Finite Group Databasebeta

← #24996881

Subgroups — #24996881

Order 11008.

654 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140410C211yesmaximal, characteristic
2C2×#14582830C211yesmaximal, characteristic
3#19134681C211yesmaximal, characteristic
4C2×#14582636C211yesmaximal, characteristic
5C2×#14582624C211yesmaximal, characteristic
6#19132475C211yesmaximal, characteristic
7C2×C43×#483C211yesmaximal, characteristic
8C22×Dic43⋊C4—21no—
9C22×Dic43⋊C4C2211yescharacteristic
10C2×C22⋊(C43⋊C8)C2211yescharacteristic
11#14582837—21no—
12#14582832—22no—
13#14582830—22no—
14#14582830—22no—
15#14582818—21no—
16#14582771—21no—
17#14582760—21no—
18#14582759C2211yescharacteristic
19C2×C43⋊#95—21no—
20C2×C43⋊#95C2211yescharacteristic
21#14582661—22no—
22#14582636—22no—
23#14582624—22no—
24C2×C22⋊Q8×C43C2211yescharacteristic
25C22×C4⋊C4×C43C2211yescharacteristic
26C43×#483—22no—
27C43×#483—22no—
28C2×#106×C43—21no—
29C2×#103×C43—21no—
30C2×C22⋊C8×C43C2211yescharacteristic
31C23×Dic43—21no—
32C23×Dic43D411yescharacteristic
33C23×Dic43D411yescharacteristic
34C22×C43⋊C8—21no—
35C2×C4⋊Dic43D412yes—
36C2×Dic43⋊C4—24no—
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—21no—
40C2×Dic43⋊C4—21no—
41C2×Dic43⋊C4—21no—
42C2×Dic43⋊C4—21no—
43C2×Dic43⋊C4—22no—
44C2×Dic43⋊C4—42no—
45C2×Dic43⋊C4—42no—
46C2×C22⋊Dic43—21no—
47C22⋊(C43⋊C8)—21no—
48C22⋊(C43⋊C8)—21no—
49C43⋊#95—22no—
50C43⋊#95—24no—
51C43⋊#95—22no—
52C43⋊#95—22no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C43⋊#95D412yes—
56C22×Q8×C43D411yescharacteristic
57C23×C4×C43—21no—
58C23×C4×C43C2311yescharacteristic
59C22×C8×C43—21no—
60C22⋊Q8×C43—21no—
61C22⋊Q8×C43—21no—
62C22⋊Q8×C43—21no—
63C22⋊Q8×C43—21no—
64C2×C4⋊C4×C43—21no—
65C2×C4⋊C4×C43—21no—
66C2×C4⋊C4×C43—21no—
67C2×C4⋊C4×C43—21no—
68C2×C4⋊C4×C43—21no—
69C2×C4⋊C4×C43—21no—
70C2×C4⋊C4×C43D412yes—
71C2×C4⋊C4×C43D411yescharacteristic
72C2×C22⋊C4×C43—21no—
73#106×C43—24no—
74#103×C43—24no—
75C22⋊C8×C43—21no—
76C22⋊C8×C43D412yes—
77C24×C43C2×D411yescharacteristic
78C2×Q8×C43—21no—
79C2×Q8×C43—21no—
80C2×Q8×C43—42no—
81C22×C4×C43—21no—
82C22×C4×C43—21no—
83C22×C4×C43—22no—
84C22×C4×C43—42no—
85C22×C4×C43—41no—
86C22×C4×C43—41no—
87C22×C4×C43—41no—
88C22×C4×C43—41no—
89C22×C4×C43—41no—
90C22×C4×C43—41no—
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43C2×D411yescharacteristic
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43#4111yescharacteristic
97C22×Dic43—24no—
98C22×Dic43—21no—
99C22×Dic43—22no—
100C22×Dic43—21no—
101C22×Dic43—22no—
102C22×Dic43—21no—
103C22×Dic43—21no—
104C22×Dic43—21no—
105C22×Dic43—21no—
106C22×Dic43—21no—
107C22×Dic43—21no—
108C22×Dic43—21no—
109C22×Dic43—42no—
110C22×Dic43—42no—
111C22×Dic43—41no—
112C22×Dic43—41no—
113C22×Dic43SD1612yes—
114C2×C8×C43—22no—
115C2×C8×C43—42no—
116C4⋊C4×C43—22no—
117C4⋊C4×C43—21no—
118C4⋊C4×C43—22no—
119C4⋊C4×C43—21no—
120C4⋊C4×C43—41no—
121C4⋊C4×C43—41no—
122C4⋊C4×C43—41no—
123C4⋊C4×C43—41no—
124C22⋊C4×C43—41no—
125C22⋊C4×C43—41no—
126C22⋊Dic43—41no—
127C22⋊Dic43—41no—
128C4⋊Dic43—42no—
129Dic43⋊C4—48no—
130Dic43⋊C4—41no—
131Dic43⋊C4—41no—
132Dic43⋊C4—41no—
133Dic43⋊C4—41no—
134Dic43⋊C4—82no—
135C2×C43⋊C8—42no—
136C2×C43⋊C8—41no—
137C23×C43—22no—
138C23×C43—22no—
