Finite Group Databasebeta

← #24989093

Subgroups — #24989093

Order 11008.

1040 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 1040 conjugacy classes of subgroups — too many to draw. Only its 115 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×#14583477C211yesmaximal, characteristic
2#19134523C211yesmaximal, characteristic, complemented
3#19133127C212yesmaximal, complemented
4#19133123C212yesmaximal, complemented
5C43×#1782C211yesmaximal, characteristic, complemented
6C22×#10621898C411yescharacteristic, complemented
7#14583477—24no—
8#14583477—24no—
9C2×#13063304C411yescharacteristic, complemented
10C2×#13063304C2211yescharacteristic
11C2×#13063301—21no—
12C2×#13063299C411yescharacteristic, complemented
13C2×#13063299C2211yescharacteristic
14C2×#13063297—21no—
15C2×#13063297—21no—
16C2×#13063296—21no—
17C22×C4⋊Dic43C411yescharacteristic, complemented
18C2×#13063244—21no—
19C2×#13063242—21no—
20#14582863C2212yes—
21#14582635—24no—
22#14582632—24no—
23C22×#41×C43C2211yescharacteristic
24C2×#99×C43—21no—
25C2×#99×C43—21no—
26C43×#381C2212yes—
27C2×#10621898—22no—
28C2×#10621898—22no—
29C2×#10621898—42no—
30C2×#10621898—42no—
31C22×Dic86C2×C411yescharacteristic
32C22×D172C2×C411yescharacteristic
33C22×C22⋊D43—21no—
34C22×C22⋊D43—21no—
35C22×C22⋊D43—21no—
36C23×Dic43—21no—
37C22×C4×D43—21no—
38C2×#10621877—22no—
39#13063304—22no—
40#13063304—22no—
41#13063304—22no—
42#13063304D414yes—
43#13063301—28no—
44#13063299—22no—
45#13063299—22no—
46#13063299—22no—
47#13063299D414yes—
48#13063297—28no—
49#13063297—28no—
50#13063296—28no—
51C2×C4⋊Dic43—21no—
52C2×C4⋊Dic43—22no—
53C2×C4⋊Dic43—22no—
54C2×C4⋊Dic43C2×C411yescharacteristic
55C2×C4⋊Dic43C2×C411yescharacteristic
56C2×Dic43⋊C4—21no—
57C2×Dic43⋊C4—21no—
58C2×C22⋊Dic43—21no—
59C2×C22⋊Dic43—21no—
60C2×(C2×D43)⋊C4—21no—
61C2×(C2×D43)⋊C4—21no—
62#13063244—42no—
63#13063242—42no—
64C22⋊(C43⋊C8)—22no—
65C22⋊(C43⋊C8)—22no—
66C2×#41×C43—22no—
67C2×#41×C43—22no—
68C2×#41×C43—42no—
69C2×#41×C43—42no—
70C22×Q8×C43D411yescharacteristic
71C22×D4×C43D411yescharacteristic
72C22×D4×C43D411yescharacteristic
73C22×D4×C43D411yescharacteristic
74C23×C4×C43C2×C411yescharacteristic
75C23×C4×C43C2×C411yescharacteristic
76C23×C4×C43C2311yescharacteristic
77C2×C22⋊C4×C43—22no—
78#99×C43—42no—
79#99×C43—42no—
80#95×C43—22no—
81#95×C43—22no—
82C24×C43C22⋊C411yescharacteristic
83C24×C43C22⋊C411yescharacteristic
84C24×C43C2×D411yescharacteristic
85C23×D43—21no—
86#41×C43—48no—
87#41×C43—48no—
88C2×Q8×C43—22no—
89C2×Q8×C43—22no—
90C2×Q8×C43—41no—
91C2×D4×C43—22no—
92C2×D4×C43—22no—
93C2×D4×C43—22no—
94C2×D4×C43—22no—
95C2×D4×C43—22no—
96C2×D4×C43—22no—
97C2×D4×C43—41no—
98C2×D4×C43—41no—
99C2×D4×C43—41no—
100C22×C4×C43—22no—
101C22×C4×C43—21no—
102C22×C4×C43—21no—
