Finite Group Databasebeta

← #24994610

Subgroups — #24994610

Order 11008.

518 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 91 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
1#19143634C211yesmaximal, characteristic
2#19139944C211yesmaximal, characteristic
3#19132931C211yesmaximal, characteristic
4#19132924C211yesmaximal, characteristic, complemented
5#19132924C211yesmaximal, characteristic, complemented
6#19132501C211yesmaximal, characteristic, complemented
7C43×#1305C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊D43C2211yescharacteristic
9C22×Dic43⋊C4C2211yescharacteristic
10#14582975—22no—
11#14582974—22no—
12#14582949—21no—
13#14582863C2211yescharacteristic
14#14582863C2211yescharacteristic
15#14582861—21no—
16#14582829—21no—
17#14582821—21no—
18#14582784—21no—
19#14582776C411yescharacteristic
20#14582776C411yescharacteristic
21#14582774C411yescharacteristic
22#14582774C411yescharacteristic
23#14582773—21no—
24#14582624—21no—
25#14582624—22no—
26#14582624—22no—
27#14582622—21no—
28C43×#407C2211yescharacteristic
29C43×#407C2211yescharacteristic
30C43×#380C2211yescharacteristic
31C22×C22⋊D43C2×C411yescharacteristic
32C23×Dic43C2×C411yescharacteristic
33C23×Dic43C2×C411yescharacteristic
34C22×C4×D43D411yescharacteristic
35C2×#10621877—21no—
36C2×#10621877—21no—
37C2×#10621872—22no—
38C4×C22⋊D43—21no—
39C4×C22⋊D43—21no—
40C4×C22⋊D43—21no—
41C4×C22⋊D43—21no—
42C2×C4⋊Dic43—21no—
43C2×C4⋊Dic43—21no—
44C2×Dic43⋊C4—21no—
45C2×Dic43⋊C4—21no—
46C2×Dic43⋊C4—21no—
47C2×Dic43⋊C4—21no—
48C2×Dic43⋊C4—21no—
49C2×Dic43⋊C4—21no—
50C2×Dic43⋊C4D411yescharacteristic
51C2×C22⋊Dic43C2×C411yescharacteristic
52C2×(C2×D43)⋊C4—21no—
53C2×(C2×D43)⋊C4—21no—
54C2×(C2×D43)⋊C4D411yescharacteristic
55C2×C4×Dic43D411yescharacteristic
56Dic43⋊C8—22no—
57C22⋊(C43⋊C8)—21no—
58C22⋊(C43⋊C8)—21no—
59C22⋊(C43⋊C8)—21no—
60C22⋊(C43⋊C8)D412yes—
61(C2×D43)⋊C8—22no—
62C8×Dic43—22no—
63C43⋊#95—21no—
64C43⋊#95—21no—
65C43⋊#95—21no—
66C43⋊#95—21no—
67C23×C4×C43C2311yescharacteristic
68C2×M16×C43—21no—
69C2×M16×C43—21no—
70C2×C4⋊C4×C43—21no—
71C2×C22⋊C4×C43C2×C411yescharacteristic
72C2×C22⋊C4×C43C2×C411yescharacteristic
73C22⋊C8×C43—21no—
74C22⋊C8×C43—21no—
75C22⋊C8×C43—21no—
76C22⋊C8×C43D412yes—
77#95×C43—21no—
78C24×C43C22×C411yescharacteristic
79C23×D43C22⋊C411yescharacteristic
80C22×C4×C43—21no—
81C22×C4×C43—21no—
82C22×C4×C43—81no—
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43#4111yescharacteristic
88C22×C4×C43#4111yescharacteristic
89C2×C22⋊D43—22no—
90C2×C22⋊D43—21no—
91C2×C22⋊D43—21no—
92C2×C22⋊D43—41no—
93C22×Dic43—21no—
94C22×Dic43—21no—
95C22×Dic43—21no—
96C22×Dic43—21no—
97C22×Dic43—21no—
98C22×Dic43—21no—
99C22×Dic43—42no—
100C22×Dic43—81no—
101C22×Dic43C22⋊C411yescharacteristic
102C22×Dic43C22⋊C411yescharacteristic
103C22×Dic43C22⋊C411yescharacteristic
104C2×C4×D43—21no—
105C2×C4×D43—21no—
106C2×C4×D43—81no—
107M16×C43—81no—
108M16×C43—81no—
109C2×C8×C43—22no—
110C2×C8×C43—41no—
111C4⋊C4×C43—81no—
112C22⋊C4×C43—41no—
113C22⋊C4×C43—41no—
114C22⋊Dic43—21no—
115C22⋊Dic43—21no—
116(C2×D43)⋊C4—21no—
117(C2×D43)⋊C4—21no—
118(C2×D43)⋊C4—42no—
119(C2×D43)⋊C4—81no—
120C4⋊Dic43—42no—
121C4⋊Dic43—81no—
122Dic43⋊C4—21no—
123Dic43⋊C4—21no—
124Dic43⋊C4—41no—
125Dic43⋊C4—41no—
126Dic43⋊C4—41no—
127Dic43⋊C4—41no—
