Finite Group Databasebeta

← #24997827

Subgroups — #24997827

Order 11008.

654 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583247C211yesmaximal, characteristic
2C2×#14583181C211yesmaximal, characteristic, complemented
3#19139597C211yesmaximal, characteristic
4C2×#14582642C211yesmaximal, characteristic
5C2×#14582629C211yesmaximal, characteristic, complemented
6#19132436C211yesmaximal, characteristic, complemented
7C43×#1981C211yesmaximal, characteristic, complemented
8C2×#13063322C2211yescharacteristic
9C2×#13063313—21no—
10C2×C4×Dic86C2211yescharacteristic
11#14583247—22no—
12#14583247—22no—
13#14583181—22no—
14#14583181—22no—
15C2×#13063256—21no—
16C2×C4⋊(C43⋊C8)C2211yescharacteristic
17C2×#13063248—21no—
18C2×#13063245—22no—
19C2×C4×C43⋊C8C2211yescharacteristic
20#14582817—22no—
21#14582801—21no—
22#14582800—22no—
23#14582642—22no—
24#14582629—22no—
25C2×C4⋊Q8×C43C2211yescharacteristic
26C2×C4⋊C8×C43C2211yescharacteristic
27C2×#103×C43—22no—
28C4×C4⋊C4×C43C2211yescharacteristic
29C22×Dic86D411yescharacteristic
30C22×D172—21no—
31C22×D172—21no—
32C22×D172D412yes—
33C22×C43⋊C8—21no—
34C22×C43⋊C8—21no—
35#13063322—21no—
36#13063322—21no—
37#13063322—21no—
38#13063322—21no—
39#13063313—42no—
40#13063313—42no—
41C4×Dic86—21no—
42C4×Dic86—21no—
43C4×Dic86—21no—
44C4×Dic86—21no—
45C2×C4⋊Dic43D411yescharacteristic
46C2×Dic43⋊C4—21no—
47C2×(C2×D43)⋊C4—24no—
48C2×(C2×D43)⋊C4—24no—
49C2×C4×Dic43—21no—
50#13063256—24no—
51C4⋊(C43⋊C8)—21no—
52C4⋊(C43⋊C8)D412yes—
53#13063248—24no—
54#13063245—28no—
55C4×C43⋊C8—21no—
56C4×C43⋊C8D412yes—
57C22×Q8×C43—21no—
58C22×C8×C43—21no—
59C4⋊Q8×C43—21no—
60C4⋊Q8×C43—21no—
61C4⋊Q8×C43—21no—
62C4⋊Q8×C43D412yes—
63C2×C4⋊C4×C43—21no—
64C2×C4⋊C4×C43—21no—
65C2×C4⋊C4×C43D412yes—
66C2×C42×C43—21no—
67C2×C42×C43C2311yescharacteristic
68C4⋊C8×C43—21no—
69C4⋊C8×C43—21no—
70#103×C43—44no—
71#95×C43—21no—
72C23×D43—22no—
73C2×Q8×C43—22no—
74C2×Q8×C43—41no—
75C2×Q8×C43—42no—
76C2×Q8×C43—42no—
77C22×C4×C43—22no—
78C22×C4×C43—41no—
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43C2×D411yescharacteristic
82C22×Dic43—21no—
83C22×Dic43—21no—
84C2×D172—22no—
85C2×D172—22no—
86C2×D172—41no—
87C2×D172—41no—
88C2×D172—41no—
89C2×D172—41no—
90C2×D172—41no—
91C2×D172—42no—
92C2×D172—41no—
93C2×D172—41no—
94C2×D172—42no—
95C2×D172—41no—
96C2×D172—44no—
97C2×Dic86—21no—
98C2×Dic86—21no—
99C2×Dic86—21no—
100C2×Dic86—21no—
101C2×Dic86—21no—
102C2×Dic86SD1612yes—
103C2×C8×C43—41no—
104C2×C8×C43—42no—
105C4⋊C4×C43—22no—
106C4⋊C4×C43—22no—
107C4⋊C4×C43—22no—
108C4⋊C4×C43—22no—
109C4⋊C4×C43—41no—
110C4⋊C4×C43—41no—
111C42×C43—41no—
112C42×C43—41no—
113C42×C43C2×D411yescharacteristic
114C42×C43C2×D411yescharacteristic
115C42×C43C2×D411yescharacteristic
116C42×C43#4111yescharacteristic
117(C2×D43)⋊C4—48no—
118(C2×D43)⋊C4—84no—
119C4⋊Dic43—21no—
120C4⋊Dic43—21no—
121Dic43⋊C4—41no—
122Dic43⋊C4—41no—
123C4×Dic43—41no—
124C4×Dic43—41no—
125C2×C43⋊C8—22no—
126C2×C43⋊C8—22no—
127C2×C43⋊C8—42no—
128C2×C43⋊C8—41no—
129C2×C43⋊C8—41no—
130C23×C43#12011yescharacteristic
131C22×D43—42no—
132C22×D43—44no—
133C22×D43—42no—
134C22×D43—42no—
135C22×D43—44no—
136Q8×C43—44no—
