Finite Group Databasebeta

← #24991237

Subgroups — #24991237

Order 11008.

540 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#19143712C211yesmaximal, characteristic, complemented
2#19135390C211yesmaximal, characteristic, complemented
3#19132986C211yesmaximal, characteristic, complemented
4#19132977C211yesmaximal, characteristic, complemented
5#19132446C211yesmaximal, characteristic, complemented
6#19132433C211yesmaximal, characteristic, complemented
7C4×AGL(1,ℤ/8)×C43C211yesmaximal, characteristic
8#14583030—21no—
9#14582977—21no—
10#14582971—22no—
11#14582956—21no—
12#14582952C2211yescharacteristic
13#14582952C2211yescharacteristic
14#14582923—21no—
15C2×C4⋊(C43⋊C8)C2211yescharacteristic
16C2×C22⋊(C43⋊C8)—22no—
17C2×C4×C43⋊C8C2211yescharacteristic
18Q8⋊(C43⋊C8)—21no—
19D4⋊(C43⋊C8)—21no—
20D4⋊(C43⋊C8)—21no—
21D4⋊(C43⋊C8)—21no—
22C2×AGL(1,ℤ/8)×C43C411yescharacteristic
23C4×#41×C43C2211yescharacteristic
24C2×C4×D4×C43C2211yescharacteristic
25C43×#442—21no—
26C43×#440—21no—
27C4×SD16×C43—21no—
28C4×D8×C43—21no—
29C43×#428C411yescharacteristic
30C43×#418C411yescharacteristic
31C43×#417C411yescharacteristic
32C4×M16×C43C2211yescharacteristic
33C2×#10621877—22no—
34C22×C43⋊C8—21no—
35C22×C43⋊C8D412yes—
36C4⋊(C43⋊C8)—22no—
37C4⋊(C43⋊C8)—21no—
38C4⋊(C43⋊C8)—21no—
39C4⋊(C43⋊C8)—21no—
40C4⋊(C43⋊C8)D411yescharacteristic
41C4⋊(C43⋊C8)D411yescharacteristic
42C22⋊(C43⋊C8)—22no—
43C22⋊(C43⋊C8)—21no—
44C22⋊(C43⋊C8)—21no—
45C22⋊(C43⋊C8)—44no—
46#13063236—22no—
47C4×C43⋊C8—21no—
48C4×C43⋊C8—21no—
49C4×C43⋊C8—21no—
50C4×C43⋊C8—21no—
51C2×#41×C43C2×C411yescharacteristic
52C22×D4×C43C2×C411yescharacteristic
53C23×C4×C43—21no—
54AGL(1,ℤ/8)×C43—22no—
55AGL(1,ℤ/8)×C43—22no—
56C2×SD16×C43—21no—
57C2×D8×C43—21no—
58C2×M16×C43C2×C411yescharacteristic
59C2×M16×C43C2×C411yescharacteristic
60C4×Q8×C43D411yescharacteristic
61C4×Q8×C43D411yescharacteristic
62C4×D4×C43—21no—
63C4×D4×C43—21no—
64C4×D4×C43—21no—
65C4×D4×C43—21no—
66C4×D4×C43—21no—
67C4×D4×C43—21no—
68C4×D4×C43D411yescharacteristic
69C4×D4×C43D411yescharacteristic
70#117×C43—21no—
71#117×C43C2×C411yescharacteristic
72C2×C4⋊C4×C43C2×C411yescharacteristic
73C2×C22⋊C4×C43—21no—
74C2×C42×C43—21no—
75C2×C42×C43C2311yescharacteristic
76#107×C43—21no—
77#106×C43—21no—
78#103×C43—21no—
79#102×C43—21no—
80#102×C43—21no—
81#102×C43—21no—
82#97×C43—21no—
83C4×C8×C43—21no—
84C24×C43—21no—
85#41×C43—21no—
86#41×C43—21no—
87#41×C43—21no—
88#41×C43—21no—
89C2×Q8×C43C22⋊C411yescharacteristic
90C2×D4×C43—21no—
91C2×D4×C43—21no—
92C2×D4×C43—21no—
93C2×D4×C43—21no—
94C2×D4×C43—21no—
95C2×D4×C43—21no—
96C2×D4×C43C22⋊C411yescharacteristic
97C2×D4×C43M1612yescomplemented
98C22×C4×C43—21no—