103C22×C4×C43—21no—
104C22×C4×C43—21no—
105C22×C4×C43—22no—
106C22×C4×C43—41no—
107C22×C4×C43—41no—
108C22×C4×C43—41no—
109C22×C4×C43—41no—
110C22×C4×C43—42no—
111C22×C4×C43C22⋊C411yescharacteristic
112C22×C4×C43C22⋊C411yescharacteristic
113C22×C4×C43C22×C411yescharacteristic
114C22×C4×C43C2×D411yescharacteristic
115C22×C4×C43C2×D412yes—
116C22×C4×C43C2×D412yes—
117C2×C22⋊D43—24no—
118C2×C22⋊D43—24no—
119C2×C22⋊D43—24no—
120C2×C22⋊D43—42no—
121C2×C22⋊D43—42no—
122C2×C22⋊D43—82no—
123C2×C22⋊D43—82no—
124C22×Dic43—24no—
125C22×Dic43—21no—
126C22×Dic43—21no—
127C22×Dic43—21no—
128C22×Dic43—82no—
129#10621898—48no—
130#10621898—48no—
131C2×D172—21no—
132C2×D172—41no—
133C2×D172—41no—
134C2×D172C22⋊C412yes—
135C2×C4×D43—24no—
136C2×C4×D43—42no—
137C2×C4×D43—42no—
138C2×Dic86—21no—
139C2×Dic86—41no—
140C2×Dic86—41no—
141C2×Dic86C22⋊C412yes—
142C22⋊C4×C43—42no—
143C22⋊C4×C43—42no—
144C22⋊Dic43—24no—
145C22⋊Dic43—24no—
146(C2×D43)⋊C4—24no—
147(C2×D43)⋊C4—24no—
148C4⋊Dic43—24no—
149C4⋊Dic43—21no—
150C4⋊Dic43—21no—
151C4⋊Dic43C22⋊C412yes—
152C4⋊Dic43C22⋊C412yes—
153Dic43⋊C4—24no—
154Dic43⋊C4—24no—
155#10621877—42no—
156#10621877—42no—
157C2×C43⋊C8—42no—
158C23×C43—21no—
159C23×C43—21no—
160C23×C43—21no—
161C23×C43—21no—
162C23×C43—21no—
163C23×C43—21no—
164C23×C43—21no—
165C23×C43—41no—
166C23×C43—41no—
167C23×C43—41no—
168C23×C43—41no—
169C23×C43—41no—
170C23×C43—41no—
171C23×C43#9912yes—
172C23×C43C2×C22⋊C411yescharacteristic
173C23×C43#12012yes—
174C22×D43—22no—
175C22×D43—42no—
176C22×D43—42no—
177C22×D43—41no—
178C22×D43—41no—
179Q8×C43—44no—
180D4×C43—44no—
181D4×C43—44no—
182D4×C43—44no—
183C2×C4×C43—24no—
184C2×C4×C43—24no—
185C2×C4×C43—21no—
186C2×C4×C43—21no—
187C2×C4×C43—21no—
188C2×C4×C43—21no—
189C2×C4×C43—21no—
190C2×C4×C43—21no—
191C2×C4×C43—21no—
192C2×C4×C43—21no—
193C2×C4×C43—21no—
194C2×C4×C43—42no—
195C2×C4×C43—42no—
196C2×C4×C43—42no—
197C2×C4×C43—42no—
198C2×C4×C43—82no—
199C2×C4×C43—82no—
200C2×C4×C43—82no—
201C2×C4×C43#9912yes—
202C2×C4×C43C2×C22⋊C411yescharacteristic
203C2×C4×C43C2×C22⋊C411yescharacteristic
204C2×C4×C43#12012yes—
205C22⋊D43—48no—
206C22⋊D43—84no—
207C22⋊D43—84no—
208C2×Dic43—22no—
209C2×Dic43—22no—
210C2×Dic43—22no—
211C2×Dic43—42no—
212C2×Dic43—42no—
213C2×Dic43—41no—
214C2×Dic43—41no—
215C2×Dic43—84no—
216D172—42no—
217D172—42no—
218C4×D43—48no—
219Dic86—42no—
220Dic86—42no—
221C43⋊C8—82no—
222#8517—431nomaximal, Sylow
223C22×C43—21no—
224C22×C43—21no—
225C22×C43—22no—
226C22×C43—22no—
227C22×C43—22no—
228C22×C43—22no—
229C22×C43—42no—
230C22×C43—42no—
231C22×C43—41no—
232C22×C43—41no—
233C22×C43—41no—
234C22×C43—41no—
235C22×C43—41no—
236C22×C43—81no—
237C22×C43—81no—
238C22×C43—81no—
239C22×C43—81no—
240C22×C43#37911yescharacteristic
