Finite Group Databasebeta

← #24992877

Subgroups — #24992877

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#19144604C211yesmaximal, characteristic
2#19137056C211yesmaximal, characteristic
3#19135571C211yesmaximal, characteristic, complemented
4#19133093C211yesmaximal, characteristic, complemented
5#19133019C211yesmaximal, characteristic
6#19132427C211yesmaximal, characteristic, complemented
7C43×#1303C211yesmaximal, characteristic, complemented
8#14583456C2211yescharacteristic
9C2×C4×D172C2211yescharacteristic
10C2×#13063282—21no—
11#14583230—21no—
12#14583190C412yescomplemented
13#14583105C412yescomplemented
14#14583052—21no—
15C4×#10621873—22no—
16#14582952C2211yescharacteristic
17#14582800—21no—
18#14582795—21no—
19#14582788—22no—
20C4×(C2×D43)⋊C4—21no—
21C42×Dic43C2211yescharacteristic
22#14582660—21no—
23#14582660—21no—
24#14582635—22no—
25#14582626—22no—
26C43×#431C2211yescharacteristic
27C43×#423C2211yescharacteristic
28C4×C4⋊C4×C43C2211yescharacteristic
29C22×D172D411yescharacteristic
30C22×C4×D43—21no—
31C2×#10621873—22no—
32#13063325C2×C411yescharacteristic
33#13063325C2×C411yescharacteristic
34#13063317—21no—
35#13063304—21no—
36#13063304—21no—
37C4×Dic86—21no—
38C4×Dic86—21no—
39C4×D172—21no—
40C4×D172—21no—
41C4×D172C2×C412yes—
42C4×D172D412yes—
43#13063284—21no—
44#13063282—42no—
45#13063282—42no—
46C2×C4⋊Dic43D411yescharacteristic
47C2×Dic43⋊C4—22no—
48C2×(C2×D43)⋊C4—21no—
49C2×(C2×D43)⋊C4—22no—
50C2×(C2×D43)⋊C4—22no—
51C2×C4×Dic43—21no—
52C2×C4×Dic43—21no—
53C2×C4×Dic43D411yescharacteristic
54C2×C4×Dic43D411yescharacteristic
55#13063257—22no—
56C4⋊(C43⋊C8)—21no—
57#13063250—22no—
58#13063247—22no—
59C22⋊(C43⋊C8)—21no—
60C4×C43⋊C8—21no—
61C43⋊#95—22no—
62C2×M16×C43—21no—
63C2×C4⋊C4×C43—21no—
64C2×C42×C43—21no—
65C2×C42×C43C2311yescharacteristic
66C4⋊C8×C43—21no—
67C4⋊C8×C43—21no—
68C4⋊C8×C43C2×C412yes—
69C22⋊C8×C43—21no—
70C4×C8×C43—21no—
71#95×C43D412yes—
72C23×D43—21no—
73C22×C4×C43—22no—
74C22×C4×C43C2×D411yescharacteristic
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×Dic43—21no—
78C22×Dic43—21no—
79C22×Dic43—21no—
80C2×D172—21no—
81C2×D172—42no—
82C2×D172C22⋊C412yes—
83C2×C4×D43—22no—
84C2×C4×D43—22no—
85C2×C4×D43—41no—
86C2×C4×D43—41no—
87C2×C4×D43—41no—
88C2×C4×D43—41no—
89C2×Dic86—21no—
90C2×Dic86—21no—
91M16×C43—41no—
92M16×C43—41no—
93C2×C8×C43—22no—
94C2×C8×C43—41no—
95C4⋊C4×C43—42no—
96C42×C43—41no—
97C42×C43—41no—
98C42×C43C22×C411yescharacteristic
99C42×C43C2×D411yescharacteristic
100C42×C43#4111yescharacteristic
101C42×C43#4111yescharacteristic
102C22⋊Dic43—41no—
103(C2×D43)⋊C4—22no—
104(C2×D43)⋊C4—22no—
105(C2×D43)⋊C4—44no—
106(C2×D43)⋊C4—44no—
107C4⋊Dic43—21no—
108C4⋊Dic43—21no—
109C4⋊Dic43—21no—
110C4⋊Dic43—21no—
111C4⋊Dic43—21no—
112C4⋊Dic43C22⋊C412yes—
113Dic43⋊C4—44no—
114Dic43⋊C4—41no—
115Dic43⋊C4—41no—
116C4×Dic43—21no—
117C4×Dic43—21no—
118C4×Dic43—21no—
119C4×Dic43—42no—
120C4×Dic43—42no—
121C4×Dic43—41no—
122C4×Dic43SD1612yescomplemented
123C2×C43⋊C8—41no—
124#10621873—44no—
125C23×C43#12011yescharacteristic
126C22×D43—22no—
127C22×D43—42no—
128C22×D43—42no—
129C22×D43—41no—
130C22×D43—41no—
131C2×C4×C43—22no—
132C2×C4×C43—41no—
133C2×C4×C43—42no—
134C2×C4×C43—42no—
135C2×C4×C43—42no—
136C2×C4×C43C2×C22⋊C411yescharacteristic
137C2×C4×C43C4×D411yescharacteristic
138C2×C4×C43C4×D411yescharacteristic
139C2×C4×C43#12111yescharacteristic
140C2×C4×C43#12111yescharacteristic
141C2×C4×C43#12311yescharacteristic
142C2×C4×C43C2×SD1611yescharacteristic
143C2×C4×C43#13511yescharacteristic
144C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C43#13711yescharacteristic
146C2×Dic43—22no—
147C2×Dic43—22no—
148C2×Dic43—22no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157D172—22no—
158D172—22no—
159D172—42no—
160C4×D43—42no—
161C4×D43—42no—
162C4×D43—42no—
163C4×D43—42no—
164Dic86—42no—
165Dic86—81no—
166C8×C43—42no—
167C8×C43—81no—
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#42112yes—
185C4×C43C4×SD1611yescharacteristic
