Finite Group Databasebeta

← #24991643

Subgroups — #24991643

Order 11008.

768 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582825C211yesmaximal, characteristic
2#19137208C211yesmaximal, characteristic
3#19134681C211yesmaximal, characteristic, complemented
4C2×#14582622C211yesmaximal, characteristic
5#19132475C211yesmaximal, characteristic, complemented
6#19132473C211yesmaximal, characteristic, complemented
7C43×#1823C211yesmaximal, characteristic, complemented
8C22×(C2×D43)⋊C4—21no—
9C22×(C2×D43)⋊C4C2211yescharacteristic
10C2×C22⋊C4×D43—21no—
11C2×C22⋊(C43⋊C8)C2211yescharacteristic
12#14582825—22no—
13#14582825C414yescomplemented
14#14582773—22no—
15#14582770—22no—
16#14582759C2211yescharacteristic
17#14582757—21no—
18C2×C43⋊#95—21no—
19C2×C43⋊#95C2211yescharacteristic
20#14582661—22no—
21#14582622—22no—
22C22×C4⋊C4×C43C2211yescharacteristic
23C2×C22⋊C8×C43C2211yescharacteristic
24C43×#380C2211yescharacteristic
25C43×#340—22no—
26C24×D43D411yescharacteristic
27C23×Dic43—21no—
28C23×Dic43D411yescharacteristic
29C22×C4×D43—22no—
30C22×C43⋊C8—21no—
31C2×C4⋊Dic43D412yes—
32C2×Dic43⋊C4—22no—
33C2×C22⋊Dic43—21no—
34C2×(C2×D43)⋊C4—21no—
35C2×(C2×D43)⋊C4—21no—
36C2×(C2×D43)⋊C4—21no—
37C2×(C2×D43)⋊C4—21no—
38C2×(C2×D43)⋊C4—22no—
39C2×(C2×D43)⋊C4—24no—
40C2×(C2×D43)⋊C4—42no—
41C2×(C2×D43)⋊C4—42no—
42C2×(C2×D43)⋊C4C2×C412yes—
43C2×(C2×D43)⋊C4D412yes—
44C22⋊C4×D43—42no—
45C22⋊C4×D43—42no—
46C22⋊(C43⋊C8)—21no—
47C22⋊(C43⋊C8)—21no—
48C43⋊#95—22no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C43⋊#95—24no—
52C43⋊#95C2×C412yescomplemented
53C23×C4×C43—21no—
54C23×C4×C43C2311yescharacteristic
55C22×C8×C43—21no—
56C2×C4⋊C4×C43—21no—
57C2×C4⋊C4×C43—21no—
58C2×C4⋊C4×C43—21no—
59C2×C4⋊C4×C43—21no—
60C2×C4⋊C4×C43—21no—
61C2×C4⋊C4×C43C2×C412yescomplemented
62C2×C4⋊C4×C43D412yes—
63C2×C22⋊C4×C43—21no—
64C22⋊C8×C43—21no—
65C22⋊C8×C43—21no—
66#95×C43—21no—
67C24×C43C2×D411yescharacteristic
68C23×D43—21no—
69C23×D43—21no—
70C23×D43—21no—
71C23×D43—21no—
72C23×D43—42no—
73C23×D43—42no—
74C23×D43C22⋊C412yes—
75C23×D43D812yes—
76C23×D43SD1612yes—
77C22×C4×C43—22no—
78C22×C4×C43—22no—
79C22×C4×C43—42no—
80C22×C4×C43—41no—
81C22×C4×C43—41no—
82C22×C4×C43—41no—
83C22×C4×C43—41no—
84C22×C4×C43—41no—
85C22×C4×C43—41no—
86C22×C4×C43C22×C411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43#4111yescharacteristic
91C22×C4×C43#4111yescharacteristic
92C22×Dic43—22no—
93C22×Dic43—21no—
94C22×Dic43—22no—
95C22×Dic43—21no—
96C22×Dic43—42no—
97C22×Dic43—42no—
98C22×Dic43—42no—
99C22×Dic43—41no—
100C22×Dic43—41no—
101C22×Dic43C22⋊C412yes—
102C2×C4×D43—44no—
103C2×C4×D43—82no—
104C2×C4×D43—82no—
105C2×C8×C43—42no—
106C2×C8×C43—41no—
107C4⋊C4×C43—22no—
108C4⋊C4×C43—22no—
109C4⋊C4×C43—42no—
110C4⋊C4×C43—41no—
111C4⋊C4×C43—41no—
112C22⋊C4×C43—41no—
113C22⋊C4×C43—41no—
114C22⋊Dic43—41no—
115C22⋊Dic43—41no—
116(C2×D43)⋊C4—22no—
117(C2×D43)⋊C4—22no—
118(C2×D43)⋊C4—22no—
119(C2×D43)⋊C4—22no—
120(C2×D43)⋊C4—44no—
121(C2×D43)⋊C4—48no—
122C4⋊Dic43—42no—
123Dic43⋊C4—82no—
124C2×C43⋊C8—42no—
125C2×C43⋊C8—41no—
126C23×C43—22no—
127C23×C43—22no—
128C23×C43C2×C22⋊C411yescharacteristic
129C23×C43#12011yescharacteristic
130C23×C43#12311yescharacteristic
131C23×C43C2×D811yescharacteristic
132C23×C43C2×SD1611yescharacteristic
133C23×C43AGL(1,ℤ/8)11yescharacteristic
134C23×C43#13711yescharacteristic
135C22×D43—22no—
136C22×D43—22no—
137C22×D43—22no—
