Finite Group Databasebeta

← #24992991

Subgroups — #24992991

Order 11008.

528 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583176C211yesmaximal, characteristic
2M16×D172C211yesmaximal, characteristic
3#19133267C211yesmaximal, characteristic, complemented
4#19133019C211yesmaximal, characteristic
5#19132469C211yesmaximal, characteristic, complemented
6#19132446C211yesmaximal, characteristic, complemented
7C43×#1966C211yesmaximal, characteristic, complemented
8C2×M16×D43—21no—
9C2×C4×D172C2211yescharacteristic
10#14583176—21no—
11#14583176—21no—
12#14583176—21no—
13#14583176—21no—
14#14582978—21no—
15#14582972—22no—
16C8×D172—21no—
17#14582952C2211yescharacteristic
18C2×#13063258C412yes—
19#14582923C2211yescharacteristic
20C2×C4⋊(C43⋊C8)C2211yescharacteristic
21C2×#13063245C412yes—
22#14582862—21no—
23#14582645—22no—
24#14582626—21no—
25#14582626—21no—
26C2×C4⋊Q8×C43C2211yescharacteristic
27C43×#423C2211yescharacteristic
28C2×#101×C43—21no—
29C2×#101×C43—21no—
30C4×M16×C43C2211yescharacteristic
31C22×D172C2×C411yescharacteristic
32C22×C4×D43—21no—
33C2×#10621877—21no—
34C2×#10621872—22no—
35M16×D43—42no—
36M16×D43—42no—
37C22×C43⋊C8C2×C412yes—
38C2×C8×D43—22no—
39C4×D172—21no—
40C4×D172—21no—
41C4×D172D411yescharacteristic
42C4×D172D411yescharacteristic
43C4×D172D411yescharacteristic
44C4×D172D411yescharacteristic
45C2×C4⋊Dic43C2×C411yescharacteristic
46C2×(C2×D43)⋊C4—21no—
47#13063258—22no—
48#13063258—22no—
49C4⋊(C43⋊C8)—21no—
50C4⋊(C43⋊C8)—21no—
51C4⋊(C43⋊C8)—21no—
52C4⋊(C43⋊C8)—21no—
53C4⋊(C43⋊C8)D412yes—
54#13063245—22no—
55#13063245—22no—
56C22⋊(C43⋊C8)—21no—
57(C2×D43)⋊C8—22no—
58(C2×D43)⋊C8—22no—
59C4×C43⋊C8—21no—
60C22×Q8×C43—21no—
61C2×M16×C43—21no—
62C2×M16×C43D411yescharacteristic
63C2×M16×C43D411yescharacteristic
64C4⋊Q8×C43—21no—
65C4⋊Q8×C43—21no—
66C4⋊Q8×C43—21no—
67C4⋊Q8×C43—21no—
68C2×C4⋊C4×C43—21no—
69C2×C4⋊C4×C43C2×C412yes—
70C2×C42×C43C2311yescharacteristic
71C4⋊C8×C43—21no—
72C4⋊C8×C43—21no—
73#101×C43—42no—
74#101×C43—42no—
75#97×C43—21no—
76C4×C8×C43—21no—
77C23×D43—21no—
78C2×Q8×C43—41no—
79C2×Q8×C43—41no—
80C2×Q8×C43—41no—
81C2×Q8×C43—41no—
82C2×Q8×C43—41no—
83C2×Q8×C43—41no—
84C22×C4×C43—22no—
85C22×C4×C43C22×C411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43#4111yescharacteristic
88C22×Dic43—21no—
89C2×D172—21no—
90C2×D172—22no—
91C2×D172—41no—
92C2×D172C22⋊C411yescharacteristic
93C2×D172C22⋊C411yescharacteristic
94C2×C4×D43—21no—
95C2×C4×D43—21no—
96C2×C4×D43—21no—
97C2×C4×D43—21no—
98C2×C4×D43—41no—
99C2×C4×D43—41no—
100C2×C4×D43—41no—
101C2×C4×D43—41no—
102M16×C43—21no—
103M16×C43—21no—
104M16×C43—21no—
105M16×C43—41no—
106M16×C43—41no—
107M16×C43D812yes—
108C2×C8×C43—21no—
109C2×C8×C43—21no—
110C2×C8×C43—41no—
111C4⋊C4×C43—22no—
112C4⋊C4×C43—22no—
113C4⋊C4×C43—41no—
114C4⋊C4×C43—41no—
115C42×C43C2×D411yescharacteristic
116C42×C43C2×D411yescharacteristic
117C42×C43C2×D411yescharacteristic
118C42×C43#4111yescharacteristic
119(C2×D43)⋊C4—21no—
120(C2×D43)⋊C4—21no—
121(C2×D43)⋊C4—21no—
122(C2×D43)⋊C4—21no—
123C4⋊Dic43—21no—
124C4⋊Dic43C22⋊C411yescharacteristic
125C4⋊Dic43C22⋊C411yescharacteristic
126#10621877—41no—
127#10621877—41no—
128C2×C43⋊C8—22no—
129C2×C43⋊C8—22no—
130C2×C43⋊C8—42no—
131C2×C43⋊C8—41no—
132#10621872—44no—
133C8×D43—44no—
134C23×C43C4×D411yescharacteristic
