Finite Group Databasebeta

← #24993049

Subgroups — #24993049

Order 11008.

594 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583212C211yesmaximal, characteristic
2#19137464C211yesmaximal, characteristic, complemented
3#19135430C211yesmaximal, characteristic
4#19133164C211yesmaximal, characteristic
5#19132462C211yesmaximal, characteristic, complemented
6#19132441C211yesmaximal, characteristic, complemented
7C43×#1823C211yesmaximal, characteristic, complemented
8C2×#13063299C2211yescharacteristic
9C2×#13063284—21no—
10#14583212—21no—
11#14583212—21no—
12#14583212—22no—
13C2×#13063258C412yescomplemented
14C2×#13063245C412yescomplemented
15C2×#13063239—21no—
16C2×#13063239—21no—
17C2×C22⋊(C43⋊C8)C2211yescharacteristic
18#14582798—21no—
19#14582785—22no—
20#14582762—21no—
21#14582759C2211yescharacteristic
22C4⋊C4×Dic43—21no—
23C4×C22⋊Dic43C2211yescharacteristic
24#14582634—22no—
25C22×C4⋊C4×C43C2211yescharacteristic
26C2×C22⋊C8×C43C2211yescharacteristic
27C43×#380C2211yescharacteristic
28C43×#340—22no—
29C22×D172C2×C411yescharacteristic
30C22×C22⋊D43—21no—
31C22×C43⋊C8C2×C412yes—
32#13063299—21no—
33#13063299—21no—
34#13063299—21no—
35#13063299—21no—
36#13063284—42no—
37#13063284—42no—
38C2×C4⋊Dic43—22no—
39C2×C4⋊Dic43—21no—
40C2×C4⋊Dic43C2×C411yescharacteristic
41C2×C22⋊Dic43—21no—
42C2×C22⋊Dic43D411yescharacteristic
43C2×C22⋊Dic43D411yescharacteristic
44C2×(C2×D43)⋊C4—21no—
45C2×C4×Dic43—22no—
46C2×C4×Dic43—21no—
47#13063258—22no—
48#13063258—22no—
49#13063245—22no—
50#13063245—22no—
51#13063239—42no—
52#13063239—42no—
53C22⋊(C43⋊C8)—21no—
54C22⋊(C43⋊C8)—21no—
55C43⋊#95—22no—
56C43⋊#95—22no—
57C43⋊#95—21no—
58C43⋊#95D412yes—
59C23×C4×C43—21no—
60C23×C4×C43C2311yescharacteristic
61C22×C8×C43—21no—
62C2×C4⋊C4×C43—21no—
63C2×C4⋊C4×C43—21no—
64C2×C4⋊C4×C43—21no—
65C2×C4⋊C4×C43—21no—
66C2×C4⋊C4×C43C2×C412yes—
67C2×C4⋊C4×C43D411yescharacteristic
68C2×C4⋊C4×C43D411yescharacteristic
69C2×C4⋊C4×C43D412yes—
70C2×C22⋊C4×C43—21no—
71C22⋊C8×C43—21no—
72C22⋊C8×C43—21no—
73#95×C43—21no—
74C24×C43C2×D411yescharacteristic
75C23×D43—21no—
76C22×C4×C43—22no—
77C22×C4×C43—21no—
78C22×C4×C43—21no—
79C22×C4×C43—22no—
80C22×C4×C43—42no—
81C22×C4×C43—41no—
82C22×C4×C43—41no—
83C22×C4×C43—41no—
84C22×C4×C43—41no—
85C22×C4×C43—41no—
86C22×C4×C43C22×C411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43#4111yescharacteristic
91C22×C4×C43#4111yescharacteristic
92C2×C22⋊D43—41no—
93C2×C22⋊D43—41no—
94C2×C22⋊D43—41no—
95C2×C22⋊D43—41no—
96C2×C22⋊D43—41no—
97C2×C22⋊D43—41no—
98C22×Dic43—21no—
99C22×Dic43—21no—
100C22×Dic43—21no—
101C22×Dic43—22no—
102C2×D172—21no—
103C2×D172—21no—
104C2×D172—42no—
105C2×C8×C43—42no—
106C2×C8×C43—41no—
107C4⋊C4×C43—22no—
108C4⋊C4×C43—22no—
109C4⋊C4×C43—21no—
110C4⋊C4×C43—21no—
111C4⋊C4×C43—42no—
112C4⋊C4×C43C22⋊C412yes—
113C4⋊C4×C43C22⋊C412yes—
114C22⋊C4×C43—41no—
115C22⋊C4×C43—41no—
116C22⋊Dic43—21no—
117C22⋊Dic43—21no—
118C22⋊Dic43—21no—
119C22⋊Dic43—41no—
120C22⋊Dic43—41no—
121C22⋊Dic43D812yes—
122(C2×D43)⋊C4—41no—
123(C2×D43)⋊C4—41no—
124C4⋊Dic43—21no—
125C4⋊Dic43—21no—
126C4⋊Dic43—44no—
127C4⋊Dic43—42no—
128C4×Dic43—44no—
129C4×Dic43—42no—
130C2×C43⋊C8—22no—
131C2×C43⋊C8—42no—
132C23×C43—41no—
133C23×C43—41no—
134C23×C43C4×D411yescharacteristic
135C23×C43#12011yescharacteristic
136C23×C43#12111yescharacteristic
137C23×C43C2×D811yescharacteristic
