Finite Group Databasebeta

← #24991487

Subgroups — #24991487

Order 11008.

530 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144044C211yesmaximal, characteristic
2#19143160C211yesmaximal, characteristic, complemented
3#19133046C211yesmaximal, characteristic, complemented
4#19132975C211yesmaximal, characteristic, complemented
5#19132491C211yesmaximal, characteristic, complemented
6#19132429C211yesmaximal, characteristic, complemented
7C43×#1480C211yesmaximal, characteristic, complemented
8C2×#13063345—21no—
9C2×#13063331—21no—
10C4×#10621898C2211yescharacteristic
11#14583118—21no—
12#14583111—21no—
13#14583106C411yescharacteristic
14#14583101C411yescharacteristic
15#14583096C411yescharacteristic
16#14583091C411yescharacteristic
17#14582925—21no—
18#14582924—22no—
19#14582923C2211yescharacteristic
20#14582921—21no—
21C2×C4⋊(C43⋊C8)C2211yescharacteristic
22C4⋊C8×D43—21no—
23#14582895—21no—
24C2×C4×C43⋊C8C2211yescharacteristic
25#14582629—21no—
26D4⋊(C43⋊C8)—22no—
27#14582626—21no—
28C43×#532C2211yescharacteristic
29C43×#431C2211yescharacteristic
30C2×C4⋊C8×C43C2211yescharacteristic
31C43×D4⋊C8—21no—
32C43×D4⋊C8—21no—
33C2×#10621898D411yescharacteristic
34#13063345—42no—
35#13063345—42no—
36C2×#10621885—21no—
37C2×#10621883—21no—
38C2×#10621884—21no—
39C2×#10621882—21no—
40#13063331—42no—
41#13063331—42no—
42C2×#10621877—21no—
43C2×#10621872—22no—
44C22×C43⋊C8—21no—
45C22×C43⋊C8—21no—
46C2×C8×D43—22no—
47C4×Dic86C2×C411yescharacteristic
48C4×Dic86D411yescharacteristic
49C4×D172C2×C411yescharacteristic
50C4×D172D411yescharacteristic
51C4×C22⋊D43—21no—
52C4×C22⋊D43—21no—
53#13063284D411yescharacteristic
54#13063282—21no—
55C42×D43—21no—
56C4⋊(C43⋊C8)—21no—
57C4⋊(C43⋊C8)—21no—
58C4⋊(C43⋊C8)C2×C411yescharacteristic
59C4⋊(C43⋊C8)C2×C411yescharacteristic
60C4⋊(C43⋊C8)D412yes—
61Dic43⋊C8—22no—
62Dic43⋊C8—22no—
63#13063249—21no—
64#13063249—21no—
65#13063246—21no—
66#13063246—21no—
67C4×C43⋊C8—21no—
68C4×C43⋊C8—21no—
69C2×#41×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×C43—21no—
81C4⋊C8×C43D411yescharacteristic
82C4⋊C8×C43D411yescharacteristic
83C22⋊C8×C43—21no—
84C4×C8×C43—21no—
85#41×C43—41no—
86#41×C43—41no—
87#41×C43—41no—
88#41×C43—41no—
89C2×Q8×C43—21no—
90C2×D4×C43—21no—
91C2×D4×C43—21no—
92C2×D4×C43—21no—
93C2×D4×C43—41no—
94C22×C4×C43—41no—
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43#4111yescharacteristic
97C22×C4×C43#4111yescharacteristic
98C2×C22⋊D43—21no—
99#10621898—21no—
100#10621898—21no—
101#10621898D812yes—
102#10621898SD1612yes—
103C2×D172C22⋊C411yescharacteristic
104C2×C4×D43—21no—
105C2×C4×D43—21no—
106C2×C4×D43—21no—
107C2×Dic86C22⋊C411yescharacteristic
108C2×C8×C43—21no—
109C2×C8×C43—21no—
110C2×C8×C43—41no—
111C2×C8×C43—41no—
112C2×C8×C43—41no—
113C4⋊C4×C43—21no—
114C4⋊C4×C43—21no—
115C22⋊C4×C43—41no—
116C22⋊C4×C43—41no—
117C42×C43C22×C411yescharacteristic
118C42×C43C2×D411yescharacteristic
119C42×C43C2×D411yescharacteristic
120C42×C43C2×D411yescharacteristic
121C22⋊Dic43—21no—
122#10621885—42no—
123#10621884—42no—
124#10621883—42no—
125#10621882—42no—
126(C2×D43)⋊C4—21no—
127(C2×D43)⋊C4—21no—
128C4⋊Dic43C22⋊C411yescharacteristic
129C4⋊Dic43C22⋊C411yescharacteristic
130Dic43⋊C4—21no—
131Dic43⋊C4—21no—
132C4×Dic43—21no—
133C4×Dic43—21no—
134C4×Dic43—21no—
135#10621877—41no—
136#10621877—41no—
137C2×C43⋊C8—22no—
138C2×C43⋊C8—21no—
139C2×C43⋊C8—21no—
140C2×C43⋊C8—22no—
141C2×C43⋊C8—41no—
