Finite Group Databasebeta

← #24995940

Subgroups — #24995940

Order 11008.

514 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#19145021C211yesmaximal, characteristic
2C4⋊C4×C43⋊C8C211yesmaximal, characteristic, complemented
3#19133341C211yesmaximal, characteristic, complemented
4#19133089C211yesmaximal, characteristic, complemented
5#19132995C211yesmaximal, characteristic, complemented
6#19132994C211yesmaximal, characteristic, complemented
7C43×#1502C211yesmaximal, characteristic, complemented
8C2×#13063345—21no—
9C2×#13063345—21no—
10#14583449C2211yescharacteristic
11#14583281—21no—
12#14583281—21no—
13#14583278C411yescharacteristic, complemented
14#14583275C411yescharacteristic, complemented
15#14583273C411yescharacteristic, complemented
16#14583271C411yescharacteristic, complemented
17#14582952C2211yescharacteristic
18C2×C4⋊(C43⋊C8)C2211yescharacteristic
19C2×C4×C43⋊C8—21no—
20C2×C4×C43⋊C8C2211yescharacteristic
21#14582654—21no—
22#14582651—21no—
23#14582649—21no—
24#14582632—22no—
25#14582628—22no—
26D4⋊(C43⋊C8)—22no—
27C43×#532C2211yescharacteristic
28C43×#431C2211yescharacteristic
29C4×C4⋊C4×C43C2211yescharacteristic
30C43×#327—22no—
31C2×#10621898—21no—
32#13063345—42no—
33#13063345—42no—
34#13063345—42no—
35#13063345—42no—
36C2×#10621885—21no—
37C2×#10621885—21no—
38C2×#10621883—21no—
39C2×#10621883—21no—
40C2×#10621884—21no—
41C2×#10621884—21no—
42C2×#10621882—21no—
43C2×#10621882—21no—
44C22×C43⋊C8—21no—
45C22×C43⋊C8D411yescharacteristic
46C22×C43⋊C8D411yescharacteristic
47#13063325C2×C411yescharacteristic
48#13063322C2×C411yescharacteristic
49#13063313—21no—
50#13063299—21no—
51#13063299—21no—
52C4×D172—21no—
53C4×D172—21no—
54C4⋊(C43⋊C8)—21no—
55C4⋊(C43⋊C8)—21no—
56C4⋊(C43⋊C8)D412yes—
57C22⋊(C43⋊C8)—21no—
58C4×C43⋊C8—21no—
59C4×C43⋊C8—42no—
60C4×C43⋊C8C2×C411yescharacteristic
61C4×C43⋊C8C2×C411yescharacteristic
62C4×C43⋊C8D411yescharacteristic
63C4×C43⋊C8D411yescharacteristic
64C2×#41×C43—21no—
65C4⋊Q8×C43C2×C411yescharacteristic
66#127×C43C2×C411yescharacteristic
67#124×C43—21no—
68#121×C43—21no—
69#121×C43—21no—
70C4×D4×C43—21no—
71C4×D4×C43—21no—
72C2×C4⋊C4×C43—21no—
73C2×C42×C43—21no—
74C2×C42×C43C2311yescharacteristic
75C4⋊C8×C43—21no—
76C22⋊C8×C43—21no—
77C4×C8×C43—21no—
78#95×C43D412yes—
79#41×C43—41no—
80#41×C43—41no—
81#41×C43—41no—
82#41×C43—41no—
83C2×Q8×C43—21no—
84C2×D4×C43—21no—
85C2×D4×C43—21no—
86C2×D4×C43—21no—
87C2×D4×C43—41no—
88C22×C4×C43—22no—
89C22×C4×C43—41no—
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43#4111yescharacteristic
93C2×C22⋊D43—41no—
94#10621898—41no—
95#10621898—41no—
96#10621898—41no—
97#10621898—41no—
98C2×D172—21no—
99C2×D172—21no—
100C2×D172—21no—
101C2×C4×D43—41no—
102C2×Dic86—21no—
103C2×C8×C43—41no—
104C4⋊C4×C43—24no—
105C4⋊C4×C43—21no—
106C4⋊C4×C43—21no—
107C22⋊C4×C43—41no—
108C22⋊C4×C43—41no—
109C42×C43—41no—
110C42×C43—41no—
111C42×C43C22×C411yescharacteristic
112C42×C43C2×D411yescharacteristic
113C42×C43C2×D411yescharacteristic
114C42×C43#4111yescharacteristic
115#10621885—42no—
116#10621885—42no—
117#10621884—42no—
118#10621884—42no—
119#10621883—42no—
120#10621883—42no—
121#10621882—42no—
122#10621882—42no—
123(C2×D43)⋊C4—41no—
124(C2×D43)⋊C4—41no—
125C4⋊Dic43—21no—
126C4⋊Dic43—21no—
127C2×C43⋊C8—21no—
128C2×C43⋊C8—21no—
129C2×C43⋊C8—22no—
130C2×C43⋊C8—41no—
131C2×C43⋊C8—41no—
132C2×C43⋊C8—41no—
