Finite Group Databasebeta

← #24992480

Subgroups — #24992480

Order 11008.

464 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144078C211yesmaximal, characteristic
2#19143263C211yesmaximal, characteristic
3C2×#14582645C211yesmaximal, characteristic, complemented
4#19132983C211yesmaximal, characteristic
5#19132491C211yesmaximal, characteristic, complemented
6#19132469C211yesmaximal, characteristic, complemented
7C43×#1546C211yesmaximal, characteristic, complemented
8C2×#13063356—21no—
9C4×#10621898C2211yescharacteristic
10#14583106—21no—
11#14583106C412yes—
12#14583101—21no—
13#14583101C412yes—
14#14582959—22no—
15#14582955—21no—
16#14582951—21no—
17#14582923C2211yescharacteristic
18C2×C4⋊(C43⋊C8)C2211yescharacteristic
19C2×C4⋊(C43⋊C8)C2211yescharacteristic
20#14582908—21no—
21#14582867—21no—
22#14582857—21no—
23#14582645—21no—
24#14582645—21no—
25#14582631—21no—
26#14582628—21no—
27C2×C4⋊Q8×C43C2211yescharacteristic
28C43×#431C2211yescharacteristic
29C43×#423C2211yescharacteristic
30C43×#332—22no—
31C2×#10621898D411yescharacteristic
32#13063356—42no—
33#13063356—42no—
34C2×#10621885—22no—
35C2×#10621884—22no—
36C2×#10621877—21no—
37C22×C43⋊C8—21no—
38C22×C43⋊C8—21no—
39C4×Dic86C2×C411yescharacteristic
40C4×Dic86D411yescharacteristic
41C4×D172C2×C411yescharacteristic
42C4×D172D411yescharacteristic
43C4×C22⋊D43—21no—
44C4×C22⋊D43—21no—
45#13063284D411yescharacteristic
46#13063282—21no—
47C42×D43—21no—
48C4⋊(C43⋊C8)—21no—
49C4⋊(C43⋊C8)—21no—
50C4⋊(C43⋊C8)—21no—
51C4⋊(C43⋊C8)—21no—
52C4⋊(C43⋊C8)C2×C412yes—
53C4⋊(C43⋊C8)D411yescharacteristic
54C4⋊(C43⋊C8)D411yescharacteristic
55#13063249—22no—
56#13063249—22no—
57(C2×D43)⋊C8—22no—
58(C2×D43)⋊C8—22no—
59#13063235—22no—
60C8×Dic43—22no—
61C22×Q8×C43—21no—
62C2×M16×C43—21no—
63C4⋊Q8×C43—21no—
64C4⋊Q8×C43—21no—
65C4⋊Q8×C43—21no—
66C4⋊Q8×C43C2×C412yes—
67C2×C4⋊C4×C43—21no—
68C2×C4⋊C4×C43—21no—
69C2×C42×C43C2311yescharacteristic
70C4⋊C8×C43—21no—
71C4⋊C8×C43—21no—
72C4⋊C8×C43D412yes—
73C22⋊C8×C43—21no—
74C4×C8×C43—21no—
75C2×Q8×C43—22no—
76C2×Q8×C43—41no—
77C2×Q8×C43—41no—
78C2×Q8×C43—41no—
79C2×Q8×C43—41no—
80C2×Q8×C43—41no—
81C22×C4×C43—41no—
82C22×C4×C43C2×D411yescharacteristic
83C22×C4×C43#4111yescharacteristic
84C22×C4×C43#4111yescharacteristic
85C2×C22⋊D43—21no—
86#10621898—21no—
87#10621898—21no—
88#10621898—21no—
89#10621898—21no—
90C2×D172C22⋊C411yescharacteristic
91C2×C4×D43—21no—
92C2×C4×D43—21no—
93C2×C4×D43—21no—
94C2×Dic86C22⋊C411yescharacteristic
95M16×C43—41no—
96M16×C43—41no—
97C2×C8×C43—22no—
98C2×C8×C43—41no—
99C4⋊C4×C43—22no—
100C4⋊C4×C43—22no—
101C4⋊C4×C43—41no—
102C4⋊C4×C43—41no—
103C42×C43C22×C411yescharacteristic
104C42×C43C2×D411yescharacteristic
105C42×C43C2×D411yescharacteristic
106C42×C43C2×D411yescharacteristic
107C22⋊Dic43—21no—
108#10621885—44no—
109#10621884—44no—
110(C2×D43)⋊C4—21no—
111(C2×D43)⋊C4—21no—
112C4⋊Dic43C22⋊C411yescharacteristic
113C4⋊Dic43C22⋊C411yescharacteristic
114Dic43⋊C4—21no—
115Dic43⋊C4—21no—
116C4×Dic43—21no—
117C4×Dic43—21no—
118C4×Dic43—21no—
