Finite Group Databasebeta

← #24993050

Subgroups — #24993050

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×#14583213C211yesmaximal, characteristic
2#19137462C211yesmaximal, characteristic, complemented
3#19135431C211yesmaximal, characteristic
4#19134682C211yesmaximal, characteristic, complemented
5#19133164C211yesmaximal, characteristic
6#19132463C211yesmaximal, characteristic, complemented
7C43×#1282C211yesmaximal, characteristic, complemented
8C2×#13063299C2211yescharacteristic
9C2×#13063281—21no—
10C22×C4⋊Dic43C2211yescharacteristic
11#14583213—21no—
12#14583213—22no—
13#14583213—21no—
14C2×#13063259C412yescomplemented
15C2×#13063247C412yescomplemented
16C2×#13063239—21no—
17C2×#13063239—21no—
18#14582797—21no—
19#14582784—22no—
20#14582760—21no—
21#14582759C2211yescharacteristic
22#14582759C2211yescharacteristic
23C4×C4⋊Dic43—21no—
24#14582662—22no—
25#14582634—22no—
26C2×C22⋊C8×C43C2211yescharacteristic
27C2×C22⋊C8×C43C2211yescharacteristic
28C4×C22⋊C4×C43C2211yescharacteristic
29C22×D172C2×C411yescharacteristic
30C22×C22⋊D43—21no—
31C23×Dic43—21no—
32#13063299—21no—
33#13063299—21no—
34#13063299—21no—
35#13063299—21no—
36#13063281—42no—
37#13063281—42no—
38C2×C4⋊Dic43—21no—
39C2×C4⋊Dic43—21no—
40C2×C4⋊Dic43—21no—
41C2×C4⋊Dic43—21no—
42C2×C4⋊Dic43—21no—
43C2×C4⋊Dic43C2×C411yescharacteristic
44C2×C4⋊Dic43C2×C412yes—
45C2×C4⋊Dic43D411yescharacteristic
46C2×C4⋊Dic43D412yes—
47C2×C4⋊Dic43D411yescharacteristic
48C2×Dic43⋊C4—22no—
49C2×C22⋊Dic43—21no—
50C2×C22⋊Dic43—21no—
51C2×(C2×D43)⋊C4—21no—
52C2×C4×Dic43—22no—
53#13063259—22no—
54#13063259—22no—
55#13063247—22no—
56#13063247—22no—
57#13063239—42no—
58#13063239—42no—
59C43⋊#95—22no—
60C43⋊#95—22no—
61C43⋊#95—21no—
62C43⋊#95D412yes—
63C23×C4×C43C2311yescharacteristic
64C22×C8×C43—21no—
65C22×C8×C43C2×C412yes—
66C2×C22⋊C4×C43D411yescharacteristic
67C2×C22⋊C4×C43D411yescharacteristic
68C2×C42×C43—21no—
69C22⋊C8×C43—21no—
70C22⋊C8×C43—21no—
71C22⋊C8×C43—21no—
72C22⋊C8×C43—21no—
73#95×C43—21no—
74C24×C43C2×D411yescharacteristic
75C23×D43—21no—
76C22×C4×C43—21no—
77C22×C4×C43—21no—
78C22×C4×C43—42no—
79C22×C4×C43C22×C411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43C2×D411yescharacteristic
83C22×C4×C43#4111yescharacteristic
84C22×C4×C43#4111yescharacteristic
85C2×C22⋊D43—41no—
86C2×C22⋊D43—41no—
87C2×C22⋊D43—41no—
88C2×C22⋊D43—41no—
89C2×C22⋊D43—41no—
90C2×C22⋊D43—41no—
91C22×Dic43—22no—
92C22×Dic43—21no—
93C22×Dic43—21no—
94C22×Dic43—21no—
95C22×Dic43—22no—
96C22×Dic43—22no—
97C22×Dic43—41no—
98C22×Dic43—41no—
99C22×Dic43—41no—
100C22×Dic43—41no—
101C22×Dic43—41no—
102C2×D172—21no—
103C2×D172—21no—
104C2×D172—42no—
105C2×C8×C43—22no—
106C2×C8×C43—42no—
107C2×C8×C43—42no—
108C2×C8×C43—41no—
109C22⋊C4×C43—21no—
110C22⋊C4×C43—21no—
111C22⋊C4×C43—21no—
112C22⋊C4×C43D812yes—
113C42×C43—42no—
114C22⋊Dic43—41no—
115C22⋊Dic43—41no—
116C22⋊Dic43—41no—
