Finite Group Databasebeta

← #24993483

Subgroups — #24993483

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#19144075C211yesmaximal, characteristic
2#19143712C211yesmaximal, characteristic, complemented
3#19135522C211yesmaximal, characteristic, complemented
4#19133264C211yesmaximal, characteristic, complemented
5#19132498C211yesmaximal, characteristic, complemented
6#19132469C211yesmaximal, characteristic, complemented
7C43×#1806C211yesmaximal, characteristic, complemented
8C2×#13063350—21no—
9C2×#13063322C2211yescharacteristic
10#14583099—21no—
11#14583099C412yescomplemented
12#14583094—21no—
13#14583094C412yescomplemented
14#14583030—21no—
15#14582977—21no—
16#14582971—22no—
17#14582956—21no—
18#14582952C2211yescharacteristic
19#14582923—21no—
20#14582923C2211yescharacteristic
21C2×C4⋊(C43⋊C8)C2211yescharacteristic
22#14582903—21no—
23C2×#13063245—22no—
24#14582642—21no—
25#14582642—21no—
26C4×#41×C43C2211yescharacteristic
27C43×#423C2211yescharacteristic
28C2×#104×C43—21no—
29C4×C4⋊C4×C43C2211yescharacteristic
30C43×#339—21no—
31C22×D172—21no—
32C22×D172—21no—
33C22×D172—21no—
34#13063350—42no—
35#13063350—42no—
36C2×#10621884—22no—
37C2×#10621882—22no—
38C2×#10621877—21no—
39C2×#10621877—22no—
40C22×C43⋊C8D412yes—
41#13063322—21no—
42#13063322—21no—
43#13063322—21no—
44#13063322C2×C412yes—
45C4⋊(C43⋊C8)—22no—
46C4⋊(C43⋊C8)—21no—
47C4⋊(C43⋊C8)—21no—
48C4⋊(C43⋊C8)—21no—
49C4⋊(C43⋊C8)C2×C412yes—
50C4⋊(C43⋊C8)D411yescharacteristic
51C4⋊(C43⋊C8)D411yescharacteristic
52#13063245—22no—
53#13063245—22no—
54#13063245—44no—
55C22⋊(C43⋊C8)—22no—
56C22⋊(C43⋊C8)—21no—
57#13063236—22no—
58C4×C43⋊C8—21no—
59C2×#41×C43D411yescharacteristic
60C2×M16×C43—21no—
61C4×Q8×C43C2×C411yescharacteristic
62C4×Q8×C43D411yescharacteristic
63C4×D4×C43—21no—
64C4×D4×C43—21no—
65C4×D4×C43C2×C411yescharacteristic
66C4×D4×C43D411yescharacteristic
67#117×C43—21no—
68#117×C43D411yescharacteristic
69C2×C4⋊C4×C43—21no—
70C2×C42×C43—21no—
71C2×C42×C43—21no—
72C2×C42×C43C2311yescharacteristic
73C4⋊C8×C43—21no—
74C4⋊C8×C43—21no—
75#104×C43—42no—
76#95×C43—21no—
77C23×D43—41no—
78#41×C43—21no—
79#41×C43—21no—
80#41×C43—21no—
81#41×C43—21no—
82C2×Q8×C43C22⋊C411yescharacteristic
83C2×D4×C43—21no—
84C2×D4×C43C22⋊C411yescharacteristic
85C22×C4×C43—21no—
86C22×C4×C43—21no—
87C22×C4×C43—21no—
88C22×C4×C43—41no—
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43#4111yescharacteristic
92C2×D172—22no—
93C2×D172—22no—
94C2×D172—22no—
95C2×D172—41no—
96C2×D172—41no—
97C2×D172—41no—
98C2×D172—42no—
99C2×D172—42no—
100C2×D172—41no—
101C2×D172—41no—
102C2×D172—41no—
103C2×D172—41no—
104C2×D172—82no—
105M16×C43—41no—
106M16×C43—41no—
107C2×C8×C43—41no—
108C4⋊C4×C43—21no—
109C4⋊C4×C43—21no—
110C4⋊C4×C43—22no—
111C4⋊C4×C43—41no—
112C4⋊C4×C43C22⋊C411yescharacteristic
113C4⋊C4×C43C22⋊C411yescharacteristic
114C22⋊C4×C43—21no—
115C22⋊C4×C43—21no—
116C22⋊C4×C43—21no—
117C42×C43—21no—
118C42×C43—21no—
119C42×C43—21no—
120C42×C43—41no—
121C42×C43—41no—
122C42×C43C22×C411yescharacteristic
123C42×C43C2×D411yescharacteristic
124C42×C43C2×D411yescharacteristic
125C42×C43#4111yescharacteristic
126#10621884—44no—
127#10621882—44no—
128#10621877—41no—
129#10621877—41no—
130#10621877—82no—
131C2×C43⋊C8—22no—
