Finite Group Databasebeta

← #24991695

Subgroups — #24991695

Order 11008.

612 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143157C211yesmaximal, characteristic, complemented
2#19137835C211yesmaximal, characteristic
3#19133021C211yesmaximal, characteristic, complemented
4#19133019C211yesmaximal, characteristic, complemented
5#19132907C211yesmaximal, characteristic, complemented
6#19132498C211yesmaximal, characteristic, complemented
7C43×#1303C211yesmaximal, characteristic, complemented
8C2×M16×D43—21no—
9C2×C4×D172—21no—
10C2×C4×D172C2211yescharacteristic
11C2×#13063282C2211yescharacteristic
12#14582952C2211yescharacteristic
13#14582924—22no—
14#14582924—22no—
15#14582923C2211yescharacteristic
16#14582922—21no—
17#14582831C411yescharacteristic
18#14582826C411yescharacteristic
19#14582821—21no—
20#14582817C411yescharacteristic
21#14582816—21no—
22#14582809C411yescharacteristic
23C4×(C2×D43)⋊C4—21no—
24#14582628—22no—
25#14582626—22no—
26#14582624—21no—
27#14582622—21no—
28C43×#431C2211yescharacteristic
29C43×#423C2211yescharacteristic
30C4×C4⋊C4×C43C2211yescharacteristic
31C22×D172—21no—
32C22×D172C2×C411yescharacteristic
33C22×C4×D43—21no—
34C22×C4×D43D411yescharacteristic
35C2×#10621877—21no—
36C2×#10621872—22no—
37M16×D43—42no—
38M16×D43—42no—
39C2×C8×D43—22no—
40C4×D172—21no—
41C4×D172—21no—
42C4×D172—21no—
43C4×D172—21no—
44C4×D172—42no—
45C4×D172—42no—
46#13063282—21no—
47#13063282—21no—
48#13063282—21no—
49#13063282—21no—
50C2×C4⋊Dic43—21no—
51C2×C4⋊Dic43C2×C411yescharacteristic
52C2×Dic43⋊C4C2×C411yescharacteristic
53C2×Dic43⋊C4D411yescharacteristic
54C2×(C2×D43)⋊C4—21no—
55C2×(C2×D43)⋊C4—21no—
56C2×(C2×D43)⋊C4—21no—
57C2×(C2×D43)⋊C4—21no—
58C2×(C2×D43)⋊C4—21no—
59C2×(C2×D43)⋊C4C2×C411yescharacteristic
60C2×(C2×D43)⋊C4D411yescharacteristic
61C2×C4×Dic43D411yescharacteristic
62C4⋊(C43⋊C8)—21no—
63C4⋊(C43⋊C8)—21no—
64C4⋊(C43⋊C8)D412yescomplemented
65Dic43⋊C8—24no—
66C22⋊(C43⋊C8)—21no—
67C4×C43⋊C8—21no—
68C43⋊#95—21no—
69C43⋊#95—21no—
70C2×M16×C43—21no—
71C2×C4⋊C4×C43—21no—
72C2×C42×C43—21no—
73C2×C42×C43C2311yescharacteristic
74C4⋊C8×C43—21no—
75C4⋊C8×C43—21no—
76C4⋊C8×C43D412yescomplemented
77C22⋊C8×C43—21no—
78C4×C8×C43—21no—
79#95×C43C2×C411yescharacteristic
80#95×C43C2×C411yescharacteristic
81C23×D43—21no—
82C23×D43C22⋊C411yescharacteristic
83C22×C4×C43—21no—
84C22×C4×C43—21no—
85C22×C4×C43C22×C411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×Dic43—21no—
89C22×Dic43C22⋊C411yescharacteristic
90C22×Dic43C22⋊C411yescharacteristic
91C22×Dic43C22⋊C411yescharacteristic
92C2×D172—21no—
93C2×D172—21no—
94C2×D172—42no—
95C2×D172—42no—
96C2×D172—42no—
97C2×D172—42no—
98C2×C4×D43—21no—
99C2×C4×D43—21no—
100C2×C4×D43—21no—
101C2×C4×D43—21no—
