Finite Group Databasebeta

← #24991284

Subgroups — #24991284

Order 11008.

626 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
1#19143617C211yesmaximal, characteristic
2C4×#13063308C211yesmaximal, characteristic
3#19134663C211yesmaximal, characteristic, complemented
4#19132911C211yesmaximal, characteristic
5#19132442C211yesmaximal, characteristic, complemented
6#19132441C211yesmaximal, characteristic, complemented
7C43×#1817C211yesmaximal, characteristic, complemented
8C2×#13063308C411yescharacteristic
9C2×C4×C22⋊D43C2211yescharacteristic
10C8×C22⋊D43—22no—
11(C22⋊D43)⋊C8—22no—
12#14582949—21no—
13C2×C22⋊(C43⋊C8)C2211yescharacteristic
14C2×C22⋊(C43⋊C8)C2211yescharacteristic
15C22⋊C8×D43—21no—
16#14582790—21no—
17#14582783—21no—
18#14582778C411yescharacteristic
19#14582772C411yescharacteristic
20#14582762C411yescharacteristic
21C4×Dic43⋊C4—21no—
22C4×(C2×D43)⋊C4—21no—
23C4×C22⋊Dic43C2211yescharacteristic
24#14582654—22no—
25#14582624—21no—
26#14582622—21no—
27C22×C42×C43C2211yescharacteristic
28C2×C22⋊C8×C43C2211yescharacteristic
29C2×C22⋊C8×C43C2211yescharacteristic
30C43×#336—22no—
31C22×C22⋊D43C2×C411yescharacteristic
32C22×C4×D43D411yescharacteristic
33C22×C43⋊C8—21no—
34C22×C43⋊C8D412yes—
35C2×C8×D43—22no—
36#13063308—22no—
37#13063308C814yescomplemented
38C4×C22⋊D43—21no—
39C4×C22⋊D43—21no—
40C4×C22⋊D43—21no—
41C4×C22⋊D43—21no—
42C2×Dic43⋊C4—21no—
43C2×Dic43⋊C4—21no—
44C2×Dic43⋊C4D411yescharacteristic
45C2×C22⋊Dic43C2×C411yescharacteristic
46C2×C22⋊Dic43C2×C411yescharacteristic
47C2×C22⋊Dic43C2×C411yescharacteristic
48C2×(C2×D43)⋊C4—21no—
49C2×(C2×D43)⋊C4—21no—
50C2×(C2×D43)⋊C4D411yescharacteristic
51C2×C4×Dic43—21no—
52C2×C4×Dic43D411yescharacteristic
53Dic43⋊C8—22no—
54C22⋊(C43⋊C8)—21no—
55C22⋊(C43⋊C8)—21no—
56C22⋊(C43⋊C8)—21no—
57C22⋊(C43⋊C8)—21no—
58(C2×D43)⋊C8—22no—
59C8×Dic43—22no—
60C43⋊#95—21no—
61C43⋊#95—21no—
62C43⋊#95—21no—
63C43⋊#95—21no—
64C43⋊#95—21no—
65C23×C4×C43C2×C411yescharacteristic
66C23×C4×C43C2×C411yescharacteristic
67C23×C4×C43C2311yescharacteristic
68C22×C8×C43—21no—
69C22×C8×C43D412yes—
70C2×C42×C43—21no—
71C2×C42×C43—21no—
72C2×C42×C43—21no—
73C2×C42×C43—21no—
74C2×C42×C43—21no—
75C2×C42×C43—21no—
76C22⋊C8×C43—21no—
77C22⋊C8×C43—21no—
78C22⋊C8×C43—21no—
79C22⋊C8×C43—21no—
80C24×C43C22×C411yescharacteristic
81C23×D43C22⋊C411yescharacteristic
82C22×C4×C43—21no—
83C22×C4×C43—21no—
84C22×C4×C43—21no—
85C22×C4×C43—21no—
86C22×C4×C43—21no—
87C22×C4×C43—21no—
88C22×C4×C43—21no—
89C22×C4×C43—21no—
90C22×C4×C43—21no—
91C22×C4×C43—42no—
92C22×C4×C43—42no—
93C22×C4×C43C2×C812yescomplemented
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43#4111yescharacteristic
99C22×C4×C43#4111yescharacteristic
