Finite Group Databasebeta

← #25070635

Subgroups — #25070635

Order 11008.

1188 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147928C211yesmaximal, characteristic
2#19145716C212yesmaximal, complemented
3#19133597C214yesmaximal, complemented
4#19133580C214yesmaximal, complemented
5#19133154C212yesmaximal, complemented
6#19132909C211yesmaximal, characteristic, complemented
7C43×#2621C211yesmaximal, characteristic, complemented
8C22×#10621898—21no—
9#14583480—21no—
10#14583480C2212yes—
11#14583475—22no—
12#14583468—22no—
13#14583461—21no—
14#14583461C2212yes—
15#14583449—21no—
16#14583449C2212yes—
17#14583411—24no—
18#14583302—22no—
19#14583247—22no—
20#14583212C2218yescomplemented
21#14583176—24no—
22#14582952C2212yescomplemented
23#14582632C2218yescomplemented
24#14582625C2212yescomplemented
25#14582623C2212yes—
26C2×C4⋊Q8×C43C2211yescharacteristic, complemented
27C2×C22⋊Q8×C43—21no—
28C2×#117×C43C2211yescharacteristic
29C43×#398—21no—
30C43×#398C2212yescomplemented
31C43×#397—21no—
32C43×#397C2212yes—
33C43×#391—21no—
34C43×#382C2211yescharacteristic, complemented
35C2×#10621898—22no—
36C2×#10621898—22no—
37C2×#10621898—22no—
38C2×#10621898—22no—
39C2×#10621898—44no—
40C2×#10621898—44no—
41C22×Dic86—21no—
42C22×D172—21no—
43C22×C22⋊D43—22no—
44C22×C4×D43—22no—
45#13063325—21no—
46#13063325D412yes—
47#13063322—21no—
48#13063322D412yes—
49#13063313—22no—
50#13063313—22no—
51#13063309—24no—
52#13063309—24no—
53#13063305—24no—
54#13063305—24no—
55#13063300—24no—
56#13063300—24no—
57#13063299—22no—
58#13063299—22no—
59#13063299—22no—
60#13063299C2314yes—
61#13063295—24no—
62#13063295—24no—
63C4×D172—22no—
64C4×D172—22no—
65C4×D172—22no—
66C4×D172D414yes—
67#13063258—28no—
68C4⋊(C43⋊C8)—22no—
69#13063245—28no—
70C22⋊(C43⋊C8)C2314yes—
71C4×C43⋊C8—22no—
72C22×Q8×C43—21no—
73C23×C4×C43D411yescharacteristic
74C4⋊Q8×C43—22no—
75C4⋊Q8×C43—22no—
76C22⋊Q8×C43—44no—
77#117×C43—22no—
78#117×C43—22no—
79C2×C4⋊C4×C43—21no—
80C2×C4⋊C4×C43—22no—
81C2×C4⋊C4×C43—21no—
82C2×C4⋊C4×C43D411yescharacteristic
83C2×C4⋊C4×C43C2312yes—
84C2×C4⋊C4×C43C2311yescharacteristic
85C2×C22⋊C4×C43—22no—
86C2×C22⋊C4×C43D411yescharacteristic
87C2×C22⋊C4×C43C2311yescharacteristic
88C2×C42×C43D411yescharacteristic
89C2×C42×C43C2311yescharacteristic
90#95×C43—21no—
91#95×C43—22no—
92#95×C43—22no—
93#95×C43C2312yes—
94C24×C43C2×D411yescharacteristic
95C23×D43—22no—
96C2×Q8×C43—41no—
97C2×Q8×C43—41no—
98C2×Q8×C43—42no—
99C2×Q8×C43—42no—
100C22×C4×C43—21no—
101C22×C4×C43—21no—
102C22×C4×C43—22no—
103C22×C4×C43—22no—
104C22×C4×C43—22no—
105C22×C4×C43D814yes—
106C22×C4×C43C2×D411yescharacteristic
107C22×C4×C43C2×D411yescharacteristic