117C22⋊Dic43—41no—
118(C2×D43)⋊C4—41no—
119(C2×D43)⋊C4—41no—
120C4⋊Dic43—22no—
121C4⋊Dic43—22no—
122C4⋊Dic43—21no—
123C4⋊Dic43—21no—
124C4⋊Dic43—21no—
125C4⋊Dic43—21no—
126C4⋊Dic43—42no—
127C4⋊Dic43—42no—
128C4⋊Dic43C22⋊C412yes—
129C4⋊Dic43C22⋊C412yes—
130Dic43⋊C4—44no—
131C4×Dic43—44no—
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—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×C43C2×C22⋊C411yescharacteristic
159C2×C4×C43C4×D411yescharacteristic
160C2×C4×C43#12111yescharacteristic
161C2×C4×C43#12311yescharacteristic
162C22⋊D43—81no—
163C22⋊D43—81no—
164C22⋊D43—81no—
165C22⋊D43—81no—
166C2×Dic43—22no—
167C2×Dic43—22no—
168C2×Dic43—42no—
169C2×Dic43—42no—
170C2×Dic43—41no—
171C2×Dic43—41no—
172C2×Dic43—41no—
173C2×Dic43—41no—
174C2×Dic43—42no—
175C2×Dic43—42no—
176C2×Dic43—42no—
177C2×Dic43—42no—
178C2×Dic43—41no—
179C2×Dic43—41no—
180C2×Dic43—41no—
181C2×Dic43—42no—
182C2×Dic43—81no—
183C2×Dic43—81no—
184C2×Dic43—81no—
185D172—42no—
186D172—81no—
187C8×C43—42no—
188C8×C43—81no—
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—81no—
217C4×C43#41012yes—
218Dic43—42no—
219Dic43—42no—
220Dic43—82no—
221Dic43—81no—
222Dic43—161no—
223C2×#480—431no—
224#2344—431no—
225#1964—431no—
226#1823—431no—
227#1519—431no—
228#1289—431no—
229#1282D4311yescharacteristic, complemented
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⋊C4—431no—
243#480—862no—
244#480—861no—
245#480—861no—
246C2×#107—432no—
247C2×#102—432no—
248C2×#99—861no—
249C2×#99—861no—
250C2×C22⋊C8C2×D4311yescharacteristic
251C2×C22⋊C8C2×D4311yescharacteristic
252#389—861no—
253#387—862no—
254#381—861no—
255#380—431no—
256#380—431no—
257C4×C4⋊C4—861no—
258C4×C22⋊C4C2×D4311yescharacteristic
259#340—862no—
260#327—862no—
261C43#926011yescharacteristic, complemented, Sylow
262C22×D4—431no—
263C22×D4—861no—
264C23×C4—861no—
265C23×C4C22×D4311yescharacteristic
266C22×C8—21no—
267C22×C8C4×D4312yes—
268#121—861no—
269#121—861no—
270#121—861no—
271#121—861no—
272#117—1722no—
273#117—1722no—
274C2×C4⋊C4—432no—
275C2×C4⋊C4—432no—
276C2×C4⋊C4—431no—
277C2×C4⋊C4—431no—
278C2×C4⋊C4—431no—
279C2×C4⋊C4—861no—
280C2×C4⋊C4—861no—
281C2×C4⋊C4—861no—
282C2×C4⋊C4—862no—
283C2×C4⋊C4—861no—
284C2×C4⋊C4—861no—
285C2×C22⋊C4—861no—
286C2×C22⋊C4—861no—
287C2×C22⋊C4—861no—
288C2×C22⋊C4D17211yescharacteristic
289C2×C22⋊C4D17211yescharacteristic
290C2×C42—21no—
291C2×C42—862no—
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—21no—
301C22⋊C8—21no—
302#95—21no—
303#95—432no—
304#95—862no—
305#95—862no—
306#95—861no—
307C24—861no—
308C24C2×D17211yescharacteristic
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—21no—
319C22×C4—21no—
320C22×C4—42no—
321C22×C4—862no—
322C22×C4—861no—
323C22×C4—861no—
324C22×C4—862no—
325C22×C4—861no—
326C22×C4—862no—
327C22×C4—1721no—
328C22×C4—1721no—
329C22×C4—1721no—
330C22×C4—1721no—
331C22×C4—1721no—
332C22×C4C2×C4×D4311yescharacteristic
