Finite Group Databasebeta

← #24984626

Subgroups — #24984626

Order 11008.

606 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137111C211yesmaximal, characteristic
2#19134662C211yesmaximal, characteristic, complemented
3#19134352C211yesmaximal, characteristic, complemented
4#19132419C211yesmaximal, characteristic, complemented
5#19132417C211yesmaximal, characteristic, complemented
6#19132416C211yesmaximal, characteristic, complemented
7C43×#1270C211yesmaximal, characteristic, complemented
8C2×#13063296C411yescharacteristic
9C2×D4×Dic43C411yescharacteristic
10C2×(C22⋊D43)⋊C4—21no—
11C2×C42×D43C2211yescharacteristic
12C2×(C2×D43)⋊C8—21no—
13C2×(C2×D43)⋊C8—21no—
14C2×C8×Dic43—21no—
15#14582797C2211yescharacteristic
16#14582793—21no—
17#14582775—21no—
18#14582756C411yescharacteristic
19C4⋊C4×Dic43C411yescharacteristic
20C22⋊C4×Dic43—21no—
21#14582654C2211yescharacteristic
22#14582654C2211yescharacteristic
23#14582653—21no—
24C43×#390C2211yescharacteristic
25C43×#336C2211yescharacteristic
26C43×#336C2211yescharacteristic
27C22×C22⋊D43—21no—
28C23×Dic43—21no—
29C22×C4×D43C2×C411yescharacteristic
30C22×C4×D43D411yescharacteristic
31C22×C4×D43D411yescharacteristic
32C22×C43⋊C8—21no—
33C22×C43⋊C8—21no—
34#13063296—22no—
35#13063296C814yescomplemented
36D4×Dic43—42no—
37(C22⋊D43)⋊C4—42no—
38(C22⋊D43)⋊C4—42no—
39C2×C4⋊Dic43C2×C411yescharacteristic
40C2×C4⋊Dic43C2×C411yescharacteristic
41C2×Dic43⋊C4—21no—
42C2×C22⋊Dic43—21no—
43C2×C22⋊Dic43—21no—
44C2×(C2×D43)⋊C4—21no—
45C2×C4×Dic43—21no—
46C2×C4×Dic43C2×C411yescharacteristic
47C2×C4×Dic43D411yescharacteristic
48C2×C4×Dic43D411yescharacteristic
49C42×D43—42no—
50(C2×D43)⋊C8—24no—
51(C2×D43)⋊C8—42no—
52C8×Dic43—42no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C22×D4×C43C2×C411yescharacteristic
57C22×C8×C43—21no—
58C22×C8×C43—21no—
59C2×C4⋊C4×C43C2×C411yescharacteristic
60C2×C22⋊C4×C43—21no—
61C2×C22⋊C4×C43—21no—
62C2×C42×C43C2311yescharacteristic
63C24×C43—21no—
64C23×D43C22⋊C411yescharacteristic
65C2×D4×C43—21no—
66C2×D4×C43—41no—
67C2×D4×C43—41no—
68C2×D4×C43C2×C812yes—
69C22×C4×C43—21no—
70C22×C4×C43C22×C411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C2×C22⋊D43—24no—
74C2×C22⋊D43—42no—
75C2×C22⋊D43—42no—
76C22×Dic43—21no—
77C22×Dic43—21no—
78C22×Dic43—42no—
79C22×Dic43—42no—
80C22×Dic43—42no—
81C22×Dic43C22⋊C411yescharacteristic
82C22×Dic43C22⋊C411yescharacteristic
83C22×Dic43C22⋊C411yescharacteristic
84C2×C4×D43—21no—
85C2×C4×D43—21no—
86C2×C4×D43—21no—
87C2×C4×D43—21no—
88C2×C4×D43—22no—
89C2×C4×D43—22no—
90C2×C4×D43—41no—
91C2×C4×D43—41no—
92C2×C4×D43—41no—
93C2×C4×D43—41no—
94C2×C4×D43C2×C812yes—
95C2×C4×D43M1612yes—
96C2×C8×C43—22no—
97C2×C8×C43—41no—
98C2×C8×C43—41no—
99C2×C8×C43—41no—
100C2×C8×C43—41no—
101C2×C8×C43—41no—
102C4⋊C4×C43—41no—
103C22⋊C4×C43—41no—
104C22⋊C4×C43—41no—
105C22⋊C4×C43—41no—
106C22⋊C4×C43—41no—
107C42×C43—41no—
108C22⋊Dic43—24no—
109C22⋊Dic43—42no—
110(C2×D43)⋊C4—42no—
111C4⋊Dic43—21no—
112C4⋊Dic43—41no—
113C4⋊Dic43C2×C812yes—
114Dic43⋊C4—41no—
115Dic43⋊C4—41no—
116C4×Dic43—22no—
117C4×Dic43—22no—
118C4×Dic43—41no—
119C4×Dic43—42no—
120C2×C43⋊C8—22no—
121C2×C43⋊C8—41no—
122C2×C43⋊C8—41no—
123C2×C43⋊C8—41no—
124C2×C43⋊C8—41no—
125C2×C43⋊C8—41no—
126C23×C43—22no—
127C23×C43—41no—
128C23×C43—41no—
129C23×C43—41no—
130C23×C43—41no—
131C23×C43—41no—
132C23×C43—41no—
