Finite Group Databasebeta

← #24991488

Subgroups — #24991488

Order 11008.

484 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144044C211yesmaximal, characteristic
2#19143263C211yesmaximal, characteristic, complemented
3#19132994C211yesmaximal, characteristic, complemented
4#19132978C211yesmaximal, characteristic, complemented
5#19132490C211yesmaximal, characteristic, complemented
6#19132430C211yesmaximal, characteristic, complemented
7C43×#1492C211yesmaximal, characteristic, complemented
8C2×#13063345—21no—
9C4×#10621898C2211yescharacteristic
10#14583118—21no—
11#14583111—21no—
12#14583106C411yescharacteristic
13#14583101C411yescharacteristic
14#14583096C411yescharacteristic
15#14583091C411yescharacteristic
16#14582959—22no—
17#14582955—21no—
18#14582952C2211yescharacteristic
19#14582951—21no—
20C2×C4⋊(C43⋊C8)C2211yescharacteristic
21C2×C4⋊(C43⋊C8)C2211yescharacteristic
22#14582895—21no—
23#14582867—21no—
24#14582857—21no—
25#14582631—21no—
26#14582628—21no—
27D4⋊(C43⋊C8)—21no—
28D4⋊(C43⋊C8)—21no—
29C43×#532C2211yescharacteristic
30C43×#423C2211yescharacteristic
31C2×C4×C8×C43C2211yescharacteristic
32C43×D4⋊C8—22no—
33C2×#10621898D411yescharacteristic
34#13063345—42no—
35#13063345—42no—
36C2×#10621885—21no—
37C2×#10621883—21no—
38C2×#10621884—21no—
39C2×#10621882—21no—
40C22×C43⋊C8—21no—
41C22×C43⋊C8—21no—
42C4×Dic86C2×C411yescharacteristic
43C4×Dic86D411yescharacteristic
44C4×D172C2×C411yescharacteristic
45C4×D172D411yescharacteristic
46C4×C22⋊D43—21no—
47C4×C22⋊D43—21no—
48#13063284D411yescharacteristic
49#13063282—21no—
50C42×D43—21no—
51C4⋊(C43⋊C8)—21no—
52C4⋊(C43⋊C8)—21no—
53C4⋊(C43⋊C8)—21no—
54C4⋊(C43⋊C8)C2×C411yescharacteristic
55C4⋊(C43⋊C8)C2×C411yescharacteristic
56C4⋊(C43⋊C8)D411yescharacteristic
57C4⋊(C43⋊C8)D411yescharacteristic
58#13063249—21no—
59#13063249—21no—
60#13063246—21no—
61#13063246—21no—
62C22⋊(C43⋊C8)—21no—
63(C2×D43)⋊C8—22no—
64(C2×D43)⋊C8—22no—
65#13063235—22no—
66C4×C43⋊C8—21no—
67C8×Dic43—22no—
68C2×#41×C43—21no—
69C2×M16×C43—21no—
70C22×C8×C43—21no—
71C4⋊Q8×C43C2×C411yescharacteristic
72#127×C43C2×C411yescharacteristic
73#124×C43—21no—
74#121×C43—21no—
75#121×C43—21no—
76C4×D4×C43—21no—
77C4×D4×C43—21no—
78C2×C42×C43C2311yescharacteristic
79C4⋊C8×C43—21no—
80C4⋊C8×C43D412yes—
81C4×C8×C43—21no—
82C4×C8×C43—21no—
83#41×C43—41no—
84#41×C43—41no—
85#41×C43—41no—
86#41×C43—41no—
87C2×Q8×C43—21no—
88C2×D4×C43—21no—
89C2×D4×C43—21no—
90C2×D4×C43—21no—
91C2×D4×C43—41no—
92C22×C4×C43—41no—
93C22×C4×C43C2×D411yescharacteristic
94C22×C4×C43#4111yescharacteristic
95C22×C4×C43#4111yescharacteristic
96C2×C22⋊D43—21no—
97#10621898—21no—
98#10621898—21no—
99#10621898—21no—
100#10621898—21no—
101C2×D172C22⋊C411yescharacteristic
102C2×C4×D43—21no—
103C2×C4×D43—21no—
104C2×C4×D43—21no—
105C2×Dic86C22⋊C411yescharacteristic
106M16×C43—41no—
107M16×C43—41no—
108C2×C8×C43—22no—
109C2×C8×C43—22no—
110C2×C8×C43—41no—
111C2×C8×C43—41no—
112C4⋊C4×C43—21no—
113C4⋊C4×C43—21no—
114C22⋊C4×C43—41no—
115C22⋊C4×C43—41no—
116C42×C43C22×C411yescharacteristic
117C42×C43C2×D411yescharacteristic
118C42×C43C2×D411yescharacteristic
119C42×C43C2×D411yescharacteristic
120C22⋊Dic43—21no—
121#10621885—42no—
122#10621884—42no—
123#10621883—42no—
124#10621882—42no—
125(C2×D43)⋊C4—21no—
126(C2×D43)⋊C4—21no—
127C4⋊Dic43C22⋊C411yescharacteristic
128C4⋊Dic43C22⋊C411yescharacteristic
129Dic43⋊C4—21no—
130Dic43⋊C4—21no—
131C4×Dic43—21no—
