Finite Group Databasebeta

← #24997826

Subgroups — #24997826

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
2#19139594C211yesmaximal, characteristic
3#19135519C211yesmaximal, characteristic, complemented
4C2×#14582642C211yesmaximal, characteristic
5C2×Q8⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
6#19132434C211yesmaximal, characteristic, complemented
7C2×C43×#475C211yesmaximal, characteristic, complemented
8C2×#13063322C2211yescharacteristic
9C2×#13063314—21no—
10#14583247—22no—
11#14583247—22no—
12C2×C4⋊(C43⋊C8)C2211yescharacteristic
13C2×#13063249—22no—
14C2×#13063245—22no—
15C2×C4×C43⋊C8C2211yescharacteristic
16#14582816—22no—
17#14582801—22no—
18#14582800—21no—
19C4×C4⋊Dic43C2211yescharacteristic
20#14582642—22no—
21Q8⋊(C43⋊C8)—22no—
22C2×C4⋊Q8×C43C2211yescharacteristic
23C2×C4×Q8×C43C2211yescharacteristic
24C43×#475—22no—
25C43×#475—22no—
26C2×#106×C43—21no—
27C2×C4⋊C8×C43C2211yescharacteristic
28C2×#103×C43—21no—
29C22×D172—21no—
30C22×D172—21no—
31C22×D172D412yes—
32C22×C43⋊C8—21no—
33C22×C43⋊C8—21no—
34#13063322—21no—
35#13063322—21no—
36#13063322—21no—
37#13063322—21no—
38#13063314—42no—
39#13063314—42no—
40C2×C4⋊Dic43D412yes—
41C2×(C2×D43)⋊C4—24no—
42C2×(C2×D43)⋊C4—24no—
43C2×C4×Dic43—21no—
44C4⋊(C43⋊C8)—21no—
45C4⋊(C43⋊C8)—21no—
46#13063249—44no—
47#13063245—28no—
48C4×C43⋊C8—21no—
49C4×C43⋊C8D412yes—
50C43⋊#95—21no—
51C22×Q8×C43—21no—
52C22×Q8×C43D411yescharacteristic
53C22×C8×C43—21no—
54C4⋊Q8×C43—21no—
55C4⋊Q8×C43—21no—
56C4⋊Q8×C43—21no—
57C4⋊Q8×C43D412yes—
58C4×Q8×C43—21no—
59C4×Q8×C43—21no—
60C4×Q8×C43—21no—
61C4×Q8×C43—21no—
62C2×C4⋊C4×C43—21no—
63C2×C4⋊C4×C43—21no—
64C2×C4⋊C4×C43—21no—
65C2×C4⋊C4×C43D411yescharacteristic
66C2×C42×C43—21no—
67C2×C42×C43C2311yescharacteristic
68#106×C43—24no—
69C4⋊C8×C43—21no—
70C4⋊C8×C43D412yes—
71#103×C43—24no—
72C23×D43—22no—
73C2×Q8×C43—21no—
74C2×Q8×C43—21no—
75C2×Q8×C43—21no—
76C2×Q8×C43—22no—
77C2×Q8×C43—21no—
78C2×Q8×C43—21no—
79C2×Q8×C43—41no—
80C2×Q8×C43—42no—
81C2×Q8×C43—42no—
82C2×Q8×C43SD1612yes—
83C22×C4×C43—21no—
84C22×C4×C43—21no—
85C22×C4×C43—41no—
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×Dic43—22no—
90C2×D172—22no—
91C2×D172—22no—
92C2×D172—41no—
93C2×D172—41no—
94C2×D172—41no—
95C2×D172—41no—
96C2×D172—41no—
97C2×D172—42no—
98C2×D172—41no—
99C2×D172—41no—
100C2×D172—42no—
101C2×D172—41no—
102C2×D172—44no—
103C2×C8×C43—22no—
104C2×C8×C43—41no—
105C2×C8×C43—41no—
106C4⋊C4×C43—22no—
107C4⋊C4×C43—21no—
108C4⋊C4×C43—22no—
109C4⋊C4×C43—21no—
110C4⋊C4×C43—41no—
111C4⋊C4×C43—41no—
112C4⋊C4×C43—41no—
113C4⋊C4×C43—41no—
114C42×C43—41no—
115C42×C43—41no—
116C42×C43C2×D411yescharacteristic
117C42×C43C2×D411yescharacteristic
118C42×C43C2×D411yescharacteristic
119C42×C43#4111yescharacteristic
120(C2×D43)⋊C4—48no—
121(C2×D43)⋊C4—84no—
122C4⋊Dic43—22no—
123C4⋊Dic43—22no—