333C22×C4#1062189811yescharacteristic
334C22×C4D4×D4311yescharacteristic
335C22×C4D4×D4311yescharacteristic
336C22×C4D4×D4311yescharacteristic
337C22×C4#1062190211yescharacteristic
338C2×C8—22no—
339C2×C8—42no—
340C2×C8—42no—
341C2×C8—41no—
342C4⋊C4—432no—
343C4⋊C4—432no—
344C4⋊C4—862no—
345C4⋊C4—862no—
346C4⋊C4—861no—
347C4⋊C4—861no—
348C4⋊C4—861no—
349C4⋊C4—861no—
350C4⋊C4—1722no—
351C4⋊C4—1724no—
352C4⋊C4—1722no—
353C22⋊C4—21no—
354C22⋊C4—21no—
355C22⋊C4—21no—
356C22⋊C4—1721no—
357C22⋊C4—1721no—
358C22⋊C4—1721no—
359C22⋊C4—1721no—
360C22⋊C4—1721no—
361C22⋊C4—1721no—
362C22⋊C4D34412yes—
363C42—42no—
364C42—1724no—
365C23—41no—
366C23—41no—
367C23—3441no—
368C23—3441no—
369C23—1721no—
370C23—1721no—
371C23—1721no—
372C23C4×D17211yescharacteristic
373C23#1306329511yescharacteristic
374C23#1306330011yescharacteristic
375C23C2×D34411yescharacteristic
376C23#1306334711yescharacteristic
377C23#1306335311yescharacteristic
378C23#1306335311yescharacteristic
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—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—862no—
398C2×C4—862no—
399C2×C4—3441no—
400C2×C4—3441no—
401C2×C4—3441no—
402C2×C4—1722no—
403C2×C4—1722no—
404C2×C4—1721no—
405C2×C4—1721no—
406C2×C4—1721no—
407C2×C4—1722no—
408C2×C4—1721no—
409C2×C4—1721no—
410C2×C4—1722no—
411C2×C4—1722no—
412C2×C4—1722no—
413C2×C4—1722no—
414C2×C4—1721no—
415C2×C4—1721no—
416C2×C4C22⋊C4×D4311yescharacteristic
417C2×C4#1306328711yescharacteristic
418C2×C4#1306329811yescharacteristic
419C2×C4#1306331011yescharacteristic
420C8—42no—
421C8—81no—
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#1458277711yescharacteristic
438C22C4×D34411yescharacteristic
439C22#1458301211yescharacteristic
440C22#1458303511yescharacteristic
441C22#1458304611yescharacteristic
442C22#1458309511yescharacteristic
443C22#1458311511yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—42no—
448C4—81no—
449C4—3442no—
450C4—3441no—
451C4—1722no—
452C4—1722no—
453C4—6881no—
454C4#1458287112yes—
455C2—21no—
456C2—21no—
457C2—21no—
458C2—21no—
459C2—21no—
460C2—21no—
461C2—6881no—
462C2#1913494211yescharacteristic
463C2#1913505211yescharacteristic
464C2#1913508811yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1282C2
socleC22×C43#386
prime radicalC2×#13063299C22
cosocleC23×C4×C43C23
hypercenter#1282D43
hypocenterC43#9260
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1282

Complements

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

NH ≅ G/Ntype
2. #19137462C2semidirect
4. #19134682C2semidirect
6. #19132463C2semidirect
7. C43×#1282C2semidirect
14. C2×#13063259C4semidirect
15. C2×#13063247C4semidirect
229. #1282D43semidirect
261. C43#9260semidirect

Maximal subgroups

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

subgroupindex
C2×#145832132
#191374622
#191354312
#191346822
#191331642
#191324632
C43×#12822
#926043