Finite Group Databasebeta

← #24992932

Subgroups — #24992932

Order 11008.

514 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583114C211yesmaximal, characteristic
2#19133194C211yesmaximal, characteristic, complemented
3#19133038C211yesmaximal, characteristic, complemented
4#19132946C211yesmaximal, characteristic, complemented
5#19132464C211yesmaximal, characteristic, complemented
6#19132444C211yesmaximal, characteristic, complemented
7C43×#2974C211yesmaximal, characteristic, complemented
8C22×#10621883C411yescharacteristic
9C22×#10621882C411yescharacteristic
10C2×#13063313C2211yescharacteristic
11#14583114—21no—
12#14583114—21no—
13#14583114—21no—
14#14583114—21no—
15#14582956C2211yescharacteristic
16C2×C4⋊(C43⋊C8)C2211yescharacteristic
17C2×#13063248C411yescharacteristic
18C2×#13063245C411yescharacteristic
19C4×#10621877C2211yescharacteristic
20#14582638—22no—
21D4⋊(C43⋊C8)—21no—
22D4⋊(C43⋊C8)—21no—
23#14582622—21no—
24#14582622—21no—
25C2×C4×D4×C43C2211yescharacteristic
26C43×#436—21no—
27C43×#435—22no—
28C8×D4×C43—21no—
29C43×#432C2211yescharacteristic
30C43×#431C2211yescharacteristic
31C43×#407—21no—
32C2×C22⋊C8×C43—21no—
33C22×Dic86C2×C411yescharacteristic
34C22×D172C2×C411yescharacteristic
35C2×#10621883—21no—
36C2×#10621883—21no—
37C2×#10621883—42no—
38C2×#10621882—21no—
39C2×#10621882—21no—
40C2×#10621882—42no—
41C2×#10621877—21no—
42C22×C43⋊C8C2×C411yescharacteristic
43C22×C43⋊C8C2×C411yescharacteristic
44#13063313—21no—
45#13063313—21no—
46#13063313—21no—
47#13063313—21no—
48C2×(C2×D43)⋊C4—21no—
49C2×(C2×D43)⋊C4—21no—
50C4⋊(C43⋊C8)—21no—
51C4⋊(C43⋊C8)—21no—
52C4⋊(C43⋊C8)—21no—
53#13063248—21no—
54#13063248—21no—
55#13063245—21no—
56#13063245—21no—
57C22⋊(C43⋊C8)—21no—
58#13063236—21no—
59#13063236—21no—
60C4×C43⋊C8—21no—
61C22×D4×C43C2×C411yescharacteristic
62C23×C4×C43—21no—
63C2×M16×C43—22no—
64C22×C8×C43—22no—
65C4×D4×C43—21no—
66C4×D4×C43—21no—
67C4×D4×C43D411yescharacteristic
68C4×D4×C43D411yescharacteristic
69C4×D4×C43D411yescharacteristic
70C4×D4×C43D411yescharacteristic
71C2×C4⋊C4×C43C2×C411yescharacteristic
72C2×C22⋊C4×C43—21no—
73C2×C42×C43C2311yescharacteristic
74C4⋊C8×C43—21no—
75C4⋊C8×C43—21no—
76C22⋊C8×C43—22no—
77C22⋊C8×C43—22no—
78C22⋊C8×C43—21no—
79C22⋊C8×C43D411yescharacteristic
80C22⋊C8×C43D411yescharacteristic
81#97×C43D412yes—
82C4×C8×C43—21no—
83C24×C43—21no—
84C23×D43—21no—
85C2×D4×C43—21no—
86C2×D4×C43—22no—
87C2×D4×C43—41no—
88C2×D4×C43C22⋊C411yescharacteristic
89C2×D4×C43C22⋊C411yescharacteristic
90C22×C4×C43—21no—
91C22×C4×C43—21no—
92C22×C4×C43—21no—
93C22×C4×C43—21no—
94C22×C4×C43—21no—
95C22×C4×C43—82no—
96C22×C4×C43C22×C411yescharacteristic
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43#4111yescharacteristic
99C22×Dic43—21no—
100C2×D172—21no—
101C2×D172—21no—
102C2×D172—41no—
103C2×D172—41no—
104C2×Dic86—21no—
105C2×Dic86—21no—
106C2×Dic86—41no—
107C2×Dic86—41no—
108M16×C43—82no—
109C2×C8×C43—21no—
110C2×C8×C43—21no—
111C2×C8×C43—22no—
112C2×C8×C43—82no—
113C4⋊C4×C43—21no—
114C4⋊C4×C43C22⋊C411yescharacteristic
115C4⋊C4×C43C22⋊C411yescharacteristic
116C22⋊C4×C43—21no—
117C22⋊C4×C43—21no—
118C22⋊C4×C43—21no—
119C22⋊C4×C43—21no—
120C42×C43C2×D411yescharacteristic
121C42×C43C2×D411yescharacteristic
122C42×C43C2×D411yescharacteristic
123C42×C43#4111yescharacteristic
124#10621883—42no—
125#10621883—42no—
126#10621882—42no—
127#10621882—42no—
128(C2×D43)⋊C4—41no—
