Finite Group Databasebeta

← #24988207

Subgroups — #24988207

Order 11008.

782 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 782 conjugacy classes of subgroups — too many to draw. Only its 113 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×#14583620C211yesmaximal, characteristic
2#19134695C211yesmaximal, characteristic, complemented
3#19134692C211yesmaximal, characteristic, complemented
4C4×#13063239C211yesmaximal, characteristic
5#19133115C211yesmaximal, characteristic, complemented
6#19132931C211yesmaximal, characteristic
7C43×#1508C211yesmaximal, characteristic, complemented
8#14583620—22no—
9#14583620—22no—
10#14583620—22no—
11#14583620—22no—
12C2×#13063324C411yescharacteristic, complemented
13C2×#13063320—21no—
14C2×#13063318—21no—
15C2×#13063311—21no—
16C2×#13063301C411yescharacteristic, complemented
17C2×Q8×Dic43C411yescharacteristic, complemented
18C2×#13063290—21no—
19C2×C4×C22⋊D43C2211yescharacteristic
20C2×#13063284C2211yescharacteristic
21C2×#13063283C411yescharacteristic, complemented
22C2×#13063239—21no—
23#14582863C2211yescharacteristic
24C4×C22⋊Dic43C2211yescharacteristic
25#14582665—21no—
26#14582660—22no—
27#14582659—22no—
28#14582636—22no—
29#14582624—21no—
30#14582622—21no—
31C2×C22⋊Q8×C43C2211yescharacteristic
32C43×#407C2211yescharacteristic
33C4×C22⋊C4×C43C2211yescharacteristic
34C43×#328—22no—
35C22×Dic86—21no—
36C22×C22⋊D43D411yescharacteristic
37C22×C4×D43C2×C411yescharacteristic
38C2×#10621877—21no—
39#13063324—22no—
40#13063324—22no—
41#13063320—24no—
42#13063320—24no—
43#13063318—24no—
44#13063318—24no—
45#13063311—24no—
46#13063311—24no—
47#13063301—22no—
48#13063301—22no—
49Q8×Dic43—22no—
50Q8×Dic43—22no—
51#13063290—24no—
52#13063290—24no—
53C4×C22⋊D43—21no—
54C4×C22⋊D43—21no—
55C4×C22⋊D43—21no—
56C4×C22⋊D43—21no—
57#13063284—21no—
58#13063284—21no—
59#13063284D412yes—
60#13063284D412yes—
61#13063283—22no—
62#13063283—22no—
63C2×C4⋊Dic43—21no—
64C2×C4⋊Dic43C2×C411yescharacteristic
65C2×C4⋊Dic43C2×C411yescharacteristic
66C2×Dic43⋊C4—21no—
67C2×Dic43⋊C4—21no—
68C2×Dic43⋊C4D411yescharacteristic
69C2×C22⋊Dic43—21no—
70C2×C22⋊Dic43—21no—
71C2×C22⋊Dic43D411yescharacteristic
72C2×(C2×D43)⋊C4—21no—
73C2×(C2×D43)⋊C4—21no—
74C2×(C2×D43)⋊C4D411yescharacteristic
75C2×C4×Dic43—21no—
76C2×C4×Dic43—21no—
77C2×C4×Dic43—21no—
78C2×C4×Dic43—21no—
79C2×C4×Dic43C2×C411yescharacteristic
80#13063239—24no—
81C22⋊(C43⋊C8)—21no—
82C22⋊(C43⋊C8)—21no—
83C43⋊#95—21no—
84C22×Q8×C43C2×C411yescharacteristic
85C23×C4×C43C2311yescharacteristic
86C2×M16×C43—21no—
87C22⋊Q8×C43—21no—
88C22⋊Q8×C43—21no—
89C22⋊Q8×C43D412yes—
90C22⋊Q8×C43D412yes—
91C2×C4⋊C4×C43—21no—
92C2×C4⋊C4×C43C2×C411yescharacteristic
93C2×C22⋊C4×C43—21no—
94C2×C22⋊C4×C43—21no—
95C2×C42×C43—21no—
96C22⋊C8×C43—21no—
97C22⋊C8×C43—21no—
98#95×C43—21no—
99C24×C43C2×D411yescharacteristic
100C23×D43C22⋊C411yescharacteristic
101C2×Q8×C43—21no—
102C2×Q8×C43—42no—
