Finite Group Databasebeta

← #24993488

Subgroups — #24993488

Order 11008.

558 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144071C211yesmaximal, characteristic
2#19143713C211yesmaximal, characteristic, complemented
3#19134616C211yesmaximal, characteristic, complemented
4#19133263C211yesmaximal, characteristic, complemented
5#19132498C211yesmaximal, characteristic, complemented
6#19132470C211yesmaximal, characteristic, complemented
7C43×#1982C211yesmaximal, characteristic, complemented
8C2×#13063351—21no—
9C4×#10621898C2211yescharacteristic
10#14583096—21no—
11#14583096C412yescomplemented
12#14583091—21no—
13#14583091C412yescomplemented
14#14583026—21no—
15#14582976—21no—
16#14582970—22no—
17#14582955—21no—
18#14582952C2211yescharacteristic
19#14582923C2211yescharacteristic
20#14582923C2211yescharacteristic
21#14582921—21no—
22C2×#13063253—21no—
23#14582904—21no—
24#14582659—21no—
25#14582643—21no—
26#14582643—21no—
27C2×#127×C43C2211yescharacteristic
28C2×C4⋊C8×C43C2211yescharacteristic
29C2×#102×C43—22no—
30C4×C4⋊C4×C43C2211yescharacteristic
31C2×#10621898D411yescharacteristic
32#13063351—42no—
33#13063351—42no—
34C2×#10621883—22no—
35C2×#10621882—22no—
36C2×#10621877—21no—
37C2×#10621877—21no—
38C2×#10621872—22no—
39C4×Dic86C2×C411yescharacteristic
40C4×Dic86D411yescharacteristic
41C4×D172C2×C411yescharacteristic
42C4×D172D411yescharacteristic
43C4×C22⋊D43—21no—
44C4×C22⋊D43—21no—
45#13063284D411yescharacteristic
46#13063282—21no—
47C42×D43—21no—
48C4⋊(C43⋊C8)—21no—
49C4⋊(C43⋊C8)—21no—
50C4⋊(C43⋊C8)—21no—
51C4⋊(C43⋊C8)C2×C412yes—
52C4⋊(C43⋊C8)D411yescharacteristic
53C4⋊(C43⋊C8)D411yescharacteristic
54Dic43⋊C8—22no—
55#13063253—42no—
56#13063246—22no—
57#13063246—22no—
58C22⋊(C43⋊C8)—21no—
59(C2×D43)⋊C8—22no—
60#13063235—22no—
61C4×C43⋊C8—21no—
62C22×D4×C43—21no—
63C22×D4×C43—21no—
64C22×D4×C43—21no—
65C22×C8×C43D412yes—
66#127×C43—21no—
67#127×C43—21no—
68#127×C43—21no—
69#127×C43C2×C412yes—
70C2×C4⋊C4×C43—21no—
71C2×C42×C43—21no—
72C2×C42×C43C2311yescharacteristic
73C4⋊C8×C43—21no—
74C4⋊C8×C43—21no—
75#102×C43—44no—
76#95×C43—21no—
77C24×C43—41no—
78C2×D4×C43—22no—
79C2×D4×C43—22no—
80C2×D4×C43—22no—
81C2×D4×C43—41no—
82C2×D4×C43—41no—
83C2×D4×C43—41no—
84C2×D4×C43—42no—
85C2×D4×C43—42no—
86C2×D4×C43—41no—
87C2×D4×C43—41no—
88C2×D4×C43—41no—
89C2×D4×C43—41no—
90C2×D4×C43—82no—
91C22×C4×C43—41no—
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43C2×D411yescharacteristic
94C22×C4×C43#4111yescharacteristic
95C2×C22⋊D43—21no—
96#10621898—21no—
97#10621898—21no—
98#10621898—21no—
99#10621898—21no—
100C2×D172C22⋊C411yescharacteristic
101C2×C4×D43—21no—
102C2×C4×D43—21no—
103C2×C4×D43—21no—
104C2×Dic86C22⋊C411yescharacteristic
105C2×C8×C43—22no—
106C2×C8×C43—42no—
107C4⋊C4×C43—22no—
108C4⋊C4×C43—41no—
109C42×C43—41no—
110C42×C43—41no—
111C42×C43C22×C411yescharacteristic
112C42×C43C2×D411yescharacteristic
113C42×C43C2×D411yescharacteristic
114C42×C43#4111yescharacteristic
115C22⋊Dic43—21no—
116#10621883—44no—
117#10621882—44no—
118(C2×D43)⋊C4—21no—
119(C2×D43)⋊C4—21no—
120C4⋊Dic43C22⋊C411yescharacteristic
121C4⋊Dic43C22⋊C411yescharacteristic
122Dic43⋊C4—21no—
123Dic43⋊C4—21no—
124C4×Dic43—21no—
125C4×Dic43—21no—
126C4×Dic43—21no—
127#10621877—41no—
128#10621877—41no—
129#10621877—41no—
130#10621877—41no—