108C22×C4×C43C2×D411yescharacteristic
109C22×C4×C43C2×D411yescharacteristic
110C22×C4×C43C2×D411yescharacteristic
111C22×C4×C43C2411yescharacteristic
112C2×C22⋊D43—24no—
113C2×C22⋊D43—24no—
114C2×C22⋊D43—44no—
115C2×C22⋊D43—44no—
116C22×Dic43—22no—
117#10621898—44no—
118#10621898—48no—
119#10621898—48no—
120#10621898—44no—
121#10621898—44no—
122#10621898—44no—
123C2×D172—22no—
124C2×D172—22no—
125C2×D172—22no—
126C2×D172—22no—
127C2×D172—22no—
128C2×D172—44no—
129C2×D172C2×D414yes—
130C2×C4×D43—24no—
131C2×C4×D43—24no—
132C2×C4×D43—48no—
133C2×Dic86—22no—
134C2×Dic86—22no—
135C2×Dic86—44no—
136C4⋊C4×C43—22no—
137C4⋊C4×C43—22no—
138C4⋊C4×C43—24no—
139C4⋊C4×C43—42no—
140C4⋊C4×C43—42no—
141C4⋊C4×C43—44no—
142C22⋊C4×C43—22no—
143C22⋊C4×C43—22no—
144C22⋊C4×C43—44no—
145C42×C43—21no—
146C42×C43—21no—
147C42×C43C2×D412yes—
148C42×C43C2×D412yes—
149(C2×D43)⋊C4—24no—
150(C2×D43)⋊C4—24no—
151(C2×D43)⋊C4—24no—
152(C2×D43)⋊C4—24no—
153C4⋊Dic43—22no—
154C4⋊Dic43—22no—
155C4⋊Dic43—22no—
156C4⋊Dic43C2×D414yes—
157C2×C43⋊C8—24no—
158C23×C43—21no—
159C23×C43—21no—
160C23×C43—41no—
161C23×C43—41no—
162C23×C43C2×D812yes—
163C23×C43C22×D411yescharacteristic
164C22×D43—24no—
165C22×D43—44no—
166C22×D43—82no—
167C22×D43—82no—
168Q8×C43—82no—
169Q8×C43—82no—
170C2×C4×C43—21no—
171C2×C4×C43—21no—
172C2×C4×C43—24no—
173C2×C4×C43—24no—
174C2×C4×C43—21no—
175C2×C4×C43—21no—
176C2×C4×C43—41no—
177C2×C4×C43—41no—
178C2×C4×C43—41no—
179C2×C4×C43—41no—
180C2×C4×C43—42no—
181C2×C4×C43—42no—
182C2×C4×C43—42no—
183C2×C4×C43—42no—
184C2×C4×C43—42no—
185C2×C4×C43—42no—
186C2×C4×C43#12012yes—
187C2×C4×C43#12011yescharacteristic
188C2×C4×C43#12011yescharacteristic
189C2×C4×C43C2×D812yes—
190C2×C4×C43C2×D812yes—
191C2×C4×C43AGL(1,ℤ/8)12yes—
192C2×C4×C43C22×D412yes—
193C22⋊D43—48no—
194C22⋊D43—44no—
195C22⋊D43—44no—
196C2×Dic43—24no—
197C2×Dic43—44no—
198D172—44no—
199D172—44no—
200D172—44no—
201D172—82no—
202D172—82no—
203D172—82no—
204C4×D43—48no—
205C4×D43—48no—
206Dic86—44no—
207Dic86—44no—
208C43⋊C8—44no—
209#18308—431nomaximal, Sylow
210C22×C43—21no—
211C22×C43—21no—
212C22×C43—22no—
213C22×C43—42no—
214C22×C43—41no—
215C22×C43—41no—
216C22×C43—81no—
217C22×C43C2×#12011yescharacteristic
218C22×C43C22×D811yescharacteristic
219C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
220C2×D43—44no—
221C2×D43—44no—
222C2×D43—44no—
223C2×D43—88no—
224C4×C43—22no—
225C4×C43—22no—
226C4×C43—22no—
227C4×C43—41no—
228C4×C43—41no—
229C4×C43—82no—
230C4×C43—82no—
231C4×C43#44712yes—
232C4×C43#44712yes—
233Dic43—44no—
234#3449—431no—
235#3226—432no—
236#2621D4311yescharacteristic, complemented
237#1610—434no—