142C2×C43⋊C8—41no—
143C2×C43⋊C8—41no—
144C2×C43⋊C8—41no—
145#10621872—44no—
146C8×D43—44no—
147C23×C43—41no—
148C23×C43#12311yescharacteristic
149C22×D43—21no—
150Q8×C43—41no—
151Q8×C43—41no—
152D4×C43—42no—
153D4×C43—41no—
154D4×C43—41no—
155D4×C43—41no—
156D4×C43—41no—
157D4×C43—81no—
158D4×C43—81no—
159C2×C4×C43—21no—
160C2×C4×C43—21no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43—81no—
164C2×C4×C43—81no—
165C2×C4×C43C2×C22⋊C411yescharacteristic
166C2×C4×C43C4×D411yescharacteristic
167C2×C4×C43C4×D411yescharacteristic
168C2×C4×C43#12011yescharacteristic
169C2×C4×C43#12111yescharacteristic
170C2×C4×C43#12111yescharacteristic
171C2×C4×C43C2×D811yescharacteristic
172C2×C4×C43C2×SD1611yescharacteristic
173C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C43#13711yescharacteristic
175C22⋊D43—22no—
176C22⋊D43—22no—
177C2×Dic43—21no—
178C2×Dic43—21no—
179C2×Dic43—21no—
180D172—21no—
181D172#10212yes—
182C4×D43—22no—
183C4×D43—22no—
184C4×D43—41no—
185C4×D43—41no—
186C4×D43—81no—
187Dic86—21no—
188Dic86#10212yes—
189C8×C43—41no—
190C8×C43—41no—
191C8×C43—81no—
192C43⋊C8—42no—
193C43⋊C8—41no—
194C43⋊C8—41no—
195C43⋊C8—42no—
196#8995—431nomaximal, Sylow
197C22×C43—21no—
198C22×C43—21no—
199C22×C43—81no—
200C22×C43—81no—
201C22×C43—81no—
202C22×C43#38611yescharacteristic
203C22×C43#48011yescharacteristic
204C22×C43#48111yescharacteristic
205C2×D43—22no—
206C2×D43—41no—
207C2×D43—41no—
208C4×C43—21no—
209C4×C43—21no—
210C4×C43—21no—
211C4×C43—81no—
212C4×C43C2×#10211yescharacteristic
213C4×C43#41711yescharacteristic
214C4×C43#44311yescharacteristic
215C4×C43#44411yescharacteristic
216C4×C43#44711yescharacteristic
217C4×C43#44811yescharacteristic
218Dic43—22no—
219Dic43—41no—
220Dic43—41no—
221#3035—431no—
222#2906—431no—
223#1492—431no—
224#1480D4311yescharacteristic, complemented
225#1476—431no—
226#1301—431no—
227#1277—431no—
228C2×C43—21no—
229C2×C43—21no—
230C2×C43—161no—
231C2×C43#187411yescharacteristic
232C2×C43#187611yescharacteristic
233C2×C43#188111yescharacteristic
234D43—42no—
235C2×#135—861no—
236C2×#131—861no—
237#532C2×D4311yescharacteristic
238C4×#41—431no—
239#464—861no—
240#463—861no—
241#462—431no—
242#461—431no—
243#460—431no—
244#459—431no—
245#431C2×D4311yescharacteristic
246#424—862no—
247#424—861no—
248#423—431no—
249#423—861no—
250C2×C4⋊C8—431no—
251C2×C4⋊C8—861no—
252C2×C4⋊C8C2×D4311yescharacteristic
253#416—861no—
254C2×C4×C8—431no—
255Q8⋊C8—861no—
256D4⋊C8—21no—
257D4⋊C8—21no—
258D4⋊C8—861no—
259D4⋊C8—862no—
260C43#899511yescharacteristic, complemented, Sylow
261C2×#41—21no—
262C2×#41—431no—
263#135—1722no—
264#135—1722no—
265C2×Q16—861no—
266C2×SD16—861no—
267C2×SD16—861no—
268C2×D8—861no—
269#131—1722no—
270#131—1722no—
271C2×M16—862no—
272C2×M16—861no—
273C22×C8—21no—
274C22×C8—862no—
275C22×C8—861no—
276C22×C8—861no—
277C4⋊Q8C4×D4311yescharacteristic
278#127C4×D4311yescharacteristic
279#124—21no—
280#121—21no—
281#121—21no—
282C4×Q8—431no—
283C4×Q8—431no—
284C4×D4—21no—
285C4×D4—21no—
286C4×D4—431no—
287C4×D4—431no—
288C4×D4—861no—
289C4×D4—861no—
290#117—431no—
291#117—861no—
292C2×C42—861no—
293C2×C42C22×D4311yescharacteristic
294C4⋊C8—21no—
295C4⋊C8—21no—
296C4⋊C8—431no—
297C4⋊C8—431no—
298C4⋊C8—432no—
299C4⋊C8—862no—
300C4⋊C8—862no—
301C4⋊C8—861no—
302C4⋊C8—861no—
303C4⋊C8C22⋊D4311yescharacteristic
304C4⋊C8C22⋊D4311yescharacteristic
305#103—861no—
306#103—861no—
307#102—861no—