138C23×C43#13511yescharacteristic
139C23×C43AGL(1,ℤ/8)11yescharacteristic
140C23×C43AGL(1,ℤ/8)11yescharacteristic
141C22×D43—41no—
142C22×D43—41no—
143C22×D43—41no—
144C22×D43—81no—
145C22×D43—81no—
146C2×C4×C43—22no—
147C2×C4×C43—22no—
148C2×C4×C43—22no—
149C2×C4×C43—22no—
150C2×C4×C43—22no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—41no—
154C2×C4×C43—42no—
155C2×C4×C43—42no—
156C2×C4×C43—41no—
157C2×C4×C43—41no—
158C2×C4×C43—41no—
159C2×C4×C43—41no—
160C2×C4×C43—42no—
161C2×C4×C43—42no—
162C2×C4×C43—81no—
163C2×C4×C43—81no—
164C2×C4×C43—81no—
165C2×C4×C43C2×C22⋊C411yescharacteristic
166C2×C4×C43C4×D411yescharacteristic
167C2×C4×C43#12111yescharacteristic
168C2×C4×C43#12311yescharacteristic
169C22⋊D43—81no—
170C22⋊D43—81no—
171C22⋊D43—81no—
172C22⋊D43—81no—
173C2×Dic43—22no—
174C2×Dic43—41no—
175C2×Dic43—41no—
176C2×Dic43—41no—
177C2×Dic43—42no—
178C2×Dic43—41no—
179C2×Dic43—42no—
180C2×Dic43—41no—
181C2×Dic43—41no—
182C2×Dic43—41no—
183C2×Dic43—42no—
184C2×Dic43—41no—
185D172—42no—
186D172—81no—
187C8×C43—81no—
188C43⋊C8—42no—
189#9260—431nomaximal, Sylow
190C22×C43—21no—
191C22×C43—21no—
192C22×C43—21no—
193C22×C43—21no—
194C22×C43—21no—
195C22×C43—21no—
196C22×C43—41no—
197C22×C43—41no—
198C22×C43—41no—
199C22×C43—41no—
200C22×C43#38611yescharacteristic
201C22×C43C4×D811yescharacteristic
202C22×C43#44211yescharacteristic
203C22×C43#44711yescharacteristic
204C22×C43#44911yescharacteristic
205C22×C43#45911yescharacteristic
206C22×C43#46311yescharacteristic
207C2×D43—81no—
208C2×D43—81no—
209C2×D43—81no—
210C2×D43—161no—
211C2×D43—161no—
212C4×C43—21no—
213C4×C43—21no—
214C4×C43—21no—
215C4×C43—42no—
216C4×C43—42no—
217C4×C43—161no—
218C4×C43#41012yes—
219Dic43—42no—
220Dic43—82no—
221Dic43—81no—
222Dic43—81no—
223C2×#480—431no—
224#2344—431no—
225#1964—431no—
226#1823D4311yescharacteristic, complemented
227#1519—431no—
228#1289—431no—
229#1282—431no—
230C2×C43—21no—
231C2×C43—21no—
232C2×C43—21no—
233C2×C43—21no—
234C2×C43—21no—
235C2×C43—21no—
236C2×C43#187911yescharacteristic
237C2×C43#189911yescharacteristic
238C2×C43#190511yescharacteristic
239D43—161no—
240C2×#121—431no—
241C2×#117—861no—
242C22×C4⋊C4C2×D4311yescharacteristic
243#480—861no—
244#480—861no—
245#480—862no—
246C2×#107—432no—
247C2×#102—432no—
248C2×#99—861no—
249C2×#99—861no—
250C2×C22⋊C8—431no—
251C2×C22⋊C8C2×D4311yescharacteristic
252#389—861no—
253#387—862no—
254#381—861no—
255#380—431no—
256#380C2×D4311yescharacteristic
257C4×C4⋊C4—861no—
258C4×C22⋊C4—431no—
259#340—22no—
260#327—862no—
261C43#926011yescharacteristic, complemented, Sylow
262C22×D4—431no—
263C22×D4—861no—
264C23×C4—21no—
265C23×C4C22×D4311yescharacteristic
266C22×C8—21no—
267C22×C8—432no—
268#121—861no—
269#121—861no—
270#121—861no—
271#121—861no—
272#117—1722no—
273#117—1722no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—431no—
279C2×C4⋊C4—862no—
280C2×C4⋊C4—861no—
281C2×C4⋊C4C4×D4312yes—
282C2×C4⋊C4D17211yescharacteristic
283C2×C4⋊C4D17211yescharacteristic
284C2×C4⋊C4C22⋊D4312yes—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—431no—
287C2×C22⋊C4—431no—
288C2×C22⋊C4—861no—
289C2×C22⋊C4—861no—
290C2×C42—862no—
291C2×C42—861no—
292#107—862no—
293#107—862no—
294#102—862no—
295#102—862no—
296#99—1722no—
297#99—1722no—
298C22⋊C8—21no—
299C22⋊C8—21no—
300C22⋊C8—861no—
301C22⋊C8—861no—
