Finite Group Databasebeta

← #24992678

Subgroups — #24992678

Order 11008.

478 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144383C211yesmaximal, characteristic
2#41×C43⋊C8C211yesmaximal, characteristic
3#19133093C211yesmaximal, characteristic, complemented
4#19133049C211yesmaximal, characteristic, complemented
5#19132490C211yesmaximal, characteristic, complemented
6#19132436C211yesmaximal, characteristic, complemented
7C43×#1806C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9#14583206—21no—
10#14583199—21no—
11#14583194C411yescharacteristic, complemented
12#14583189C411yescharacteristic, complemented
13#14583184C411yescharacteristic, complemented
14#14583179C411yescharacteristic, complemented
15Q8×C43⋊C8—21no—
16D4×C43⋊C8—22no—
17D4×C43⋊C8—21no—
18#14582952—21no—
19#14582952C2211yescharacteristic
20#14582935—21no—
21C2×C4⋊(C43⋊C8)C2211yescharacteristic
22#14582895—21no—
23C2×C4×C43⋊C8—21no—
24C2×C4×C43⋊C8C2211yescharacteristic
25#14582635—22no—
26#14582629—21no—
27#14582629—21no—
28C4×#41×C43C2211yescharacteristic
29C43×#423C2211yescharacteristic
30C2×#104×C43—21no—
31C4×C4⋊C4×C43C2211yescharacteristic
32C43×#339—21no—
33C22×C43⋊C8—22no—
34C22×C43⋊C8—21no—
35C22×C43⋊C8—21no—
36#13063325C2×C411yescharacteristic
37#13063325C2×C411yescharacteristic
38#13063317—21no—
39#13063304—21no—
40#13063304—21no—
41C4×Dic86—21no—
42C4×Dic86—21no—
43#13063284—21no—
44#13063258—21no—
45#13063258—21no—
46#13063256—21no—
47#13063256—21no—
48C4⋊(C43⋊C8)—22no—
49C4⋊(C43⋊C8)—21no—
50C4⋊(C43⋊C8)—21no—
51C4⋊(C43⋊C8)C2×C411yescharacteristic
52C4⋊(C43⋊C8)C2×C411yescharacteristic
53#13063249—21no—
54#13063249—21no—
55#13063246—21no—
56#13063246—21no—
57C22⋊(C43⋊C8)—22no—
58C22⋊(C43⋊C8)D412yes—
59C4×C43⋊C8—22no—
60C4×C43⋊C8—21no—
61C4×C43⋊C8—21no—
62C4×C43⋊C8D411yescharacteristic
63C4×C43⋊C8D411yescharacteristic
64C2×#41×C43D411yescharacteristic
65C2×M16×C43—21no—
66C4×Q8×C43C2×C411yescharacteristic
67C4×Q8×C43D411yescharacteristic
68C4×D4×C43—21no—
69C4×D4×C43—21no—
70C4×D4×C43C2×C411yescharacteristic
71C4×D4×C43D411yescharacteristic
72#117×C43—21no—
73#117×C43D411yescharacteristic
74C2×C4⋊C4×C43—21no—
75C2×C42×C43—21no—
76C2×C42×C43—21no—
77C2×C42×C43C2311yescharacteristic
78C4⋊C8×C43—21no—
79C4⋊C8×C43—21no—
80#104×C43—42no—
81#95×C43—21no—
82#41×C43—21no—
83#41×C43—21no—
84#41×C43SD1612yes—
85#41×C43Q1612yes—
86C2×Q8×C43C22⋊C411yescharacteristic
87C2×D4×C43—21no—
88C2×D4×C43C22⋊C411yescharacteristic
89C22×C4×C43—21no—
90C22×C4×C43—21no—
91C22×C4×C43—21no—
92C22×C4×C43—41no—
93C22×C4×C43C2×D411yescharacteristic
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43#4111yescharacteristic
96C2×Dic86—21no—
97C2×Dic86—21no—
98M16×C43—41no—
99M16×C43—41no—
100C2×C8×C43—41no—
101C4⋊C4×C43—21no—
102C4⋊C4×C43—21no—
103C4⋊C4×C43—22no—
104C4⋊C4×C43—41no—
105C4⋊C4×C43C22⋊C411yescharacteristic
106C4⋊C4×C43C22⋊C411yescharacteristic
107C22⋊C4×C43—21no—
108C22⋊C4×C43—21no—
109C22⋊C4×C43—21no—
110C42×C43—21no—
111C42×C43—21no—
112C42×C43—21no—
113C42×C43—41no—
114C42×C43—41no—
115C42×C43C22×C411yescharacteristic
116C42×C43C2×D411yescharacteristic
117C42×C43C2×D411yescharacteristic
