Finite Group Databasebeta

← #24992487

Subgroups — #24992487

Order 11008.

562 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144071C211yesmaximal, characteristic
2#19143164C211yesmaximal, characteristic, complemented
3C2×#14582643C211yesmaximal, characteristic, complemented
4#19132983C211yesmaximal, characteristic, complemented
5#19132491C211yesmaximal, characteristic, complemented
6#19132469C211yesmaximal, characteristic, complemented
7C43×#1545C211yesmaximal, characteristic, complemented
8C2×#13063351—21no—
9C2×#13063333—21no—
10C4×#10621898C2211yescharacteristic
11#14583096—21no—
12#14583096C412yes—
13#14583091—21no—
14#14583091C412yes—
15#14582927—21no—
16#14582924—22no—
17#14582923C2211yescharacteristic
18#14582921—21no—
19C2×C4⋊(C43⋊C8)C2211yescharacteristic
20C2×C4⋊(C43⋊C8)C2211yescharacteristic
21C4⋊C8×D43—21no—
22#14582904—21no—
23#14582643—21no—
24#14582643—21no—
25#14582631—21no—
26#14582628—21no—
27C2×#127×C43C2211yescharacteristic
28C43×#431C2211yescharacteristic
29C43×#423C2211yescharacteristic
30C43×#331—22no—
31C2×#10621898D411yescharacteristic
32#13063351—42no—
33#13063351—42no—
34C2×#10621883—22no—
35C2×#10621882—22no—
36#13063333—42no—
37#13063333—42no—
38C2×#10621877—21no—
39C2×#10621872—22no—
40C22×C43⋊C8—21no—
41C22×C43⋊C8—21no—
42C2×C8×D43—22no—
43C4×Dic86C2×C411yescharacteristic
44C4×Dic86D411yescharacteristic
45C4×D172C2×C411yescharacteristic
46C4×D172D411yescharacteristic
47C4×C22⋊D43—21no—
48C4×C22⋊D43—21no—
49#13063284D411yescharacteristic
50#13063282—21no—
51C42×D43—21no—
52C4⋊(C43⋊C8)—21no—
53C4⋊(C43⋊C8)—21no—
54C4⋊(C43⋊C8)—21no—
55C4⋊(C43⋊C8)—21no—
56C4⋊(C43⋊C8)C2×C412yes—
57C4⋊(C43⋊C8)D411yescharacteristic
58C4⋊(C43⋊C8)D411yescharacteristic
59Dic43⋊C8—22no—
60Dic43⋊C8—22no—
61#13063246—22no—
62#13063246—22no—
63C22×D4×C43—21no—
64C22×D4×C43—21no—
65C22×D4×C43—21no—
66C2×M16×C43—21no—
67#127×C43—21no—
68#127×C43—21no—
69#127×C43—21no—
70#127×C43C2×C412yes—
71C2×C42×C43C2311yescharacteristic
72C4⋊C8×C43—21no—
73C4⋊C8×C43—21no—
74C4⋊C8×C43D412yes—
75C22⋊C8×C43—21no—
76C4×C8×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—41no—
85C2×D4×C43—41no—
86C2×D4×C43—41no—
87C2×D4×C43—41no—
88C2×D4×C43—81no—
89C2×D4×C43—81no—
90C2×D4×C43—82no—
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43#4111yescharacteristic
93C22×C4×C43#4111yescharacteristic
94C2×C22⋊D43—21no—
95#10621898—21no—
96#10621898—21no—
97#10621898D812yes—
98#10621898SD1612yes—
99C2×D172C22⋊C411yescharacteristic
100C2×C4×D43—21no—
101C2×C4×D43—21no—
102C2×C4×D43—21no—
103C2×Dic86C22⋊C411yescharacteristic
104M16×C43—41no—
105M16×C43—41no—
106C2×C8×C43—22no—
107C2×C8×C43—41no—
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—
126C2×C43⋊C8—22no—
127C2×C43⋊C8—21no—
128C2×C43⋊C8—21no—
129C2×C43⋊C8—41no—
130C2×C43⋊C8—41no—
131C2×C43⋊C8—41no—
132C2×C43⋊C8—81no—
133#10621872—44no—
134C8×D43—44no—
135C23×C43—42no—
136C23×C43—82no—
137C23×C43—82no—
138C23×C43—81no—
139C23×C43—81no—
140C23×C43#12311yescharacteristic
141C22×D43—21no—
142D4×C43—42no—
143D4×C43—42no—
144D4×C43—82no—
145D4×C43—82no—