99C22×C4×C43—21no—
100C22×C4×C43—21no—
101C22×C4×C43—21no—
102C22×C4×C43—42no—
103C22×C4×C43—42no—
104C22×C4×C43—41no—
105C22×C4×C43—41no—
106C22×C4×C43C22×C411yescharacteristic
107C22×C4×C43C2×D411yescharacteristic
108C22×C4×C43#4111yescharacteristic
109SD16×C43—24no—
110D8×C43—24no—
111M16×C43—21no—
112M16×C43—21no—
113M16×C43—21no—
114M16×C43M1612yescomplemented
115C2×C8×C43—21no—
116C2×C8×C43—21no—
117C4⋊C4×C43—21no—
118C4⋊C4×C43—21no—
119C4⋊C4×C43—21no—
120C4⋊C4×C43—21no—
121C4⋊C4×C43C22⋊C411yescharacteristic
122C4⋊C4×C43C22⋊C411yescharacteristic
123C22⋊C4×C43—21no—
124C22⋊C4×C43—21no—
125C22⋊C4×C43—21no—
126C22⋊C4×C43—41no—
127C22⋊C4×C43—41no—
128C42×C43—21no—
129C42×C43—21no—
130C42×C43—21no—
131C42×C43C2×D411yescharacteristic
132C42×C43C2×D411yescharacteristic
133C42×C43C2×D411yescharacteristic
134C42×C43#4111yescharacteristic
135#10621877—82no—
136C2×C43⋊C8—22no—
137C2×C43⋊C8—21no—
138C2×C43⋊C8—21no—
139C2×C43⋊C8—22no—
140C2×C43⋊C8—41no—
141C2×C43⋊C8—41no—
142C2×C43⋊C8—42no—
143C2×C43⋊C8—41no—
144C23×C43—21no—
145C23×C43—22no—
146C23×C43—42no—
147C23×C43—42no—
148C23×C43—41no—
149C23×C43—41no—
150C23×C43C4×D411yescharacteristic
151Q8×C43—21no—
152Q8×C43—21no—
153D4×C43—21no—
154D4×C43—22no—
155D4×C43—21no—
156D4×C43—22no—
157D4×C43—41no—
158D4×C43—41no—
159D4×C43—41no—
160D4×C43—41no—
161C2×C4×C43—21no—
162C2×C4×C43—21no—
163C2×C4×C43—21no—
164C2×C4×C43—21no—
165C2×C4×C43—21no—
166C2×C4×C43—41no—
167C2×C4×C43—41no—
168C2×C4×C43—41no—
169C2×C4×C43—41no—
170C2×C4×C43—41no—
171C2×C4×C43—42no—
172C2×C4×C43—41no—
173C2×C4×C43—81no—
174C2×C4×C43—82no—
175C2×C4×C43—81no—
176C2×C4×C43—81no—
177C2×C4×C43C2×C22⋊C411yescharacteristic
178C2×C4×C43C4×D411yescharacteristic
179C2×C4×C43#12011yescharacteristic
180C2×C4×C43#12111yescharacteristic
181C2×C4×C43#12111yescharacteristic
182C2×C4×C43#12311yescharacteristic
183C2×C4×C43C2×M1611yescharacteristic
184C2×C4×C43C2×M1611yescharacteristic
185C2×C4×C43#13111yescharacteristic
186C2×C4×C43#13111yescharacteristic
187C8×C43—22no—
188C8×C43—41no—
189C43⋊C8—42no—
190C43⋊C8—42no—
191C43⋊C8—41no—
192C43⋊C8—41no—
193C43⋊C8—81no—
194#8956—431nomaximal, Sylow
195C22×C43—21no—
196C22×C43—21no—
197C22×C43—44no—
198C22×C43—42no—
199C22×C43—41no—
200C22×C43—41no—
201C22×C43—41no—
202C22×C43—82no—
203C22×C43—81no—
204C22×C43—81no—
205C22×C43#38611yescharacteristic
206C22×C43#43511yescharacteristic
207C22×C43#43611yescharacteristic
208C4×C43—21no—
209C4×C43—21no—
210C4×C43—21no—
211C4×C43—41no—
212C4×C43—41no—
213C4×C43—41no—
214C4×C43—81no—
215C4×C43#40711yescharacteristic
216C4×C43#40811yescharacteristic
217C4×C43#43511yescharacteristic
218C4×C43#43611yescharacteristic
