Finite Group Databasebeta

← #24992896

Subgroups — #24992896

Order 11008.

512 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144627C211yesmaximal, characteristic
2#19137072C211yesmaximal, characteristic, complemented
3#19135423C211yesmaximal, characteristic
4#19133091C211yesmaximal, characteristic
5#19133025C211yesmaximal, characteristic, complemented
6#19132497C211yesmaximal, characteristic, complemented
7C43×#1276C211yesmaximal, characteristic, complemented
8#14583449C2211yescharacteristic
9C2×C4×Dic86C2211yescharacteristic
10#14583218—21no—
11#14583185C412yescomplemented
12#14583100C412yescomplemented
13#14583040—21no—
14C4×#10621873—22no—
15#14582923C2211yescharacteristic
16C2×#13063253—21no—
17C2×#13063253—21no—
18#14582805—21no—
19#14582797—21no—
20#14582783—22no—
21C4×Dic43⋊C4—21no—
22C4×C4⋊Dic43C2211yescharacteristic
23#14582745—21no—
24#14582634—22no—
25#14582631—22no—
26C43×#431C2211yescharacteristic
27C43×#431C2211yescharacteristic
28C43×C43C2211yescharacteristic
29C2×#10621898—21no—
30C22×Dic86D411yescharacteristic
31C2×#10621873—22no—
32C2×#10621877—21no—
33#13063325C2×C411yescharacteristic
34#13063322C2×C411yescharacteristic
35#13063313—21no—
36#13063299—21no—
37#13063299—21no—
38C4×Dic86—21no—
39C4×Dic86—21no—
40C4×Dic86C2×C412yes—
41C4×Dic86D412yes—
42C4×D172—21no—
43C4×D172—21no—
44C2×C4⋊Dic43—21no—
45C2×C4⋊Dic43D411yescharacteristic
46C2×Dic43⋊C4—21no—
47C2×Dic43⋊C4—22no—
48C2×C4×Dic43—21no—
49C2×C4×Dic43—21no—
50#13063257—22no—
51C4⋊(C43⋊C8)—21no—
52C4⋊(C43⋊C8)—21no—
53#13063253—42no—
54#13063253—42no—
55#13063250—22no—
56#13063247—22no—
57C43⋊#95—22no—
58C43⋊#95—22no—
59C43⋊#95—22no—
60C43⋊#95D412yes—
61C2×C42×C43—21no—
62C2×C42×C43—21no—
63C2×C42×C43D411yescharacteristic
64C2×C42×C43D411yescharacteristic
65C2×C42×C43C2311yescharacteristic
66C4⋊C8×C43—21no—
67C4⋊C8×C43C2×C412yes—
68C22⋊C8×C43—21no—
69C22⋊C8×C43—21no—
70C4×C8×C43—21no—
71C4×C8×C43—21no—
72C22×C4×C43—21no—
73C22×C4×C43—21no—
74C22×C4×C43C2×D411yescharacteristic
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C2×C22⋊D43—41no—
78C22×Dic43—21no—
79C22×Dic43—21no—
80C22×Dic43—22no—
81#10621898—41no—
82#10621898—41no—
83#10621898—41no—
84#10621898—41no—
85C2×D172—21no—
86C2×D172—21no—
87C2×D172—21no—
88C2×C4×D43—41no—
89C2×Dic86—21no—
90C2×Dic86—21no—
91C2×Dic86—42no—
92C2×Dic86C22⋊C412yes—
93C2×C8×C43—22no—
94C2×C8×C43—41no—
95C42×C43—21no—
96C42×C43—21no—
97C42×C43—21no—
98C42×C43—42no—
99C42×C43—42no—
100C42×C43SD1612yescomplemented
101C42×C43C22×C411yescharacteristic
102C42×C43C2×D411yescharacteristic
103C42×C43#4111yescharacteristic
104C42×C43#4111yescharacteristic
105(C2×D43)⋊C4—41no—
106(C2×D43)⋊C4—41no—
107C4⋊Dic43—21no—
108C4⋊Dic43—21no—
109C4⋊Dic43—21no—
110C4⋊Dic43—42no—
111C4⋊Dic43C22⋊C412yes—
112Dic43⋊C4—22no—
113Dic43⋊C4—22no—
114Dic43⋊C4—44no—
115C4×Dic43—22no—
116C4×Dic43—22no—
117C4×Dic43—41no—
118C4×Dic43—41no—
119#10621877—41no—
120#10621877—41no—
121C2×C43⋊C8—41no—
122#10621873—44no—
123C23×C43#12011yescharacteristic
124C22×D43—41no—
