Finite Group Databasebeta

← #24990146

Subgroups — #24990146

Order 11008.

530 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137499C211yesmaximal, characteristic
2#19134580C211yesmaximal, characteristic
3#19132911C211yesmaximal, characteristic
4#19132475C211yesmaximal, characteristic, complemented
5#19132473C211yesmaximal, characteristic, complemented
6#19132462C211yesmaximal, characteristic, complemented
7C43×#1289C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊D43C2211yescharacteristic
9C2×(C22⋊D43)⋊C4—21no—
10C2×#13063239—21no—
11C2×C22⋊(C43⋊C8)C2211yescharacteristic
12#14582794—21no—
13#14582771—21no—
14#14582770—21no—
15#14582763C411yescharacteristic, complemented
16#14582759C2211yescharacteristic
17#14582758C411yescharacteristic, complemented
18#14582750C411yescharacteristic, complemented
19C2×C43⋊#95C2211yescharacteristic
20#95×D43C411yescharacteristic, complemented
21#14582665—21no—
22#14582624—21no—
23#14582622—21no—
24C2×C22⋊C8×C43C2211yescharacteristic
25C43×#380C2211yescharacteristic
26C43×#380C2211yescharacteristic
27C22×C22⋊D43D411yescharacteristic
28C23×Dic43—21no—
29C22×C4×D43—21no—
30C22×C4×D43C2×C411yescharacteristic
31C22×C43⋊C8—21no—
32C4×C22⋊D43—21no—
33C4×C22⋊D43—21no—
34C4×C22⋊D43—21no—
35C4×C22⋊D43—21no—
36(C22⋊D43)⋊C4—42no—
37(C22⋊D43)⋊C4—42no—
38C2×C4⋊Dic43—21no—
39C2×Dic43⋊C4—21no—
40C2×Dic43⋊C4—21no—
41C2×Dic43⋊C4—21no—
42C2×Dic43⋊C4D411yescharacteristic
43C2×C22⋊Dic43—21no—
44C2×C22⋊Dic43D411yescharacteristic
45C2×(C2×D43)⋊C4—21no—
46C2×(C2×D43)⋊C4D411yescharacteristic
47C2×C4×Dic43—21no—
48C2×C4×Dic43C2×C411yescharacteristic
49#13063239—42no—
50C22⋊(C43⋊C8)—21no—
51C22⋊(C43⋊C8)—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C43⋊#95C2×C411yescharacteristic
57C43⋊#95C2×C411yescharacteristic
58C23×C4×C43C2311yescharacteristic
59C22×C8×C43—21no—
60C2×C4⋊C4×C43—21no—
61C2×C4⋊C4×C43—21no—
62C2×C22⋊C4×C43—21no—
63C2×C22⋊C4×C43—21no—
64C22⋊C8×C43—21no—
65C22⋊C8×C43—21no—
66#95×C43—21no—
67#95×C43C2×C411yescharacteristic
68#95×C43C2×C411yescharacteristic
69C24×C43C2×D411yescharacteristic
70C23×D43C22⋊C411yescharacteristic
71C22×C4×C43—21no—
72C22×C4×C43—21no—
73C22×C4×C43—41no—
74C22×C4×C43—81no—
75C22×C4×C43C22×C411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43#4111yescharacteristic
78C22×C4×C43#4111yescharacteristic
79C22×C4×C43#4111yescharacteristic
80C22×C4×C43#4111yescharacteristic
81C2×C22⋊D43—21no—
82C2×C22⋊D43—21no—
83C2×C22⋊D43—21no—
84C2×C22⋊D43—21no—
85C2×C22⋊D43SD1612yes—
86C2×C22⋊D43Q1612yes—
87C22×Dic43—21no—
88C22×Dic43—21no—
89C22×Dic43—42no—
90C22×Dic43—41no—
91C22×Dic43—41no—
92C22×Dic43—41no—
93C22×Dic43—81no—
94C22×Dic43C22⋊C411yescharacteristic
95C22×Dic43C22⋊C411yescharacteristic
96C22×Dic43C22⋊C411yescharacteristic
97C2×C4×D43—21no—
98C2×C4×D43—21no—
99C2×C4×D43—42no—
100C2×C4×D43—42no—
101C2×C4×D43—81no—
102C2×C4×D43—81no—
103C2×C8×C43—41no—
104C2×C8×C43—81no—
105C4⋊C4×C43—81no—
106C4⋊C4×C43—81no—
107C22⋊C4×C43—41no—
108C22⋊C4×C43—41no—
109C22⋊C4×C43—41no—
110C22⋊C4×C43—41no—
111C22⋊Dic43—21no—
112C22⋊Dic43—21no—
113C22⋊Dic43—41no—
114C22⋊Dic43—41no—
115(C2×D43)⋊C4—21no—
116(C2×D43)⋊C4—21no—
117(C2×D43)⋊C4—42no—
118C4⋊Dic43—81no—
119Dic43⋊C4—21no—
120Dic43⋊C4—21no—
121Dic43⋊C4—42no—
122Dic43⋊C4—42no—
123Dic43⋊C4—81no—
124C4×Dic43—21no—
125C4×Dic43—21no—
126C4×Dic43—42no—
127C2×C43⋊C8—41no—
128C2×C43⋊C8—81no—
129C23×C43—41no—
130C23×C43—41no—
131C23×C43C2×C22⋊C411yescharacteristic
132C23×C43#12311yescharacteristic
