Finite Group Databasebeta

← #24996876

Subgroups — #24996876

Order 11008.

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

normal subgroups only

This group has 734 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×#14583227C211yesmaximal, characteristic, complemented
2#19140402C211yesmaximal, characteristic
3C2×#14582826C211yesmaximal, characteristic
4#19134682C211yesmaximal, characteristic, complemented
5C2×#14582622C211yesmaximal, characteristic
6#19132474C211yesmaximal, characteristic, complemented
7C2×C43×#328C211yesmaximal, characteristic, complemented
8C22×C4⋊Dic43C2211yescharacteristic
9C22×(C2×D43)⋊C4—21no—
10C22×(C2×D43)⋊C4C2211yescharacteristic
11#14583227—22no—
12#14583227—22no—
13C2×#13063256—21no—
14C2×#13063249—21no—
15C2×C22⋊(C43⋊C8)C2211yescharacteristic
16#14582834—21no—
17#14582826—22no—
18#14582826—22no—
19#14582821—22no—
20#14582810—21no—
21#14582771—21no—
22#14582759C2211yescharacteristic
23#14582754—21no—
24C2×C43⋊#95—21no—
25#14582662—22no—
26#14582622—22no—
27C2×C22⋊Q8×C43C2211yescharacteristic
28C2×C22⋊C8×C43C2211yescharacteristic
29C2×#95×C43C2211yescharacteristic
30C43×#328—22no—
31C24×D43D411yescharacteristic
32C23×Dic43—21no—
33C23×Dic43D411yescharacteristic
34C22×C43⋊C8—21no—
35C2×C4⋊Dic43—21no—
36C2×C4⋊Dic43—21no—
37C2×C4⋊Dic43—21no—
38C2×C4⋊Dic43—21no—
39C2×C4⋊Dic43—21no—
40C2×C4⋊Dic43D412yes—
41C2×C4⋊Dic43D412yes—
42C2×Dic43⋊C4—22no—
43C2×C22⋊Dic43—21no—
44C2×(C2×D43)⋊C4—24no—
45C2×(C2×D43)⋊C4—21no—
46C2×(C2×D43)⋊C4—21no—
47C2×(C2×D43)⋊C4—21no—
48C2×(C2×D43)⋊C4—21no—
49C2×(C2×D43)⋊C4—21no—
50C2×(C2×D43)⋊C4—21no—
51C2×(C2×D43)⋊C4—22no—
52C2×(C2×D43)⋊C4—22no—
53C2×(C2×D43)⋊C4—42no—
54C2×(C2×D43)⋊C4—42no—
55#13063256—24no—
56#13063249—24no—
57C22⋊(C43⋊C8)—21no—
58C22⋊(C43⋊C8)D412yes—
59C43⋊#95—22no—
60C43⋊#95—24no—
61C43⋊#95—21no—
62C22×Q8×C43D411yescharacteristic
63C23×C4×C43—21no—
64C23×C4×C43C2311yescharacteristic
65C22×C8×C43—21no—
66C22⋊Q8×C43—21no—
67C22⋊Q8×C43—21no—
68C22⋊Q8×C43—21no—
69C22⋊Q8×C43—21no—
70C2×C4⋊C4×C43—21no—
71C2×C4⋊C4×C43D411yescharacteristic
72C2×C22⋊C4×C43—21no—
73C22⋊C8×C43—21no—
74C22⋊C8×C43—21no—
75#95×C43—21no—
76#95×C43D412yes—
77C24×C43C2×D411yescharacteristic
78C23×D43—21no—
79C23×D43—21no—
80C23×D43—21no—
81C23×D43—21no—
82C23×D43—21no—
83C23×D43—21no—
84C23×D43—42no—
85C23×D43—42no—
86C23×D43SD1612yes—
87C2×Q8×C43—21no—
88C2×Q8×C43—21no—
89C2×Q8×C43—42no—
90C22×C4×C43—22no—
91C22×C4×C43—21no—
92C22×C4×C43—21no—
93C22×C4×C43—42no—
94C22×C4×C43—42no—
95C22×C4×C43—42no—
96C22×C4×C43—41no—
97C22×C4×C43—41no—
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43C2×D411yescharacteristic
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43#4111yescharacteristic
104C22×Dic43—21no—
