacteristic
67C4×C8×C43—21no—
68C4×C8×C43—21no—
69C23×D43—21no—
70C2×Q8×C43—41no—
71C2×Q8×C43—41no—
72C2×Q8×C43—41no—
73C2×Q8×C43—41no—
74C2×Q8×C43—41no—
75C2×Q8×C43—41no—
76C22×C4×C43—22no—
77C22×C4×C43—41no—
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×Dic43—21no—
82C22×Dic43—21no—
83C22×Dic43—21no—
84C2×D172—21no—
85C2×D172—21no—
86C2×D172—21no—
87C2×D172—21no—
88C2×D172—21no—
89C2×D172SD1612yes—
90C2×C4×D43—41no—
91C2×C4×D43—41no—
92C2×C4×D43—41no—
93C2×C4×D43—41no—
94C2×C4×D43—41no—
95C2×C4×D43—41no—
96C2×C8×C43—22no—
97C2×C8×C43—41no—
98C2×C8×C43—41no—
99C4⋊C4×C43—22no—
100C4⋊C4×C43—22no—
101C4⋊C4×C43—42no—
102C4⋊C4×C43—41no—
103C4⋊C4×C43—41no—
104C4⋊C4×C43—41no—
105C4⋊C4×C43—41no—
106C4⋊C4×C43—41no—
107C4⋊C4×C43—41no—
108C42×C43C2×D411yescharacteristic
109C42×C43#4111yescharacteristic
110C42×C43#4111yescharacteristic
111C42×C43#4111yescharacteristic
112(C2×D43)⋊C4—44no—
113(C2×D43)⋊C4—44no—
114(C2×D43)⋊C4—41no—
115(C2×D43)⋊C4—41no—
116C4⋊Dic43—21no—
117C4⋊Dic43—21no—
118C4⋊Dic43—21no—
119C4⋊Dic43—21no—
120C4⋊Dic43D812yes—
121C4⋊Dic43SD1612yes—
122Dic43⋊C4—44no—
123Dic43⋊C4—44no—
124C4×Dic43—41no—
125C4×Dic43—41no—
126C2×C43⋊C8—22no—
127C2×C43⋊C8—41no—
128C2×C43⋊C8—41no—
129C2×C43⋊C8—41no—
130C2×C43⋊C8—41no—
131C2×C43⋊C8—41no—
132C23×C43#12011yescharacteristic
133C22×D43—22no—
134C22×D43—41no—
135C22×D43—41no—
136C22×D43—41no—
137C22×D43—41no—
138C22×D43—41no—
139C22×D43—41no—
140Q8×C43—81no—
141Q8×C43—81no—
142Q8×C43—81no—
143Q8×C43—81no—
144C2×C4×C43—21no—
145C2×C4×C43—21no—
146C2×C4×C43—42no—
147C2×C4×C43—42no—
148C2×C4×C43—42no—
149C2×C4×C43—81no—
150C2×C4×C43—81no—
151C2×C4×C43—81no—
152C2×C4×C43#12111yescharacteristic
153C2×C4×C43#12111yescharacteristic
154C2×C4×C43#12111yescharacteristic
155C2×C4×C43#12311yescharacteristic
156C2×C4×C43#12311yescharacteristic
157C2×C4×C43#12411yescharacteristic
158C2×C4×C43C2×D811yescharacteristic
159C2×C4×C43C2×SD1611yescharacteristic
160C2×C4×C43C2×SD1611yescharacteristic
161C2×C4×C43#13511yescharacteristic
162C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C43#13711yescharacteristic
165C2×C4×C43#13711yescharacteristic
166C2×Dic43—22no—
167C2×Dic43—22no—
168C2×Dic43—41no—
169C2×Dic43—41no—
170C2×Dic43—41no—
171C2×Dic43—41no—
172C2×Dic43—41no—
173C2×Dic43—41no—
174C2×Dic43—41no—
175D172—22no—
176D172—22no—
177D172—41no—
178D172—41no—
179C4×D43—81no—
180C4×D43—81no—
181C4×D43—81no—
182C4×D43—81no—
183C8×C43—42no—
184C43⋊C8—42no—
185C43⋊C8—81no—
186#10420—431nomaximal, Sylow
187C22×C43#39411yescharacteristic
188C22×C43#44711yescharacteristic
189C22×C43#44811yescharacteristic
190C22×C43#45011yescharacteristic
191C22×C43#45211yescharacteristic
192C22×C43#45411yescharacteristic
193C22×C43#45611yescharacteristic
194C2×D43—42no—
195C2×D43—42no—
196C2×D43—42no—
197C2×D43—81no—
198C2×D43—81no—
199C2×D43—81no—
200C2×D43—81no—
