Finite Group Databasebeta

← #24989965

Subgroups — #24989965

Order 11008.

496 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19136991C211yesmaximal, characteristic
2#19134572C211yesmaximal, characteristic
3C4×(C2×D43)⋊C8C211yesmaximal, characteristic
4#19132436C211yesmaximal, characteristic, complemented
5#19132435C211yesmaximal, characteristic, complemented
6#19132434C211yesmaximal, characteristic, complemented
7C43×#1279C211yesmaximal, characteristic, complemented
8C2×C42×D43C2211yescharacteristic
9C2×C4⋊(C43⋊C8)C2211yescharacteristic
10C2×(C2×D43)⋊C8—21no—
11C2×(C2×D43)⋊C8—21no—
12C2×C4×C43⋊C8C2211yescharacteristic
13#14582766—21no—
14#14582764C411yescharacteristic
15#14582764C411yescharacteristic
16#14582761—21no—
17#14582756C411yescharacteristic
18#14582756C411yescharacteristic
19C4×C4⋊Dic43C2211yescharacteristic
20C4×(C2×D43)⋊C4—21no—
21#14582745—21no—
22#14582653—21no—
23#14582653—21no—
24C2×C4⋊C8×C43C2211yescharacteristic
25C2×C4×C8×C43C2211yescharacteristic
26C4×C4⋊C4×C43C2211yescharacteristic
27C22×C4×D43C2×C411yescharacteristic
28C22×C4×D43D411yescharacteristic
29C22×C4×D43D411yescharacteristic
30C22×C43⋊C8—21no—
31C22×C43⋊C8—21no—
32C2×C4⋊Dic43C2×C411yescharacteristic
33C2×C4⋊Dic43C2×C411yescharacteristic
34C2×(C2×D43)⋊C4—21no—
35C2×(C2×D43)⋊C4—21no—
36C2×C4×Dic43—21no—
37C2×C4×Dic43C2×C411yescharacteristic
38C2×C4×Dic43D411yescharacteristic
39C2×C4×Dic43D411yescharacteristic
40C42×D43—21no—
41C42×D43—21no—
42C42×D43—21no—
43C42×D43—21no—
44C4⋊(C43⋊C8)—21no—
45C4⋊(C43⋊C8)—21no—
46(C2×D43)⋊C8—24no—
47(C2×D43)⋊C8—42no—
48C4×C43⋊C8—21no—
49C4×C43⋊C8—21no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C43⋊#95—21no—
57C22×C8×C43—21no—
58C22×C8×C43—21no—
59C2×C4⋊C4×C43C2×C411yescharacteristic
60C2×C4⋊C4×C43C2×C411yescharacteristic
61C2×C42×C43—21no—
62C2×C42×C43C2311yescharacteristic
63C4⋊C8×C43—21no—
64C4⋊C8×C43—21no—
65C4×C8×C43—21no—
66C4×C8×C43—21no—
67#95×C43—21no—
68C23×D43C22⋊C411yescharacteristic
69C22×C4×C43—21no—
70C22×C4×C43—21no—
71C22×C4×C43C22×C411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C22×Dic43—21no—
75C22×Dic43—21no—
76C22×Dic43C22⋊C411yescharacteristic
77C22×Dic43C22⋊C411yescharacteristic
78C22×Dic43C22⋊C411yescharacteristic
79C2×C4×D43—21no—
80C2×C4×D43—21no—
81C2×C4×D43—21no—
82C2×C4×D43—21no—
83C2×C4×D43—21no—
84C2×C4×D43—21no—
85C2×C4×D43—21no—
86C2×C4×D43—21no—
87C2×C4×D43—21no—
88C2×C4×D43—21no—
89C2×C4×D43—21no—
90C2×C4×D43—21no—
91C2×C4×D43—21no—
92C2×C4×D43—21no—
93C2×C4×D43—22no—
94C2×C4×D43—41no—
95C2×C8×C43—22no—
96C2×C8×C43—41no—
97C2×C8×C43—41no—
98C2×C8×C43—41no—
99C2×C8×C43—41no—
100C2×C8×C43—41no—
101C4⋊C4×C43—21no—
102C4⋊C4×C43—21no—
103C4⋊C4×C43—21no—
104C4⋊C4×C43—21no—
105C42×C43—41no—
106C42×C43—41no—
107C42×C43#4111yescharacteristic
108C42×C43#4111yescharacteristic
109C42×C43#4111yescharacteristic
110C42×C43#4111yescharacteristic
111(C2×D43)⋊C4—42no—
112(C2×D43)⋊C4—42no—
113C4⋊Dic43—21no—
114C4⋊Dic43—21no—
115C4⋊Dic43—21no—
116C4⋊Dic43—21no—
117C4×Dic43—21no—
118C4×Dic43—21no—
119C4×Dic43—21no—
120C4×Dic43—21no—
121C4×Dic43—21no—
122C4×Dic43—21no—
123C4×Dic43—41no—
124C4×Dic43—41no—
125C2×C43⋊C8—22no—
126C2×C43⋊C8—41no—
127C2×C43⋊C8—41no—
128C2×C43⋊C8—41no—
129C2×C43⋊C8—41no—
130C2×C43⋊C8—41no—
131C23×C43C2×C22⋊C411yescharacteristic
132C22×D43—21no—
133C22×D43—21no—
134C22×D43—21no—
135C22×D43—21no—
136C22×D43—21no—
137C22×D43—21no—
138C22×D43#10412yes—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43#11711yescharacteristic
148C2×C4×C43#11711yescharacteristic
149C2×C4×C43#12311yescharacteristic
