Finite Group Databasebeta

← #24984606

Subgroups — #24984606

Order 11008.

708 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137082C211yesmaximal, characteristic
2#19134662C211yesmaximal, characteristic, complemented
3#336×D43C211yesmaximal, characteristic, complemented
4#19132420C211yesmaximal, characteristic, complemented
5#19132420C211yesmaximal, characteristic, complemented
6#19132416C211yesmaximal, characteristic, complemented
7C43×#1270C211yesmaximal, characteristic, complemented
8C22×#10621900C411yescharacteristic
9C22×C8×D43—21no—
10C2×#13063283C411yescharacteristic
11C2×C42×D43C2211yescharacteristic
12C2×(C2×D43)⋊C8—21no—
13#14582805C2211yescharacteristic
14#14582804C411yescharacteristic
15#14582802C411yescharacteristic
16#14582775—21no—
17#14582775—21no—
18C22⋊C4×Dic43—21no—
19C22⋊C4×Dic43—21no—
20#14582654C2211yescharacteristic
21#14582654C2211yescharacteristic
22#14582653—21no—
23#14582653—21no—
24C43×#390C2211yescharacteristic
25C43×#336C2211yescharacteristic
26C43×#336C2211yescharacteristic
27C2×#10621900—22no—
28C2×#10621900—42no—
29C2×#10621900—42no—
30C2×#10621900C814yescomplemented
31C22×Dic86C2×C411yescharacteristic
32C22×C22⋊D43—21no—
33C23×Dic43—21no—
34C22×C4×D43C2×C411yescharacteristic
35C22×C4×D43D411yescharacteristic
36C22×C4×D43D411yescharacteristic
37C22×C43⋊C8—21no—
38C22×C43⋊C8—21no—
39C2×C8×D43—24no—
40C2×C8×D43—42no—
41C2×C8×D43—42no—
42#13063283—42no—
43C2×C4⋊Dic43C2×C411yescharacteristic
44C2×C22⋊Dic43—21no—
45C2×C22⋊Dic43—21no—
46C2×(C2×D43)⋊C4—21no—
47C2×C4×Dic43—21no—
48C2×C4×Dic43C2×C411yescharacteristic
49C2×C4×Dic43D411yescharacteristic
50C2×C4×Dic43D411yescharacteristic
51C42×D43—42no—
52(C2×D43)⋊C8—42no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C43⋊#95—21no—
57C22×D4×C43C2×C411yescharacteristic
58C22×C8×C43—21no—
59C22×C8×C43—21no—
60C2×C4⋊C4×C43C2×C411yescharacteristic
61C2×C22⋊C4×C43—21no—
62C2×C22⋊C4×C43—21no—
63C2×C42×C43C2311yescharacteristic
64C24×C43—21no—
65C23×D43C22⋊C411yescharacteristic
66C2×D4×C43—21no—
67C2×D4×C43—41no—
68C2×D4×C43—41no—
69C2×D4×C43C2×C812yescomplemented
70C22×C4×C43—21no—
71C22×C4×C43C22×C411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C2×C22⋊D43—24no—
75C2×C22⋊D43—42no—
76C2×C22⋊D43—42no—
77C22×Dic43—24no—
78C22×Dic43—21no—
79C22×Dic43—21no—
80C22×Dic43—42no—
81C22×Dic43—42no—
82C22×Dic43C22⋊C411yescharacteristic
83C22×Dic43C22⋊C411yescharacteristic
84C22×Dic43C22⋊C411yescharacteristic
85#10621900—48no—
86#10621900—48no—
87C2×C4×D43—21no—
88C2×C4×D43—21no—
89C2×C4×D43—22no—
90C2×C4×D43—21no—
91C2×C4×D43—21no—
92C2×C4×D43—22no—
93C2×C4×D43—22no—
94C2×C4×D43—22no—
95C2×C4×D43—22no—
96C2×C4×D43—41no—
97C2×C4×D43C2×C812yes—
98C2×C4×D43M1612yes—
99C2×Dic86—21no—
100C2×Dic86—41no—
101C2×Dic86—41no—
102C2×Dic86C2×C812yescomplemented
103C2×C8×C43—22no—
104C2×C8×C43—41no—
105C2×C8×C43—41no—
106C2×C8×C43—41no—
107C2×C8×C43—41no—
108C2×C8×C43—41no—
109C4⋊C4×C43—41no—
110C22⋊C4×C43—41no—
111C22⋊C4×C43—41no—
112C22⋊C4×C43—41no—
113C22⋊C4×C43—41no—
114C42×C43—41no—
115C22⋊Dic43—42no—
116C22⋊Dic43—42no—
117(C2×D43)⋊C4—42no—
118C4⋊Dic43—41no—
119C4×Dic43—41no—
120C4×Dic43—41no—
121C4×Dic43—41no—
122C4×Dic43—42no—
123C2×C43⋊C8—22no—
124C2×C43⋊C8—41no—
125C2×C43⋊C8—41no—
126C2×C43⋊C8—41no—
127C2×C43⋊C8—41no—
128C2×C43⋊C8—41no—
129C8×D43—48no—
130C23×C43—22no—
131C23×C43—41no—
132C23×C43—41no—
133C23×C43—41no—
134C23×C43—41no—
135C23×C43—41no—
136C23×C43—41no—
137C23×C43C2×C22⋊C411yescharacteristic
138C22×D43—21no—
