Finite Group Databasebeta

← #24992216

Subgroups — #24992216

Order 11008.

600 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582954C211yesmaximal, characteristic, complemented
2#19142897C211yesmaximal, characteristic
3#19134358C211yesmaximal, characteristic, complemented
4C2×#14582638C211yesmaximal, characteristic, complemented
5C2×#14582638C211yesmaximal, characteristic, complemented
6#19132476C211yesmaximal, characteristic, complemented
7C43×#1295C211yesmaximal, characteristic, complemented
8C2×#13063313C2211yescharacteristic
9C2×#13063305C411yescharacteristic
10C2×#13063300C411yescharacteristic
11C2×C42×D43C2211yescharacteristic
12#14582954—22no—
13#14582954—22no—
14C2×Dic43⋊C8—21no—
15C2×(C2×D43)⋊C8—21no—
16C2×(C2×D43)⋊C8—21no—
17C2×#13063236C2211yescharacteristic
18C2×#13063236C2211yescharacteristic
19#14582804C411yescharacteristic
20#14582800C411yescharacteristic
21#14582791—21no—
22#14582791—21no—
23#14582777—21no—
24#14582777—21no—
25#14582653—21no—
26#14582638—22no—
27#14582638—22no—
28C2×#97×C43C2211yescharacteristic
29C2×#97×C43C2211yescharacteristic
30C43×#382C2211yescharacteristic
31C22×Dic86C2×C411yescharacteristic
32C22×D172—21no—
33C22×D172C2×C411yescharacteristic
34C22×C4×D43C2×C411yescharacteristic
35C22×C4×D43D411yescharacteristic
36C22×C4×D43D411yescharacteristic
37C22×C43⋊C8—21no—
38C22×C43⋊C8—21no—
39#13063313—21no—
40#13063313—21no—
41#13063313—21no—
42#13063313—21no—
43#13063305—42no—
44#13063300—42no—
45C2×C4⋊Dic43—21no—
46C2×(C2×D43)⋊C4—21no—
47C2×(C2×D43)⋊C4—21no—
48C2×(C2×D43)⋊C4—21no—
49C2×(C2×D43)⋊C4—21no—
50C2×(C2×D43)⋊C4—21no—
51C2×(C2×D43)⋊C4—21no—
52C2×C4×Dic43C2×C411yescharacteristic
53C2×C4×Dic43D411yescharacteristic
54C2×C4×Dic43D411yescharacteristic
55C42×D43—21no—
56C42×D43—21no—
57C42×D43—21no—
58C42×D43—21no—
59Dic43⋊C8—24no—
60(C2×D43)⋊C8—24no—
61(C2×D43)⋊C8—24no—
62#13063236—21no—
63#13063236—21no—
64#13063236—21no—
65#13063236D412yescomplemented
66C43⋊#95—21no—
67C43⋊#95—21no—
68C22×C8×C43—21no—
69C22×C8×C43—21no—
70C2×C4⋊C4×C43C2×C411yescharacteristic
71C2×C4⋊C4×C43C2×C411yescharacteristic
72C2×C42×C43C2311yescharacteristic
73#97×C43—21no—
74#97×C43—21no—
75#97×C43—21no—
76#97×C43D412yescomplemented
77#95×C43—21no—
78#95×C43—21no—
79C23×D43—21no—
80C23×D43C22⋊C411yescharacteristic
81C22×C4×C43—21no—
82C22×C4×C43—21no—
83C22×C4×C43C22×C411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43C2×D411yescharacteristic
86C22×Dic43—21no—
87C22×Dic43C22⋊C411yescharacteristic
88C22×Dic43C22⋊C411yescharacteristic
89C22×Dic43C22⋊C411yescharacteristic
90C2×D172—21no—
91C2×D172—21no—
92C2×D172—42no—
93C2×D172—42no—
94C2×D172—42no—
95C2×D172—41no—
96C2×D172—41no—
97C2×C4×D43—21no—
98C2×C4×D43—21no—
99C2×C4×D43—21no—
100C2×C4×D43—21no—
101C2×C4×D43—21no—