219C4×C43#45311yescharacteristic
220C4×C43#45411yescharacteristic
221#2989—431no—
222C4×AGL(1,ℤ/8)D4311yescharacteristic
223#1954—431no—
224#1478—431no—
225#1476—431no—
226#1283—431no—
227#1278—431no—
228C2×C43—21no—
229C2×C43—21no—
230C2×C43—81no—
231C2×C43—82no—
232C2×C43#187011yescharacteristic
233C2×C43#188111yescharacteristic
234C2×C43#188311yescharacteristic
235C2×AGL(1,ℤ/8)Dic4311yescharacteristic
236C4×#41C2×D4311yescharacteristic
237C2×C4×D4C2×D4311yescharacteristic
238#446—861no—
239#442—21no—
240#440—21no—
241C4×SD16—21no—
242C4×D8—21no—
243#436—861no—
244#435—862no—
245#432—861no—
246#431—431no—
247#431—431no—
248#428Dic4311yescharacteristic
249#423—861no—
250C2×C4⋊C8—431no—
251#418Dic4311yescharacteristic
252#417Dic4311yescharacteristic
253C2×C22⋊C8—862no—
254C4×M16C2×D4311yescharacteristic
255C2×C4×C8—431no—
256Q8⋊C8—861no—
257D4⋊C8—861no—
258D4⋊C8—861no—
259D4⋊C8—861no—
260C43#895611yescharacteristic, complemented, Sylow
261C2×#41C2×Dic4311yescharacteristic
262C22×D4C2×Dic4311yescharacteristic
263C23×C4—21no—
264AGL(1,ℤ/8)—22no—
265AGL(1,ℤ/8)—22no—
266C2×SD16—21no—
267C2×D8—21no—
268C2×M16—862no—
269C2×M16C2×Dic4311yescharacteristic
270C2×M16C2×Dic4311yescharacteristic
271C22×C8—432no—
272C22×C8—861no—
273C4×Q8C22⋊D4311yescharacteristic
274C4×Q8C22⋊D4311yescharacteristic
275C4×D4—21no—
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—21no—
279C4×D4—21no—
280C4×D4—21no—
281C4×D4C22⋊D4311yescharacteristic
282C4×D4C22⋊D4311yescharacteristic
283#117—21no—
284#117C2×Dic4311yescharacteristic
285C2×C4⋊C4C2×Dic4311yescharacteristic
286C2×C22⋊C4—21no—
287C2×C42—21no—
288C2×C42C22×D4311yescharacteristic
289#107—21no—
290#106—21no—
291C4⋊C8—431no—
292C4⋊C8—431no—
293C4⋊C8—862no—
294C4⋊C8—861no—
295C4⋊C8—861no—
296C4⋊C8—861no—
297#103—21no—
298#102—21no—
299#102—21no—
300#102—21no—
301C22⋊C8—862no—
302C22⋊C8—861no—
303C22⋊C8—861no—
304C22⋊C8—1724no—
305#97—21no—
306#97—862no—
307C4×C8—21no—
308C4×C8—861no—
309C4×C8—861no—
310C4×C8—861no—
311C4×C8—861no—
312C24—21no—
313#41—21no—
314#41—21no—
315#41—21no—
316#41—21no—
317C2×Q8C22⋊Dic4311yescharacteristic
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—21no—
324C2×D4#1062187712yescomplemented
325C2×D4C22⋊Dic4311yescharacteristic
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—42no—
331C22×C4—42no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4D4×D4311yescharacteristic
335C22×C4#1062190011yescharacteristic
336C22×C4C22×Dic4311yescharacteristic
337SD16—24no—
338D8—24no—
339M16—21no—
340M16—21no—
341M16—21no—
342M16—3442no—
343M16#1062187712yescomplemented
344C2×C8—21no—
345C2×C8—21no—
346C2×C8—862no—
347C2×C8—861no—
348C2×C8—861no—
349C2×C8—862no—