139C22×D43—21no—
140C22×D43—21no—
141C22×D43—21no—
142C22×D43C22⋊C812yes—
143C22×D43#9912yes—
144C22×D43#10012yes—
145D4×C43—42no—
146D4×C43—42no—
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43—21no—
150C2×C4×C43—21no—
151C2×C4×C43—21no—
152C2×C4×C43—21no—
153C2×C4×C43—41no—
154C2×C4×C43—41no—
155C2×C4×C43—41no—
156C2×C4×C43C22×C811yescharacteristic
157C2×C4×C43C2×M1611yescharacteristic
158C2×C4×C43#13511yescharacteristic
159C2×C4×C43#13511yescharacteristic
160C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C43#13711yescharacteristic
162C22⋊D43—48no—
163C2×Dic43—21no—
164C2×Dic43—21no—
165C2×Dic43—21no—
166C2×Dic43—21no—
167C2×Dic43—22no—
168C2×Dic43—21no—
169C2×Dic43—21no—
170C2×Dic43—21no—
171C2×Dic43—48no—
172C2×Dic43—41no—
173C2×Dic43—41no—
174C2×Dic43—41no—
175C2×Dic43—41no—
176C2×Dic43—41no—
177C2×Dic43C22⋊C812yes—
178C2×Dic43#10412yes—
179C4×D43—24no—
180C4×D43—24no—
181C4×D43—24no—
182C4×D43—24no—
183C4×D43—42no—
184C4×D43—42no—
185Dic86—42no—
186Dic86—42no—
187C8×C43—42no—
188C8×C43—81no—
189C43⋊C8—42no—
190C43⋊C8—81no—
191#7578—431nomaximal, Sylow
192C22×C43—42no—
193C22×C43—42no—
194C22×C43—42no—
195C22×C43—81no—
196C22×C43—81no—
197C22×C43—81no—
198C22×C43—81no—
199C22×C43C2×C22⋊C811yescharacteristic
200C22×C43C2×#9911yescharacteristic
201C22×C43C2×#10011yescharacteristic
202C22×C43#41611yescharacteristic
203C22×C43#41711yescharacteristic
204C22×C43C2×#10411yescharacteristic
205C22×C43#42111yescharacteristic
206C2×D43—22no—
207C2×D43—22no—
208C2×D43—22no—
209C2×D43—22no—
210C2×D43—22no—
211C2×D43—22no—
212C2×D43#32314yes—
213C4×C43—21no—
214C4×C43—21no—
215C4×C43—21no—
216C4×C43—21no—
217C4×C43—21no—
218C4×C43—21no—
219C4×C43—81no—
220Dic43—22no—
221Dic43—22no—
222Dic43—42no—
223Dic43—41no—
224Dic43—81no—
225#2297—431no—
226#1817—431no—
227C2×#336—431no—
228#1272—431no—
229#1272—431no—
230#1270—431no—
231#1270D4311yescharacteristic, complemented
232C2×C43—82no—
233C2×C43C2×#32311yescharacteristic
234C2×C43#147611yescharacteristic
235C2×C43#147711yescharacteristic
236C2×C43#150411yescharacteristic
237C2×C43#151611yescharacteristic
238C2×C43#153011yescharacteristic
239C2×C43#155111yescharacteristic
240D43—24no—
241C22×#41—431no—
242C23×C8—861no—
243C2×#117—431no—
244C22×C42—431no—
245C2×C22⋊C8—861no—
246#391—431no—
247#391—431no—
248#390—431no—
249#390C2×D4311yescharacteristic
250#386—861no—
251#386—861no—
252C4×C22⋊C4—861no—
253C4×C22⋊C4—861no—
254#336—431no—
255#336—431no—
256#336—861no—
257#336—861no—
258#336C2×D4311yescharacteristic
259#336C2×D4311yescharacteristic
260C43#757811yescharacteristic, complemented, Sylow
261C2×#41—434no—
262C2×#41—862no—
263C2×#41—1722no—
264C2×#41—1722no—
265C22×Q8—431no—
266C22×D4—861no—
267C22×D4C4×D4311yescharacteristic
268C23×C4—431no—
269C23×C4—431no—
270C23×C4—431no—
271C23×C4—861no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—864no—
275C22×C8—861no—
276C22×C8—861no—
277C22×C8—1722no—
278C22×C8—1722no—
279#117—1722no—
280C2×C4⋊C4—431no—
281C2×C4⋊C4C4×D4311yescharacteristic
282C2×C22⋊C4—21no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—861no—
285C2×C22⋊C4—861no—
286C2×C22⋊C4—861no—
287C2×C42—431no—
288C2×C42—431no—
289C2×C42—431no—
290C2×C42—861no—
291C2×C42—1722no—
292C2×C42C22×D4311yescharacteristic
293C22⋊C8—1722no—
294#95—861no—
295#95—861no—
296#95—861no—
297#95—861no—
298C24—21no—
299C24—431no—
300#41—1728no—
301#41—1728no—
302C2×Q8—432no—
303C2×Q8—861no—
304C2×Q8—1721no—
305C2×Q8—1721no—