137Q8×C43—81no—
138Q8×C43—81no—
139C2×C4×C43—22no—
140C2×C4×C43—42no—
141C2×C4×C43—42no—
142C2×C4×C43—42no—
143C2×C4×C43—42no—
144C2×C4×C43—82no—
145C2×C4×C43#12011yescharacteristic
146C2×C4×C43#12011yescharacteristic
147C2×C4×C43#12111yescharacteristic
148C2×C4×C43#12111yescharacteristic
149C2×C4×C43#12111yescharacteristic
150C2×C4×C43#12711yescharacteristic
151C2×C4×C43C2×SD1611yescharacteristic
152C2×C4×C43#13512yes—
153C2×C4×C43#13511yescharacteristic
154C2×C4×C43AGL(1,ℤ/8)12yes—
155C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C43#13711yescharacteristic
157C2×Dic43—22no—
158C2×Dic43—41no—
159C2×Dic43—41no—
160C2×Dic43—41no—
161C2×Dic43—42no—
162D172—44no—
163D172—82no—
164D172—81no—
165D172—81no—
166D172—82no—
167D172—81no—
168D172—81no—
169D172—81no—
170D172—81no—
171Dic86—22no—
172Dic86—22no—
173Dic86—41no—
174Dic86—41no—
175C8×C43—81no—
176C43⋊C8—42no—
177C43⋊C8—42no—
178#10071—431nomaximal, Sylow
179C22×C43#39211yescharacteristic
180C22×C43#44912yes—
181C22×C43#45011yescharacteristic
182C22×C43#45211yescharacteristic
183C22×C43#45512yes—
184C2×D43—84no—
185C2×D43—84no—
186C2×D43—82no—
187C2×D43—82no—
188C2×D43—82no—
189C4×C43—21no—
190C4×C43—21no—
191C4×C43—82no—
192C4×C43—82no—
193C4×C43#44811yescharacteristic
194C4×C43#44911yescharacteristic
195C4×C43#46312yes—
196C4×C43#46511yescharacteristic
197C4×C43#46811yescharacteristic
198C4×C43#49511yescharacteristic
199C4×C43#49611yescharacteristic
200Dic43—42no—
201Dic43—81no—
202C2×#486—431no—
203C2×#475—431no—
204#2548—431no—
205#1981D4311yescharacteristic, complemented
206C2×#331—431no—
207C2×Q8⋊C8—431no—
208#1279—431no—
209C2×C43#164012yes—
210C2×C43#164212yes—
211C2×C43#200011yescharacteristic
212C2×C43#200411yescharacteristic
213C2×C43#201211yescharacteristic
214D43—162no—
215C2×C4⋊Q8C2×D4311yescharacteristic
216C2×#127—431no—
217C2×#124—861no—
218C2×C4×Q8—431no—
219#486—862no—
220#486—862no—
221#475—862no—
222#475—862no—
223C2×#106—861no—
224C2×C4⋊C8—431no—
225C2×C4⋊C8C2×D4311yescharacteristic
226C2×#103—22no—
227C2×#103—861no—
228C2×#102—862no—
229C2×C4×C8—431no—
230#394—862no—
231#390—861no—
232#390—862no—
233C4×C4⋊C4C2×D4311yescharacteristic
234#331—862no—
235Q8⋊C8—862no—
236C43#1007111yescharacteristic, complemented, Sylow
237C22×Q8—21no—
238C22×Q8—431no—
239C22×D4—432no—
240C22×D4—861no—
241C22×D4—861no—
242C22×C8—21no—
243C22×C8—861no—
244C22×C8—861no—
245C4⋊Q8—21no—
246C4⋊Q8—21no—
247C4⋊Q8—21no—
248C4⋊Q8D17212yes—
249#127—861no—
250#127—861no—
251#127—861no—
252#127—861no—
253#124—1722no—
254#124—1722no—
255C4×Q8—861no—
256C4×Q8—861no—
257C4×Q8—861no—
258C4×Q8—861no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—431no—
262C2×C4⋊C4—861no—
263C2×C4⋊C4C22⋊D4312yes—
264C2×C22⋊C4—864no—
265C2×C22⋊C4—864no—
266C2×C42—21no—
267C2×C42—861no—
268C2×C42C22×D4311yescharacteristic
269#106—864no—
270C4⋊C8—21no—
271C4⋊C8—21no—
272C4⋊C8—432no—
273C4⋊C8—861no—
274#103—44no—
275#103—864no—
276#102—868no—
277C4×C8—432no—
278C4×C8—861no—
279#95—21no—
280C24—862no—
281C2×Q8—22no—
282C2×Q8—41no—
283C2×Q8—42no—
284C2×Q8—42no—
285C2×Q8—432no—
286C2×Q8—861no—
287C2×Q8—861no—
288C2×Q8—861no—
289C2×Q8—861no—
290C2×Q8—861no—