131C2×C43⋊C8—22no—
132C2×C43⋊C8—21no—
133C2×C43⋊C8—21no—
134C2×C43⋊C8—41no—
135#10621872—82no—
136C23×C43—42no—
137C23×C43—82no—
138C23×C43—82no—
139C23×C43—81no—
140C23×C43—81no—
141C23×C43#12111yescharacteristic
142C22×D43—21no—
143D4×C43—44no—
144D4×C43—42no—
145D4×C43—42no—
146D4×C43—82no—
147D4×C43—82no—
148D4×C43—81no—
149D4×C43—81no—
150D4×C43—81no—
151D4×C43—81no—
152C2×C4×C43—21no—
153C2×C4×C43—21no—
154C2×C4×C43—41no—
155C2×C4×C43—42no—
156C2×C4×C43—81no—
157C2×C4×C43—81no—
158C2×C4×C43C2×C22⋊C411yescharacteristic
159C2×C4×C43C4×D411yescharacteristic
160C2×C4×C43C4×D411yescharacteristic
161C2×C4×C43#12011yescharacteristic
162C2×C4×C43#12111yescharacteristic
163C2×C4×C43#12311yescharacteristic
164C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C43#13711yescharacteristic
168C22⋊D43—41no—
169C22⋊D43—41no—
170C2×Dic43—21no—
171C2×Dic43—21no—
172C2×Dic43—21no—
173D172—21no—
174D172—21no—
175C4×D43—41no—
176C4×D43—41no—
177C4×D43—41no—
178C4×D43—41no—
179C4×D43—81no—
180Dic86—21no—
181Dic86—21no—
182C8×C43—42no—
183C43⋊C8—42no—
184C43⋊C8—41no—
185C43⋊C8—41no—
186C43⋊C8—81no—
187#9322—431nomaximal, Sylow
188C22×C43—21no—
189C22×C43—21no—
190C22×C43—82no—
191C22×C43—82no—
192C22×C43—82no—
193C22×C43—162no—
194C22×C43—162no—
195C22×C43#38611yescharacteristic
196C22×C43#46811yescharacteristic
197C22×C43#46911yescharacteristic
198C2×D43—41no—
199C2×D43—41no—
200C2×D43—41no—
201C4×C43—21no—
202C4×C43—21no—
203C4×C43—21no—
204C4×C43—82no—
205C4×C43#41711yescharacteristic
206C4×C43#41811yescharacteristic
207C4×C43#45311yescharacteristic
208C4×C43#45411yescharacteristic
209C4×C43#46811yescharacteristic
210C4×C43#46911yescharacteristic
211Dic43—41no—
212Dic43—41no—
213Dic43—41no—
214#3038—431no—
215#2989—431no—
216#1982D4311yescharacteristic, complemented
217#1806—431no—
218#1545—431no—
219#1303—431no—
220#1292—431no—
221C2×C43—21no—
222C2×C43—21no—
223C2×C43—162no—
224C2×C43#188311yescharacteristic
225C2×C43#189511yescharacteristic
226C2×C43#190311yescharacteristic
227D43—81no—
228C2×AGL(1,ℤ/8)—861no—
229C2×#127C2×D4311yescharacteristic
230C4×#41—431no—
231#460—432no—
232#460—861no—
233#459—432no—
234#459—861no—
235#446—861no—
236#436—861no—
237#435—862no—
238#432—861no—
239#431—431no—
240#423—431no—
241#423—431no—
242#423—861no—
243C2×C4⋊C8C2×D4311yescharacteristic
244C2×#104—861no—
245#418—861no—
246C2×#102—22no—
247C4×C4⋊C4C2×D4311yescharacteristic
248#339—861no—
249#331—861no—
250#331—861no—
251C43#932211yescharacteristic, complemented, Sylow
252C2×#41—431no—
253C22×D4—21no—
254C22×D4—21no—
255C22×D4—21no—
256AGL(1,ℤ/8)—1722no—
257AGL(1,ℤ/8)—1722no—
258C2×SD16—862no—
259C2×D8—862no—
260C2×M16—862no—
261C2×M16—861no—
262C2×M16—861no—
263C22×C8C22⋊D4312yes—
264#127—21no—
265#127—21no—
266#127—21no—
267#127C4×D4312yes—
268C4×Q8—431no—
269C4×Q8—431no—
270C4×D4—431no—
271C4×D4—431no—
272C4×D4—861no—
273C4×D4—861no—
274#117—431no—
275#117—861no—
276C2×C4⋊C4—21no—
277C2×C42—21no—
278C2×C42—861no—
279C2×C42C22×D4311yescharacteristic
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8—432no—
283C4⋊C8—431no—
284C4⋊C8—431no—
285C4⋊C8—862no—
286C4⋊C8—861no—
287C4⋊C8—861no—
288C4⋊C8—861no—
289#104—1722no—
290#102—44no—
291#102—862no—
292#102—862no—
293C22⋊C8—862no—
294C22⋊C8—861no—
295#97—862no—
296C4×C8—861no—
297#95—21no—
298C24—41no—