133C23×C43#12311yescharacteristic
134C23×C43C2×SD1611yescharacteristic
135C23×C43C2×Q1611yescharacteristic
136C23×C43AGL(1,ℤ/8)11yescharacteristic
137C23×C43AGL(1,ℤ/8)11yescharacteristic
138C22×D43—21no—
139C22×D43—21no—
140C22×D43—41no—
141C22×D43—41no—
142C22×D43#10312yes—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—41no—
154C2×C4×C43—41no—
155C2×C4×C43—81no—
156C2×C4×C43—81no—
157C2×C4×C43—81no—
158C2×C4×C43#11711yescharacteristic
159C2×C4×C43#11711yescharacteristic
160C2×C4×C43#12311yescharacteristic
161C2×C4×C43#12311yescharacteristic
162C22⋊D43—22no—
163C22⋊D43—22no—
164C22⋊D43—22no—
165C22⋊D43—22no—
166C2×Dic43—21no—
167C2×Dic43—21no—
168C2×Dic43—22no—
169C2×Dic43—21no—
170C2×Dic43—21no—
171C2×Dic43—41no—
172C2×Dic43—41no—
173C2×Dic43—41no—
174C2×Dic43—41no—
175C2×Dic43—41no—
176C2×Dic43—41no—
177C2×Dic43—41no—
178C2×Dic43—82no—
179C2×Dic43—82no—
180C2×Dic43—81no—
181C2×Dic43—81no—
182C2×Dic43—81no—
183C2×Dic43#10312yes—
184C4×D43—81no—
185C4×D43—81no—
186C4×D43—84no—
187C8×C43—81no—
188C43⋊C8—81no—
189#8761—431nomaximal, Sylow
190C22×C43—21no—
191C22×C43—21no—
192C22×C43—21no—
193C22×C43—21no—
194C22×C43—21no—
195C22×C43—21no—
196C22×C43—41no—
197C22×C43—41no—
198C22×C43—41no—
199C22×C43—41no—
200C22×C43#38111yescharacteristic
201C22×C43C2×#10311yescharacteristic
202C22×C43#41811yescharacteristic
203C22×C43#48111yescharacteristic
204C22×C43#48111yescharacteristic
205C22×C43#48411yescharacteristic
206C22×C43#48411yescharacteristic
207C2×D43—22no—
208C2×D43—42no—
209C2×D43—41no—
210C2×D43—41no—
211C2×D43—42no—
212C4×C43—21no—
213C4×C43—21no—
214C4×C43—21no—
215C4×C43—21no—
216C4×C43—81no—
217C4×C43—81no—
218C4×C43—161no—
219Dic43—22no—
220Dic43—42no—
221Dic43—41no—
222Dic43—41no—
223Dic43—81no—
224Dic43—161no—
225#2349—431no—
226#1799—431no—
227#1459—431no—
228#1294—431no—
229#1294—431no—
230#1289—431no—
231#1289D4311yescharacteristic, complemented
232C2×C43—21no—
233C2×C43—21no—
234C2×C43—21no—
235C2×C43—21no—
236C2×C43—21no—
237C2×C43—21no—
238C2×C43#182411yescharacteristic
239C2×C43#182711yescharacteristic
240C2×C43#182811yescharacteristic
241D43—42no—
242C2×C4×D4—431no—
243C2×C4×D4—861no—
244C2×#99—861no—
245C2×C22⋊C8—431no—
246C2×C22⋊C8C2×D4311yescharacteristic
247#389—861no—
248#385—861no—
249#385—861no—
250#382—431no—
251#380—431no—
252#380—431no—
253#380C2×D4311yescharacteristic
254#380C2×D4311yescharacteristic
255C4×C4⋊C4—431no—
256C2×#95—431no—
257C2×#95—431no—
258#342—861no—
259#324—861no—
260#323—861no—
261C43#876111yescharacteristic, complemented, Sylow
262C22×D4—431no—
263C23×C4—431no—
264C23×C4—861no—
265C23×C4—861no—
266C23×C4C22×D4311yescharacteristic
267C22×C8—21no—
268C22×C8—861no—
269C4×D4—861no—
270C4×D4—861no—
271C4×D4—861no—
272C4×D4—861no—
273C4×D4—1722no—
274C4×D4—1722no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—431no—
278C2×C4⋊C4—861no—
279C2×C4⋊C4—861no—
280C2×C4⋊C4—861no—
281C2×C4⋊C4—861no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—431no—
285C2×C22⋊C4—431no—
286C2×C22⋊C4—861no—
287C2×C22⋊C4—861no—
288C2×C42—431no—
289C2×C42—861no—
290#99—1722no—
291C22⋊C8—21no—
292C22⋊C8—21no—
293C22⋊C8—861no—
294C22⋊C8—861no—
295#95—21no—
296#95—431no—
297#95—431no—
298#95—861no—
299#95—861no—
300#95—861no—
301#95—861no—
302#95C4×D4311yescharacteristic
303#95C4×D4311yescharacteristic
304C24—431no—
305C24D4×D4311yescharacteristic
306C2×D4—432no—
307C2×D4—432no—
308C2×D4—861no—
309C2×D4—861no—
310C2×D4—861no—