118C42×C43#4111yescharacteristic
119C22⋊Dic43—41no—
120C4⋊Dic43—21no—
121C4⋊Dic43—21no—
122C4⋊Dic43—21no—
123C4⋊Dic43—21no—
124Dic43⋊C4—41no—
125Dic43⋊C4—41no—
126C4×Dic43—41no—
127C2×C43⋊C8—21no—
128C2×C43⋊C8—21no—
129C2×C43⋊C8—21no—
130C2×C43⋊C8—22no—
131C2×C43⋊C8—21no—
132C2×C43⋊C8—42no—
133C2×C43⋊C8—44no—
134C2×C43⋊C8—41no—
135C2×C43⋊C8—41no—
136C23×C43—21no—
137C23×C43#12111yescharacteristic
138Q8×C43—21no—
139Q8×C43#10312yes—
140D4×C43—22no—
141D4×C43—22no—
142D4×C43—21no—
143D4×C43#10312yes—
144C2×C4×C43—21no—
145C2×C4×C43—21no—
146C2×C4×C43—21no—
147C2×C4×C43—22no—
148C2×C4×C43—22no—
149C2×C4×C43—21no—
150C2×C4×C43—21no—
151C2×C4×C43—41no—
152C2×C4×C43—42no—
153C2×C4×C43—41no—
154C2×C4×C43—41no—
155C2×C4×C43—42no—
156C2×C4×C43—81no—
157C2×C4×C43—81no—
158C2×C4×C43C2×C22⋊C411yescharacteristic
159C2×C4×C43C4×D411yescharacteristic
160C2×C4×C43C4×D411yescharacteristic
161C2×C4×C43#12011yescharacteristic
162C2×C4×C43#12111yescharacteristic
163C2×C4×C43#12311yescharacteristic
164C2×C4×C43C2×SD1611yescharacteristic
165C2×C4×C43C2×Q1611yescharacteristic
166C2×C4×C43#13511yescharacteristic
167C2×C4×C43#13511yescharacteristic
168C2×Dic43—41no—
169C2×Dic43—41no—
170Dic86—41no—
171Dic86—41no—
172Dic86—81no—
173C8×C43—81no—
174C43⋊C8—22no—
175C43⋊C8—42no—
176C43⋊C8—41no—
177C43⋊C8—41no—
178C43⋊C8—41no—
179#9207—431nomaximal, Sylow
180C22×C43—21no—
181C22×C43—21no—
182C22×C43—22no—
183C22×C43—41no—
184C22×C43—41no—
185C22×C43#38611yescharacteristic
186C22×C43#46511yescharacteristic
187C22×C43#46711yescharacteristic
188C4×C43—21no—
189C4×C43—22no—
190C4×C43—21no—
191C4×C43—21no—
192C4×C43—41no—
193C4×C43—41no—
194C4×C43—82no—
195C4×C43C2×#10311yescharacteristic
196C4×C43#41611yescharacteristic
197C4×C43#44311yescharacteristic
198C4×C43#44411yescharacteristic
199C4×C43#46511yescharacteristic
200C4×C43#46711yescharacteristic
201Dic43—81no—
202Dic43—81no—
203#3076—431no—
204C8×#41—431no—
205#1806D4311yescharacteristic
206#1503—431no—
207#1493—431no—
208#1301—431no—
209#1279—431no—
210C2×C43—21no—
211C2×C43—21no—
212C2×C43—42no—
213C2×C43#187611yescharacteristic
214C2×C43#189211yescharacteristic
215C2×C43#190611yescharacteristic
216#533—431no—
217C4×#41C2×D4311yescharacteristic
218#479—861no—
219#478—861no—
220#477—431no—
221#476—431no—
222#475—431no—
223#474—431no—
224C8×Q8—861no—
225C8×D4—862no—
226C8×D4—861no—
227#431—431no—
228#431—861no—
229#427—861no—
230#423C2×D4311yescharacteristic
231C2×C4⋊C8—431no—
232C2×#104—21no—
233#416—861no—
234C2×C4×C8—431no—
235C2×C4×C8—861no—
236C4×C4⋊C4C2×D4311yescharacteristic
237#339—21no—
238#328—862no—
239Q8⋊C8—861no—
240Q8⋊C8—861no—
241C43#920711yescharacteristic, complemented, Sylow
242C2×#41C22⋊D4311yescharacteristic
243C2×M16—21no—
244C22×C8—862no—
245C22×C8—861no—
246C22×C8—861no—
247C4⋊Q8—431no—
248C4⋊Q8—431no—
249#125—861no—
250C22⋊Q8—861no—
251C22⋊Q8—861no—
252C4×Q8—861no—
253C4×Q8—861no—
254C4×Q8C4×D4311yescharacteristic
255C4×Q8D17211yescharacteristic
256C4×D4—21no—
257C4×D4—21no—
258C4×D4C4×D4311yescharacteristic
259C4×D4D17211yescharacteristic
260#117—21no—
261#117—861no—
262#117C22⋊D4311yescharacteristic
263C2×C4⋊C4—21no—
