Finite Group Databasebeta

← #25013461

Subgroups — #25013461

Order 11008.

494 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M32×D43C211yesmaximal, characteristic, complemented
2#19143291C211yesmaximal, characteristic
3C2×#14582684C211yesmaximal, characteristic, complemented
4C2×#14582682C211yesmaximal, characteristic, complemented
5C2×(C2×D43)⋊C16C211yesmaximal, characteristic, complemented
6#19132684C211yesmaximal, characteristic, complemented
7C43×#1379C211yesmaximal, characteristic, complemented
8C2×#13063331C2211yescharacteristic
9C22×C8×D43C2211yescharacteristic
10#14583411C411yescharacteristic
11C2×#13063265C2211yescharacteristic
12C2×#13063264—21no—
13M32×D43—22no—
14M32×D43—22no—
15C22×C43⋊C16C2211yescharacteristic
16C2×C16×D43—21no—
17#14582972—21no—
18#14582972—21no—
19C8×D172—21no—
20C8×D172—21no—
21#14582926C411yescharacteristic
22#14582867C411yescharacteristic
23#14582862C411yescharacteristic
24#14582684—22no—
25#14582682—22no—
26(C2×D43)⋊C16—21no—
27(C2×D43)⋊C16—21no—
28C2×M32×C43C2211yescharacteristic
29C22×C16×C43C2211yescharacteristic
30C43×#405C2211yescharacteristic
31C2×#10621898C2×C411yescharacteristic
32C22×C4×D43C2×C411yescharacteristic
33#13063331—21no—
34#13063331—21no—
35#13063331—21no—
36#13063331—21no—
37C2×#10621877C2×C411yescharacteristic
38C2×#10621872—21no—
39C22×C43⋊C8C2×C411yescharacteristic
40C2×C8×D43—21no—
41C2×C8×D43—21no—
42C2×C8×D43—21no—
43C2×C8×D43—21no—
44C2×C8×D43—21no—
45C2×C8×D43D411yescharacteristic
46C2×C8×D43D411yescharacteristic
47C2×C8×D43D411yescharacteristic
48C2×C8×D43D411yescharacteristic
49#13063309—21no—
50#13063305C811yescharacteristic
51#13063305C811yescharacteristic
52#13063300C811yescharacteristic
53#13063300C811yescharacteristic
54#13063295—21no—
55C4×D172—21no—
56C4×D172—21no—
57#13063265—21no—
58#13063265D412yescomplemented
59#13063264—24no—
60C2×C43⋊C16—21no—
61C2×C43⋊C16—21no—
62C2×C43⋊C16—21no—
63C2×C43⋊C16—21no—
64C16×D43—24no—
65C4⋊(C43⋊C8)—21no—
66C4⋊(C43⋊C8)—21no—
67(C2×D43)⋊C8—21no—
68(C2×D43)⋊C8—21no—
69(C2×D43)⋊C8—21no—
70(C2×D43)⋊C8—21no—
71C2×M16×C43C2×C411yescharacteristic
72C22×C8×C43C2311yescharacteristic
73#117×C43C2×C411yescharacteristic
74M32×C43—21no—
75M32×C43D412yescomplemented
76C2×C16×C43—21no—
77C2×C16×C43—21no—
78C2×C16×C43—21no—
79C2×C16×C43—21no—
80#97×C43—21no—
81C4×C8×C43—21no—
82C23×D43M1611yescharacteristic
83C22×C4×C43C22×C411yescharacteristic
84C2×C22⋊D43—21no—
85C22×Dic43M1611yescharacteristic
86#10621898—21no—
87#10621898—21no—
88#10621898—21no—
89#10621898—21no—
90C2×D172—21no—
91C2×D172—21no—
92C2×D172C2×C811yescharacteristic
93C2×C4×D43—21no—
94C2×C4×D43—21no—
95C2×C4×D43—21no—
96C2×C4×D43—21no—
97C2×C4×D43—21no—
