Finite Group Databasebeta

← #24995991

Subgroups — #24995991

Order 11008.

478 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#19145021C211yesmaximal, characteristic
2#19134725C211yesmaximal, characteristic, complemented
3#19133156C211yesmaximal, characteristic, complemented
4#19133155C211yesmaximal, characteristic, complemented
5#19133154C211yesmaximal, characteristic, complemented
6#19132888C211yesmaximal, characteristic, complemented
7C43×#1517C211yesmaximal, 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⋊C8C2211yescharacteristic
19#14582765C2211yescharacteristic
20#14582661—21no—
21#14582661—21no—
22#14582634—22no—
23#14582633—22no—
24#14582632—22no—
25#14582621—21no—
26#14582620—21no—
27C43×#532C2211yescharacteristic
28C43×#431C2211yescharacteristic
29C43×#382C2211yescharacteristic
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⋊C8D411yescharacteristic
45C22×C43⋊C8D411yescharacteristic
46#13063325C2×C411yescharacteristic
47#13063322C2×C411yescharacteristic
48#13063313—21no—
49#13063299—21no—
50#13063299—21no—
51C4×D172—21no—
52C4×D172—21no—
53C2×C4⋊Dic43—21no—
54C4⋊(C43⋊C8)—21no—
55C22⋊(C43⋊C8)D412yes—
56C4×C43⋊C8—21no—
57C4×C43⋊C8C2×C411yescharacteristic
58C4×C43⋊C8C2×C411yescharacteristic
59C4×C43⋊C8D411yescharacteristic
60C4×C43⋊C8D411yescharacteristic
61C43⋊#95—21no—
62C43⋊#95—21no—
63C2×#41×C43—21no—
64C4⋊Q8×C43C2×C411yescharacteristic
65#127×C43C2×C411yescharacteristic
66#124×C43—21no—
67#121×C43—21no—
68#121×C43—21no—
69C4×D4×C43—21no—
70C4×D4×C43—21no—
71C2×C4⋊C4×C43—21no—
72C2×C42×C43C2311yescharacteristic
73C4⋊C8×C43—21no—
74C22⋊C8×C43D412yes—
75C4×C8×C43—21no—
76#95×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—21no—
86C2×D4×C43—41no—
87C22×C4×C43—41no—
88C22×C4×C43—41no—
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C2×C22⋊D43—41no—
93C22×Dic43—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—22no—
104C4⋊C4×C43—21no—
105C4⋊C4×C43—21no—
106C4⋊C4×C43—41no—
107C4⋊C4×C43—41no—
108C22⋊C4×C43—41no—
109C22⋊C4×C43—41no—
110C42×C43C22×C411yescharacteristic
111C42×C43C2×D411yescharacteristic
112C42×C43#4111yescharacteristic
113C42×C43#4111yescharacteristic
114#10621885—42no—
115#10621885—42no—
116#10621884—42no—
117#10621884—42no—
118#10621883—42no—
119#10621883—42no—
120#10621882—42no—
121#10621882—42no—
122(C2×D43)⋊C4—41no—
123(C2×D43)⋊C4—41no—
124C4⋊Dic43—21no—
125C4⋊Dic43—21no—
126C4⋊Dic43—41no—
127C4⋊Dic43—41no—
128C2×C43⋊C8—21no—
129C2×C43⋊C8—21no—
130C2×C43⋊C8—21no—
131C2×C43⋊C8—21no—
132C2×C43⋊C8—22no—
133C2×C43⋊C8C22⋊C411yescharacteristic
134C2×C43⋊C8C22⋊C411yescharacteristic
135C2×C43⋊C8C22⋊C411yescharacteristic
136C2×C43⋊C8C22⋊C411yescharacteristic
137C23×C43—41no—
138C23×C43#12711yescharacteristic
139C22×D43—41no—
140Q8×C43—41no—
141Q8×C43—41no—
142D4×C43—41no—
143D4×C43—41no—
144D4×C43—81no—
145D4×C43—81no—
146D4×C43—81no—
147D4×C43—81no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—81no—
