Finite Group Databasebeta

← #24989097

Subgroups — #24989097

Order 11008.

818 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 818 conjugacy classes of subgroups — too many to draw. Only its 107 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×#14583502C211yesmaximal, characteristic
2#19134676C211yesmaximal, characteristic, complemented
3#19134670C211yesmaximal, characteristic, complemented
4#19133125C211yesmaximal, characteristic, complemented
5#19133124C211yesmaximal, characteristic, complemented
6#19133123C211yesmaximal, characteristic, complemented
7C43×#1510C211yesmaximal, characteristic, complemented
8#14583502—22no—
9#14583502—22no—
10#14583502—22no—
11#14583502—22no—
12C2×#13063321C411yescharacteristic, complemented
13C2×#13063316C411yescharacteristic, complemented
14C2×#13063309—21no—
15C2×#13063307—21no—
16C2×#13063299C2211yescharacteristic
17C2×#13063297—21no—
18C2×#13063296—21no—
19C2×D4×Dic43C411yescharacteristic, complemented
20C2×#13063287C411yescharacteristic, complemented
21C2×#13063284C2211yescharacteristic
22#14582863C2211yescharacteristic
23#14582762C2211yescharacteristic
24#14582667—21no—
25#14582667—21no—
26#14582665—21no—
27#14582665—21no—
28#14582634—22no—
29#14582633—22no—
30#14582632—22no—
31C2×#121×C43C2211yescharacteristic
32C43×#407C2211yescharacteristic
33C43×#381C2211yescharacteristic
34C43×#327—22no—
35C22×D172C2×C411yescharacteristic
36C22×C22⋊D43—21no—
37C22×C22⋊D43—21no—
38C22×C22⋊D43—21no—
39C23×Dic43—21no—
40C22×C4×D43—21no—
41C2×#10621877—21no—
42#13063321—22no—
43#13063321—22no—
44#13063316—22no—
45#13063316—22no—
46#13063309—24no—
47#13063309—24no—
48#13063307—24no—
49#13063307—24no—
50#13063299—21no—
51#13063299—21no—
52#13063299D412yes—
53#13063299D412yes—
54#13063297—24no—
55#13063297—24no—
56#13063296—24no—
57#13063296—24no—
58D4×Dic43—22no—
59D4×Dic43—22no—
60#13063287—22no—
61#13063287—22no—
62#13063284—21no—
63#13063284—21no—
64#13063284—21no—
65#13063284—21no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43C2×C411yescharacteristic
68C2×C4⋊Dic43D411yescharacteristic
69C2×C4⋊Dic43D411yescharacteristic
70C2×Dic43⋊C4—21no—
71C2×C22⋊Dic43—21no—
72C2×C22⋊Dic43—21no—
73C2×C22⋊Dic43D411yescharacteristic
74C2×C22⋊Dic43D411yescharacteristic
75C2×(C2×D43)⋊C4—21no—
76C2×(C2×D43)⋊C4—21no—
77C2×C4×Dic43C2×C411yescharacteristic
78C2×C4×Dic43C2×C411yescharacteristic
79C22⋊(C43⋊C8)—21no—
80C22⋊(C43⋊C8)—21no—
81C43⋊#95—21no—
82C43⋊#95—21no—
83C22×D4×C43—21no—
84C22×D4×C43C2×C411yescharacteristic
85C23×C4×C43C2311yescharacteristic
86C2×M16×C43—21no—
87#121×C43—21no—
88#121×C43—21no—
89#121×C43D412yes—
90#121×C43D412yes—
91C2×C4⋊C4×C43C2×C411yescharacteristic
92C2×C22⋊C4×C43—21no—
93C2×C22⋊C4×C43—21no—
94C22⋊C8×C43—21no—
95C22⋊C8×C43—21no—
96#95×C43—21no—
97#95×C43—21no—
98C24×C43—21no—
99C24×C43C2×D411yescharacteristic
100C23×D43—21no—
101C2×D4×C43—21no—