146D4×C43—82no—
147D4×C43—81no—
148D4×C43—81no—
149D4×C43—81no—
150D4×C43—81no—
151C2×C4×C43—21no—
152C2×C4×C43—21no—
153C2×C4×C43—41no—
154C2×C4×C43C2×C22⋊C411yescharacteristic
155C2×C4×C43C4×D411yescharacteristic
156C2×C4×C43C4×D411yescharacteristic
157C2×C4×C43#12011yescharacteristic
158C2×C4×C43#12111yescharacteristic
159C2×C4×C43#12111yescharacteristic
160C2×C4×C43C2×D811yescharacteristic
161C2×C4×C43C2×SD1611yescharacteristic
162C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C43#13711yescharacteristic
164C22⋊D43—22no—
165C22⋊D43—22no—
166C2×Dic43—21no—
167C2×Dic43—21no—
168C2×Dic43—21no—
169D172—21no—
170D172#10212yes—
171C4×D43—22no—
172C4×D43—22no—
173C4×D43—41no—
174C4×D43—41no—
175C4×D43—81no—
176Dic86—21no—
177Dic86#10212yes—
178C8×C43—42no—
179C8×C43—81no—
180C43⋊C8—42no—
181C43⋊C8—41no—
182C43⋊C8—41no—
183C43⋊C8—81no—
184#9173—431nomaximal, Sylow
185C22×C43—21no—
186C22×C43—21no—
187C22×C43—82no—
188C22×C43—82no—
189C22×C43—82no—
190C22×C43—162no—
191C22×C43—162no—
192C22×C43#38611yescharacteristic
193C22×C43#48011yescharacteristic
194C22×C43#48111yescharacteristic
195C2×D43—22no—
196C2×D43—41no—
197C2×D43—41no—
198C4×C43—21no—
199C4×C43—21no—
200C4×C43—21no—
201C4×C43C2×#10211yescharacteristic
202C4×C43#41711yescharacteristic
203C4×C43#44711yescharacteristic
204C4×C43#44811yescharacteristic
205C4×C43#47111yescharacteristic
206C4×C43#47211yescharacteristic
207Dic43—22no—
208Dic43—41no—
209Dic43—41no—
210#3038—431no—
211#2906—431no—
212#1545D4311yescharacteristic, complemented
213C2×#331—431no—
214#1477—431no—
215#1301—431no—
216#1292—431no—
217C2×C43—21no—
218C2×C43—21no—
219C2×C43—162no—
220C2×C43#187411yescharacteristic
221C2×C43#190311yescharacteristic
222C2×C43#190711yescharacteristic
223D43—42no—
224C2×AGL(1,ℤ/8)—861no—
225C2×#131—861no—
226C2×#127C2×D4311yescharacteristic
227C4×#41—431no—
228#460—432no—
229#460—861no—
230#459—432no—
231#459—861no—
232#431C2×D4311yescharacteristic
233#424—861no—
234#424—862no—
235#423—431no—
236#423—861no—
237#423C2×D4311yescharacteristic
238C2×C4⋊C8—431no—
239C2×C4⋊C8—431no—
240C2×C4⋊C8—861no—
241#418—861no—
242#331—22no—
243#331—861no—
244#331—861no—
245Q8⋊C8—861no—
246D4⋊C8—861no—
247C43#917311yescharacteristic, complemented, Sylow
248C2×#41—431no—
249C22×D4—21no—
250C22×D4—21no—
251C22×D4—21no—
252AGL(1,ℤ/8)—1722no—
253AGL(1,ℤ/8)—1722no—
254C2×SD16—862no—
255C2×D8—862no—
256#131—1722no—
257#131—1722no—
258C2×M16—21no—
259C2×M16—862no—
260C2×M16—861no—
261C22×C8—862no—
262C22×C8—861no—
263C22×C8—861no—
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×C42—861no—
277C2×C42C22×D4311yescharacteristic
278C4⋊C8—21no—
279C4⋊C8—21no—
280C4⋊C8—432no—
281C4⋊C8—431no—
282C4⋊C8—431no—
283C4⋊C8—862no—
284C4⋊C8—862no—
285C4⋊C8—861no—
286C4⋊C8—861no—
287C4⋊C8—861no—
288C4⋊C8—861no—
289C4⋊C8C22⋊D4312yes—
290#102—862no—
291#102—862no—
292C22⋊C8—21no—
293C4×C8—21no—
294C24—41no—
295#41—432no—
296#41—432no—
297#41—861no—
298#41—861no—
299C2×Q8—431no—
300C2×D4—22no—
301C2×D4—22no—
302C2×D4—22no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—81no—