133C23×C43C2×C22⋊C411yescharacteristic
134C22×D43—21no—
135C22×D43—21no—
136C22×D43—21no—
137C22×D43—21no—
138C22×D43—21no—
139C22×D43—21no—
140C22×D43C22⋊C812yes—
141D4×C43—42no—
142D4×C43—42no—
143C2×C4×C43—21no—
144C2×C4×C43—21no—
145C2×C4×C43—21no—
146C2×C4×C43—21no—
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43C22×C811yescharacteristic
153C2×C4×C43C2×M1611yescharacteristic
154C2×C4×C43#13511yescharacteristic
155C2×C4×C43#13511yescharacteristic
156C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
158C22⋊D43—48no—
159C2×Dic43—21no—
160C2×Dic43—21no—
161C2×Dic43—21no—
162C2×Dic43—21no—
163C2×Dic43—21no—
164C2×Dic43—21no—
165C2×Dic43—22no—
166C2×Dic43—41no—
167C2×Dic43—41no—
168C2×Dic43—41no—
169C2×Dic43—41no—
170C2×Dic43—41no—
171C2×Dic43—84no—
172C2×Dic43C22⋊C812yes—
173C2×Dic43#9912yes—
174C2×Dic43#10412yes—
175C4×D43—42no—
176C4×D43—42no—
177C4×D43—42no—
178C4×D43—42no—
179C4×D43—42no—
180C4×D43—42no—
181C8×C43—42no—
182C8×C43—81no—
183C43⋊C8—42no—
184C43⋊C8—81no—
185#7582—431nomaximal, Sylow
186C22×C43—42no—
187C22×C43—42no—
188C22×C43—42no—
189C22×C43—81no—
190C22×C43—81no—
191C22×C43—81no—
192C22×C43—81no—
193C22×C43C2×C22⋊C811yescharacteristic
194C22×C43C2×#9911yescharacteristic
195C22×C43#41311yescharacteristic
196C22×C43#41611yescharacteristic
197C22×C43#41811yescharacteristic
198C22×C43C2×#10411yescharacteristic
199C22×C43#42111yescharacteristic
200C2×D43—22no—
201C2×D43—22no—
202C2×D43—22no—
203C2×D43—41no—
204C2×D43—41no—
205C2×D43—41no—
206C2×D43—41no—
207C4×C43—21no—
208C4×C43—21no—
209C4×C43—21no—
210C4×C43—21no—
211C4×C43—21no—
212C4×C43—21no—
213C4×C43—81no—
214Dic43—22no—
215Dic43—22no—
216Dic43—22no—
217Dic43—42no—
218Dic43—81no—
219C4×#121—431no—
220#1817—431no—
221C4×C22⋊C8—431no—
222#1271—431no—
223#1271—431no—
224#1270—431no—
225#1270D4311yescharacteristic, complemented
226C2×C43—82no—
227C2×C43#145911yescharacteristic
228C2×C43#147611yescharacteristic
229C2×C43#147811yescharacteristic
230C2×C43#150711yescharacteristic
231C2×C43#151611yescharacteristic
232C2×C43#152911yescharacteristic
233C2×C43#155311yescharacteristic
234D43—42no—
235C2×#121—431no—
236C2×C4×D4—431no—
237C2×C4×D4—861no—
238C22×C42—431no—
239C2×C22⋊C8—861no—
240C2×C22⋊C8—861no—
241C2×C4×C8—861no—
242#390C2×D4311yescharacteristic
243#389—431no—
244#388—861no—
245#386—861no—
246#380—431no—
247C4×C4⋊C4—431no—
248C4×C22⋊C4—861no—
249#336—431no—
250#336—431no—
251#336—861no—
252#336C2×D4311yescharacteristic
253#336C2×D4311yescharacteristic
254C43#758211yescharacteristic, complemented, Sylow
255C22×D4—861no—
256C22×D4C4×D4311yescharacteristic
257C23×C4—431no—
258C23×C4—431no—
259C23×C4—431no—
260C23×C4—861no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—861no—
264C22×C8—861no—
265#121—434no—
266#121—862no—
267C4×D4—1722no—
268C4×D4—1722no—
269C4×D4—1722no—
270C2×C4⋊C4—431no—
271C2×C4⋊C4—431no—
272C2×C4⋊C4—861no—
273C2×C4⋊C4C4×D4311yescharacteristic
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—861no—
277C2×C22⋊C4—861no—
278C2×C22⋊C4—861no—
279C2×C42—431no—
280C2×C42—431no—
281C2×C42—431no—
282C2×C42—861no—
283C2×C42—1722no—
284C2×C42C22×D4311yescharacteristic
285C22⋊C8—864no—
286C22⋊C8—1722no—
287C4×C8—1722no—
288#95—861no—
289#95—861no—
290#95—861no—
291C24—21no—
292C24—431no—
293C2×D4—21no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—864no—
297C2×D4—1722no—
