Finite Group Databasebeta

← #24992817

Subgroups — #24992817

Order 11008.

562 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583176C211yesmaximal, characteristic
2C2×#14582976C211yesmaximal, characteristic
3#19135398C211yesmaximal, characteristic, complemented
4#19134596C211yesmaximal, characteristic
5#19132479C211yesmaximal, characteristic, complemented
6#19132429C211yesmaximal, characteristic, complemented
7C2×C43×#332C211yesmaximal, characteristic, complemented
8C22×#10621872—21no—
9C2×C4×D172C2211yescharacteristic
10#14583176—22no—
11#14583176C414yescomplemented
12#14582976—22no—
13#14582976—22no—
14C2×#13063258—21no—
15C2×C4⋊(C43⋊C8)C2211yescharacteristic
16C2×#13063249—21no—
17C2×#13063249—21no—
18C2×#13063247—21no—
19C2×#13063245—21no—
20C2×(C2×D43)⋊C8—21no—
21C2×C4×C43⋊C8C2211yescharacteristic
22#14582769C2211yescharacteristic
23#14582662—21no—
24C2×C4⋊Q8×C43C2211yescharacteristic
25C2×C4⋊C8×C43C2211yescharacteristic
26C2×C4⋊C8×C43C2211yescharacteristic
27C43×#332—22no—
28C22×D172D411yescharacteristic
29C22×C4×D43—21no—
30C2×#10621872—24no—
31C2×#10621872—42no—
32C2×#10621872—42no—
33C22×C43⋊C8—21no—
34C22×C43⋊C8D411yescharacteristic
35C22×C43⋊C8D411yescharacteristic
36C4×D172—21no—
37C4×D172—21no—
38C4×D172C2×C412yes—
39C4×D172D412yes—
40C2×C4⋊Dic43—21no—
41C2×C4⋊Dic43—21no—
42C2×C4⋊Dic43—21no—
43C2×C4⋊Dic43D411yescharacteristic
44C2×(C2×D43)⋊C4—21no—
45#13063258—24no—
46C4⋊(C43⋊C8)—21no—
47C4⋊(C43⋊C8)C2×C412yes—
48#13063249—42no—
49#13063249—42no—
50#13063247—42no—
51#13063245—24no—
52(C2×D43)⋊C8—24no—
53C4×C43⋊C8—21no—
54C4×C43⋊C8—21no—
55C22×Q8×C43—21no—
56C22×C8×C43—21no—
57C22×C8×C43—21no—
58C4⋊Q8×C43—21no—
59C4⋊Q8×C43—21no—
60C4⋊Q8×C43—21no—
61C4⋊Q8×C43C2×C412yes—
62C2×C4⋊C4×C43—21no—
63C2×C4⋊C4×C43—21no—
64C2×C42×C43C2311yescharacteristic
65C4⋊C8×C43—21no—
66C4⋊C8×C43—21no—
67C4⋊C8×C43—21no—
68C4⋊C8×C43D412yes—
69C23×D43—21no—
70C2×Q8×C43—22no—
71C2×Q8×C43—41no—
72C2×Q8×C43—41no—
73C2×Q8×C43—41no—
74C2×Q8×C43—41no—
75C2×Q8×C43—41no—
76C22×C4×C43—41no—
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43#4111yescharacteristic
80C22×Dic43—21no—
81C22×Dic43—41no—
82C2×D172—21no—
83C2×D172—21no—
84C2×D172—21no—
85C2×D172—21no—
86C2×D172—21no—
87C2×D172C22⋊C412yes—
88C2×C4×D43—22no—
89C2×C4×D43—22no—
90C2×C4×D43—41no—
91C2×C4×D43—41no—
92C2×C4×D43—41no—
93C2×C4×D43—41no—
94C2×C8×C43—22no—
95C2×C8×C43—41no—
96C2×C8×C43—41no—
97C2×C8×C43—41no—
98C2×C8×C43—41no—
99C2×C8×C43—41no—
100C4⋊C4×C43—22no—
101C4⋊C4×C43—22no—
102C4⋊C4×C43—41no—
103C4⋊C4×C43—41no—
104C42×C43C22×C411yescharacteristic
105C42×C43C2×D411yescharacteristic
106C42×C43C2×D411yescharacteristic
107C42×C43#4111yescharacteristic
108(C2×D43)⋊C4—22no—
109(C2×D43)⋊C4—22no—
110C4⋊Dic43—21no—
111C4⋊Dic43—41no—
112C4⋊Dic43—41no—
113C4⋊Dic43—41no—
114C4⋊Dic43—41no—
115C4⋊Dic43—81no—
116C4⋊Dic43C22⋊C412yes—
117C2×C43⋊C8—21no—
118C2×C43⋊C8—21no—
119C2×C43⋊C8—22no—
120C2×C43⋊C8—21no—
121C2×C43⋊C8—21no—
122C2×C43⋊C8—21no—
123C2×C43⋊C8—41no—
124C2×C43⋊C8—41no—
125C2×C43⋊C8D812yes—
126#10621872—48no—
127C23×C43#12111yescharacteristic
128C22×D43—22no—
129C22×D43—41no—
130C22×D43—41no—
131C22×D43—41no—
132C22×D43—41no—
133C22×D43—41no—
134C22×D43—41no—
135Q8×C43—42no—
136Q8×C43—42no—
137Q8×C43—81no—
138Q8×C43—81no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—42no—
142C2×C4×C43—81no—
143C2×C4×C43—81no—
