Finite Group Databasebeta

← #25013500

Subgroups — #25013500

Order 11008.

510 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×M32×D43C211yesmaximal, characteristic, complemented
2C2×#14582972C211yesmaximal, characteristic
3C2×#14582680C211yesmaximal, characteristic, complemented
4C2×#14582680C211yesmaximal, characteristic, complemented
5#19136205C211yesmaximal, characteristic, complemented
6#19132679C211yesmaximal, characteristic, complemented
7C43×#1377C211yesmaximal, characteristic, complemented
8C22×#10621872C2211yescharacteristic
9C22×C8×D43C2211yescharacteristic
10C2×C4×D172C411yescharacteristic
11C2×#13063265C2211yescharacteristic
12C2×#13063265C2211yescharacteristic
13C2×#13063264—21no—
14M32×D43—22no—
15M32×D43—22no—
16C2×C16×D43—21no—
17#14582972—21no—
18#14582972—21no—
19#14582972—21no—
20#14582972—21no—
21C2×C4⋊(C43⋊C8)C411yescharacteristic
22C2×(C2×D43)⋊C8C411yescharacteristic
23C2×(C2×D43)⋊C8C411yescharacteristic
24#14582680—22no—
25#14582680—22no—
26(C2×D43)⋊C16—21no—
27(C2×D43)⋊C16—21no—
28C2×M32×C43C2211yescharacteristic
29C2×M32×C43C2211yescharacteristic
30C2×#97×C43C2211yescharacteristic
31C22×D172C811yescharacteristic
32C22×C4×D43C2×C411yescharacteristic
33C22×C4×D43C2×C411yescharacteristic
34C2×#10621872—21no—
35C2×#10621872—21no—
36C2×#10621872—21no—
37C2×#10621872—21no—
38C2×#10621872—21no—
39C2×#10621872—21no—
40C22×C43⋊C8C2×C411yescharacteristic
41C22×C43⋊C8C2×C411yescharacteristic
42C2×C8×D43—21no—
43C2×C8×D43—21no—
44C2×C8×D43—21no—
45C2×C8×D43—21no—
46C2×C8×D43D411yescharacteristic
47C2×C8×D43D411yescharacteristic
48C2×C8×D43D411yescharacteristic
49C2×C8×D43D411yescharacteristic
50C4×D172—21no—
51C4×D172—21no—
52C4×D172—21no—
53C4×D172—21no—
54C2×C4⋊Dic43C811yescharacteristic
55C2×(C2×D43)⋊C4C811yescharacteristic
56C2×(C2×D43)⋊C4C811yescharacteristic
57#13063265—21no—
58#13063265—21no—
59#13063265—21no—
60#13063265D412yescomplemented
61#13063264—24no—
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—
71C22×C8×C43C2×C411yescharacteristic
72C22×C8×C43C2311yescharacteristic
73C2×C42×C43C2×C411yescharacteristic
74M32×C43—21no—
75M32×C43—21no—
76M32×C43—21no—
77M32×C43D412yescomplemented
78C2×C16×C43—21no—
79C2×C16×C43—21no—
80#97×C43—21no—
81#97×C43—21no—
82C23×D43C2×C811yescharacteristic
83C23×D43C2×C811yescharacteristic
84C22×C4×C43C2×C811yescharacteristic
85C22×C4×C43C2×C811yescharacteristic
86C22×C4×C43C22×C411yescharacteristic
87C22×Dic43C2×C811yescharacteristic
88C22×Dic43C2×C811yescharacteristic
89C2×D172—21no—
90C2×D172—21no—
91C2×D172—42no—
92C2×C4×D43—21no—
93C2×C4×D43—21no—
94C2×C4×D43—21no—
95C2×C4×D43—21no—
96C2×C4×D43—21no—
97C2×C4×D43—21no—
98C2×C4×D43—21no—
99C2×C4×D43—21no—
100C2×C4×D43—21no—
101C2×C4×D43—21no—
