Finite Group Databasebeta

← #24988268

Subgroups — #24988268

Order 11008.

1060 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 1060 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583558C211yesmaximal, characteristic
2#19134583C211yesmaximal, characteristic, complemented
3#19134531C212yesmaximal, complemented
4#19133164C212yesmaximal, complemented
5C43×#1459C211yesmaximal, characteristic, complemented
6C22×#10621898C411yescharacteristic, complemented
7C23×Dic86C2211yescharacteristic
8#14583558—24no—
9#14583558—24no—
10C2×#13063313C411yescharacteristic, complemented
11C2×#13063311—21no—
12C2×#13063304C411yescharacteristic, complemented
13C2×#13063303—21no—
14C2×#13063299C2211yescharacteristic
15C2×#13063297—21no—
16C2×C4×Dic86C411yescharacteristic, complemented
17C2×(C22⋊D43)⋊C4—21no—
18C2×#13063250—24no—
19C2×#13063240—21no—
20#14582759C2212yes—
21#14582666—21no—
22#14582634—24no—
23C2×C4×D4×C43C2211yescharacteristic
24C2×C22⋊C8×C43C2212yes—
25C43×#324—21no—
26C43×#323—21no—
27C2×#10621898—22no—
28C2×#10621898—22no—
29C2×#10621898—44no—
30C22×Dic86—22no—
31C22×Dic86—21no—
32C22×Dic86—44no—
33C22×Dic86C2×C411yescharacteristic
34C22×Dic86C2×C411yescharacteristic
35C22×Dic86D414yes—
36C22×D172C2×C411yescharacteristic
37C22×C22⋊D43—21no—
38C22×C22⋊D43—21no—
39C23×Dic43—21no—
40C22×C4×D43—21no—
41#13063313—22no—
42#13063313—22no—
43#13063311—28no—
44#13063304—22no—
45#13063304—22no—
46#13063303—28no—
47#13063299—22no—
48#13063299D414yes—
49#13063297—28no—
50C4×Dic86—22no—
51C4×Dic86—22no—
52(C22⋊D43)⋊C4—28no—
53C2×C4⋊Dic43—22no—
54C2×C4⋊Dic43C2×C411yescharacteristic
55C2×Dic43⋊C4—21no—
56C2×Dic43⋊C4—21no—
57C2×C22⋊Dic43—21no—
58C2×C22⋊Dic43—22no—
59C2×(C2×D43)⋊C4—21no—
60C2×(C2×D43)⋊C4—21no—
61C2×(C2×D43)⋊C4—21no—
62C2×C4×Dic43—21no—
63#13063250—48no—
64#13063240—42no—
65C43⋊#95—22no—
66C22×D4×C43D411yescharacteristic
67C23×C4×C43C2×C411yescharacteristic
68C23×C4×C43C2311yescharacteristic
69C22×C8×C43—22no—
70C4×D4×C43—22no—
71C4×D4×C43—22no—
72C2×C4⋊C4×C43D411yescharacteristic
73C2×C22⋊C4×C43D411yescharacteristic
74C2×C22⋊C4×C43D411yescharacteristic
75C2×C42×C43C2×C411yescharacteristic
76C22⋊C8×C43—22no—
77C22⋊C8×C43—22no—
78C24×C43C22⋊C411yescharacteristic
79C24×C43C2×D411yescharacteristic
80C23×D43—21no—
81C2×D4×C43—22no—
82C2×D4×C43—22no—
83C2×D4×C43—21no—
84C2×D4×C43—21no—
85C22×C4×C43—21no—
86C22×C4×C43—21no—
87C22×C4×C43—42no—
88C22×C4×C43—42no—
89C22×C4×C43C22⋊C411yescharacteristic
90C22×C4×C43C22⋊C411yescharacteristic
91C22×C4×C43C22⋊C411yescharacteristic
92C22×C4×C43C22×C411yescharacteristic
93C22×C4×C43C2×D411yescharacteristic
94C22×C4×C43C2×D412yes—
95C22×C4×C43C2×D412yes—
96C2×C22⋊D43—24no—
97C2×C22⋊D43—24no—