119#10621877—41no—
120#10621877—41no—
121C2×C43⋊C8—22no—
122C2×C43⋊C8—21no—
123C2×C43⋊C8—21no—
124C2×C43⋊C8—41no—
125C2×C43⋊C8—41no—
126C2×C43⋊C8—41no—
127C2×C43⋊C8—81no—
128C23×C43#12311yescharacteristic
129C22×D43—21no—
130Q8×C43—42no—
131Q8×C43—42no—
132Q8×C43—81no—
133Q8×C43—81no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—41no—
137C2×C4×C43—42no—
138C2×C4×C43—81no—
139C2×C4×C43—81no—
140C2×C4×C43C2×C22⋊C411yescharacteristic
141C2×C4×C43C4×D411yescharacteristic
142C2×C4×C43C4×D411yescharacteristic
143C2×C4×C43#12011yescharacteristic
144C2×C4×C43#12111yescharacteristic
145C2×C4×C43#12111yescharacteristic
146C2×C4×C43#13511yescharacteristic
147C2×C4×C43#13511yescharacteristic
148C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
150C22⋊D43—41no—
151C22⋊D43—41no—
152C2×Dic43—21no—
153C2×Dic43—21no—
154C2×Dic43—21no—
155D172—21no—
156D172—21no—
157C4×D43—41no—
158C4×D43—41no—
159C4×D43—41no—
160C4×D43—41no—
161C4×D43—81no—
162Dic86—21no—
163Dic86—21no—
164C8×C43—42no—
165C8×C43—81no—
166C43⋊C8—42no—
167C43⋊C8—41no—
168C43⋊C8—41no—
169C43⋊C8—81no—
170#9172—431nomaximal, Sylow
171C22×C43—21no—
172C22×C43—21no—
173C22×C43#38611yescharacteristic
174C22×C43#48211yescharacteristic
175C22×C43#48211yescharacteristic
176C2×D43—41no—
177C2×D43—41no—
178C2×D43—41no—
179C4×C43—21no—
180C4×C43—21no—
181C4×C43—21no—
182C4×C43—82no—
183C4×C43#41611yescharacteristic
184C4×C43#41811yescharacteristic
185C4×C43#44911yescharacteristic
186C4×C43#44911yescharacteristic
187C4×C43#47111yescharacteristic
188C4×C43#47311yescharacteristic
189Dic43—41no—
190Dic43—41no—
191Dic43—41no—
192#3039—431no—
193#2925—431no—
194#1546D4311yescharacteristic, complemented
195C2×#332—431no—
196#1477—431no—
197#1301—431no—
198#1292—431no—
199C2×C43—21no—
200C2×C43—21no—
201C2×C43#187511yescharacteristic
202C2×C43#190211yescharacteristic
203C2×C43#190811yescharacteristic
204D43—81no—
205C2×#137—861no—
206C2×C4⋊Q8C2×D4311yescharacteristic
207C4×#41—431no—
208#462—432no—
209#462—861no—
210#461—432no—
211#461—861no—
212#433—862no—
213#432—861no—
214#431—861no—
215#431C2×D4311yescharacteristic
216#423—431no—
217#423C2×D4311yescharacteristic
218C2×C4⋊C8—431no—
219C2×C4⋊C8—431no—
220#419—861no—
221#408—861no—
222#405—861no—
223#332—22no—
224#332—861no—
225#332—861no—
226Q8⋊C8—861no—
227D4⋊C8—861no—
228C43#917211yescharacteristic, complemented, Sylow
229C2×#41—431no—
230C22×Q8—21no—
231#137—1722no—
232#137—1722no—
233C2×Q16—862no—
234C2×SD16—862no—
235C2×M16—21no—
236C2×M16—861no—
237C22×C8—861no—
238C22×C8—861no—
239C4⋊Q8—21no—
240C4⋊Q8—21no—
241C4⋊Q8—21no—
242C4⋊Q8C4×D4312yes—
243C4×Q8—431no—
244C4×Q8—431no—
245C4×D4—431no—
246C4×D4—431no—
247C4×D4—861no—
248C4×D4—861no—
249#117—431no—
250#117—861no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C42—861no—
254C2×C42C22×D4311yescharacteristic
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—432no—
258C4⋊C8—431no—
259C4⋊C8—431no—
260C4⋊C8—861no—
261C4⋊C8—861no—
262C4⋊C8—861no—
263C4⋊C8—861no—
264C4⋊C8C22⋊D4312yes—
265#103—862no—