152C2×C4×C43—81no—
153C2×C4×C43—81no—
154C2×C4×C43—81no—
155C2×C4×C43—81no—
156C2×C4×C43C2×C22⋊C411yescharacteristic
157C2×C4×C43C4×D411yescharacteristic
158C2×C4×C43C4×D411yescharacteristic
159C2×C4×C43#12111yescharacteristic
160C2×C4×C43#12111yescharacteristic
161C2×C4×C43#12411yescharacteristic
162C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
166C22⋊D43—81no—
167C22⋊D43—81no—
168C2×Dic43—41no—
169C2×Dic43—81no—
170C2×Dic43—81no—
171C2×Dic43—81no—
172D172—41no—
173D172—41no—
174D172—81no—
175D172—81no—
176C4×D43—81no—
177C4×D43—81no—
178Dic86—41no—
179Dic86—41no—
180C8×C43—42no—
181C43⋊C8—21no—
182C43⋊C8—21no—
183C43⋊C8—21no—
184C43⋊C8—21no—
185C43⋊C8—42no—
186#9760—431nomaximal, Sylow
187C22×C43—21no—
188C22×C43—21no—
189C22×C43—81no—
190C22×C43—81no—
191C22×C43—81no—
192C22×C43#39011yescharacteristic
193C22×C43#49611yescharacteristic
194C22×C43#49611yescharacteristic
195C2×D43—81no—
196C2×D43—81no—
197C2×D43—81no—
198C4×C43—21no—
199C4×C43—21no—
200C4×C43—21no—
201C4×C43—21no—
202C4×C43—81no—
203C4×C43—161no—
204C4×C43#41811yescharacteristic
205C4×C43#41811yescharacteristic
206C4×C43#49011yescharacteristic
207C4×C43#49011yescharacteristic
208Dic43—81no—
209Dic43—161no—
210#3147—431no—
211#1835—431no—
212#1517—431no—
213#1517—431no—
214#1517—431no—
215#1517D4311yescharacteristic, complemented
216#1452—431no—
217C2×C43—21no—
218C2×C43—21no—
219C2×C43—161no—
220C2×C43#196111yescharacteristic
221C2×C43#197611yescharacteristic
222C2×C43#197611yescharacteristic
223D43—161no—
224C2×#135—861no—
225C2×#135—861no—
226#532—431no—
227#532C2×D4311yescharacteristic
228#495—861no—
229#495—861no—
230#494—431no—
231#493—431no—
232#492—431no—
233#492—431no—
234#431—431no—
235#431C2×D4311yescharacteristic
236C2×C4×C8—431no—
237#382—431no—
238#382C2×D4311yescharacteristic
239#340—861no—
240#340—861no—
241#327—22no—
242#327—862no—
243#327—862no—
244#327—862no—
245#322—861no—
246#322—861no—
247C43#976011yescharacteristic, complemented, Sylow
248C2×#41—21no—
249C2×#41—861no—
250#135—1722no—
251#135—1722no—
252#135—1722no—
253#135—1722no—
254C2×Q16—861no—
255C2×Q16—861no—
256C2×SD16—861no—
257C2×SD16—861no—
258C2×SD16—861no—
259C2×SD16—861no—
260C2×D8—861no—
261C2×D8—861no—
262C22×C8—431no—
263C22×C8—431no—
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×C4⋊C4—861no—
280C2×C42C22×D4311yescharacteristic
281C4⋊C8—21no—
282C4⋊C8—861no—
283C22⋊C8—432no—
284C22⋊C8C22⋊D4312yes—
285C4×C8—21no—
286C4×C8—431no—
287C4×C8—431no—
288C4×C8—431no—
289C4×C8—431no—
290C4×C8—861no—
291#95—21no—
292#95—21no—
293#95—861no—
294#95—861no—
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—41no—
314C22×C4—41no—
315C22×C4—1721no—
316C22×C4—1721no—
317C22×C4D4×D4311yescharacteristic
318C22×C4D4×D4311yescharacteristic
319C22×C4C2×C22⋊D4311yescharacteristic
320Q16—1722no—
321Q16—1722no—
322SD16—1722no—
323SD16—1722no—
324SD16—1722no—
325SD16—1722no—
