Finite Group Databasebeta

← #24998907

Subgroups — #24998907

Order 11008.

676 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583100C211yesmaximal, characteristic
2C2×#14583099C211yesmaximal, characteristic
3#19139965C211yesmaximal, characteristic, complemented
4#19135401C211yesmaximal, characteristic
5C2×#14582631C211yesmaximal, characteristic, complemented
6#19132479C211yesmaximal, characteristic, complemented
7C2×C43×Q8⋊C8C211yesmaximal, characteristic, complemented
8C22×#10621873—21no—
9C22×#10621884—21no—
10C2×#13063322C2211yescharacteristic
11C2×C4×Dic86C2211yescharacteristic
12#14583100—22no—
13#14583100—22no—
14#14583099—22no—
15#14583099—22no—
16C2×C4⋊(C43⋊C8)C2211yescharacteristic
17C2×#13063247—21no—
18C2×#13063247—22no—
19C2×#13063245—21no—
20#14582832—22no—
21#14582806—21no—
22#14582805—21no—
23#14582797—21no—
24#14582795—21no—
25#14582769C2211yescharacteristic
26#14582631—22no—
27C2×C4×Q8×C43C2211yescharacteristic
28C2×C4⋊C8×C43C2211yescharacteristic
29C2×C4×C8×C43C2211yescharacteristic
30C43×Q8⋊C8—22no—
31C22×Dic86D411yescharacteristic
32C22×D172—21no—
33C22×D172—21no—
34C22×D172—21no—
35C2×#10621873—24no—
36C2×#10621873—42no—
37C2×#10621873—42no—
38C2×#10621884—24no—
39C2×#10621884—42no—
40C2×#10621884—42no—
41C22×C43⋊C8—21no—
42#13063322—21no—
43#13063322—21no—
44#13063322—21no—
45#13063322D412yes—
46C4×Dic86—21no—
47C4×Dic86—21no—
48C4×Dic86—21no—
49C4×Dic86—21no—
50C2×C4⋊Dic43—21no—
51C2×C4⋊Dic43—21no—
52C2×C4⋊Dic43D411yescharacteristic
53C2×C4⋊Dic43D412yes—
54C2×Dic43⋊C4—21no—
55C2×Dic43⋊C4—22no—
56C2×C4×Dic43—21no—
57C4⋊(C43⋊C8)—21no—
58C4⋊(C43⋊C8)D412yes—
59#13063247—24no—
60#13063247—44no—
61#13063245—24no—
62C43⋊#95—22no—
63C43⋊#95—22no—
64C43⋊#95—22no—
65C22×Q8×C43D411yescharacteristic
66C22×C8×C43—21no—
67C22×C8×C43—21no—
68C4×Q8×C43—21no—
69C4×Q8×C43—21no—
70C4×Q8×C43—21no—
71C4×Q8×C43—21no—
72C2×C4⋊C4×C43—21no—
73C2×C4⋊C4×C43D411yescharacteristic
74C2×C42×C43—21no—
75C2×C42×C43C2311yescharacteristic
76C4⋊C8×C43—21no—
77C4⋊C8×C43D412yes—
78C4×C8×C43—21no—
79C4×C8×C43—21no—
80C23×D43—41no—
81C2×Q8×C43—21no—
82C2×Q8×C43—21no—
83C2×Q8×C43—21no—
84C2×Q8×C43—21no—
85C2×Q8×C43—21no—
86C2×Q8×C43SD1612yescomplemented
87C22×C4×C43—21no—
88C22×C4×C43—21no—
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×Dic43—21no—
93C22×Dic43—22no—
94C22×Dic43—21no—
95C2×D172—22no—
96C2×D172—22no—
97C2×D172—22no—
98C2×D172—41no—
99C2×D172—41no—
100C2×D172—41no—
101C2×D172—42no—
102C2×D172—42no—
103C2×D172—41no—
104C2×D172—41no—
105C2×D172—41no—
106C2×D172—41no—
107C2×D172—41no—
108C2×D172—41no—
109C2×D172—41no—
110C2×D172—41no—
111C2×Dic86—21no—
112C2×Dic86—21no—
113C2×Dic86—21no—
114C2×Dic86—21no—
115C2×Dic86—21no—
116C2×Dic86SD1612yescomplemented
117C2×C8×C43—22no—
118C2×C8×C43—22no—
119C2×C8×C43—41no—
120C2×C8×C43—41no—