128C4×Dic43—21no—
129C4×Dic43—21no—
130#10621877—81no—
131#10621877—81no—
132C2×C43⋊C8—22no—
133C2×C43⋊C8—41no—
134#10621872—82no—
135C23×C43—21no—
136C23×C43—21no—
137C23×C43—41no—
138C23×C43—41no—
139C23×C43C2×C22⋊C411yescharacteristic
140C23×C43C4×D411yescharacteristic
141C23×C43C4×D411yescharacteristic
142C22×D43—21no—
143C22×D43—21no—
144C22×D43—21no—
145C22×D43—41no—
146C22×D43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
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—41no—
157C2×C4×C43—41no—
158C2×C4×C43—41no—
159C2×C4×C43#12011yescharacteristic
160C2×C4×C43#12111yescharacteristic
161C2×C4×C43#12111yescharacteristic
162C2×C4×C43#12311yescharacteristic
163C22⋊D43—42no—
164C22⋊D43—42no—
165C2×Dic43—21no—
166C2×Dic43—21no—
167C2×Dic43—22no—
168C2×Dic43—22no—
169C2×Dic43—22no—
170C2×Dic43—21no—
171C2×Dic43—21no—
172C2×Dic43—41no—
173C2×Dic43—41no—
174C2×Dic43—41no—
175C2×Dic43—41no—
176C2×Dic43—41no—
177C2×Dic43—41no—
178C2×Dic43—41no—
179C2×Dic43—41no—
180C2×Dic43—41no—
181C2×Dic43—81no—
182C2×Dic43—81no—
183C2×Dic43#10112yes—
184C4×D43—42no—
185C4×D43—81no—
186C8×C43—42no—
187C8×C43—81no—
188C43⋊C8—42no—
189C43⋊C8—81no—
190#9518—431nomaximal, Sylow
191C22×C43—21no—
192C22×C43—21no—
193C22×C43—21no—
194C22×C43—21no—
195C22×C43—21no—
196C22×C43—21no—
197C22×C43—21no—
198C22×C43—21no—
199C22×C43—42no—
200C22×C43—42no—
201C22×C43#38611yescharacteristic
202C22×C43C2×#10111yescharacteristic
203C22×C43#41311yescharacteristic
204C2×D43—42no—
205C2×D43—41no—
206C2×D43—41no—
207C2×D43—41no—
208C2×D43—81no—
209C4×C43—21no—
210C4×C43—21no—
211C4×C43—21no—
212C4×C43—21no—
213C4×C43—81no—
214C4×C43—81no—
215Dic43—22no—
216Dic43—42no—
217Dic43—41no—
218Dic43—41no—
219Dic43—81no—
220#2975—431no—
221#2579—431no—
222#1465—431no—
223#1463—431no—
224#1463—431no—
225#1305—431no—
226#1305D4311yescharacteristic, complemented
227C2×C43—21no—
228C2×C43—21no—
229C2×C43—41no—
230C2×C43—41no—
231C2×C43#189111yescharacteristic
232C2×C43#190111yescharacteristic
233C2×C43#191311yescharacteristic
234D43—81no—
235C2×C4×D4—431no—
236C22×C4⋊C4—431no—
237#436—862no—
238#436—862no—
239#431—861no—
240#407—431no—
241#407—431no—
242#407—861no—
243#407C2×D4311yescharacteristic
244#407C2×D4311yescharacteristic
245#398—861no—
246#396—861no—
247#387—861no—
248#386—431no—
249#386—431no—
250#385—431no—
251#385—431no—
252#385—861no—
253#380C2×D4311yescharacteristic
254#324—862no—
255#324—861no—
256#324—862no—
257#323—861no—
258C43#951811yescharacteristic, complemented, Sylow
259C22×D4—431no—
260C23×C4—431no—
261C23×C4—431no—
262C23×C4—431no—
263C23×C4C22×D4311yescharacteristic
264C2×M16—21no—
265C2×M16—21no—
266C2×M16—862no—
267C2×M16—861no—
268C2×M16—861no—
269C4×D4—861no—
270C4×D4—861no—
271C4×D4—861no—
272C4×D4—861no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—431no—
275C2×C4⋊C4—861no—
276C2×C4⋊C4—861no—
277C2×C4⋊C4—861no—
278C2×C4⋊C4—861no—
279C2×C4⋊C4—861no—
280C2×C4⋊C4—861no—
281C2×C4⋊C4—861no—
282C2×C4⋊C4—861no—
283C2×C22⋊C4—431no—
284C2×C22⋊C4—431no—
285C2×C22⋊C4—861no—
286C2×C22⋊C4—861no—
287C2×C22⋊C4C4×D4311yescharacteristic
288C2×C22⋊C4C4×D4311yescharacteristic
289C2×C42—431no—
290C4⋊C8—862no—
291C22⋊C8—21no—
292C22⋊C8—21no—
293C22⋊C8—21no—
294C22⋊C8—432no—
295C22⋊C8—862no—
296C22⋊C8—861no—
297C22⋊C8—861no—