129(C2×D43)⋊C4—41no—
130(C2×D43)⋊C4—41no—
131(C2×D43)⋊C4—41no—
132#10621877—22no—
133#10621877—41no—
134C2×C43⋊C8—21no—
135C2×C43⋊C8—21no—
136C2×C43⋊C8—41no—
137C2×C43⋊C8—41no—
138C2×C43⋊C8—41no—
139C2×C43⋊C8—41no—
140C23×C43—21no—
141C23×C43—21no—
142C23×C43—42no—
143C23×C43—41no—
144C23×C43—41no—
145C23×C43—81no—
146C23×C43C4×D411yescharacteristic
147C22×D43—41no—
148C22×D43—41no—
149C22×D43—41no—
150C22×D43—81no—
151C22×D43—81no—
152D4×C43—21no—
153D4×C43—21no—
154D4×C43—21no—
155D4×C43—42no—
156D4×C43#10012yes—
157C2×C4×C43—21no—
158C2×C4×C43—21no—
159C2×C4×C43—21no—
160C2×C4×C43—21no—
161C2×C4×C43—21no—
162C2×C4×C43—21no—
163C2×C4×C43—41no—
164C2×C4×C43—42no—
165C2×C4×C43—42no—
166C2×C4×C43—81no—
167C2×C4×C43—81no—
168C2×C4×C43—81no—
169C2×C4×C43C2×C22⋊C411yescharacteristic
170C2×C4×C43C4×D411yescharacteristic
171C2×C4×C43#12011yescharacteristic
172C2×C4×C43#12111yescharacteristic
173C2×C4×C43#12111yescharacteristic
174C2×C4×C43#12311yescharacteristic
175C2×Dic43—41no—
176C2×Dic43—81no—
177D172—41no—
178D172—41no—
179D172—81no—
180Dic86—41no—
181Dic86—41no—
182Dic86—81no—
183C8×C43—41no—
184C8×C43—42no—
185C8×C43—41no—
186C43⋊C8—42no—
187C43⋊C8—41no—
188C43⋊C8—41no—
189C43⋊C8—81no—
190#9243—431nomaximal, Sylow
191C22×C43—21no—
192C22×C43—21no—
193C22×C43—22no—
194C22×C43—41no—
195C22×C43—41no—
196C22×C43—41no—
197C22×C43—41no—
198C22×C43—41no—
199C22×C43—82no—
200C22×C43—82no—
201C22×C43#38611yescharacteristic
202C22×C43#44311yescharacteristic
203C22×C43#44411yescharacteristic
204C2×D43—81no—
205C2×D43—81no—
206C2×D43—81no—
207C2×D43—161no—
208C2×D43—161no—
209C4×C43—21no—
210C4×C43—21no—
211C4×C43—21no—
212C4×C43—21no—
213C4×C43—21no—
214C4×C43—41no—
215C4×C43—41no—
216C4×C43C2×#10011yescharacteristic
217C4×C43#41311yescharacteristic
218Dic43—81no—
219C2×#463—431no—
220#2974D4311yescharacteristic, complemented
221#1527—431no—
222#1490—431no—
223#1469—431no—
224#1290—431no—
225#1283—431no—
226C2×C43—21no—
227C2×C43—21no—
228C2×C43—42no—
229C2×C43—81no—
230C2×C43#187611yescharacteristic
231C2×C43#190011yescharacteristic
232C2×C43#190411yescharacteristic
233D43—161no—
234C22×SD16—431no—
235C22×D8—431no—
236C2×#124—431no—
237C2×C4×D4C2×D4311yescharacteristic
238#463—861no—
239#463—861no—
240#463—861no—
241#463—861no—
242#436—21no—
243#435—22no—
244C8×D4—21no—
245#432—431no—
246#432C2×D4311yescharacteristic
247#431C2×D4311yescharacteristic
248C2×C4⋊C8—431no—
249C2×#103—431no—
250C2×#102—431no—
251#407—21no—
252C2×C22⋊C8—21no—
253C4×M16—431no—
254#329—862no—
255D4⋊C8—861no—
256D4⋊C8—861no—
257#323—861no—
258#323—861no—
259C43#924311yescharacteristic, complemented, Sylow
260C22×Q8—431no—
261C22×D4—431no—
262C22×D4C4×D4311yescharacteristic
263C23×C4—21no—
264C2×SD16—861no—
265C2×SD16—861no—
266C2×SD16—1722no—
267C2×D8—861no—
268C2×D8—861no—
269C2×D8—1722no—
270C2×M16—22no—
271C2×M16—861no—
272C22×C8—22no—
273C22×C8—431no—
274C22×C8—431no—
275#124—861no—
276#124—861no—
277#124—861no—
278#124—861no—
279C4×D4—21no—
280C4×D4—21no—
281C4×D4D17211yescharacteristic
282C4×D4D17211yescharacteristic
283C4×D4C22⋊D4311yescharacteristic
284C4×D4C22⋊D4311yescharacteristic
285C2×C4⋊C4C4×D4311yescharacteristic
286C2×C22⋊C4—21no—
287C2×C22⋊C4—861no—
288C2×C22⋊C4—861no—
289C2×C42C22×D4311yescharacteristic
290C4⋊C8—21no—
291C4⋊C8—21no—
292C4⋊C8—861no—
293C4⋊C8—861no—
294C4⋊C8—861no—
295#103—861no—
296#103—861no—
