Finite Group Databasebeta

← #24992165

Subgroups — #24992165

Order 11008.

694 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582952C211yesmaximal, characteristic, complemented
2#19142926C211yesmaximal, characteristic
3C2×#14582632C212yesmaximal
4#19132474C212yesmaximal, complemented
5C43×#1434C211yesmaximal, characteristic, complemented
6C2×#13063308—21no—
7C2×#13063299C2211yescharacteristic
8#14582952—24no—
9C2×C4⋊(C43⋊C8)—21no—
10C2×C22⋊(C43⋊C8)C2212yes—
11C2×C4×C43⋊C8—21no—
12#14582801C411yescharacteristic, complemented
13#14582801C411yescharacteristic, complemented
14#14582797C411yescharacteristic, complemented
15#14582797C411yescharacteristic, complemented
16#14582790—21no—
17#14582790—21no—
18#14582778—21no—
19#14582759C2211yescharacteristic
20#14582632—24no—
21C22×C42×C43C2211yescharacteristic
22C2×#95×C43—21no—
23C2×#95×C43—21no—
24C2×#95×C43C2212yes—
25C22×D172C2×C411yescharacteristic
26C22×C22⋊D43—21no—
27C22×C43⋊C8—22no—
28#13063308—42no—
29#13063308—42no—
30#13063299—22no—
31#13063299—22no—
32C2×C4⋊Dic43C2×C411yescharacteristic
33C2×C4⋊Dic43C2×C411yescharacteristic
34C2×C4⋊Dic43C2×C411yescharacteristic
35C2×Dic43⋊C4—21no—
36C2×Dic43⋊C4—21no—
37C2×C22⋊Dic43—21no—
38C2×(C2×D43)⋊C4—21no—
39C2×(C2×D43)⋊C4—21no—
40C2×(C2×D43)⋊C4—21no—
41C2×(C2×D43)⋊C4—21no—
42C2×(C2×D43)⋊C4—21no—
43C4⋊(C43⋊C8)—24no—
44C22⋊(C43⋊C8)—22no—
45C22⋊(C43⋊C8)D414yes—
46C4×C43⋊C8—24no—
47C43⋊#95—21no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C23×C4×C43—22no—
51C23×C4×C43D411yescharacteristic
52C23×C4×C43D411yescharacteristic
53C23×C4×C43C2311yescharacteristic
54C2×C42×C43—22no—
55C2×C42×C43—22no—
56C2×C42×C43C2×C411yescharacteristic
57C2×C42×C43C2×C411yescharacteristic
58C2×C42×C43D411yescharacteristic
59C2×C42×C43D411yescharacteristic
60#95×C43—24no—
61#95×C43—22no—
62#95×C43—22no—
63#95×C43—42no—
64C24×C43C2×D411yescharacteristic
65C23×D43—21no—
66C22×C4×C43—22no—
67C22×C4×C43—24no—
68C22×C4×C43—22no—
69C22×C4×C43—22no—
70C22×C4×C43—22no—
71C22×C4×C43—41no—
72C22×C4×C43—41no—
73C22×C4×C43—41no—
74C22×C4×C43—42no—
75C22×C4×C43—42no—
76C22×C4×C43—42no—
77C22×C4×C43—42no—
78C22×C4×C43—42no—
79C22×C4×C43—42no—
80C22×C4×C43C22⋊C411yescharacteristic
81C22×C4×C43C22⋊C411yescharacteristic
82C22×C4×C43C22⋊C411yescharacteristic
83C22×C4×C43C22⋊C411yescharacteristic
84C22×C4×C43D812yes—
85C22×C4×C43SD1612yes—
86C22×C4×C43C22×C411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D412yes—
89C22×C4×C43#4112yes—
90C2×C22⋊D43—42no—
91C2×C22⋊D43—41no—
92C2×C22⋊D43—41no—
93C2×C22⋊D43—42no—
94C22×Dic43—21no—
95C22×Dic43—21no—
96C22×Dic43—21no—
97C2×D172—22no—
98C2×D172—41no—
99C2×D172—41no—
100C42×C43—22no—
101C42×C43—22no—
102C42×C43—21no—
103C42×C43—21no—
104C42×C43—21no—
105C42×C43—21no—
106C22⋊Dic43—41no—
107C22⋊Dic43—41no—
108(C2×D43)⋊C4—42no—
109(C2×D43)⋊C4—42no—
110(C2×D43)⋊C4—42no—
111(C2×D43)⋊C4—42no—
112(C2×D43)⋊C4—41no—
113(C2×D43)⋊C4—41no—
114C4⋊Dic43—22no—
115C4⋊Dic43—41no—
116C4⋊Dic43—41no—
117Dic43⋊C4—42no—
118Dic43⋊C4—42no—
119C2×C43⋊C8—24no—
120C2×C43⋊C8—42no—
121C2×C43⋊C8—42no—
122C23×C43—21no—
123C23×C43—21no—
124C23×C43—21no—
125C23×C43—21no—
126C23×C43C2×C22⋊C411yescharacteristic
127C23×C43#12112yes—
128C23×C43C2×D811yescharacteristic
129C23×C43C2×SD1611yescharacteristic
130C23×C43#13512yes—
131C22×D43—41no—
132C22×D43—41no—
133C22×D43—41no—
134C22×D43—41no—
135C22×D43—41no—