150C2×C4×C43#12311yescharacteristic
151C2×C4×C43#12311yescharacteristic
152C2×C4×C43#12311yescharacteristic
153C2×C4×C43#13111yescharacteristic
154C2×C4×C43#13111yescharacteristic
155C2×C4×C43#13111yescharacteristic
156C2×C4×C43#13111yescharacteristic
157C2×C4×C43#13511yescharacteristic
158C2×C4×C43#13511yescharacteristic
159C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C43#13711yescharacteristic
161C2×Dic43—21no—
162C2×Dic43—21no—
163C2×Dic43—21no—
164C2×Dic43—21no—
165C2×Dic43—21no—
166C2×Dic43—21no—
167C2×Dic43—21no—
168C2×Dic43—21no—
169C2×Dic43—21no—
170C2×Dic43—41no—
171C2×Dic43—41no—
172C2×Dic43—41no—
173C2×Dic43—41no—
174C2×Dic43—41no—
175C2×Dic43—41no—
176C4×D43—42no—
177C4×D43—42no—
178C4×D43—41no—
179C4×D43—41no—
180C4×D43—41no—
181C4×D43—41no—
182C4×D43—41no—
183C4×D43—41no—
184C4×D43—41no—
185C4×D43—41no—
186C8×C43—42no—
187C8×C43—81no—
188C43⋊C8—42no—
189C43⋊C8—81no—
190#8711—431nomaximal, Sylow
191C22×C43#38111yescharacteristic
192C22×C43#40811yescharacteristic
193C22×C43#40811yescharacteristic
194C22×C43#41611yescharacteristic
195C22×C43#41711yescharacteristic
196C22×C43C2×#10411yescharacteristic
197C22×C43#42111yescharacteristic
198C2×D43—22no—
199C2×D43—22no—
200C2×D43—22no—
201C2×D43—41no—
202C2×D43—41no—
203C2×D43—41no—
204C2×D43—41no—
205C4×C43—21no—
206C4×C43—21no—
207C4×C43—81no—
208C4×C43—81no—
209C4×C43#43311yescharacteristic
210C4×C43#43311yescharacteristic
211C4×C43#43311yescharacteristic
212C4×C43#43311yescharacteristic
213C4×C43#48211yescharacteristic
214C4×C43#48211yescharacteristic
215C4×C43#48511yescharacteristic
216C4×C43#48511yescharacteristic
217Dic43—41no—
218Dic43—41no—
219Dic43—41no—
220Dic43—81no—
221Dic43—81no—
222#2283—431no—
223#1797—431no—
224C4×C22⋊C8—431no—
225#1279—431no—
226#1279—431no—
227#1279—431no—
228#1279D4311yescharacteristic, complemented
229C2×C43#148211yescharacteristic
230C2×C43#148311yescharacteristic
231C2×C43#149411yescharacteristic
232C2×C43#149511yescharacteristic
233C2×C43#181811yescharacteristic
234C2×C43#182511yescharacteristic
235C2×C43#182611yescharacteristic
236D43—42no—
237C22×C42—431no—
238C2×C4⋊C8—431no—
239C2×C4⋊C8C2×D4311yescharacteristic
240C2×C22⋊C8—861no—
241C2×C22⋊C8—861no—
242C2×C4×C8—431no—
243C2×C4×C8C2×D4311yescharacteristic
244#383—861no—
245#382—431no—
246#382—431no—
247#381—861no—
248#380—431no—
249#380—431no—
250C4×C4⋊C4—431no—
251C4×C4⋊C4C2×D4311yescharacteristic
252C4×C22⋊C4—861no—
253#376—861no—
254#336—861no—
255#336—861no—
256C43#871111yescharacteristic, complemented, Sylow
257C23×C4—431no—
258C23×C4—431no—
259C23×C4—431no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—861no—
263C22×C8—861no—
264C2×C4⋊C4—431no—
265C2×C4⋊C4—431no—
266C2×C4⋊C4C4×D4311yescharacteristic
267C2×C4⋊C4C4×D4311yescharacteristic
268C2×C22⋊C4—861no—
269C2×C22⋊C4—861no—
270C2×C42—21no—
271C2×C42—431no—
272C2×C42—431no—
273C2×C42—431no—
274C2×C42—861no—
275C2×C42—861no—
276C2×C42—861no—
277C2×C42—861no—
278C2×C42—861no—
279C2×C42C22×D4311yescharacteristic
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8—861no—
283C4⋊C8—861no—
284C22⋊C8—864no—
285C22⋊C8—1722no—
286C4×C8—21no—
287C4×C8—21no—
288C4×C8—861no—
289C4×C8—861no—
290#95—21no—
291#95—861no—
292#95—861no—
293#95—861no—
294#95—861no—
295#95—861no—
296#95—861no—
297#95—861no—
298C24—431no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—431no—
302C22×C4—431no—
303C22×C4—431no—
304C22×C4—862no—
305C22×C4—861no—
306C22×C4—861no—
307C22×C4—861no—
308C22×C4—861no—
309C22×C4—861no—
310C22×C4—861no—
311C22×C4—861no—