125C2×C4×C43—22no—
126C2×C4×C43—22no—
127C2×C4×C43—22no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43C2×C22⋊C411yescharacteristic
134C2×C4×C43C4×D411yescharacteristic
135C2×C4×C43C4×D411yescharacteristic
136C2×C4×C43#12111yescharacteristic
137C2×C4×C43#12111yescharacteristic
138C2×C4×C43#12311yescharacteristic
139C2×C4×C43C2×SD1611yescharacteristic
140C2×C4×C43#13511yescharacteristic
141C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C43#13711yescharacteristic
143C22⋊D43—81no—
144C22⋊D43—81no—
145C2×Dic43—22no—
146C2×Dic43—22no—
147C2×Dic43—42no—
148C2×Dic43—42no—
149C2×Dic43—42no—
150C2×Dic43—42no—
151C2×Dic43—41no—
152C2×Dic43—42no—
153D172—42no—
154D172—41no—
155D172—41no—
156D172—81no—
157C4×D43—81no—
158C4×D43—81no—
159Dic86—22no—
160Dic86—22no—
161Dic86—42no—
162Dic86—41no—
163Dic86—41no—
164C8×C43—42no—
165C8×C43—81no—
166C43⋊C8—81no—
167#9238—431nomaximal, Sylow
168C22×C43—21no—
169C22×C43—21no—
170C22×C43#38611yescharacteristic
171C22×C43#44811yescharacteristic
172C22×C43#44911yescharacteristic
173C2×D43—81no—
174C2×D43—81no—
175C2×D43—81no—
176C4×C43—21no—
177C4×C43—21no—
178C4×C43—21no—
179C4×C43—42no—
180C4×C43—42no—
181C4×C43#42112yes—
182C4×C43C4×SD1611yescharacteristic
183C4×C43#44011yescharacteristic
184C4×C43#46011yescharacteristic
185C4×C43#46411yescharacteristic
186Dic43—42no—
187Dic43—42no—
188Dic43—82no—
189Dic43—81no—
190#3103—431no—
191#2295—431no—
192#1962—431no—
193#1502—431no—
194#1487—431no—
195#1303—431no—
196#1276D4311yescharacteristic, complemented
197C2×C43—21no—
198C2×C43—21no—
199C2×C43#188011yescharacteristic
200C2×C43#189711yescharacteristic
201C2×C43#190611yescharacteristic
202D43—161no—
203#532—431no—
204C2×C4×Q8—431no—
205#481—861no—
206#475—432no—
207#460—432no—
208#448—861no—
209C4×SD16—862no—
210#431C2×D4311yescharacteristic
211#431C2×D4311yescharacteristic
212#423—431no—
213C2×#104—861no—
214C2×#104—861no—
215#391—861no—
216#389—861no—
217#387—862no—
218C4×C4⋊C4—431no—
219C4×C4⋊C4—861no—
220#376—861no—
221C43C2×D4311yescharacteristic
222#327—862no—
223Q8⋊C8—862no—
224C43#923811yescharacteristic, complemented, Sylow
225C2×#41—861no—
226C22×Q8—431no—
227C2×SD16—862no—
228C2×M16—861no—
229C4⋊Q8—431no—
230#127—431no—
231#124—861no—
232#121—861no—
233#121—861no—
234C4×Q8—432no—
235C4×Q8—432no—
236C4×Q8—861no—
237C4×Q8—861no—
238C4×D4—861no—
239C4×D4—861no—
240C2×C4⋊C4—431no—
241C2×C4⋊C4—861no—
242C2×C4⋊C4—862no—
243C2×C4⋊C4—861no—
244C2×C42—21no—
245C2×C42—21no—
246C2×C42—861no—
247C2×C42—861no—
248C2×C42D17211yescharacteristic
249C2×C42D17211yescharacteristic
250C2×C42C22×D4311yescharacteristic
251#106—862no—
252C4⋊C8—21no—
253C4⋊C8—861no—
254C4⋊C8—861no—
255C4⋊C8C4×D4312yes—
256#104—1722no—
257#104—1722no—
258#103—862no—
259#102—862no—
260C22⋊C8—21no—
261C22⋊C8—21no—
262C4×C8—21no—
263C4×C8—21no—
264#95—432no—
265#95—862no—
266#95—862no—
267#95—862no—
268#41—1721no—
269#41—1721no—
270#41—1721no—
271#41—1721no—
272C2×Q8—432no—
273C2×Q8—861no—
274C2×Q8—861no—
275C2×Q8—1722no—
276C2×D4—861no—