350C2×C8—1721no—
351C2×C8—1721no—
352C2×C8—1721no—
353C2×C8—1722no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4C22⋊Dic4311yescharacteristic
359C4⋊C4C22⋊Dic4311yescharacteristic
360C22⋊C4—21no—
361C22⋊C4—21no—
362C22⋊C4—21no—
363C22⋊C4—41no—
364C22⋊C4—41no—
365C42—21no—
366C42—21no—
367C42—21no—
368C42D4×D4311yescharacteristic
369C42#1062190011yescharacteristic
370C42C2×C22⋊D4311yescharacteristic
371C42C2×C22⋊D4311yescharacteristic
372C23—22no—
373C23—21no—
374C23—42no—
375C23—42no—
376C23—41no—
377C23—41no—
378C23D4×Dic4311yescharacteristic
379Q8—21no—
380Q8—21no—
381D4—21no—
382D4—22no—
383D4—21no—
384D4—22no—
385D4—41no—
386D4—41no—
387D4—41no—
388D4—41no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—42no—
400C2×C4—41no—
401C2×C4—81no—
402C2×C4—82no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4C2×C22⋊Dic4311yescharacteristic
406C2×C4D4×Dic4311yescharacteristic
407C2×C4#1306329311yescharacteristic
408C2×C4#1306329711yescharacteristic
409C2×C4#1306329711yescharacteristic
410C2×C4#1306330611yescharacteristic
411C2×C4C2×#1062187711yescharacteristic
412C2×C4C2×#1062187711yescharacteristic
413C2×C4#1306333211yescharacteristic
414C2×C4#1306333211yescharacteristic
415C8—22no—
416C8—41no—
417C8—3441no—
418C8—1722no—
419C8—1722no—
420C8—1721no—
421C8—1721no—
422C22—21no—
423C22—21no—
424C22—44no—
425C22—41no—
426C22—42no—
427C22—41no—
428C22—41no—
429C22—82no—
430C22—81no—
431C22—81no—
432C22#1458277911yescharacteristic
433C22#1458297111yescharacteristic
434C22#1458297711yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—41no—
439C4—41no—
440C4—41no—
441C4—81no—
442C4#1458286311yescharacteristic
443C4#1458286611yescharacteristic
444C4#1458297111yescharacteristic
445C4#1458297711yescharacteristic
446C4#1458306511yescharacteristic
447C4#1458307011yescharacteristic
448C2—21no—
449C2—21no—
450C2—82no—
451C2—81no—
452C2#1913489311yescharacteristic
453C2#1913495911yescharacteristic
454C2#1913497311yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC4×AGL(1,ℤ/8)×C43C2
socleC22×C43#386
prime radicalC2×AGL(1,ℤ/8)×C43C4
cosocleC2×C42×C43C23
hypercenterC4×AGL(1,ℤ/8)D43
hypocenterC43#8956
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #19143712C2semidirect
2. #19135390C2semidirect
3. #19132986C2semidirect
4. #19132977C2semidirect
5. #19132446C2semidirect
6. #19132433C2semidirect
97. C2×D4×C43M16semidirect
114. M16×C43M16semidirect
260. C43#8956semidirect
324. C2×D4#10621877semidirect
343. M16#10621877semidirect

Maximal subgroups

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

subgroupindex
#191437122
#191353902
#191329862
#191329772
#191324462
#191324332
C4×AGL(1,ℤ/8)×C432
#895643