297#102—861no—
298#102—861no—
299C22⋊C8—22no—
300C22⋊C8—22no—
301C22⋊C8—21no—
302C22⋊C8—861no—
303C22⋊C8C22⋊D4311yescharacteristic
304C22⋊C8C22⋊D4311yescharacteristic
305#97—861no—
306#97—861no—
307#97C22⋊D4312yes—
308C4×C8—21no—
309C4×C8—861no—
310C24—21no—
311C24—861no—
312C2×Q8—861no—
313C2×Q8—861no—
314C2×Q8—1721no—
315C2×Q8—1721no—
316C2×D4—22no—
317C2×D4—21no—
318C2×D4—41no—
319C2×D4—861no—
320C2×D4—861no—
321C2×D4—1721no—
322C2×D4—1721no—
323C2×D4(C2×D43)⋊C411yescharacteristic
324C2×D4(C2×D43)⋊C411yescharacteristic
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—82no—
331C22×C4—861no—
332C22×C4C2×C4×D4311yescharacteristic
333C22×C4#1062189811yescharacteristic
334C22×C4C2×C22⋊D4311yescharacteristic
335SD16—1722no—
336SD16—1722no—
337D8—1722no—
338D8—1722no—
339M16—82no—
340M16—862no—
341M16—1721no—
342C2×C8—21no—
343C2×C8—21no—
344C2×C8—22no—
345C2×C8—82no—
346C2×C8—861no—
347C2×C8—861no—
348C2×C8—1721no—
349C2×C8—1721no—
350C2×C8—1721no—
351C2×C8—1721no—
352C4⋊C4—21no—
353C4⋊C4(C2×D43)⋊C411yescharacteristic
354C4⋊C4(C2×D43)⋊C411yescharacteristic
355C22⋊C4—21no—
356C22⋊C4—21no—
357C22⋊C4—21no—
358C22⋊C4—21no—
359C22⋊C4—1721no—
360C22⋊C4—1721no—
361C22⋊C4—1721no—
362C22⋊C4—1721no—
363C42C2×D17211yescharacteristic
364C42#1062189811yescharacteristic
365C42C2×C22⋊D4311yescharacteristic
366C42C2×C22⋊D4311yescharacteristic
367C23—21no—
368C23—21no—
369C23—42no—
370C23—41no—
371C23—41no—
372C23—81no—
373C23—3441no—
374C23—3441no—
375C23—1721no—
376C23—1721no—
377C23—1721no—
378C23C4×C22⋊D4311yescharacteristic
379Q8—3441no—
380Q8—1721no—
381Q8—1721no—
382D4—21no—
383D4—21no—
384D4—21no—
385D4—42no—
386D4—3441no—
387D4—1721no—
388D4—1721no—
389D4#1306324112yes—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—3441no—
403C2×C4—1721no—
404C2×C4C2×(C2×D43)⋊C411yescharacteristic
405C2×C4C4×C22⋊D4311yescharacteristic
406C2×C4#1306329411yescharacteristic
407C2×C4#1306329911yescharacteristic
408C2×C4#1306329911yescharacteristic
409C2×C4#1306330811yescharacteristic
410C8—41no—
411C8—42no—
412C8—41no—
413C8—3441no—
414C8—1722no—
415C8—1721no—
416C8—1721no—
417C22—21no—
418C22—21no—
419C22—22no—
420C22—41no—
421C22—41no—
422C22—41no—
423C22—41no—
424C22—41no—
425C22—82no—
426C22—82no—
427C22—3441no—
428C22—3441no—
429C22—3441no—
430C22—6881no—
431C22—6881no—
432C22#1458277811yescharacteristic
433C22#1458301411yescharacteristic
434C22#1458301911yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—41no—
441C4—41no—
442C4—3441no—
443C4C2×#1306324111yescharacteristic
444C4#1458288111yescharacteristic
445C2—21no—
446C2—21no—
447C2—42no—
448C2—81no—
449C2—6881no—
450C2#1913492211yescharacteristic
451C2#1913505811yescharacteristic
452C2#1913508211yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2974C2
socleC22×C43#386
prime radicalC22×#10621882C4
cosocleC2×C42×C43C23
hypercenter#2974D43
hypocenterC43#9243
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2974

Complements

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

NH ≅ G/Ntype
2. #19133194C2semidirect
3. #19133038C2semidirect
4. #19132946C2semidirect
5. #19132464C2semidirect
6. #19132444C2semidirect
7. C43×#2974C2semidirect
220. #2974D43semidirect
259. C43#9243semidirect

Maximal subgroups

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

subgroupindex
C2×#145831142
#191331942
#191330382
#191329462
#191324642
#191324442
C43×#29742
#924343