Finite Group Databasebeta

← #24999152

Subgroups — #24999152

Order 11008.

658 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583272C211yesmaximal, characteristic
2C2×#14583184C211yesmaximal, characteristic, complemented
3C2×#14583099C211yesmaximal, characteristic
4C2×#14582646C211yesmaximal, characteristic, complemented
5C2×#14582642C211yesmaximal, characteristic
6#19132430C211yesmaximal, characteristic, complemented
7C43×#1984C211yesmaximal, characteristic, complemented
8C22×#10621873—22no—
9C22×#10621884—21no—
10C2×#13063325C2211yescharacteristic
11C2×#13063322C2211yescharacteristic
12#14583272—22no—
13#14583272—22no—
14#14583184—22no—
15#14583184—22no—
16#14583099—22no—
17#14583099—22no—
18C2×#13063256—21no—
19C2×C4⋊(C43⋊C8)C2211yescharacteristic
20C2×C4⋊(C43⋊C8)C2211yescharacteristic
21C2×#13063249—21no—
22C2×#13063245—21no—
23#14582646—22no—
24#14582642—22no—
25C2×C4×Q8×C43C2211yescharacteristic
26C2×C4⋊C8×C43C2211yescharacteristic
27C2×C4×C8×C43C2211yescharacteristic
28C43×#336—22no—
29C22×Dic86—21no—
30C22×D172—21no—
31C22×D172—21no—
32C22×D172—21no—
33C2×#10621873—28no—
34C2×#10621873—44no—
35C2×#10621873—44no—
36C2×#10621884—24no—
37C2×#10621884—42no—
38C2×#10621884—42no—
39C22×C43⋊C8—21no—
40C22×C43⋊C8—21no—
41#13063325—21no—
42#13063325—21no—
43#13063325—21no—
44#13063325D412yes—
45#13063322—21no—
46#13063322—21no—
47#13063322—21no—
48#13063322D412yes—
49C2×C4⋊Dic43—21no—
50C2×C4⋊Dic43—21no—
51#13063256—24no—
52C4⋊(C43⋊C8)—21no—
53C4⋊(C43⋊C8)—21no—
54C4⋊(C43⋊C8)D412yes—
55C4⋊(C43⋊C8)D412yes—
56#13063249—24no—
57#13063245—24no—
58C22×Q8×C43D411yescharacteristic
59C22×C8×C43—21no—
60C22×C8×C43D412yes—
61C4×Q8×C43—21no—
62C4×Q8×C43—21no—
63C4×Q8×C43—21no—
64C4×Q8×C43—21no—
65C2×C4⋊C4×C43—21no—
66C2×C4⋊C4×C43D411yescharacteristic
67C2×C42×C43—21no—
68C2×C42×C43C2311yescharacteristic
69C4⋊C8×C43—21no—
70C4⋊C8×C43—21no—
71C4×C8×C43—21no—
72C4×C8×C43—21no—
73C23×D43—41no—
74C2×Q8×C43—21no—
75C2×Q8×C43—21no—
76C2×Q8×C43—21no—
77C2×Q8×C43—21no—
78C2×Q8×C43—21no—
79C2×Q8×C43SD1612yescomplemented
80C22×C4×C43—21no—
81C22×C4×C43—21no—
82C22×C4×C43C2×D411yescharacteristic
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43#4111yescharacteristic
85C22×Dic43—41no—
86C2×D172—22no—
87C2×D172—22no—
88C2×D172—22no—
89C2×D172—41no—
90C2×D172—41no—
91C2×D172—41no—
92C2×D172—41no—
93C2×D172—42no—
94C2×D172—41no—
95C2×D172—41no—
96C2×D172—42no—
97C2×D172—41no—
98C2×D172—82no—
99C2×Dic86—22no—
100C2×Dic86—42no—
101C2×Dic86—42no—
102C2×Dic86—41no—
103C2×C8×C43—22no—
104C2×C8×C43—22no—
105C2×C8×C43—41no—
106C2×C8×C43—42no—
107C2×C8×C43SD1614yescomplemented
108C4⋊C4×C43—21no—
109C4⋊C4×C43—21no—
110C4⋊C4×C43—41no—
111C4⋊C4×C43—41no—
112C42×C43—41no—
113C42×C43—41no—
114C42×C43C2×D411yescharacteristic
115C42×C43C2×D411yescharacteristic
116C42×C43C2×D411yescharacteristic
117C42×C43C2×D411yescharacteristic
118#10621884—48no—
119C4⋊Dic43—22no—
120C4⋊Dic43—22no—
121C4⋊Dic43—41no—
122C4⋊Dic43—41no—
123C2×C43⋊C8—22no—
124C2×C43⋊C8—22no—
125C2×C43⋊C8—41no—
126C2×C43⋊C8—41no—
127C2×C43⋊C8—41no—
128C2×C43⋊C8—41no—
129#10621873—416no—
130C23×C43#12111yescharacteristic
131C22×D43—42no—
132C22×D43—82no—
133C22×D43—81no—
134C22×D43—81no—
