Finite Group Databasebeta

← #24996973

Subgroups — #24996973

Order 11008.

768 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 768 conjugacy classes of subgroups — too many to draw. Only its 85 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#19144531C211yesmaximal, characteristic, complemented
2#19138869C211yesmaximal, characteristic, complemented
3#19134695C211yesmaximal, characteristic, complemented
4#19133124C211yesmaximal, characteristic, complemented
5#19132922C211yesmaximal, characteristic, complemented
6#19132448C211yesmaximal, characteristic, complemented
7C43×#2539C211yesmaximal, characteristic
8C2×#13063284C2211yescharacteristic
9#14583220—22no—
10#14583215—21no—
11#14583210—21no—
12#14582939—21no—
13#14582904—21no—
14#14582863C2211yescharacteristic
15#14582863C2211yescharacteristic
16#14582835—21no—
17#14582824—21no—
18#14582787—22no—
19#14582772—21no—
20#14582762C2211yescharacteristic
21#14582755—21no—
22#14582659—22no—
23#14582633—22no—
24#14582623—22no—
25C2×#123×C43—21no—
26C2×#121×C43C2211yescharacteristic
27C2×#120×C43—21no—
28C22×C22⋊C4×C43C2211yescharacteristic
29C43×#399—21no—
30C43×#392—21no—
31C43×#390—22no—
32C4×C22⋊C4×C43C2211yescharacteristic
33C2×#10621877—21no—
34C2×#10621877—21no—
35#13063284—21no—
36#13063284—21no—
37#13063284—21no—
38#13063284—21no—
39C2×C4⋊Dic43D411yescharacteristic, complemented
40C2×C4⋊Dic43D411yescharacteristic, complemented
41C2×Dic43⋊C4—22no—
42C2×C22⋊Dic43—22no—
43C2×C22⋊Dic43—21no—
44C2×C22⋊Dic43—21no—
45C2×C22⋊Dic43—22no—
46C2×C4×Dic43—21no—
47#13063258—22no—
48#13063256—22no—
49#13063246—22no—
50#13063246—22no—
51C22⋊(C43⋊C8)—21no—
52C22⋊(C43⋊C8)—21no—
53C22⋊(C43⋊C8)—21no—
54C22⋊(C43⋊C8)D412yescomplemented
55C43⋊#95—22no—
56C43⋊#95—21no—
57C43⋊#95D412yescomplemented
58C25×C43D411yescharacteristic
59C22×D4×C43—21no—
60C22×D4×C43—22no—
61C22×D4×C43D411yescharacteristic
62C23×C4×C43D411yescharacteristic
63C23×C4×C43C2311yescharacteristic
64#123×C43—44no—
65#121×C43—21no—
66#121×C43—21no—
67#121×C43—21no—
68#121×C43—21no—
69#120×C43—44no—
70C2×C4⋊C4×C43—22no—
71C2×C4⋊C4×C43D411yescharacteristic
72C2×C22⋊C4×C43—21no—
73C2×C22⋊C4×C43—22no—
74C2×C22⋊C4×C43—22no—
75C2×C22⋊C4×C43—21no—
76C2×C22⋊C4×C43—21no—
77C2×C22⋊C4×C43—21no—
78C2×C22⋊C4×C43—21no—
79C2×C22⋊C4×C43—21no—
80C2×C22⋊C4×C43—21no—
81C2×C22⋊C4×C43—21no—
82C2×C42×C43D412yes—
83#95×C43—21no—
84C24×C43—21no—
85C24×C43—21no—
86C24×C43—21no—
87C24×C43—21no—
88C24×C43—42no—
89C24×C43—42no—
90C24×C43—42no—
91C24×C43C2×D411yescharacteristic
92C2×D4×C43—21no—
93C2×D4×C43—21no—
94C2×D4×C43—42no—
95C2×D4×C43—42no—
96C2×D4×C43—44no—
97C2×D4×C43—44no—
98C2×D4×C43—41no—
99C2×D4×C43—41no—
100C2×D4×C43—42no—
101C2×D4×C43—82no—
102C22×C4×C43—22no—
103C22×C4×C43—21no—
104C22×C4×C43—21no—
105C22×C4×C43—21no—
106C22×C4×C43—21no—
107C22×C4×C43—42no—
108C22×C4×C43—42no—
109C22×C4×C43C2×D411yescharacteristic
110C22×C4×C43C2×D411yescharacteristic
111C22×C4×C43C2×D411yescharacteristic
112C22×C4×C43C2×D411yescharacteristic
113C22×C4×C43C2×D411yescharacteristic
114C22×C4×C43#4111yescharacteristic
115C22×Dic43—22no—
116C22×Dic43—21no—
117C22×Dic43—21no—
118C4⋊C4×C43—21no—
119C4⋊C4×C43—21no—
120C4⋊C4×C43—44no—
121C22⋊C4×C43—24no—
122C22⋊C4×C43—44no—
123C22⋊C4×C43—44no—
124C22⋊C4×C43—41no—
125C22⋊C4×C43—41no—
126C22⋊C4×C43—41no—
127C22⋊C4×C43—41no—
128C22⋊C4×C43—41no—
129C22⋊C4×C43—41no—
130C42×C43—42no—
131C22⋊Dic43—42no—
132C22⋊Dic43—44no—
133C22⋊Dic43—41no—
134C22⋊Dic43—41no—
135C22⋊Dic43—82no—
136C4⋊Dic43—21no—
137C4⋊Dic43—21no—
138C4⋊Dic43—21no—
139C4⋊Dic43—21no—