266#103—862no—
267C22⋊C8—21no—
268C22⋊C8—862no—
269C22⋊C8—862no—
270#97—862no—
271C4×C8—21no—
272C4×C8—862no—
273#41—861no—
274#41—861no—
275#41—861no—
276#41—861no—
277C2×Q8—22no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×Q8—41no—
283C2×Q8—431no—
284C2×D4—431no—
285C2×D4—861no—
286C22×C4—41no—
287C22×C4—861no—
288C22×C4—861no—
289C22×C4—861no—
290C22×C4#1062189811yescharacteristic
291C22×C4D4×D4311yescharacteristic
292C22×C4#1062190011yescharacteristic
293Q16—1724no—
294SD16—1724no—
295M16—41no—
296M16—41no—
297M16—1721no—
298M16—1721no—
299C2×C8—22no—
300C2×C8—41no—
301C2×C8—862no—
302C2×C8—861no—
303C2×C8—861no—
304C2×C8—3441no—
305C2×C8—1721no—
306C2×C8—1721no—
307C2×C8—1721no—
308C4⋊C4—22no—
309C4⋊C4—22no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—431no—
313C4⋊C4—431no—
314C4⋊C4—861no—
315C4⋊C4—861no—
316C22⋊C4—861no—
317C22⋊C4—861no—
318C22⋊C4—861no—
319C42—861no—
320C42—861no—
321C42—861no—
322C42C2×C4×D4311yescharacteristic
323C42D4×D4311yescharacteristic
324C42D4×D4311yescharacteristic
325C42C2×C22⋊D4311yescharacteristic
326C23—861no—
327C23#1306330711yescharacteristic
328Q8—42no—
329Q8—42no—
330Q8—81no—
331Q8—81no—
332Q8—861no—
333Q8—861no—
334D4—861no—
335D4—861no—
336D4—1721no—
337D4—1721no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—861no—
345C2×C4—861no—
346C2×C4—861no—
347C2×C4—3441no—
348C2×C4—1721no—
349C2×C4—1721no—
350C2×C4—1721no—
351C2×C4—1721no—
352C2×C4C22⋊C4×D4311yescharacteristic
353C2×C4(C22⋊D43)⋊C411yescharacteristic
354C2×C4C4×C22⋊D4311yescharacteristic
355C2×C4#1306329311yescharacteristic
356C2×C4#1306329611yescharacteristic
357C2×C4#1306329811yescharacteristic
358C2×C4#1306334411yescharacteristic
359C2×C4#1306334611yescharacteristic
360C2×C4#1306334911yescharacteristic
361C2×C4#1306335211yescharacteristic
362C8—42no—
363C8—81no—
364C8—3441no—
365C8—1721no—
366C8—1721no—
367C8—1722no—
368C22—21no—
369C22—21no—
370C22—1721no—
371C22—1721no—
372C22—1721no—
373C22#1458277511yescharacteristic
374C22#1458322111yescharacteristic
375C22#1458322211yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—82no—
380C4—1721no—
381C4—1721no—
382C4—1721no—
383C4#1458289211yescharacteristic
384C4#1458290211yescharacteristic
385C4#1458304111yescharacteristic
386C4#1458304311yescharacteristic
387C4#1458316511yescharacteristic
388C4#1458317311yescharacteristic
389C2—21no—
390C2—21no—
391C2—3441no—
392C2#1913491411yescharacteristic
393C2#1913506511yescharacteristic
394C2#1913510711yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1546C2
socleC22×C43#386
prime radicalC2×#10621898D4
cosocleC2×C42×C43C23
hypercenter#1546D43
hypocenterC43#9172
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
3. C2×#14582645C2semidirect
5. #19132491C2semidirect
6. #19132469C2semidirect
7. C43×#1546C2semidirect
194. #1546D43semidirect
228. C43#9172semidirect

Maximal subgroups

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

subgroupindex
#191440782
#191432632
C2×#145826452
#191329832
#191324912
#191324692
C43×#15462
#917243