138C22×D43—22no—
139C22×D43—22no—
140C22×D43—22no—
141C22×D43—42no—
142C22×D43—42no—
143C22×D43—42no—
144C22×D43—42no—
145C22×D43—44no—
146C22×D43—44no—
147C22×D43—82no—
148C22×D43—82no—
149C22×D43—81no—
150C22×D43—81no—
151C22×D43#10214yes—
152C2×C4×C43—22no—
153C2×C4×C43—22no—
154C2×C4×C43—41no—
155C2×C4×C43—41no—
156C2×C4×C43—41no—
157C2×C4×C43—41no—
158C2×C4×C43—42no—
159C2×C4×C43—42no—
160C2×C4×C43—42no—
161C2×C4×C43—42no—
162C2×C4×C43—42no—
163C2×C4×C43—42no—
164C2×C4×C43—81no—
165C2×C4×C43—81no—
166C2×C4×C43—81no—
167C2×C4×C43—81no—
168C2×C4×C43C4×D411yescharacteristic
169C2×C4×C43C4×D411yescharacteristic
170C2×C4×C43#12111yescharacteristic
171C2×C4×C43#12111yescharacteristic
172C2×Dic43—22no—
173C2×Dic43—42no—
174C2×Dic43—42no—
175C2×Dic43—42no—
176C2×Dic43—42no—
177C2×Dic43—42no—
178C2×Dic43—42no—
179C2×Dic43—42no—
180C2×Dic43—42no—
181C2×Dic43—81no—
182C2×Dic43—82no—
183C2×Dic43—82no—
184C4×D43—88no—
185C8×C43—81no—
186C43⋊C8—81no—
187#9025—431nomaximal, Sylow
188C22×C43—22no—
189C22×C43—22no—
190C22×C43—22no—
191C22×C43—22no—
192C22×C43—21no—
193C22×C43—21no—
194C22×C43—21no—
195C22×C43—21no—
196C22×C43#38611yescharacteristic
197C22×C43C2×#10211yescharacteristic
198C22×C43#41711yescharacteristic
199C22×C43#44711yescharacteristic
200C22×C43#44811yescharacteristic
201C22×C43#45512yes—
202C22×C43#45812yes—
203C22×C43#48011yescharacteristic
204C22×C43#48111yescharacteristic
205C2×D43—24no—
206C2×D43—44no—
207C2×D43—44no—
208C2×D43—42no—
209C2×D43—42no—
210C2×D43—44no—
211C2×D43—82no—
212C2×D43—82no—
213C2×D43—82no—
214C4×C43—21no—
215C4×C43—21no—
216C4×C43—21no—
217C4×C43—21no—
218C4×C43—82no—
219C4×C43—82no—
220Dic43—42no—
221Dic43—82no—
222Dic43—82no—
223C2×#397—431no—
224#2315—431no—
225#1823—431no—
226#1823D4311yescharacteristic, complemented
227C2×#323—431no—
228#1294—431no—
229#1294—431no—
230C2×C43—21no—
231C2×C43—21no—
232C2×C43—21no—
233C2×C43—21no—
234C2×C43#160712yes—
235C2×C43#160812yes—
236C2×C43#187411yescharacteristic
237C2×C43#188511yescharacteristic
238C2×C43#189011yescharacteristic
239D43—44no—
240C22×C4⋊C4C2×D4311yescharacteristic
241C22×C22⋊C4—431no—
242C22×C22⋊C4—861no—
243C22×C22⋊C4—861no—
244C2×C22⋊C8—431no—
245C2×C22⋊C8C2×D4311yescharacteristic
246#397—434no—
247#397—862no—
248#385—862no—
249#385—862no—
250#380—431no—
251#380—861no—
252#380C2×D4311yescharacteristic
253C2×#95—431no—
254C2×#95—861no—
255#340—22no—
256#340—862no—
257#323—862no—
258C43#902511yescharacteristic, complemented, Sylow
259C25—431no—
260C23×C4—21no—
261C23×C4—431no—
262C23×C4—862no—
263C23×C4—861no—
264C23×C4C22×D4311yescharacteristic
265C22×C8—21no—
266C22×C8—861no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—432no—
273C2×C4⋊C4—862no—
274C2×C4⋊C4C4×D4312yescomplemented
275C2×C4⋊C4C22⋊D4312yes—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—432no—
278C2×C22⋊C4—432no—
279C2×C22⋊C4—861no—
280C2×C22⋊C4—861no—
281C2×C22⋊C4—861no—
282C2×C22⋊C4—861no—
283C2×C22⋊C4—864no—
284C2×C22⋊C4—862no—
285C2×C22⋊C4—861no—
286C2×C22⋊C4—1722no—
287C2×C22⋊C4—1722no—
288C2×C22⋊C4—1722no—
289C2×C22⋊C4—1722no—
290C22⋊C8—21no—
291C22⋊C8—21no—
292C22⋊C8—861no—
293C22⋊C8—861no—
294#95—21no—
295#95—432no—
296#95—864no—
297#95—862no—
298#95—861no—
299#95—861no—
300C24—432no—
301C24—432no—
302C24—432no—
303C24—861no—
304C24—861no—
305C24—861no—
306C24—861no—
307C24—1722no—
308C24—1722no—
309C24D4×D4311yescharacteristic