105C22×Dic43—22no—
106C22×Dic43—21no—
107C22×Dic43—22no—
108C22×Dic43—21no—
109C22×Dic43—42no—
110C22×Dic43—41no—
111C22×Dic43—41no—
112C22×Dic43—41no—
113C22×Dic43—41no—
114C22×Dic43—41no—
115C22×Dic43—41no—
116C2×C8×C43—42no—
117C2×C8×C43—41no—
118C4⋊C4×C43—21no—
119C4⋊C4×C43—21no—
120C4⋊C4×C43—41no—
121C4⋊C4×C43—41no—
122C22⋊C4×C43—41no—
123C22⋊C4×C43—41no—
124C22⋊Dic43—41no—
125C22⋊Dic43—41no—
126(C2×D43)⋊C4—48no—
127(C2×D43)⋊C4—41no—
128(C2×D43)⋊C4—41no—
129(C2×D43)⋊C4—41no—
130(C2×D43)⋊C4—41no—
131(C2×D43)⋊C4—82no—
132(C2×D43)⋊C4—82no—
133C4⋊Dic43—22no—
134C4⋊Dic43—22no—
135C4⋊Dic43—41no—
136C4⋊Dic43—41no—
137C4⋊Dic43—42no—
138Dic43⋊C4—82no—
139C2×C43⋊C8—22no—
140C2×C43⋊C8—42no—
141C23×C43—22no—
142C23×C43—22no—
143C23×C43#12011yescharacteristic
144C23×C43#12011yescharacteristic
145C23×C43#12111yescharacteristic
146C23×C43C2×SD1611yescharacteristic
147C23×C43#13511yescharacteristic
148C23×C43AGL(1,ℤ/8)11yescharacteristic
149C23×C43#13711yescharacteristic
150C22×D43—22no—
151C22×D43—22no—
152C22×D43—22no—
153C22×D43—44no—
154C22×D43—44no—
155C22×D43—42no—
156C22×D43—42no—
157C22×D43—41no—
158C22×D43—41no—
159C22×D43—41no—
160C22×D43—42no—
161C22×D43—42no—
162C22×D43—41no—
163C22×D43—82no—
164C22×D43—82no—
165C22×D43—81no—
166C22×D43—81no—
167Q8×C43—42no—
168Q8×C43—81no—
169C2×C4×C43—22no—
170C2×C4×C43—22no—
171C2×C4×C43—41no—
172C2×C4×C43—41no—
173C2×C4×C43—41no—
174C2×C4×C43—41no—
175C2×C4×C43—42no—
176C2×C4×C43—42no—
177C2×C4×C43—41no—
178C2×C4×C43—41no—
179C2×C4×C43—42no—
180C2×C4×C43—42no—
181C2×C4×C43—42no—
182C2×C4×C43—82no—
183C2×C4×C43—82no—
184C2×C4×C43#12011yescharacteristic
185C2×C4×C43#12111yescharacteristic
186C2×C4×C43#12111yescharacteristic
187C2×C4×C43#12711yescharacteristic
188C2×Dic43—42no—
189C2×Dic43—42no—
190C2×Dic43—41no—
191C2×Dic43—42no—
192C2×Dic43—42no—
193C2×Dic43—42no—
194C2×Dic43—42no—
195C2×Dic43—42no—
196C2×Dic43—42no—
197C2×Dic43—81no—
198C2×Dic43—81no—
199C2×Dic43—81no—
200C2×Dic43—81no—
201C2×Dic43—81no—
202C8×C43—81no—
203C43⋊C8—42no—
204#9926—431nomaximal, Sylow
205C22×C43—22no—
206C22×C43—22no—
207C22×C43—22no—
208C22×C43—22no—
209C22×C43—21no—
210C22×C43—21no—
211C22×C43—21no—
212C22×C43—21no—
213C22×C43#39211yescharacteristic
214C22×C43#44811yescharacteristic
215C22×C43#44911yescharacteristic
216C22×C43#45011yescharacteristic
217C22×C43#45211yescharacteristic
218C22×C43#45512yes—
219C22×C43#45812yes—
220C22×C43#46511yescharacteristic
221C22×C43#46811yescharacteristic
222C2×D43—44no—
223C2×D43—44no—
224C2×D43—42no—
225C2×D43—82no—
226C2×D43—82no—
227C2×D43—82no—
228C2×D43—81no—
229C2×D43—81no—
230C2×D43—82no—
231C4×C43—21no—
232C4×C43—21no—
233C4×C43—21no—
234C4×C43—21no—
235C4×C43—82no—
236C4×C43—81no—
