Finite Group Databasebeta

← #24988135

Subgroups — #24988135

Order 11008.

834 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148398C211yesmaximal, characteristic
2#19135016C212yesmaximal, complemented
3#19134888C211yesmaximal, characteristic
4#19133166C212yesmaximal, complemented
5C43×#1799C211yesmaximal, characteristic
6C23×C43⋊C8C2211yescharacteristic
7#14583608—24no—
8#14583606—22no—
9D4×Dic86—22no—
10#14583530C412yescomplemented
11#14583525—21no—
12#14583525C412yescomplemented
13#14583456—21no—
14C2×#13063304—21no—
15C2×#13063304C2212yes—
16#14583374—21no—
17C2×#13063248—22no—
18C2×C22⋊(C43⋊C8)—21no—
19C2×C22⋊(C43⋊C8)C2211yescharacteristic
20#14582661—22no—
21#14582654—21no—
22#14582635—24no—
23C2×C4×D4×C43C2211yescharacteristic
24C2×#99×C43—21no—
25C43×#380C2212yes—
26C43×#342—21no—
27C22×Dic86—21no—
28C22×Dic86D412yes—
29C22×C43⋊C8—21no—
30C22×C43⋊C8—22no—
31C22×C43⋊C8—21no—
32C22×C43⋊C8—42no—
33#13063325—21no—
34#13063325—21no—
35#13063324—24no—
36#13063317—22no—
37#13063316—24no—
38#13063304—22no—
39#13063304—22no—
40#13063304—22no—
41#13063304—22no—
42#13063304—22no—
43#13063304—22no—
44#13063304C2×C414yes—
45#13063304D414yes—
46#13063302—24no—
47#13063302—24no—
48#13063302—24no—
49#13063302—24no—
50C4×Dic86—22no—
51C4×Dic86—22no—
52D4×Dic43—24no—
53D4×Dic43—24no—
54#13063284—22no—
55C2×C4⋊Dic43—21no—
56C2×C4⋊Dic43D412yes—
57C2×Dic43⋊C4—22no—
58C2×Dic43⋊C4—22no—
59C2×C22⋊Dic43—22no—
60C2×C22⋊Dic43—22no—
61#13063248—44no—
62C22⋊(C43⋊C8)—22no—
63C22⋊(C43⋊C8)—42no—
64C22×D4×C43D411yescharacteristic
65C23×C4×C43D411yescharacteristic
66C23×C4×C43C2311yescharacteristic
67C4×D4×C43—22no—
68C4×D4×C43—22no—
69C2×C4⋊C4×C43—22no—
70C2×C4⋊C4×C43C2×C411yescharacteristic
71C2×C22⋊C4×C43—22no—
72C2×C22⋊C4×C43C2×C411yescharacteristic
73C2×C22⋊C4×C43D411yescharacteristic
74C2×C42×C43D411yescharacteristic
75#99×C43—42no—
76#95×C43—22no—
77C24×C43C22⋊C411yescharacteristic
78C24×C43C2×D411yescharacteristic
79C2×D4×C43—22no—
80C2×D4×C43—22no—
81C2×D4×C43SD1612yes—
82C2×D4×C43Q1612yes—
83C22×C4×C43—21no—
84C22×C4×C43—21no—
85C22×C4×C43—41no—
86C22×C4×C43—41no—
87C22×C4×C43—41no—
88C22×C4×C43—41no—
89C22×C4×C43—42no—
90C22×C4×C43C22⋊C411yescharacteristic
91C22×C4×C43C22⋊C411yescharacteristic
92C22×C4×C43C22⋊C411yescharacteristic
93C22×C4×C43C22×C411yescharacteristic
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43C2×D412yes—
96C22×C4×C43C2×D412yes—
97C22×Dic43—22no—
98C22×Dic43—22no—
99C22×Dic43—22no—
100C22×Dic43—22no—
101C2×Dic86—22no—
102C2×Dic86—22no—
103C2×Dic86—22no—
104C2×Dic86—42no—
105C2×Dic86—42no—
106C2×Dic86—81no—
107C2×Dic86—81no—
108C2×Dic86C22⋊C414yes—
109C4⋊C4×C43—22no—
110C4⋊C4×C43—42no—
111C4⋊C4×C43—42no—
112C22⋊C4×C43—22no—
113C22⋊C4×C43—22no—
114C22⋊C4×C43—42no—
115C22⋊C4×C43—42no—
116C42×C43—21no—
117C42×C43—21no—
118C22⋊Dic43—24no—
119C22⋊Dic43—24no—
120C22⋊Dic43—24no—
121C4⋊Dic43—22no—
122C4⋊Dic43—22no—
123C4⋊Dic43—22no—
124C4⋊Dic43—22no—
125C4⋊Dic43—22no—
126C4⋊Dic43C22⋊C414yes—
127Dic43⋊C4—24no—
128Dic43⋊C4—24no—
129Dic43⋊C4—24no—
130Dic43⋊C4—24no—
131C4×Dic43—24no—
132C2×C43⋊C8—22no—
133C2×C43⋊C8—24no—
134C2×C43⋊C8—41no—
135C2×C43⋊C8—42no—
136C2×C43⋊C8—41no—
137C2×C43⋊C8—41no—
138C2×C43⋊C8—41no—
139C2×C43⋊C8—41no—
140C23×C43—21no—