306C2×D4—21no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—864no—
310C2×D4—1722no—
311C2×D4—1722no—
312C2×D4C8×D4312yescomplemented
313C22×C4—21no—
314C22×C4—431no—
315C22×C4—431no—
316C22×C4—432no—
317C22×C4—432no—
318C22×C4—431no—
319C22×C4—862no—
320C22×C4—862no—
321C22×C4—862no—
322C22×C4—862no—
323C22×C4—862no—
324C22×C4—864no—
325C22×C4—861no—
326C22×C4—861no—
327C22×C4—861no—
328C22×C4—861no—
329C22×C4—861no—
330C22×C4—861no—
331C22×C4—1721no—
332C22×C4—1722no—
333C22×C4—1722no—
334C22×C4C2×C4×D4311yescharacteristic
335C22×C4D4×D4311yescharacteristic
336C22×C4D4×D4311yescharacteristic
337C2×C8—22no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—41no—
343C2×C8—862no—
344C2×C8—1728no—
345C2×C8—1721no—
346C2×C8—1721no—
347C2×C8—1721no—
348C2×C8—1721no—
349C2×C8—1721no—
350C4⋊C4—41no—
351C4⋊C4—1721no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—1722no—
357C22⋊C4—1722no—
358C22⋊C4—1722no—
359C42—41no—
360C42—1721no—
361C42—1721no—
362C42—1721no—
363C42—1722no—
364C23—22no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—432no—
372C23—432no—
373C23—432no—
374C23—861no—
375C23—861no—
376C23—861no—
377C23—861no—
378C23C22⋊C4×D4311yescharacteristic
379Q8—1722no—
380Q8—1722no—
381D4—42no—
382D4—42no—
383D4—1728no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—432no—
394C2×C4—432no—
395C2×C4—864no—
396C2×C4—864no—
397C2×C4—864no—
398C2×C4—864no—
399C2×C4—861no—
400C2×C4—861no—
401C2×C4—861no—
402C2×C4—861no—
403C2×C4—862no—
404C2×C4—861no—
405C2×C4—861no—
406C2×C4—861no—
407C2×C4—1722no—
408C2×C4—1722no—
409C2×C4—1728no—
410C2×C4—1721no—
411C2×C4—1721no—
412C2×C4—1721no—
413C2×C4—1721no—
414C2×C4—1721no—
415C2×C4C2×C8×D4311yescharacteristic
416C2×C4M16×D4311yescharacteristic
417C2×C4#1306334411yescharacteristic
418C2×C4#1306334611yescharacteristic
419C2×C4#1306334911yescharacteristic
420C2×C4#1306335411yescharacteristic
421C8—42no—
422C8—81no—
423C8—3441no—
424C8—1722no—
425C22—42no—
426C22—42no—
427C22—42no—
428C22—81no—
429C22—81no—
430C22—81no—
431C22—81no—
432C22—434no—
433C22—862no—
434C22—862no—
435C22—862no—
436C22—862no—
437C22—862no—
438C22—862no—
439C22C22⋊C8×D4311yescharacteristic
440C22#99×D4311yescharacteristic
441C22#100×D4311yescharacteristic
442C22#1458289211yescharacteristic
443C22#1458289711yescharacteristic
444C22#104×D4311yescharacteristic
445C22#1458291411yescharacteristic
446C4—21no—
447C4—21no—
448C4—21no—
449C4—21no—
450C4—21no—
451C4—21no—
452C4—81no—
453C4—862no—
454C4—862no—
455C4—3441no—
456C4—1721no—
457C4—1722no—
458C2—82no—
459C2—864no—
460C2#323×D4311yescharacteristic
461C2#1913297411yescharacteristic
462C2#1913297911yescharacteristic
463C2#1913309611yescharacteristic
464C2#1913314811yescharacteristic
465C2#1913320411yescharacteristic
466C2#1913328711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC2×C4×C43C22×C8
FrattiniC2×C42C22×D43
FittingC43×#1270C2
socleC23×C43C2×C22⋊C4
prime radicalC22×#10621900C4
cosocleC2×C42×C43C23
hypercenter#1270D43
hypocenterC43#7578
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #19134662C2semidirect
3. #336×D43C2semidirect
4. #19132420C2semidirect
5. #19132420C2semidirect
6. #19132416C2semidirect
7. C43×#1270C2semidirect
30. C2×#10621900C8semidirect
69. C2×D4×C43C2×C8semidirect
102. C2×Dic86C2×C8semidirect
231. #1270D43semidirect
260. C43#7578semidirect
312. C2×D4C8×D43semidirect

Maximal subgroups

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

subgroupindex
#191370822
#191346622
#336×D432
#191324202
#191324162
C43×#12702
#757843