102C2×C4×D43—21no—
103C2×C4×D43—22no—
104C2×C4×D43—22no—
105C2×C4×D43—41no—
106C2×C4×D43—41no—
107C2×C4×D43—41no—
108C2×C4×D43—41no—
109C2×Dic86—21no—
110C2×Dic86—21no—
111C2×Dic86—41no—
112C2×Dic86—41no—
113C2×C8×C43—22no—
114C2×C8×C43—22no—
115C2×C8×C43—41no—
116C2×C8×C43—41no—
117C2×C8×C43—41no—
118C2×C8×C43—41no—
119C4⋊C4×C43—41no—
120C4⋊C4×C43—41no—
121C42×C43C2×D411yescharacteristic
122C42×C43C2×D411yescharacteristic
123C42×C43#4111yescharacteristic
124C42×C43#4111yescharacteristic
125(C2×D43)⋊C4—42no—
126(C2×D43)⋊C4—42no—
127(C2×D43)⋊C4—41no—
128(C2×D43)⋊C4—41no—
129(C2×D43)⋊C4—41no—
130(C2×D43)⋊C4—41no—
131(C2×D43)⋊C4—42no—
132(C2×D43)⋊C4—42no—
133C4⋊Dic43—42no—
134C4×Dic43—21no—
135C4×Dic43—21no—
136C4×Dic43—21no—
137C4×Dic43—21no—
138C4×Dic43—21no—
139C4×Dic43—21no—
140C2×C43⋊C8—22no—
141C2×C43⋊C8—22no—
142C2×C43⋊C8—41no—
143C2×C43⋊C8—41no—
144C2×C43⋊C8—41no—
145C2×C43⋊C8—41no—
146C23×C43C2×C22⋊C411yescharacteristic
147C22×D43—21no—
148C22×D43—21no—
149C22×D43—21no—
150C22×D43—21no—
151C22×D43—21no—
152C22×D43—21no—
153C22×D43—41no—
154C22×D43—41no—
155C22×D43—41no—
156C22×D43—41no—
157C22×D43—41no—
158C22×D43—41no—
159C22×D43—41no—
160C22×D43#10012yes—
161C2×C4×C43—21no—
162C2×C4×C43—21no—
163C2×C4×C43—21no—
164C2×C4×C43—21no—
165C2×C4×C43—21no—
166C2×C4×C43—21no—
167C2×C4×C43—41no—
168C2×C4×C43—41no—
169C2×C4×C43—41no—
170C2×C4×C43—41no—
171C2×C4×C43—41no—
172C2×C4×C43—41no—
173C2×C4×C43C4×D411yescharacteristic
174C2×C4×C43C4×D411yescharacteristic
175C2×C4×C43#12011yescharacteristic
176C2×C4×C43#12111yescharacteristic
177C2×C4×C43#12111yescharacteristic
178C2×C4×C43#12311yescharacteristic
179C2×Dic43—21no—
180C2×Dic43—21no—
181C2×Dic43—21no—
182C2×Dic43—21no—
183C2×Dic43—21no—
184C2×Dic43—21no—
185C2×Dic43—21no—
186C2×Dic43—21no—
187C2×Dic43—41no—
188C2×Dic43—41no—
189C2×Dic43—41no—
190C2×Dic43#10412yes—
191D172—81no—
192D172—81no—
193D172—84no—
194C4×D43—42no—
195C4×D43—42no—
196C4×D43—42no—
197C4×D43—42no—
198C4×D43—42no—
199C4×D43—42no—
200Dic86—81no—
201Dic86—81no—
202C8×C43—42no—
203C8×C43—42no—
204C43⋊C8—42no—
205C43⋊C8—42no—
206#9124—431nomaximal, Sylow
207C22×C43#38611yescharacteristic
208C22×C43C2×#10011yescharacteristic
209C22×C43#41311yescharacteristic
210C22×C43C2×#10411yescharacteristic
211C22×C43#42111yescharacteristic
212C22×C43#42111yescharacteristic
213C22×C43#42111yescharacteristic
214C2×D43—22no—
215C2×D43—22no—
216C2×D43—22no—
217C2×D43—41no—
218C2×D43—41no—
219C2×D43—41no—
220C2×D43—41no—
221C2×D43—81no—
222C2×D43—81no—
223C2×D43—81no—
224C2×D43—81no—
225C2×D43—81no—
226C2×D43—81no—
227C2×D43—81no—
228C4×C43—21no—
229C4×C43—21no—
230C4×C43—21no—
231C4×C43—21no—
232C4×C43—21no—
233C4×C43—21no—
234C4×C43—81no—
235C4×C43—81no—
236Dic43—22no—
237Dic43—41no—