102C2×D4×C43—22no—
103C2×D4×C43—22no—
104C2×D4×C43—42no—
105C2×D4×C43—82no—
106C2×D4×C43C22⋊C412yes—
107C22×C4×C43—21no—
108C22×C4×C43—42no—
109C22×C4×C43—41no—
110C22×C4×C43C22×C411yescharacteristic
111C22×C4×C43C2×D411yescharacteristic
112C22×C4×C43C2×D411yescharacteristic
113C22×C4×C43C2×D411yescharacteristic
114C22×C4×C43C2×D411yescharacteristic
115C22×C4×C43C2×D411yescharacteristic
116C2×C22⋊D43—24no—
117C2×C22⋊D43—24no—
118C2×C22⋊D43—22no—
119C2×C22⋊D43—22no—
120C2×C22⋊D43—82no—
121C2×C22⋊D43—82no—
122C2×C22⋊D43—82no—
123C22×Dic43—24no—
124C22×Dic43—21no—
125C22×Dic43—41no—
126C22×Dic43—82no—
127C22×Dic43C22⋊C411yescharacteristic
128C22×Dic43C22⋊C411yescharacteristic
129C22×Dic43C22⋊C411yescharacteristic
130C22×Dic43C22⋊C411yescharacteristic
131C2×D172—21no—
132C2×D172—42no—
133C2×D172C22⋊C412yes—
134C2×C4×D43—24no—
135C2×C4×D43—82no—
136M16×C43—42no—
137C2×C8×C43—41no—
138C4⋊C4×C43—21no—
139C4⋊C4×C43C22⋊C412yes—
140C22⋊C4×C43—22no—
141C22⋊C4×C43—22no—
142C22⋊C4×C43—42no—
143C22⋊Dic43—24no—
144C22⋊Dic43—21no—
145C22⋊Dic43—21no—
146C22⋊Dic43—21no—
147C22⋊Dic43—21no—
148C22⋊Dic43—42no—
149(C2×D43)⋊C4—24no—
150(C2×D43)⋊C4—22no—
151(C2×D43)⋊C4—22no—
152C4⋊Dic43—24no—
153C4⋊Dic43—21no—
154C4⋊Dic43—21no—
155C4⋊Dic43—21no—
156C4⋊Dic43—21no—
157C4⋊Dic43—21no—
158C4⋊Dic43C22⋊C412yes—
159Dic43⋊C4—24no—
160C4×Dic43—21no—
161C4×Dic43—21no—
162C4×Dic43—21no—
163C4×Dic43—21no—
164#10621877—42no—
165C2×C43⋊C8—41no—
166C23×C43—22no—
167C23×C43—22no—
168C23×C43—41no—
169C23×C43—41no—
170C23×C43—42no—
171C23×C43—42no—
172C23×C43—42no—
173C23×C43C2×C22⋊C411yescharacteristic
174C23×C43#12011yescharacteristic
175C23×C43#12011yescharacteristic
176C22×D43—22no—
177C22×D43—42no—
178C22×D43—42no—
179C22×D43—42no—
180D4×C43—42no—
181D4×C43—42no—
182D4×C43—82no—
183D4×C43—82no—
184C2×C4×C43—22no—
185C2×C4×C43—22no—
186C2×C4×C43—22no—
187C2×C4×C43—41no—
188C2×C4×C43—41no—
189C2×C4×C43—41no—
190C2×C4×C43—41no—
191C2×C4×C43—42no—
192C2×C4×C43—81no—
193C2×C4×C43—81no—
194C2×C4×C43—81no—
195C2×C4×C43C2×C22⋊C411yescharacteristic
196C2×C4×C43C2×C22⋊C411yescharacteristic
197C2×C4×C43#12011yescharacteristic
198C2×C4×C43#12011yescharacteristic
199C22⋊D43—82no—
200C22⋊D43—82no—
201C22⋊D43—84no—
202C22⋊D43—84no—
203C2×Dic43—21no—
204C2×Dic43—21no—
205C2×Dic43—21no—
206C2×Dic43—21no—
207C2×Dic43—22no—
208C2×Dic43—42no—
209C2×Dic43—41no—
210C2×Dic43—41no—
211C2×Dic43—41no—
212C2×Dic43—41no—
213C2×Dic43—84no—
214C2×Dic43—81no—
215C2×Dic43—81no—
216C2×Dic43—81no—
217D172—42no—
218D172—42no—
219C4×D43—84no—
220C8×C43—81no—
221C43⋊C8—81no—
222#8518—431nomaximal, Sylow
223C22×C43—21no—
224C22×C43—21no—
225C22×C43—21no—
226C22×C43—21no—
227C22×C43—21no—
228C22×C43—21no—
229C22×C43—21no—
230C22×C43—21no—
231C22×C43—42no—
232C22×C43—42no—
233C22×C43—42no—
234C22×C43—82no—
235C22×C43—84no—
236C22×C43#37911yescharacteristic
237C22×C43#41012yes—