103C2×Q8×C43C22⋊C412yes—
104C22×C4×C43—21no—
105C22×C4×C43—21no—
106C22×C4×C43—42no—
107C22×C4×C43—41no—
108C22×C4×C43C22×C411yescharacteristic
109C22×C4×C43C2×D411yescharacteristic
110C22×C4×C43C2×D411yescharacteristic
111C22×C4×C43C2×D411yescharacteristic
112C22×C4×C43C2×D411yescharacteristic
113C22×C4×C43C2×D411yescharacteristic
114C2×C22⋊D43—22no—
115C2×C22⋊D43—21no—
116C2×C22⋊D43—21no—
117C2×C22⋊D43—41no—
118C22×Dic43—21no—
119C22×Dic43—21no—
120C22×Dic43—41no—
121C22×Dic43C22⋊C411yescharacteristic
122C22×Dic43C22⋊C411yescharacteristic
123C22×Dic43C22⋊C411yescharacteristic
124C2×C4×D43—21no—
125C2×C4×D43—21no—
126C2×C4×D43—42no—
127C2×Dic86—24no—
128C2×Dic86—42no—
129C2×Dic86—42no—
130M16×C43—42no—
131C2×C8×C43—41no—
132C4⋊C4×C43—21no—
133C4⋊C4×C43—22no—
134C4⋊C4×C43—22no—
135C4⋊C4×C43C22⋊C412yes—
136C22⋊C4×C43—22no—
137C22⋊C4×C43—22no—
138C22⋊C4×C43—22no—
139C22⋊C4×C43—41no—
140C42×C43—42no—
141C22⋊Dic43—22no—
142C22⋊Dic43—22no—
143C22⋊Dic43—22no—
144C22⋊Dic43—21no—
145C22⋊Dic43—21no—
146C22⋊Dic43—41no—
147(C2×D43)⋊C4—24no—
148(C2×D43)⋊C4—24no—
149(C2×D43)⋊C4—21no—
150(C2×D43)⋊C4—21no—
151C4⋊Dic43—24no—
152C4⋊Dic43—21no—
153C4⋊Dic43—21no—
154C4⋊Dic43C22⋊C412yes—
155C4⋊Dic43C22⋊C412yes—
156Dic43⋊C4—24no—
157Dic43⋊C4—24no—
158Dic43⋊C4—21no—
159Dic43⋊C4—21no—
160C4×Dic43—24no—
161C4×Dic43—24no—
162C4×Dic43—21no—
163C4×Dic43—21no—
164C4×Dic43—22no—
165C4×Dic43—22no—
166C4×Dic43—42no—
167#10621877—42no—
168C2×C43⋊C8—41no—
169C23×C43—21no—
170C23×C43—21no—
171C23×C43—41no—
172C23×C43—41no—
173C23×C43C2×C22⋊C411yescharacteristic
174C23×C43#12011yescharacteristic
175C23×C43#12011yescharacteristic
176C22×D43—21no—
177C22×D43—21no—
178C22×D43—21no—
179C22×D43—41no—
180C22×D43—41no—
181Q8×C43—42no—
182Q8×C43—42no—
183C2×C4×C43—22no—
184C2×C4×C43—22no—
185C2×C4×C43—22no—
186C2×C4×C43—22no—
187C2×C4×C43—22no—
188C2×C4×C43—41no—
189C2×C4×C43—41no—
190C2×C4×C43—41no—
191C2×C4×C43—42no—
192C2×C4×C43—41no—
193C2×C4×C43—41no—
194C2×C4×C43—42no—
195C2×C4×C43—81no—
196C2×C4×C43—81no—
197C2×C4×C43C2×C22⋊C411yescharacteristic
198C2×C4×C43C2×C22⋊C411yescharacteristic
199C2×C4×C43#12011yescharacteristic
200C2×C4×C43#12011yescharacteristic
201C22⋊D43—42no—
202C22⋊D43—42no—
203C2×Dic43—21no—
204C2×Dic43—21no—
205C2×Dic43—22no—
206C2×Dic43—21no—
207C2×Dic43—21no—
208C2×Dic43—22no—
209C2×Dic43—42no—
210C2×Dic43—41no—
211C2×Dic43—41no—
212C2×Dic43—41no—
213C2×Dic43—41no—
214C2×Dic43—42no—
215C2×Dic43—81no—
216C2×Dic43—81no—
217C2×Dic43#10412yes—
218C4×D43—42no—
219C4×D43—42no—
220Dic86—48no—
221C8×C43—81no—
222C43⋊C8—81no—
223#8365—431nomaximal, Sylow
224C22×C43—21no—
225C22×C43—21no—
226C22×C43—21no—
227C22×C43—21no—
228C22×C43—21no—
229C22×C43—21no—
230C22×C43—21no—
231C22×C43—21no—
232C22×C43—81no—
233C22×C43—81no—
234C22×C43#37911yescharacteristic
235C22×C43C2×#10411yescharacteristic
236C22×C43#42111yescharacteristic
237C2×D43—41no—
238C2×D43—41no—
239C2×D43—41no—
240C2×D43—81no—