326D8—1722no—
327D8—1722no—
328C2×C8—22no—
329C2×C8—431no—
330C2×C8—431no—
331C2×C8—431no—
332C2×C8—431no—
333C2×C8—861no—
334C2×C8—861no—
335C2×C8—861no—
336C2×C8—861no—
337C2×C8—862no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—861no—
343C4⋊C4—861no—
344C4⋊C4—1721no—
345C4⋊C4—1721no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—1721no—
349C22⋊C4—1721no—
350C42C2×C4×D4311yescharacteristic
351C42#1062189811yescharacteristic
352C42D4×D4311yescharacteristic
353C42#1062190011yescharacteristic
354C23—41no—
355C23—1721no—
356C23#1306332111yescharacteristic
357Q8—41no—
358Q8—41no—
359Q8—1721no—
360Q8—1721no—
361D4—41no—
362D4—41no—
363D4—81no—
364D4—81no—
365D4—81no—
366D4—81no—
367D4—3441no—
368D4—3441no—
369D4—3441no—
370D4—3441no—
371D4—1721no—
372D4—1721no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—81no—
377C2×C4—81no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4—81no—
381C2×C4—3441no—
382C2×C4—3441no—
383C2×C4—3441no—
384C2×C4—3441no—
385C2×C4—3441no—
386C2×C4—1721no—
387C2×C4C22⋊C4×D4311yescharacteristic
388C2×C4(C22⋊D43)⋊C411yescharacteristic
389C2×C4C4×C22⋊D4311yescharacteristic
390C2×C4#1306329711yescharacteristic
391C2×C4#1306329811yescharacteristic
392C2×C4#1306331111yescharacteristic
393C2×C4#1306334911yescharacteristic
394C2×C4#1306334911yescharacteristic
395C2×C4#1306335211yescharacteristic
396C2×C4#1306335211yescharacteristic
397C8—42no—
398C8—861no—
399C8—861no—
400C8—861no—
401C8—861no—
402C8—1722no—
403C22—21no—
404C22—21no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22—3441no—
409C22—3441no—
410C22—3441no—
411C22#1458279911yescharacteristic
412C22#1458328511yescharacteristic
413C22#1458328711yescharacteristic
414C4—21no—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—81no—
419C4—161no—
420C4—3441no—
421C4—6881no—
422C4#1458290211yescharacteristic
423C4#1458290211yescharacteristic
424C4#1458326211yescharacteristic
425C4#1458326211yescharacteristic
426C2—21no—
427C2—21no—
428C2—161no—
429C2—6881no—
430C2#1913541711yescharacteristic
431C2#1913549011yescharacteristic
432C2#1913549211yescharacteristic
subgroupG/H
centerC22#14582799
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1517C2
socleC22×C43#390
prime radical#19145021C2
cosocleC2×C42×C43C23
hypercenter#1517D43
hypocenterC43#9760
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1517

Complements

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

NH ≅ G/Ntype
2. #19134725C2semidirect
3. #19133156C2semidirect
4. #19133155C2semidirect
5. #19133154C2semidirect
6. #19132888C2semidirect
7. C43×#1517C2semidirect
13. #14583278C4semidirect
14. #14583275C4semidirect
15. #14583273C4semidirect
16. #14583271C4semidirect
215. #1517D43semidirect
247. C43#9760semidirect

Maximal subgroups

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

subgroupindex
#191450212
#191347252
#191331562
#191331552
#191331542
#191328882
C43×#15172
#976043