136C22×D43—41no—
137C22×D43—41no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—21no—
145C2×C4×C43—21no—
146C2×C4×C43—21no—
147C2×C4×C43—21no—
148C2×C4×C43—24no—
149C2×C4×C43—24no—
150C2×C4×C43—21no—
151C2×C4×C43—21no—
152C2×C4×C43—21no—
153C2×C4×C43—42no—
154C2×C4×C43—42no—
155C2×C4×C43—44no—
156C2×C4×C43—44no—
157C2×C4×C43—44no—
158C2×C4×C43—44no—
159C2×C4×C43—82no—
160C2×C4×C43—82no—
161C2×C4×C43—82no—
162C2×C4×C43—82no—
163C2×C4×C43#10212yes—
164C2×C4×C43#10212yes—
165C2×C4×C43#10412yes—
166C2×C4×C43C4×D412yes—
167C2×C4×C43#12011yescharacteristic
168C2×C4×C43#12311yescharacteristic
169C22⋊D43—82no—
170C22⋊D43—82no—
171C2×Dic43—41no—
172C2×Dic43—41no—
173C2×Dic43—41no—
174C2×Dic43—41no—
175C2×Dic43—41no—
176C2×Dic43—41no—
177C2×Dic43—41no—
178C2×Dic43—41no—
179C2×Dic43—41no—
180D172—82no—
181C43⋊C8—44no—
182#9114—431nomaximal, Sylow
183C22×C43—22no—
184C22×C43—22no—
185C22×C43—22no—
186C22×C43—21no—
187C22×C43—21no—
188C22×C43—21no—
189C22×C43—21no—
190C22×C43—22no—
191C22×C43#38611yescharacteristic
192C22×C43#41011yescharacteristic
193C22×C43#41011yescharacteristic
194C22×C43C2×#10211yescharacteristic
195C22×C43#41611yescharacteristic
196C22×C43C2×#10411yescharacteristic
197C22×C43#42111yescharacteristic
198C22×C43#46512yes—
199C22×C43#46612yes—
200C2×D43—81no—
201C2×D43—81no—
202C2×D43—81no—
203C2×D43—81no—
204C2×D43—81no—
205C2×D43—81no—
206C2×D43—81no—
207C4×C43—22no—
208C4×C43—22no—
209C4×C43—22no—
210C4×C43—21no—
211C4×C43—22no—
212C4×C43—21no—
213C4×C43—41no—
214C4×C43—84no—
215Dic43—81no—
216Dic43—81no—
217Dic43—81no—
218C2×#431—431no—
219#2854—431no—
220C2×#327—432no—
221#1434D4311yescharacteristic, complemented
222#1294—432no—
223C2×C43—22no—
224C2×C43—22no—
225C2×C43#150011yescharacteristic
226C2×C43#150211yescharacteristic
227C2×C43#151711yescharacteristic
228C2×C43#152111yescharacteristic
229C2×C43#187111yescharacteristic
230C2×C43#189311yescharacteristic
231C2×C43#189911yescharacteristic
232D43—161no—
233C2×#123—861no—
234C2×#121—431no—
235C22×C42C2×D4311yescharacteristic
236#431—864no—
237C2×C4⋊C8—861no—
238C2×C22⋊C8—432no—
239C2×C4×C8—861no—
240#390—431no—
241#390—431no—
242#389—431no—
243#389—431no—
244#388—861no—
245#388—861no—
246#386—861no—
247#380—431no—
248C2×#95—21no—
249C2×#95—21no—
250C2×#95C2×D4312yes—
251#327—864no—
252C43#911411yescharacteristic, complemented, Sylow
253C22×D4—431no—
254C22×D4—861no—
255C23×C4—22no—
256C23×C4C22⋊D4311yescharacteristic
257C23×C4C22⋊D4311yescharacteristic
258C23×C4C22×D4311yescharacteristic
259C22×C8—862no—
260#123—1722no—
261#123—1722no—
262#121—862no—
263#121—862no—
264C2×C4⋊C4—431no—
265C2×C4⋊C4—431no—
266C2×C4⋊C4—431no—
267C2×C4⋊C4—861no—
268C2×C4⋊C4—861no—
269C2×C22⋊C4—861no—
270C2×C22⋊C4—861no—
271C2×C22⋊C4—861no—
272C2×C22⋊C4—861no—
273C2×C22⋊C4—861no—
274C2×C22⋊C4—861no—
275C2×C42—22no—
276C2×C42—22no—
277C2×C42C4×D4311yescharacteristic
278C2×C42C4×D4311yescharacteristic
279C2×C42D17211yescharacteristic
280C2×C42D17211yescharacteristic
281C4⋊C8—864no—
282C22⋊C8—434no—
283C22⋊C8—862no—
284C4×C8—864no—
285#95—24no—
286#95—22no—
287#95—22no—
288#95—42no—
289#95—861no—
290#95—861no—
291#95—861no—
292C24—861no—
293C24C2×C22⋊D4311yescharacteristic
294C2×D4—862no—
295C2×D4—1721no—
296C2×D4—1721no—
297C2×D4—1722no—
298C2×D4—1721no—
299C2×D4—1721no—
300C2×D4—1722no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—24no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—861no—