135C22×D43—21no—
136C22×D43—21no—
137C22×D43—42no—
138C22×D43—41no—
139C22×D43—41no—
140C22×D43—81no—
141Q8×C43—81no—
142Q8×C43—81no—
143Q8×C43—81no—
144Q8×C43—81no—
145C2×C4×C43—21no—
146C2×C4×C43—21no—
147C2×C4×C43—41no—
148C2×C4×C43—42no—
149C2×C4×C43—42no—
150C2×C4×C43—42no—
151C2×C4×C43C2×C22⋊C411yescharacteristic
152C2×C4×C43C4×D411yescharacteristic
153C2×C4×C43#12011yescharacteristic
154C2×C4×C43#12111yescharacteristic
155C2×C4×C43#12111yescharacteristic
156C2×C4×C43#12311yescharacteristic
157C2×C4×C43C2×D811yescharacteristic
158C2×C4×C43#13511yescharacteristic
159C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
161C2×Dic43—21no—
162C2×Dic43—21no—
163C2×Dic43—41no—
164C2×Dic43—41no—
165D172—21no—
166D172—21no—
167D172—21no—
168D172—42no—
169D172#10112yescomplemented
170C4×D43—41no—
171C4×D43—41no—
172C4×D43—41no—
173C4×D43—41no—
174C4×D43—41no—
175C4×D43—41no—
176C4×D43—41no—
177C4×D43—41no—
178C8×C43—22no—
179C8×C43—41no—
180C8×C43—81no—
181C43⋊C8—42no—
182C43⋊C8—42no—
183C43⋊C8—81no—
184#9251—431nomaximal, Sylow
185C22×C43—21no—
186C22×C43—21no—
187C22×C43#38611yescharacteristic
188C22×C43C4×D811yescharacteristic
189C22×C43#44211yescharacteristic
190C2×D43—22no—
191C2×D43—41no—
192C2×D43—41no—
193C2×D43—41no—
194C2×D43—41no—
195C2×D43—41no—
196C2×D43—82no—
197C2×D43—82no—
198C4×C43—21no—
199C4×C43—21no—
200C4×C43—21no—
201C4×C43—82no—
202C4×C43C2×#10111yescharacteristic
203C4×C43#41311yescharacteristic
204C4×C43#44711yescharacteristic
205C4×C43#44911yescharacteristic
206C4×C43#45911yescharacteristic
207C4×C43#46311yescharacteristic
208Dic43—41no—
209Dic43—41no—
210C2×#474—431no—
211D4×M16—431no—
212#1966D4311yescharacteristic, complemented
213#1546—431no—
214#1486—431no—
215#1292—431no—
216#1283—431no—
217C2×C43—21no—
218C2×C43—21no—
219C2×C43#187911yescharacteristic
220C2×C43#190111yescharacteristic
221C2×C43#190211yescharacteristic
222D43—42no—
223D43—81no—
224C22×M16—861no—
225C2×C4⋊Q8C2×D4311yescharacteristic
226C2×C4×D4—431no—
227#474—861no—
228#474—861no—
229#474—861no—
230#474—861no—
231#436—861no—
232#435—862no—
233C8×D4—861no—
234#431—431no—
235C2×#107—432no—
236#423—431no—
237#423C2×D4311yescharacteristic
238C2×C4⋊C8—431no—
239C2×#102—432no—
240C2×#101—21no—
241C2×#101—21no—
242#407—861no—
243C4×M16C2×D4311yescharacteristic
244#332—862no—
245D4⋊C8—861no—
246D4⋊C8—861no—
247C43#925111yescharacteristic, complemented, Sylow
248C22×Q8—21no—
249C22×D4—431no—
250C23×C4—861no—
251C2×M16—21no—
252C2×M16—862no—
253C2×M16—861no—
254C2×M16—1722no—
255C2×M16—1722no—
256C2×M16C22⋊D4311yescharacteristic
257C2×M16C22⋊D4311yescharacteristic
258C22×C8—432no—
259C22×C8—862no—
260C4⋊Q8—21no—
261C4⋊Q8—21no—
262C4⋊Q8—21no—
263C4⋊Q8—21no—
264C4×D4—431no—
265C4×D4—431no—
266C4×D4—431no—
267C4×D4—431no—
268C4×D4—861no—
269C4×D4—861no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—431no—
272C2×C4⋊C4C4×D4312yes—
273C2×C22⋊C4—861no—
274C2×C42C22×D4311yescharacteristic
275#107—862no—
276#107—862no—
277C4⋊C8—21no—
278C4⋊C8—21no—
279C4⋊C8—432no—
280C4⋊C8—861no—
281C4⋊C8—861no—
282C4⋊C8—861no—
283C4⋊C8—861no—
284#102—862no—
285#102—862no—
286#101—42no—
287#101—42no—
288C22⋊C8—862no—
289C22⋊C8—862no—
290C22⋊C8—861no—
291#97—21no—
292C4×C8—21no—
293C4×C8—861no—
294C24—861no—
295C2×Q8—41no—
296C2×Q8—41no—
