Finite Group Databasebeta

← #24991818

Subgroups — #24991818

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#19135514C211yesmaximal, characteristic, complemented
3#19133090C211yesmaximal, characteristic, complemented
4#19132993C211yesmaximal, characteristic, complemented
5#19132434C211yesmaximal, characteristic, complemented
6#19132433C211yesmaximal, characteristic, complemented
7C43×#2935C211yesmaximal, characteristic, complemented
8#14583449C2211yescharacteristic
9#14583302C411yescharacteristic, complemented
10#14583275C411yescharacteristic, complemented
11#14583247C411yescharacteristic, complemented
12#14583245C411yescharacteristic, complemented
13#14583133—22no—
14C4×#10621882—22no—
15#14582952C2211yescharacteristic
16C2×#13063251—21no—
17C2×#13063251—21no—
18C2×C4×C43⋊C8C2211yescharacteristic
19C4×C4⋊Dic43C2211yescharacteristic
20#14582633—22no—
21#14582626—21no—
22#14582626—21no—
23C2×#131×C43—21no—
24C43×#532C2211yescharacteristic
25C43×#436—21no—
26C43×#435—22no—
27C8×D4×C43—21no—
28C2×C4⋊C8×C43C2211yescharacteristic
29C43×#408—21no—
30C4×M16×C43C2211yescharacteristic
31C2×#10621898—21no—
32C2×#10621882—22no—
33C22×C43⋊C8—21no—
34#13063325C2×C411yescharacteristic
35#13063322C2×C411yescharacteristic
36#13063313—21no—
37#13063299—21no—
38#13063299—21no—
39C4×D172—21no—
40C4×D172—21no—
41C2×C4⋊Dic43—21no—
42C2×C4×Dic43—21no—
43#13063258—22no—
44C4⋊(C43⋊C8)—21no—
45#13063251—42no—
46#13063251—42no—
47#13063246—22no—
48#13063245—22no—
49C22⋊(C43⋊C8)—21no—
50C4×C43⋊C8—21no—
51C4×C43⋊C8—21no—
52C4×C43⋊C8C2×C411yescharacteristic
53C4×C43⋊C8C2×C411yescharacteristic
54C43⋊#95—21no—
55C2×#41×C43—21no—
56#131×C43—42no—
57#131×C43—42no—
58C2×M16×C43—22no—
59C2×M16×C43D411yescharacteristic
60C2×M16×C43D411yescharacteristic
61C22×C8×C43—22no—
62C22×C8×C43—21no—
63C4⋊Q8×C43C2×C411yescharacteristic
64#127×C43C2×C411yescharacteristic
65#124×C43—21no—
66#121×C43—21no—
67#121×C43D412yes—
68C4×D4×C43—21no—
69C4×D4×C43D412yes—
70C2×C42×C43C2311yescharacteristic
71C4⋊C8×C43—21no—
72C4⋊C8×C43D411yescharacteristic
73C4⋊C8×C43D411yescharacteristic
74C22⋊C8×C43—22no—
75C22⋊C8×C43—22no—
76#97×C43—21no—
77C4×C8×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×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43#4111yescharacteristic
91C2×C22⋊D43—41no—
92C22×Dic43—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—
102M16×C43—21no—
103M16×C43—21no—
104M16×C43—21no—
105M16×C43—44no—
106M16×C43D812yescomplemented
107C2×C8×C43—21no—
108C2×C8×C43—21no—
109C2×C8×C43—21no—
110C2×C8×C43—21no—
111C2×C8×C43—44no—
112C2×C8×C43—41no—
113C2×C8×C43—41no—
114C4⋊C4×C43—21no—
115C4⋊C4×C43C22⋊C412yes—
116C22⋊C4×C43—22no—
117C22⋊C4×C43—22no—
118C42×C43C22×C411yescharacteristic
119C42×C43C2×D411yescharacteristic
120C42×C43C2×D411yescharacteristic
121C42×C43#4111yescharacteristic
122#10621882—44no—
123(C2×D43)⋊C4—41no—
124(C2×D43)⋊C4—41no—
125C4⋊Dic43—22no—
126C4⋊Dic43—21no—
127C4⋊Dic43—21no—
128C4⋊Dic43—41no—
129C4×Dic43—41no—
130C4×Dic43—41no—
131C2×C43⋊C8—21no—
132C2×C43⋊C8—21no—
133C2×C43⋊C8—42no—
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×C43C2×C22⋊C411yescharacteristic
154C2×C4×C43C4×D411yescharacteristic
155C2×C4×C43C4×D411yescharacteristic
156C2×C4×C43#12011yescharacteristic
157C2×C4×C43#12111yescharacteristic
158C2×C4×C43#12311yescharacteristic
159C2×C4×C43C2×D811yescharacteristic
160C2×C4×C43#13511yescharacteristic
161C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
163C22⋊D43—81no—
164C22⋊D43—81no—
165C2×Dic43—42no—
166C2×Dic43—41no—
167C2×Dic43—81no—
168C2×Dic43—81no—
169D172—42no—
170D172—41no—
171D172—41no—
172D172—41no—
173D172—41no—
174C4×D43—81no—
175C4×D43—81no—
176Dic86—41no—
177Dic86—41no—
178C8×C43—22no—
179C8×C43—41no—
180C8×C43—41no—
181C8×C43—41no—
182C43⋊C8—22no—
183C43⋊C8—41no—
184C43⋊C8—81no—
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×C43C4×D811yescharacteristic
202C4×C43#44211yescharacteristic
203C4×C43#44311yescharacteristic
204C4×C43#44411yescharacteristic
205C4×C43#44711yescharacteristic
206C4×C43#44911yescharacteristic
207Dic43—82no—
208Dic43—81no—
209#3169—431no—
210#2935D4311yescharacteristic, complemented
211#1980—431no—
212#1502—431no—