102C2×C4×D43—41no—
103C2×C4×D43—41no—
104C2×C4×D43—41no—
105C2×C4×D43—41no—
106C2×C4×D43—41no—
107C2×C4×D43—41no—
108C2×C4×D43D812yes—
109C2×C4×D43SD1612yes—
110M16×C43—41no—
111M16×C43—41no—
112C2×C8×C43—22no—
113C2×C8×C43—41no—
114C4⋊C4×C43—42no—
115C42×C43—41no—
116C42×C43—41no—
117C42×C43C2×D411yescharacteristic
118C42×C43C2×D411yescharacteristic
119C42×C43#4111yescharacteristic
120C42×C43#4111yescharacteristic
121(C2×D43)⋊C4—21no—
122(C2×D43)⋊C4—21no—
123(C2×D43)⋊C4—21no—
124(C2×D43)⋊C4—21no—
125(C2×D43)⋊C4—42no—
126(C2×D43)⋊C4—42no—
127(C2×D43)⋊C4—41no—
128(C2×D43)⋊C4—41no—
129(C2×D43)⋊C4—42no—
130(C2×D43)⋊C4—42no—
131C4⋊Dic43—21no—
132C4⋊Dic43—21no—
133C4⋊Dic43—42no—
134Dic43⋊C4—21no—
135Dic43⋊C4—21no—
136Dic43⋊C4—21no—
137Dic43⋊C4—21no—
138C4×Dic43—21no—
139C4×Dic43—21no—
140#10621877—41no—
141#10621877—41no—
142C2×C43⋊C8—22no—
143C2×C43⋊C8—41no—
144#10621872—44no—
145C8×D43—44no—
146C23×C43C2×C22⋊C411yescharacteristic
147C22×D43—21no—
148C22×D43—21no—
149C22×D43—22no—
150C22×D43—41no—
151C22×D43—41no—
152C22×D43—41no—
153C22×D43—41no—
154C22×D43—41no—
155C22×D43—41no—
156C22×D43—41no—
157C22×D43—41no—
158C22×D43#10212yes—
159C2×C4×C43—22no—
160C2×C4×C43—41no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43—41no—
164C2×C4×C43—41no—
165C2×C4×C43—41no—
166C2×C4×C43—41no—
167C2×C4×C43C4×D411yescharacteristic
168C2×C4×C43C4×D411yescharacteristic
169C2×C4×C43#12011yescharacteristic
170C2×C4×C43#12111yescharacteristic
171C2×C4×C43#12111yescharacteristic
172C2×C4×C43#12311yescharacteristic
173C2×C4×C43C2×D811yescharacteristic
174C2×C4×C43C2×SD1611yescharacteristic
175C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
176C2×C4×C43#13711yescharacteristic
177C2×Dic43—21no—
178C2×Dic43—21no—
179C2×Dic43—21no—
180C2×Dic43—21no—
181C2×Dic43—41no—
182C2×Dic43—41no—
183C2×Dic43—41no—
184C2×Dic43—41no—
185C2×Dic43—41no—
186C2×Dic43#10212yes—
187D172—22no—
188D172—22no—
189D172—41no—
190D172—41no—
191D172—48no—
192C4×D43—22no—
193C4×D43—22no—
194C4×D43—22no—
195C4×D43—22no—
196C4×D43—81no—
197C4×D43—81no—
198C4×D43—81no—
199C4×D43—81no—
200C8×C43—42no—
201C8×C43—81no—
202C43⋊C8—42no—
203C43⋊C8—81no—
204#9035—431nomaximal, Sylow
205C22×C43—21no—
206C22×C43—21no—
207C22×C43#38611yescharacteristic
208C22×C43C2×#10211yescharacteristic
209C22×C43#41711yescharacteristic
210C2×D43—22no—
211C2×D43—41no—
212C2×D43—41no—
213C2×D43—42no—
214C2×D43—42no—
215C2×D43—42no—
216C2×D43—42no—
217C2×D43—81no—
218C2×D43—81no—
219C2×D43—81no—
220C2×D43—81no—
221C2×D43—81no—
222C4×C43—21no—
223C4×C43—21no—
224C4×C43—21no—
225C4×C43—21no—
226C4×C43—42no—
227C4×C43—81no—
228C4×C43#44711yescharacteristic
229C4×C43#44811yescharacteristic
230C4×C43#48011yescharacteristic
