Finite Group Databasebeta

← #24991816

Subgroups — #24991816

Order 11008.

538 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145170C211yesmaximal, characteristic
2#19143339C211yesmaximal, characteristic, complemented
3#19135513C211yesmaximal, characteristic, complemented
4#19132995C211yesmaximal, characteristic, complemented
5#19132436C211yesmaximal, characteristic, complemented
6#19132431C211yesmaximal, characteristic, complemented
7C43×#1502C211yesmaximal, characteristic, complemented
8C2×#13063332—21no—
9#14583449C2211yescharacteristic
10#14583302C411yescharacteristic, complemented
11#14583275C411yescharacteristic, complemented
12#14583247C411yescharacteristic, complemented
13#14583245C411yescharacteristic, complemented
14#14583133—22no—
15C4×#10621882—22no—
16#14582977—21no—
17#14582971—22no—
18D4×C43⋊C8—21no—
19C2×C4⋊(C43⋊C8)C2211yescharacteristic
20C2×#13063253—21no—
21C2×#13063253—21no—
22#14582866—21no—
23C4×#10621877C2211yescharacteristic
24C2×C4×C43⋊C8C2211yescharacteristic
25#14582628—21no—
26#14582628—21no—
27C43×#532C2211yescharacteristic
28C43×#431C2211yescharacteristic
29C4×C4⋊C4×C43C2211yescharacteristic
30C43×#327—22no—
31C2×#10621898—21no—
32C2×#10621882—22no—
33#13063332—42no—
34#13063332—42no—
35C2×#10621877—22no—
36C2×#10621877D411yescharacteristic
37C2×#10621877D411yescharacteristic
38C22×C43⋊C8—22no—
39C22×C43⋊C8—21no—
40C22×C43⋊C8—21no—
41#13063325C2×C411yescharacteristic
42#13063322C2×C411yescharacteristic
43#13063313—21no—
44#13063299—21no—
45#13063299—21no—
46C4×D172—21no—
47C4×D172—21no—
48#13063258—22no—
49C4⋊(C43⋊C8)—21no—
50C4⋊(C43⋊C8)D411yescharacteristic
51C4⋊(C43⋊C8)D411yescharacteristic
52#13063253—42no—
53#13063253—42no—
54#13063246—22no—
55#13063245—22no—
56C22⋊(C43⋊C8)—22no—
57C22⋊(C43⋊C8)—22no—
58#13063236—21no—
59C4×C43⋊C8—21no—
60C4×C43⋊C8—21no—
61C4×C43⋊C8C2×C411yescharacteristic
62C4×C43⋊C8C2×C411yescharacteristic
63C2×#41×C43—21no—
64C4⋊Q8×C43C2×C411yescharacteristic
65#127×C43C2×C411yescharacteristic
66#124×C43—21no—
67#121×C43—21no—
68#121×C43D412yes—
69C4×D4×C43—21no—
70C4×D4×C43D412yes—
71C2×C4⋊C4×C43—21no—
72C2×C42×C43—21no—
73C2×C42×C43C2311yescharacteristic
74C4⋊C8×C43—21no—
75C22⋊C8×C43—21no—
76C4×C8×C43—21no—
77#95×C43—21no—
78#41×C43—41no—
79#41×C43—41no—
80#41×C43—41no—
81#41×C43—41no—
82C2×Q8×C43—21no—
83C2×D4×C43—21no—
84C2×D4×C43—21no—
85C2×D4×C43—22no—
86C2×D4×C43C22⋊C412yes—
87C22×C4×C43—22no—
88C22×C4×C43—41no—
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43#4111yescharacteristic
92C2×C22⋊D43—41no—
93#10621898—41no—
94#10621898—41no—
95#10621898—41no—
96#10621898—41no—
97C2×D172—21no—
98C2×D172—21no—
99C2×D172—21no—
100C2×C4×D43—41no—
101C2×Dic86—21no—
102C2×C8×C43—41no—
103C4⋊C4×C43—21no—
104C4⋊C4×C43—22no—
105C4⋊C4×C43—41no—
106C4⋊C4×C43C22⋊C412yes—
107C22⋊C4×C43—22no—
108C22⋊C4×C43—22no—
109C42×C43—41no—
110C42×C43—41no—
111C42×C43C22×C411yescharacteristic
112C42×C43C2×D411yescharacteristic
113C42×C43C2×D411yescharacteristic
114C42×C43#4111yescharacteristic
115#10621882—44no—
116(C2×D43)⋊C4—41no—
117(C2×D43)⋊C4—41no—
118C4⋊Dic43—21no—
119C4⋊Dic43—21no—
120#10621877—21no—
121#10621877—21no—
122#10621877—21no—
123#10621877—44no—
124#10621877D812yescomplemented
125C2×C43⋊C8—21no—
126C2×C43⋊C8—21no—
127C2×C43⋊C8—21no—
128C2×C43⋊C8—21no—
129C2×C43⋊C8—21no—
130C2×C43⋊C8—21no—
131C2×C43⋊C8—42no—