98C2×C22⋊D43—44no—
99C2×C22⋊D43—42no—
100C2×C22⋊D43—41no—
101C2×C22⋊D43—41no—
102C22×Dic43—21no—
103C22×Dic43—21no—
104C22×Dic43—21no—
105C22×Dic43—24no—
106C22×Dic43—44no—
107C22×Dic43—42no—
108#10621898—48no—
109#10621898—44no—
110#10621898—44no—
111C2×D172—21no—
112C2×D172—42no—
113C2×D172C22⋊C412yes—
114C2×C4×D43—24no—
115C2×C4×D43—44no—
116C2×Dic86—21no—
117C2×Dic86—24no—
118C2×Dic86—28no—
119C2×Dic86—21no—
120C2×Dic86—24no—
121C2×Dic86—42no—
122C2×Dic86—44no—
123C2×Dic86—48no—
124C2×Dic86—44no—
125C2×Dic86C22⋊C412yes—
126C2×Dic86C22⋊C412yes—
127C2×C8×C43—44no—
128C2×C8×C43—42no—
129C4⋊C4×C43—22no—
130C22⋊C4×C43—22no—
131C22⋊C4×C43—22no—
132C42×C43—21no—
133C42×C43—21no—
134C22⋊Dic43—24no—
135C22⋊Dic43—42no—
136C22⋊Dic43—42no—
137(C2×D43)⋊C4—24no—
138(C2×D43)⋊C4—24no—
139(C2×D43)⋊C4—24no—
140C4⋊Dic43—21no—
141C4⋊Dic43—44no—
142C4⋊Dic43C22⋊C412yes—
143Dic43⋊C4—24no—
144Dic43⋊C4—24no—
145C4×Dic43—24no—
146C23×C43—21no—
147C23×C43—21no—
148C23×C43—21no—
149C23×C43—41no—
150C23×C43—41no—
151C23×C43—41no—
152C23×C43—41no—
153C23×C43C2×C22⋊C411yescharacteristic
154C23×C43#12012yes—
155C23×C43#13512yes—
156C23×C43AGL(1,ℤ/8)11yescharacteristic
157C23×C43#13711yescharacteristic
158C22×D43—22no—
159C22×D43—42no—
160C22×D43—42no—
161C22×D43—41no—
162C22×D43—41no—
163D4×C43—42no—
164D4×C43—42no—
165C2×C4×C43—24no—
166C2×C4×C43—22no—
167C2×C4×C43—21no—
168C2×C4×C43—21no—
169C2×C4×C43—21no—
170C2×C4×C43—21no—
171C2×C4×C43—21no—
172C2×C4×C43—42no—
173C2×C4×C43—41no—
174C2×C4×C43—42no—
175C2×C4×C43—42no—
176C2×C4×C43—41no—
177C2×C4×C43—41no—
178C2×C4×C43C2×C22⋊C411yescharacteristic
179C2×C4×C43C2×C22⋊C411yescharacteristic
180C2×C4×C43#12012yes—
181C22⋊D43—48no—
182C22⋊D43—44no—
183C22⋊D43—44no—
184C2×Dic43—24no—
185C2×Dic43—22no—
186C2×Dic43—22no—
187C2×Dic43—22no—
188C2×Dic43—48no—
189C2×Dic43—42no—
190C2×Dic43—41no—
191C2×Dic43—41no—
192C2×Dic43—82no—
193C2×Dic43—82no—
194C2×Dic43—82no—
195D172—42no—
196D172—42no—
197C4×D43—48no—
198Dic86—24no—
199Dic86—22no—
200Dic86—24no—
201Dic86—48no—
202Dic86—42no—
203Dic86#9914yescomplemented
204C8×C43—82no—
205#8377—431nomaximal, Sylow
206C22×C43—21no—
207C22×C43—22no—
208C22×C43—21no—
209C22×C43—22no—
210C22×C43—42no—
211C22×C43—41no—
212C22×C43—41no—
213C22×C43—41no—
214C22×C43—41no—
215C22×C43—41no—
216C22×C43—81no—
217C22×C43—81no—
218C22×C43#37911yescharacteristic
219C22×C43#41611yescharacteristic
220C22×C43#41711yescharacteristic
221C22×C43#44912yes—
222C22×C43#45212yes—
223C2×D43—42no—
224C2×D43—42no—
225C2×D43—42no—
226C2×D43—82no—
227C2×D43—82no—
228C4×C43—22no—
229C4×C43—21no—
230C4×C43—41no—
231C4×C43—41no—
232C4×C43—41no—
233C4×C43C2×#9912yes—
234Dic43—24no—
235Dic43—42no—