291C2×D4—862no—
292C2×D4—862no—
293C2×D4—1724no—
294C2×D4—1721no—
295C2×D4—1721no—
296C2×D4—1721no—
297C2×D4—1721no—
298C2×D4—1721no—
299C2×D4—1722no—
300C2×D4—1721no—
301C2×D4—1722no—
302C2×D4—1721no—
303C2×D4—1721no—
304C22×C4—22no—
305C22×C4—41no—
306C22×C4—861no—
307C22×C4—861no—
308C22×C4D4×D4311yescharacteristic
309C22×C4D4×D4311yescharacteristic
310C22×C4C2×C22⋊D4311yescharacteristic
311C2×C8—41no—
312C2×C8—42no—
313C2×C8—862no—
314C2×C8—862no—
315C2×C8—1722no—
316C2×C8—1721no—
317C2×C8—1721no—
318C4⋊C4—22no—
319C4⋊C4—22no—
320C4⋊C4—22no—
321C4⋊C4—22no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—861no—
325C4⋊C4—861no—
326C4⋊C4—1721no—
327C4⋊C4—1721no—
328C22⋊C4—3444no—
329C22⋊C4—1728no—
330C42—41no—
331C42—41no—
332C42—1721no—
333C42—1721no—
334C42C2×D17211yescharacteristic
335C42#1062189811yescharacteristic
336C42D4×D4311yescharacteristic
337C42D4×D4311yescharacteristic
338C23—1724no—
339C23—1722no—
340C23—1722no—
341C23—1722no—
342C23—1724no—
343C23#1306329311yescharacteristic
344Q8—44no—
345Q8—81no—
346Q8—81no—
347Q8—862no—
348Q8—862no—
349Q8—1721no—
350Q8—1721no—
351D4—3442no—
352D4—3441no—
353D4—3442no—
354D4—3441no—
355D4—3441no—
356D4—3441no—
357D4—3441no—
358D4—3441no—
359D4—1724no—
360C2×C4—22no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—82no—
366C2×C4—862no—
367C2×C4—1721no—
368C2×C4—1722no—
369C2×C4—1721no—
370C2×C4—1721no—
371C2×C4#1306329511yescharacteristic
372C2×C4#1306329511yescharacteristic
373C2×C4#1306329811yescharacteristic
374C2×C4#1306329811yescharacteristic
375C2×C4#1306329911yescharacteristic
376C2×C4#1306332111yescharacteristic
377C2×C4SD16×D4311yescharacteristic
378C2×C4#1306334512yes—
379C2×C4#1306334811yescharacteristic
380C2×C4#1306335112yes—
381C2×C4#1306335211yescharacteristic
382C2×C4#1306335711yescharacteristic
383C8—81no—
384C8—1722no—
385C8—1722no—
386C22—3444no—
387C22—3444no—
388C22—3442no—
389C22—3442no—
390C22—3442no—
391C22#1458280811yescharacteristic
392C22#1458304212yes—
393C22#1458304811yescharacteristic
394C22#1458306011yescharacteristic
395C22#1458307512yes—
396C4—21no—
397C4—21no—
398C4—82no—
399C4—82no—
400C4—3441no—
401C4—1722no—
402C4#1458303911yescharacteristic
403C4#1458304711yescharacteristic
404C4#1458311412yes—
405C4#1458313111yescharacteristic
406C4#1458314811yescharacteristic
407C4#1458328111yescharacteristic
408C4#1458328611yescharacteristic
409C2—6882no—
410C2#1913377912yes—
411C2#1913379312yes—
412C2#1913559711yescharacteristic
413C2#1913562511yescharacteristic
414C2#1913567111yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1981C2
socleC23×C43#120
prime radicalC2×#13063322C22
hypercenter#1981D43
hypocenterC43#10071
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1981

Complements

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

NH ≅ G/Ntype
2. C2×#14583181C2semidirect
5. C2×#14582629C2semidirect
6. #19132436C2semidirect
7. C43×#1981C2semidirect
205. #1981D43semidirect
236. C43#10071semidirect

Maximal subgroups

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

subgroupindex
C2×#145832472
C2×#145831812
#191395972
C2×#145826422
C2×#145826292
#191324362
C43×#19812
#1007143