238C2×D43—42no—
239C2×D43—42no—
240C2×D43—42no—
241C2×D43—84no—
242C4×C43—21no—
243C4×C43—21no—
244C4×C43—21no—
245C4×C43—21no—
246C4×C43—42no—
247C4×C43—161no—
248Dic43—41no—
249Dic43—42no—
250Dic43—41no—
251Dic43—41no—
252Dic43—41no—
253Dic43—161no—
254C2×#540—431no—
255#1822—431no—
256#1820—431no—
257#1510—431no—
258#1510—431no—
259#1510—431no—
260#1510D4311yescharacteristic, complemented
261C2×C43—22no—
262C2×C43—41no—
263C2×C43—41no—
264C2×C43—82no—
265C2×C43#178211yescharacteristic
266C2×C43#179511yescharacteristic
267C2×C43#179511yescharacteristic
268D43—82no—
269#540—862no—
270#540—862no—
271#540—862no—
272#540—862no—
273C2×#127—431no—
274C2×#125—431no—
275C2×#123—861no—
276C2×#123—861no—
277C2×#121—431no—
278C2×#121—861no—
279C2×#121—861no—
280C2×#121C2×D4311yescharacteristic
281C2×C4×D4—431no—
282C2×C4×D4—431no—
283C2×#117—431no—
284#407—431no—
285#407C2×D4311yescharacteristic
286#381—431no—
287#381C2×D4311yescharacteristic
288#343—861no—
289#343—861no—
290#342—861no—
291#342—861no—
292#327—22no—
293#327—862no—
294#327—862no—
295#327—862no—
296C43#851811yescharacteristic, complemented, Sylow
297C22×D4—21no—
298C22×D4—431no—
299C22×D4—861no—
300C22×D4—861no—
301C22×D4—861no—
302C22×D4C4×D4311yescharacteristic
303C23×C4—861no—
304C23×C4—861no—
305C23×C4C22×D4311yescharacteristic
306C2×M16—21no—
307C2×M16—861no—
308#127—862no—
309#127—862no—
310#125—862no—
311#125—862no—
312#123—864no—
313#123—864no—
314#123—864no—
315#123—864no—
316#121—21no—
317#121—21no—
318#121—432no—
319#121—432no—
320#121—864no—
321#121—864no—
322#121—864no—
323#121—864no—
324#121—861no—
325#121—861no—
326#121D17212yes—
327#121C22⋊D4312yes—
328C4×D4—862no—
329C4×D4—862no—
330C4×D4—862no—
331C4×D4—862no—
332#117—861no—
333#117—861no—
334#117—861no—
335#117—861no—
336C2×C4⋊C4—431no—
337C2×C4⋊C4—431no—
338C2×C4⋊C4—431no—
339C2×C4⋊C4—861no—
340C2×C4⋊C4—861no—
341C2×C4⋊C4C4×D4311yescharacteristic
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—431no—
345C2×C22⋊C4—431no—
346C2×C22⋊C4—861no—
347C2×C22⋊C4—861no—
348C2×C22⋊C4—861no—
349C2×C22⋊C4—861no—
350C2×C42—431no—
351C2×C42—431no—
352C22⋊C8—21no—
353C22⋊C8—21no—
354C22⋊C8—861no—
355C22⋊C8—861no—
356#95—21no—
357#95—21no—
358#95—861no—
359#95—861no—
360C24—21no—
361C24—861no—
362C24D4×D4311yescharacteristic
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—21no—
366C2×D4—42no—
367C2×D4—82no—
368C2×D4—432no—
369C2×D4—864no—
370C2×D4—864no—
371C2×D4—862no—
372C2×D4—862no—
373C2×D4—861no—
374C2×D4—3442no—
375C2×D4—3442no—
376C2×D4—3442no—
377C2×D4—1722no—
378C2×D4(C2×D43)⋊C412yes—
379C22×C4—21no—
380C22×C4—42no—
381C22×C4—41no—
382C22×C4—431no—
383C22×C4—431no—
384C22×C4—431no—
385C22×C4—431no—
386C22×C4—864no—
387C22×C4—864no—
388C22×C4—861no—
389C22×C4—3442no—
390C22×C4—3442no—
391C22×C4—1721no—
392C22×C4C2×C4×D4311yescharacteristic
393C22×C4C2×D17211yescharacteristic
