Finite Group Databasebeta

← #24992500

Subgroups — #24992500

Order 11008.

516 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144071C211yesmaximal, characteristic
2#19143260C211yesmaximal, characteristic, complemented
3#19133263C211yesmaximal, characteristic, complemented
4#19132980C211yesmaximal, characteristic, complemented
5#19132492C211yesmaximal, characteristic, complemented
6#19132470C211yesmaximal, characteristic, complemented
7C2×C43×#331C211yesmaximal, characteristic, complemented
8C2×#13063351—21no—
9C4×#10621898C2211yescharacteristic
10#14583096—21no—
11#14583096C412yes—
12#14583091—21no—
13#14583091C412yes—
14#14582959—22no—
15#14582955—21no—
16#14582952C2211yescharacteristic
17#14582951—21no—
18#14582923C2211yescharacteristic
19#14582923C2211yescharacteristic
20#14582904—21no—
21#14582865—21no—
22#14582854—21no—
23#14582643—22no—
24#14582629—21no—
25#14582626—21no—
26C2×#127×C43C2211yescharacteristic
27C2×C4⋊C8×C43C2211yescharacteristic
28C2×C4⋊C8×C43C2211yescharacteristic
29C43×#331—21no—
30C43×#331—21no—
31C2×#10621898D411yescharacteristic
32#13063351—42no—
33#13063351—42no—
34C2×#10621883—22no—
35C2×#10621882—22no—
36C2×#10621877—21no—
37C2×#10621877—21no—
38C4×Dic86C2×C411yescharacteristic
39C4×Dic86D411yescharacteristic
40C4×D172C2×C411yescharacteristic
41C4×D172D411yescharacteristic
42C4×C22⋊D43—21no—
43C4×C22⋊D43—21no—
44#13063284D411yescharacteristic
45#13063282—21no—
46C42×D43—21no—
47C4⋊(C43⋊C8)—21no—
48C4⋊(C43⋊C8)—21no—
49C4⋊(C43⋊C8)—21no—
50C4⋊(C43⋊C8)C2×C412yes—
51C4⋊(C43⋊C8)D412yes—
52#13063246—22no—
53#13063246—22no—
54C22⋊(C43⋊C8)—21no—
55(C2×D43)⋊C8—22no—
56(C2×D43)⋊C8—22no—
57#13063235—22no—
58C4×C43⋊C8—21no—
59C8×Dic43—22no—
60C22×D4×C43—21no—
61C22×D4×C43—21no—
62C22×D4×C43—21no—
63C22×C8×C43—21no—
64C22×C8×C43—21no—
65#127×C43—21no—
66#127×C43—21no—
67#127×C43—21no—
68#127×C43C2×C412yes—
69C2×C42×C43C2311yescharacteristic
70C4⋊C8×C43—21no—
71C4⋊C8×C43—21no—
72C4⋊C8×C43—21no—
73C4⋊C8×C43D411yescharacteristic
74C4⋊C8×C43D411yescharacteristic
75C24×C43—41no—
76C2×D4×C43—22no—
77C2×D4×C43—22no—
78C2×D4×C43—22no—
79C2×D4×C43—41no—
80C2×D4×C43—41no—
81C2×D4×C43—41no—
82C2×D4×C43—41no—
83C2×D4×C43—41no—
84C2×D4×C43—41no—
85C2×D4×C43—41no—
86C2×D4×C43—81no—
87C2×D4×C43—81no—
88C2×D4×C43—82no—
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43#4111yescharacteristic
91C22×C4×C43#4111yescharacteristic
92C2×C22⋊D43—21no—
93#10621898—21no—
94#10621898—21no—
95#10621898—21no—
96#10621898—21no—
97C2×D172C22⋊C411yescharacteristic
98C2×C4×D43—21no—
99C2×C4×D43—21no—
100C2×C4×D43—21no—
101C2×Dic86C22⋊C411yescharacteristic
102C2×C8×C43—21no—
103C2×C8×C43—21no—
104C2×C8×C43—41no—
105C2×C8×C43—41no—
106C2×C8×C43—41no—
107C2×C8×C43—81no—
108C42×C43C22×C411yescharacteristic
109C42×C43C2×D411yescharacteristic
110C42×C43C2×D411yescharacteristic
111C42×C43C2×D411yescharacteristic
112C22⋊Dic43—21no—
113#10621883—44no—
114#10621882—44no—
115(C2×D43)⋊C4—21no—
116(C2×D43)⋊C4—21no—
117C4⋊Dic43C22⋊C411yescharacteristic
118C4⋊Dic43C22⋊C411yescharacteristic
119Dic43⋊C4—21no—
120Dic43⋊C4—21no—
121C4×Dic43—21no—
122C4×Dic43—21no—
123C4×Dic43—21no—
124#10621877—41no—
125#10621877—41no—
126#10621877—41no—
127#10621877—41no—
128C2×C43⋊C8—22no—