238#1607—434no—
239#1517—432no—
240#1458—431no—
241C2×C43—21no—
242C2×C43—21no—
243C2×C43—42no—
244C2×C43C2×#44711yescharacteristic
245C2×C43#302211yescharacteristic
246C2×C43#302811yescharacteristic
247D43—84no—
248C22×#41—861no—
249#537—432no—
250#537—861no—
251#536—862no—
252#535—862no—
253#534—432no—
254#534—861no—
255#532—432no—
256#532—861no—
257C2×C4⋊Q8C2×D4311yescharacteristic, complemented
258#525—864no—
259C2×C22⋊Q8—21no—
260C2×#117C2×D4311yescharacteristic
261#500—862no—
262#486—862no—
263#480—438no—
264#474—864no—
265#431—432no—
266#398—21no—
267#398C2×D4312yescomplemented
268#397—21no—
269#397C2×D4312yes—
270#391—21no—
271#382C2×D4311yescharacteristic, complemented
272#327—438no—
273#324—432no—
274#323—432no—
275C43#1830811yescharacteristic, complemented, Sylow
276C2×#41—862no—
277C2×#41—862no—
278C2×#41—862no—
279C2×#41—862no—
280C2×#41—1724no—
281C2×#41—1724no—
282C22×Q8—21no—
283C22×Q8—861no—
284C22×D4—861no—
285C22×D4—862no—
286C23×C4—862no—
287C23×C4C22⋊D4311yescharacteristic
288C4⋊Q8—22no—
289C4⋊Q8—22no—
290C4⋊Q8—432no—
291C4⋊Q8—861no—
292#127—432no—
293#127—861no—
294#124—862no—
295#124—862no—
296#123—864no—
297#123—864no—
298C22⋊Q8—44no—
299C22⋊Q8—864no—
300C22⋊Q8—864no—
301#121—434no—
302#121—864no—
303#121—864no—
304#121—862no—
305#121—862no—
306#121—862no—
307#120—864no—
308#120—864no—
309C4×D4—434no—
310C4×D4—862no—
311C4×D4—862no—
312C4×D4—862no—
313#117—22no—
314#117—22no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4C22⋊D4311yescharacteristic
319C2×C4⋊C4C22×D4312yes—
320C2×C4⋊C4C22×D4311yescharacteristic
321C2×C22⋊C4—22no—
322C2×C22⋊C4C22⋊D4311yescharacteristic
323C2×C22⋊C4C22×D4311yescharacteristic
324C2×C42C22⋊D4311yescharacteristic
325C2×C42C22×D4311yescharacteristic
326#107—868no—
327C4⋊C8—862no—
328#102—868no—
329C22⋊C8—434no—
330C4×C8—862no—
331#95—21no—
332#95—22no—
333#95—22no—
334#95C22×D4312yes—
335C24—862no—
336C24C2×C22⋊D4311yescharacteristic
337#41—1724no—
338#41—1728no—
339#41—1728no—
340#41—1724no—
341#41—1724no—
342#41—1724no—
343C2×Q8—41no—
344C2×Q8—41no—
345C2×Q8—42no—
346C2×Q8—42no—
347C2×Q8—862no—
348C2×Q8—862no—
349C2×Q8—1724no—
350C2×D4—434no—
351C2×D4—862no—
352C2×D4—862no—
353C2×D4—862no—
354C2×D4—864no—
355C2×D4—864no—
356C2×D4—862no—
357C2×D4—862no—
358C2×D4—1724no—
359C2×D4—1724no—
360C2×D4—1724no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—864no—
367C22×C4—862no—
368C22×C4—864no—
369C22×C4—1728no—
370C22×C4#1062188214yes—
371C22×C4C2×C22⋊D4311yescharacteristic
372C22×C4C2×C22⋊D4311yescharacteristic
373C22×C4C2×C22⋊D4311yescharacteristic
374C22×C4C2×C22⋊D4311yescharacteristic
375C22×C4C2×C22⋊D4311yescharacteristic