277C2×D4—861no—
278C2×D4—861no—
279C2×D4—1721no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—861no—
283C22×C4—861no—
284C22×C4—862no—
285C22×C4—1721no—
286C22×C4C2×D17211yescharacteristic
287C22×C4D4×D4311yescharacteristic
288C22×C4D4×D4311yescharacteristic
289SD16—1724no—
290M16—1721no—
291M16—1721no—
292C2×C8—22no—
293C2×C8—41no—
294C2×C8—1721no—
295C4⋊C4—432no—
296C4⋊C4—862no—
297C4⋊C4—862no—
298C4⋊C4—861no—
299C4⋊C4—861no—
300C4⋊C4—861no—
301C4⋊C4—1724no—
302C4⋊C4—1722no—
303C22⋊C4—1721no—
304C22⋊C4—1721no—
305C42—21no—
306C42—21no—
307C42—21no—
308C42—42no—
309C42—42no—
310C42—862no—
311C42—862no—
312C42—1721no—
313C42—1721no—
314C42#1062187312yescomplemented
315C42C2×C4×D4311yescharacteristic
316C42#1062189811yescharacteristic
317C42D4×D4311yescharacteristic
318C42#1062190211yescharacteristic
319C23—1721no—
320C23#1306329511yescharacteristic
321Q8—862no—
322Q8—862no—
323Q8—1722no—
324Q8—1721no—
325Q8—1721no—
326D4—3441no—
327D4—3441no—
328D4—3441no—
329D4—1722no—
330D4—1721no—
331D4—1721no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—862no—
341C2×C4—862no—
342C2×C4—3441no—
343C2×C4—3441no—
344C2×C4—1722no—
345C2×C4—1722no—
346C2×C4—1722no—
347C2×C4—1721no—
348C2×C4—1722no—
349C2×C4—1722no—
350C2×C4C22⋊C4×D4311yescharacteristic
351C2×C4#1306328711yescharacteristic
352C2×C4C4×D17211yescharacteristic
353C2×C4#1306329811yescharacteristic
354C2×C4#1306330011yescharacteristic
355C2×C4#1306331011yescharacteristic
356C2×C4C2×#1062187311yescharacteristic
357C2×C4#1306334711yescharacteristic
358C2×C4#1306335311yescharacteristic
359C2×C4#1306335811yescharacteristic
360C8—42no—
361C8—81no—
362C8—3441no—
363C22—21no—
364C22—21no—
365C22—3441no—
366C22—3441no—
367C22—3441no—
368C22#1458277711yescharacteristic
369C22#1458304011yescharacteristic
370C22#1458304611yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—42no—
375C4—42no—
376C4—3442no—
377C4—3441no—
378C4—1722no—
379C4—1722no—
380C4#1458291412yes—
381C4C4×#1062187311yescharacteristic
382C4#1458300111yescharacteristic
383C4#1458310011yescharacteristic
384C4#1458312211yescharacteristic
385C2—21no—
386C2—21no—
387C2—6881no—
388C2#1913494911yescharacteristic
389C2#1913504211yescharacteristic
390C2#1913509511yescharacteristic
subgroupG/H
centerC2×C4#13063300
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1276C2
socleC22×C43#386
prime radical#14583449C22
cosocleC2×C42×C43C23
hypercenter#1276D43
hypocenterC43#9238
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1276

Complements

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

NH ≅ G/Ntype
2. #19137072C2semidirect
5. #19133025C2semidirect
6. #19132497C2semidirect
7. C43×#1276C2semidirect
11. #14583185C4semidirect
12. #14583100C4semidirect
100. C42×C43SD16semidirect
196. #1276D43semidirect
224. C43#9238semidirect
314. C42#10621873semidirect

Maximal subgroups

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

subgroupindex
#191446272
#191370722
#191354232
#191330912
#191330252
#191324972
C43×#12762
#923843