Finite Group Databasebeta

← #24999988

Subgroups — #24999988

Order 11008.

516 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139769C211yesmaximal, characteristic
2#19135351C211yesmaximal, characteristic, complemented
3#19134592C211yesmaximal, characteristic
4C2×#14582648C211yesmaximal, characteristic, complemented
5C2×#14582628C211yesmaximal, characteristic
6#19132435C211yesmaximal, characteristic, complemented
7C43×#1956C211yesmaximal, characteristic, complemented
8C2×C4×D172C2211yescharacteristic
9C2×#13063258—21no—
10C2×C4⋊(C43⋊C8)C2211yescharacteristic
11C2×C4⋊(C43⋊C8)C2211yescharacteristic
12C2×#13063245—21no—
13#14582810—22no—
14#14582800—21no—
15#14582764—21no—
16#14582756—21no—
17#14582756—21no—
18C4×C4⋊Dic43C2211yescharacteristic
19#14582661—21no—
20#14582661—21no—
21#14582648—22no—
22#14582628—22no—
23C2×C4⋊Q8×C43C2211yescharacteristic
24C2×#103×C43—22no—
25C2×C4×C8×C43C2211yescharacteristic
26C43×#384C2211yescharacteristic
27C22×D172D411yescharacteristic
28C22×C4×D43—21no—
29C22×C43⋊C8—21no—
30C22×C43⋊C8—21no—
31C4×D172—21no—
32C4×D172—21no—
33C4×D172—21no—
34C4×D172—21no—
35C2×C4⋊Dic43D411yescharacteristic
36C2×C4⋊Dic43D411yescharacteristic
37C2×C4⋊Dic43D411yescharacteristic
38C2×(C2×D43)⋊C4—21no—
39C2×(C2×D43)⋊C4—22no—
40C2×(C2×D43)⋊C4—22no—
41C2×C4×Dic43—21no—
42#13063258—42no—
43C4⋊(C43⋊C8)—21no—
44C4⋊(C43⋊C8)—21no—
45C4⋊(C43⋊C8)—21no—
46C4⋊(C43⋊C8)D412yes—
47#13063245—42no—
48C43⋊#95—22no—
49C43⋊#95—22no—
50C43⋊#95—21no—
51C22×Q8×C43D412yes—
52C22×C8×C43—21no—
53C4⋊Q8×C43—21no—
54C4⋊Q8×C43—21no—
55C4⋊Q8×C43—21no—
56C4⋊Q8×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×C43—21no—
62C2×C42×C43C2311yescharacteristic
63#103×C43—44no—
64C4×C8×C43—21no—
65C4×C8×C43—21no—
66C23×D43—21no—
67C2×Q8×C43—22no—
68C2×Q8×C43—22no—
69C2×Q8×C43—42no—
70C2×Q8×C43—42no—
71C22×C4×C43—22no—
72C22×C4×C43—41no—
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C22×C4×C43C2×D411yescharacteristic
76C22×Dic43—21no—
77C22×Dic43—21no—
78C22×Dic43—21no—
79C2×D172—21no—
80C2×D172—21no—
81C2×D172—21no—
82C2×D172—21no—
83C2×D172—21no—
84C2×D172Q1612yes—
85C2×C4×D43—41no—
86C2×C4×D43—41no—
87C2×C4×D43—41no—
88C2×C4×D43—41no—
89C2×C4×D43—41no—
90C2×C4×D43—41no—
91C2×C8×C43—22no—
92C2×C8×C43—41no—
93C2×C8×C43—41no—
94C4⋊C4×C43—42no—
95C4⋊C4×C43—41no—
96C4⋊C4×C43—41no—
97C4⋊C4×C43—41no—
98C4⋊C4×C43—41no—
99C4⋊C4×C43—41no—
100C4⋊C4×C43—41no—
101C4⋊C4×C43—41no—
102C4⋊C4×C43—41no—
103C42×C43C2×D411yescharacteristic
104C42×C43#4111yescharacteristic
105C42×C43#4111yescharacteristic
106C42×C43#4111yescharacteristic
107(C2×D43)⋊C4—41no—
108(C2×D43)⋊C4—41no—
109(C2×D43)⋊C4—82no—
110(C2×D43)⋊C4—82no—
111C4⋊Dic43—21no—
112C4⋊Dic43—21no—
113C4⋊Dic43—21no—
114C4⋊Dic43—21no—
115C4⋊Dic43—21no—
116C4⋊Dic43—21no—
117C4×Dic43—41no—
118C4×Dic43—41no—
119C2×C43⋊C8—22no—
120C2×C43⋊C8—41no—
121C2×C43⋊C8—41no—
122C2×C43⋊C8—41no—
123C2×C43⋊C8—41no—
124C2×C43⋊C8—41no—
125C23×C43#12011yescharacteristic
126C22×D43—22no—
127C22×D43—41no—
128C22×D43—41no—
129C22×D43—41no—
130C22×D43—41no—
131C22×D43—41no—
132C22×D43—41no—
133Q8×C43—44no—
134Q8×C43—82no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43—42no—
138C2×C4×C43—42no—
139C2×C4×C43—42no—
140C2×C4×C43—81no—
141C2×C4×C43—81no—
142C2×C4×C43—81no—
143C2×C4×C43#12111yescharacteristic
144C2×C4×C43#12111yescharacteristic