121C2×C8×C43—41no—
122C2×C8×C43—41no—
123C4⋊C4×C43—21no—
124C4⋊C4×C43—21no—
125C4⋊C4×C43—41no—
126C4⋊C4×C43—41no—
127C42×C43—41no—
128C42×C43—41no—
129C42×C43C2×D411yescharacteristic
130C42×C43C2×D411yescharacteristic
131C42×C43C2×D411yescharacteristic
132C42×C43#4111yescharacteristic
133#10621884—48no—
134C4⋊Dic43—21no—
135C4⋊Dic43—21no—
136C4⋊Dic43—41no—
137C4⋊Dic43—41no—
138C4⋊Dic43—41no—
139C4⋊Dic43—41no—
140C4⋊Dic43—42no—
141Dic43⋊C4—41no—
142Dic43⋊C4—41no—
143Dic43⋊C4—82no—
144C4×Dic43—41no—
145C4×Dic43—41no—
146C2×C43⋊C8—22no—
147C2×C43⋊C8—41no—
148C2×C43⋊C8—41no—
149#10621873—48no—
150C23×C43#12011yescharacteristic
151C22×D43—42no—
152C22×D43—81no—
153C22×D43—81no—
154C22×D43—81no—
155C22×D43—81no—
156C22×D43—81no—
157C22×D43—81no—
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×C43#12011yescharacteristic
171C2×C4×C43#12011yescharacteristic
172C2×C4×C43#12111yescharacteristic
173C2×C4×C43#12111yescharacteristic
174C2×C4×C43#12111yescharacteristic
175C2×C4×C43#12711yescharacteristic
176C2×C4×C43C2×SD1611yescharacteristic
177C2×C4×C43C2×SD1611yescharacteristic
178C2×C4×C43#13511yescharacteristic
179C2×C4×C43#13511yescharacteristic
180C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
181C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
182C2×C4×C43#13711yescharacteristic
183C2×C4×C43#13711yescharacteristic
184C2×Dic43—22no—
185C2×Dic43—41no—
186C2×Dic43—41no—
187C2×Dic43—41no—
188C2×Dic43—42no—
189C2×Dic43—42no—
190C2×Dic43—41no—
191C2×Dic43—42no—
192C2×Dic43—41no—
193D172—44no—
194D172—42no—
195D172—42no—
196D172—42no—
197D172—42no—
198D172—82no—
199D172—81no—
200D172—81no—
201D172—81no—
202D172—81no—
203Dic86—22no—
204Dic86—22no—
205Dic86—41no—
206Dic86—41no—
207C8×C43—42no—
208C8×C43—42no—
209C43⋊C8—42no—
210#10230—431nomaximal, Sylow
211C22×C43#39211yescharacteristic
212C22×C43#44811yescharacteristic
213C22×C43#44811yescharacteristic
214C22×C43#44911yescharacteristic
215C22×C43#44911yescharacteristic
216C22×C43#45311yescharacteristic
217C22×C43#45411yescharacteristic
218C2×D43—82no—
219C2×D43—82no—
220C2×D43—82no—
221C2×D43—161no—
222C2×D43—161no—
223C2×D43—161no—
224C2×D43—161no—
225C4×C43—21no—
226C4×C43—21no—
227C4×C43—42no—
228C4×C43—81no—
229C4×C43#45011yescharacteristic
230C4×C43#45011yescharacteristic
231C4×C43#45211yescharacteristic
232C4×C43#45211yescharacteristic
233C4×C43#46511yescharacteristic
234C4×C43#46511yescharacteristic
235C4×C43#46811yescharacteristic
236C4×C43#46811yescharacteristic
237Dic43—42no—
238Dic43—82no—
239Dic43—81no—
240C2×#460—431no—
241C2×#460—431no—
242#2582—431no—
243#1957—431no—
244C2×Q8⋊C8—431no—
245C2×Q8⋊C8D4311yescharacteristic, complemented
246#1296—431no—
247C2×C43#162011yescharacteristic
248C2×C43#162311yescharacteristic
249C2×C43#162611yescharacteristic