316C22×C4—861no—
317C22×C4—861no—
318C22×C4(C2×D43)⋊C411yescharacteristic
319C22×C4(C2×D43)⋊C411yescharacteristic
320C22×C4(C2×D43)⋊C411yescharacteristic
321C22×C4(C2×D43)⋊C411yescharacteristic
322C22×C4#1062188212yes—
323C22×C4#1062188412yes—
324C22×C4C2×C4×D4311yescharacteristic
325C22×C4C2×D17211yescharacteristic
326C22×C4D4×D4312yes—
327C22×C4#1062190012yes—
328C2×C8—864no—
329C2×C8—1722no—
330C2×C8—1722no—
331C4⋊C4—862no—
332C4⋊C4—1721no—
333C4⋊C4—1721no—
334C4⋊C4—1722no—
335C4⋊C4—1722no—
336C22⋊C4—1722no—
337C22⋊C4—1721no—
338C22⋊C4—1721no—
339C22⋊C4—1722no—
340C22⋊C4—1722no—
341C22⋊C4—1722no—
342C22⋊C4—1721no—
343C22⋊C4—1721no—
344C42—22no—
345C42—22no—
346C42—21no—
347C42—21no—
348C42—21no—
349C42—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—1721no—
355C23—1721no—
356C23—1721no—
357C23—1721no—
358C23—1721no—
359C23—1721no—
360C23—1721no—
361C23C2×(C2×D43)⋊C411yescharacteristic
362C23#1306329712yes—
363C23C2×#1062188211yescharacteristic
364C23C2×#1062188411yescharacteristic
365C23#1306334512yes—
366D4—3442no—
367D4—3442no—
368D4—3442no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—24no—
374C2×C4—24no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—44no—
387C2×C4—44no—
388C2×C4—44no—
389C2×C4—44no—
390C2×C4—82no—
391C2×C4—82no—
392C2×C4—82no—
393C2×C4—82no—
394C2×C4—1721no—
395C2×C4—1721no—
396C2×C4—1721no—
397C2×C4—1721no—
398C2×C4—1721no—
399C2×C4—1721no—
400C2×C4—1721no—
401C2×C4—1721no—
402C2×C4—1721no—
403C2×C4#1306324512yes—
404C2×C4#1306324512yes—
405C2×C4#1306325312yes—
406C2×C4(C22⋊D43)⋊C412yes—
407C2×C4#1306329511yescharacteristic
408C2×C4#1306330911yescharacteristic
409C8—1724no—
410C22—22no—
411C22—22no—
412C22—21no—
413C22—21no—
414C22—22no—
415C22—21no—
416C22—21no—
417C22—22no—
418C22—3441no—
419C22—3441no—
420C22—3441no—
421C22—3441no—
422C22—3441no—
423C22—3441no—
424C22—3441no—
425C22#1458277611yescharacteristic
426C22#1458287211yescharacteristic
427C22#1458287211yescharacteristic
428C22C2×#1306324511yescharacteristic
429C22#1458289311yescharacteristic
430C22C2×#1306325311yescharacteristic
431C22#1458291711yescharacteristic
432C22#1458313012yes—
433C22#1458313312yes—
434C4—22no—
435C4—22no—
436C4—21no—
437C4—22no—
438C4—21no—
439C4—22no—
440C4—41no—
441C4—84no—
442C4—3441no—
443C4—3441no—
444C4—3441no—
445C2—22no—
446C2—22no—
447C2—6881no—
448C2#1913307911yescharacteristic
449C2#1913308911yescharacteristic
450C2#1913315411yescharacteristic
451C2#1913317011yescharacteristic
452C2#1913489511yescharacteristic
453C2#1913502111yescharacteristic
454C2#1913505111yescharacteristic
subgroupG/H
centerC23C2×(C2×D43)⋊C4
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1434C2
socleC23×C43C2×C22⋊C4
prime radicalC2×#13063299C22
cosocleC23×C4×C43C23
hypercenter#1434D43
hypocenterC43#9114
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1434

Complements

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

NH ≅ G/Ntype
1. C2×#14582952C2semidirect
4. #19132474C2semidirect
5. C43×#1434C2semidirect
12. #14582801C4semidirect
13. #14582801C4semidirect
14. #14582797C4semidirect
15. #14582797C4semidirect
221. #1434D43semidirect
252. C43#9114semidirect

Maximal subgroups

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

subgroupindex
C2×#145829522
#191429262
C2×#145826322
#191324742
C43×#14342
#911443