139C23×C43#12011yescharacteristic
140C23×C43#12011yescharacteristic
141C23×C43#12111yescharacteristic
142C23×C43C2×SD1611yescharacteristic
143C23×C43#13511yescharacteristic
144C23×C43AGL(1,ℤ/8)11yescharacteristic
145C23×C43#13711yescharacteristic
146Q8×C43—42no—
147Q8×C43—81no—
148C2×C4×C43—22no—
149C2×C4×C43—22no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—41no—
154C2×C4×C43—41no—
155C2×C4×C43—41no—
156C2×C4×C43—42no—
157C2×C4×C43—42no—
158C2×C4×C43—42no—
159C2×C4×C43—42no—
160C2×C4×C43—42no—
161C2×C4×C43—81no—
162C2×C4×C43—81no—
163C2×C4×C43—81no—
164C2×C4×C43—81no—
165C2×C4×C43#12011yescharacteristic
166C2×C4×C43#12111yescharacteristic
167C2×C4×C43#12111yescharacteristic
168C2×C4×C43#12711yescharacteristic
169C2×Dic43—24no—
170C2×Dic43—22no—
171C2×Dic43—22no—
172C2×Dic43—22no—
173C2×Dic43—44no—
174C2×Dic43—44no—
175C2×Dic43—42no—
176C2×Dic43—41no—
177C2×Dic43—41no—
178C2×Dic43—42no—
179C2×Dic43—41no—
180C2×Dic43—41no—
181C2×Dic43—42no—
182C2×Dic43—41no—
183C2×Dic43—42no—
184C2×Dic43—42no—
185C2×Dic43—42no—
186C2×Dic43—42no—
187C2×Dic43—81no—
188C8×C43—42no—
189C43⋊C8—81no—
190#9927—431nomaximal, Sylow
191C22×C43—22no—
192C22×C43—22no—
193C22×C43—22no—
194C22×C43—22no—
195C22×C43—21no—
196C22×C43—21no—
197C22×C43—21no—
198C22×C43—21no—
199C22×C43#39211yescharacteristic
200C22×C43#44811yescharacteristic
201C22×C43#44911yescharacteristic
202C22×C43#45011yescharacteristic
203C22×C43#45211yescharacteristic
204C22×C43#45612yes—
205C22×C43#45812yes—
206C22×C43#46511yescharacteristic
207C22×C43#46811yescharacteristic
208C4×C43—21no—
209C4×C43—21no—
210C4×C43—21no—
211C4×C43—21no—
212C4×C43—82no—
213C4×C43—81no—
214C4×C43—81no—
215Dic43—44no—
216Dic43—42no—
217Dic43—82no—
218Dic43—81no—
219C2×#483D4311yescharacteristic
220#2627—431no—
221C2×#398—431no—
222#1823—431no—
223C2×#328—431no—
224C2×#324—431no—
225#1294—431no—
226C2×C43—21no—
227C2×C43—21no—
228C2×C43—21no—
229C2×C43—21no—
230C2×C43#160912yes—
231C2×C43#161112yes—
232C2×C43#200011yescharacteristic
233C2×C43#200511yescharacteristic
234C2×C43#202211yescharacteristic
235C2×C22⋊Q8C2×D4311yescharacteristic
236C22×C4⋊C4—431no—
237C22×C4⋊C4—861no—
238C22×C4⋊C4C2×D4311yescharacteristic
239#483—22no—
240#483—22no—
241C2×#106—21no—
242C2×#103—21no—
243C2×C22⋊C8—431no—
244C2×C22⋊C8C2×D4311yescharacteristic
245#400—861no—
246#398—862no—
247#398—862no—
248#398—862no—
249#395—861no—
250#385—861no—
251#381—861no—
252#380—431no—
253C2×#95—431no—
254C2×#95—861no—
255#340—862no—
256#328—862no—
257#324—862no—
258C43#992711yescharacteristic, complemented, Sylow
259C22×Q8C22⋊D4311yescharacteristic
260C23×C4—21no—
261C23×C4—431no—
262C23×C4—431no—
263C23×C4—861no—
264C23×C4C22×D4311yescharacteristic
265C22×C8—21no—
266C22×C8—861no—
267C22⋊Q8—21no—
268C22⋊Q8—21no—
269C22⋊Q8—21no—
270C22⋊Q8—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—432no—
278C2×C4⋊C4—862no—
279C2×C4⋊C4—864no—
280C2×C4⋊C4—861no—
281C2×C4⋊C4—861no—
282C2×C4⋊C4—861no—
283C2×C4⋊C4—861no—
284C2×C4⋊C4—861no—
285C2×C4⋊C4—861no—
286C2×C4⋊C4—1722no—
287C2×C4⋊C4—1722no—
288C2×C4⋊C4C22⋊D4312yes—
289C2×C4⋊C4C22⋊D4311yescharacteristic
290C2×C22⋊C4—21no—
291C2×C22⋊C4—861no—
292#106—24no—
293#103—24no—
294C22⋊C8—21no—
295C22⋊C8—861no—