102C2×C4×D43C22⋊C411yescharacteristic
103C2×C4×D43C22⋊C411yescharacteristic
104C2×C4×D43M1611yescharacteristic
105C2×C4×D43M1611yescharacteristic
106C2×C8×C43—21no—
107C2×C8×C43—21no—
108C2×C8×C43—21no—
109C2×C8×C43C2×D411yescharacteristic
110C2×C8×C43C2×D411yescharacteristic
111C2×C8×C43C2×D411yescharacteristic
112C2×C8×C43C2×D411yescharacteristic
113C2×C8×C43#4111yescharacteristic
114C2×C8×C43#4111yescharacteristic
115C42×C43—21no—
116C42×C43—21no—
117(C2×D43)⋊C4—21no—
118(C2×D43)⋊C4—21no—
119(C2×D43)⋊C4—21no—
120(C2×D43)⋊C4—21no—
121C4⋊Dic43—21no—
122C4⋊Dic43—21no—
123C2×C43⋊C8—21no—
124C2×C43⋊C8—21no—
125C2×C43⋊C8—21no—
126C2×C43⋊C8—21no—
127C2×C43⋊C8—21no—
128C2×C43⋊C8C22⋊C411yescharacteristic
129C2×C43⋊C8C22⋊C411yescharacteristic
130#10621872—41no—
131#10621872—41no—
132#10621872—41no—
133#10621872—41no—
134C8×D43—21no—
135C8×D43—21no—
136C8×D43—21no—
137C8×D43—21no—
138C8×D43—21no—
139C8×D43—21no—
140C8×D43—21no—
141C8×D43—21no—
142C16×C43—22no—
143C16×C43—41no—
144C43⋊C16—22no—
145C43⋊C16—41no—
146C23×C43C22×C811yescharacteristic
147C22×D43—21no—
148C22×D43—21no—
149C22×D43—22no—
150C22×D43—21no—
151C22×D43—21no—
152C22×D43—21no—
153C22×D43—41no—
154C22×D43—41no—
155C22×D43—41no—
156C22×D43C22⋊C811yescharacteristic
157C22×D43C22⋊C811yescharacteristic
158C2×C4×C43—21no—
159C2×C4×C43—21no—
160C2×C4×C43—41no—
161C2×C4×C43—41no—
162C2×C4×C43C2×C22⋊C411yescharacteristic
163C2×C4×C43C4×D411yescharacteristic
164C2×C4×C43C4×D411yescharacteristic
165C2×C4×C43C2×M1611yescharacteristic
166C2×C4×C43#13111yescharacteristic
167C2×C4×C43#13111yescharacteristic
168C2×Dic43—21no—
169C2×Dic43—21no—
170C2×Dic43—21no—
171C2×Dic43—21no—
172C2×Dic43—21no—
173C2×Dic43C22⋊C811yescharacteristic
174C2×Dic43C22⋊C811yescharacteristic
175D172—42no—
176D172—42no—
177C4×D43—21no—
178C4×D43—21no—
179C4×D43—21no—
180C4×D43—21no—
181C4×D43—21no—
182C4×D43—21no—
183C4×D43—21no—
184C4×D43—21no—
185C4×D43—41no—
186C4×D43—41no—
187C4×D43—41no—
188C4×D43—41no—
189C8×C43—41no—
190C8×C43#12011yescharacteristic
191C8×C43#12111yescharacteristic
192C8×C43#12111yescharacteristic
193C8×C43#12311yescharacteristic
194C43⋊C8—21no—
195C43⋊C8—21no—
196C43⋊C8—41no—
197#12985—431nomaximal, Sylow
198C22×C43—21no—
199C22×C43—21no—
200C22×C43C2×C22⋊C811yescharacteristic
201C22×C43C8×D411yescharacteristic
202C22×C43C8×D411yescharacteristic
203C2×D43—21no—
204C2×D43—21no—
205C2×D43—21no—
206C2×D43—21no—
207C2×D43—21no—
208C2×D43—42no—
209C2×D43—42no—
210C2×D43—41no—
211C2×D43—41no—
212C2×D43—41no—
213C2×D43—81no—
214C2×D43—81no—
215C2×D43#34912yescomplemented
216C4×C43—41no—
217C4×C43—41no—
218C4×C43#38611yescharacteristic
219C4×C43#40811yescharacteristic
220C4×C43#43511yescharacteristic
221C4×C43#43511yescharacteristic
222Dic43—21no—