302#95—21no—
303#95—432no—
304#95—862no—
305#95—862no—
306#95—861no—
307C24—861no—
308C24D4×D4311yescharacteristic
309C2×D4—861no—
310C2×D4—861no—
311C2×D4—1722no—
312C2×D4—1721no—
313C2×D4—1721no—
314C2×D4—1721no—
315C2×D4—1721no—
316C2×D4—1721no—
317C2×D4—1721no—
318C22×C4—22no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—22no—
322C22×C4—42no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—861no—
329C22×C4—861no—
330C22×C4—862no—
331C22×C4—861no—
332C22×C4C2×C4×D4311yescharacteristic
333C22×C4C2×D17211yescharacteristic
334C22×C4D4×D4311yescharacteristic
335C22×C4#1062190011yescharacteristic
336C22×C4#1062190011yescharacteristic
337C22×C4C2×C22⋊D4311yescharacteristic
338C2×C8—42no—
339C2×C8—41no—
340C2×C8—862no—
341C2×C8—1722no—
342C4⋊C4—22no—
343C4⋊C4—22no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—42no—
347C4⋊C4—861no—
348C4⋊C4—861no—
349C4⋊C4—1722no—
350C4⋊C4—1724no—
351C4⋊C4(C2×D43)⋊C412yes—
352C4⋊C4(C2×D43)⋊C412yes—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—432no—
356C22⋊C4—861no—
357C22⋊C4—861no—
358C22⋊C4—861no—
359C22⋊C4—1721no—
360C22⋊C4—1721no—
361C22⋊C4—1721no—
362C22⋊C4—1721no—
363C42—1722no—
364C42—1724no—
365C23—41no—
366C23—41no—
367C23—3441no—
368C23—3441no—
369C23—1721no—
370C23—1721no—
371C23—1721no—
372C23(C22⋊D43)⋊C411yescharacteristic
373C23#1306329511yescharacteristic
374C23#1306329711yescharacteristic
375C23D8×D4311yescharacteristic
376C23#1306334611yescharacteristic
377C23#1306334911yescharacteristic
378C23#1306335211yescharacteristic
379D4—3441no—
380D4—3441no—
381D4—3441no—
382D4—3441no—
383D4—3441no—
384D4—1722no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4—862no—
405C2×C4—1721no—
406C2×C4—1722no—
407C2×C4—1722no—
408C2×C4—1721no—
409C2×C4—1721no—
410C2×C4—1721no—
411C2×C4—1721no—
412C2×C4—1721no—
413C2×C4—1722no—
414C2×C4—1721no—
415C2×C4—1721no—
416C2×C4C2×(C2×D43)⋊C411yescharacteristic
417C2×C4(C22⋊D43)⋊C411yescharacteristic
418C2×C4#1306329711yescharacteristic
419C2×C4#1306330911yescharacteristic
420C8—81no—
421C8—1722no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—3441no—
433C22—3441no—
434C22—3441no—
435C22—6881no—
436C22—6881no—
437C22#1458277611yescharacteristic
438C22#1458297911yescharacteristic
439C22#1458300811yescharacteristic
440C22#1458303411yescharacteristic
441C22#1458304511yescharacteristic
442C22#1458309211yescharacteristic
443C22#1458311611yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—42no—
448C4—42no—
449C4—161no—
450C4—3442no—
451C4—3441no—
452C4—3441no—
453C4—1722no—
454C4#1458287212yes—
455C2—21no—
456C2—21no—
457C2—21no—
458C2—21no—
459C2—21no—
460C2—21no—
461C2—6881no—
462C2#1913494111yescharacteristic
463C2#1913505111yescharacteristic
464C2#1913508711yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1823C2
socleC22×C43#386
prime radicalC2×#13063299C22
cosocleC23×C4×C43C23
hypercenter#1823D43
hypocenterC43#9260
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
2. #19137464C2semidirect
5. #19132462C2semidirect
6. #19132441C2semidirect
7. C43×#1823C2semidirect
13. C2×#13063258C4semidirect
14. C2×#13063245C4semidirect
226. #1823D43semidirect
261. C43#9260semidirect

Maximal subgroups

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

subgroupindex
C2×#145832122
#191374642
#191354302
#191331642
#191324622
#191324412
C43×#18232
#926043