241C2×D43—81no—
242C4×C43—21no—
243C4×C43—21no—
244C4×C43—21no—
245C4×C43—42no—
246C4×C43—42no—
247C4×C43—82no—
248C4×C43#41012yes—
249Dic43—22no—
250Dic43—41no—
251Dic43—42no—
252Dic43—41no—
253Dic43—42no—
254Dic43—82no—
255C2×#556—431no—
256#1826—431no—
257#1826—431no—
258C4×#99—431no—
259#1508—431no—
260#1508D4311yescharacteristic, complemented
261#1465—431no—
262C2×C43—21no—
263C2×C43—21no—
264C2×C43—41no—
265C2×C43—41no—
266C2×C43#178211yescharacteristic
267C2×C43#178911yescharacteristic
268C2×C43#179611yescharacteristic
269D43—81no—
270#556—862no—
271#556—862no—
272#556—862no—
273#556—862no—
274C2×C4⋊Q8—431no—
275C2×#126—861no—
276C2×#126—861no—
277C2×#124—861no—
278C2×C22⋊Q8—431no—
279C2×C22⋊Q8C2×D4311yescharacteristic
280C2×C4×Q8—431no—
281C2×C4×Q8—861no—
282C2×C4×D4—431no—
283C2×#117—431no—
284C2×#117—431no—
285C2×#99—861no—
286#407—431no—
287#407C2×D4311yescharacteristic
288C4×C22⋊C4—431no—
289C4×C22⋊C4C2×D4311yescharacteristic
290#342—861no—
291#339—862no—
292#339—862no—
293#328—22no—
294#328—862no—
295#324—861no—
296#323—861no—
297C43#836511yescharacteristic, complemented, Sylow
298C22×Q8—861no—
299C22×Q8C4×D4311yescharacteristic
300C22×D4—431no—
301C23×C4—431no—
302C23×C4C22×D4311yescharacteristic
303C2×M16—21no—
304C2×M16—861no—
305C4⋊Q8—862no—
306C4⋊Q8—862no—
307#126—864no—
308#126—864no—
309#126—864no—
310#126—864no—
311#124—864no—
312#124—864no—
313C22⋊Q8—21no—
314C22⋊Q8—21no—
315C22⋊Q8—862no—
316C22⋊Q8—862no—
317C22⋊Q8D17212yes—
318C22⋊Q8C22⋊D4312yes—
319C4×Q8—864no—
320C4×Q8—864no—
321C4×Q8—862no—
322C4×Q8—862no—
323C4×D4—861no—
324C4×D4—861no—
325C4×D4—861no—
326C4×D4—861no—
327#117—432no—
328#117—432no—
329#117—862no—
330#117—861no—
331#117—861no—
332#117—862no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—431no—
335C2×C4⋊C4—431no—
336C2×C4⋊C4—431no—
337C2×C4⋊C4—861no—
338C2×C4⋊C4—861no—
339C2×C4⋊C4—861no—
340C2×C4⋊C4C4×D4311yescharacteristic
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—431no—
344C2×C22⋊C4—431no—
345C2×C22⋊C4—861no—
346C2×C22⋊C4—861no—
347C2×C22⋊C4—861no—
348C2×C22⋊C4—861no—
349C2×C42—21no—
350C2×C42—431no—
351C2×C42—861no—
352C2×C42—861no—
353C2×C42—861no—
354C2×C42—861no—
355#99—864no—
356C22⋊C8—21no—
357C22⋊C8—21no—
358C22⋊C8—861no—
359C22⋊C8—861no—
360#95—21no—
361#95—861no—
362C24—431no—
363C24D4×D4311yescharacteristic
364C2×Q8—21no—
365C2×Q8—42no—
366C2×Q8—864no—
367C2×Q8—1722no—
368C2×Q8—1722no—
369C2×Q8(C2×D43)⋊C412yes—
370C2×D4—862no—
371C2×D4—861no—
372C2×D4—861no—
373C2×D4—1721no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—42no—
377C22×C4—41no—
378C22×C4—431no—
379C22×C4—431no—
380C22×C4—431no—
381C22×C4—861no—
382C22×C4—861no—
383C22×C4—861no—
384C22×C4—861no—
385C22×C4—1722no—
386C22×C4—1721no—
387C22×C4C2×C4×D4311yescharacteristic
388C22×C4C2×D17211yescharacteristic
389C22×C4D4×D4311yescharacteristic
390C22×C4D4×D4311yescharacteristic
391C22×C4D4×D4311yescharacteristic
