Finite Group Databasebeta

← #24993177

Subgroups — #24993177

Order 11008.

564 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145348C211yesmaximal, characteristic
2#19135431C211yesmaximal, characteristic
3#19133167C211yesmaximal, characteristic, complemented
4C2×#14582632C211yesmaximal, characteristic
5#19132474C211yesmaximal, characteristic, complemented
6#19132443C211yesmaximal, characteristic, complemented
7C43×#2368C211yesmaximal, characteristic, complemented
8C2×#13063299C2211yescharacteristic
9#14583227C412yescomplemented
10#14583217—21no—
11#14583130—22no—
12#14583049C412yescomplemented
13#14583038—21no—
14C2×#13063239—21no—
15C2×#13063239—21no—
16C2×C22⋊(C43⋊C8)C2211yescharacteristic
17C2×C22⋊(C43⋊C8)C2211yescharacteristic
18#14582759C2211yescharacteristic
19#14582636—22no—
20#14582632—21no—
21#14582632—21no—
22C2×C22⋊Q8×C43C2211yescharacteristic
23C43×#391—21no—
24C43×#387—21no—
25C43×#387—21no—
26C43×#385—21no—
27C4×C4⋊C4×C43—21no—
28C4×C22⋊C4×C43—21no—
29C4×C22⋊C4×C43C2211yescharacteristic
30C2×#95×C43C2211yescharacteristic
31C22×D172C2×C411yescharacteristic
32C22×C22⋊D43—21no—
33C2×#10621884—22no—
34C22×C43⋊C8—21no—
35C22×C43⋊C8—21no—
36#13063299—21no—
37#13063299—21no—
38#13063299—21no—
39#13063299—21no—
40C2×C4⋊Dic43—21no—
41C2×C4⋊Dic43C2×C411yescharacteristic
42C2×C22⋊Dic43—21no—
43C2×(C2×D43)⋊C4—21no—
44#13063256—22no—
45#13063249—22no—
46#13063245—22no—
47#13063239—42no—
48#13063239—42no—
49C22⋊(C43⋊C8)—21no—
50C22⋊(C43⋊C8)—21no—
51C22⋊(C43⋊C8)—21no—
52C22⋊(C43⋊C8)C2×C412yes—
53C43⋊#95—21no—
54C22×Q8×C43D411yescharacteristic
55C23×C4×C43—21no—
56C23×C4×C43C2311yescharacteristic
57C22⋊Q8×C43—21no—
58C22⋊Q8×C43—21no—
59C22⋊Q8×C43C2×C412yes—
60C22⋊Q8×C43D412yes—
61C2×C4⋊C4×C43—21no—
62C2×C4⋊C4×C43—21no—
63C2×C4⋊C4×C43—21no—
64C2×C4⋊C4×C43D411yescharacteristic
65C2×C22⋊C4×C43—21no—
66C2×C22⋊C4×C43D411yescharacteristic
67C2×C22⋊C4×C43D411yescharacteristic
68C2×C42×C43—21no—
69C2×C42×C43—21no—
70C2×C42×C43—21no—
71#95×C43—21no—
72#95×C43—21no—
73#95×C43—21no—
74#95×C43—21no—
75#95×C43—21no—
76#95×C43—21no—
77#95×C43D411yescharacteristic
78#95×C43D411yescharacteristic
79C24×C43C2×D411yescharacteristic
80C23×D43—21no—
81C2×Q8×C43—21no—
82C2×Q8×C43—81no—
83C2×Q8×C43C22⋊C412yes—
84C22×C4×C43—21no—
85C22×C4×C43—21no—
86C22×C4×C43—21no—
87C22×C4×C43—21no—
88C22×C4×C43—21no—
89C22×C4×C43—21no—
90C22×C4×C43—42no—
91C22×C4×C43—41no—
92C22×C4×C43—41no—
93C22×C4×C43—81no—
94C22×C4×C43—81no—
95C22×C4×C43C22×C411yescharacteristic
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43#4111yescharacteristic
100C22×C4×C43#4111yescharacteristic
101C2×C22⋊D43—41no—
