Finite Group Databasebeta

← #24992498

Subgroups — #24992498

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#19144076C211yesmaximal, characteristic
2#19143263C211yesmaximal, characteristic, complemented
3#19133264C211yesmaximal, characteristic, complemented
4C2×#14582642C211yesmaximal, characteristic, complemented
5#19132980C211yesmaximal, characteristic, complemented
6#19132490C211yesmaximal, characteristic, complemented
7C43×#1292C211yesmaximal, characteristic, complemented
8C2×#13063353—21no—
9C2×#13063322C2211yescharacteristic
10C4×#10621898C2211yescharacteristic
11#14583100—21no—
12#14583100C412yes—
13#14583095—21no—
14#14583095C412yes—
15#14582959—22no—
16#14582955—21no—
17#14582952C2211yescharacteristic
18#14582951—21no—
19C2×C4⋊(C43⋊C8)C2211yescharacteristic
20#14582905—21no—
21#14582867—21no—
22#14582857—21no—
23#14582642—21no—
24#14582642—21no—
25#14582642—22no—
26#14582629—21no—
27#14582626—21no—
28C43×#423C2211yescharacteristic
29C43×#423C2211yescharacteristic
30C2×C4⋊C8×C43C2211yescharacteristic
31C2×#10621898D411yescharacteristic
32C22×D172—21no—
33C22×D172—21no—
34C22×D172—21no—
35#13063353—42no—
36#13063353—42no—
37C2×#10621873—22no—
38C2×D344—22no—
39C22×C43⋊C8—21no—
40#13063322—21no—
41#13063322—21no—
42#13063322—21no—
43#13063322C2×C412yes—
44C4×Dic86C2×C411yescharacteristic
45C4×Dic86D411yescharacteristic
46C4×D172C2×C411yescharacteristic
47C4×D172D411yescharacteristic
48C4×C22⋊D43—21no—
49C4×C22⋊D43—21no—
50#13063284D411yescharacteristic
51#13063282—21no—
52C42×D43—21no—
53C4⋊(C43⋊C8)—21no—
54C4⋊(C43⋊C8)—21no—
55C4⋊(C43⋊C8)D411yescharacteristic
56C4⋊(C43⋊C8)D411yescharacteristic
57#13063247—22no—
58#13063247—22no—
59C22⋊(C43⋊C8)—21no—
60(C2×D43)⋊C8—22no—
61(C2×D43)⋊C8—22no—
62#13063235—22no—
63C4×C43⋊C8—21no—
64C8×Dic43—22no—
65C2×M16×C43—21no—
66C2×M16×C43—21no—
67C22×C8×C43—21no—
68C2×C42×C43C2311yescharacteristic
69C4⋊C8×C43—21no—
70C4⋊C8×C43—21no—
71C4⋊C8×C43—21no—
72C4⋊C8×C43—21no—
73C4⋊C8×C43C2×C412yes—
74C4⋊C8×C43D412yes—
75C23×D43—41no—
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43#4111yescharacteristic
78C22×C4×C43#4111yescharacteristic
79C2×C22⋊D43—21no—
80#10621898—21no—
81#10621898—21no—
82#10621898—21no—
83#10621898—21no—
84C2×D172—22no—
85C2×D172—22no—
86C2×D172—22no—
87C2×D172—41no—
88C2×D172—41no—
89C2×D172—41no—
90C2×D172—41no—
91C2×D172—41no—
92C2×D172—41no—
93C2×D172—41no—
94C2×D172—81no—
95C2×D172—81no—
96C2×D172—82no—
97C2×D172C22⋊C411yescharacteristic
98C2×C4×D43—21no—
99C2×C4×D43—21no—
100C2×C4×D43—21no—
101C2×Dic86C22⋊C411yescharacteristic
102M16×C43—41no—
103M16×C43—41no—
104M16×C43—41no—
105M16×C43—41no—
106C2×C8×C43—22no—
107C2×C8×C43—22no—
108C2×C8×C43—41no—
109C2×C8×C43—81no—
110C42×C43C22×C411yescharacteristic
111C42×C43C2×D411yescharacteristic
112C42×C43C2×D411yescharacteristic
113C42×C43C2×D411yescharacteristic