392C22×C4C2×C22⋊D4311yescharacteristic
393M16—42no—
394M16—1722no—
395C2×C8—41no—
396C2×C8—1721no—
397C4⋊C4—21no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—432no—
401C4⋊C4—432no—
402C4⋊C4—864no—
403C4⋊C4—864no—
404C4⋊C4—864no—
405C4⋊C4—861no—
406C4⋊C4—861no—
407C4⋊C4—861no—
408C4⋊C4—861no—
409C4⋊C4(C2×D43)⋊C412yes—
410C22⋊C4—22no—
411C22⋊C4—22no—
412C22⋊C4—22no—
413C22⋊C4—41no—
414C22⋊C4—864no—
415C22⋊C4—864no—
416C22⋊C4—861no—
417C22⋊C4—862no—
418C22⋊C4—861no—
419C22⋊C4—862no—
420C22⋊C4—861no—
421C22⋊C4—861no—
422C22⋊C4—862no—
423C22⋊C4—1721no—
424C42—42no—
425C42—864no—
426C42—864no—
427C42—861no—
428C42—861no—
429C42—862no—
430C42—862no—
431C42—1722no—
432C23—21no—
433C23—21no—
434C23—41no—
435C23—41no—
436C23—861no—
437C23—861no—
438C23—861no—
439C23—1721no—
440C23—1721no—
441C23C22⋊C4×D4311yescharacteristic
442C23#1306329311yescharacteristic
443C23#1306329511yescharacteristic
444Q8—42no—
445Q8—42no—
446Q8—1728no—
447D4—1722no—
448D4—1722no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—42no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—42no—
461C2×C4—81no—
462C2×C4—81no—
463C2×C4—432no—
464C2×C4—861no—
465C2×C4—861no—
466C2×C4—862no—
467C2×C4—861no—
468C2×C4—862no—
469C2×C4—861no—
470C2×C4—3441no—
471C2×C4—3441no—
472C2×C4—1722no—
473C2×C4—1722no—
474C2×C4—1722no—
475C2×C4—1721no—
476C2×C4—1721no—
477C2×C4—1722no—
478C2×C4—1721no—
479C2×C4—1721no—
480C2×C4C22⋊C4×D4311yescharacteristic
481C2×C4C2×(C2×D43)⋊C411yescharacteristic
482C2×C4#1306329311yescharacteristic
483C2×C4#1306329511yescharacteristic
484C8—81no—
485C8—3441no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—81no—
495C22—81no—
496C22—3441no—
497C22—3441no—
498C22—1721no—
499C22—1721no—
500C22—1721no—
501C22#1458275411yescharacteristic
502C22#104×D4311yescharacteristic
503C22#1458291411yescharacteristic
504C4—21no—
505C4—21no—
506C4—21no—
507C4—42no—
508C4—42no—
509C4—82no—
510C4—862no—
511C4—3442no—
512C4—1721no—
513C4—1722no—
514C4—1722no—
515C4—1721no—
516C4#1458287112yes—
517C2—21no—
518C2—21no—
519C2—41no—
520C2—41no—
521C2—3441no—
522C2#1913451111yescharacteristic
523C2#1913453711yescharacteristic
524C2#1913456711yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1508C2
socleC22×C43#379
prime radicalC22×C22⋊D43D4
cosocleC23×C4×C43C23
hypercenter#1508D43
hypocenterC43#8365
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1508

Complements

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

NH ≅ G/Ntype
2. #19134695C2semidirect
3. #19134692C2semidirect
5. #19133115C2semidirect
7. C43×#1508C2semidirect
12. C2×#13063324C4semidirect
16. C2×#13063301C4semidirect
17. C2×Q8×Dic43C4semidirect
21. C2×#13063283C4semidirect
260. #1508D43semidirect
297. C43#8365semidirect

Maximal subgroups

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

subgroupindex
C2×#145836202
#191346952
#191346922
C4×#130632392
#191331152
#191329312
C43×#15082
#836543