186C4×C43#44011yescharacteristic
187C4×C43#46111yescharacteristic
188C4×C43#46311yescharacteristic
189Dic43—42no—
190Dic43—42no—
191Dic43—42no—
192Dic43—81no—
193Dic43—81no—
194#3101—431no—
195#2293—431no—
196#1994—431no—
197#1503—431no—
198#1486—431no—
199#1303D4311yescharacteristic, complemented
200#1276—431no—
201C2×C43—21no—
202C2×C43—21no—
203C2×C43#187711yescharacteristic
204C2×C43#189711yescharacteristic
205C2×C43#190611yescharacteristic
206D43—82no—
207#533—431no—
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#423C2×D4311yescharacteristic
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—862no—
227D4⋊C8—862no—
228C43#923511yescharacteristic, complemented, Sylow
229C22×D4—431no—
230C23×C4—861no—
231C2×SD16—862no—
232C2×M16—21no—
233C4⋊Q8—431no—
234C4⋊Q8—431no—
235#125—861no—
236C22⋊Q8—861no—
237C22⋊Q8—861no—
238C4×Q8—861no—
239C4×Q8—861no—
240C4×D4—432no—
241C4×D4—432no—
242C4×D4—861no—
243C4×D4—861no—
244#117—861no—
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—21no—
262C4⋊C8—861no—
263C4⋊C8C4×D4312yes—
264#103—862no—
265#102—862no—
266C22⋊C8—21no—
267C22⋊C8—861no—
268C4×C8—21no—
269C4×C8—861no—
270#95—862no—
271#95D17212yes—
272C24—861no—
273C2×Q8—861no—
274C2×Q8—861no—
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×C4C2×D17211yescharacteristic
289C22×C4D4×D4311yescharacteristic
290C22×C4D4×D4311yescharacteristic
291SD16—1724no—
292M16—41no—
293M16—41no—
294C2×C8—22no—
295C2×C8—41no—
296C2×C8—1721no—
297C4⋊C4—42no—
298C4⋊C4—432no—
299C4⋊C4—861no—
300C4⋊C4—861no—
301C4⋊C4—861no—
302C4⋊C4—861no—
303C4⋊C4—861no—
304C4⋊C4—1724no—
305C4⋊C4—1721no—
306C4⋊C4—1721no—
307C22⋊C4—862no—
308C22⋊C4—862no—
309C22⋊C4—1724no—
310C22⋊C4—1724no—
311C22⋊C4—1721no—
312C42—41no—
313C42—41no—
314C42—432no—
315C42—861no—
316C42—861no—
317C42—861no—
318C42—1722no—
319C42—1722no—
320C42—1721no—
321C42C2×C4×D4311yescharacteristic
322C42#1062189811yescharacteristic
323C42D4×D4311yescharacteristic
324C42#1062190211yescharacteristic
325C23—862no—
326C23—1722no—
327C23—1722no—
328C23—1721no—
329C23—1721no—
330C23#1306329511yescharacteristic
331Q8—3441no—
332Q8—1722no—
333D4—862no—
334D4—862no—
335D4—1722no—
336C2×C4—22no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—862no—
342C2×C4—862no—
343C2×C4—862no—
344C2×C4—1721no—
345C2×C4—1721no—
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#1306328711yescharacteristic
358C2×C4C4×D17211yescharacteristic
359C2×C4#1306329811yescharacteristic
360C2×C4#1306330011yescharacteristic
361C2×C4#1306331011yescharacteristic
362C2×C4SD16×D4311yescharacteristic
363C2×C4#1306334611yescharacteristic
364C2×C4#1306334911yescharacteristic
365C2×C4#1306335711yescharacteristic
366C8—42no—
367C8—81no—
368C8—3441no—
369C22—21no—
370C22—21no—
371C22—3442no—
372C22—3442no—
373C22—1722no—
374C22—1722no—
375C22—1722no—
376C22#1458277711yescharacteristic
377C22#1458305111yescharacteristic
378C22#1458306411yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—82no—
383C4—3441no—
384C4—3441no—
385C4—1722no—
386C4—1722no—
387C4—1722no—
388C4#1458291412yes—
389C4#1458298611yescharacteristic
390C4#1458299811yescharacteristic
391C4#1458310311yescharacteristic
392C4#1458311311yescharacteristic
393C2—21no—
394C2—21no—
395C2—3442no—
396C2#1913493011yescharacteristic
397C2#1913504211yescharacteristic
398C2#1913509711yescharacteristic
subgroupG/H
centerC2×C4#13063298
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1303C2
socleC22×C43#386
prime radicalC22×D172D4
cosocleC2×C42×C43C23
hypercenter#1303D43
hypocenterC43#9235
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
3. #19135571C2semidirect
4. #19133093C2semidirect
6. #19132427C2semidirect
7. C43×#1303C2semidirect
12. #14583190C4semidirect
13. #14583105C4semidirect
122. C4×Dic43SD16semidirect
199. #1303D43semidirect
228. C43#9235semidirect

Maximal subgroups

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

subgroupindex
#191446042
#191370562
#191355712
#191330932
#191330192
#191324272
C43×#13032
#923543