140Dic43⋊C4—82no—
141C4×Dic43—41no—
142C4×Dic43—41no—
143#10621877—42no—
144#10621877—42no—
145C2×C43⋊C8—22no—
146C2×C43⋊C8—41no—
147C23×C43—22no—
148C23×C43—22no—
149C23×C43—22no—
150C23×C43—22no—
151C23×C43—22no—
152C23×C43—41no—
153C23×C43—42no—
154C23×C43—41no—
155C23×C43—41no—
156C23×C43—42no—
157C23×C43—41no—
158C23×C43—41no—
159C23×C43—41no—
160C23×C43—42no—
161C23×C43—41no—
162C23×C43—42no—
163C23×C43—42no—
164C23×C43—41no—
165C23×C43—42no—
166C23×C43—81no—
167C23×C43—81no—
168C23×C43—88no—
169C23×C43#12011yescharacteristic
170C23×C43#12011yescharacteristic
171C23×C43#12111yescharacteristic
172D4×C43—42no—
173D4×C43—81no—
174D4×C43—88no—
175D4×C43—82no—
176D4×C43—82no—
177C2×C4×C43—22no—
178C2×C4×C43—22no—
179C2×C4×C43—24no—
180C2×C4×C43—41no—
181C2×C4×C43—41no—
182C2×C4×C43—41no—
183C2×C4×C43—41no—
184C2×C4×C43—42no—
185C2×C4×C43—42no—
186C2×C4×C43—41no—
187C2×C4×C43—42no—
188C2×C4×C43—41no—
189C2×C4×C43—41no—
190C2×C4×C43—41no—
191C2×C4×C43—42no—
192C2×C4×C43—81no—
193C2×C4×C43#12011yescharacteristic
194C2×C4×C43#12111yescharacteristic
195C2×C4×C43#12111yescharacteristic
196C2×C4×C43#12711yescharacteristic
197C2×Dic43—42no—
198C2×Dic43—42no—
199C2×Dic43—42no—
200C2×Dic43—41no—
201C2×Dic43—41no—
202C2×Dic43—42no—
203C2×Dic43—42no—
204C43⋊C8—42no—
205C43⋊C8—81no—
206#9940—431nomaximal, Sylow
207C22×C43—21no—
208C22×C43—21no—
209C22×C43—21no—
210C22×C43—21no—
211C22×C43—21no—
212C22×C43—21no—
213C22×C43—21no—
214C22×C43—44no—
215C22×C43—44no—
216C22×C43—44no—
217C22×C43—42no—
218C22×C43—82no—
219C22×C43—82no—
220C22×C43—82no—
221C22×C43—82no—
222C22×C43—82no—
223C22×C43—82no—
224C22×C43—81no—
225C22×C43—81no—
226C22×C43—81no—
227C22×C43—81no—
228C22×C43—81no—
229C22×C43#39211yescharacteristic
230C22×C43#45312yes—
231C22×C43#45812yes—
232C4×C43—21no—
233C4×C43—21no—
234C4×C43—21no—
235C4×C43—21no—
236C4×C43—44no—
237C4×C43—81no—
238C4×C43—81no—
239Dic43—82no—
240Dic43—81no—
241Dic43—81no—
242#3094—431no—
243#2539D4311yescharacteristic
244#2482—431no—
245#1826—431no—
246#1510—431no—
247#1462—431no—
248#1284—431no—
249C2×C43—22no—
250C2×C43—22no—
251C2×C43—41no—
252C2×C43—82no—
253C2×C43—161no—
254C2×C43#200211yescharacteristic
255C2×C43#201011yescharacteristic
256C2×C43#202211yescharacteristic
257C2×#123—21no—
258C2×#121C2×D4311yescharacteristic
259C2×#120—21no—
260C2×#117—431no—
261C22×C22⋊C4C2×D4311yescharacteristic
262#482—862no—
263#481—861no—
264#480—861no—
265#428—861no—
266#418—861no—
267#407—431no—
268#407—431no—
269#399—21no—
270#399—861no—
271#397—861no—
272#392—21no—
273#390—22no—
274#388—862no—
275#385—861no—
276#381—431no—
277#379—861no—
278C4×C22⋊C4C2×D4311yescharacteristic
279#339—862no—
280#327—862no—
281#323—862no—
282C43#994011yescharacteristic, complemented, Sylow
283C25C22⋊D4311yescharacteristic
284C22×D4—21no—
285C22×D4—22no—
286C22×D4C22⋊D4311yescharacteristic
287C23×C4C22⋊D4311yescharacteristic
288C23×C4C22×D4311yescharacteristic
289C2×M16—861no—
290C2×M16—861no—
291#123—44no—
292#121—21no—
293#121—21no—
294#121—21no—
295#121—21no—
296#120—44no—
297#117—861no—
298#117—861no—
299#117—861no—
300#117—861no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—431no—
303C2×C4⋊C4—431no—
304C2×C4⋊C4—862no—
305C2×C4⋊C4C22⋊D4311yescharacteristic
306C2×C22⋊C4—21no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—22no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—862no—
317C2×C22⋊C4—862no—
318C2×C22⋊C4—861no—
319C2×C22⋊C4—861no—
320C2×C42—861no—
321C2×C42C22⋊D4312yes—
322#107—862no—
323#106—862no—
324#102—862no—
325#102—862no—