132C2×C43⋊C8—44no—
133C2×C43⋊C8—41no—
134C2×C43⋊C8—41no—
135C23×C43—22no—
136C23×C43#12111yescharacteristic
137C22×D43—41no—
138Q8×C43—41no—
139Q8×C43—41no—
140D4×C43—42no—
141D4×C43—42no—
142D4×C43—42no—
143D4×C43—41no—
144D4×C43—41no—
145D4×C43—41no—
146D4×C43—41no—
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43—22no—
150C2×C4×C43—41no—
151C2×C4×C43—42no—
152C2×C4×C43—42no—
153C2×C4×C43—42no—
154C2×C4×C43—81no—
155C2×C4×C43—81no—
156C2×C4×C43C2×C22⋊C411yescharacteristic
157C2×C4×C43C4×D411yescharacteristic
158C2×C4×C43C4×D411yescharacteristic
159C2×C4×C43#12011yescharacteristic
160C2×C4×C43#12111yescharacteristic
161C2×C4×C43#12311yescharacteristic
162C2×C4×C43C2×D811yescharacteristic
163C2×C4×C43#13511yescharacteristic
164C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
166C22⋊D43—81no—
167C22⋊D43—81no—
168C2×Dic43—41no—
169D172—42no—
170D172—41no—
171D172—41no—
172D172—41no—
173D172—41no—
174C4×D43—81no—
175C4×D43—81no—
176Dic86—41no—
177Dic86—41no—
178C8×C43—81no—
179C43⋊C8—22no—
180C43⋊C8—22no—
181C43⋊C8—41no—
182C43⋊C8—41no—
183C43⋊C8—41no—
184C43⋊C8—41no—
185#9053—431nomaximal, Sylow
186C22×C43—21no—
187C22×C43—21no—
188C22×C43—42no—
189C22×C43—42no—
190C22×C43—42no—
191C22×C43#38611yescharacteristic
192C22×C43#45911yescharacteristic
193C22×C43#46311yescharacteristic
194C2×D43—81no—
195C2×D43—81no—
196C2×D43—81no—
197C4×C43—21no—
198C4×C43—21no—
199C4×C43—21no—
200C4×C43—42no—
201C4×C43—82no—
202C4×C43C4×D811yescharacteristic
203C4×C43#44211yescharacteristic
204C4×C43#44311yescharacteristic
205C4×C43#44411yescharacteristic
206C4×C43#44711yescharacteristic
207C4×C43#44911yescharacteristic
208Dic43—81no—
209#3169—431no—
210#2935—431no—
211#1980—431no—
212#1502D4311yescharacteristic, complemented
213#1480—431no—
214#1279—431no—
215#1278—431no—
216C2×C43—21no—
217C2×C43—21no—
218C2×C43—82no—
219C2×C43#187611yescharacteristic
220C2×C43#187911yescharacteristic
221C2×C43#188411yescharacteristic
222D43—161no—
223C2×#131—861no—
224#532—431no—
225#532C2×D4311yescharacteristic
226#500—431no—
227#493—431no—
228#486—431no—
229#486—431no—
230#466—862no—
231C4×D8—862no—
232#436—861no—
233#435—862no—
234C8×D4—861no—
235#431C2×D4311yescharacteristic
236C2×C4⋊C8—431no—
237C2×#104—861no—
238C2×#104—861no—
239#408—861no—
240C4×M16—431no—
241C2×C4×C8—431no—
242C4×C4⋊C4C2×D4311yescharacteristic
243#327—22no—
244D4⋊C8—861no—
245D4⋊C8—861no—
246C43#905311yescharacteristic, complemented, Sylow
247C2×#41—21no—
248C2×#41—861no—
249C2×D8—862no—
250#131—1722no—
251#131—1722no—
252C2×M16—431no—
253C2×M16—431no—
254C2×M16—862no—
255C22×C8—862no—
256C22×C8—861no—
257C22×C8—861no—
258C4⋊Q8—431no—
259C4⋊Q8C4×D4311yescharacteristic
260#127—431no—
261#127C4×D4311yescharacteristic
262#124—21no—
263#124—861no—
264#121—21no—
265#121—861no—
266#121—861no—
267#121C22⋊D4312yes—
268C4×D4—21no—
269C4×D4—861no—
270C4×D4—861no—
271C4×D4D17212yes—
272C2×C4⋊C4—21no—
273C2×C42—21no—
274C2×C42C22×D4311yescharacteristic
275#107—862no—
276C4⋊C8—21no—
277C4⋊C8—431no—
278C4⋊C8—431no—
279C4⋊C8—861no—
280#104—1722no—
281#104—1722no—
282#102—862no—
283#102—862no—
284C22⋊C8—21no—
285C22⋊C8—862no—
286C22⋊C8—862no—
287#97—861no—
288C4×C8—21no—
289C4×C8—431no—
290C4×C8—431no—
291C4×C8—861no—
292C4×C8—861no—
293#95—21no—
294#41—41no—
295#41—41no—
296#41—41no—
297#41—41no—
298#41—1721no—
299#41—1721no—
300#41—1721no—