124C4×Dic43—41no—
125C4×Dic43—41no—
126C2×C43⋊C8—22no—
127C2×C43⋊C8—42no—
128C2×C43⋊C8—41no—
129C2×C43⋊C8—42no—
130C23×C43#12011yescharacteristic
131C22×D43—42no—
132C22×D43—44no—
133C22×D43—42no—
134C22×D43—42no—
135C22×D43—44no—
136Q8×C43—22no—
137Q8×C43—22no—
138Q8×C43—41no—
139Q8×C43—41no—
140Q8×C43—44no—
141Q8×C43—81no—
142Q8×C43—81no—
143C2×C4×C43—22no—
144C2×C4×C43—22no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—42no—
149C2×C4×C43—42no—
150C2×C4×C43—82no—
151C2×C4×C43#12011yescharacteristic
152C2×C4×C43#12011yescharacteristic
153C2×C4×C43#12111yescharacteristic
154C2×C4×C43#12111yescharacteristic
155C2×C4×C43#12111yescharacteristic
156C2×C4×C43#12711yescharacteristic
157C2×C4×C43C2×SD1611yescharacteristic
158C2×C4×C43#13511yescharacteristic
159C2×C4×C43#13512yes—
160C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C43AGL(1,ℤ/8)12yes—
162C2×C4×C43#13711yescharacteristic
163C2×Dic43—42no—
164C2×Dic43—42no—
165C2×Dic43—42no—
166D172—44no—
167D172—82no—
168D172—81no—
169D172—81no—
170D172—82no—
171D172—81no—
172D172—81no—
173D172—81no—
174D172—81no—
175C8×C43—42no—
176C43⋊C8—42no—
177C43⋊C8—81no—
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—42no—
192C4×C43—81no—
193C4×C43—82no—
194C4×C43#44811yescharacteristic
195C4×C43#44911yescharacteristic
196C4×C43#46312yes—
197C4×C43#46511yescharacteristic
198C4×C43#46811yescharacteristic
199C4×C43#49511yescharacteristic
200C4×C43#49611yescharacteristic
201Dic43—82no—
202C2×#486—431no—
203C2×#475D4311yescharacteristic, complemented
204#2548—431no—
205#1981—431no—
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×Q8C2×D4311yescharacteristic
219#486—862no—
220#486—862no—
221#475—22no—
222#475—22no—
223C2×#106—21no—
224C2×C4⋊C8—431no—
225C2×C4⋊C8C2×D4311yescharacteristic
226C2×#103—21no—
227C2×#103—862no—
228C2×#102—862no—
229C2×C4×C8—431no—
230#394—862no—
231#390—862no—
232#390—861no—
233C4×C4⋊C4—431no—
234#331—862no—
235Q8⋊C8—862no—
236C43#1007111yescharacteristic, complemented, Sylow
237C22×Q8—21no—
238C22×Q8C22⋊D4311yescharacteristic
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⋊Q8C22⋊D4312yes—
249#127—861no—
250#127—861no—
251#127—861no—
252#127—861no—
253#124—1722no—
254#124—1722no—
255C4×Q8—21no—
256C4×Q8—21no—
257C4×Q8—21no—
258C4×Q8—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—432no—
263C2×C4⋊C4C22⋊D4311yescharacteristic
264C2×C22⋊C4—864no—
265C2×C22⋊C4—864no—
266C2×C42—21no—
267C2×C42—861no—
268C2×C42C22×D4311yescharacteristic
269#106—24no—
270C4⋊C8—21no—
271C4⋊C8—861no—
272C4⋊C8—861no—
273C4⋊C8C22⋊D4312yes—
274#103—24no—
275#103—1724no—
276#102—868no—
277C4×C8—432no—
278C4×C8—861no—
279#95—861no—
280C24—862no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—22no—
285C2×Q8—21no—
286C2×Q8—21no—
287C2×Q8—41no—
288C2×Q8—42no—
289C2×Q8—42no—
290C2×Q8#1062188412yes—