129C2×C43⋊C8—22no—
130C2×C43⋊C8—41no—
131C23×C43—42no—
132C23×C43—82no—
133C23×C43—82no—
134C23×C43—81no—
135C23×C43—81no—
136C23×C43#12311yescharacteristic
137C22×D43—21no—
138D4×C43—42no—
139D4×C43—42no—
140D4×C43—82no—
141D4×C43—82no—
142D4×C43—82no—
143D4×C43—81no—
144D4×C43—81no—
145D4×C43—81no—
146D4×C43—81no—
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43—41no—
150C2×C4×C43C2×C22⋊C411yescharacteristic
151C2×C4×C43C4×D411yescharacteristic
152C2×C4×C43C4×D411yescharacteristic
153C2×C4×C43#12011yescharacteristic
154C2×C4×C43#12111yescharacteristic
155C2×C4×C43#12111yescharacteristic
156C2×C4×C43#13511yescharacteristic
157C2×C4×C43#13511yescharacteristic
158C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
160C22⋊D43—41no—
161C22⋊D43—41no—
162C2×Dic43—21no—
163C2×Dic43—21no—
164C2×Dic43—21no—
165D172—21no—
166D172—21no—
167C4×D43—41no—
168C4×D43—41no—
169C4×D43—41no—
170C4×D43—41no—
171C4×D43—81no—
172Dic86—21no—
173Dic86—21no—
174C8×C43—41no—
175C8×C43—41no—
176C8×C43—81no—
177C43⋊C8—42no—
178C43⋊C8—42no—
179C43⋊C8—81no—
180#9174—431nomaximal, Sylow
181C22×C43—21no—
182C22×C43—21no—
183C22×C43—82no—
184C22×C43—82no—
185C22×C43—82no—
186C22×C43—162no—
187C22×C43—162no—
188C22×C43#38611yescharacteristic
189C22×C43#48211yescharacteristic
190C22×C43#48211yescharacteristic
191C2×D43—41no—
192C2×D43—41no—
193C2×D43—41no—
194C4×C43—21no—
195C4×C43—21no—
196C4×C43—21no—
197C4×C43#41611yescharacteristic
198C4×C43#41811yescharacteristic
199C4×C43#44911yescharacteristic
200C4×C43#44911yescharacteristic
201C4×C43#47111yescharacteristic
202C4×C43#47211yescharacteristic
203Dic43—41no—
204Dic43—41no—
205Dic43—41no—
206#3038—431no—
207#2925—431no—
208#1545—431no—
209C2×#331D4311yescharacteristic, complemented
210#1477—431no—
211#1301—431no—
212#1292—431no—
213C2×C43—21no—
214C2×C43—21no—
215C2×C43—162no—
216C2×C43#187511yescharacteristic
217C2×C43#190311yescharacteristic
218C2×C43#190711yescharacteristic
219D43—81no—
220C2×AGL(1,ℤ/8)—861no—
221C2×#127C2×D4311yescharacteristic
222C4×#41—431no—
223#460—432no—
224#460—861no—
225#459—432no—
226#459—861no—
227#433—862no—
228#432—861no—
229#431—431no—
230#431—861no—
231#423—431no—
232#423—431no—
233C2×C4⋊C8C2×D4311yescharacteristic
234C2×C4⋊C8C2×D4311yescharacteristic
235#418—861no—
236#408—861no—
237#405—861no—
238#331—21no—
239#331—21no—
240#331—862no—
241Q8⋊C8—861no—
242D4⋊C8—861no—
243C43#917411yescharacteristic, complemented, Sylow
244C2×#41—431no—
245C22×D4—21no—
246C22×D4—21no—
247C22×D4—21no—
248AGL(1,ℤ/8)—1722no—
249AGL(1,ℤ/8)—1722no—
250C2×SD16—862no—
251C2×D8—862no—
252C2×M16—861no—
253C2×M16—861no—
254C22×C8—21no—
255C22×C8—21no—
256#127—21no—
257#127—21no—
258#127—21no—
259#127C4×D4312yes—
260C4×Q8—431no—
261C4×Q8—431no—
262C4×D4—431no—
263C4×D4—431no—
264C4×D4—861no—
265C4×D4—861no—
266#117—431no—
267#117—861no—
268C2×C42—861no—
269C2×C42C22×D4311yescharacteristic
270C4⋊C8—21no—
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8—432no—
274C4⋊C8—432no—
275C4⋊C8—861no—
276C4⋊C8—861no—
277C4⋊C8—861no—
278C4⋊C8C22⋊D4311yescharacteristic
279C4⋊C8C22⋊D4311yescharacteristic
280#102—862no—
281#102—862no—
282C22⋊C8—862no—
283C22⋊C8—862no—
284C22⋊C8—861no—
285#97—862no—
286C4×C8—862no—
287C4×C8—861no—
288C24—41no—