98C2×C4×D43C22⋊C411yescharacteristic
99C2×C4×D43C22⋊C411yescharacteristic
100C2×C4×D43C2×C811yescharacteristic
101C2×C4×D43C2×C811yescharacteristic
102C2×Dic86C2×C811yescharacteristic
103M16×C43—21no—
104M16×C43—21no—
105C2×C8×C43—21no—
106C2×C8×C43C2×D411yescharacteristic
107C2×C8×C43C2×D411yescharacteristic
108C2×C8×C43C2×D411yescharacteristic
109C2×C8×C43C2×D411yescharacteristic
110C2×C8×C43#4111yescharacteristic
111C2×C8×C43#4111yescharacteristic
112C4⋊C4×C43C2×C811yescharacteristic
113C4⋊C4×C43C2×C811yescharacteristic
114C22⋊C4×C43—21no—
115C42×C43—21no—
116(C2×D43)⋊C4—21no—
117(C2×D43)⋊C4—21no—
118(C2×D43)⋊C4—21no—
119(C2×D43)⋊C4—21no—
120C4⋊Dic43—21no—
121C4⋊Dic43—21no—
122#10621877—21no—
123#10621877—21no—
124C2×C43⋊C8—21no—
125C2×C43⋊C8—21no—
126C2×C43⋊C8—21no—
127C2×C43⋊C8C22⋊C411yescharacteristic
128C2×C43⋊C8C22⋊C411yescharacteristic
129#10621872—41no—
130#10621872—41no—
131C8×D43—21no—
132C8×D43—21no—
133C8×D43—21no—
134C8×D43—21no—
135C8×D43—21no—
136C8×D43—21no—
137C8×D43—21no—
138C8×D43—21no—
139C8×D43—41no—
140C8×D43—41no—
141C16×C43—22no—
142C16×C43—41no—
143C43⋊C16—22no—
144C43⋊C16—41no—
145C23×C43C2×M1611yescharacteristic
146C22×D43—21no—
147C22×D43—21no—
148C22×D43—22no—
149C22×D43—21no—
150C22×D43—41no—
151C22×D43C22⋊C811yescharacteristic
152C22×D43C22⋊C811yescharacteristic
153C2×C4×C43—21no—
154C2×C4×C43—21no—
155C2×C4×C43C2×C22⋊C411yescharacteristic
156C2×C4×C43C4×D411yescharacteristic
157C2×C4×C43C4×D411yescharacteristic
158C2×C4×C43C22×C811yescharacteristic
159C2×C4×C43#13111yescharacteristic
160C2×C4×C43#13111yescharacteristic
161C22⋊D43—41no—
162C22⋊D43—41no—
163C2×Dic43—21no—
164C2×Dic43—21no—
165C2×Dic43—21no—
166C2×Dic43C22⋊C811yescharacteristic
167C2×Dic43C22⋊C811yescharacteristic
168D172—21no—
169D172—21no—
170D172—42no—
171D172—42no—
172C4×D43—21no—
173C4×D43—21no—
174C4×D43—21no—
175C4×D43—21no—
176C4×D43—21no—
177C4×D43—21no—
178C4×D43—21no—
179C4×D43—21no—
180C4×D43—41no—
181C4×D43—41no—
182Dic86—21no—
183Dic86—21no—
184C8×C43—41no—
185C8×C43#12011yescharacteristic
186C8×C43#12111yescharacteristic
187C8×C43#12111yescharacteristic
188C8×C43#12311yescharacteristic
189C43⋊C8—21no—
190C43⋊C8—21no—
191C43⋊C8—41no—
192#12978—431nomaximal, Sylow
193C22×C43—21no—
194C22×C43—21no—
195C22×C43C2×C22⋊C811yescharacteristic
196C22×C43#43511yescharacteristic
197C22×C43#43511yescharacteristic
198C2×D43—21no—
199C2×D43—21no—
200C2×D43—21no—
201C2×D43—21no—
202C2×D43—21no—
203C2×D43—42no—
204C2×D43—42no—
205C2×D43—41no—
206C2×D43—41no—
207C2×D43—41no—
208C2×D43#35012yescomplemented
209C4×C43—41no—
210C4×C43—41no—
211C4×C43#38611yescharacteristic
212C4×C43#40811yescharacteristic
213C4×C43C8×D411yescharacteristic
