Finite Group Databasebeta

← #24991945

Subgroups — #24991945

Order 11008.

606 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582950C211yesmaximal, characteristic
2C4×#13063301C211yesmaximal, characteristic
3#19134572C211yesmaximal, characteristic
4C2×Q8⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
5#19132435C211yesmaximal, characteristic, complemented
6#19132434C211yesmaximal, characteristic, complemented
7C2×C43×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#13063301C411yescharacteristic
9C2×C42×D43C2211yescharacteristic
10#14582950—22no—
11#14582950—22no—
12C2×C4⋊(C43⋊C8)C2211yescharacteristic
13C2×Dic43⋊C8—21no—
14C2×(C2×D43)⋊C8—21no—
15C2×(C2×D43)⋊C8—21no—
16C2×C4×C43⋊C8C2211yescharacteristic
17#14582806C411yescharacteristic
18#14582795C411yescharacteristic
19#14582780—21no—
20#14582770—21no—
21#14582756C411yescharacteristic
22C4×Dic43⋊C4—21no—
23C4×C4⋊Dic43C2211yescharacteristic
24C4×(C2×D43)⋊C4—21no—
25#14582653—21no—
26Q8⋊(C43⋊C8)—22no—
27C2×C4×Q8×C43C2211yescharacteristic
28C2×C4⋊C8×C43C2211yescharacteristic
29C2×C4×C8×C43C2211yescharacteristic
30C43×Q8⋊C8—22no—
31C22×C4×D43C2×C411yescharacteristic
32C22×C4×D43D411yescharacteristic
33C22×C4×D43D411yescharacteristic
34C22×C43⋊C8—21no—
35C22×C43⋊C8—21no—
36#13063301—22no—
37#13063301—22no—
38C2×C4⋊Dic43C2×C411yescharacteristic
39C2×C4⋊Dic43C2×C411yescharacteristic
40C2×Dic43⋊C4—21no—
41C2×Dic43⋊C4—21no—
42C2×(C2×D43)⋊C4—21no—
43C2×(C2×D43)⋊C4—21no—
44C2×C4×Dic43—21no—
45C2×C4×Dic43C2×C411yescharacteristic
46C2×C4×Dic43D411yescharacteristic
47C2×C4×Dic43D411yescharacteristic
48C42×D43—21no—
49C42×D43—21no—
50C42×D43—21no—
51C42×D43—21no—
52C4⋊(C43⋊C8)—21no—
53C4⋊(C43⋊C8)—21no—
54Dic43⋊C8—24no—
55(C2×D43)⋊C8—24no—
56(C2×D43)⋊C8—42no—
57C4×C43⋊C8—21no—
58C4×C43⋊C8D412yes—
59C43⋊#95—21no—
60C43⋊#95—21no—
61C43⋊#95—21no—
62C43⋊#95—21no—
63C43⋊#95—21no—
64C22×Q8×C43C2×C411yescharacteristic
65C22×C8×C43—21no—
66C22×C8×C43—21no—
67C4×Q8×C43—21no—
68C4×Q8×C43—21no—
69C4×Q8×C43—21no—
70C4×Q8×C43—21no—
71C2×C4⋊C4×C43—21no—
72C2×C4⋊C4×C43C2×C411yescharacteristic
73C2×C42×C43—21no—
74C2×C42×C43C2311yescharacteristic
75C4⋊C8×C43—21no—
76C4⋊C8×C43—21no—
77C4×C8×C43—21no—
78C4×C8×C43D412yes—
79C23×D43C22⋊C411yescharacteristic
80C2×Q8×C43—21no—
81C2×Q8×C43—21no—
82C2×Q8×C43—21no—
83C2×Q8×C43—21no—
84C2×Q8×C43—21no—
85C2×Q8×C43M1612yes—
86C22×C4×C43—21no—
87C22×C4×C43—21no—
88C22×C4×C43C22×C411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×Dic43—21no—
92C22×Dic43—21no—
93C22×Dic43C22⋊C411yescharacteristic
94C22×Dic43C22⋊C411yescharacteristic
95C22×Dic43C22⋊C411yescharacteristic
96C2×C4×D43—21no—
97C2×C4×D43—21no—
98C2×C4×D43—21no—
99C2×C4×D43—21no—
100C2×C4×D43—21no—
101C2×C4×D43—21no—
102C2×C4×D43—21no—
103C2×C4×D43—21no—
104C2×C4×D43—21no—
105C2×C4×D43—21no—
106C2×C4×D43—21no—
107C2×C4×D43—21no—
108C2×C4×D43—41no—
109C2×C4×D43—41no—
110C2×C4×D43SD1612yes—
111C2×C4×D43Q1612yes—
112C2×C8×C43—22no—
113C2×C8×C43—41no—