145C2×C4×C43#12111yescharacteristic
146C2×C4×C43#12311yescharacteristic
147C2×C4×C43#12311yescharacteristic
148C2×C4×C43#12411yescharacteristic
149C2×C4×C43C2×Q1611yescharacteristic
150C2×C4×C43#13511yescharacteristic
151C2×C4×C43#13511yescharacteristic
152C2×C4×C43#13511yescharacteristic
153C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C43#13711yescharacteristic
156C2×C4×C43#13711yescharacteristic
157C2×Dic43—41no—
158C2×Dic43—41no—
159C2×Dic43—41no—
160C2×Dic43—41no—
161C2×Dic43—41no—
162C2×Dic43—41no—
163C2×Dic43—41no—
164C2×Dic43—41no—
165C2×Dic43—41no—
166D172—22no—
167D172—22no—
168D172—41no—
169D172—41no—
170C4×D43—81no—
171C4×D43—81no—
172C4×D43—81no—
173C4×D43—81no—
174C8×C43—42no—
175C43⋊C8—42no—
176C43⋊C8—81no—
177#10413—431nomaximal, Sylow
178C22×C43#39411yescharacteristic
179C22×C43#44911yescharacteristic
180C22×C43#44911yescharacteristic
181C22×C43#45111yescharacteristic
182C22×C43#45211yescharacteristic
183C22×C43#45311yescharacteristic
184C22×C43#45511yescharacteristic
185C2×D43—42no—
186C2×D43—42no—
187C2×D43—42no—
188C2×D43—81no—
189C2×D43—81no—
190C2×D43—81no—
191C2×D43—81no—
192C4×C43—21no—
193C4×C43—21no—
194C4×C43—82no—
195C4×C43—161no—
196C4×C43#46311yescharacteristic
197C4×C43#46411yescharacteristic
198C4×C43#46711yescharacteristic
199C4×C43#46811yescharacteristic
200C4×C43#48411yescharacteristic
201C4×C43#48511yescharacteristic
202C4×C43#48811yescharacteristic
203C4×C43#48911yescharacteristic
204Dic43—81no—
205Dic43—81no—
206Dic43—81no—
207#2563—431no—
208#1956D4311yescharacteristic, complemented
209#1947—431no—
210#1802—431no—
211C2×#333—431no—
212C2×D4⋊C8—431no—
213#1279—431no—
214C2×C43#162411yescharacteristic
215C2×C43#163211yescharacteristic
216C2×C43#164411yescharacteristic
217C2×C43#164611yescharacteristic
218C2×C43#203611yescharacteristic
219C2×C43#203711yescharacteristic
220C2×C43#204211yescharacteristic
221D43—82no—
222C2×C4⋊Q8C2×D4311yescharacteristic
223C2×C4×D4—431no—
224C2×#107—861no—
225C2×C4⋊C8—431no—
226C2×C4⋊C8—431no—
227C2×#103—22no—
228C2×#102—861no—
229C2×C4×C8C2×D4311yescharacteristic
230#393—862no—
231#390—861no—
232#384C2×D4311yescharacteristic
233#382—861no—
234#380—861no—
235#380—861no—
236C4×C4⋊C4—431no—
237#340—861no—
238#340—861no—
239#333—862no—
240D4⋊C8—862no—
241C43#1041311yescharacteristic, complemented, Sylow
242C22×Q8C22⋊D4312yes—
243C22×D4—431no—
244C23×C4—861no—
245C22×C8—21no—
246C22×C8—861no—
247C22×C8—861no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8—21no—
251C4⋊Q8—21no—
252C4×D4—861no—
253C4×D4—861no—
254C4×D4—861no—
255C4×D4—861no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—431no—
262C2×C4⋊C4—431no—
263C2×C4⋊C4—431no—
264C2×C22⋊C4—862no—
265C2×C22⋊C4—862no—
266C2×C22⋊C4—861no—
267C2×C42—861no—
268C2×C42C22×D4311yescharacteristic
269#107—1722no—
270C4⋊C8—432no—
271C4⋊C8—861no—
272C4⋊C8—861no—
273C4⋊C8—861no—
274#103—44no—
275#102—1722no—
276C4×C8—21no—
277C4×C8—21no—
278#95—862no—
279#95—862no—
280#95—861no—
281C24—861no—
282C2×Q8—22no—
283C2×Q8—22no—
284C2×Q8—42no—
285C2×Q8—42no—
286C2×D4—432no—
287C2×D4—861no—
288C2×D4—861no—
289C2×D4—861no—
290C2×D4—861no—
291C2×D4—861no—
292C22×C4—22no—
293C22×C4—41no—
294C22×C4—861no—
295C22×C4—861no—
296C22×C4—861no—
297C22×C4—1721no—
298C22×C4—1721no—
299C22×C4—1721no—
300C22×C4—1721no—
