Finite Group Databasebeta

← #24996887

Subgroups — #24996887

Order 11008.

654 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 654 conjugacy classes of subgroups — too many to draw. Only its 115 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×#14583230C211yesmaximal, characteristic
2#19140411C211yesmaximal, characteristic
3C2×#14582831C211yesmaximal, characteristic
4#19134679C211yesmaximal, characteristic
5C2×#14582635C211yesmaximal, characteristic
6C2×#14582624C211yesmaximal, characteristic
7C43×#1294C211yesmaximal, characteristic
8C2×#13063304C2211yescharacteristic
9C22×C4⋊Dic43—21no—
10C22×C4⋊Dic43C2211yescharacteristic
11C22×Dic43⋊C4C2211yescharacteristic
12#14583230—22no—
13#14583230—22no—
14C2×#13063257—21no—
15C2×#13063250—21no—
16C2×C22⋊(C43⋊C8)C2211yescharacteristic
17#14582839—21no—
18#14582831—22no—
19#14582831—22no—
20#14582829—22no—
21#14582820—21no—
22#14582774—21no—
23#14582760—21no—
24C2×C43⋊#95—21no—
25#14582661—22no—
26#14582635—22no—
27#14582624—22no—
28C2×C22⋊C8×C43C2211yescharacteristic
29C43×#380C2211yescharacteristic
30C2×#95×C43C2211yescharacteristic
31C22×Dic86D411yescharacteristic
32C23×Dic43—21no—
33C23×Dic43D411yescharacteristic
34C23×Dic43D411yescharacteristic
35C22×C43⋊C8—21no—
36#13063304—21no—
37#13063304—21no—
38#13063304—21no—
39#13063304—21no—
40C2×C4⋊Dic43—21no—
41C2×C4⋊Dic43—21no—
42C2×C4⋊Dic43—21no—
43C2×C4⋊Dic43—21no—
44C2×C4⋊Dic43—24no—
45C2×C4⋊Dic43—21no—
46C2×C4⋊Dic43—22no—
47C2×C4⋊Dic43—42no—
48C2×C4⋊Dic43—42no—
49C2×C4⋊Dic43D412yes—
50C2×C4⋊Dic43D411yescharacteristic
51C2×Dic43⋊C4—21no—
52C2×Dic43⋊C4—21no—
53C2×Dic43⋊C4—21no—
54C2×Dic43⋊C4—21no—
55C2×Dic43⋊C4—21no—
56C2×Dic43⋊C4—21no—
57C2×Dic43⋊C4—21no—
58C2×C22⋊Dic43—21no—
59#13063257—24no—
60#13063250—24no—
61C22⋊(C43⋊C8)—21no—
62C22⋊(C43⋊C8)—21no—
63C43⋊#95—22no—
64C43⋊#95—22no—
65C43⋊#95—22no—
66C43⋊#95—24no—
67C23×C4×C43—21no—
68C23×C4×C43C2311yescharacteristic
69C22×C8×C43—21no—
70C2×C4⋊C4×C43D412yes—
71C2×C22⋊C4×C43—21no—
72C22⋊C8×C43—21no—
73C22⋊C8×C43D412yes—
74#95×C43—21no—
75#95×C43—21no—
76#95×C43D412yes—
77C24×C43C2×D411yescharacteristic
78C22×C4×C43—24no—
79C22×C4×C43—22no—
80C22×C4×C43—22no—
81C22×C4×C43—42no—
82C22×C4×C43—42no—
83C22×C4×C43—41no—
84C22×C4×C43—41no—
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43#4111yescharacteristic
91C22×Dic43—21no—
92C22×Dic43—21no—
93C22×Dic43—21no—
94C22×Dic43—21no—
95C22×Dic43—21no—
96C22×Dic43—21no—
97C22×Dic43—22no—
98C22×Dic43—21no—
99C22×Dic43—21no—
100C22×Dic43—21no—
101C22×Dic43—21no—
102C22×Dic43—21no—
103C22×Dic43—42no—
104C22×Dic43—41no—
105C22×Dic43—41no—
106C22×Dic43—41no—
107C22×Dic43—41no—
108C22×Dic43—41no—
109C22×Dic43—41no—
110C22×Dic43SD1612yes—
111C2×Dic86—21no—
112C2×Dic86—21no—
113C2×Dic86—42no—
114C2×C8×C43—22no—
115C2×C8×C43—42no—
116C4⋊C4×C43—42no—
117C22⋊C4×C43—41no—
118C22⋊C4×C43—41no—