132C2×C43⋊C8—21no—
133C2×C43⋊C8—21no—
134C2×C43⋊C8—22no—
135C2×C43⋊C8—42no—
136C23×C43—21no—
137C23×C43#12111yescharacteristic
138C22×D43—42no—
139C22×D43—82no—
140C22×D43—82no—
141C22×D43—81no—
142C22×D43—81no—
143Q8×C43—21no—
144Q8×C43—21no—
145D4×C43—21no—
146D4×C43—21no—
147D4×C43—41no—
148D4×C43—41no—
149C2×C4×C43—21no—
150C2×C4×C43—21no—
151C2×C4×C43—21no—
152C2×C4×C43—21no—
153C2×C4×C43—21no—
154C2×C4×C43—41no—
155C2×C4×C43—41no—
156C2×C4×C43—41no—
157C2×C4×C43—41no—
158C2×C4×C43—41no—
159C2×C4×C43—42no—
160C2×C4×C43—81no—
161C2×C4×C43—81no—
162C2×C4×C43—81no—
163C2×C4×C43C2×C22⋊C411yescharacteristic
164C2×C4×C43C4×D411yescharacteristic
165C2×C4×C43C4×D411yescharacteristic
166C2×C4×C43#12011yescharacteristic
167C2×C4×C43#12111yescharacteristic
168C2×C4×C43#12311yescharacteristic
169C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C43#13711yescharacteristic
173D172—44no—
174D172—42no—
175D172—42no—
176D172—82no—
177D172—82no—
178D172—81no—
179D172—81no—
180D172—81no—
181D172—81no—
182C8×C43—81no—
183C43⋊C8—42no—
184C43⋊C8—42no—
185C43⋊C8—41no—
186C43⋊C8—41no—
187#9322—431nomaximal, Sylow
188C22×C43—21no—
189C22×C43—21no—
190C22×C43—41no—
191C22×C43—41no—
192C22×C43—41no—
193C22×C43#38611yescharacteristic
194C22×C43#46811yescharacteristic
195C22×C43#46911yescharacteristic
196C2×D43—82no—
197C2×D43—82no—
198C2×D43—82no—
199C2×D43—162no—
200C2×D43—162no—
201C4×C43—21no—
202C4×C43—21no—
203C4×C43—21no—
204C4×C43—41no—
205C4×C43—41no—
206C4×C43—41no—
207C4×C43—82no—
208C4×C43#41711yescharacteristic
209C4×C43#41811yescharacteristic
210C4×C43#45311yescharacteristic
211C4×C43#45411yescharacteristic
212C4×C43#46811yescharacteristic
213C4×C43#46911yescharacteristic
214#3038—431no—
215#2989—431no—
216#1982—431no—
217#1806D4311yescharacteristic, complemented
218#1545—431no—
219#1303—431no—
220#1292—431no—
221C2×C43—21no—
222C2×C43—21no—
223C2×C43—81no—
224C2×C43#188311yescharacteristic
225C2×C43#189511yescharacteristic
226C2×C43#190311yescharacteristic
227D43—162no—
228C2×AGL(1,ℤ/8)—861no—
229C2×#127—431no—
230C4×#41C2×D4311yescharacteristic
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—861no—
242#423C2×D4311yescharacteristic
243C2×C4⋊C8—431no—
244C2×#104—21no—
245#418—861no—
246C2×#102—862no—
247C4×C4⋊C4C2×D4311yescharacteristic
248#339—21no—
249#331—861no—
250#331—861no—
251C43#932211yescharacteristic, complemented, Sylow
252C2×#41C22⋊D4311yescharacteristic
253C22×D4—861no—
254C22×D4—861no—
255C22×D4—861no—
256AGL(1,ℤ/8)—1722no—
257AGL(1,ℤ/8)—1722no—
258C2×SD16—862no—
259C2×D8—862no—
260C2×M16—21no—
261C2×M16—862no—
262C2×M16—861no—
263C22×C8—432no—
264#127—432no—
265#127—861no—
266#127—861no—
267#127—861no—
268C4×Q8C4×D4311yescharacteristic
269C4×Q8D17211yescharacteristic
270C4×D4—21no—
271C4×D4—21no—
272C4×D4C4×D4311yescharacteristic
273C4×D4D17211yescharacteristic
274#117—21no—
275#117C22⋊D4311yescharacteristic
276C2×C4⋊C4—21no—
277C2×C42—21no—
278C2×C42—21no—
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—42no—
290#102—862no—
291#102—862no—
292#102—1724no—
293C22⋊C8—862no—
294C22⋊C8—861no—
295#97—862no—
296C4×C8—861no—
297#95—21no—
298C24—1721no—
299#41—21no—
300#41—21no—
301#41—21no—
302#41—21no—
303C2×Q8(C2×D43)⋊C411yescharacteristic
304C2×D4—21no—