301C22×C4—1721no—
302C22×C4—1721no—
303C22×C4D4×D4311yescharacteristic
304C22×C4D4×D4311yescharacteristic
305C22×C4C2×C22⋊D4311yescharacteristic
306C2×C8—22no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—862no—
310C2×C8—1721no—
311C2×C8—1721no—
312C2×C8—1721no—
313C2×C8—1721no—
314C2×C8—1721no—
315C4⋊C4—42no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—861no—
325C4⋊C4—861no—
326C4⋊C4—861no—
327C4⋊C4—861no—
328C4⋊C4—861no—
329C4⋊C4—861no—
330C22⋊C4—3442no—
331C22⋊C4—3442no—
332C22⋊C4—1721no—
333C22⋊C4—1721no—
334C42—1721no—
335C42—1721no—
336C42#1062189811yescharacteristic
337C42#1062189811yescharacteristic
338C42D4×D4311yescharacteristic
339C42#1062190011yescharacteristic
340C23—862no—
341C23—1721no—
342C23—1721no—
343C23—1721no—
344C23—1721no—
345C23—1721no—
346C23—1721no—
347C23#1306329311yescharacteristic
348Q8—44no—
349Q8—82no—
350D4—862no—
351D4—862no—
352D4—1721no—
353D4—1721no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4—3441no—
363C2×C4—3441no—
364C2×C4—3441no—
365C2×C4—3441no—
366C2×C4—1721no—
367C2×C4—1721no—
368C2×C4—1721no—
369C2×C4—1721no—
370C2×C4—1721no—
371C2×C4—1721no—
372C2×C4—1721no—
373C2×C4—1721no—
374C2×C4—1721no—
375C2×C4#1306329711yescharacteristic
376C2×C4#1306329811yescharacteristic
377C2×C4#1306329811yescharacteristic
378C2×C4#1306330711yescharacteristic
379C2×C4#1306330811yescharacteristic
380C2×C4#1306331111yescharacteristic
381C2×C4Q16×D4311yescharacteristic
382C2×C4#1306334611yescharacteristic
383C2×C4#1306334611yescharacteristic
384C2×C4#1306334811yescharacteristic
385C2×C4#1306335211yescharacteristic
386C2×C4#1306335211yescharacteristic
387C2×C4#1306335711yescharacteristic
388C2×C4#1306335711yescharacteristic
389C8—42no—
390C8—3441no—
391C8—1722no—
392C22—3441no—
393C22—3441no—
394C22—3441no—
395C22—3441no—
396C22—1722no—
397C22—1722no—
398C22—1722no—
399C22#1458281411yescharacteristic
400C22#1458304311yescharacteristic
401C22#1458304311yescharacteristic
402C22#1458305311yescharacteristic
403C22#1458306011yescharacteristic
404C22#1458306611yescharacteristic
405C22#1458307611yescharacteristic
406C4—21no—
407C4—21no—
408C4—82no—
409C4—161no—
410C4—3441no—
411C4—3441no—
412C4—3441no—
413C4#1458311711yescharacteristic
414C4#1458312411yescharacteristic
415C4#1458313911yescharacteristic
416C4#1458314811yescharacteristic
417C4#1458323311yescharacteristic
418C4#1458323811yescharacteristic
419C4#1458325511yescharacteristic
420C4#1458326011yescharacteristic
421C2—3442no—
422C2#1913367611yescharacteristic
423C2#1913372611yescharacteristic
424C2#1913380611yescharacteristic
425C2#1913382011yescharacteristic
426C2#1913579611yescharacteristic
427C2#1913580511yescharacteristic
428C2#1913583211yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1956C2
socleC23×C43#120
prime radicalC22×D172D4
hypercenter#1956D43
hypocenterC43#10413
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1956

Complements

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

NH ≅ G/Ntype
2. #19135351C2semidirect
4. C2×#14582648C2semidirect
6. #19132435C2semidirect
7. C43×#1956C2semidirect
208. #1956D43semidirect
241. C43#10413semidirect

Maximal subgroups

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

subgroupindex
#191397692
#191353512
#191345922
C2×#145826482
C2×#145826282
#191324352
C43×#19562
#1041343