231C4×C43#48111yescharacteristic
232Dic43—22no—
233Dic43—41no—
234Dic43—41no—
235Dic43—81no—
236#2905—431no—
237#2392—431no—
238#1486—431no—
239#1486—431no—
240#1458—431no—
241#1303—431no—
242#1303D4311yescharacteristic, complemented
243C2×C43—21no—
244C2×C43—21no—
245C2×C43#187411yescharacteristic
246C2×C43#188411yescharacteristic
247C2×C43#189111yescharacteristic
248D43—42no—
249D43—82no—
250C22×M16—861no—
251C2×C4×D4—431no—
252C2×C4×D4—861no—
253C2×#117—431no—
254#431—431no—
255#431C2×D4311yescharacteristic
256#424—862no—
257#424—862no—
258#423—431no—
259#423—861no—
260#423C2×D4311yescharacteristic
261#398—431no—
262#397—431no—
263#396—861no—
264#394—431no—
265#394—861no—
266#392—431no—
267C4×C4⋊C4C2×D4311yescharacteristic
268C4×C22⋊C4—861no—
269D4⋊C8—862no—
270D4⋊C8—862no—
271#324—861no—
272#323—861no—
273C43#903511yescharacteristic, complemented, Sylow
274C22×D4—431no—
275C22×D4—861no—
276C23×C4—431no—
277C23×C4—861no—
278C2×M16—21no—
279C2×M16—862no—
280C2×M16—861no—
281C2×M16—1722no—
282C2×M16—1722no—
283C22×C8—862no—
284C4×D4—861no—
285C4×D4—861no—
286C4×D4—861no—
287C4×D4—861no—
288C4×D4—1722no—
289C4×D4—1722no—
290#117—861no—
291#117—861no—
292#117—861no—
293#117—861no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—431no—
296C2×C4⋊C4—431no—
297C2×C4⋊C4—431no—
298C2×C4⋊C4—861no—
299C2×C22⋊C4—431no—
300C2×C22⋊C4—431no—
301C2×C22⋊C4—861no—
302C2×C22⋊C4—861no—
303C2×C22⋊C4—861no—
304C2×C22⋊C4—861no—
305C2×C22⋊C4—861no—
306C2×C42—21no—
307C2×C42—431no—
308C2×C42C22×D4311yescharacteristic
309C4⋊C8—21no—
310C4⋊C8—21no—
311C4⋊C8—432no—
312C4⋊C8—864no—
313C4⋊C8—861no—
314C4⋊C8—861no—
315C4⋊C8D17212yescomplemented
316C22⋊C8—21no—
317C22⋊C8—861no—
318C4×C8—21no—
319C4×C8—861no—
320#95—861no—
321#95—861no—
322#95C4×D4311yescharacteristic
323#95C4×D4311yescharacteristic
324C24—431no—
325C24—861no—
326C2×D4—861no—
327C2×D4—861no—
328C2×D4—1722no—
329C2×D4—1722no—
330C2×D4—1722no—
331C2×D4—1722no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—431no—
335C22×C4—432no—
336C22×C4—432no—
337C22×C4—431no—
338C22×C4—431no—
339C22×C4—861no—
340C22×C4—861no—
341C22×C4—861no—
342C22×C4—861no—
343C22×C4—861no—
344C22×C4—1721no—
345C22×C4—1721no—
346C22×C4—1721no—
347C22×C4—1721no—
348C22×C4—1721no—
349C22×C4—1721no—
350C22×C4C2×C4×D4311yescharacteristic
351C22×C4D4×D4311yescharacteristic
352C22×C4D4×D4311yescharacteristic
353M16—41no—
354M16—41no—
355M16—1724no—
356M16—1721no—
357M16—1721no—
358C2×C8—22no—
359C2×C8—41no—
360C2×C8—862no—
361C2×C8—1724no—
362C2×C8—1721no—
363C4⋊C4—42no—
364C4⋊C4—861no—
365C4⋊C4—861no—
366C4⋊C4—861no—
367C4⋊C4—861no—
368C4⋊C4—861no—
369C4⋊C4—861no—
370C4⋊C4—1722no—
371C22⋊C4—861no—
372C22⋊C4—861no—
373C22⋊C4—861no—
374C22⋊C4—861no—
375C22⋊C4—1722no—