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—1721no—
300C2×D4—1722no—
301C2×D4—1721no—
302C2×D4—1722no—
303C2×D4—1721no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—41no—
307C22×C4—862no—
308C22×C4D4×D4311yescharacteristic
309C22×C4D4×D4311yescharacteristic
310C22×C4C2×C22⋊D4311yescharacteristic
311C2×C8—22no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—862no—
315C2×C8—1721no—
316C2×C8—1722no—
317C2×C8—1722no—
318C4⋊C4—22no—
319C4⋊C4—22no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—862no—
327C4⋊C4—862no—
328C22⋊C4—3444no—
329C22⋊C4—1728no—
330C42—41no—
331C42—41no—
332C42—1721no—
333C42—1721no—
334C42D4×D4311yescharacteristic
335C42#1062190011yescharacteristic
336C42C2×C22⋊D4311yescharacteristic
337C42C2×C22⋊D4311yescharacteristic
338C23—1724no—
339C23—1722no—
340C23—1722no—
341C23—1722no—
342C23—1724no—
343C23#1306329311yescharacteristic
344Q8—22no—
345Q8—22no—
346Q8—41no—
347Q8—41no—
348Q8—44no—
349Q8—81no—
350Q8—81no—
351D4—3442no—
352D4—3441no—
353D4—3442no—
354D4—3441no—
355D4—3441no—
356D4—3441no—
357D4—3441no—
358D4—3441no—
359D4—1724no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—82no—
368C2×C4—1722no—
369C2×C4—1722no—
370C2×C4—1722no—
371C2×C4#1306329311yescharacteristic
372C2×C4#1306329411yescharacteristic
373C2×C4#1306329611yescharacteristic
374C2×C4#1306329711yescharacteristic
375C2×C4#1306329711yescharacteristic
376C2×C4#1306332111yescharacteristic
377C2×C4C2×#1062188411yescharacteristic
378C2×C4#1306334511yescharacteristic
379C2×C4#1306334612yes—
380C2×C4#1306335011yescharacteristic
381C2×C4#1306335212yes—
382C2×C4#1306335611yescharacteristic
383C8—42no—
384C8—3441no—
385C8—1722no—
386C22—3444no—
387C22—3444no—
388C22—3442no—
389C22—3442no—
390C22—3442no—
391C22#1458280711yescharacteristic
392C22#1458304312yes—
393C22#1458304911yescharacteristic
394C22#1458305911yescharacteristic
395C22#1458307512yes—
396C4—21no—
397C4—21no—
398C4—42no—
399C4—81no—
400C4—82no—
401C4—3442no—
402C4#1458303811yescharacteristic
403C4#1458304411yescharacteristic
404C4#1458311612yes—
405C4#1458313011yescharacteristic
406C4#1458314711yescharacteristic
407C4#1458328011yescharacteristic
408C4#1458328511yescharacteristic
409C2—6882no—
410C2#1913378012yes—
411C2#1913379412yes—
412C2#1913559611yescharacteristic
413C2#1913562111yescharacteristic
414C2#1913566911yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC2×C43×#475C2
socleC23×C43#120
prime radicalC2×#13063322C22
hypercenterC2×#475D43
hypocenterC43#10071
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
3. #19135519C2semidirect
5. C2×Q8⋊(C43⋊C8)C2semidirect
6. #19132434C2semidirect
7. C2×C43×#475C2semidirect
203. C2×#475D43semidirect
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
#191395942
#191355192
C2×#145826422
C2×Q8⋊(C43⋊C8)2
#191324342
C2×C43×#4752
#1007143