100C2×C22⋊D43—21no—
101C2×C22⋊D43—21no—
102C2×C22⋊D43—21no—
103C2×C22⋊D43—21no—
104C2×C22⋊D43C2×C812yes—
105C2×C22⋊D43M1612yes—
106C22×Dic43—21no—
107C22×Dic43—21no—
108C22×Dic43C22⋊C411yescharacteristic
109C22×Dic43C22⋊C411yescharacteristic
110C22×Dic43C22⋊C411yescharacteristic
111C2×C4×D43—21no—
112C2×C4×D43—21no—
113C2×C4×D43—42no—
114C2×C8×C43—22no—
115C2×C8×C43—42no—
116C2×C8×C43—42no—
117C2×C8×C43—41no—
118C42×C43—41no—
119C42×C43—41no—
120C42×C43—41no—
121C42×C43—41no—
122C22⋊Dic43—21no—
123C22⋊Dic43—21no—
124C22⋊Dic43—21no—
125C22⋊Dic43—21no—
126C22⋊Dic43—21no—
127C22⋊Dic43C2×C812yescomplemented
128(C2×D43)⋊C4—21no—
129(C2×D43)⋊C4—21no—
130(C2×D43)⋊C4—24no—
131(C2×D43)⋊C4—42no—
132Dic43⋊C4—21no—
133Dic43⋊C4—21no—
134Dic43⋊C4—24no—
135Dic43⋊C4—42no—
136C4×Dic43—21no—
137C4×Dic43—21no—
138C4×Dic43—42no—
139C2×C43⋊C8—22no—
140C2×C43⋊C8—42no—
141C2×C43⋊C8—42no—
142C2×C43⋊C8—41no—
143C8×D43—82no—
144C23×C43—41no—
145C23×C43—41no—
146C23×C43C2×C22⋊C411yescharacteristic
147C23×C43C4×D411yescharacteristic
148C23×C43C4×D411yescharacteristic
149C23×C43C22×C811yescharacteristic
150C23×C43C2×M1611yescharacteristic
151C23×C43#13111yescharacteristic
152C23×C43#13111yescharacteristic
153C22×D43—21no—
154C22×D43—21no—
155C22×D43—41no—
156C22×D43—41no—
157C22×D43C22⋊C812yes—
158C2×C4×C43—22no—
159C2×C4×C43—22no—
160C2×C4×C43—22no—
161C2×C4×C43—22no—
162C2×C4×C43—22no—
163C2×C4×C43—22no—
164C2×C4×C43—22no—
165C2×C4×C43—22no—
166C2×C4×C43—22no—
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×C43—41no—
174C2×C4×C43—41no—
175C2×C4×C43—41no—
176C2×C4×C43—41no—
177C2×C4×C43—41no—
178C2×C4×C43#12011yescharacteristic
179C2×C4×C43#12111yescharacteristic
180C2×C4×C43#12111yescharacteristic
181C2×C4×C43#12311yescharacteristic
182C22⋊D43—22no—
183C22⋊D43—22no—
184C22⋊D43—22no—
185C22⋊D43—22no—
186C2×Dic43—21no—
187C2×Dic43—21no—
188C2×Dic43—21no—
189C2×Dic43—21no—
190C2×Dic43—22no—
191C2×Dic43—41no—
192C2×Dic43—41no—
193C2×Dic43—41no—
194C2×Dic43—41no—
195C2×Dic43—41no—
196C2×Dic43—41no—
197C2×Dic43—41no—
198C2×Dic43C22⋊C812yes—
199C4×D43—42no—
200C4×D43—81no—
201C8×C43—42no—
202C8×C43—81no—
203C43⋊C8—42no—
204C43⋊C8—81no—
205#8966—431nomaximal, Sylow
206C22×C43—21no—
207C22×C43—21no—
208C22×C43—21no—
209C22×C43—21no—
210C22×C43—21no—
211C22×C43—21no—
212C22×C43—41no—
213C22×C43—41no—
214C22×C43—41no—
215C22×C43—41no—
216C22×C43#38611yescharacteristic
217C22×C43C2×C22⋊C811yescharacteristic
218C22×C43#40811yescharacteristic
219C22×C43C8×D411yescharacteristic
220C22×C43C8×D411yescharacteristic
221C22×C43#43511yescharacteristic
222C22×C43#43511yescharacteristic
223C2×D43—22no—
224C2×D43—41no—
225C2×D43—41no—
226C2×D43—42no—
227C2×D43—81no—
228C4×C43—21no—