201C4×C43—21no—
202C4×C43—21no—
203C4×C43—82no—
204C4×C43—161no—
205C4×C43#45911yescharacteristic
206C4×C43#46011yescharacteristic
207C4×C43#46511yescharacteristic
208C4×C43#47011yescharacteristic
209C4×C43#48311yescharacteristic
210C4×C43#48511yescharacteristic
211C4×C43#48611yescharacteristic
212C4×C43#49011yescharacteristic
213Dic43—42no—
214Dic43—42no—
215Dic43—81no—
216#2542—431no—
217#1990D4311yescharacteristic, complemented
218#1948—431no—
219#1802—431no—
220C2×#332—431no—
221C2×D4⋊C8—431no—
222#1279—431no—
223C2×C43#162711yescharacteristic
224C2×C43#163511yescharacteristic
225C2×C43#164711yescharacteristic
226C2×C43#165111yescharacteristic
227C2×C43#203511yescharacteristic
228C2×C43#203811yescharacteristic
229C2×C43#204111yescharacteristic
230D43—82no—
231C2×C4⋊Q8C2×D4311yescharacteristic
232C2×C22⋊Q8—861no—
233C2×C22⋊Q8—861no—
234C2×C4×D4—431no—
235C2×#106—861no—
236C2×C4⋊C8—431no—
237C2×C4⋊C8—431no—
238C2×#102—861no—
239C2×C4×C8C2×D4311yescharacteristic
240#399—862no—
241#390—861no—
242#384—861no—
243#384C2×D4311yescharacteristic
244C4×C4⋊C4—431no—
245#340—22no—
246#340—861no—
247#340—861no—
248#332—862no—
249D4⋊C8—862no—
250C43#1042011yescharacteristic, complemented, Sylow
251C22×Q8—21no—
252C22×D4—431no—
253C23×C4—861no—
254C22×C8—21no—
255C22×C8—861no—
256C22×C8—861no—
257C4⋊Q8—21no—
258C4⋊Q8—21no—
259C4⋊Q8—21no—
260C4⋊Q8—21no—
261C22⋊Q8—1722no—
262C22⋊Q8—1722no—
263C22⋊Q8—1722no—
264C22⋊Q8—1722no—
265C4×D4—861no—
266C4×D4—861no—
267C4×D4—861no—
268C4×D4—861no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—431no—
274C2×C4⋊C4—431no—
275C2×C4⋊C4—431no—
276C2×C4⋊C4—862no—
277C2×C4⋊C4—862no—
278C2×C4⋊C4C22⋊D4312yes—
279C2×C22⋊C4—862no—
280C2×C22⋊C4—862no—
281C2×C22⋊C4—861no—
282C2×C42—861no—
283C2×C42C22×D4311yescharacteristic
284#106—1722no—
285C4⋊C8—432no—
286C4⋊C8—861no—
287C4⋊C8—861no—
288C4⋊C8—861no—
289#102—1722no—
290C4×C8—21no—
291C4×C8—21no—
292#95—861no—
293C24—861no—
294C2×Q8—41no—
295C2×Q8—41no—
296C2×Q8—41no—
297C2×Q8—41no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×D4—432no—
301C2×D4—861no—
302C2×D4—861no—
303C2×D4—861no—
304C2×D4—861no—
305C2×D4—861no—
306C22×C4—22no—
307C22×C4—41no—
308C22×C4—861no—
309C22×C4—861no—
310C22×C4—861no—
311C22×C4—1721no—
312C22×C4—1721no—
313C22×C4—1721no—
314C22×C4—1721no—
315C22×C4—1721no—
316C22×C4—1721no—
317C22×C4D4×D4311yescharacteristic
318C22×C4D4×D4311yescharacteristic
319C22×C4C2×C22⋊D4311yescharacteristic
320C2×C8—22no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—862no—
324C2×C8—1721no—
325C2×C8—1721no—
326C2×C8—1721no—
327C2×C8—1721no—
328C2×C8—1721no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—42no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—432no—
339C4⋊C4—432no—
340C4⋊C4—861no—
341C4⋊C4—861no—
342C4⋊C4—861no—
343C4⋊C4—861no—
344C4⋊C4—1724no—
345C4⋊C4—1724no—