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—42no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—432no—
320C22×C4—861no—
321C22×C4—861no—
322C22×C4—862no—
323C22×C4—862no—
324C22×C4—3442no—
325C22×C4—3442no—
326C22×C4—1724no—
327C22×C4—1722no—
328C22×C4—1722no—
329C22×C4—1721no—
330C22×C4—1721no—
331C22×C4—1722no—
332C22×C4C2×C4×D4311yescharacteristic
333C22×C4#1062189811yescharacteristic
334C22×C4D4×D4311yescharacteristic
335C22×C4D4×D4311yescharacteristic
336C22×C4#1062190011yescharacteristic
337C22×C4C2×C22⋊D4311yescharacteristic
338C2×C8—42no—
339C2×C8—41no—
340C2×C8—1722no—
341C2×C8—1721no—
342C4⋊C4—22no—
343C4⋊C4—22no—
344C4⋊C4—42no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—3442no—
348C4⋊C4—1722no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—862no—
352C22⋊C4—862no—
353C22⋊C4—862no—
354C22⋊C4—862no—
355C22⋊C4—1728no—
356C22⋊C4—1724no—
357C22⋊C4—1721no—
358C22⋊C4—1721no—
359C23—22no—
360C23—22no—
361C23—434no—
362C23—862no—
363C23—862no—
364C23—862no—
365C23—862no—
366C23—862no—
367C23—862no—
368C23—3441no—
369C23—3441no—
370C23—3442no—
371C23—3442no—
372C23—1722no—
373C23—1722no—
374C23—1724no—
375C23—1724no—
376C23—1722no—
377C23—1722no—
378C23C22⋊C4×D4311yescharacteristic
379C23#1306329311yescharacteristic
380C23#1306330711yescharacteristic
381C23D8×D4311yescharacteristic
382C23SD16×D4311yescharacteristic
383C23#1306334911yescharacteristic
384C23#1306335411yescharacteristic
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4—862no—
402C2×C4—3448no—
403C2×C4—3442no—
404C2×C4—3442no—
405C2×C4—3441no—
406C2×C4—1722no—
407C2×C4—1722no—
408C2×C4—1722no—
409C2×C4—1722no—
410C2×C4—1722no—
411C2×C4—1722no—
412C2×C4—1722no—
413C2×C4—1722no—
414C2×C4(C22⋊D43)⋊C411yescharacteristic
415C2×C4C4×C22⋊D4311yescharacteristic
416C2×C4#1306329611yescharacteristic
417C2×C4#1306329811yescharacteristic
418C8—81no—
419C8—3441no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—22no—
425C22—22no—
426C22—22no—
427C22—22no—
428C22—864no—
429C22—3442no—
430C22—3442no—
431C22—3442no—
432C22—1724no—
433C22—1722no—
434C22—1722no—
435C22—1724no—
436C22—1724no—
437C22#1458277511yescharacteristic
438C22#102×D4311yescharacteristic
439C22#1458289711yescharacteristic
440C22#1458303111yescharacteristic
441C22#1458303611yescharacteristic
442C22#1458307512yes—
443C22#1458308812yes—
444C22#1458321111yescharacteristic
445C22#1458321611yescharacteristic
446C4—21no—
447C4—21no—
448C4—21no—
449C4—21no—
450C4—82no—
451C4—82no—
452C4—3442no—
453C4—3442no—
454C4—1722no—
455C2—21no—
456C2—21no—
457C2—21no—
458C2—21no—
459C2—1724no—
460C2#1913357912yes—
461C2#1913358412yes—
462C2#1913490911yescharacteristic
463C2#1913498011yescharacteristic
464C2#1913500511yescharacteristic
subgroupG/H
centerC23#13063293
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1823C2
socleC23×C43#120
prime radicalC24×D43D4
cosocleC23×C4×C43C23
hypercenter#1823D43
hypocenterC43#9025
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
3. #19134681C2semidirect
5. #19132475C2semidirect
6. #19132473C2semidirect
7. C43×#1823C2semidirect
13. #14582825C4semidirect
52. C43⋊#95C2×C4semidirect
61. C2×C4⋊C4×C43C2×C4semidirect
226. #1823D43semidirect
258. C43#9025semidirect
274. C2×C4⋊C4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145828252
#191372082
#191346812
C2×#145826222
#191324752
#191324732
C43×#18232
#902543