102C2×C22⋊D43—41no—
103C2×C22⋊D43—41no—
104C2×C22⋊D43—41no—
105C2×C22⋊D43—41no—
106C2×C22⋊D43—41no—
107C22×Dic43—21no—
108C22×Dic43—41no—
109C2×D172—21no—
110C2×D172—21no—
111C2×D172—81no—
112C4⋊C4×C43—22no—
113C4⋊C4×C43—22no—
114C4⋊C4×C43—21no—
115C4⋊C4×C43—42no—
116C4⋊C4×C43—81no—
117C4⋊C4×C43C22⋊C412yes—
118C22⋊C4×C43—22no—
119C22⋊C4×C43—22no—
120C22⋊C4×C43—21no—
121C22⋊C4×C43—21no—
122C22⋊C4×C43—21no—
123C22⋊C4×C43SD1612yescomplemented
124C42×C43—42no—
125C42×C43—81no—
126C42×C43—81no—
127C22⋊Dic43—41no—
128C22⋊Dic43—41no—
129#10621884—82no—
130(C2×D43)⋊C4—41no—
131(C2×D43)⋊C4—41no—
132C4⋊Dic43—21no—
133C4⋊Dic43—21no—
134C4⋊Dic43—81no—
135C2×C43⋊C8—22no—
136C2×C43⋊C8—41no—
137C2×C43⋊C8—81no—
138C2×C43⋊C8—81no—
139C23×C43—41no—
140C23×C43—41no—
141C23×C43C4×D411yescharacteristic
142C23×C43#12011yescharacteristic
143C23×C43#12111yescharacteristic
144C23×C43C2×SD1611yescharacteristic
145C23×C43#13511yescharacteristic
146C23×C43AGL(1,ℤ/8)11yescharacteristic
147C23×C43#13711yescharacteristic
148C22×D43—41no—
149C22×D43—41no—
150C22×D43—41no—
151C22×D43—81no—
152C22×D43—81no—
153Q8×C43—42no—
154Q8×C43—81no—
155C2×C4×C43—22no—
156C2×C4×C43—22no—
157C2×C4×C43—22no—
158C2×C4×C43—22no—
159C2×C4×C43—41no—
160C2×C4×C43—41no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43—41no—
164C2×C4×C43—41no—
165C2×C4×C43—41no—
166C2×C4×C43—41no—
167C2×C4×C43—41no—
168C2×C4×C43—41no—
169C2×C4×C43—41no—
170C2×C4×C43—41no—
171C2×C4×C43—41no—
172C2×C4×C43—41no—
173C2×C4×C43—41no—
174C2×C4×C43—41no—
175C2×C4×C43—41no—
176C2×C4×C43—41no—
177C2×C4×C43—41no—
178C2×C4×C43—41no—
179C2×C4×C43—82no—
180C2×C4×C43—82no—
181C2×C4×C43C2×C22⋊C411yescharacteristic
182C2×C4×C43C4×D411yescharacteristic
183C2×C4×C43#12111yescharacteristic
184C2×C4×C43#12311yescharacteristic
185C22⋊D43—81no—
186C22⋊D43—81no—
187C22⋊D43—81no—
188C22⋊D43—81no—
189C2×Dic43—41no—
190C2×Dic43—41no—
191C2×Dic43—41no—
192C2×Dic43—81no—
193C2×Dic43—81no—
194C2×Dic43—81no—
195D172—42no—
196D172—81no—
197C43⋊C8—42no—
198C43⋊C8—81no—
199#9278—431nomaximal, Sylow
200C22×C43—21no—
201C22×C43—21no—
202C22×C43—21no—
203C22×C43—21no—
204C22×C43—21no—
205C22×C43—21no—
206C22×C43—41no—
207C22×C43—41no—
208C22×C43—41no—
209C22×C43—41no—
210C22×C43#38611yescharacteristic
211C22×C43C4×SD1611yescharacteristic
212C22×C43#44011yescharacteristic
213C22×C43#44811yescharacteristic
214C22×C43#44911yescharacteristic
215C22×C43#46011yescharacteristic
216C22×C43#46411yescharacteristic
217C2×D43—81no—
218C2×D43—81no—
219C2×D43—81no—
220C2×D43—161no—
221C2×D43—161no—
222C4×C43—21no—
223C4×C43—21no—
224C4×C43—21no—
225C4×C43—21no—
226C4×C43—42no—