135C22×D43—82no—
136Q8×C43—22no—
137Q8×C43—22no—
138Q8×C43—41no—
139Q8×C43—41no—
140C2×C4×C43—22no—
141C2×C4×C43—22no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—42no—
146C2×C4×C43#12011yescharacteristic
147C2×C4×C43#12011yescharacteristic
148C2×C4×C43#12011yescharacteristic
149C2×C4×C43#12111yescharacteristic
150C2×C4×C43#12111yescharacteristic
151C2×C4×C43#12711yescharacteristic
152C2×C4×C43C2×SD1612yes—
153C2×C4×C43C2×SD1611yescharacteristic
154C2×C4×C43#13511yescharacteristic
155C2×C4×C43AGL(1,ℤ/8)12yes—
156C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C43#13711yescharacteristic
158C2×Dic43—42no—
159C2×Dic43—82no—
160D172—44no—
161D172—42no—
162D172—42no—
163D172—82no—
164D172—82no—
165D172—81no—
166D172—81no—
167D172—81no—
168D172—81no—
169Dic86—44no—
170Dic86—81no—
171Dic86—81no—
172C8×C43—24no—
173C8×C43—81no—
174C43⋊C8—42no—
175C43⋊C8—42no—
176#10268—431nomaximal, Sylow
177C22×C43#39211yescharacteristic
178C22×C43#46012yes—
179C22×C43#46511yescharacteristic
180C22×C43#46811yescharacteristic
181C22×C43#47112yes—
182C2×D43—82no—
183C2×D43—82no—
184C2×D43—82no—
185C2×D43—162no—
186C2×D43—162no—
187C4×C43—21no—
188C4×C43—21no—
189C4×C43—42no—
190C4×C43—81no—
191C4×C43#44811yescharacteristic
192C4×C43#44911yescharacteristic
193C4×C43#45012yes—
194C4×C43#45011yescharacteristic
195C4×C43#45211yescharacteristic
196C4×C43#49211yescharacteristic
197C4×C43#49611yescharacteristic
198Dic43—82no—
199C2×#492—431no—
200C2×#475—431no—
201C2×#460—431no—
202#1984D4311yescharacteristic, complemented
203C2×#332—431no—
204C2×#331—431no—
205#1277—431no—
206C2×C43#166612yes—
207C2×C43#168612yes—
208C2×C43#200011yescharacteristic
209C2×C43#201411yescharacteristic
210C2×C43#201911yescharacteristic
211D43—162no—
212C22×SD16—861no—
213C22×SD16—862no—
214C2×C4⋊Q8—431no—
215C2×#127—431no—
216C2×C4×Q8C2×D4311yescharacteristic
217#492—862no—
218#492—862no—
219#475—862no—
220#475—862no—
221#460—862no—
222#460—862no—
223C2×#106—861no—
224C2×C4⋊C8—431no—
225C2×C4⋊C8—431no—
226C2×C4⋊C8C2×D4311yescharacteristic
227C2×#103—861no—
228C2×#102—861no—
229C2×C4×C8C2×D4311yescharacteristic
230#336—22no—
231#332—862no—
232#331—862no—
233C43#1026811yescharacteristic, complemented, Sylow
234C22×Q8—861no—
235C22×Q8D17211yescharacteristic
236C22×D4—861no—
237C22×D4—861no—
238C22×D4—861no—
239C2×SD16—868no—
240C2×SD16—864no—
241C2×SD16—1724no—
242C2×SD16—1722no—
243C2×SD16—1722no—
244C2×SD16—1724no—
245C22×C8—21no—
246C22×C8—861no—
247C22×C8—861no—
248C22×C8C22⋊D4312yes—
249C4⋊Q8—432no—
250C4⋊Q8—861no—
251C4⋊Q8—861no—
252C4⋊Q8—861no—
253#127—432no—
254#127—861no—
255#127—861no—
256#127—861no—
257C4×Q8—21no—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—861no—
263C2×C4⋊C4—861no—
264C2×C4⋊C4D17211yescharacteristic
265C2×C42—21no—
266C2×C42C22×D4311yescharacteristic
267#106—864no—
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8—432no—
271C4⋊C8—432no—
272C4⋊C8—861no—
273C4⋊C8—861no—
274#103—864no—
275#102—864no—
276C4×C8—21no—
277C4×C8—21no—
278C24—1721no—
279C2×Q8—21no—
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—862no—
285C2×Q8—1722no—
286C2×Q8—1722no—
287C2×Q8—1721no—
288C2×Q8#1062187312yescomplemented
289C2×D4—862no—
290C2×D4—862no—