214C4×C43C8×D411yescharacteristic
215Dic43—21no—
216Dic43—21no—
217Dic43—41no—
218C22×M32—431no—
219#2929—431no—
220C2×#350—431no—
221C2×#350—431no—
222C2×C22⋊C16—431no—
223#1379—431no—
224#1379D4311yescharacteristic, complemented
225C2×C43—21no—
226C2×C43—21no—
227C2×C43#186911yescharacteristic
228C2×C43C2×#35011yescharacteristic
229C2×C43#211711yescharacteristic
230D43—22no—
231D43—41no—
232D43—81no—
233C2×#131—431no—
234C23×C8—431no—
235#525—431no—
236C2×M32—431no—
237C2×M32—861no—
238C2×M32—862no—
239C2×M32—862no—
240C2×M32C2×D4311yescharacteristic
241C22×C16—431no—
242C22×C16—861no—
243C22×C16C2×D4311yescharacteristic
244#435—861no—
245#435—861no—
246C8×D4—861no—
247C8×D4—861no—
248#424—431no—
249#408—431no—
250#407—431no—
251#405C2×D4311yescharacteristic
252#350—862no—
253#350—862no—
254C22⋊C16—861no—
255C22⋊C16—861no—
256C43#1297811yescharacteristic, complemented, Sylow
257C2×#41—431no—
258C23×C4—431no—
259#131—861no—
260#131—861no—
261#131—861no—
262#131—861no—
263C2×M16—431no—
264C2×M16—861no—
265C2×M16C4×D4311yescharacteristic
266C22×C8—431no—
267C22×C8—431no—
268C22×C8—431no—
269C22×C8—431no—
270C22×C8—431no—
271C22×C8—861no—
272C22×C8—861no—
273C22×C8—861no—
274C22×C8—861no—
275C22×C8—861no—
276C22×C8C22×D4311yescharacteristic
277#123—861no—
278C22⋊Q8—431no—
279C22⋊Q8—431no—
280#121—431no—
281#121—431no—
282#120—861no—
283C4×D4—861no—
284C4×D4—861no—
285#117C4×D4311yescharacteristic
286M32—21no—
287M32—432no—
288M32—864no—
289M32—861no—
290M32D17212yescomplemented
291C2×C16—21no—
292C2×C16—21no—
293C2×C16—21no—
294C2×C16—21no—
295C2×C16—864no—
296C2×C16—861no—
297C2×C16—861no—
298C2×C16—861no—
299C2×C16—861no—
300C4⋊C8—861no—
301C4⋊C8—861no—
302C22⋊C8—861no—
303C22⋊C8—861no—
304C22⋊C8—861no—
305C22⋊C8—861no—
306#97—21no—
307C4×C8—21no—
308C24—431no—
309#41—861no—
310#41—861no—
311#41—861no—
312#41—861no—
313C2×Q8—431no—
314C2×D4—431no—
315C2×D4—861no—
316C2×D4—861no—
317C2×D4—861no—
318C22×C4—431no—
319C22×C4—431no—
320C22×C4—431no—
321C22×C4—431no—
322C22×C4—431no—
323C22×C4—861no—
324C22×C4—861no—
325C22×C4—861no—
326C22×C4—861no—
327C22×C4—861no—
328C22×C4C2×C4×D4311yescharacteristic
329M16—21no—
330M16—21no—
331M16—861no—
332M16—861no—
333M16—1721no—
334M16—1721no—
335C2×C8—21no—
336C2×C8—431no—
337C2×C8—431no—
338C2×C8—861no—
339C2×C8—861no—
340C2×C8—861no—
341C2×C8—861no—
342C2×C8—861no—
343C2×C8—861no—
344C2×C8—861no—
345C2×C8—861no—
346C2×C8—861no—
347C2×C8—861no—
348C2×C8—861no—
349C2×C8—1721no—
350C2×C8—1721no—
351C2×C8C2×D17211yescharacteristic
352C2×C8#1062189811yescharacteristic
353C2×C8D4×D4311yescharacteristic
354C2×C8D4×D4311yescharacteristic
355C2×C8D4×D4311yescharacteristic
356C2×C8#1062190211yescharacteristic