227C4×C43—42no—
228C4×C43—42no—
229C4×C43—42no—
230C4×C43—81no—
231C4×C43—81no—
232Dic43—81no—
233Dic43—161no—
234#3187—431no—
235#2368D4311yescharacteristic, complemented
236#1964—431no—
237#1520—431no—
238C2×#327—431no—
239#1294—431no—
240#1282—431no—
241C2×C43—21no—
242C2×C43—21no—
243C2×C43—21no—
244C2×C43—21no—
245C2×C43—21no—
246C2×C43—21no—
247C2×C43#188011yescharacteristic
248C2×C43#190611yescharacteristic
249C2×C43#191311yescharacteristic
250D43—161no—
251C2×C22⋊Q8C2×D4311yescharacteristic
252C2×#121—431no—
253#483—432no—
254#481—861no—
255#465—862no—
256#450—432no—
257#448—861no—
258C2×#99—861no—
259C2×#99—861no—
260C2×C22⋊C8—431no—
261C2×C22⋊C8—431no—
262#391—21no—
263#387—21no—
264#387—21no—
265#385—21no—
266#380—431no—
267C4×C4⋊C4—21no—
268C4×C22⋊C4—21no—
269C4×C22⋊C4C2×D4311yescharacteristic
270C2×#95C2×D4311yescharacteristic
271#328—862no—
272#327—861no—
273#327—861no—
274C43#927811yescharacteristic, complemented, Sylow
275C22×Q8C22⋊D4311yescharacteristic
276C22×D4—431no—
277C22×D4—861no—
278C23×C4—21no—
279C23×C4C22×D4311yescharacteristic
280C2×SD16—862no—
281C22×C8—861no—
282C22×C8—861no—
283C22⋊Q8—21no—
284C22⋊Q8—21no—
285C22⋊Q8C4×D4312yes—
286C22⋊Q8D17212yes—
287#121—861no—
288#121—861no—
289#121—861no—
290#121—861no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—431no—
295C2×C4⋊C4—861no—
296C2×C4⋊C4C22⋊D4311yescharacteristic
297C2×C22⋊C4—21no—
298C2×C22⋊C4—861no—
299C2×C22⋊C4—861no—
300C2×C22⋊C4C22⋊D4311yescharacteristic
301C2×C22⋊C4C22⋊D4311yescharacteristic
302C2×C42—21no—
303C2×C42—21no—
304C2×C42—21no—
305#106—862no—
306#103—862no—
307#102—862no—
308#99—1722no—
309#99—1722no—
310C22⋊C8—432no—
311C22⋊C8—861no—
312C22⋊C8—861no—
313C22⋊C8—861no—
314#95—21no—
315#95—21no—
316#95—21no—
317#95—21no—
318#95—21no—
319#95—21no—
320#95—861no—
321#95C22⋊D4311yescharacteristic
322#95C22⋊D4311yescharacteristic
323C24—861no—
324C24C2×C22⋊D4311yescharacteristic
325C2×Q8—21no—
326C2×Q8—81no—
327C2×Q8(C2×D43)⋊C412yes—
328C2×D4—861no—
329C2×D4—861no—
330C2×D4—3441no—
331C2×D4—1721no—
332C2×D4—1721no—
333C2×D4—1721no—
334C2×D4—1721no—
335C2×D4—1721no—
336C2×D4—1721no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—42no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—81no—
347C22×C4—81no—
348C22×C4—861no—
349C22×C4—1721no—
350C22×C4C2×C4×D4311yescharacteristic
351C22×C4C2×D17211yescharacteristic
352C22×C4#1062189811yescharacteristic
353C22×C4#1062189811yescharacteristic
354C22×C4C2×C22⋊D4311yescharacteristic
355C22×C4C2×C22⋊D4311yescharacteristic
356SD16—3442no—
357C2×C8—862no—
358C2×C8—3441no—
359C2×C8—3441no—
360C2×C8—1721no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—21no—