229C4×C43—21no—
230C4×C43—21no—
231C4×C43—42no—
232C4×C43—42no—
233C4×C43#45812yes—
234Dic43—22no—
235Dic43—42no—
236Dic43—41no—
237Dic43—41no—
238Dic43—81no—
239#2972—431no—
240C4×#123—431no—
241#1817—431no—
242#1817D4311yescharacteristic, complemented
243#1459—431no—
244#1282—431no—
245#1282—431no—
246C2×C43—21no—
247C2×C43—21no—
248C2×C43—21no—
249C2×C43—21no—
250C2×C43—21no—
251C2×C43—21no—
252C2×C43#186911yescharacteristic
253C2×C43#189011yescharacteristic
254C2×C43#189111yescharacteristic
255D43—42no—
256C2×#123—431no—
257C2×C4×D4—431no—
258C22×C42C2×D4311yescharacteristic
259C8×D4—862no—
260C8×D4—862no—
261#431—861no—
262C2×C22⋊C8—431no—
263C2×C22⋊C8—431no—
264C2×C22⋊C8—861no—
265C2×C22⋊C8C2×D4311yescharacteristic
266C2×C22⋊C8C2×D4311yescharacteristic
267#388—861no—
268#387—861no—
269#386—431no—
270#385—431no—
271#381—431no—
272C4×C4⋊C4—861no—
273C4×C22⋊C4—431no—
274C4×C22⋊C4—861no—
275#336—22no—
276#336—862no—
277#324—861no—
278#323—861no—
279C43#896611yescharacteristic, complemented, Sylow
280C22×D4—431no—
281C23×C4—431no—
282C23×C4C4×D4311yescharacteristic
283C23×C4C4×D4311yescharacteristic
284C23×C4C22×D4311yescharacteristic
285C22×C8—21no—
286C22×C8—432no—
287C22×C8—862no—
288C22×C8—861no—
289C22×C8C22⋊D4312yes—
290#123—434no—
291#123—862no—
292C4×D4—861no—
293C4×D4—861no—
294C4×D4—861no—
295C4×D4—861no—
296C2×C4⋊C4—431no—
297C2×C4⋊C4—861no—
298C2×C4⋊C4—861no—
299C2×C22⋊C4—431no—
300C2×C22⋊C4—431no—
301C2×C22⋊C4—431no—
302C2×C22⋊C4—431no—
303C2×C22⋊C4—861no—
304C2×C22⋊C4—861no—
305C2×C42—21no—
306C2×C42—21no—
307C2×C42—21no—
308C2×C42—21no—
309C2×C42—21no—
310C2×C42—21no—
311C2×C42—431no—
312C2×C42—861no—
313C4⋊C8—862no—
314C22⋊C8—21no—
315C22⋊C8—21no—
316C22⋊C8—21no—
317C22⋊C8—21no—
318C22⋊C8—862no—
319C22⋊C8—861no—
320C22⋊C8—861no—
321C22⋊C8—861no—
322C22⋊C8—861no—
323C4×C8—862no—
324#95—861no—
325#95—861no—
326#95—861no—
327#95—861no—
328#95—861no—
329C24—431no—
330C24C2×C4×D4311yescharacteristic
331C2×D4—432no—
332C2×D4—432no—
333C2×D4—861no—
334C2×D4—861no—
335C2×D4—861no—
336C2×D4—861no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—42no—
347C22×C4—42no—
348C22×C4—431no—
349C22×C4—431no—
350C22×C4—431no—
351C22×C4—861no—
352C22×C4—861no—
353C22×C4—861no—
354C22×C4—861no—
355C22×C4—1722no—
356C22×C4C8×D4312yescomplemented
357C22×C4#1062189811yescharacteristic
358C22×C4D4×D4311yescharacteristic
359C22×C4D4×D4311yescharacteristic
360C22×C4D4×D4311yescharacteristic
361C22×C4#1062190011yescharacteristic
362C22×C4C2×C22⋊D4311yescharacteristic
363C2×C8—22no—
364C2×C8—42no—
365C2×C8—42no—
366C2×C8—41no—
367C2×C8—862no—
368C2×C8—3442no—
369C2×C8—1722no—
370C2×C8—1721no—
371C2×C8—1722no—
372C4⋊C4—864no—
373C4⋊C4—861no—