357C4⋊C4—861no—
358C4⋊C4—861no—
359C4⋊C4C8×D4311yescharacteristic
360C4⋊C4C8×D4311yescharacteristic
361C22⋊C4—21no—
362C22⋊C4—861no—
363C22⋊C4—861no—
364C22⋊C4—861no—
365C22⋊C4—861no—
366C42—21no—
367C16—22no—
368C16—41no—
369C16—862no—
370C16—1721no—
371C23—431no—
372C23—431no—
373C23—862no—
374C23—861no—
375C23—861no—
376C23—861no—
377C23—1721no—
378C23M16×D4311yescharacteristic
379Q8—861no—
380Q8—861no—
381D4—861no—
382D4—861no—
383D4—1722no—
384D4—1722no—
385D4—1721no—
386D4—1721no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—431no—
390C2×C4—431no—
391C2×C4—861no—
392C2×C4—861no—
393C2×C4—861no—
394C2×C4—861no—
395C2×C4—861no—
396C2×C4—861no—
397C2×C4—861no—
398C2×C4—861no—
399C2×C4—861no—
400C2×C4—861no—
401C2×C4—861no—
402C2×C4—1721no—
403C2×C4—1721no—
404C2×C4C22⋊C4×D4311yescharacteristic
405C2×C4#1306328711yescharacteristic
406C2×C4C4×D17211yescharacteristic
407C2×C4C2×C8×D4311yescharacteristic
408C2×C4#1306333111yescharacteristic
409C2×C4#1306333311yescharacteristic
410C8—41no—
411C8—861no—
412C8—861no—
413C8—1721no—
414C8#1306329511yescharacteristic
415C8#1306329811yescharacteristic
416C8#1306330011yescharacteristic
417C8#1306331011yescharacteristic
418C22—21no—
419C22—21no—
420C22—432no—
421C22—861no—
422C22—861no—
423C22—861no—
424C22—861no—
425C22—861no—
426C22—1722no—
427C22—1722no—
428C22—1721no—
429C22—1721no—
430C22—1721no—
431C22C22⋊C8×D4311yescharacteristic
432C22#1458296911yescharacteristic
433C22#1458297211yescharacteristic
434C4—41no—
435C4—41no—
436C4—861no—
437C4—861no—
438C4—1721no—
439C4#1458277711yescharacteristic
440C4#1458286411yescharacteristic
441C4#1458296411yescharacteristic
442C4C8×D17211yescharacteristic
443C2—21no—
444C2—21no—
445C2—862no—
446C2—3441no—
447C2—1721no—
448C2#1913488611yescharacteristic
449C2#350×D4311yescharacteristic
450C2#1913622111yescharacteristic
subgroupG/H
centerC2×C8D4×D43
commutatorC2×C4×C43C22×C8
FrattiniC22×C8C22×D43
FittingC43×#1379C2
socleC22×C43C2×C22⋊C8
prime radical#14583411C4
cosocleC22×C8×C43C23
hypercenter#1379D43
hypocenterC43#12978
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ #1379

Complements

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

NH ≅ G/Ntype
1. C2×M32×D43C2semidirect
3. C2×#14582684C2semidirect
4. C2×#14582682C2semidirect
5. C2×(C2×D43)⋊C16C2semidirect
6. #19132684C2semidirect
7. C43×#1379C2semidirect
58. #13063265D4semidirect
75. M32×C43D4semidirect
208. C2×D43#350semidirect
224. #1379D43semidirect
256. C43#12978semidirect
290. M32D172semidirect

Maximal subgroups

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

subgroupindex
C2×M32×D432
#191432912
C2×#145826842
C2×#145826822
C2×(C2×D43)⋊C162
#191326842
C43×#13792
#1297843