376C22⋊C4—1722no—
377C22⋊C4—1722no—
378C22⋊C4—1722no—
379C22⋊C4—1721no—
380C22⋊C4—1721no—
381C42—41no—
382C42—41no—
383C42—861no—
384C42—861no—
385C42C2×D17211yescharacteristic
386C42#1062189811yescharacteristic
387C42D4×D4311yescharacteristic
388C42#1062190211yescharacteristic
389C23—432no—
390C23—862no—
391C23—861no—
392C23—861no—
393C23—1721no—
394C23—1721no—
395C23—1721no—
396C23—1721no—
397C23—1721no—
398C23—1721no—
399C23—1721no—
400C23—1721no—
401C23C22⋊C4×D4311yescharacteristic
402D4—862no—
403D4—862no—
404D4—1721no—
405D4—1721no—
406D4—1728no—
407C2×C4—22no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—432no—
416C2×C4—861no—
417C2×C4—861no—
418C2×C4—862no—
419C2×C4—862no—
420C2×C4—862no—
421C2×C4—862no—
422C2×C4—861no—
423C2×C4—861no—
424C2×C4—3441no—
425C2×C4—3441no—
426C2×C4—3441no—
427C2×C4—3441no—
428C2×C4—1721no—
429C2×C4—1721no—
430C2×C4—1721no—
431C2×C4—1721no—
432C2×C4—1721no—
433C2×C4#1306328711yescharacteristic
434C2×C4C4×D17211yescharacteristic
435C2×C4#1306329511yescharacteristic
436C2×C4#1306329811yescharacteristic
437C2×C4#1306330011yescharacteristic
438C2×C4#1306331011yescharacteristic
439C2×C4D8×D4311yescharacteristic
440C2×C4SD16×D4311yescharacteristic
441C2×C4#1306335211yescharacteristic
442C2×C4#1306335711yescharacteristic
443C8—42no—
444C8—81no—
445C8—3441no—
446C8—1722no—
447C22—21no—
448C22—21no—
449C22—862no—
450C22—3441no—
451C22—3441no—
452C22—3441no—
453C22—3441no—
454C22—3441no—
455C22—1722no—
456C22—1722no—
457C22—1722no—
458C22—1722no—
459C22—1721no—
460C22—1721no—
461C22#1458277711yescharacteristic
462C22#102×D4311yescharacteristic
463C22#1458289911yescharacteristic
464C4—21no—
465C4—21no—
466C4—21no—
467C4—21no—
468C4—42no—
469C4—81no—
470C4—862no—
471C4—3441no—
472C4—1721no—
473C4—1721no—
474C4#1458303411yescharacteristic
475C4#1458303911yescharacteristic
476C4#1458321411yescharacteristic
477C4#1458321911yescharacteristic
478C2—21no—
479C2—21no—
480C2—3442no—
481C2—1722no—
482C2#1913491111yescharacteristic
483C2#1913497711yescharacteristic
484C2#1913501211yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1303C2
socleC22×C43#386
prime radical#14582809C4
cosocleC2×C42×C43C23
hypercenter#1303D43
hypocenterC43#9035
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
1. #19143157C2semidirect
3. #19133021C2semidirect
4. #19133019C2semidirect
5. #19132907C2semidirect
6. #19132498C2semidirect
7. C43×#1303C2semidirect
64. C4⋊(C43⋊C8)D4semidirect
76. C4⋊C8×C43D4semidirect
242. #1303D43semidirect
273. C43#9035semidirect
315. C4⋊C8D172semidirect

Maximal subgroups

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

subgroupindex
#191431572
#191378352
#191330212
#191330192
#191329072
#191324982
C43×#13032
#903543