237C4×C43—81no—
238Dic43—82no—
239Dic43—82no—
240Dic43—81no—
241C2×#483—431no—
242#2626—431no—
243C2×#397—431no—
244#1823—431no—
245C2×#328D4311yescharacteristic, complemented
246C2×#323—431no—
247#1294—431no—
248C2×C43—21no—
249C2×C43—21no—
250C2×C43—21no—
251C2×C43—21no—
252C2×C43#160812yes—
253C2×C43#161212yes—
254C2×C43#200011yescharacteristic
255C2×C43#200411yescharacteristic
256C2×C43#202211yescharacteristic
257D43—82no—
258C2×C22⋊Q8C2×D4311yescharacteristic
259C22×C4⋊C4—431no—
260C22×C22⋊C4—431no—
261C22×C22⋊C4—861no—
262#483—862no—
263#483—862no—
264C2×#106—861no—
265C2×#103—861no—
266C2×C22⋊C8—431no—
267C2×C22⋊C8C2×D4311yescharacteristic
268#399—861no—
269#397—862no—
270#397—862no—
271#396—862no—
272#393—861no—
273#385—861no—
274#380—431no—
275#379—861no—
276C2×#95—861no—
277C2×#95C2×D4311yescharacteristic
278#340—862no—
279#328—22no—
280#323—862no—
281C43#992611yescharacteristic, complemented, Sylow
282C25—431no—
283C22×Q8D17211yescharacteristic
284C23×C4—21no—
285C23×C4—431no—
286C23×C4—861no—
287C23×C4C22×D4311yescharacteristic
288C22×C8—21no—
289C22×C8—861no—
290C22⋊Q8—21no—
291C22⋊Q8—21no—
292C22⋊Q8—21no—
293C22⋊Q8—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—432no—
296C2×C4⋊C4—432no—
297C2×C4⋊C4—861no—
298C2×C4⋊C4—861no—
299C2×C4⋊C4—861no—
300C2×C4⋊C4—861no—
301C2×C4⋊C4—862no—
302C2×C4⋊C4—861no—
303C2×C4⋊C4D17211yescharacteristic
304C2×C22⋊C4—21no—
305C2×C22⋊C4—862no—
306C2×C22⋊C4—862no—
307C2×C22⋊C4—864no—
308C2×C22⋊C4—861no—
309C2×C22⋊C4—861no—
310C2×C22⋊C4—861no—
311C2×C22⋊C4—861no—
312C2×C22⋊C4—861no—
313C2×C22⋊C4—861no—
314C2×C22⋊C4—861no—
315C2×C22⋊C4—1722no—
316C2×C22⋊C4—1722no—
317#106—864no—
318#103—864no—
319C22⋊C8—21no—
320C22⋊C8—21no—
321C22⋊C8—432no—
322C22⋊C8—861no—
323#95—21no—
324#95—864no—
325#95—862no—
326#95—861no—
327#95C22⋊D4312yes—
328C24—432no—
329C24—861no—
330C24—861no—
331C24—861no—
332C24—861no—
333C24—861no—
334C24—861no—
335C24—1722no—
336C24—1722no—
337C24D4×D4311yescharacteristic
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—42no—
341C22×C4—22no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—42no—
345C22×C4—42no—
346C22×C4—42no—
347C22×C4—41no—
348C22×C4—41no—
349C22×C4—861no—
350C22×C4—861no—
351C22×C4—862no—
352C22×C4—862no—
353C22×C4—861no—
354C22×C4—1721no—
355C22×C4—1721no—
356C22×C4—1721no—
357C22×C4—1721no—
358C22×C4—1721no—
359C22×C4—1721no—
360C22×C4—1722no—
361C22×C4C2×D17211yescharacteristic
362C22×C4#1062189811yescharacteristic
363C22×C4D4×D4311yescharacteristic
364C22×C4D4×D4311yescharacteristic
365C22×C4D4×D4311yescharacteristic
366C22×C4C2×C22⋊D4311yescharacteristic
367C2×C8—42no—
368C2×C8—41no—
369C2×C8—862no—
370C2×C8—1722no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—862no—