299#41—861no—
300#41—861no—
301#41—861no—
302#41—861no—
303C2×Q8—431no—
304C2×D4—22no—
305C2×D4—22no—
306C2×D4—22no—
307C2×D4—42no—
308C2×D4—42no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—82no—
317C2×D4—431no—
318C2×D4—861no—
319C22×C4—41no—
320C22×C4—861no—
321C22×C4—861no—
322C22×C4—861no—
323C22×C4D4×D4311yescharacteristic
324C22×C4#1062190011yescharacteristic
325C22×C4C2×C22⋊D4311yescharacteristic
326SD16—1724no—
327D8—1724no—
328M16—3442no—
329M16—1721no—
330M16—1721no—
331M16—1721no—
332M16—1721no—
333C2×C8—22no—
334C2×C8—42no—
335C2×C8—862no—
336C2×C8—861no—
337C2×C8—861no—
338C2×C8—1721no—
339C4⋊C4—22no—
340C4⋊C4—41no—
341C4⋊C4—431no—
342C4⋊C4—431no—
343C4⋊C4—861no—
344C4⋊C4—861no—
345C22⋊C4—861no—
346C22⋊C4—861no—
347C22⋊C4—861no—
348C42—41no—
349C42—41no—
350C42—861no—
351C42—861no—
352C42—861no—
353C42C2×C4×D4311yescharacteristic
354C42#1062189811yescharacteristic
355C42D4×D4311yescharacteristic
356C42D4×D4311yescharacteristic
357C23—42no—
358C23—82no—
359C23—82no—
360C23—81no—
361C23—81no—
362C23—861no—
363C23#1306329611yescharacteristic
364Q8—861no—
365Q8—861no—
366D4—44no—
367D4—42no—
368D4—42no—
369D4—82no—
370D4—82no—
371D4—81no—
372D4—81no—
373D4—81no—
374D4—81no—
375D4—861no—
376D4—861no—
377D4—1721no—
378D4—1721no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—861no—
386C2×C4—861no—
387C2×C4—861no—
388C2×C4—3441no—
389C2×C4—1721no—
390C2×C4—1721no—
391C2×C4—1721no—
392C2×C4—1721no—
393C2×C4C22⋊C4×D4311yescharacteristic
394C2×C4(C22⋊D43)⋊C411yescharacteristic
395C2×C4C4×C22⋊D4311yescharacteristic
396C2×C4#1306329311yescharacteristic
397C2×C4#1306329811yescharacteristic
398C2×C4#1306330711yescharacteristic
399C2×C4#1306334911yescharacteristic
400C2×C4#1306334911yescharacteristic
401C2×C4#1306335211yescharacteristic
402C2×C4#1306335411yescharacteristic
403C8—42no—
404C8—3441no—
405C8—1721no—
406C8—1721no—
407C8—1722no—
408C22—21no—
409C22—21no—
410C22—82no—
411C22—82no—
412C22—82no—
413C22—162no—
414C22—162no—
415C22—1721no—
416C22—1721no—
417C22—1721no—
418C22#1458277511yescharacteristic
419C22#1458314211yescharacteristic
420C22#1458314911yescharacteristic
421C4—21no—
422C4—21no—
423C4—21no—
424C4—82no—
425C4—1721no—
426C4—1721no—
427C4—1721no—
428C4#1458289711yescharacteristic
429C4#1458290211yescharacteristic
430C4#1458306611yescharacteristic
431C4#1458307111yescharacteristic
432C4#1458314411yescharacteristic
433C4#1458315111yescharacteristic
434C2—21no—
435C2—21no—
436C2—162no—
437C2—3441no—
438C2#1913497411yescharacteristic
439C2#1913503011yescharacteristic
440C2#1913507211yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1982C2
socleC22×C43#386
prime radical#19144071C2
cosocleC2×C42×C43C23
hypercenter#1982D43
hypocenterC43#9322
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1982

Complements

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

NH ≅ G/Ntype
2. #19143713C2semidirect
3. #19134616C2semidirect
4. #19133263C2semidirect
5. #19132498C2semidirect
6. #19132470C2semidirect
7. C43×#1982C2semidirect
11. #14583096C4semidirect
13. #14583091C4semidirect
216. #1982D43semidirect
251. C43#9322semidirect

Maximal subgroups

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

subgroupindex
#191440712
#191437132
#191346162
#191332632
#191324982
#191324702
C43×#19822
#932243