119C22⋊Dic43—41no—
120C22⋊Dic43—41no—
121C4⋊Dic43—22no—
122C4⋊Dic43—21no—
123C4⋊Dic43—22no—
124C4⋊Dic43—21no—
125C4⋊Dic43—48no—
126C4⋊Dic43—41no—
127C4⋊Dic43—41no—
128C4⋊Dic43—82no—
129Dic43⋊C4—41no—
130Dic43⋊C4—41no—
131Dic43⋊C4—41no—
132Dic43⋊C4—41no—
133Dic43⋊C4—41no—
134Dic43⋊C4—41no—
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
146C2×C4×C43—22no—
147C2×C4×C43—22no—
148C2×C4×C43—24no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—44no—
154C2×C4×C43—44no—
155C2×C4×C43—42no—
156C2×C4×C43—42no—
157C2×C4×C43—42no—
158C2×C4×C43—42no—
159C2×C4×C43—42no—
160C2×C4×C43#12011yescharacteristic
161C2×C4×C43#12111yescharacteristic
162C2×C4×C43#12111yescharacteristic
163C2×C4×C43#12711yescharacteristic
164C2×Dic43—22no—
165C2×Dic43—22no—
166C2×Dic43—22no—
167C2×Dic43—41no—
168C2×Dic43—41no—
169C2×Dic43—41no—
170C2×Dic43—41no—
171C2×Dic43—42no—
172C2×Dic43—41no—
173C2×Dic43—41no—
174C2×Dic43—41no—
175C2×Dic43—42no—
176C2×Dic43—42no—
177C2×Dic43—42no—
178C2×Dic43—42no—
179C2×Dic43—42no—
180C2×Dic43—42no—
181C2×Dic43—81no—
182C2×Dic43—81no—
183C2×Dic43—81no—
184C2×Dic43—81no—
185C2×Dic43—81no—
186Dic86—42no—
187Dic86—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—44no—
213C4×C43—82no—
214Dic43—42no—
215Dic43—82no—
216Dic43—81no—
217Dic43—81no—
218Dic43—81no—
219C2×#483—431no—
220#2627—431no—
221C2×#398—431no—
222#1823—431no—
223C2×#328—431no—
224C2×#324—431no—
225#1294D4311yescharacteristic
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⋊Q8—431no—
236C22×C4⋊C4—431no—
237C22×C4⋊C4—431no—
238C22×C4⋊C4—861no—
239#483—862no—
240#483—862no—
241C2×#106—861no—
242C2×#103—861no—
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#380C2×D4311yescharacteristic
253C2×#95—861no—
254C2×#95C2×D4311yescharacteristic
255#340—862no—
256#328—862no—
257#324—862no—
258C43#992711yescharacteristic, complemented, Sylow
259C22×Q8—431no—
260C23×C4—21no—
261C23×C4—431no—
262C23×C4—431no—
263C23×C4—861no—
264C23×C4C22×D4311yescharacteristic
265C22×C8—21no—
266C22×C8—861no—
267C22⋊Q8—861no—
268C22⋊Q8—861no—
269C22⋊Q8—861no—
270C22⋊Q8—861no—
271C2×C4⋊C4—432no—
272C2×C4⋊C4—431no—
273C2×C4⋊C4—861no—
274C2×C4⋊C4—861no—
275C2×C4⋊C4—861no—
276C2×C4⋊C4—861no—
277C2×C4⋊C4—862no—
278C2×C4⋊C4—864no—
279C2×C4⋊C4—861no—
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—861no—
287C2×C4⋊C4—1722no—
288C2×C4⋊C4—1722no—
289C2×C4⋊C4D17212yes—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—861no—
292#106—864no—
293#103—864no—
294C22⋊C8—21no—
295C22⋊C8—861no—
296C22⋊C8—861no—
297C22⋊C8D17212yes—
298#95—21no—
299#95—21no—
300#95—864no—
301#95—862no—
302#95—862no—
303#95—862no—
304#95D17212yes—
305C24D4×D4311yescharacteristic
306C2×Q8—861no—
307C2×Q8—861no—
308C2×Q8—1722no—
309C22×C4—24no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—432no—
317C22×C4—861no—
318C22×C4—861no—
319C22×C4—861no—