311C2×D4—81no—
312C2×D4—82no—
313C2×D4—431no—
314C2×D4—861no—
315C22×C4—861no—
316C22×C4—861no—
317C22×C4—861no—
318C22×C4#1062189811yescharacteristic
319C22×C4D4×D4311yescharacteristic
320C22×C4#1062190011yescharacteristic
321SD16—1724no—
322D8—1724no—
323M16—41no—
324M16—41no—
325M16—1724no—
326M16—1721no—
327M16—1721no—
328C2×C8—22no—
329C2×C8—41no—
330C2×C8—862no—
331C2×C8—861no—
332C2×C8—861no—
333C2×C8—3441no—
334C2×C8—1724no—
335C2×C8—1721no—
336C2×C8—1721no—
337C2×C8—1721no—
338C4⋊C4—431no—
339C4⋊C4—431no—
340C4⋊C4—861no—
341C4⋊C4—861no—
342C22⋊C4—861no—
343C22⋊C4—861no—
344C22⋊C4—861no—
345C42—861no—
346C42—861no—
347C42—861no—
348C42C2×C4×D4311yescharacteristic
349C42D4×D4311yescharacteristic
350C42D4×D4311yescharacteristic
351C42C2×C22⋊D4311yescharacteristic
352C23—42no—
353C23—82no—
354C23—82no—
355C23—81no—
356C23—81no—
357C23—861no—
358C23#1306330711yescharacteristic
359Q8—432no—
360Q8—861no—
361D4—42no—
362D4—42no—
363D4—82no—
364D4—82no—
365D4—82no—
366D4—81no—
367D4—81no—
368D4—81no—
369D4—81no—
370D4—432no—
371D4—862no—
372D4—862no—
373D4—861no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—41no—
377C2×C4—861no—
378C2×C4—862no—
379C2×C4—862no—
380C2×C4—861no—
381C2×C4—861no—
382C2×C4—3441no—
383C2×C4—1721no—
384C2×C4—1721no—
385C2×C4C22⋊C4×D4311yescharacteristic
386C2×C4(C22⋊D43)⋊C411yescharacteristic
387C2×C4C4×C22⋊D4311yescharacteristic
388C2×C4#1306329311yescharacteristic
389C2×C4#1306329611yescharacteristic
390C2×C4#1306329811yescharacteristic
391C2×C4D8×D4311yescharacteristic
392C2×C4SD16×D4311yescharacteristic
393C2×C4#1306334911yescharacteristic
394C2×C4#1306335411yescharacteristic
395C8—42no—
396C8—81no—
397C8—3441no—
398C8—1722no—
399C8—1721no—
400C8—1721no—
401C22—21no—
402C22—21no—
403C22—82no—
404C22—82no—
405C22—82no—
406C22—162no—
407C22—162no—
408C22—862no—
409C22—1721no—
410C22—1721no—
411C22#1458277511yescharacteristic
412C22#1458321111yescharacteristic
413C22#1458321611yescharacteristic
414C4—21no—
415C4—21no—
416C4—21no—
417C4—862no—
418C4—1721no—
419C4—1721no—
420C4#102×D4311yescharacteristic
421C4#1458289711yescharacteristic
422C4#1458303111yescharacteristic
423C4#1458303611yescharacteristic
424C4#1458316111yescharacteristic
425C4#1458316811yescharacteristic
426C2—21no—
427C2—21no—
428C2—162no—
429C2—1722no—
430C2#1913490911yescharacteristic
431C2#1913507211yescharacteristic
432C2#1913510011yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1545C2
socleC22×C43#386
prime radical#19144071C2
cosocleC2×C42×C43C23
hypercenter#1545D43
hypocenterC43#9173
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1545

Complements

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

NH ≅ G/Ntype
2. #19143164C2semidirect
3. C2×#14582643C2semidirect
4. #19132983C2semidirect
5. #19132491C2semidirect
6. #19132469C2semidirect
7. C43×#1545C2semidirect
212. #1545D43semidirect
247. C43#9173semidirect

Maximal subgroups

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

subgroupindex
#191440712
#191431642
C2×#145826432
#191329832
#191324912
#191324692
C43×#15452
#917343