312C22×C4—861no—
313C22×C4—861no—
314C22×C4—861no—
315C22×C4—861no—
316C22×C4—861no—
317C22×C4—861no—
318C22×C4—861no—
319C22×C4—861no—
320C22×C4—861no—
321C22×C4—1721no—
322C22×C4C2×C4×D4311yescharacteristic
323C22×C4D4×D4311yescharacteristic
324C22×C4D4×D4311yescharacteristic
325C2×C8—22no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—862no—
332C2×C8—1721no—
333C2×C8—1721no—
334C2×C8—1721no—
335C2×C8—1721no—
336C2×C8—1721no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—861no—
342C4⋊C4—861no—
343C4⋊C4—861no—
344C4⋊C4—861no—
345C22⋊C4—1722no—
346C22⋊C4—1722no—
347C42—41no—
348C42—41no—
349C42—861no—
350C42—861no—
351C42—861no—
352C42—861no—
353C42—861no—
354C42—861no—
355C42—1721no—
356C42—1721no—
357C42#1062189811yescharacteristic
358C42#1062189811yescharacteristic
359C42#1062190011yescharacteristic
360C42#1062190211yescharacteristic
361C23—432no—
362C23—861no—
363C23—861no—
364C23—861no—
365C23—861no—
366C23—861no—
367C23—861no—
368C23C22⋊C4×D4311yescharacteristic
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—861no—
378C2×C4—861no—
379C2×C4—861no—
380C2×C4—861no—
381C2×C4—861no—
382C2×C4—861no—
383C2×C4—861no—
384C2×C4—861no—
385C2×C4—861no—
386C2×C4—1722no—
387C2×C4—1722no—
388C2×C4—1721no—
389C2×C4—1721no—
390C2×C4—1721no—
391C2×C4—1721no—
392C2×C4—1721no—
393C2×C4—1721no—
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#1306328211yescharacteristic
403C2×C4#1306328311yescharacteristic
404C2×C4#1306330711yescharacteristic
405C2×C4#1306330711yescharacteristic
406C2×C4#1306331011yescharacteristic
407C2×C4#1306331011yescharacteristic
408C2×C4#1306333111yescharacteristic
409C2×C4#1306333111yescharacteristic
410C2×C4#1306333311yescharacteristic
411C2×C4#1306333311yescharacteristic
412C2×C4#1306334611yescharacteristic
413C2×C4#1306334811yescharacteristic
414C2×C4#1306334911yescharacteristic
415C2×C4#1306335411yescharacteristic
416C8—42no—
417C8—81no—
418C8—3441no—
419C8—1722no—
420C22—862no—
421C22—862no—
422C22—862no—
423C22—1721no—
424C22—1721no—
425C22—1721no—
426C22—1721no—
427C22#1458276111yescharacteristic
428C22#1458286411yescharacteristic
429C22#1458286411yescharacteristic
430C22#1458289411yescharacteristic
431C22#1458289711yescharacteristic
432C22#104×D4311yescharacteristic
433C22#1458291411yescharacteristic
434C4—21no—
435C4—21no—
436C4—81no—
437C4—81no—
438C4—3441no—
439C4—3441no—
440C4—1721no—
441C4—1721no—
442C4—1721no—
443C4#1458295811yescharacteristic
444C4#1458295911yescharacteristic
445C4#1458295911yescharacteristic
446C4#1458296111yescharacteristic
447C4#1458322211yescharacteristic
448C4#1458322611yescharacteristic
449C4#1458323911yescharacteristic
450C4#1458324311yescharacteristic
451C2—1722no—
452C2#1913300211yescharacteristic
453C2#1913300511yescharacteristic
454C2#1913305411yescharacteristic
455C2#1913305711yescharacteristic
456C2#1913466511yescharacteristic
457C2#1913468911yescharacteristic
458C2#1913469311yescharacteristic
subgroupG/H
centerC22×C4D4×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1279C2
socleC23×C43C2×C22⋊C4
prime radicalC23×D43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1279D43
hypocenterC43#8711
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
4. #19132436C2semidirect
5. #19132435C2semidirect
6. #19132434C2semidirect
7. C43×#1279C2semidirect
228. #1279D43semidirect
256. C43#8711semidirect

Maximal subgroups

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

subgroupindex
#191369912
#191345722
C4×(C2×D43)⋊C82
#191324362
#191324352
#191324342
C43×#12792
#871143