298C22⋊C8—861no—
299C22⋊C8D17212yes—
300C4×C8—862no—
301#95—21no—
302#95—861no—
303#95—861no—
304#95—861no—
305#95—861no—
306C24—431no—
307C24C2×C4×D4311yescharacteristic
308C2×D4—862no—
309C2×D4—861no—
310C2×D4—861no—
311C2×D4—1721no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—81no—
315C22×C4—431no—
316C22×C4—431no—
317C22×C4—431no—
318C22×C4—861no—
319C22×C4—861no—
320C22×C4—861no—
321C22×C4—861no—
322C22×C4—861no—
323C22×C4—861no—
324C22×C4—861no—
325C22×C4—861no—
326C22×C4—3441no—
327C22×C4—3441no—
328C22×C4—1722no—
329C22×C4C2×D17211yescharacteristic
330C22×C4#1062189811yescharacteristic
331C22×C4D4×D4311yescharacteristic
332C22×C4D4×D4311yescharacteristic
333C22×C4D4×D4311yescharacteristic
334C22×C4#1062190211yescharacteristic
335M16—81no—
336M16—81no—
337M16—3442no—
338M16—3441no—
339M16—3441no—
340C2×C8—22no—
341C2×C8—41no—
342C2×C8—862no—
343C2×C8—1721no—
344C4⋊C4—81no—
345C4⋊C4—861no—
346C4⋊C4—861no—
347C4⋊C4—3441no—
348C4⋊C4—1722no—
349C4⋊C4—1721no—
350C4⋊C4—1721no—
351C4⋊C4—1721no—
352C4⋊C4—1721no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—861no—
356C22⋊C4—861no—
357C22⋊C4—861no—
358C22⋊C4—861no—
359C22⋊C4—3441no—
360C22⋊C4—1722no—
361C42—861no—
362C42—861no—
363C23—21no—
364C23—21no—
365C23—41no—
366C23—41no—
367C23—861no—
368C23—861no—
369C23—861no—
370C23—1721no—
371C23—1721no—
372C23C22⋊C4×D4311yescharacteristic
373C23#1306328711yescharacteristic
374C23C4×D17211yescharacteristic
375D4—1722no—
376D4—1722no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—432no—
390C2×C4—861no—
391C2×C4—861no—
392C2×C4—862no—
393C2×C4—862no—
394C2×C4—862no—
395C2×C4—861no—
396C2×C4—861no—
397C2×C4—3441no—
398C2×C4—3441no—
399C2×C4—3441no—
400C2×C4—1722no—
401C2×C4—1721no—
402C2×C4—1721no—
403C2×C4—1721no—
404C2×C4—1721no—
405C2×C4—1721no—
406C2×C4—1721no—
407C2×C4—1721no—
408C2×C4—1721no—
409C2×C4—1721no—
410C2×C4#1306329511yescharacteristic
411C2×C4#1306329811yescharacteristic
412C2×C4#1306330011yescharacteristic
413C2×C4#1306331011yescharacteristic
414C8—42no—
415C8—81no—
416C8—3441no—
417C8—1722no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—42no—
427C22—42no—
428C22—3441no—
429C22—1722no—
430C22—1721no—
431C22—1721no—
432C22—1721no—
433C22#1458277711yescharacteristic
434C22#101×D4311yescharacteristic
435C22#1458288011yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—81no—
441C4—81no—
442C4—862no—
443C4—3441no—
444C4—1722no—
445C4—1721no—
446C4—1721no—
447C2—21no—
448C2—21no—
449C2—41no—
450C2—41no—
451C2—3441no—
452C2#1913501211yescharacteristic
453C2#1913506211yescharacteristic
454C2#1913513611yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC24×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1305C2
socleC22×C43#386
prime radicalC22×C22⋊D43C2×C4
cosocleC23×C4×C43C23
hypercenter#1305D43
hypocenterC43#9518
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1305

Complements

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

NH ≅ G/Ntype
4. #19132924C2semidirect
5. #19132924C2semidirect
6. #19132501C2semidirect
7. C43×#1305C2semidirect
226. #1305D43semidirect
258. C43#9518semidirect

Maximal subgroups

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

subgroupindex
#191436342
#191399442
#191329312
#191329242
#191325012
C43×#13052
#951843