296C22⋊C8—861no—
297C22⋊C8C22⋊D4312yes—
298#95—432no—
299#95—864no—
300#95—862no—
301#95—862no—
302#95—862no—
303#95—861no—
304#95—861no—
305C24D4×D4311yescharacteristic
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—42no—
309C22×C4—22no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—42no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—432no—
320C22×C4—864no—
321C22×C4—862no—
322C22×C4—861no—
323C22×C4—861no—
324C22×C4—861no—
325C22×C4—861no—
326C22×C4—861no—
327C22×C4—861no—
328C22×C4—861no—
329C22×C4—861no—
330C22×C4—862no—
331C22×C4—861no—
332C22×C4—1722no—
333C22×C4—1722no—
334C22×C4—1721no—
335C22×C4—1721no—
336C22×C4D4×D4311yescharacteristic
337C22×C4D4×D4311yescharacteristic
338C22×C4#1062190011yescharacteristic
339C22×C4C2×C22⋊D4311yescharacteristic
340C22×C4C2×C22⋊D4311yescharacteristic
341C22×C4C2×C22⋊D4311yescharacteristic
342C2×C8—22no—
343C2×C8—42no—
344C2×C8—1722no—
345C2×C8—1721no—
346C4⋊C4—22no—
347C4⋊C4—21no—
348C4⋊C4—22no—
349C4⋊C4—21no—
350C4⋊C4—41no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C4⋊C4—41no—
354C4⋊C4—3442no—
355C4⋊C4—1722no—
356C4⋊C4—1728no—
357C4⋊C4—1721no—
358C4⋊C4—1721no—
359C4⋊C4—1721no—
360C4⋊C4—1721no—
361C22⋊C4—41no—
362C22⋊C4—41no—
363C22⋊C4—1721no—
364C22⋊C4—1721no—
365C23—22no—
366C23—22no—
367C23#1306329311yescharacteristic
368C23#1306329311yescharacteristic
369C23#1306329611yescharacteristic
370C23SD16×D4311yescharacteristic
371C23#1306334611yescharacteristic
372C23#1306335211yescharacteristic
373C23#1306335411yescharacteristic
374Q8—42no—
375Q8—81no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—864no—
394C2×C4—862no—
395C2×C4—862no—
396C2×C4—862no—
397C2×C4—3441no—
398C2×C4—1722no—
399C2×C4—1722no—
400C2×C4—1721no—
401C2×C4—1722no—
402C2×C4—1722no—
403C2×C4—1722no—
404C2×C4—1724no—
405C2×C4—1724no—
406C2×C4—1722no—
407C2×C4—1721no—
408C2×C4—1722no—
409C2×C4—1721no—
410C2×C4—1721no—
411C2×C4—1721no—
412C2×C4#1306329411yescharacteristic
413C2×C4#1306329711yescharacteristic
414C2×C4#1306329711yescharacteristic
415C2×C4#1306332111yescharacteristic
416C8—42no—
417C8—3441no—
418C22—21no—
419C22—21no—
420C22—22no—
421C22—22no—
422C22—22no—
423C22—22no—
424C22—21no—
425C22—21no—
426C22#1458280711yescharacteristic
427C22#1458303611yescharacteristic
428C22#1458304311yescharacteristic
429C22#1458304811yescharacteristic
430C22#1458305811yescharacteristic
431C22#1458308012yes—
432C22#1458308812yes—
433C22#1458312511yescharacteristic
434C22#1458314211yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—82no—
440C4—81no—
441C4—81no—
442C4—3442no—
443C4—3441no—
444C4—1724no—
445C4—1722no—
446C2—21no—
447C2—21no—
448C2—21no—
449C2—21no—
450C2#1913359112yes—
451C2#1913360112yes—
452C2#1913559511yescharacteristic
453C2#1913562811yescharacteristic
454C2#1913572311yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC2×C43×#483C2
socleC23×C43#120
prime radicalC24×C43C2×D4
hypercenterC2×#483D43
hypocenterC43#9927
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
258. C43#9927semidirect

Maximal subgroups

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

subgroupindex
#191404102
C2×#145828302
#191346812
C2×#145826362
C2×#145826242
#191324752
C2×C43×#4832
#992743