241C22×C43C2×#9911yescharacteristic
242C22×C43C2×#9911yescharacteristic
243C2×D43—42no—
244C2×D43—42no—
245C2×D43—42no—
246C2×D43—82no—
247C2×D43—82no—
248C4×C43—22no—
249C4×C43—21no—
250C4×C43—21no—
251C4×C43—22no—
252C4×C43—41no—
253C4×C43—162no—
254Dic43—42no—
255Dic43—42no—
256Dic43—42no—
257C2×#537—431no—
258#1785—431no—
259#1782D4311yescharacteristic, complemented
260#1511—432no—
261#1510—432no—
262C2×C43—21no—
263C2×C43—21no—
264C2×C43—42no—
265C2×C43—42no—
266C2×C43—81no—
267C2×C43#178111yescharacteristic
268C2×C43#179511yescharacteristic
269C2×C43#179611yescharacteristic
270D43—82no—
271C22×#41—431no—
272C22×#41C2×D4311yescharacteristic
273#537—864no—
274#537—864no—
275C2×C22⋊Q8—431no—
276C2×C22⋊Q8—431no—
277C2×C22⋊Q8—861no—
278C2×#121—431no—
279C2×#121—431no—
280C2×#121—861no—
281C2×#121—861no—
282C2×#121—861no—
283C22×C4⋊C4—431no—
284C2×#101—861no—
285C2×#100—861no—
286C2×#99—21no—
287C2×#99—21no—
288#407—432no—
289#381C2×D4312yes—
290#328—864no—
291#327—864no—
292C43#851711yescharacteristic, complemented, Sylow
293C2×#41—22no—
294C2×#41—22no—
295C2×#41—42no—
296C2×#41—42no—
297C2×#41—862no—
298C2×#41—862no—
299C2×#41—1722no—
300C2×#41—1722no—
301C22×Q8—431no—
302C22×Q8D17211yescharacteristic
303C22×D4—431no—
304C22×D4—861no—
305C22×D4—861no—
306C22×D4—861no—
307C22×D4D17211yescharacteristic
308C22×D4C22⋊D4311yescharacteristic
309C22×D4C22⋊D4311yescharacteristic
310C23×C4—861no—
311C23×C4—861no—
312C23×C4C4×D4311yescharacteristic
313C23×C4C4×D4311yescharacteristic
314C23×C4C22×D4311yescharacteristic
315C2×M16—862no—
316C22⋊Q8—434no—
317C22⋊Q8—862no—
318C22⋊Q8—862no—
319C22⋊Q8—868no—
320C22⋊Q8—862no—
321#121—434no—
322#121—862no—
323#121—862no—
324#121—868no—
325#121—868no—
326#121—868no—
327#121—862no—
328C2×C4⋊C4—431no—
329C2×C4⋊C4—431no—
330C2×C4⋊C4—862no—
331C2×C4⋊C4—862no—
332C2×C4⋊C4—861no—
333C2×C4⋊C4—861no—
334C2×C4⋊C4—861no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—861no—
337C2×C22⋊C4—861no—
338C2×C22⋊C4—861no—
339C2×C22⋊C4—861no—
340#101—1722no—
341#100—1722no—
342#99—42no—
343#99—42no—
344C22⋊C8—862no—
345C22⋊C8—862no—
346#95—22no—
347#95—22no—
348C24—861no—
349C24(C2×D43)⋊C411yescharacteristic
350C24(C2×D43)⋊C411yescharacteristic
351C24C2×C22⋊D4311yescharacteristic
352#41—48no—
353#41—48no—
354#41—1728no—
355#41—1728no—
356C2×Q8—22no—
357C2×Q8—22no—
358C2×Q8—41no—
359C2×Q8—432no—
360C2×Q8—861no—
361C2×Q8—1721no—
362C2×Q8—1721no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—432no—
373C2×D4—864no—
374C2×D4—864no—
375C2×D4—864no—
376C2×D4—861no—
377C2×D4—3442no—
378C2×D4—3442no—
379C2×D4—1721no—
380C2×D4—1721no—
381C2×D4—1722no—
382C2×D4—1722no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4—42no—
394C22×C4—864no—
395C22×C4—864no—
396C22×C4—861no—
397C22×C4—861no—