114C22⋊Dic43—21no—
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—
124C2×C43⋊C8—21no—
125C2×C43⋊C8—21no—
126C2×C43⋊C8—41no—
127C2×C43⋊C8—41no—
128C2×C43⋊C8—41no—
129D344—44no—
130#10621873—44no—
131C23×C43#12311yescharacteristic
132C22×D43—21no—
133C22×D43—42no—
134C22×D43—82no—
135C22×D43—82no—
136C22×D43—81no—
137C22×D43—81no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—41no—
141C2×C4×C43C2×C22⋊C411yescharacteristic
142C2×C4×C43C4×D411yescharacteristic
143C2×C4×C43C4×D411yescharacteristic
144C2×C4×C43#12011yescharacteristic
145C2×C4×C43#12111yescharacteristic
146C2×C4×C43#12111yescharacteristic
147C2×C4×C43#13511yescharacteristic
148C2×C4×C43#13511yescharacteristic
149C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
151C22⋊D43—41no—
152C22⋊D43—41no—
153C2×Dic43—21no—
154C2×Dic43—21no—
155C2×Dic43—21no—
156D172—21no—
157D172—21no—
158D172—42no—
159D172—42no—
160D172—82no—
161D172—82no—
162D172—82no—
163D172—81no—
164D172—81no—
165D172—81no—
166D172—81no—
167C4×D43—41no—
168C4×D43—41no—
169C4×D43—41no—
170C4×D43—41no—
171C4×D43—81no—
172Dic86—21no—
173Dic86—21no—
174C8×C43—42no—
175C8×C43—42no—
176C8×C43—81no—
177C43⋊C8—41no—
178C43⋊C8—41no—
179C43⋊C8—81no—
180#9174—431nomaximal, Sylow
181C22×C43—21no—
182C22×C43—21no—
183C22×C43#38611yescharacteristic
184C22×C43#48211yescharacteristic
185C22×C43#48211yescharacteristic
186C2×D43—41no—
187C2×D43—41no—
188C2×D43—41no—
189C2×D43—82no—
190C2×D43—82no—
191C2×D43—82no—
192C2×D43—162no—
193C2×D43—162no—
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×#331—431no—
210#1477—431no—
211#1301—431no—
212#1292D4311yescharacteristic, complemented
213C2×C43—21no—
214C2×C43—21no—
215C2×C43#187511yescharacteristic
216C2×C43#190311yescharacteristic
217C2×C43#190711yescharacteristic
218D43—81no—
219D43—162no—
220C2×AGL(1,ℤ/8)—861no—
221C2×#127—431no—
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#423C2×D4311yescharacteristic
232#423C2×D4311yescharacteristic
233C2×C4⋊C8—431no—
234C2×C4⋊C8C2×D4311yescharacteristic
235#418—861no—
236#408—861no—
237#405—861no—
238#331—861no—
239#331—861no—
240#331—862no—
241Q8⋊C8—861no—
242D4⋊C8—861no—
243C43#917411yescharacteristic, complemented, Sylow
244C2×#41—431no—
245C22×D4—861no—
246C22×D4—861no—
247C22×D4—861no—
248AGL(1,ℤ/8)—1722no—
249AGL(1,ℤ/8)—1722no—
250C2×SD16—862no—
251C2×D8—862no—
252C2×M16—21no—
253C2×M16—21no—
254C22×C8—21no—
255C22×C8—861no—
256#127—432no—
257#127—861no—
258#127—861no—
259#127—861no—
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—21no—
274C4⋊C8—431no—
275C4⋊C8—431no—
276C4⋊C8—861no—
277C4⋊C8—861no—
278C4⋊C8C4×D4312yes—
279C4⋊C8D17212yes—
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—1721no—
289#41—861no—
290#41—861no—
291#41—861no—
292#41—861no—
293C2×Q8—431no—
294C2×D4—431no—
295C2×D4—861no—
296C2×D4—862no—
297C2×D4—862no—
298C2×D4—862no—