289#41—861no—
290#41—861no—
291#41—861no—
292#41—861no—
293C2×Q8—431no—
294C2×D4—22no—
295C2×D4—22no—
296C2×D4—22no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—81no—
305C2×D4—81no—
306C2×D4—82no—
307C2×D4—431no—
308C2×D4—861no—
309C22×C4—861no—
310C22×C4—861no—
311C22×C4—861no—
312C22×C4#1062189811yescharacteristic
313C22×C4D4×D4311yescharacteristic
314C22×C4#1062190011yescharacteristic
315SD16—1724no—
316D8—1724no—
317M16—1721no—
318M16—1721no—
319M16—1721no—
320M16—1721no—
321C2×C8—21no—
322C2×C8—21no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—81no—
327C2×C8—862no—
328C2×C8—862no—
329C2×C8—1721no—
330C4⋊C4—431no—
331C4⋊C4—431no—
332C4⋊C4—861no—
333C4⋊C4—861no—
334C22⋊C4—861no—
335C22⋊C4—861no—
336C22⋊C4—861no—
337C42—861no—
338C42—861no—
339C42—861no—
340C42C2×C4×D4311yescharacteristic
341C42D4×D4311yescharacteristic
342C42D4×D4311yescharacteristic
343C42C2×C22⋊D4311yescharacteristic
344C23—42no—
345C23—82no—
346C23—82no—
347C23—81no—
348C23—81no—
349C23—861no—
350C23#1306330711yescharacteristic
351Q8—861no—
352Q8—861no—
353D4—42no—
354D4—42no—
355D4—82no—
356D4—82no—
357D4—82no—
358D4—81no—
359D4—81no—
360D4—81no—
361D4—81no—
362D4—861no—
363D4—861no—
364D4—1721no—
365D4—1721no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—41no—
369C2×C4—861no—
370C2×C4—861no—
371C2×C4—861no—
372C2×C4—3441no—
373C2×C4—1721no—
374C2×C4—1721no—
375C2×C4—1721no—
376C2×C4—1721no—
377C2×C4C22⋊C4×D4311yescharacteristic
378C2×C4(C22⋊D43)⋊C411yescharacteristic
379C2×C4C4×C22⋊D4311yescharacteristic
380C2×C4#1306329311yescharacteristic
381C2×C4#1306329611yescharacteristic
382C2×C4#1306329811yescharacteristic
383C2×C4#1306334411yescharacteristic
384C2×C4#1306334611yescharacteristic
385C2×C4#1306334911yescharacteristic
386C2×C4#1306335211yescharacteristic
387C8—41no—
388C8—41no—
389C8—81no—
390C8—3441no—
391C8—1722no—
392C8—1722no—
393C22—21no—
394C22—21no—
395C22—82no—
396C22—82no—
397C22—82no—
398C22—162no—
399C22—162no—
400C22—1721no—
401C22—1721no—
402C22—1721no—
403C22#1458277511yescharacteristic
404C22#1458322111yescharacteristic
405C22#1458322211yescharacteristic
406C4—21no—
407C4—21no—
408C4—21no—
409C4—1721no—
410C4—1721no—
411C4—1721no—
412C4#1458289211yescharacteristic
413C4#1458290211yescharacteristic
414C4#1458304111yescharacteristic
415C4#1458304311yescharacteristic
416C4#1458315911yescharacteristic
417C4#1458316611yescharacteristic
418C2—21no—
419C2—21no—
420C2—162no—
421C2—3441no—
422C2#1913491411yescharacteristic
423C2#1913507811yescharacteristic
424C2#1913510611yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC2×C43×#331C2
socleC22×C43#386
prime radical#19144071C2
cosocleC2×C42×C43C23
hypercenterC2×#331D43
hypocenterC43#9174
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#331

Complements

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

NH ≅ G/Ntype
2. #19143260C2semidirect
3. #19133263C2semidirect
4. #19132980C2semidirect
5. #19132492C2semidirect
6. #19132470C2semidirect
7. C2×C43×#331C2semidirect
209. C2×#331D43semidirect
243. C43#9174semidirect

Maximal subgroups

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

subgroupindex
#191440712
#191432602
#191332632
#191329802
#191324922
#191324702
C2×C43×#3312
#917443