308#102—861no—
309C22⋊C8—21no—
310C4×C8—21no—
311C4×C8—861no—
312C4×C8—861no—
313#41—41no—
314#41—41no—
315#41—41no—
316#41—41no—
317#41—432no—
318#41—432no—
319#41—861no—
320#41—861no—
321C2×Q8—21no—
322C2×Q8—431no—
323C2×D4—21no—
324C2×D4—21no—
325C2×D4—21no—
326C2×D4—41no—
327C2×D4—431no—
328C2×D4—861no—
329C22×C4—41no—
330C22×C4—861no—
331C22×C4—861no—
332C22×C4—861no—
333C22×C4#1062189811yescharacteristic
334C22×C4D4×D4311yescharacteristic
335C22×C4#1062190011yescharacteristic
336Q16—1722no—
337SD16—1722no—
338SD16—1722no—
339D8—1722no—
340M16—1724no—
341M16—1721no—
342M16—1721no—
343C2×C8—21no—
344C2×C8—21no—
345C2×C8—41no—
346C2×C8—41no—
347C2×C8—41no—
348C2×C8—862no—
349C2×C8—861no—
350C2×C8—861no—
351C2×C8—862no—
352C2×C8—1724no—
353C2×C8—1721no—
354C2×C8—1721no—
355C2×C8—1721no—
356C2×C8—1721no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—431no—
360C4⋊C4—431no—
361C4⋊C4—861no—
362C4⋊C4—861no—
363C22⋊C4—41no—
364C22⋊C4—41no—
365C22⋊C4—861no—
366C22⋊C4—861no—
367C22⋊C4—861no—
368C42—861no—
369C42—861no—
370C42—861no—
371C42C2×C4×D4311yescharacteristic
372C42D4×D4311yescharacteristic
373C42D4×D4311yescharacteristic
374C42C2×C22⋊D4311yescharacteristic
375C23—41no—
376C23—861no—
377C23#1306330711yescharacteristic
378Q8—41no—
379Q8—41no—
380Q8—432no—
381Q8—861no—
382D4—42no—
383D4—41no—
384D4—41no—
385D4—41no—
386D4—41no—
387D4—81no—
388D4—81no—
389D4—432no—
390D4—862no—
391D4—862no—
392D4—861no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—861no—
400C2×C4—862no—
401C2×C4—862no—
402C2×C4—861no—
403C2×C4—861no—
404C2×C4—3441no—
405C2×C4—1721no—
406C2×C4—1721no—
407C2×C4C22⋊C4×D4311yescharacteristic
408C2×C4(C22⋊D43)⋊C411yescharacteristic
409C2×C4C4×C22⋊D4311yescharacteristic
410C2×C4#1306329311yescharacteristic
411C2×C4#1306329611yescharacteristic
412C2×C4#1306329811yescharacteristic
413C2×C4D8×D4311yescharacteristic
414C2×C4SD16×D4311yescharacteristic
415C2×C4#1306334911yescharacteristic
416C2×C4#1306335411yescharacteristic
417C8—41no—
418C8—41no—
419C8—81no—
420C8—1722no—
421C8—1721no—
422C8—1721no—
423C8—1722no—
424C22—21no—
425C22—21no—
426C22—81no—
427C22—81no—
428C22—81no—
429C22—862no—
430C22—1721no—
431C22—1721no—
432C22#1458277511yescharacteristic
433C22#1458321111yescharacteristic
434C22#1458321611yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—81no—
439C4—862no—
440C4—1721no—
441C4—1721no—
442C4#102×D4311yescharacteristic
443C4#1458289711yescharacteristic
444C4#1458301411yescharacteristic
445C4#1458301911yescharacteristic
446C4#1458303111yescharacteristic
447C4#1458303611yescharacteristic
448C2—21no—
449C2—21no—
450C2—161no—
451C2—1722no—
452C2#1913490911yescharacteristic
453C2#1913492511yescharacteristic
454C2#1913495411yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1480C2
socleC22×C43#386
prime radical#19144044C2
cosocleC2×C42×C43C23
hypercenter#1480D43
hypocenterC43#8995
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1480

Complements

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

NH ≅ G/Ntype
2. #19143160C2semidirect
3. #19133046C2semidirect
4. #19132975C2semidirect
5. #19132491C2semidirect
6. #19132429C2semidirect
7. C43×#1480C2semidirect
224. #1480D43semidirect
260. C43#8995semidirect

Maximal subgroups

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

subgroupindex
#191440442
#191431602
#191330462
#191329752
#191324912
#191324292
C43×#14802
#899543