320C22×C4—861no—
321C22×C4—861no—
322C22×C4—861no—
323C22×C4—861no—
324C22×C4—861no—
325C22×C4—862no—
326C22×C4—861no—
327C22×C4—861no—
328C22×C4—861no—
329C22×C4—1721no—
330C22×C4—1721no—
331C22×C4—1721no—
332C22×C4—1721no—
333C22×C4—1721no—
334C22×C4—1721no—
335C22×C4—1722no—
336C22×C4C2×D17211yescharacteristic
337C22×C4C2×D17211yescharacteristic
338C22×C4C2×D17211yescharacteristic
339C22×C4D4×D4311yescharacteristic
340C22×C4D4×D4311yescharacteristic
341C22×C4#1062190211yescharacteristic
342C2×C8—22no—
343C2×C8—42no—
344C2×C8—1722no—
345C2×C8—1721no—
346C4⋊C4—42no—
347C4⋊C4—862no—
348C4⋊C4—861no—
349C4⋊C4—862no—
350C4⋊C4—861no—
351C4⋊C4—3442no—
352C4⋊C4—1728no—
353C4⋊C4—1721no—
354C4⋊C4—1721no—
355C4⋊C4—1721no—
356C4⋊C4—1721no—
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#1306329511yescharacteristic
368C23#1306329511yescharacteristic
369C23#1306330011yescharacteristic
370C23SD16×D4311yescharacteristic
371C23#1306334611yescharacteristic
372C23#1306334911yescharacteristic
373C23#1306335711yescharacteristic
374Q8—3441no—
375Q8—1722no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—24no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—44no—
384C2×C4—44no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—862no—
391C2×C4—862no—
392C2×C4—862no—
393C2×C4—3441no—
394C2×C4—3441no—
395C2×C4—3441no—
396C2×C4—3441no—
397C2×C4—3441no—
398C2×C4—1722no—
399C2×C4—1722no—
400C2×C4—1722no—
401C2×C4—1721no—
402C2×C4—1721no—
403C2×C4—1722no—
404C2×C4—1721no—
405C2×C4—1722no—
406C2×C4—1722no—
407C2×C4—1722no—
408C2×C4—1721no—
409C2×C4—1721no—
410C2×C4—1721no—
411C2×C4—1721no—
412C2×C4#1306329511yescharacteristic
413C2×C4#1306330011yescharacteristic
414C2×C4#1306330011yescharacteristic
415C2×C4#1306332211yescharacteristic
416C8—42no—
417C8—3441no—
418C22—21no—
419C22—21no—
420C22—22no—
421C22—22no—
422C22—22no—
423C22—22no—
424C22—21no—
425C22—21no—
426C22#1458280911yescharacteristic
427C22#1458303911yescharacteristic
428C22#1458304511yescharacteristic
429C22#1458305111yescharacteristic
430C22#1458306411yescharacteristic
431C22#1458308312yes—
432C22#1458309012yes—
433C22#1458312911yescharacteristic
434C22#1458314611yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—44no—
440C4—82no—
441C4—3442no—
442C4—3441no—
443C4—3441no—
444C4—3441no—
445C4—1722no—
446C2—21no—
447C2—21no—
448C2—21no—
449C2—21no—
450C2#1913359312yes—
451C2#1913360412yes—
452C2#1913560111yescharacteristic
453C2#1913563411yescharacteristic
454C2#1913572711yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#1294C2
socleC23×C43#120
prime radicalC24×C43C2×D4
hypercenter#1294D43
hypocenterC43#9927
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

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
C2×#145832302
#191404112
C2×#145828312
#191346792
C2×#145826352
C2×#145826242
C43×#12942
#992743