141C23×C43—21no—
142C23×C43—41no—
143C23×C43—41no—
144C23×C43—41no—
145C23×C43—41no—
146C23×C43#10312yescomplemented
147C23×C43C2×C22⋊C411yescharacteristic
148C23×C43#12012yes—
149C23×C43C2×SD1611yescharacteristic
150C23×C43C2×Q1611yescharacteristic
151C23×C43#13712yes—
152D4×C43—24no—
153D4×C43—24no—
154C2×C4×C43—21no—
155C2×C4×C43—21no—
156C2×C4×C43—21no—
157C2×C4×C43—22no—
158C2×C4×C43—21no—
159C2×C4×C43—22no—
160C2×C4×C43—21no—
161C2×C4×C43—21no—
162C2×C4×C43—41no—
163C2×C4×C43—42no—
164C2×C4×C43—41no—
165C2×C4×C43—41no—
166C2×C4×C43—41no—
167C2×C4×C43—41no—
168C2×C4×C43—81no—
169C2×C4×C43—82no—
170C2×C4×C43—82no—
171C2×C4×C43—82no—
172C2×C4×C43#10312yescomplemented
173C2×C4×C43C2×C22⋊C412yes—
174C2×C4×C43#12011yescharacteristic
175C2×C4×C43#12011yescharacteristic
176C2×Dic43—24no—
177C2×Dic43—24no—
178C2×Dic43—82no—
179C2×Dic43—82no—
180C2×Dic43—82no—
181C2×Dic43—82no—
182Dic86—42no—
183Dic86—42no—
184Dic86—44no—
185Dic86—82no—
186Dic86—82no—
187C43⋊C8—42no—
188C43⋊C8—81no—
189#8351—431nomaximal, Sylow
190C22×C43—21no—
191C22×C43—22no—
192C22×C43—21no—
193C22×C43—22no—
194C22×C43—22no—
195C22×C43—41no—
196C22×C43—41no—
197C22×C43—42no—
198C22×C43—42no—
199C22×C43—41no—
200C22×C43—41no—
201C22×C43—81no—
202C22×C43#37911yescharacteristic
203C22×C43C2×#10311yescharacteristic
204C22×C43#41911yescharacteristic
205C22×C43#44812yes—
206C22×C43#45112yes—
207C4×C43—22no—
208C4×C43—21no—
209C4×C43—22no—
210C4×C43—41no—
211C4×C43—41no—
212C4×C43—162no—
213C4×C43B(4,𝔽2)11yescharacteristic
214C4×C43#45811yescharacteristic
215Dic43—44no—
216Dic43—44no—
217#3501—431no—
218#1892—432no—
219#1869—431no—
220#1799D4311yescharacteristic
221#1520—432no—
222C2×C43—22no—
223C2×C43—21no—
224C2×C43—21no—
225C2×C43—22no—
226C2×C43—42no—
227C2×C43#178711yescharacteristic
228C2×C43#179011yescharacteristic
229C2×C43#179411yescharacteristic
230C23×C8—431no—
231#554—862no—
232#554—864no—
233D4×Q8—862no—
234#544—432no—
235#543—432no—
236#543—861no—
237#533—861no—
238C2×C22⋊Q8—432no—
239C2×C22⋊Q8—861no—
240#518—861no—
241C2×C4×D4C2×D4311yescharacteristic
242C2×#103—862no—
243C2×#99—21no—
244C2×C22⋊C8—431no—
245C2×C22⋊C8—861no—
246#380C2×D4312yes—
247#342—21no—
248#340—862no—
249#336—861no—
250#328—864no—
251C43#835111yescharacteristic, complemented, Sylow
252C22×Q8—432no—
253C22×Q8—861no—
254C22×D4C22⋊D4311yescharacteristic
255C23×C4D17211yescharacteristic
256C23×C4C22×D4311yescharacteristic
257C22×C8—861no—
258C22×C8—862no—
259C22×C8—861no—
260C22×C8—1722no—
261C4⋊Q8—861no—
262C4⋊Q8—861no—
263C4⋊Q8—864no—
264#125—862no—
265#125—864no—
266C22⋊Q8—434no—
267C22⋊Q8—434no—
268C22⋊Q8—864no—
269C22⋊Q8—864no—
270C22⋊Q8—864no—
271C22⋊Q8—864no—
272C22⋊Q8—862no—
273C22⋊Q8—862no—
274C22⋊Q8—862no—
275C22⋊Q8—862no—
276C22⋊Q8—862no—
277C22⋊Q8—862no—
278C4×Q8—862no—
279C4×Q8—862no—
280C4×D4—22no—
281C4×D4—22no—
282C4×D4—864no—
283C4×D4—864no—
284#117—862no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—432no—
287C2×C4⋊C4—862no—
288C2×C4⋊C4—861no—
289C2×C4⋊C4—862no—
290C2×C4⋊C4C4×D4311yescharacteristic
291C2×C22⋊C4—22no—
292C2×C22⋊C4—862no—
293C2×C22⋊C4—862no—
294C2×C22⋊C4C4×D4311yescharacteristic
295C2×C22⋊C4C22⋊D4311yescharacteristic
296C2×C42D17211yescharacteristic
297#103—1724no—
298#99—42no—
299C22⋊C8—862no—
