Finite Group Databasebeta

← #24992873

Subgroups — #24992873

Order 11008.

550 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 550 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144599C211yesmaximal, characteristic
2#19137056C211yesmaximal, characteristic
3#19135573C211yesmaximal, characteristic, complemented
4#19133021C211yesmaximal, characteristic
5#19132498C211yesmaximal, characteristic, complemented
6#19132427C211yesmaximal, characteristic, complemented
7C43×#1503C211yesmaximal, characteristic, complemented
8C2×C4×D172C2211yescharacteristic
9C2×#13063282—21no—
10#14583227—21no—
11#14583186C412yescomplemented
12#14583101C412yescomplemented
13#14583049—21no—
14C4×#10621884—22no—
15#14582952C2211yescharacteristic
16#14582923C2211yescharacteristic
17#14582800—21no—
18#14582795—21no—
19#14582788—22no—
20C4×(C2×D43)⋊C4—21no—
21C42×Dic43C2211yescharacteristic
22#14582658—21no—
23#14582658—21no—
24#14582628—22no—
25C43×#533C2211yescharacteristic
26C43×#431C2211yescharacteristic
27C4×C4⋊C4×C43C2211yescharacteristic
28C43×#328—22no—
29C22×D172D411yescharacteristic
30C22×C4×D43—21no—
31C2×#10621884—22no—
32C2×#10621877—21no—
33C4×D172—21no—
34C4×D172—21no—
35C4×D172C2×C412yes—
36C4×D172D412yes—
37#13063282—42no—
38#13063282—42no—
39C2×C4⋊Dic43D411yescharacteristic
40C2×Dic43⋊C4—22no—
41C2×(C2×D43)⋊C4—21no—
42C2×(C2×D43)⋊C4—22no—
43C2×(C2×D43)⋊C4—22no—
44C2×C4×Dic43—21no—
45C2×C4×Dic43—21no—
46C2×C4×Dic43D411yescharacteristic
47C2×C4×Dic43D411yescharacteristic
48#13063256—22no—
49C4⋊(C43⋊C8)—21no—
50C4⋊(C43⋊C8)—21no—
51C4⋊(C43⋊C8)C2×C412yes—
52#13063249—22no—
53#13063245—22no—
54C22⋊(C43⋊C8)—21no—
55C4×C43⋊C8—21no—
56C43⋊#95—22no—
57C4⋊Q8×C43C2×C411yescharacteristic
58C4⋊Q8×C43C2×C411yescharacteristic
59#125×C43—21no—
60C22⋊Q8×C43—21no—
61C22⋊Q8×C43—21no—
62C4×Q8×C43—21no—
63C4×Q8×C43—21no—
64#117×C43—21no—
65C2×C4⋊C4×C43—21no—
66C2×C42×C43—21no—
67C2×C42×C43C2311yescharacteristic
68C4⋊C8×C43—21no—
69C22⋊C8×C43—21no—
70C4×C8×C43—21no—
71#95×C43D412yes—
72C23×D43—21no—
73C2×Q8×C43—21no—
74C2×Q8×C43—21no—
75C22×C4×C43—22no—
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C22×Dic43—21no—
80C22×Dic43—21no—
81C22×Dic43—21no—
82C2×D172—21no—
83C2×D172—42no—
84C2×D172C22⋊C412yes—
85C2×C4×D43—22no—
86C2×C4×D43—22no—
87C2×C4×D43—41no—
88C2×C4×D43—41no—
89C2×C4×D43—41no—
90C2×C4×D43—41no—
91C2×C8×C43—41no—
92C4⋊C4×C43—21no—
93C4⋊C4×C43—21no—
94C4⋊C4×C43—21no—
95C4⋊C4×C43—21no—
96C4⋊C4×C43—42no—
97C4⋊C4×C43—41no—
98C4⋊C4×C43—41no—
99C22⋊C4×C43—41no—
100C42×C43—41no—
101C42×C43—41no—
102C42×C43—41no—
103C42×C43C22×C411yescharacteristic
104C42×C43C2×D411yescharacteristic
105C42×C43#4111yescharacteristic
106C42×C43#4111yescharacteristic
107#10621884—44no—
108(C2×D43)⋊C4—22no—
109(C2×D43)⋊C4—22no—
110(C2×D43)⋊C4—44no—
111(C2×D43)⋊C4—44no—
112C4⋊Dic43—21no—
113C4⋊Dic43C22⋊C412yes—
114Dic43⋊C4—44no—
115C4×Dic43—21no—
116C4×Dic43—21no—
117C4×Dic43—21no—
118C4×Dic43—42no—
119C4×Dic43—42no—
120C4×Dic43SD1612yescomplemented
121#10621877—41no—
122#10621877—41no—
123C2×C43⋊C8—22no—
124C2×C43⋊C8—41no—
125C23×C43#12011yescharacteristic