114C2×C8×C43—41no—
115C2×C8×C43—41no—
116C2×C8×C43—41no—
117C2×C8×C43—41no—
118C4⋊C4×C43—21no—
119C4⋊C4×C43—21no—
120C4⋊C4×C43—41no—
121C4⋊C4×C43—41no—
122C42×C43—41no—
123C42×C43—41no—
124C42×C43C2×D411yescharacteristic
125C42×C43C2×D411yescharacteristic
126C42×C43#4111yescharacteristic
127C42×C43#4111yescharacteristic
128(C2×D43)⋊C4—24no—
129(C2×D43)⋊C4—42no—
130C4⋊Dic43—21no—
131C4⋊Dic43—21no—
132C4⋊Dic43—21no—
133C4⋊Dic43M1612yes—
134Dic43⋊C4—24no—
135Dic43⋊C4—42no—
136C4×Dic43—21no—
137C4×Dic43—21no—
138C4×Dic43—21no—
139C4×Dic43—21no—
140C4×Dic43—21no—
141C4×Dic43—21no—
142C4×Dic43—41no—
143C4×Dic43—41no—
144C2×C43⋊C8—22no—
145C2×C43⋊C8—41no—
146C2×C43⋊C8—41no—
147C2×C43⋊C8—41no—
148C2×C43⋊C8—41no—
149C2×C43⋊C8—41no—
150C23×C43C2×C22⋊C411yescharacteristic
151C22×D43—21no—
152C22×D43—21no—
153C22×D43—21no—
154C22×D43—21no—
155C22×D43—21no—
156C22×D43—21no—
157C22×D43#10312yes—
158Q8×C43—22no—
159Q8×C43—22no—
160Q8×C43—41no—
161Q8×C43—41no—
162C2×C4×C43—21no—
163C2×C4×C43—21no—
164C2×C4×C43—22no—
165C2×C4×C43—41no—
166C2×C4×C43—41no—
167C2×C4×C43—41no—
168C2×C4×C43—41no—
169C2×C4×C43—41no—
170C2×C4×C43C4×D411yescharacteristic
171C2×C4×C43C4×D411yescharacteristic
172C2×C4×C43#12011yescharacteristic
173C2×C4×C43#12111yescharacteristic
174C2×C4×C43#12111yescharacteristic
175C2×C4×C43#12311yescharacteristic
176C2×C4×C43C2×M1611yescharacteristic
177C2×C4×C43C2×M1611yescharacteristic
178C2×C4×C43#13111yescharacteristic
179C2×C4×C43#13111yescharacteristic
180C2×C4×C43C2×SD1611yescharacteristic
181C2×C4×C43C2×Q1611yescharacteristic
182C2×C4×C43#13511yescharacteristic
183C2×C4×C43#13511yescharacteristic
184C2×Dic43—21no—
185C2×Dic43—21no—
186C2×Dic43—21no—
187C2×Dic43—21no—
188C2×Dic43—21no—
189C2×Dic43—22no—
190C2×Dic43—21no—
191C2×Dic43—21no—
192C2×Dic43—21no—
193C2×Dic43—41no—
194C2×Dic43—41no—
195C2×Dic43—41no—
196C2×Dic43—41no—
197C2×Dic43—41no—
198C2×Dic43#10312yes—
199C4×D43—22no—
200C4×D43—22no—
201C4×D43—22no—
202C4×D43—22no—
203C4×D43—42no—
204C4×D43—42no—
205C4×D43—41no—
206C4×D43—41no—
207C4×D43—41no—
208C4×D43—41no—
209C8×C43—42no—
210C8×C43—81no—
211C43⋊C8—42no—
212C43⋊C8—81no—
213#9075—431nomaximal, Sylow
214C22×C43#38611yescharacteristic
215C22×C43#40711yescharacteristic
216C22×C43#40811yescharacteristic
217C22×C43C2×#10311yescharacteristic
218C22×C43#41611yescharacteristic
219C22×C43#42111yescharacteristic
220C22×C43#42111yescharacteristic
221C2×D43—22no—
222C2×D43—22no—
223C2×D43—22no—
224C2×D43—41no—
225C2×D43—41no—
226C2×D43—41no—
227C2×D43—41no—
228C4×C43—21no—
229C4×C43—21no—
230C4×C43—42no—
231C4×C43—81no—
232C4×C43#43511yescharacteristic
233C4×C43#43511yescharacteristic
234C4×C43#43611yescharacteristic
235C4×C43#43611yescharacteristic
236C4×C43#46511yescharacteristic
237C4×C43#46511yescharacteristic
238C4×C43#46711yescharacteristic
239C4×C43#46711yescharacteristic
240Dic43—22no—
241Dic43—41no—
242Dic43—41no—
243Dic43—42no—
244Dic43—81no—
245C2×#431—431no—
246C4×C22⋊Q8—431no—