144C2×C4×C43C2×C22⋊C411yescharacteristic
145C2×C4×C43C4×D411yescharacteristic
146C2×C4×C43C4×D411yescharacteristic
147C2×C4×C43#12011yescharacteristic
148C2×C4×C43#12111yescharacteristic
149C2×C4×C43#12311yescharacteristic
150C2×C4×C43C2×D811yescharacteristic
151C2×C4×C43#13511yescharacteristic
152C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C43#13711yescharacteristic
156C2×C4×C43#13711yescharacteristic
157C2×C4×C43#13711yescharacteristic
158C2×Dic43—22no—
159C2×Dic43—41no—
160C2×Dic43—41no—
161C2×Dic43—81no—
162C2×Dic43—81no—
163C2×Dic43—81no—
164D172—22no—
165D172—22no—
166D172—41no—
167D172—41no—
168C4×D43—42no—
169C4×D43—42no—
170C4×D43—42no—
171C4×D43—42no—
172C8×C43—42no—
173C8×C43—81no—
174C43⋊C8—22no—
175C43⋊C8—42no—
176C43⋊C8—41no—
177#9227—431nomaximal, Sylow
178C22×C43#38611yescharacteristic
179C22×C43#45911yescharacteristic
180C22×C43#46311yescharacteristic
181C22×C43#46811yescharacteristic
182C22×C43#47011yescharacteristic
183C22×C43#47111yescharacteristic
184C22×C43#47311yescharacteristic
185C2×D43—42no—
186C2×D43—42no—
187C2×D43—42no—
188C2×D43—81no—
189C2×D43—81no—
190C2×D43—81no—
191C2×D43—81no—
192C4×C43—21no—
193C4×C43—21no—
194C4×C43—82no—
195C4×C43#41711yescharacteristic
196C4×C43#41911yescharacteristic
197C4×C43C4×D811yescharacteristic
198C4×C43#44211yescharacteristic
199C4×C43#44711yescharacteristic
200C4×C43#44911yescharacteristic
201C4×C43#46811yescharacteristic
202C4×C43#47011yescharacteristic
203Dic43—42no—
204Dic43—161no—
205C2×#474—431no—
206C2×#436—431no—
207#1956—431no—
208#1802—431no—
209C2×#332D4311yescharacteristic, complemented
210#1296—431no—
211#1277—431no—
212C2×C43#168511yescharacteristic
213C2×C43#168911yescharacteristic
214C2×C43#169911yescharacteristic
215C2×C43#170311yescharacteristic
216C2×C43#187911yescharacteristic
217C2×C43#189411yescharacteristic
218C2×C43#190811yescharacteristic
219D43—82no—
220C22×M16—861no—
221C2×C4⋊Q8C2×D4311yescharacteristic
222C2×C4×D4—431no—
223#474—434no—
224#474—862no—
225#436—862no—
226#436—862no—
227C2×#107—861no—
228C2×C4⋊C8—431no—
229C2×C4⋊C8C2×D4311yescharacteristic
230C2×C4⋊C8C2×D4311yescharacteristic
231C2×#103—861no—
232C2×#103—861no—
233C2×#102—861no—
234C2×#102—861no—
235C2×C22⋊C8—861no—
236C2×C4×C8—431no—
237#384—431no—
238#340—861no—
239#332—22no—
240C43#922711yescharacteristic, complemented, Sylow
241C22×Q8—21no—
242C22×D4—431no—
243C23×C4—861no—
244C2×M16—864no—
245C2×M16—1722no—
246C2×M16—1722no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—431no—
250C22×C8—431no—
251C22×C8—861no—
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8C4×D4312yes—
256C4×D4—432no—
257C4×D4—432no—
258C4×D4—861no—
259C4×D4—861no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—431no—
263C2×C4⋊C4—861no—
264C2×C4⋊C4—861no—
265C2×C4⋊C4—861no—
266C2×C22⋊C4—861no—
267C2×C42C22×D4311yescharacteristic
268#107—864no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8—21no—
272C4⋊C8—432no—
273C4⋊C8—861no—
274C4⋊C8C22⋊D4312yes—
275#103—1722no—
276#103—1722no—
277#102—864no—
278#102—1722no—
279C22⋊C8—864no—
280C4×C8—861no—
281C4×C8—861no—
282C24—861no—
283C2×Q8—22no—
284C2×Q8—41no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×D4—432no—
290C2×D4—861no—
291C2×D4—861no—
292C2×D4—861no—
293C2×D4—861no—
294C2×D4—861no—
295C22×C4—41no—
296C22×C4—861no—
297C22×C4—862no—
298C22×C4—862no—
299C22×C4—1721no—