133C2×C43⋊C8C22⋊C411yescharacteristic
134C2×C43⋊C8C22⋊C411yescharacteristic
135C2×C43⋊C8C22⋊C411yescharacteristic
136C2×C43⋊C8C22⋊C411yescharacteristic
137C2×C43⋊C8D812yes—
138C2×C43⋊C8SD1612yes—
139C23×C43—41no—
140C23×C43#12111yescharacteristic
141C22×D43—41no—
142Q8×C43—41no—
143Q8×C43—41no—
144D4×C43—41no—
145D4×C43—41no—
146D4×C43—42no—
147D4×C43—81no—
148D4×C43—81no—
149D4×C43—81no—
150C2×C4×C43—22no—
151C2×C4×C43—24no—
152C2×C4×C43—41no—
153C2×C4×C43—42no—
154C2×C4×C43—42no—
155C2×C4×C43—41no—
156C2×C4×C43—81no—
157C2×C4×C43—81no—
158C2×C4×C43C2×C22⋊C411yescharacteristic
159C2×C4×C43C4×D411yescharacteristic
160C2×C4×C43C4×D411yescharacteristic
161C2×C4×C43#12111yescharacteristic
162C2×C4×C43#12411yescharacteristic
163C2×C4×C43#12711yescharacteristic
164C2×C4×C43C2×D811yescharacteristic
165C2×C4×C43C2×SD1611yescharacteristic
166C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
168C22⋊D43—81no—
169C22⋊D43—81no—
170C2×Dic43—41no—
171D172—41no—
172D172—41no—
173D172—42no—
174D172—81no—
175C4×D43—81no—
176C4×D43—81no—
177Dic86—41no—
178Dic86—41no—
179C8×C43—81no—
180C43⋊C8—21no—
181C43⋊C8—21no—
182C43⋊C8—42no—
183C43⋊C8—81no—
184C43⋊C8#10212yes—
185C43⋊C8#10212yes—
186#9750—431nomaximal, Sylow
187C22×C43—21no—
188C22×C43—21no—
189C22×C43—81no—
190C22×C43—81no—
191C22×C43—81no—
192C22×C43#39011yescharacteristic
193C22×C43#45911yescharacteristic
194C22×C43#46011yescharacteristic
195C2×D43—81no—
196C2×D43—81no—
197C2×D43—81no—
198C4×C43—21no—
199C4×C43—21no—
200C4×C43—21no—
201C4×C43—44no—
202C4×C43—81no—
203C4×C43C2×#10211yescharacteristic
204C4×C43#41811yescharacteristic
205C4×C43#44312yes—
206C4×C43#45911yescharacteristic
207C4×C43#46011yescharacteristic
208Dic43—81no—
209#3147—431no—
210C8×C4⋊C4—431no—
211#1564—431no—
212#1502—431no—
213#1502D4311yescharacteristic, complemented
214#1480—431no—
215#1480—431no—
216C2×C43—21no—
217C2×C43—21no—
218C2×C43—161no—
219C2×C43#197411yescharacteristic
220C2×C43#197611yescharacteristic
221C2×C43#198211yescharacteristic
222D43—161no—
223C2×#135—861no—
224C2×#135—861no—
225#532—431no—
226#532C2×D4311yescharacteristic
227#495—861no—
228#495—861no—
229#494—431no—
230#493—431no—
231#492—431no—
232#492—431no—
233#431—431no—
234#431C2×D4311yescharacteristic
235C2×C4⋊C8—431no—
236C2×C4×C8—431no—
237C2×C4×C8—861no—
238C4×C4⋊C4C2×D4311yescharacteristic
239#336—861no—
240#335—861no—
241#334—861no—
242#327—22no—
243#327—862no—
244D4⋊C8—862no—
245D4⋊C8—862no—
246C43#975011yescharacteristic, complemented, Sylow
247C2×#41—21no—
248C2×#41—861no—
249#135—1722no—
250#135—1722no—
251#135—1722no—
252#135—1722no—
253C2×Q16—861no—
254C2×Q16—861no—
255C2×SD16—861no—
256C2×SD16—861no—
257C2×SD16—861no—
258C2×SD16—861no—
259C2×D8—861no—
260C2×D8—861no—
261C22×C8—431no—
262C22×C8—431no—
263C22×C8—861no—
264C4⋊Q8—431no—
265C4⋊Q8C4×D4311yescharacteristic
266#127—431no—
267#127C4×D4311yescharacteristic
268#124—21no—
269#124—861no—
270#121—21no—
271#121—21no—
272#121—861no—
273#121—861no—
274C4×D4—21no—
275C4×D4—21no—
276C4×D4—861no—
277C4×D4—861no—
278C2×C4⋊C4—21no—
279C2×C42—21no—
280C2×C42C22×D4311yescharacteristic
281C4⋊C8—21no—
282C4⋊C8—432no—
283C4⋊C8—861no—
284C4⋊C8—861no—
285C22⋊C8—21no—
286C22⋊C8—861no—
287C4×C8—21no—
288C4×C8—431no—
289C4×C8—431no—
290C4×C8—431no—
291C4×C8—431no—
292C4×C8—861no—
293C4×C8—1722no—
294#95C22⋊D4312yes—