376C22×C4C23×D4311yescharacteristic
377C2×C8—864no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—24no—
381C4⋊C4—42no—
382C4⋊C4—42no—
383C4⋊C4—44no—
384C4⋊C4—434no—
385C4⋊C4—862no—
386C4⋊C4—862no—
387C4⋊C4—862no—
388C22⋊C4—22no—
389C22⋊C4—22no—
390C22⋊C4—44no—
391C22⋊C4—864no—
392C22⋊C4—864no—
393C22⋊C4—864no—
394C22⋊C4—864no—
395C42—21no—
396C42—21no—
397C42D4×D4312yes—
398C42D4×D4312yes—
399C23—21no—
400C23—21no—
401C23—41no—
402C23—41no—
403C23—864no—
404C23—3442no—
405C23—3442no—
406C23—1724no—
407C23C2×#1062188212yes—
408C23C22×C22⋊D4311yescharacteristic
409Q8—82no—
410Q8—82no—
411Q8—1724no—
412Q8—1724no—
413D4—3442no—
414D4—3442no—
415D4—3442no—
416D4—1724no—
417D4—1724no—
418D4—1728no—
419D4—1724no—
420D4—1724no—
421D4—1724no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—24no—
425C2×C4—24no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—864no—
439C2×C4—1728no—
440C2×C4—1724no—
441C2×C4—1728no—
442C2×C4#1306329312yes—
443C2×C4#1306329311yescharacteristic
444C2×C4#1306329311yescharacteristic
445C2×C4C2×#1062188212yes—
446C2×C4C2×#1062188212yes—
447C2×C4#1306335012yes—
448C2×C4C2×D4×D4312yes—
449C8—1724no—
450C22—21no—
451C22—21no—
452C22—22no—
453C22—42no—
454C22—41no—
455C22—41no—
456C22—81no—
457C22—3448no—
458C22—1724no—
459C22—1724no—
460C22—1724no—
461C22C2×#1306329311yescharacteristic
462C22C22×#1062188211yescharacteristic
463C22C2×#1306335011yescharacteristic
464C4—22no—
465C4—22no—
466C4—22no—
467C4—41no—
468C4—41no—
469C4—82no—
470C4—82no—
471C4—1724no—
472C4#1458303212yes—
473C4#1458303212yes—
474C2—21no—
475C2—21no—
476C2—42no—
477C2—3444no—
478C2C2×#1458303211yescharacteristic
479C2#1914397311yescharacteristic
480C2#1914400011yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2621C2
socleC22×C43C2×#120
prime radical#19147928C2
hypercenter#2621D43
hypocenterC43#18308
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2621

Complements

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

NH ≅ G/Ntype
2. #19145716C2semidirect
3. #19133597C2semidirect
4. #19133580C2semidirect
5. #19133154C2semidirect
6. #19132909C2semidirect
7. C43×#2621C2semidirect
20. #14583212C22semidirect
22. #14582952C22semidirect
23. #14582632C22semidirect
24. #14582625C22semidirect
26. C2×C4⋊Q8×C43C22semidirect
30. C43×#398C22semidirect
34. C43×#382C22semidirect
236. #2621D43semidirect
257. C2×C4⋊Q8C2×D43semidirect
267. #398C2×D43semidirect
271. #382C2×D43semidirect
275. C43#18308semidirect

Maximal subgroups

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

subgroupindex
#191479282
#191457162
#191335972
#191335802
#191331542
#191329092
C43×#26212
#1830843