223Dic43—21no—
224Dic43—41no—
225C22×M32—431no—
226C2×#435—431no—
227C2×#349—431no—
228C2×#349—431no—
229#2112—431no—
230#1377—431no—
231#1377D4311yescharacteristic, complemented
232C2×C43—21no—
233C2×C43—21no—
234C2×C43#186911yescharacteristic
235C2×C43C2×#34911yescharacteristic
236C2×C43#211511yescharacteristic
237D43—22no—
238D43—41no—
239D43—81no—
240C22×M16—431no—
241C23×C8—431no—
242C2×C4×D4—431no—
243C2×M32—431no—
244C2×M32—431no—
245C2×M32—861no—
246C2×M32—862no—
247C2×M32—862no—
248C2×M32C2×D4311yescharacteristic
249C2×M32C2×D4311yescharacteristic
250C22×C16—861no—
251#435—861no—
252#435—861no—
253#435—861no—
254#435—861no—
255C2×C4⋊C8—431no—
256C2×C22⋊C8—431no—
257C2×C22⋊C8—431no—
258C2×#97C2×D4311yescharacteristic
259#349—862no—
260#349—862no—
261C22⋊C16—861no—
262C22⋊C16—861no—
263C43#1298511yescharacteristic, complemented, Sylow
264C22×D4—431no—
265C23×C4—431no—
266C23×C4—431no—
267C2×M16—861no—
268C2×M16—861no—
269C2×M16—861no—
270C2×M16—861no—
271C2×M16—861no—
272C2×M16—861no—
273C22×C8—431no—
274C22×C8—431no—
275C22×C8—431no—
276C22×C8—431no—
277C22×C8—431no—
278C22×C8—431no—
279C22×C8—861no—
280C22×C8—861no—
281C22×C8—861no—
282C22×C8—861no—
283C22×C8C4×D4311yescharacteristic
284C22×C8C22×D4311yescharacteristic
285C4×D4—861no—
286C4×D4—861no—
287C4×D4—861no—
288C4×D4—861no—
289C2×C4⋊C4—431no—
290C2×C22⋊C4—431no—
291C2×C22⋊C4—431no—
292C2×C42C4×D4311yescharacteristic
293M32—21no—
294M32—21no—
295M32—21no—
296M32—432no—
297M32—864no—
298M32—861no—
299M32—861no—
300M32—861no—
301M32D17212yescomplemented
302C2×C16—21no—
303C2×C16—21no—
304C2×C16—864no—
305C2×C16—861no—
306C2×C16—861no—
307C4⋊C8—861no—
308C4⋊C8—861no—
309C22⋊C8—861no—
310C22⋊C8—861no—
311C22⋊C8—861no—
312C22⋊C8—861no—
313#97—21no—
314#97—21no—
315C24—431no—
316C24—431no—
317C2×D4—861no—
318C2×D4—861no—
319C2×D4—1722no—
320C22×C4—431no—
321C22×C4—431no—
322C22×C4—431no—
323C22×C4—431no—
324C22×C4—431no—
325C22×C4—431no—
326C22×C4—861no—
327C22×C4—861no—
328C22×C4—861no—
329C22×C4—861no—
330C22×C4—861no—
331C22×C4—861no—
332C22×C4—861no—
333C22×C4—861no—
334C22×C4—861no—
335C22×C4—861no—
336C22×C4C8×D4311yescharacteristic
337C22×C4C8×D4311yescharacteristic
338C22×C4C2×C4×D4311yescharacteristic
339M16—1721no—
340M16—1721no—
341M16—1721no—
342M16—1721no—
343C2×C8—21no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8—431no—
347C2×C8—431no—
348C2×C8—861no—
349C2×C8—861no—
350C2×C8—861no—
351C2×C8—861no—
352C2×C8—861no—
353C2×C8—861no—
354C2×C8—861no—
355C2×C8—861no—
356C2×C8—861no—
357C2×C8—861no—
358C2×C8—861no—
359C2×C8—861no—
360C2×C8—861no—
361C2×C8C2×D17211yescharacteristic
362C2×C8#1062189811yescharacteristic
363C2×C8D4×D4311yescharacteristic
364C2×C8D4×D4311yescharacteristic
365C2×C8D4×D4311yescharacteristic