326C22⋊C8—432no—
327C22⋊C8—861no—
328C22⋊C8—861no—
329C22⋊C8—861no—
330#95—21no—
331#95—432no—
332#95—862no—
333#95—861no—
334C24—21no—
335C24—21no—
336C24—21no—
337C24—21no—
338C24—42no—
339C24—42no—
340C24—42no—
341C24C2×C22⋊D4311yescharacteristic
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—42no—
345C2×D4—44no—
346C2×D4—42no—
347C2×D4—42no—
348C2×D4—44no—
349C2×D4—41no—
350C2×D4—41no—
351C2×D4—82no—
352C22×C4—22no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—42no—
358C22×C4—42no—
359C22×C4—862no—
360C22×C4—861no—
361C22×C4—861no—
362C22×C4D4×D4311yescharacteristic
363C22×C4D4×D4311yescharacteristic
364C22×C4D4×D4311yescharacteristic
365C22×C4#1062190011yescharacteristic
366C22×C4C2×C22⋊D4311yescharacteristic
367C22×C4C2×C22⋊D4311yescharacteristic
368M16—1722no—
369M16—1722no—
370C2×C8—862no—
371C2×C8—1721no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—44no—
375C4⋊C4—861no—
376C4⋊C4—861no—
377C4⋊C4—861no—
378C4⋊C4—861no—
379C4⋊C4—3442no—
380C22⋊C4—24no—
381C22⋊C4—44no—
382C22⋊C4—44no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C22⋊C4—41no—
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4—3442no—
390C22⋊C4—1722no—
391C22⋊C4—1724no—
392C22⋊C4—1721no—
393C22⋊C4—1721no—
394C42—42no—
395C42—1721no—
396C42—1721no—
397C23—22no—
398C23—22no—
399C23—22no—
400C23—22no—
401C23—22no—
402C23—41no—
403C23—42no—
404C23—41no—
405C23—41no—
406C23—42no—
407C23—41no—
408C23—41no—
409C23—41no—
410C23—42no—
411C23—41no—
412C23—42no—
413C23—42no—
414C23—41no—
415C23—42no—
416C23—81no—
417C23—81no—
418C23—88no—
419C23#1306329311yescharacteristic
420C23#1306329411yescharacteristic
421C23#1306329711yescharacteristic
422D4—42no—
423D4—81no—
424D4—88no—
425D4—82no—
426D4—82no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—24no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—41no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—81no—
443C2×C4—1722no—
444C2×C4—1722no—
445C2×C4—1722no—
446C2×C4—1721no—
447C2×C4—1721no—
448C2×C4—1722no—
449C2×C4—1722no—
450C2×C4#1306329311yescharacteristic
451C2×C4#1306329611yescharacteristic
452C2×C4#1306329711yescharacteristic
453C2×C4#1306332111yescharacteristic
454C8—3441no—
455C8—1722no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—44no—
464C22—44no—
465C22—44no—
466C22—42no—
467C22—82no—
468C22—82no—
469C22—82no—
470C22—82no—
471C22—82no—
472C22—82no—
473C22—81no—
474C22—81no—
475C22—81no—
476C22—81no—
477C22—81no—
478C22#1458280711yescharacteristic
479C22#1458306612yes—
480C22#1458308912yes—
481C4—21no—
482C4—21no—
483C4—21no—
484C4—21no—
485C4—44no—
486C4—81no—
487C4—81no—
488C4—3442no—
489C4—3441no—
490C4—3441no—
491C2—22no—
492C2—22no—
493C2—41no—
494C2—82no—
495C2—161no—
496C2#1913561011yescharacteristic
497C2#1913566011yescharacteristic
498C2#1913572411yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
Fitting, prime radicalC43×#2539C2
socleC22×C43#392
hypercenter#2539D43
hypocenterC43#9940
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2539

Complements

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

NH ≅ G/Ntype
1. #19144531C2semidirect
2. #19138869C2semidirect
3. #19134695C2semidirect
4. #19133124C2semidirect
5. #19132922C2semidirect
6. #19132448C2semidirect
39. C2×C4⋊Dic43D4semidirect
40. C2×C4⋊Dic43D4semidirect
54. C22⋊(C43⋊C8)D4semidirect
57. C43⋊#95D4semidirect
282. C43#9940semidirect

Maximal subgroups

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

subgroupindex
#191445312
#191388692
#191346952
#191331242
#191329222
#191324482
C43×#25392
#994043