132C4×Dic43—21no—
133C4×Dic43—21no—
134C2×C43⋊C8—21no—
135C2×C43⋊C8—21no—
136C2×C43⋊C8—21no—
137C2×C43⋊C8—21no—
138C2×C43⋊C8—41no—
139C2×C43⋊C8—41no—
140C2×C43⋊C8—41no—
141C2×C43⋊C8—41no—
142C2×C43⋊C8—41no—
143C23×C43—41no—
144C23×C43#12311yescharacteristic
145C22×D43—21no—
146Q8×C43—41no—
147Q8×C43—41no—
148D4×C43—42no—
149D4×C43—41no—
150D4×C43—41no—
151D4×C43—41no—
152D4×C43—41no—
153D4×C43—81no—
154D4×C43—81no—
155C2×C4×C43—21no—
156C2×C4×C43—21no—
157C2×C4×C43—41no—
158C2×C4×C43—41no—
159C2×C4×C43—81no—
160C2×C4×C43—81no—
161C2×C4×C43C2×C22⋊C411yescharacteristic
162C2×C4×C43C4×D411yescharacteristic
163C2×C4×C43C4×D411yescharacteristic
164C2×C4×C43#12011yescharacteristic
165C2×C4×C43#12111yescharacteristic
166C2×C4×C43#12111yescharacteristic
167C2×C4×C43#13511yescharacteristic
168C2×C4×C43#13511yescharacteristic
169C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
171C22⋊D43—41no—
172C22⋊D43—41no—
173C2×Dic43—21no—
174C2×Dic43—21no—
175C2×Dic43—21no—
176D172—21no—
177D172—21no—
178C4×D43—41no—
179C4×D43—41no—
180C4×D43—41no—
181C4×D43—41no—
182C4×D43—81no—
183Dic86—21no—
184Dic86—21no—
185C8×C43—42no—
186C8×C43—42no—
187C43⋊C8—41no—
188C43⋊C8—41no—
189C43⋊C8—41no—
190C43⋊C8—41no—
191C43⋊C8—81no—
192#8996—431nomaximal, Sylow
193C22×C43—21no—
194C22×C43—21no—
195C22×C43—81no—
196C22×C43—81no—
197C22×C43—81no—
198C22×C43#38611yescharacteristic
199C22×C43#48211yescharacteristic
200C22×C43#48211yescharacteristic
201C2×D43—41no—
202C2×D43—41no—
203C2×D43—41no—
204C4×C43—21no—
205C4×C43—21no—
206C4×C43—21no—
207C4×C43—81no—
208C4×C43#41611yescharacteristic
209C4×C43#41811yescharacteristic
210C4×C43#44311yescharacteristic
211C4×C43#44411yescharacteristic
212C4×C43#44911yescharacteristic
213C4×C43#44911yescharacteristic
214Dic43—41no—
215Dic43—41no—
216Dic43—41no—
217#3035—431no—
218#2925—431no—
219#1492D4311yescharacteristic, complemented
220#1480—431no—
221#1476—431no—
222#1301—431no—
223#1277—431no—
224C2×C43—21no—
225C2×C43—21no—
226C2×C43—161no—
227C2×C43#187511yescharacteristic
228C2×C43#187611yescharacteristic
229C2×C43#188111yescharacteristic
230D43—81no—
231C2×#135—861no—
232#532C2×D4311yescharacteristic
233C4×#41—431no—
234#464—861no—
235#463—861no—
236#462—431no—
237#461—431no—
238#460—431no—
239#459—431no—
240#433—862no—
241#432—861no—
242#431—431no—
243#431—861no—
244#423C2×D4311yescharacteristic
245C2×C4⋊C8—431no—
246C2×C4⋊C8—431no—
247#416—861no—
248#408—861no—
249#405—861no—
250C2×C4×C8C2×D4311yescharacteristic
251Q8⋊C8—861no—
252D4⋊C8—22no—
253D4⋊C8—861no—
254D4⋊C8—861no—
255D4⋊C8—861no—
256C43#899611yescharacteristic, complemented, Sylow
257C2×#41—21no—
258C2×#41—431no—
259#135—1722no—
260#135—1722no—
261C2×Q16—861no—
262C2×SD16—861no—
263C2×SD16—861no—
264C2×D8—861no—
265C2×M16—21no—
266C22×C8—21no—
267C22×C8—861no—
268C22×C8—861no—
269C4⋊Q8C4×D4311yescharacteristic
270#127C4×D4311yescharacteristic
271#124—21no—
272#121—21no—
273#121—21no—
274C4×Q8—431no—
275C4×Q8—431no—
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—431no—
279C4×D4—431no—
280C4×D4—861no—
281C4×D4—861no—
282#117—431no—
283#117—861no—
284C2×C42—861no—
285C2×C42C22×D4311yescharacteristic
286C4⋊C8—21no—
287C4⋊C8—431no—
288C4⋊C8—431no—
289C4⋊C8—431no—
290C4⋊C8—431no—
291C4⋊C8—861no—
292C4⋊C8—861no—
293C4⋊C8—861no—
294C4⋊C8C22⋊D4312yes—
295#103—861no—
296#103—861no—
297#102—861no—
298#102—861no—
299C22⋊C8—862no—
300C22⋊C8—862no—
301C22⋊C8—861no—