126C22×D43—22no—
127C22×D43—42no—
128C22×D43—42no—
129C22×D43—41no—
130C22×D43—41no—
131Q8×C43—42no—
132Q8×C43—81no—
133C2×C4×C43—22no—
134C2×C4×C43—41no—
135C2×C4×C43—42no—
136C2×C4×C43—42no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—42no—
140C2×C4×C43C2×C22⋊C411yescharacteristic
141C2×C4×C43C4×D411yescharacteristic
142C2×C4×C43C4×D411yescharacteristic
143C2×C4×C43#12111yescharacteristic
144C2×C4×C43#12111yescharacteristic
145C2×C4×C43#12311yescharacteristic
146C2×C4×C43C2×SD1611yescharacteristic
147C2×C4×C43#13511yescharacteristic
148C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C43#13711yescharacteristic
150C2×Dic43—22no—
151C2×Dic43—22no—
152C2×Dic43—22no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157C2×Dic43—41no—
158C2×Dic43—41no—
159D172—22no—
160D172—22no—
161D172—42no—
162C4×D43—42no—
163C4×D43—42no—
164C4×D43—42no—
165C4×D43—42no—
166C8×C43—81no—
167C43⋊C8—42no—
168C43⋊C8—81no—
169#9235—431nomaximal, Sylow
170C22×C43—21no—
171C22×C43—21no—
172C22×C43#38611yescharacteristic
173C22×C43#45011yescharacteristic
174C22×C43#45211yescharacteristic
175C2×D43—42no—
176C2×D43—42no—
177C2×D43—42no—
178C2×D43—82no—
179C2×D43—82no—
180C4×C43—21no—
181C4×C43—21no—
182C4×C43—21no—
183C4×C43—82no—
184C4×C43—81no—
185C4×C43—81no—
186C4×C43#42112yes—
187C4×C43C4×SD1611yescharacteristic
188C4×C43#44011yescharacteristic
189C4×C43#46111yescharacteristic
190C4×C43#46311yescharacteristic
191Dic43—42no—
192Dic43—42no—
193Dic43—42no—
194#3101—431no—
195#2293—431no—
196#1994—431no—
197#1503D4311yescharacteristic, complemented
198#1486—431no—
199#1303—431no—
200#1276—431no—
201C2×C43—21no—
202C2×C43—21no—
203C2×C43#187711yescharacteristic
204C2×C43#189711yescharacteristic
205C2×C43#190611yescharacteristic
206D43—82no—
207#533C2×D4311yescharacteristic
208C2×C4×D4—431no—
209C2×#117—861no—
210#483—861no—
211#476—432no—
212#461—432no—
213#450—861no—
214C4×SD16—862no—
215#431—431no—
216#431C2×D4311yescharacteristic
217#423—431no—
218#390—861no—
219#389—861no—
220#388—862no—
221C4×C4⋊C4C2×D4311yescharacteristic
222C4×C22⋊C4—861no—
223C43—431no—
224#339—861no—
225#339—861no—
226#328—22no—
227D4⋊C8—862no—
228C43#923511yescharacteristic, complemented, Sylow
229C22×D4—431no—
230C23×C4—861no—
231C2×SD16—862no—
232C2×M16—861no—
233C4⋊Q8C4×D4311yescharacteristic
234C4⋊Q8C4×D4311yescharacteristic
235#125—21no—
236C22⋊Q8—21no—
237C22⋊Q8—21no—
238C4×Q8—21no—
239C4×Q8—21no—
240C4×D4—432no—
241C4×D4—432no—
242C4×D4—861no—
243C4×D4—861no—
244#117—21no—
245#117—1722no—
246#117—1722no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—431no—
249C2×C4⋊C4—862no—
250C2×C22⋊C4—861no—
251C2×C22⋊C4—862no—
252C2×C22⋊C4—862no—
253C2×C42—21no—
254C2×C42—431no—
255C2×C42—431no—
256C2×C42—861no—
257C2×C42—861no—
258C2×C42C22×D4311yescharacteristic
259#106—862no—
260C4⋊C8—21no—
261C4⋊C8—432no—
262C4⋊C8—861no—
263C4⋊C8—861no—
264#103—862no—
265#102—862no—
266C22⋊C8—21no—
267C22⋊C8—861no—
268C4×C8—21no—
269C4×C8—861no—
270#95—862no—
271#95C22⋊D4312yes—
272C24—861no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×D4—432no—
276C2×D4—861no—
277C2×D4—1722no—