250C2×C43#162611yescharacteristic
251C2×C43#200011yescharacteristic
252C2×C43#200011yescharacteristic
253C2×C43#200611yescharacteristic
254D43—162no—
255C22×SD16—861no—
256C22×SD16—861no—
257C2×#127—431no—
258C2×C4×Q8—431no—
259C2×C4×Q8C2×D4311yescharacteristic
260#460—862no—
261#460—862no—
262#460—862no—
263#460—862no—
264C2×C4⋊C8—431no—
265C2×C4⋊C8C2×D4311yescharacteristic
266C2×#102—861no—
267C2×#102—861no—
268C2×#102—862no—
269C2×C4×C8C2×D4311yescharacteristic
270#398—862no—
271#391—861no—
272#391—861no—
273#389—861no—
274#389—861no—
275#384—431no—
276Q8⋊C8—22no—
277Q8⋊C8—862no—
278C43#1023011yescharacteristic, complemented, Sylow
279C22×Q8—431no—
280C22×Q8D17211yescharacteristic
281C22×D4—861no—
282C22×D4—861no—
283C22×D4—861no—
284C2×SD16—864no—
285C2×SD16—864no—
286C2×SD16—1722no—
287C2×SD16—1722no—
288C2×SD16—1722no—
289C2×SD16—1722no—
290C22×C8—21no—
291C22×C8—21no—
292C22×C8—861no—
293#127—432no—
294#127—861no—
295#127—861no—
296#127—861no—
297C4×Q8—21no—
298C4×Q8—21no—
299C4×Q8—21no—
300C4×Q8—21no—
301C4×Q8—861no—
302C4×Q8—861no—
303C4×Q8—861no—
304C4×Q8—861no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—431no—
307C2×C4⋊C4—432no—
308C2×C4⋊C4—862no—
309C2×C4⋊C4—861no—
310C2×C4⋊C4—861no—
311C2×C4⋊C4—861no—
312C2×C4⋊C4D17211yescharacteristic
313C2×C42—21no—
314C2×C42—861no—
315C2×C42C22×D4311yescharacteristic
316C4⋊C8—21no—
317C4⋊C8—432no—
318C4⋊C8—861no—
319C4⋊C8C22⋊D4312yes—
320#102—864no—
321#102—864no—
322#102—1724no—
323C4×C8—21no—
324C4×C8—21no—
325#95—862no—
326#95—862no—
327#95—862no—
328C24—1721no—
329C2×Q8—21no—
330C2×Q8—21no—
331C2×Q8—21no—
332C2×Q8—21no—
333C2×Q8—21no—
334C2×Q8—432no—
335C2×Q8—861no—
336C2×Q8—861no—
337C2×Q8—861no—
338C2×Q8—861no—
339C2×Q8—861no—
340C2×Q8#1062187312yescomplemented
341C2×D4—862no—
342C2×D4—862no—
343C2×D4—862no—
344C2×D4—1722no—
345C2×D4—1722no—
346C2×D4—1721no—
347C2×D4—1721no—
348C2×D4—1721no—
349C2×D4—1721no—
350C2×D4—1721no—
351C2×D4—1721no—
352C2×D4—1721no—
353C2×D4—1721no—
354C2×D4—1721no—
355C2×D4—1721no—
356C2×D4—1721no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—861no—
360C22×C4—862no—
361C22×C4—861no—
362C22×C4C2×D17211yescharacteristic
363C22×C4D4×D4311yescharacteristic
364C22×C4D4×D4311yescharacteristic
365SD16—1728no—
366SD16—1728no—
367C2×C8—22no—
368C2×C8—22no—
369C2×C8—41no—
370C2×C8—41no—
371C2×C8—41no—
372C2×C8—41no—
373C2×C8—862no—
374C2×C8—1721no—
375C2×C8—1721no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—861no—
381C4⋊C4—861no—
382C4⋊C4—3442no—
383C4⋊C4—1722no—
384C4⋊C4—1721no—
385C4⋊C4—1721no—
386C4⋊C4—1721no—
387C4⋊C4—1721no—
388C4⋊C4—1721no—
389C4⋊C4—1721no—
390C42—41no—
391C42—41no—
392C42—1721no—
393C42—1721no—
394C42#1062189811yescharacteristic
395C42D4×D4311yescharacteristic
396C42D4×D4311yescharacteristic
397C42C2×C22⋊D4311yescharacteristic