238Dic43—41no—
239Dic43—81no—
240C2×#432—431no—
241#2850—431no—
242#1749—431no—
243C2×#329—431no—
244C2×#329—431no—
245#1295—431no—
246#1295D4311yescharacteristic, complemented
247C2×C43#152911yescharacteristic
248C2×C43#153011yescharacteristic
249C2×C43#153311yescharacteristic
250C2×C43#153511yescharacteristic
251C2×C43#187111yescharacteristic
252C2×C43#189711yescharacteristic
253C2×C43#190011yescharacteristic
254D43—42no—
255D43—161no—
256C2×#124—431no—
257C2×C22⋊Q8—431no—
258C2×#121—431no—
259C22×C42—431no—
260#432—862no—
261#432—862no—
262C2×C4⋊C8—861no—
263C2×C22⋊C8—861no—
264C2×C22⋊C8—861no—
265C2×#97—431no—
266C2×#97—431no—
267C2×#97C2×D4311yescharacteristic
268C2×#97C2×D4311yescharacteristic
269#391—431no—
270#390—431no—
271#388—861no—
272#388—861no—
273#386—861no—
274#386—861no—
275#382C2×D4311yescharacteristic
276#336—861no—
277#329—862no—
278#329—862no—
279C43#912411yescharacteristic, complemented, Sylow
280C22×Q8—431no—
281C22×D4—431no—
282C22×D4—861no—
283C23×C4—431no—
284C23×C4—431no—
285C23×C4—431no—
286C22×C8—21no—
287C22×C8—21no—
288C22×C8—861no—
289C22×C8—861no—
290#124—861no—
291#124—861no—
292#124—861no—
293#124—861no—
294C22⋊Q8—1722no—
295#121—1722no—
296C2×C4⋊C4—861no—
297C2×C4⋊C4C4×D4311yescharacteristic
298C2×C4⋊C4C4×D4311yescharacteristic
299C2×C22⋊C4—861no—
300C2×C22⋊C4—861no—
301C2×C22⋊C4—861no—
302C2×C22⋊C4—861no—
303C2×C22⋊C4—861no—
304C2×C22⋊C4—861no—
305C2×C42—431no—
306C2×C42—431no—
307C2×C42—431no—
308C2×C42—861no—
309C2×C42—861no—
310C2×C42—861no—
311C2×C42—861no—
312C2×C42C22×D4311yescharacteristic
313C4⋊C8—864no—
314C22⋊C8—864no—
315C22⋊C8—864no—
316#97—21no—
317#97—21no—
318#97—21no—
319#97—432no—
320#97—861no—
321#97—861no—
322#97—861no—
323#97D17212yescomplemented
324#95—21no—
325#95—21no—
326#95—861no—
327#95—861no—
328C24—431no—
329C24—861no—
330C2×Q8—861no—
331C2×Q8—861no—
332C2×Q8—1721no—
333C2×Q8—1721no—
334C2×D4—861no—
335C2×D4—861no—
336C2×D4—1721no—
337C2×D4—1721no—
338C2×D4—1722no—
339C2×D4—1722no—
340C2×D4—1722no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—431no—
344C22×C4—431no—
345C22×C4—431no—
346C22×C4—862no—
347C22×C4—862no—
348C22×C4—861no—
349C22×C4—861no—
350C22×C4—861no—
351C22×C4—861no—
352C22×C4—861no—
353C22×C4—861no—
354C22×C4—861no—
355C22×C4—1721no—
356C22×C4—1721no—
357C22×C4—1721no—
358C22×C4—1721no—
359C22×C4C2×C4×D4311yescharacteristic
360C22×C4D4×D4311yescharacteristic
361C22×C4D4×D4311yescharacteristic
362C2×C8—22no—
363C2×C8—22no—
364C2×C8—41no—
365C2×C8—41no—
366C2×C8—41no—
367C2×C8—41no—
368C2×C8—862no—
369C2×C8—862no—
370C2×C8—1721no—
371C2×C8—1721no—
372C2×C8—1721no—
373C2×C8—1721no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—1722no—
377C22⋊C4—1722no—
378C22⋊C4—1722no—
379C22⋊C4—1722no—
380C22⋊C4—1722no—