299C2×D4—3441no—
300C2×D4—3441no—
301C2×D4—3442no—
302C2×D4—1721no—
303C2×D4—1721no—
304C2×D4—1721no—
305C2×D4—1721no—
306C2×D4—1721no—
307C2×D4—1721no—
308C2×D4—1721no—
309C22×C4—861no—
310C22×C4—861no—
311C22×C4—861no—
312C22×C4#1062189811yescharacteristic
313C22×C4D4×D4311yescharacteristic
314C22×C4#1062190211yescharacteristic
315SD16—1724no—
316D8—1724no—
317M16—41no—
318M16—41no—
319M16—41no—
320M16—41no—
321C2×C8—22no—
322C2×C8—22no—
323C2×C8—41no—
324C2×C8—81no—
325C2×C8—861no—
326C2×C8—861no—
327C2×C8—1721no—
328C2×C8—1721no—
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
341C42C2×D17211yescharacteristic
342C42D4×D4311yescharacteristic
343C42D4×D4311yescharacteristic
344C23—861no—
345C23—3442no—
346C23—3442no—
347C23—3441no—
348C23—3441no—
349C23—1722no—
350C23#1306331011yescharacteristic
351Q8—861no—
352Q8—861no—
353D4—861no—
354D4—861no—
355D4—3442no—
356D4—3442no—
357D4—3442no—
358D4—3441no—
359D4—3441no—
360D4—3441no—
361D4—3441no—
362D4—1721no—
363D4—1721no—
364D4—1722no—
365D4—1722no—
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#1306328711yescharacteristic
379C2×C4C4×D17211yescharacteristic
380C2×C4#1306329511yescharacteristic
381C2×C4#1306329811yescharacteristic
382C2×C4#1306330011yescharacteristic
383C2×C4#1306334611yescharacteristic
384C2×C4#1306334811yescharacteristic
385C2×C4#1306334911yescharacteristic
386C2×C4#1306335211yescharacteristic
387C8—42no—
388C8—42no—
389C8—81no—
390C8—3441no—
391C8—1721no—
392C8—1721no—
393C22—21no—
394C22—21no—
395C22—3442no—
396C22—3442no—
397C22—3442no—
398C22—1721no—
399C22—1721no—
400C22—1721no—
401C22—6882no—
402C22—6882no—
403C22#1458277711yescharacteristic
404C22#1458322511yescharacteristic
405C22#1458322611yescharacteristic
406C4—21no—
407C4—21no—
408C4—21no—
409C4—1721no—
410C4—1721no—
411C4—1721no—
412C4#1458289411yescharacteristic
413C4#1458290211yescharacteristic
414C4#1458304511yescharacteristic
415C4#1458304711yescharacteristic
416C4#1458316511yescharacteristic
417C4#1458316811yescharacteristic
418C2—21no—
419C2—21no—
420C2—3441no—
421C2—6882no—
422C2#1913491611yescharacteristic
423C2#1913507611yescharacteristic
424C2#1913510411yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1292C2
socleC22×C43#386
prime radical#19144076C2
cosocleC2×C42×C43C23
hypercenter#1292D43
hypocenterC43#9174
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1292

Complements

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

NH ≅ G/Ntype
2. #19143263C2semidirect
3. #19133264C2semidirect
4. C2×#14582642C2semidirect
5. #19132980C2semidirect
6. #19132490C2semidirect
7. C43×#1292C2semidirect
212. #1292D43semidirect
243. C43#9174semidirect

Maximal subgroups

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

subgroupindex
#191440762
#191432632
#191332642
C2×#145826422
#191329802
#191324902
C43×#12922
#917443