302#97—862no—
303C4×C8—21no—
304C4×C8—21no—
305C4×C8—862no—
306C4×C8—861no—
307#41—41no—
308#41—41no—
309#41—41no—
310#41—41no—
311#41—861no—
312#41—861no—
313#41—861no—
314#41—861no—
315C2×Q8—21no—
316C2×Q8—431no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—41no—
321C2×D4—431no—
322C2×D4—861no—
323C22×C4—41no—
324C22×C4—861no—
325C22×C4—861no—
326C22×C4—861no—
327C22×C4#1062189811yescharacteristic
328C22×C4D4×D4311yescharacteristic
329C22×C4#1062190011yescharacteristic
330Q16—1722no—
331SD16—1722no—
332SD16—1722no—
333D8—1722no—
334M16—41no—
335M16—41no—
336C2×C8—22no—
337C2×C8—22no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—861no—
341C2×C8—861no—
342C2×C8—861no—
343C2×C8—861no—
344C2×C8—1721no—
345C2×C8—1721no—
346C2×C8—1721no—
347C2×C8—1721no—
348C2×C8—1721no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—431no—
352C4⋊C4—431no—
353C4⋊C4—861no—
354C4⋊C4—861no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—861no—
358C22⋊C4—861no—
359C22⋊C4—861no—
360C42—861no—
361C42—861no—
362C42—861no—
363C42C2×C4×D4311yescharacteristic
364C42D4×D4311yescharacteristic
365C42D4×D4311yescharacteristic
366C42C2×C22⋊D4311yescharacteristic
367C23—41no—
368C23—861no—
369C23#1306330711yescharacteristic
370Q8—41no—
371Q8—41no—
372Q8—861no—
373Q8—861no—
374D4—42no—
375D4—41no—
376D4—41no—
377D4—41no—
378D4—41no—
379D4—81no—
380D4—81no—
381D4—861no—
382D4—861no—
383D4—1721no—
384D4—1721no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4—861no—
392C2×C4—861no—
393C2×C4—861no—
394C2×C4—3441no—
395C2×C4—1721no—
396C2×C4—1721no—
397C2×C4—1721no—
398C2×C4—1721no—
399C2×C4C22⋊C4×D4311yescharacteristic
400C2×C4(C22⋊D43)⋊C411yescharacteristic
401C2×C4C4×C22⋊D4311yescharacteristic
402C2×C4#1306329311yescharacteristic
403C2×C4#1306329611yescharacteristic
404C2×C4#1306329811yescharacteristic
405C2×C4#1306334411yescharacteristic
406C2×C4#1306334611yescharacteristic
407C2×C4#1306334911yescharacteristic
408C2×C4#1306335211yescharacteristic
409C8—42no—
410C8—42no—
411C8—3441no—
412C8—1721no—
413C8—1721no—
414C8—1721no—
415C8—1721no—
416C22—21no—
417C22—21no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—1721no—
422C22—1721no—
423C22—1721no—
424C22#1458277511yescharacteristic
425C22#1458322111yescharacteristic
426C22#1458322211yescharacteristic
427C4—21no—
428C4—21no—
429C4—21no—
430C4—81no—
431C4—1721no—
432C4—1721no—
433C4—1721no—
434C4#1458289211yescharacteristic
435C4#1458290211yescharacteristic
436C4#1458301311yescharacteristic
437C4#1458301811yescharacteristic
438C4#1458304111yescharacteristic
439C4#1458304311yescharacteristic
440C2—21no—
441C2—21no—
442C2—161no—
443C2—3441no—
444C2#1913491411yescharacteristic
445C2#1913491911yescharacteristic
446C2#1913496011yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1492C2
socleC22×C43#386
prime radical#19144044C2
cosocleC2×C42×C43C23
hypercenter#1492D43
hypocenterC43#8996
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1492

Complements

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

NH ≅ G/Ntype
2. #19143263C2semidirect
3. #19132994C2semidirect
4. #19132978C2semidirect
5. #19132490C2semidirect
6. #19132430C2semidirect
7. C43×#1492C2semidirect
219. #1492D43semidirect
256. C43#8996semidirect

Maximal subgroups

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

subgroupindex
#191440442
#191432632
#191329942
#191329782
#191324902
#191324302
C43×#14922
#899643