398C23—3441no—
399C23—3441no—
400C23—3441no—
401C23—3441no—
402C23—3441no—
403C23—3441no—
404C23—1722no—
405C23#1306329511yescharacteristic
406Q8—22no—
407Q8—22no—
408Q8—41no—
409Q8—41no—
410Q8—862no—
411Q8—862no—
412Q8—1721no—
413Q8—1721no—
414D4—3442no—
415D4—3441no—
416D4—3441no—
417D4—3441no—
418D4—3441no—
419D4—1724no—
420D4—1722no—
421D4—1722no—
422D4—1722no—
423D4—1722no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—22no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—862no—
433C2×C4—1722no—
434C2×C4—1722no—
435C2×C4—1721no—
436C2×C4—1721no—
437C2×C4—1722no—
438C2×C4—1721no—
439C2×C4—1721no—
440C2×C4—1721no—
441C2×C4#1306329311yescharacteristic
442C2×C4#1306329511yescharacteristic
443C2×C4#1306329811yescharacteristic
444C2×C4#1306329811yescharacteristic
445C2×C4#1306329911yescharacteristic
446C2×C4#1306332111yescharacteristic
447C2×C4SD16×D4311yescharacteristic
448C2×C4C2×#1062187311yescharacteristic
449C2×C4#1306334711yescharacteristic
450C2×C4#1306334811yescharacteristic
451C2×C4#1306335211yescharacteristic
452C2×C4#1306335311yescharacteristic
453C2×C4#1306335711yescharacteristic
454C2×C4#1306335811yescharacteristic
455C8—42no—
456C8—42no—
457C8—1722no—
458C22—3442no—
459C22—3442no—
460C22—3442no—
461C22—6881no—
462C22—6881no—
463C22—6881no—
464C22—6881no—
465C22#1458280811yescharacteristic
466C22#1458303911yescharacteristic
467C22#1458304011yescharacteristic
468C22#1458304611yescharacteristic
469C22#1458304711yescharacteristic
470C22#1458306811yescharacteristic
471C22#1458307311yescharacteristic
472C4—21no—
473C4—21no—
474C4—42no—
475C4—81no—
476C4—3441no—
477C4—3442no—
478C4—1722no—
479C4#1458304811yescharacteristic
480C4#1458305211yescharacteristic
481C4#1458306011yescharacteristic
482C4#1458306311yescharacteristic
483C4#1458312811yescharacteristic
484C4#1458313111yescharacteristic
485C4#1458314511yescharacteristic
486C4#1458314811yescharacteristic
487C2—6882no—
488C2#1913365611yescharacteristic
489C2#1913367511yescharacteristic
490C2#1913369311yescharacteristic
491C2#1913369411yescharacteristic
492C2#1913559711yescharacteristic
493C2#1913560011yescharacteristic
494C2#1913563811yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC2×C43×Q8⋊C8C2
socleC23×C43#120
prime radicalC2×#13063322C22
hypercenterC2×Q8⋊C8D43
hypocenterC43#10230
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
3. #19139965C2semidirect
5. C2×#14582631C2semidirect
6. #19132479C2semidirect
7. C2×C43×Q8⋊C8C2semidirect
86. C2×Q8×C43SD16semidirect
116. C2×Dic86SD16semidirect
245. C2×Q8⋊C8D43semidirect
278. C43#10230semidirect
340. C2×Q8#10621873semidirect

Maximal subgroups

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

subgroupindex
C2×#145831002
C2×#145830992
#191399652
#191354012
C2×#145826312
#191324792
C2×C43×Q8⋊C82
#1023043