295#41—41no—
296#41—41no—
297#41—41no—
298#41—41no—
299#41—1721no—
300#41—1721no—
301#41—1721no—
302#41—1721no—
303C2×Q8—21no—
304C2×Q8—861no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—41no—
309C2×D4—861no—
310C2×D4—861no—
311C2×D4—861no—
312C2×D4—1721no—
313C22×C4—22no—
314C22×C4—41no—
315C22×C4—1721no—
316C22×C4D4×D4311yescharacteristic
317C22×C4#1062190011yescharacteristic
318C22×C4C2×C22⋊D4311yescharacteristic
319Q16—1722no—
320Q16—1722no—
321SD16—1722no—
322SD16—1722no—
323SD16—1722no—
324SD16—1722no—
325D8—1722no—
326D8—1722no—
327C2×C8—41no—
328C2×C8—431no—
329C2×C8—431no—
330C2×C8—432no—
331C2×C8—432no—
332C2×C8—431no—
333C2×C8—431no—
334C2×C8—861no—
335C2×C8—861no—
336C2×C8—862no—
337C2×C8—1721no—
338C2×C8—1721no—
339C2×C8—1721no—
340C4⋊C4—24no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—861no—
344C4⋊C4—861no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C22⋊C4—1721no—
348C22⋊C4—1721no—
349C42—41no—
350C42—41no—
351C42C2×C4×D4311yescharacteristic
352C42#1062189811yescharacteristic
353C42D4×D4311yescharacteristic
354C42D4×D4311yescharacteristic
355C23—41no—
356C23—1721no—
357C23#1306329711yescharacteristic
358Q8—41no—
359Q8—41no—
360Q8—1721no—
361Q8—1721no—
362D4—41no—
363D4—41no—
364D4—42no—
365D4—81no—
366D4—81no—
367D4—81no—
368D4—3441no—
369D4—3441no—
370D4—3441no—
371D4—1721no—
372D4—1721no—
373D4—1722no—
374C2×C4—22no—
375C2×C4—24no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—41no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—3441no—
383C2×C4—3441no—
384C2×C4—1721no—
385C2×C4C22⋊C4×D4311yescharacteristic
386C2×C4(C22⋊D43)⋊C411yescharacteristic
387C2×C4C4×C22⋊D4311yescharacteristic
388C2×C4#1306329811yescharacteristic
389C2×C4#1306331111yescharacteristic
390C2×C4#1306332111yescharacteristic
391C2×C4D8×D4311yescharacteristic
392C2×C4SD16×D4311yescharacteristic
393C2×C4#1306334911yescharacteristic
394C2×C4#1306335211yescharacteristic
395C8—81no—
396C8—432no—
397C8—432no—
398C8—861no—
399C8—861no—
400C8—3441no—
401C8—1722no—
402C22—21no—
403C22—21no—
404C22—81no—
405C22—81no—
406C22—81no—
407C22—3441no—
408C22—3441no—
409C22—3441no—
410C22#1458279911yescharacteristic
411C22#1458309211yescharacteristic
412C22#1458309711yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—44no—
417C4—81no—
418C4—3441no—
419C4#102×D4311yescharacteristic
420C4#1458290211yescharacteristic
421C4#1458301312yes—
422C4#1458309311yescharacteristic
423C4#1458309811yescharacteristic
424C2—21no—
425C2—21no—
426C2—161no—
427C2—6881no—
428C2#1913548011yescharacteristic
429C2#1913549011yescharacteristic
430C2#1913552011yescharacteristic
subgroupG/H
centerC2×C4#13063298
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1502C2
socleC22×C43#390
prime radical#19145021C2
cosocleC2×C42×C43C23
hypercenter#1502D43
hypocenterC43#9750
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. C4⋊C4×C43⋊C8C2semidirect
3. #19133341C2semidirect
4. #19133089C2semidirect
5. #19132995C2semidirect
6. #19132994C2semidirect
7. C43×#1502C2semidirect
13. #14583278C4semidirect
14. #14583275C4semidirect
15. #14583273C4semidirect
16. #14583271C4semidirect
213. #1502D43semidirect
246. C43#9750semidirect

Maximal subgroups

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

subgroupindex
#191450212
C4⋊C4×C43⋊C82
#191333412
#191330892
#191329952
#191329942
C43×#15022
#975043