236Dic43—42no—
237Dic43—162no—
238C2×#548—431no—
239#1799—431no—
240#1787—432no—
241#1519—432no—
242#1459D4311yescharacteristic, complemented
243C2×C43—22no—
244C2×C43—21no—
245C2×C43—21no—
246C2×C43—22no—
247C2×C43—81no—
248C2×C43#178111yescharacteristic
249C2×C43#178811yescharacteristic
250C2×C43#179611yescharacteristic
251D43—82no—
252C22×#41—431no—
253C23×Q8—431no—
254#548—864no—
255#548—864no—
256C2×#124—431no—
257C2×#124—861no—
258C2×C22⋊Q8—431no—
259C2×C22⋊Q8—861no—
260C2×#121—431no—
261C2×#121—861no—
262C2×C4×Q8—431no—
263C2×C4×D4—861no—
264C2×C4×D4C2×D4311yescharacteristic
265C2×#103—864no—
266C2×#99—861no—
267C2×C22⋊C8C2×D4312yes—
268#380—432no—
269#342—861no—
270#327—864no—
271#324—21no—
272#323—21no—
273C43#837711yescharacteristic, complemented, Sylow
274C2×#41—862no—
275C2×#41—862no—
276C2×#41—1724no—
277C22×Q8—431no—
278C22×Q8—431no—
279C22×Q8—434no—
280C22×Q8—862no—
281C22×Q8—861no—
282C22×Q8—1724no—
283C22×D4—431no—
284C22×D4—861no—
285C22×D4—861no—
286C22×D4D17211yescharacteristic
287C23×C4—861no—
288C23×C4—861no—
289C23×C4C4×D4311yescharacteristic
290C23×C4C22×D4311yescharacteristic
291C22×C8—22no—
292#124—862no—
293#124—862no—
294#124—868no—
295C22⋊Q8—868no—
296C22⋊Q8—862no—
297C22⋊Q8—862no—
298#121—434no—
299#121—868no—
300#121—862no—
301C4×Q8—862no—
302C4×Q8—862no—
303C4×D4—22no—
304C4×D4—22no—
305C4×D4—868no—
306C2×C4⋊C4—431no—
307C2×C4⋊C4—861no—
308C2×C4⋊C4—861no—
309C2×C4⋊C4—862no—
310C2×C4⋊C4C22⋊D4311yescharacteristic
311C2×C22⋊C4—861no—
312C2×C22⋊C4—861no—
313C2×C22⋊C4—861no—
314C2×C22⋊C4—861no—
315C2×C22⋊C4—862no—
316C2×C22⋊C4D17211yescharacteristic
317C2×C22⋊C4C22⋊D4311yescharacteristic
318C2×C42—861no—
319C2×C42C4×D4311yescharacteristic
320#103—1728no—
321#99—1722no—
322C22⋊C8—22no—
323C22⋊C8—22no—
324#95—862no—
325C24—861no—
326C24(C2×D43)⋊C411yescharacteristic
327C24C2×D17211yescharacteristic
328#41—1724no—
329#41—1728no—
330#41—1724no—
331C2×Q8—432no—
332C2×Q8—432no—
333C2×Q8—864no—
334C2×Q8—868no—
335C2×Q8—861no—
336C2×Q8—861no—
337C2×Q8—864no—
338C2×Q8—1724no—
339C2×Q8—1722no—
340C2×Q8—1724no—
341C2×Q8—1728no—
342C2×D4—22no—
343C2×D4—22no—
344C2×D4—21no—
345C2×D4—21no—
346C2×D4—432no—
347C2×D4—864no—
348C2×D4—864no—
349C2×D4—861no—
350C2×D4—1722no—
351C2×D4—1724no—
352C2×D4—1722no—
353C2×D4—1721no—
354C2×D4—1721no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—42no—
358C22×C4—42no—
359C22×C4—864no—
360C22×C4—861no—
361C22×C4—861no—
362C22×C4—861no—
363C22×C4—864no—
364C22×C4—1724no—
365C22×C4—1724no—
366C22×C4—1722no—
367C22×C4(C2×D43)⋊C411yescharacteristic
368C22×C4(C2×D43)⋊C411yescharacteristic
369C22×C4(C2×D43)⋊C411yescharacteristic
370C22×C4C2×C4×D4311yescharacteristic
371C22×C4D4×D4312yes—