346C22⋊C4—1724no—
347C22⋊C4—1724no—
348C22⋊C4—1721no—
349C22⋊C4—1721no—
350C42—1721no—
351C42—1721no—
352C42#1062189811yescharacteristic
353C42#1062189811yescharacteristic
354C42D4×D4311yescharacteristic
355C42#1062190011yescharacteristic
356C23—862no—
357C23—1721no—
358C23—1721no—
359C23—1721no—
360C23—1721no—
361C23—1721no—
362C23—1721no—
363C23#1306329311yescharacteristic
364Q8—81no—
365Q8—81no—
366Q8—81no—
367Q8—81no—
368D4—862no—
369D4—862no—
370D4—1721no—
371D4—1721no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—81no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4—862no—
381C2×C4—862no—
382C2×C4—3441no—
383C2×C4—3441no—
384C2×C4—3441no—
385C2×C4—3441no—
386C2×C4—1721no—
387C2×C4—1721no—
388C2×C4—1721no—
389C2×C4—1721no—
390C2×C4—1721no—
391C2×C4—1721no—
392C2×C4—1721no—
393C2×C4#1306329711yescharacteristic
394C2×C4#1306329811yescharacteristic
395C2×C4#1306329811yescharacteristic
396C2×C4#1306330711yescharacteristic
397C2×C4#1306330811yescharacteristic
398C2×C4#1306331111yescharacteristic
399C2×C4D8×D4311yescharacteristic
400C2×C4SD16×D4311yescharacteristic
401C2×C4SD16×D4311yescharacteristic
402C2×C4#1306334811yescharacteristic
403C2×C4#1306334911yescharacteristic
404C2×C4#1306335211yescharacteristic
405C2×C4#1306335411yescharacteristic
406C2×C4#1306335711yescharacteristic
407C8—42no—
408C8—3441no—
409C8—1722no—
410C22—3441no—
411C22—3441no—
412C22—3441no—
413C22—3441no—
414C22—1722no—
415C22—1722no—
416C22—1722no—
417C22#1458281411yescharacteristic
418C22#1458303111yescharacteristic
419C22#1458303611yescharacteristic
420C22#1458304811yescharacteristic
421C22#1458306011yescharacteristic
422C22#1458307111yescharacteristic
423C22#1458308111yescharacteristic
424C4—21no—
425C4—21no—
426C4—82no—
427C4—161no—
428C4—3441no—
429C4—1722no—
430C4—1722no—
431C4#1458309311yescharacteristic
432C4#1458309811yescharacteristic
433C4#1458313111yescharacteristic
434C4#1458315611yescharacteristic
435C4#1458322811yescharacteristic
436C4#1458323911yescharacteristic
437C4#1458324411yescharacteristic
438C4#1458326211yescharacteristic
439C2—3442no—
440C2#1913369511yescharacteristic
441C2#1913374311yescharacteristic
442C2#1913382711yescharacteristic
443C2#1913385511yescharacteristic
444C2#1913578911yescharacteristic
445C2#1913581211yescharacteristic
446C2#1913582711yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1990C2
socleC23×C43#120
prime radicalC22×D172D4
hypercenter#1990D43
hypocenterC43#10420
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
2. #19135356C2semidirect
4. C2×#14582645C2semidirect
6. #19132435C2semidirect
7. C43×#1990C2semidirect
217. #1990D43semidirect
250. C43#10420semidirect

Maximal subgroups

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

subgroupindex
#191395492
#191353562
#191345922
C2×#145826452
C2×#145826282
#191324352
C43×#19902
#1042043