301#41—1721no—
302C2×Q8—21no—
303C2×Q8—861no—
304C2×D4—22no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4—861no—
308C2×D4—861no—
309C2×D4—861no—
310C2×D4—1721no—
311C2×D4(C2×D43)⋊C412yes—
312C22×C4—22no—
313C22×C4—41no—
314C22×C4—1721no—
315C22×C4D4×D4311yescharacteristic
316C22×C4#1062190011yescharacteristic
317C22×C4C2×C22⋊D4311yescharacteristic
318D8—1724no—
319M16—432no—
320M16—861no—
321M16—861no—
322M16—861no—
323M16—1724no—
324C2×C8—41no—
325C2×C8—861no—
326C2×C8—861no—
327C2×C8—861no—
328C2×C8—861no—
329C2×C8—861no—
330C2×C8—861no—
331C2×C8—1724no—
332C2×C8—1722no—
333C2×C8—1721no—
334C2×C8—1721no—
335C4⋊C4—21no—
336C4⋊C4—22no—
337C4⋊C4—41no—
338C4⋊C4—861no—
339C4⋊C4—861no—
340C4⋊C4(C2×D43)⋊C412yes—
341C22⋊C4—22no—
342C22⋊C4—22no—
343C22⋊C4—1721no—
344C22⋊C4—1721no—
345C42—41no—
346C42—41no—
347C42C2×C4×D4311yescharacteristic
348C42C2×D17211yescharacteristic
349C42D4×D4311yescharacteristic
350C42#1062190011yescharacteristic
351C23—22no—
352C23—1721no—
353C23#1306329711yescharacteristic
354Q8—41no—
355Q8—41no—
356Q8—1721no—
357Q8—1721no—
358D4—42no—
359D4—42no—
360D4—42no—
361D4—41no—
362D4—41no—
363D4—41no—
364D4—41no—
365D4—3441no—
366D4—3441no—
367D4—1722no—
368D4—1721no—
369D4—1721no—
370D4—1721no—
371D4—1721no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—22no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—81no—
380C2×C4—81no—
381C2×C4—3441no—
382C2×C4—3441no—
383C2×C4—1721no—
384C2×C4C2×(C2×D43)⋊C411yescharacteristic
385C2×C4(C22⋊D43)⋊C411yescharacteristic
386C2×C4(C22⋊D43)⋊C411yescharacteristic
387C2×C4#1306329511yescharacteristic
388C2×C4#1306329711yescharacteristic
389C2×C4#1306330911yescharacteristic
390C2×C4D8×D4311yescharacteristic
391C2×C4#1306334611yescharacteristic
392C2×C4#1306334911yescharacteristic
393C2×C4#1306335211yescharacteristic
394C8—81no—
395C8—862no—
396C8—862no—
397C8—1721no—
398C8—1721no—
399C8—1721no—
400C8—1721no—
401C22—21no—
402C22—21no—
403C22—42no—
404C22—42no—
405C22—42no—
406C22—3441no—
407C22—3441no—
408C22—3441no—
409C22#1458277611yescharacteristic
410C22#1458309211yescharacteristic
411C22#1458311611yescharacteristic
412C4—21no—
413C4—21no—
414C4—21no—
415C4—42no—
416C4—82no—
417C4—3441no—
418C4#1458297911yescharacteristic
419C4#1458300811yescharacteristic
420C4#1458301311yescharacteristic
421C4#1458301811yescharacteristic
422C4#1458303411yescharacteristic
423C4#1458304511yescharacteristic
424C2—21no—
425C2—21no—
426C2—82no—
427C2—6881no—
428C2#1913492011yescharacteristic
429C2#1913494111yescharacteristic
430C2#1913497611yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1502C2
socleC22×C43#386
prime radical#19145170C2
cosocleC2×C42×C43C23
hypercenter#1502D43
hypocenterC43#9053
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1502

Complements

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

NH ≅ G/Ntype
2. #19143339C2semidirect
3. #19135513C2semidirect
4. #19132995C2semidirect
5. #19132436C2semidirect
6. #19132431C2semidirect
7. C43×#1502C2semidirect
10. #14583302C4semidirect
11. #14583275C4semidirect
12. #14583247C4semidirect
13. #14583245C4semidirect
124. #10621877D8semidirect
212. #1502D43semidirect
246. C43#9053semidirect

Maximal subgroups

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

subgroupindex
#191451702
#191433392
#191355132
#191329952
#191324362
#191324312
C43×#15022
#905343