376C4⋊C4—862no—
377C4⋊C4—3442no—
378C4⋊C4—1722no—
379C4⋊C4—1721no—
380C4⋊C4—1721no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—3442no—
384C22⋊C4—3442no—
385C22⋊C4—1728no—
386C22⋊C4—1721no—
387C22⋊C4—1721no—
388C22⋊C4—1721no—
389C22⋊C4—1721no—
390C22⋊C4—1721no—
391C22⋊C4—1721no—
392C23—22no—
393C23—22no—
394C23—862no—
395C23—862no—
396C23—862no—
397C23—3441no—
398C23—3442no—
399C23—3441no—
400C23—3442no—
401C23—1722no—
402C23—1724no—
403C23—1722no—
404C23—1724no—
405C23—1721no—
406C23—1721no—
407C23—1721no—
408C23—1722no—
409C23—1722no—
410C23—1721no—
411C23#1306329311yescharacteristic
412C23#1306329511yescharacteristic
413C23#1306329811yescharacteristic
414C23SD16×D4311yescharacteristic
415C23#1306334811yescharacteristic
416C23#1306335211yescharacteristic
417C23#1306335711yescharacteristic
418Q8—42no—
419Q8—81no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—82no—
434C2×C4—82no—
435C2×C4—3441no—
436C2×C4—3441no—
437C2×C4—3441no—
438C2×C4—3441no—
439C2×C4—3441no—
440C2×C4—1722no—
441C2×C4—1722no—
442C2×C4—1722no—
443C2×C4—1722no—
444C2×C4—1721no—
445C2×C4—1722no—
446C2×C4—1722no—
447C2×C4—1722no—
448C2×C4—1722no—
449C2×C4#1306329511yescharacteristic
450C2×C4#1306329811yescharacteristic
451C2×C4#1306329911yescharacteristic
452C2×C4#1306332111yescharacteristic
453C8—81no—
454C8—1722no—
455C22—21no—
456C22—21no—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—21no—
462C22—21no—
463C22—3442no—
464C22—3442no—
465C22—3442no—
466C22—3441no—
467C22—3442no—
468C22—3441no—
469C22—1724no—
470C22—1722no—
471C22—1724no—
472C22#1458280811yescharacteristic
473C22#1458303911yescharacteristic
474C22#1458304711yescharacteristic
475C22#1458304811yescharacteristic
476C22#1458306011yescharacteristic
477C22#1458307812yes—
478C22#1458309012yes—
479C22#1458313111yescharacteristic
480C22#1458314811yescharacteristic
481C4—21no—
482C4—21no—
483C4—21no—
484C4—21no—
485C4—82no—
486C4—81no—
487C4—81no—
488C4—3442no—
489C4—3441no—
490C4—3442no—
491C2—21no—
492C2—21no—
493C2—21no—
494C2—21no—
495C2—3442no—
496C2#1913358712yes—
497C2#1913361212yes—
498C2#1913559711yescharacteristic
499C2#1913562311yescharacteristic
500C2#1913572511yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC2×C43×#328C2
socleC23×C43#120
prime radicalC24×D43D4
hypercenterC2×#328D43
hypocenterC43#9926
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
1. C2×#14583227C2semidirect
4. #19134682C2semidirect
6. #19132474C2semidirect
7. C2×C43×#328C2semidirect
245. C2×#328D43semidirect
281. C43#9926semidirect

Maximal subgroups

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

subgroupindex
C2×#145832272
#191404022
C2×#145828262
#191346822
C2×#145826222
#191324742
C2×C43×#3282
#992643