300C22×C4—1721no—
301C22×C4—1721no—
302C22×C4—1721no—
303C22×C4—1721no—
304C22×C4#1062189811yescharacteristic
305C22×C4D4×D4311yescharacteristic
306C22×C4D4×D4311yescharacteristic
307M16—1728no—
308C2×C8—22no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—432no—
315C2×C8—861no—
316C2×C8—861no—
317C2×C8—862no—
318C2×C8—861no—
319C2×C8—861no—
320C2×C8—861no—
321C2×C8—1721no—
322C2×C8—1721no—
323C4⋊C4—22no—
324C4⋊C4—22no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—432no—
328C4⋊C4—861no—
329C4⋊C4—3441no—
330C4⋊C4—1721no—
331C4⋊C4—1721no—
332C4⋊C4—1721no—
333C4⋊C4—1721no—
334C22⋊C4—862no—
335C22⋊C4—862no—
336C42C2×C4×D4311yescharacteristic
337C42D4×D4311yescharacteristic
338C42#1062190011yescharacteristic
339C42C2×C22⋊D4311yescharacteristic
340C23—862no—
341C23—1721no—
342C23—1721no—
343C23—1721no—
344C23—1721no—
345C23—1721no—
346C23—1721no—
347C23#1306329811yescharacteristic
348Q8—42no—
349Q8—42no—
350Q8—81no—
351Q8—81no—
352D4—862no—
353D4—862no—
354D4—1721no—
355D4—1721no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—862no—
362C2×C4—3441no—
363C2×C4—3441no—
364C2×C4—3441no—
365C2×C4—1721no—
366C2×C4—1721no—
367C2×C4—1722no—
368C2×C4—1722no—
369C2×C4—1722no—
370C2×C4—1722no—
371C2×C4C22⋊C4×D4311yescharacteristic
372C2×C4(C22⋊D43)⋊C411yescharacteristic
373C2×C4C4×C22⋊D4311yescharacteristic
374C2×C4#1306329311yescharacteristic
375C2×C4#1306329611yescharacteristic
376C2×C4#1306330711yescharacteristic
377C2×C4D8×D4311yescharacteristic
378C2×C4#1306334611yescharacteristic
379C2×C4#1306334911yescharacteristic
380C2×C4#1306335211yescharacteristic
381C2×C4#1306335211yescharacteristic
382C2×C4#1306335411yescharacteristic
383C2×C4#1306335711yescharacteristic
384C2×C4#1306335711yescharacteristic
385C8—42no—
386C8—81no—
387C8—862no—
388C8—1721no—
389C8—1722no—
390C22—3441no—
391C22—3441no—
392C22—3441no—
393C22—3441no—
394C22—1722no—
395C22—1722no—
396C22—1722no—
397C22#1458277511yescharacteristic
398C22#1458309311yescharacteristic
399C22#1458311311yescharacteristic
400C22#1458314811yescharacteristic
401C22#1458315611yescharacteristic
402C22#1458316511yescharacteristic
403C22#1458317311yescharacteristic
404C4—21no—
405C4—21no—
406C4—82no—
407C4—1722no—
408C4—6881no—
409C4#1458289911yescharacteristic
410C4#1458290611yescharacteristic
411C4#1458297911yescharacteristic
412C4#1458300811yescharacteristic
413C4#1458303111yescharacteristic
414C4#1458304311yescharacteristic
415C4#1458314211yescharacteristic
416C4#1458315411yescharacteristic
417C2—3442no—
418C2#1913406311yescharacteristic
419C2#1913408311yescharacteristic
420C2#1913414111yescharacteristic
421C2#1913416911yescharacteristic
422C2#1913494011yescharacteristic
423C2#1913502511yescharacteristic
424C2#1913510711yescharacteristic
subgroupG/H
centerC23#13063298
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC2×C43×#332C2
socleC23×C43#121
prime radicalC22×D172D4
cosocleC2×C42×C43C23
hypercenterC2×#332D43
hypocenterC43#9227
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
3. #19135398C2semidirect
5. #19132479C2semidirect
6. #19132429C2semidirect
7. C2×C43×#332C2semidirect
11. #14583176C4semidirect
209. C2×#332D43semidirect
240. C43#9227semidirect

Maximal subgroups

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

subgroupindex
C2×#145831762
C2×#145829762
#191353982
#191345962
#191324792
#191324292
C2×C43×#3322
#922743