300C22⋊C8—1722no—
301#95—22no—
302C24(C2×D43)⋊C411yescharacteristic
303C24C2×C22⋊D4311yescharacteristic
304C2×Q8—434no—
305C2×Q8—862no—
306C2×Q8—862no—
307C2×Q8—862no—
308C2×Q8—3441no—
309C2×Q8—3441no—
310C2×Q8—1722no—
311C2×Q8—1722no—
312C2×D4—22no—
313C2×D4—22no—
314C2×D4#1062188312yes—
315C2×D4#1062188512yes—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—42no—
323C22×C4—862no—
324C22×C4—862no—
325C22×C4—862no—
326C22×C4—862no—
327C22×C4(C2×D43)⋊C411yescharacteristic
328C22×C4(C2×D43)⋊C411yescharacteristic
329C22×C4(C2×D43)⋊C411yescharacteristic
330C22×C4C2×C4×D4311yescharacteristic
331C22×C4C2×D17211yescharacteristic
332C22×C4D4×D4312yes—
333C22×C4D4×D4312yes—
334C2×C8—862no—
335C2×C8—864no—
336C2×C8—1721no—
337C2×C8—1721no—
338C2×C8—1721no—
339C2×C8—1722no—
340C2×C8—1721no—
341C2×C8—1721no—
342C4⋊C4—22no—
343C4⋊C4—42no—
344C4⋊C4—42no—
345C4⋊C4—434no—
346C4⋊C4—862no—
347C4⋊C4—864no—
348C4⋊C4—862no—
349C4⋊C4—862no—
350C4⋊C4—864no—
351C4⋊C4—862no—
352C4⋊C4—864no—
353C4⋊C4—862no—
354C4⋊C4—864no—
355C22⋊C4—22no—
356C22⋊C4—22no—
357C22⋊C4—42no—
358C22⋊C4—42no—
359C22⋊C4—864no—
360C22⋊C4—864no—
361C22⋊C4—864no—
362C42—21no—
363C42—21no—
364C42—864no—
365C23—21no—
366C23—21no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23#1306324812yescomplemented
372C23C2×(C2×D43)⋊C411yescharacteristic
373C23#1306329312yes—
374C23C2×#1062188311yescharacteristic
375C23C2×#1062188511yescharacteristic
376C23#1306335512yes—
377Q8—3442no—
378Q8—3442no—
379Q8—1724no—
380Q8—1722no—
381Q8—1722no—
382D4—24no—
383D4—24no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—22no—
387C2×C4—21no—
388C2×C4—22no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—81no—
399C2×C4—82no—
400C2×C4—82no—
401C2×C4—82no—
402C2×C4—864no—
403C2×C4—864no—
404C2×C4—3442no—
405C2×C4—3442no—
406C2×C4—3442no—
407C2×C4—3442no—
408C2×C4#1306324812yescomplemented
409C2×C4C22⋊C4×D4312yes—
410C2×C4#1306329511yescharacteristic
411C2×C4#1306329511yescharacteristic
412C8—3441no—
413C8—1722no—
414C22—21no—
415C22—22no—
416C22—21no—
417C22—22no—
418C22—22no—
419C22—41no—
420C22—41no—
421C22—42no—
422C22—42no—
423C22—41no—
424C22—41no—
425C22—81no—
426C22#1458275411yescharacteristic
427C22C2×#1306324811yescharacteristic
428C22#1458290711yescharacteristic
429C22#1458303712yes—
430C22#1458305412yes—
431C4—22no—
432C4—21no—
433C4—22no—
434C4—41no—
435C4—41no—
436C4—162no—
437C4—1724no—
438C4—1724no—
439C4#1458308711yescharacteristic
440C4#1458309011yescharacteristic
441C2—22no—
442C2—21no—
443C2—21no—
444C2—22no—
445C2—42no—
446C2#1913452911yescharacteristic
447C2#1913454111yescharacteristic
448C2#1913456111yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1799C2
socleC22×C43#379
prime radicalC22×D4×C43D4
cosocleC23×C4×C43C23
hypercenter#1799D43
hypocenterC43#8351
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
2. #19135016C2semidirect
4. #19133166C2semidirect
10. #14583530C4semidirect
12. #14583525C4semidirect
146. C23×C43#103semidirect
172. C2×C4×C43#103semidirect
251. C43#8351semidirect
371. C23#13063248semidirect
408. C2×C4#13063248semidirect

Maximal subgroups

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

subgroupindex
#191483982
#191350162
#191348882
#191331662
C43×#17992
#835143