298C2×D4—1722no—
299C2×D4C8×D4312yes—
300C22×C4—21no—
301C22×C4—431no—
302C22×C4—431no—
303C22×C4—431no—
304C22×C4—432no—
305C22×C4—432no—
306C22×C4—862no—
307C22×C4—862no—
308C22×C4—861no—
309C22×C4—861no—
310C22×C4—861no—
311C22×C4—861no—
312C22×C4—861no—
313C22×C4—861no—
314C22×C4—1721no—
315C22×C4—1721no—
316C22×C4—1721no—
317C22×C4—1721no—
318C22×C4—1722no—
319C22×C4—1722no—
320C22×C4—1722no—
321C22×C4C2×C4×D4311yescharacteristic
322C22×C4D4×D4311yescharacteristic
323C22×C4D4×D4311yescharacteristic
324C2×C8—22no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—862no—
331C2×C8—1721no—
332C2×C8—1721no—
333C2×C8—1721no—
334C2×C8—1721no—
335C2×C8—1721no—
336C4⋊C4—41no—
337C4⋊C4—432no—
338C4⋊C4—861no—
339C4⋊C4—1721no—
340C4⋊C4—1721no—
341C4⋊C4—1721no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C22⋊C4—864no—
347C22⋊C4—1722no—
348C22⋊C4—1722no—
349C42—41no—
350C42—862no—
351C42—862no—
352C42—1721no—
353C42—1722no—
354C23—22no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—432no—
362C23—861no—
363C23—861no—
364C23—861no—
365C23—861no—
366C23—861no—
367C23—861no—
368C23C22⋊C4×D4311yescharacteristic
369D4—42no—
370D4—42no—
371D4—1728no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—432no—
382C2×C4—432no—
383C2×C4—432no—
384C2×C4—861no—
385C2×C4—861no—
386C2×C4—861no—
387C2×C4—861no—
388C2×C4—861no—
389C2×C4—861no—
390C2×C4—862no—
391C2×C4—3444no—
392C2×C4—1722no—
393C2×C4—1722no—
394C2×C4—1722no—
395C2×C4—1722no—
396C2×C4—1722no—
397C2×C4—1722no—
398C2×C4—1721no—
399C2×C4—1721no—
400C2×C4—1721no—
401C2×C4—1721no—
402C2×C4—1721no—
403C2×C4C2×C8×D4311yescharacteristic
404C2×C4M16×D4311yescharacteristic
405C2×C4#1306334411yescharacteristic
406C2×C4#1306334611yescharacteristic
407C2×C4#1306334911yescharacteristic
408C2×C4#1306335211yescharacteristic
409C8—42no—
410C8—81no—
411C8—3441no—
412C8—1722no—
413C22—42no—
414C22—42no—
415C22—42no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—862no—
421C22—862no—
422C22—862no—
423C22—1721no—
424C22—1721no—
425C22—1721no—
426C22—1721no—
427C22C22⋊C8×D4311yescharacteristic
428C22#99×D4311yescharacteristic
429C22#1458288011yescharacteristic
430C22#1458289211yescharacteristic
431C22#1458290211yescharacteristic
432C22#104×D4311yescharacteristic
433C22#1458291411yescharacteristic
434C4—21no—
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—81no—
441C4—862no—
442C4—862no—
443C4—862no—
444C4—3441no—
445C4—1722no—
446C2—82no—
447C2—1722no—
448C2#1913291011yescharacteristic
449C2#1913297411yescharacteristic
450C2#1913298411yescharacteristic
451C2#1913310911yescharacteristic
452C2#1913314811yescharacteristic
453C2#1913319911yescharacteristic
454C2#1913329711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC2×C4×C43C22×C8
FrattiniC2×C42C22×D43
FittingC43×#1270C2
socleC23×C43C2×C22⋊C4
prime radicalC2×#13063296C4
cosocleC2×C42×C43C23
hypercenter#1270D43
hypocenterC43#7582
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #19134662C2semidirect
3. #19134352C2semidirect
4. #19132419C2semidirect
5. #19132417C2semidirect
6. #19132416C2semidirect
7. C43×#1270C2semidirect
35. #13063296C8semidirect
225. #1270D43semidirect
254. C43#7582semidirect

Maximal subgroups

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

subgroupindex
#191371112
#191346622
#191343522
#191324192
#191324172
#191324162
C43×#12702
#758243