247#1797—431no—
248C2×Q8⋊C8—431no—
249C2×Q8⋊C8D4311yescharacteristic, complemented
250#1279—431no—
251#1279—431no—
252C2×C43#148111yescharacteristic
253C2×C43#148211yescharacteristic
254C2×C43#148711yescharacteristic
255C2×C43#148811yescharacteristic
256C2×C43#187011yescharacteristic
257C2×C43#189211yescharacteristic
258C2×C43#189711yescharacteristic
259D43—42no—
260C2×C22⋊Q8—431no—
261C2×C4×Q8C2×D4311yescharacteristic
262C22×C42—431no—
263#431—862no—
264#431—862no—
265C2×C4⋊C8—431no—
266C2×C4⋊C8—861no—
267C2×C4⋊C8C2×D4311yescharacteristic
268C2×C22⋊C8—861no—
269C2×C22⋊C8—861no—
270C2×C4×C8—431no—
271C2×C4×C8C2×D4311yescharacteristic
272#391—431no—
273#389—431no—
274#387—861no—
275#385—861no—
276#380—431no—
277C4×C4⋊C4—431no—
278C4×C4⋊C4—861no—
279C4×C22⋊C4—861no—
280#336—861no—
281Q8⋊C8—22no—
282Q8⋊C8—862no—
283C43#907511yescharacteristic, complemented, Sylow
284C22×Q8C4×D4311yescharacteristic
285C23×C4—431no—
286C23×C4—431no—
287C23×C4—431no—
288C22×C8—21no—
289C22×C8—21no—
290C22×C8—861no—
291C22×C8—861no—
292C22⋊Q8—862no—
293C22⋊Q8—862no—
294C4×Q8—21no—
295C4×Q8—21no—
296C4×Q8—21no—
297C4×Q8—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—431no—
300C2×C4⋊C4—431no—
301C2×C4⋊C4—861no—
302C2×C4⋊C4—861no—
303C2×C4⋊C4C4×D4311yescharacteristic
304C2×C22⋊C4—861no—
305C2×C22⋊C4—861no—
306C2×C42—21no—
307C2×C42—431no—
308C2×C42—431no—
309C2×C42—431no—
310C2×C42—861no—
311C2×C42—861no—
312C2×C42—861no—
313C2×C42—861no—
314C2×C42—861no—
315C2×C42C22×D4311yescharacteristic
316C4⋊C8—21no—
317C4⋊C8—21no—
318C4⋊C8—864no—
319C4⋊C8—861no—
320C4⋊C8—861no—
321C22⋊C8—864no—
322C22⋊C8—1722no—
323C4×C8—21no—
324C4×C8—432no—
325C4×C8—861no—
326C4×C8C22⋊D4312yes—
327#95—861no—
328#95—861no—
329#95—861no—
330#95—861no—
331#95—861no—
332C24—431no—
333C2×Q8—21no—
334C2×Q8—21no—
335C2×Q8—21no—
336C2×Q8—21no—
337C2×Q8—21no—
338C2×Q8#1062187212yes—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—431no—
342C22×C4—432no—
343C22×C4—432no—
344C22×C4—431no—
345C22×C4—431no—
346C22×C4—861no—
347C22×C4—861no—
348C22×C4—861no—
349C22×C4—861no—
350C22×C4—861no—
351C22×C4—861no—
352C22×C4—861no—
353C22×C4—861no—
354C22×C4—861no—
355C22×C4—861no—
356C22×C4—861no—
357C22×C4—861no—
358C22×C4—861no—
359C22×C4—861no—
360C22×C4—1721no—
361C22×C4—1721no—
362C22×C4C2×C4×D4311yescharacteristic
363C22×C4D4×D4311yescharacteristic
364C22×C4D4×D4311yescharacteristic
365C2×C8—22no—
366C2×C8—41no—
367C2×C8—41no—
368C2×C8—41no—
369C2×C8—41no—
370C2×C8—41no—
371C2×C8—862no—
372C2×C8—1721no—
373C2×C8—1721no—
374C2×C8—1721no—
375C2×C8—1721no—
376C2×C8—1721no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—432no—
382C4⋊C4—864no—
383C4⋊C4—861no—
384C4⋊C4—861no—
385C4⋊C4—861no—
386C4⋊C4—1722no—
387C22⋊C4—864no—
388C22⋊C4—1722no—
389C42—41no—
390C42—41no—
391C42—861no—
392C42—861no—
393C42—861no—
394C42—861no—
395C42—861no—
396C42—861no—
397C42—1721no—
398C42—1721no—
399C42#1062189811yescharacteristic
400C42D4×D4311yescharacteristic