366C2×C8#1062190211yescharacteristic
367C4⋊C4—861no—
368C4⋊C4—861no—
369C22⋊C4—861no—
370C22⋊C4—861no—
371C22⋊C4—861no—
372C22⋊C4—861no—
373C42—21no—
374C42—21no—
375C16—22no—
376C16—41no—
377C16—862no—
378C16—1721no—
379C23—431no—
380C23—431no—
381C23—862no—
382C23—861no—
383C23—861no—
384C23—861no—
385C23—861no—
386C23—861no—
387C23—1721no—
388C23—1721no—
389C23—1721no—
390C23C2×C8×D4311yescharacteristic
391D4—1722no—
392D4—1722no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—431no—
398C2×C4—431no—
399C2×C4—861no—
400C2×C4—861no—
401C2×C4—861no—
402C2×C4—861no—
403C2×C4—861no—
404C2×C4—861no—
405C2×C4—861no—
406C2×C4—861no—
407C2×C4—861no—
408C2×C4—861no—
409C2×C4—861no—
410C2×C4—861no—
411C2×C4—861no—
412C2×C4—1721no—
413C2×C4—1721no—
414C2×C4—1721no—
415C2×C4—1721no—
416C2×C4C22⋊C4×D4311yescharacteristic
417C2×C4#1306328711yescharacteristic
418C2×C4C4×D17211yescharacteristic
419C2×C4M16×D4311yescharacteristic
420C2×C4#1306333111yescharacteristic
421C2×C4#1306333311yescharacteristic
422C8—41no—
423C8—861no—
424C8—861no—
425C8—1721no—
426C8#1306329511yescharacteristic
427C8#1306329811yescharacteristic
428C8#1306330011yescharacteristic
429C8#1306331011yescharacteristic
430C22—21no—
431C22—21no—
432C22—432no—
433C22—861no—
434C22—861no—
435C22—861no—
436C22—861no—
437C22—861no—
438C22—3441no—
439C22—3441no—
440C22—1722no—
441C22—1722no—
442C22—1721no—
443C22—1721no—
444C22—1721no—
445C22C22⋊C8×D4311yescharacteristic
446C22#1458296411yescharacteristic
447C22C8×D17211yescharacteristic
448C4—41no—
449C4—41no—
450C4—861no—
451C4—861no—
452C4—1721no—
453C4#1458277711yescharacteristic
454C4#1458286411yescharacteristic
455C4#1458296911yescharacteristic
456C4#1458297211yescharacteristic
457C2—21no—
458C2—21no—
459C2—862no—
460C2—3441no—
461C2—1721no—
462C2#1913488611yescharacteristic
463C2#349×D4311yescharacteristic
464C2#1913621411yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D43
commutatorC23×C43C22×C8
FrattiniC22×C8C22×D43
FittingC43×#1377C2
socleC22×C43C2×C22⋊C8
prime radicalC22×D172C8
cosocleC22×C8×C43C23
hypercenter#1377D43
hypocenterC43#12985
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1377

Complements

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

NH ≅ G/Ntype
1. C2×M32×D43C2semidirect
3. C2×#14582680C2semidirect
4. C2×#14582680C2semidirect
5. #19136205C2semidirect
6. #19132679C2semidirect
7. C43×#1377C2semidirect
60. #13063265D4semidirect
77. M32×C43D4semidirect
215. C2×D43#349semidirect
231. #1377D43semidirect
263. C43#12985semidirect
301. M32D172semidirect

Maximal subgroups

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

subgroupindex
C2×M32×D432
C2×#145829722
C2×#145826802
#191362052
#191326792
C43×#13772
#1298543