305C2×D4—862no—
306C2×D4—862no—
307C2×D4—862no—
308C2×D4—3442no—
309C2×D4—1722no—
310C2×D4—1722no—
311C2×D4—1721no—
312C2×D4—1721no—
313C2×D4—1721no—
314C2×D4—1721no—
315C2×D4—1721no—
316C2×D4—1721no—
317C2×D4—1721no—
318C2×D4(C2×D43)⋊C411yescharacteristic
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—41no—
323C22×C4D4×D4311yescharacteristic
324C22×C4#1062190011yescharacteristic
325C22×C4C2×C22⋊D4311yescharacteristic
326SD16—1724no—
327D8—1724no—
328M16—41no—
329M16—41no—
330M16—3442no—
331M16—1721no—
332M16—1721no—
333C2×C8—41no—
334C2×C8—862no—
335C2×C8—861no—
336C2×C8—861no—
337C2×C8—862no—
338C2×C8—1722no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—22no—
342C4⋊C4—41no—
343C4⋊C4(C2×D43)⋊C411yescharacteristic
344C4⋊C4(C2×D43)⋊C411yescharacteristic
345C22⋊C4—21no—
346C22⋊C4—21no—
347C22⋊C4—21no—
348C42—21no—
349C42—21no—
350C42—21no—
351C42—41no—
352C42—41no—
353C42C2×C4×D4311yescharacteristic
354C42C2×D17211yescharacteristic
355C42D4×D4311yescharacteristic
356C42#1062190011yescharacteristic
357C23—21no—
358C23—3442no—
359C23—3442no—
360C23—3441no—
361C23—3441no—
362C23—1722no—
363C23#1306329711yescharacteristic
364Q8—21no—
365Q8—21no—
366D4—21no—
367D4—21no—
368D4—41no—
369D4—41no—
370D4—3442no—
371D4—3442no—
372D4—3441no—
373D4—3441no—
374D4—3441no—
375D4—3441no—
376D4—1724no—
377D4—1722no—
378D4—1722no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—42no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4C2×(C2×D43)⋊C411yescharacteristic
394C2×C4(C22⋊D43)⋊C411yescharacteristic
395C2×C4(C22⋊D43)⋊C411yescharacteristic
396C2×C4#1306329511yescharacteristic
397C2×C4#1306329711yescharacteristic
398C2×C4#1306330911yescharacteristic
399C2×C4#1306335011yescharacteristic
400C2×C4#1306335011yescharacteristic
401C2×C4#1306335111yescharacteristic
402C2×C4#1306335611yescharacteristic
403C8—81no—
404C8—1722no—
405C8—1721no—
406C8—1721no—
407C8—1722no—
408C22—21no—
409C22—21no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—3442no—
414C22—3442no—
415C22—3442no—
416C22—6882no—
417C22—6882no—
418C22#1458277611yescharacteristic
419C22#1458314711yescharacteristic
420C22#1458315011yescharacteristic
421C4—21no—
422C4—21no—
423C4—21no—
424C4—41no—
425C4—41no—
426C4—41no—
427C4—82no—
428C4#1458289811yescharacteristic
429C4#1458290311yescharacteristic
430C4#1458306811yescharacteristic
431C4#1458307311yescharacteristic
432C4#1458314711yescharacteristic
433C4#1458315011yescharacteristic
434C2—21no—
435C2—21no—
436C2—81no—
437C2—6882no—
438C2#1913496911yescharacteristic
439C2#1913503111yescharacteristic
440C2#1913507311yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1806C2
socleC22×C43#386
prime radical#19144075C2
cosocleC2×C42×C43C23
hypercenter#1806D43
hypocenterC43#9322
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
2. #19143712C2semidirect
3. #19135522C2semidirect
4. #19133264C2semidirect
5. #19132498C2semidirect
6. #19132469C2semidirect
7. C43×#1806C2semidirect
11. #14583099C4semidirect
13. #14583094C4semidirect
217. #1806D43semidirect
251. C43#9322semidirect

Maximal subgroups

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

subgroupindex
#191440752
#191437122
#191355222
#191332642
#191324982
#191324692
C43×#18062
#932243