401C42#1062190011yescharacteristic
402C42C2×C22⋊D4311yescharacteristic
403C23—432no—
404C23—861no—
405C23—861no—
406C23—861no—
407C23—861no—
408C23—861no—
409C23—861no—
410C23C22⋊C4×D4311yescharacteristic
411Q8—22no—
412Q8—22no—
413Q8—41no—
414Q8—41no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—22no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—432no—
424C2×C4—861no—
425C2×C4—861no—
426C2×C4—862no—
427C2×C4—862no—
428C2×C4—862no—
429C2×C4—862no—
430C2×C4—862no—
431C2×C4—861no—
432C2×C4—861no—
433C2×C4—861no—
434C2×C4—861no—
435C2×C4—861no—
436C2×C4—861no—
437C2×C4—1722no—
438C2×C4—1722no—
439C2×C4—1721no—
440C2×C4—1721no—
441C2×C4—1721no—
442C2×C4—1721no—
443C2×C4—1721no—
444C2×C4—1721no—
445C2×C4—1721no—
446C2×C4—1721no—
447C2×C4—1721no—
448C2×C4(C22⋊D43)⋊C411yescharacteristic
449C2×C4C4×C22⋊D4311yescharacteristic
450C2×C4#1306329311yescharacteristic
451C2×C4#1306329611yescharacteristic
452C2×C4#1306329811yescharacteristic
453C2×C4#1306330711yescharacteristic
454C2×C4M16×D4311yescharacteristic
455C2×C4C2×#1062187211yescharacteristic
456C2×C4#1306333111yescharacteristic
457C2×C4#1306333311yescharacteristic
458C2×C4SD16×D4311yescharacteristic
459C2×C4Q16×D4311yescharacteristic
460C2×C4#1306334611yescharacteristic
461C2×C4#1306334811yescharacteristic
462C8—42no—
463C8—81no—
464C8—3441no—
465C8—1722no—
466C22—862no—
467C22—862no—
468C22—862no—
469C22—1721no—
470C22—1721no—
471C22—1721no—
472C22—1721no—
473C22#1458277511yescharacteristic
474C22#1458286111yescharacteristic
475C22#1458286411yescharacteristic
476C22#103×D4311yescharacteristic
477C22#1458289411yescharacteristic
478C22#1458291411yescharacteristic
479C22#1458291411yescharacteristic
480C4—21no—
481C4—21no—
482C4—42no—
483C4—81no—
484C4—862no—
485C4—3441no—
486C4—1721no—
487C4—1722no—
488C4—1721no—
489C4#1458296711yescharacteristic
490C4#1458297011yescharacteristic
491C4#1458297411yescharacteristic
492C4#1458297511yescharacteristic
493C4#1458312511yescharacteristic
494C4#1458313111yescharacteristic
495C4#1458313711yescharacteristic
496C4#1458313911yescharacteristic
497C2—1722no—
498C2#1913299611yescharacteristic
499C2#1913300211yescharacteristic
500C2#1913302211yescharacteristic
501C2#1913302811yescharacteristic
502C2#1913488911yescharacteristic
503C2#1913501511yescharacteristic
504C2#1913504011yescharacteristic
subgroupG/H
centerC22×C4D4×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC2×C43×Q8⋊C8C2
socleC23×C43C2×C22⋊C4
prime radicalC23×D43C22⋊C4
cosocleC2×C42×C43C23
hypercenterC2×Q8⋊C8D43
hypocenterC43#9075
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
4. C2×Q8⋊(C43⋊C8)C2semidirect
5. #19132435C2semidirect
6. #19132434C2semidirect
7. C2×C43×Q8⋊C8C2semidirect
249. C2×Q8⋊C8D43semidirect
283. C43#9075semidirect

Maximal subgroups

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

subgroupindex
C2×#145829502
C4×#130633012
#191345722
C2×Q8⋊(C43⋊C8)2
#191324352
#191324342
C2×C43×Q8⋊C82
#907543