297C2×Q8—41no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×Q8—41no—
301C2×D4—431no—
302C2×D4—431no—
303C2×D4—862no—
304C2×D4—861no—
305C2×D4—1721no—
306C22×C4—22no—
307C22×C4—861no—
308C22×C4—861no—
309C22×C4—861no—
310C22×C4—861no—
311C22×C4—861no—
312C22×C4—1721no—
313C22×C4—1721no—
314C22×C4—1721no—
315C22×C4—1721no—
316C22×C4C2×C4×D4311yescharacteristic
317C22×C4#1062189811yescharacteristic
318C22×C4C2×C22⋊D4311yescharacteristic
319M16—21no—
320M16—21no—
321M16—21no—
322M16—41no—
323M16—41no—
324M16—1724no—
325M16—1721no—
326M16—1721no—
327M16#1062188212yes—
328C2×C8—21no—
329C2×C8—21no—
330C2×C8—41no—
331C2×C8—862no—
332C2×C8—862no—
333C2×C8—1724no—
334C2×C8—1721no—
335C2×C8—1722no—
336C4⋊C4—22no—
337C4⋊C4—22no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—431no—
341C4⋊C4—431no—
342C4⋊C4—861no—
343C22⋊C4—861no—
344C22⋊C4—861no—
345C22⋊C4—861no—
346C22⋊C4—861no—
347C42D4×D4311yescharacteristic
348C42D4×D4311yescharacteristic
349C42D4×D4311yescharacteristic
350C42#1062190011yescharacteristic
351C23—861no—
352C23—861no—
353C23—3441no—
354C23—1722no—
355C23—1721no—
356C23—1721no—
357C23C4×C22⋊D4311yescharacteristic
358Q8—81no—
359Q8—81no—
360Q8—81no—
361Q8—81no—
362D4—432no—
363D4—861no—
364D4—861no—
365D4—861no—
366D4—1722no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—861no—
374C2×C4—861no—
375C2×C4—1721no—
376C2×C4—1721no—
377C2×C4—1721no—
378C2×C4—1721no—
379C2×C4—1721no—
380C2×C4—1721no—
381C2×C4—1721no—
382C2×C4—1721no—
383C2×C4—1721no—
384C2×C4—1721no—
385C2×C4C22⋊C4×D4311yescharacteristic
386C2×C4(C22⋊D43)⋊C411yescharacteristic
387C2×C4#1306329311yescharacteristic
388C2×C4#1306329611yescharacteristic
389C2×C4#1306329811yescharacteristic
390C2×C4#1306330711yescharacteristic
391C2×C4C2×#1062188211yescharacteristic
392C2×C4#1306334511yescharacteristic
393C2×C4#1306335011yescharacteristic
394C2×C4#1306335111yescharacteristic
395C8—22no—
396C8—41no—
397C8—81no—
398C8—3441no—
399C8—1722no—
400C8—1722no—
401C22—21no—
402C22—21no—
403C22—862no—
404C22—3442no—
405C22—3442no—
406C22—1721no—
407C22—1721no—
408C22—1721no—
409C22—1721no—
410C22—1721no—
411C22#1458277511yescharacteristic
412C22C4×#1062188211yescharacteristic
413C22#1458300911yescharacteristic
414C4—21no—
415C4—21no—
416C4—21no—
417C4—82no—
418C4—1721no—
419C4—1721no—
420C4#101×D4311yescharacteristic
421C4#1458288211yescharacteristic
422C4#1458303211yescharacteristic
423C4#1458304211yescharacteristic
424C4#1458309111yescharacteristic
425C4#1458311111yescharacteristic
426C2—21no—
427C2—21no—
428C2—3441no—
429C2—1722no—
430C2#1913494611yescharacteristic
431C2#1913506011yescharacteristic
432C2#1913507111yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1966C2
socleC22×C43#386
prime radicalC22×D172C2×C4
cosocleC2×C42×C43C23
hypercenter#1966D43
hypocenterC43#9251
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1966

Complements

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

NH ≅ G/Ntype
3. #19133267C2semidirect
5. #19132469C2semidirect
6. #19132446C2semidirect
7. C43×#1966C2semidirect
169. D172#101semidirect
212. #1966D43semidirect
247. C43#9251semidirect

Maximal subgroups

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

subgroupindex
C2×#145831762
M16×D1722
#191332672
#191330192
#191324692
#191324462
C43×#19662
#925143