374C4⋊C4—861no—
375C4⋊C4—1722no—
376C22⋊C4—432no—
377C22⋊C4—864no—
378C22⋊C4—861no—
379C22⋊C4—861no—
380C22⋊C4—861no—
381C22⋊C4—861no—
382C22⋊C4—861no—
383C22⋊C4—861no—
384C22⋊C4—861no—
385C22⋊C4—1722no—
386C42—41no—
387C42—41no—
388C42—41no—
389C42—41no—
390C42—861no—
391C42—861no—
392C42—1722no—
393C23—41no—
394C23—41no—
395C23—432no—
396C23—861no—
397C23—861no—
398C23—1721no—
399C23—1721no—
400C23C22⋊C4×D4311yescharacteristic
401C23(C22⋊D43)⋊C411yescharacteristic
402C23C4×C22⋊D4311yescharacteristic
403C23C2×C8×D4311yescharacteristic
404C23M16×D4311yescharacteristic
405C23#1306333111yescharacteristic
406C23#1306333311yescharacteristic
407D4—862no—
408D4—862no—
409D4—862no—
410D4—862no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—432no—
432C2×C4—861no—
433C2×C4—861no—
434C2×C4—862no—
435C2×C4—861no—
436C2×C4—861no—
437C2×C4—3441no—
438C2×C4—1721no—
439C2×C4—1721no—
440C2×C4—1721no—
441C2×C4—1721no—
442C2×C4—1721no—
443C2×C4—1722no—
444C2×C4—1721no—
445C2×C4—1721no—
446C2×C4#1306329311yescharacteristic
447C2×C4#1306329611yescharacteristic
448C2×C4#1306329811yescharacteristic
449C2×C4#1306330711yescharacteristic
450C8—42no—
451C8—81no—
452C8—3441no—
453C8—1722no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—862no—
465C22—3441no—
466C22—1722no—
467C22—1721no—
468C22—1721no—
469C22#1458277511yescharacteristic
470C22C22⋊C8×D4311yescharacteristic
471C22#1458286411yescharacteristic
472C22(C22⋊D43)⋊C811yescharacteristic
473C22C8×C22⋊D4311yescharacteristic
474C22#1458296811yescharacteristic
475C22#1458297311yescharacteristic
476C4—21no—
477C4—21no—
478C4—21no—
479C4—42no—
480C4—42no—
481C4—862no—
482C4—3441no—
483C4—1722no—
484C4—1721no—
485C4—1721no—
486C4#1458308812yes—
487C2—21no—
488C2—21no—
489C2—21no—
490C2—21no—
491C2—21no—
492C2—21no—
493C2—1722no—
494C2#1913488411yescharacteristic
495C2#1913500511yescharacteristic
496C2#1913501011yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC23×C43C22×C8
FrattiniC23×C4C22×D43
FittingC43×#1817C2
socleC22×C43#386
prime radicalC22×C22⋊D43C2×C4
cosocleC23×C4×C43C23
hypercenter#1817D43
hypocenterC43#8966
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1817

Complements

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

NH ≅ G/Ntype
3. #19134663C2semidirect
5. #19132442C2semidirect
6. #19132441C2semidirect
7. C43×#1817C2semidirect
37. #13063308C8semidirect
93. C22×C4×C43C2×C8semidirect
127. C22⋊Dic43C2×C8semidirect
242. #1817D43semidirect
279. C43#8966semidirect
356. C22×C4C8×D43semidirect

Maximal subgroups

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

subgroupindex
#191436172
C4×#130633082
#191346632
#191329112
#191324422
#191324412
C43×#18172
#896643