398C22×C4—861no—
399C22×C4—3442no—
400C22×C4—1722no—
401C22×C4—1722no—
402C22×C4(C2×D43)⋊C411yescharacteristic
403C22×C4(C2×D43)⋊C411yescharacteristic
404C22×C4C2×C4×D4311yescharacteristic
405C22×C4C2×D17211yescharacteristic
406C22×C4D4×D4312yes—
407C22×C4D4×D4312yes—
408M16—1722no—
409M16—1722no—
410C2×C8—1722no—
411C4⋊C4—432no—
412C4⋊C4—432no—
413C4⋊C4—864no—
414C4⋊C4—864no—
415C4⋊C4—861no—
416C4⋊C4—861no—
417C4⋊C4—864no—
418C22⋊C4—42no—
419C22⋊C4—42no—
420C22⋊C4—864no—
421C22⋊C4—864no—
422C22⋊C4—864no—
423C22⋊C4—864no—
424C23—21no—
425C23—21no—
426C23—21no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—21no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23—862no—
438C23—1722no—
439C23—1722no—
440C23—1721no—
441C23—1721no—
442C23#1306323912yes—
443C23C2×(C2×D43)⋊C411yescharacteristic
444C23#1306329312yes—
445Q8—44no—
446Q8—1722no—
447Q8—1722no—
448D4—44no—
449D4—44no—
450D4—44no—
451D4—3444no—
452D4—3444no—
453D4—1722no—
454D4—1722no—
455D4—1728no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—82no—
472C2×C4—82no—
473C2×C4—82no—
474C2×C4—862no—
475C2×C4—862no—
476C2×C4—862no—
477C2×C4—3444no—
478C2×C4—1728no—
479C2×C4—1722no—
480C2×C4—1722no—
481C2×C4—1721no—
482C2×C4—1721no—
483C2×C4#1306323912yes—
484C2×C4C22⋊C4×D4311yescharacteristic
485C2×C4C22⋊C4×D4311yescharacteristic
486C2×C4#1306329512yes—
487C8—3442no—
488C22—21no—
489C22—21no—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—42no—
495C22—42no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—81no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22—3442no—
506C22—3442no—
507C22—1722no—
508C22—1722no—
509C22—1722no—
510C22#1458275411yescharacteristic
511C22C2×#1306323911yescharacteristic
512C22C2×#1306323911yescharacteristic
513C4—22no—
514C4—21no—
515C4—21no—
516C4—22no—
517C4—41no—
518C4—162no—
519C4—1722no—
520C4—1722no—
521C4—1722no—
522C2—21no—
523C2—21no—
524C2—42no—
525C2—42no—
526C2—81no—
527C2—3442no—
528C2#1913450911yescharacteristic
529C2#1913456311yescharacteristic
530C2#1913456811yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1782C2
socleC22×C43#379
prime radicalC2×#14583477C2
cosocleC23×C4×C43C23
hypercenter#1782D43
hypocenterC43#8517
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1782

Complements

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

NH ≅ G/Ntype
2. #19134523C2semidirect
3. #19133127C2semidirect
4. #19133123C2semidirect
5. C43×#1782C2semidirect
6. C22×#10621898C4semidirect
9. C2×#13063304C4semidirect
12. C2×#13063299C4semidirect
17. C22×C4⋊Dic43C4semidirect
259. #1782D43semidirect
292. C43#8517semidirect

Maximal subgroups

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

subgroupindex
C2×#145834772
#191345232
#191331272
#191331232
C43×#17822
#851743