381C22⋊C4—1721no—
382C22⋊C4—1721no—
383C22⋊C4—1721no—
384C22⋊C4—1721no—
385C42—861no—
386C42—861no—
387C42—861no—
388C42—861no—
389C42—861no—
390C42—861no—
391C42C2×D17211yescharacteristic
392C42#1062189811yescharacteristic
393C42D4×D4311yescharacteristic
394C42#1062190211yescharacteristic
395C23—432no—
396C23—861no—
397C23—861no—
398C23—861no—
399C23—861no—
400C23—861no—
401C23—861no—
402C23—1721no—
403C23—1721no—
404C23—1721no—
405C23—1721no—
406C23—1721no—
407C23—1721no—
408C23—1721no—
409C23C22⋊C4×D4311yescharacteristic
410Q8—3441no—
411Q8—3441no—
412D4—3441no—
413D4—3441no—
414D4—3444no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—432no—
428C2×C4—861no—
429C2×C4—861no—
430C2×C4—861no—
431C2×C4—861no—
432C2×C4—861no—
433C2×C4—861no—
434C2×C4—861no—
435C2×C4—861no—
436C2×C4—1722no—
437C2×C4—1722no—
438C2×C4—1722no—
439C2×C4—1722no—
440C2×C4—1722no—
441C2×C4—1722no—
442C2×C4—1721no—
443C2×C4—1721no—
444C2×C4—1721no—
445C2×C4#1306328711yescharacteristic
446C2×C4C4×D17211yescharacteristic
447C2×C4#1306329511yescharacteristic
448C2×C4#1306329811yescharacteristic
449C2×C4#1306330011yescharacteristic
450C2×C4#1306331011yescharacteristic
451C8—42no—
452C8—42no—
453C8—1722no—
454C8—1722no—
455C22—862no—
456C22—862no—
457C22—862no—
458C22—3441no—
459C22—3441no—
460C22—3441no—
461C22—3441no—
462C22—3441no—
463C22—3441no—
464C22—3441no—
465C22—1721no—
466C22—1721no—
467C22—1721no—
468C22—1721no—
469C22#1458277711yescharacteristic
470C22#100×D4311yescharacteristic
471C22#1458288211yescharacteristic
472C22#104×D4311yescharacteristic
473C22#1458291411yescharacteristic
474C22#1458291411yescharacteristic
475C22#1458291411yescharacteristic
476C4—21no—
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—21no—
482C4—81no—
483C4—81no—
484C4—862no—
485C4—3441no—
486C4—1721no—
487C4—1721no—
488C2—1722no—
489C2—6881no—
490C2#1913320111yescharacteristic
491C2#1913320411yescharacteristic
492C2#1913321711yescharacteristic
493C2#1913322511yescharacteristic
494C2#1913489611yescharacteristic
495C2#1913504211yescharacteristic
496C2#1913505711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1295C2
socleC23×C43C2×C22⋊C4
prime radicalC2×#13063300C4
cosocleC2×C42×C43C23
hypercenter#1295D43
hypocenterC43#9124
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
1. C2×#14582954C2semidirect
3. #19134358C2semidirect
4. C2×#14582638C2semidirect
5. C2×#14582638C2semidirect
6. #19132476C2semidirect
7. C43×#1295C2semidirect
65. #13063236D4semidirect
76. #97×C43D4semidirect
246. #1295D43semidirect
279. C43#9124semidirect
323. #97D172semidirect

Maximal subgroups

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

subgroupindex
C2×#145829542
#191428972
#191343582
C2×#145826382
#191324762
C43×#12952
#912443