364C4⋊C4—42no—
365C4⋊C4—81no—
366C4⋊C4—861no—
367C4⋊C4—861no—
368C4⋊C4—3441no—
369C4⋊C4(C2×D43)⋊C412yes—
370C22⋊C4—22no—
371C22⋊C4—22no—
372C22⋊C4—21no—
373C22⋊C4—21no—
374C22⋊C4—21no—
375C22⋊C4—1721no—
376C22⋊C4—1721no—
377C22⋊C4—1721no—
378C22⋊C4—1721no—
379C22⋊C4#1062188412yescomplemented
380C42—42no—
381C42—81no—
382C42—81no—
383C23—41no—
384C23—41no—
385C23—3441no—
386C23—3441no—
387C23—1721no—
388C23—1721no—
389C23—1721no—
390C23C4×C22⋊D4311yescharacteristic
391C23#1306329411yescharacteristic
392C23#1306329911yescharacteristic
393C23C2×#1062188411yescharacteristic
394C23#1306334511yescharacteristic
395C23#1306335011yescharacteristic
396C23#1306335611yescharacteristic
397Q8—42no—
398Q8—81no—
399D4—3441no—
400D4—3441no—
401D4—3441no—
402D4—3441no—
403D4—3441no—
404D4—1722no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—82no—
430C2×C4—82no—
431C2×C4—3441no—
432C2×C4—3441no—
433C2×C4—3441no—
434C2×C4—1721no—
435C2×C4—1721no—
436C2×C4—1721no—
437C2×C4C2×(C2×D43)⋊C411yescharacteristic
438C2×C4C4×C22⋊D4311yescharacteristic
439C2×C4#1306329911yescharacteristic
440C2×C4#1306330811yescharacteristic
441C8—3441no—
442C8—1722no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—3441no—
454C22—3441no—
455C22—3441no—
456C22—6881no—
457C22—6881no—
458C22#1458277811yescharacteristic
459C22C4×#1062188411yescharacteristic
460C22#1458299711yescharacteristic
461C22#1458303811yescharacteristic
462C22#1458304411yescharacteristic
463C22#1458309911yescharacteristic
464C22#1458312111yescharacteristic
465C4—21no—
466C4—21no—
467C4—21no—
468C4—21no—
469C4—42no—
470C4—42no—
471C4—42no—
472C4—42no—
473C4—81no—
474C4—81no—
475C4—3441no—
476C4—6881no—
477C2—21no—
478C2—21no—
479C2—21no—
480C2—21no—
481C2—21no—
482C2—21no—
483C2—6881no—
484C2#1913495011yescharacteristic
485C2#1913509611yescharacteristic
486C2#1913513711yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#2368C2
socleC22×C43#386
prime radicalC2×#13063299C22
cosocleC23×C4×C43C23
hypercenter#2368D43
hypocenterC43#9278
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2368

Complements

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

NH ≅ G/Ntype
3. #19133167C2semidirect
5. #19132474C2semidirect
6. #19132443C2semidirect
7. C43×#2368C2semidirect
9. #14583227C4semidirect
12. #14583049C4semidirect
123. C22⋊C4×C43SD16semidirect
235. #2368D43semidirect
274. C43#9278semidirect
379. C22⋊C4#10621884semidirect

Maximal subgroups

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

subgroupindex
#191453482
#191354312
#191331672
C2×#145826322
#191324742
#191324432
C43×#23682
#927843