311C2×D4—861no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—41no—
315C22×C4—81no—
316C22×C4—431no—
317C22×C4—431no—
318C22×C4—431no—
319C22×C4—861no—
320C22×C4—861no—
321C22×C4—861no—
322C22×C4—861no—
323C22×C4—3441no—
324C22×C4—3441no—
325C22×C4—3441no—
326C22×C4—1722no—
327C22×C4—1722no—
328C22×C4—1722no—
329C22×C4—1721no—
330C22×C4—1721no—
331C22×C4—1721no—
332C22×C4C2×C4×D4311yescharacteristic
333C22×C4#1062189811yescharacteristic
334C22×C4#1062189811yescharacteristic
335C22×C4D4×D4311yescharacteristic
336C22×C4#1062190011yescharacteristic
337C22×C4#1062190211yescharacteristic
338C2×C8—41no—
339C2×C8—81no—
340C2×C8—3441no—
341C2×C8—1721no—
342C4⋊C4—81no—
343C4⋊C4—81no—
344C4⋊C4—861no—
345C4⋊C4—861no—
346C4⋊C4—3441no—
347C4⋊C4—3441no—
348C4⋊C4—1722no—
349C4⋊C4—1722no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—861no—
355C22⋊C4—861no—
356C22⋊C4—861no—
357C22⋊C4—861no—
358C22⋊C4—1722no—
359C22⋊C4—1721no—
360C22⋊C4—1721no—
361C42—861no—
362C42—861no—
363C42—1722no—
364C23—41no—
365C23—41no—
366C23—432no—
367C23—861no—
368C23—861no—
369C23—1721no—
370C23—1721no—
371C23C22⋊C4×D4311yescharacteristic
372C23#1306330711yescharacteristic
373C23#1306331011yescharacteristic
374C23SD16×D4311yescharacteristic
375C23Q16×D4311yescharacteristic
376C23#1306334911yescharacteristic
377C23#1306335211yescharacteristic
378D4—862no—
379D4—862no—
380D4—862no—
381D4—862no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—432no—
398C2×C4—861no—
399C2×C4—861no—
400C2×C4—862no—
401C2×C4—861no—
402C2×C4—861no—
403C2×C4—3441no—
404C2×C4—3441no—
405C2×C4—3444no—
406C2×C4—3442no—
407C2×C4—3442no—
408C2×C4—3441no—
409C2×C4—3441no—
410C2×C4—3441no—
411C2×C4—1721no—
412C2×C4—1721no—
413C2×C4—1721no—
414C2×C4—1721no—
415C2×C4—1721no—
416C2×C4—1721no—
417C2×C4—1721no—
418C2×C4#1306328211yescharacteristic
419C2×C4#1306328311yescharacteristic
420C2×C4#1306330711yescharacteristic
421C2×C4#1306331011yescharacteristic
422C8—81no—
423C8—3441no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22—862no—
435C22—1722no—
436C22—1722no—
437C22—1721no—
438C22—1721no—
439C22#1458276111yescharacteristic
440C22#103×D4311yescharacteristic
441C22#1458290211yescharacteristic
442C22#1458321611yescharacteristic
443C22#1458321911yescharacteristic
444C22#1458323311yescharacteristic
445C22#1458323611yescharacteristic
446C4—21no—
447C4—21no—
448C4—21no—
449C4—21no—
450C4—81no—
451C4—81no—
452C4—161no—
453C4—862no—
454C4—3441no—
455C4—1722no—
456C4—1721no—
457C4—1721no—
458C4—6881no—
459C2—21no—
460C2—21no—
461C2—21no—
462C2—21no—
463C2—21no—
464C2—21no—
465C2—1722no—
466C2#1913468411yescharacteristic
467C2#1913469711yescharacteristic
468C2#1913470211yescharacteristic
subgroupG/H
centerC22#14582761
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1289C2
socleC22×C43#381
prime radicalC22×C22⋊D43D4
cosocleC23×C4×C43C23
hypercenter#1289D43
hypocenterC43#8761
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1289

Complements

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

NH ≅ G/Ntype
4. #19132475C2semidirect
5. #19132473C2semidirect
6. #19132462C2semidirect
7. C43×#1289C2semidirect
15. #14582763C4semidirect
17. #14582758C4semidirect
18. #14582750C4semidirect
20. #95×D43C4semidirect
231. #1289D43semidirect
261. C43#8761semidirect

Maximal subgroups

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

subgroupindex
#191374992
#191345802
#191329112
#191324752
#191324732
#191324622
C43×#12892
#876143