278C22×C4—22no—
279C22×C4—861no—
280C22×C4—861no—
281C22×C4—861no—
282C22×C4—862no—
283C22×C4—862no—
284C22×C4—1721no—
285C22×C4—1721no—
286C22×C4—1721no—
287C22×C4—1721no—
288C22×C4D4×D4311yescharacteristic
289C22×C4D4×D4311yescharacteristic
290C22×C4C2×C22⋊D4311yescharacteristic
291SD16—1724no—
292M16—1721no—
293M16—1721no—
294C2×C8—41no—
295C2×C8—862no—
296C2×C8—1721no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—42no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—432no—
305C4⋊C4—861no—
306C4⋊C4—1724no—
307C22⋊C4—41no—
308C22⋊C4—862no—
309C22⋊C4—862no—
310C22⋊C4—1724no—
311C22⋊C4—1724no—
312C42—41no—
313C42—41no—
314C42—41no—
315C42—432no—
316C42—861no—
317C42—861no—
318C42—861no—
319C42—1722no—
320C42—1722no—
321C42C2×C4×D4311yescharacteristic
322C42#1062189811yescharacteristic
323C42D4×D4311yescharacteristic
324C42#1062190011yescharacteristic
325C23—862no—
326C23—1722no—
327C23—1722no—
328C23—1721no—
329C23—1721no—
330C23#1306329311yescharacteristic
331Q8—42no—
332Q8—81no—
333D4—862no—
334D4—862no—
335D4—1722no—
336C2×C4—22no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—862no—
344C2×C4—862no—
345C2×C4—862no—
346C2×C4—1721no—
347C2×C4—1721no—
348C2×C4—1721no—
349C2×C4—1721no—
350C2×C4—1721no—
351C2×C4—1721no—
352C2×C4—1722no—
353C2×C4—1722no—
354C2×C4—1722no—
355C2×C4—1722no—
356C2×C4C22⋊C4×D4311yescharacteristic
357C2×C4(C22⋊D43)⋊C411yescharacteristic
358C2×C4C4×C22⋊D4311yescharacteristic
359C2×C4#1306329611yescharacteristic
360C2×C4#1306329811yescharacteristic
361C2×C4#1306330711yescharacteristic
362C2×C4SD16×D4311yescharacteristic
363C2×C4#1306334811yescharacteristic
364C2×C4#1306335211yescharacteristic
365C2×C4#1306335711yescharacteristic
366C8—81no—
367C8—3441no—
368C8—1722no—
369C22—21no—
370C22—21no—
371C22—3442no—
372C22—3442no—
373C22—1722no—
374C22—1722no—
375C22—1722no—
376C22#1458277511yescharacteristic
377C22#1458304811yescharacteristic
378C22#1458306011yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—82no—
383C4—81no—
384C4—81no—
385C4—1722no—
386C4—1722no—
387C4—1722no—
388C4#1458291412yes—
389C4#1458298411yescharacteristic
390C4#1458300211yescharacteristic
391C4#1458310311yescharacteristic
392C4#1458311711yescharacteristic
393C2—21no—
394C2—21no—
395C2—3442no—
396C2#1913492611yescharacteristic
397C2#1913504011yescharacteristic
398C2#1913509311yescharacteristic
subgroupG/H
centerC2×C4#13063298
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1503C2
socleC22×C43#386
prime radicalC22×D172D4
cosocleC2×C42×C43C23
hypercenter#1503D43
hypocenterC43#9235
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1503

Complements

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

NH ≅ G/Ntype
3. #19135573C2semidirect
5. #19132498C2semidirect
6. #19132427C2semidirect
7. C43×#1503C2semidirect
11. #14583186C4semidirect
12. #14583101C4semidirect
120. C4×Dic43SD16semidirect
197. #1503D43semidirect
228. C43#9235semidirect

Maximal subgroups

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

subgroupindex
#191445992
#191370562
#191355732
#191330212
#191324982
#191324272
C43×#15032
#923543