372C22×C4D4×D4312yes—
373C22×C4C2×C22⋊D4311yescharacteristic
374C2×C8—44no—
375C2×C8—42no—
376C4⋊C4—22no—
377C4⋊C4—432no—
378C4⋊C4—864no—
379C4⋊C4—864no—
380C4⋊C4—861no—
381C4⋊C4—1724no—
382C22⋊C4—22no—
383C22⋊C4—22no—
384C22⋊C4—864no—
385C22⋊C4—864no—
386C22⋊C4—864no—
387C22⋊C4—864no—
388C22⋊C4—1722no—
389C22⋊C4—1722no—
390C42—21no—
391C42—21no—
392C42—864no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—862no—
401C23—1722no—
402C23—1722no—
403C23—1721no—
404C23—1721no—
405C23C2×(C2×D43)⋊C411yescharacteristic
406C23#1306329512yes—
407C23#1306334712yes—
408C23#1306335311yescharacteristic
409C23#1306335811yescharacteristic
410Q8—434no—
411Q8—864no—
412Q8—862no—
413Q8—864no—
414Q8—1728no—
415Q8—1722no—
416D4—42no—
417D4—42no—
418D4—1722no—
419D4—1728no—
420D4—1724no—
421D4—1724no—
422D4—1722no—
423C2×C4—24no—
424C2×C4—22no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—42no—
431C2×C4—41no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—864no—
437C2×C4—862no—
438C2×C4—862no—
439C2×C4—862no—
440C2×C4—3442no—
441C2×C4—3442no—
442C2×C4—3442no—
443C2×C4—1728no—
444C2×C4—1728no—
445C2×C4—1722no—
446C2×C4—1721no—
447C2×C4—1721no—
448C2×C4C22⋊C4×D4311yescharacteristic
449C2×C4C22⋊C4×D4311yescharacteristic
450C2×C4#1306329312yes—
451C8—82no—
452C22—21no—
453C22—22no—
454C22—21no—
455C22—22no—
456C22—42no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—81no—
463C22—81no—
464C22—3442no—
465C22—3442no—
466C22—1722no—
467C22—1722no—
468C22—1722no—
469C22#1458275411yescharacteristic
470C22#1458289611yescharacteristic
471C22#1458290111yescharacteristic
472C22#1458304612yes—
473C22#1458306312yes—
474C4—22no—
475C4—21no—
476C4—41no—
477C4—41no—
478C4—41no—
479C4—864no—
480C4—1722no—
481C4—1722no—
482C4—6882no—
483C4#99×D4312yes—
484C2—22no—
485C2—21no—
486C2—21no—
487C2—22no—
488C2—81no—
489C2—3442no—
490C2#1913450811yescharacteristic
491C2#1913453611yescharacteristic
492C2#1913457111yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1459C2
socleC22×C43#379
prime radicalC2×#14583558C2
cosocleC23×C4×C43C23
hypercenter#1459D43
hypocenterC43#8377
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1459

Complements

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

NH ≅ G/Ntype
2. #19134583C2semidirect
3. #19134531C2semidirect
4. #19133164C2semidirect
5. C43×#1459C2semidirect
6. C22×#10621898C4semidirect
10. C2×#13063313C4semidirect
12. C2×#13063304C4semidirect
16. C2×C4×Dic86C4semidirect
203. Dic86#99semidirect
242. #1459D43semidirect
273. C43#8377semidirect

Maximal subgroups

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

subgroupindex
C2×#145835582
#191345832
#191345312
#191331642
C43×#14592
#837743