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—21no—
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—21no—
233#435—22no—
234C8×D4—21no—
235#431—431no—
236C2×C4⋊C8C2×D4311yescharacteristic
237C2×#104—861no—
238C2×#104—861no—
239#408—21no—
240C4×M16C2×D4311yescharacteristic
241C2×C4×C8—431no—
242C4×C4⋊C4—431no—
243#327—862no—
244D4⋊C8—861no—
245D4⋊C8—861no—
246C43#905311yescharacteristic, complemented, Sylow
247C2×#41—21no—
248C2×#41—861no—
249C2×D8—862no—
250#131—42no—
251#131—42no—
252C2×M16—22no—
253C2×M16C22⋊D4311yescharacteristic
254C2×M16C22⋊D4311yescharacteristic
255C22×C8—22no—
256C22×C8—21no—
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#121D17212yes—
268C4×D4—21no—
269C4×D4—861no—
270C4×D4—861no—
271C4×D4C22⋊D4312yes—
272C2×C4⋊C4—861no—
273C2×C42—861no—
274C2×C42C22×D4311yescharacteristic
275#107—862no—
276C4⋊C8—21no—
277C4⋊C8—861no—
278C4⋊C8C22⋊D4311yescharacteristic
279C4⋊C8C22⋊D4311yescharacteristic
280#104—1722no—
281#104—1722no—
282#102—862no—
283#102—862no—
284C22⋊C8—22no—
285C22⋊C8—22no—
286C22⋊C8—861no—
287#97—21no—
288C4×C8—21no—
289C4×C8—431no—
290C4×C8—431no—
291C4×C8—861no—
292C4×C8—861no—
293#95—861no—
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—1721no—
314C22×C4—1721no—
315C22×C4C2×D17211yescharacteristic
316C22×C4#1062189811yescharacteristic
317C22×C4C2×C22⋊D4311yescharacteristic
318D8—1724no—
319M16—21no—
320M16—21no—
321M16—21no—
322M16—44no—
323M16#1062188212yescomplemented
324C2×C8—21no—
325C2×C8—21no—
326C2×C8—21no—
327C2×C8—21no—
328C2×C8—44no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—861no—
332C2×C8—861no—
333C2×C8—1722no—
334C2×C8—1721no—
335C4⋊C4—21no—
336C4⋊C4—862no—
337C4⋊C4—861no—
338C4⋊C4—861no—
339C4⋊C4—1721no—
340C4⋊C4(C2×D43)⋊C412yes—
341C22⋊C4—22no—
342C22⋊C4—22no—
343C22⋊C4—1721no—
344C22⋊C4—1721no—
345C42—1721no—
346C42—1721no—
347C42C2×C4×D4311yescharacteristic
348C42#1062189811yescharacteristic
349C42C2×C22⋊D4311yescharacteristic
350C42C2×C22⋊D4311yescharacteristic
351C23—22no—
352C23—1721no—
353C23#1306329911yescharacteristic
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—3441no—
379C2×C4—3441no—
380C2×C4—3441no—
381C2×C4—3441no—
382C2×C4—1722no—
383C2×C4—1721no—
384C2×C4C2×(C2×D43)⋊C411yescharacteristic
385C2×C4C4×C22⋊D4311yescharacteristic
386C2×C4C4×C22⋊D4311yescharacteristic
387C2×C4#1306329411yescharacteristic
388C2×C4#1306329911yescharacteristic
389C2×C4#1306330811yescharacteristic
390C2×C4C2×#1062188211yescharacteristic
391C2×C4#1306334511yescharacteristic
392C2×C4#1306335011yescharacteristic
393C2×C4#1306335111yescharacteristic
394C8—22no—
395C8—41no—
396C8—41no—
397C8—41no—
398C8—862no—
399C8—3441no—
400C8—1721no—
401C22—21no—
402C22—21no—
403C22—42no—
404C22—42no—
405C22—42no—
406C22—3441no—
407C22—3441no—
408C22—3441no—
409C22#1458277811yescharacteristic
410C22#1458309411yescharacteristic
411C22#1458311411yescharacteristic
412C4—21no—
413C4—21no—
414C4—21no—
415C4—42no—
416C4—3442no—
417C4—3441no—
418C4C4×#1062188211yescharacteristic
419C4#1458300911yescharacteristic
420C4#1458301411yescharacteristic
421C4#1458301911yescharacteristic
422C4#1458303311yescharacteristic
423C4#1458304411yescharacteristic
424C2—21no—
425C2—21no—
426C2—82no—
427C2—6881no—
428C2#1913492211yescharacteristic
429C2#1913494311yescharacteristic
430C2#1913497811yescharacteristic
subgroupG/H
centerC2×C4#13063294
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2935C2
socleC22×C43#386
prime radical#19145170C2
cosocleC2×C42×C43C23
hypercenter#2935D43
hypocenterC43#9053
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2935

Complements

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

NH ≅ G/Ntype
2. #19135514C2semidirect
3. #19133090C2semidirect
4. #19132993C2semidirect
5. #19132434C2semidirect
6. #19132433C2semidirect
7. C43×#2935C2semidirect
9. #14583302C4semidirect
10. #14583275C4semidirect
11. #14583247C4semidirect
12. #14583245C4semidirect
106. M16×C43D8semidirect
210. #2935D43semidirect
246. C43#9053semidirect
323. M16#10621882semidirect

Maximal subgroups

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

subgroupindex
#191451702
#191355142
#191330902
#191329932
#191324342
#191324332
C43×#29352
#905343