394C22×C4D4×D4311yescharacteristic
395C22×C4D4×D4311yescharacteristic
396C22×C4D4×D4311yescharacteristic
397C22×C4C2×C22⋊D4311yescharacteristic
398M16—42no—
399M16—1722no—
400C2×C8—41no—
401C2×C8—1721no—
402C4⋊C4—21no—
403C4⋊C4—432no—
404C4⋊C4—864no—
405C4⋊C4—864no—
406C4⋊C4—861no—
407C4⋊C4—861no—
408C4⋊C4—861no—
409C4⋊C4—861no—
410C4⋊C4—861no—
411C4⋊C4(C2×D43)⋊C412yes—
412C22⋊C4—22no—
413C22⋊C4—22no—
414C22⋊C4—42no—
415C22⋊C4—864no—
416C22⋊C4—864no—
417C22⋊C4—861no—
418C22⋊C4—861no—
419C22⋊C4—861no—
420C22⋊C4—861no—
421C22⋊C4—862no—
422C22⋊C4—862no—
423C22⋊C4—1722no—
424C42—861no—
425C42—861no—
426C42—861no—
427C42—861no—
428C23—22no—
429C23—22no—
430C23—41no—
431C23—41no—
432C23—42no—
433C23—42no—
434C23—42no—
435C23—862no—
436C23—1722no—
437C23—1722no—
438C23—1722no—
439C23C22⋊C4×D4311yescharacteristic
440C23#1306329311yescharacteristic
441C23#1306329511yescharacteristic
442D4—42no—
443D4—42no—
444D4—82no—
445D4—82no—
446D4—3442no—
447D4—3442no—
448D4—3444no—
449D4—3444no—
450D4—1722no—
451D4—1722no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—42no—
460C2×C4—81no—
461C2×C4—81no—
462C2×C4—81no—
463C2×C4—861no—
464C2×C4—861no—
465C2×C4—861no—
466C2×C4—861no—
467C2×C4—862no—
468C2×C4—3444no—
469C2×C4—3444no—
470C2×C4—3441no—
471C2×C4—3441no—
472C2×C4—3441no—
473C2×C4—1722no—
474C2×C4—1721no—
475C2×C4—1721no—
476C2×C4—1721no—
477C2×C4—1721no—
478C2×C4C22⋊C4×D4311yescharacteristic
479C2×C4C2×(C2×D43)⋊C411yescharacteristic
480C2×C4#1306329311yescharacteristic
481C2×C4#1306329511yescharacteristic
482C8—81no—
483C8—3441no—
484C22—21no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22—82no—
496C22—84no—
497C22—3444no—
498C22—1722no—
499C22—1722no—
500C22—1722no—
501C22#1458275411yescharacteristic
502C22#1458287112yes—
503C4—21no—
504C4—21no—
505C4—21no—
506C4—21no—
507C4—42no—
508C4—161no—
509C4—1721no—
510C4—1721no—
511C4—1721no—
512C4—1722no—
513C4—1721no—
514C4—6881no—
515C2—22no—
516C2—41no—
517C2—41no—
518C2—82no—
519C2—3442no—
520C2#1913451111yescharacteristic
521C2#1913456211yescharacteristic
522C2#1913456411yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1510C2
socleC22×C43#379
prime radicalC2×#14583502C2
cosocleC23×C4×C43C23
hypercenter#1510D43
hypocenterC43#8518
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1510

Complements

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

NH ≅ G/Ntype
2. #19134676C2semidirect
3. #19134670C2semidirect
4. #19133125C2semidirect
5. #19133124C2semidirect
6. #19133123C2semidirect
7. C43×#1510C2semidirect
12. C2×#13063321C4semidirect
13. C2×#13063316C4semidirect
19. C2×D4×Dic43C4semidirect
20. C2×#13063287C4semidirect
260. #1510D43semidirect
296. C43#8518semidirect

Maximal subgroups

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

subgroupindex
C2×#145835022
#191346762
#191346702
#191331252
#191331242
#191331232
C43×#15102
#851843