291C2×D4—862no—
292C2×D4—3442no—
293C2×D4—1721no—
294C2×D4—1721no—
295C2×D4—1721no—
296C2×D4—1722no—
297C2×D4—1721no—
298C2×D4—1721no—
299C2×D4—1722no—
300C2×D4—1721no—
301C2×D4—1721no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—1721no—
305C22×C4C2×D17211yescharacteristic
306C22×C4#1062189811yescharacteristic
307C22×C4C2×C22⋊D4311yescharacteristic
308SD16—17216no—
309SD16—1728no—
310C2×C8—22no—
311C2×C8—22no—
312C2×C8—41no—
313C2×C8—42no—
314C2×C8—862no—
315C2×C8—862no—
316C2×C8—1721no—
317C2×C8—1721no—
318C2×C8—1721no—
319C2×C8—1721no—
320C2×C8#1062188414yescomplemented
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—862no—
326C4⋊C4—862no—
327C4⋊C4—1721no—
328C4⋊C4—1721no—
329C42—41no—
330C42—41no—
331C42D4×D4311yescharacteristic
332C42D4×D4311yescharacteristic
333C42D4×D4311yescharacteristic
334C42D4×D4311yescharacteristic
335C23—3442no—
336C23—3441no—
337C23—3441no—
338C23—3442no—
339C23—1722no—
340C23#1306329911yescharacteristic
341Q8—22no—
342Q8—22no—
343Q8—41no—
344Q8—41no—
345Q8—3441no—
346Q8—3441no—
347Q8—1724no—
348D4—3442no—
349D4—3442no—
350D4—3441no—
351D4—3441no—
352D4—3441no—
353D4—3441no—
354D4—1724no—
355D4—1722no—
356D4—1722no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—3442no—
364C2×C4—1722no—
365C2×C4#1306329311yescharacteristic
366C2×C4#1306329511yescharacteristic
367C2×C4#1306329511yescharacteristic
368C2×C4#1306329811yescharacteristic
369C2×C4#1306329811yescharacteristic
370C2×C4#1306332111yescharacteristic
371C2×C4C2×#1062188412yes—
372C2×C4C2×#1062187311yescharacteristic
373C2×C4#1306334711yescharacteristic
374C2×C4#1306335012yes—
375C2×C4#1306335311yescharacteristic
376C2×C4#1306335811yescharacteristic
377C8—24no—
378C8—81no—
379C8—1722no—
380C8—1722no—
381C22—3442no—
382C22—3442no—
383C22—3442no—
384C22—6882no—
385C22—6882no—
386C22#1458280811yescharacteristic
387C22#1458309912yes—
388C22#1458312811yescharacteristic
389C22#1458314511yescharacteristic
390C22#1458316212yes—
391C4—21no—
392C4—21no—
393C4—42no—
394C4—81no—
395C4—3442no—
396C4#1458304011yescharacteristic
397C4#1458304611yescharacteristic
398C4#1458304912yes—
399C4#1458305211yescharacteristic
400C4#1458306311yescharacteristic
401C4#1458327311yescharacteristic
402C4#1458328911yescharacteristic
403C2—6882no—
404C2#1913394312yes—
405C2#1913406712yes—
406C2#1913560011yescharacteristic
407C2#1913568211yescharacteristic
408C2#1913571011yescharacteristic
subgroupG/H
centerC23#13063299
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1984C2
socleC23×C43#121
prime radicalC2×#13063322C22
hypercenter#1984D43
hypocenterC43#10268
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1984

Complements

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

NH ≅ G/Ntype
2. C2×#14583184C2semidirect
4. C2×#14582646C2semidirect
6. #19132430C2semidirect
7. C43×#1984C2semidirect
79. C2×Q8×C43SD16semidirect
107. C2×C8×C43SD16semidirect
202. #1984D43semidirect
233. C43#10268semidirect
288. C2×Q8#10621873semidirect
320. C2×C8#10621884semidirect

Maximal subgroups

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

subgroupindex
C2×#145832722
C2×#145831842
C2×#145830992
C2×#145826462
C2×#145826422
#191324302
C43×#19842
#1026843