264C2×C42—21no—
265C2×C42—21no—
266C2×C42C22×D4311yescharacteristic
267#107—861no—
268#107—861no—
269#106—861no—
270#106—861no—
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8—431no—
274C4⋊C8—431no—
275C4⋊C8—862no—
276C4⋊C8—861no—
277C4⋊C8—861no—
278#104—42no—
279#103—861no—
280#103—861no—
281#102—861no—
282#102—861no—
283C22⋊C8—432no—
284C22⋊C8—862no—
285C4×C8—431no—
286C4×C8—431no—
287C4×C8—862no—
288C4×C8—861no—
289C4×C8—861no—
290#95—21no—
291#41—21no—
292#41—21no—
293#41#1062188312yes—
294#41#1062188512yes—
295C2×Q8—861no—
296C2×Q8—861no—
297C2×Q8(C2×D43)⋊C411yescharacteristic
298C2×D4—21no—
299C2×D4(C2×D43)⋊C411yescharacteristic
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—41no—
304C22×C4D4×D4311yescharacteristic
305C22×C4#1062190011yescharacteristic
306C22×C4C2×C22⋊D4311yescharacteristic
307M16—41no—
308M16—41no—
309C2×C8—41no—
310C2×C8—861no—
311C2×C8—861no—
312C2×C8—861no—
313C2×C8—861no—
314C2×C8—862no—
315C2×C8—1722no—
316C2×C8—1724no—
317C2×C8—1721no—
318C2×C8—1721no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—22no—
322C4⋊C4—41no—
323C4⋊C4—861no—
324C4⋊C4—861no—
325C4⋊C4—861no—
326C4⋊C4—861no—
327C4⋊C4—1721no—
328C4⋊C4—1721no—
329C4⋊C4(C2×D43)⋊C411yescharacteristic
330C4⋊C4(C2×D43)⋊C411yescharacteristic
331C22⋊C4—21no—
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—1721no—
335C42—21no—
336C42—21no—
337C42—21no—
338C42—41no—
339C42—41no—
340C42—1721no—
341C42C2×C4×D4311yescharacteristic
342C42C2×D17211yescharacteristic
343C42D4×D4311yescharacteristic
344C42#1062190011yescharacteristic
345C23—21no—
346C23#1306329711yescharacteristic
347Q8—21no—
348Q8—3441no—
349Q8—1721no—
350Q8—1721no—
351Q8#1306324812yes—
352D4—22no—
353D4—22no—
354D4—21no—
355D4#1306324812yes—
356C2×C4—21no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—41no—
364C2×C4—42no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—1721no—
371C2×C4—1721no—
372C2×C4C2×(C2×D43)⋊C411yescharacteristic
373C2×C4(C22⋊D43)⋊C411yescharacteristic
374C2×C4(C22⋊D43)⋊C411yescharacteristic
375C2×C4#1306329511yescharacteristic
376C2×C4#1306329711yescharacteristic
377C2×C4#1306330911yescharacteristic
378C2×C4C2×#1062188311yescharacteristic
379C2×C4C2×#1062188511yescharacteristic
380C2×C4#1306334511yescharacteristic
381C2×C4#1306334511yescharacteristic
382C8—81no—
383C8—862no—
384C8—1721no—
385C8—1722no—
386C8—1721no—
387C8—1721no—
388C22—21no—
389C22—21no—
390C22—22no—
391C22—41no—
392C22—41no—
393C22#1458277611yescharacteristic
394C22#1458312611yescharacteristic
395C22#1458313811yescharacteristic
396C4—22no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—82no—
403C4—3441no—
404C4—3441no—
405C4C2×#1306324811yescharacteristic
406C4#1458289311yescharacteristic
407C4#1458301311yescharacteristic
408C4#1458301811yescharacteristic
409C4#1458312611yescharacteristic
410C4#1458313811yescharacteristic
411C2—21no—
412C2—21no—
413C2—42no—
414C2#1913492011yescharacteristic
415C2#1913501611yescharacteristic
416C2#1913509411yescharacteristic
subgroupG/H
centerC2×C4#13063297
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1806C2
socleC22×C43#386
prime radicalC2×#41×C43D4
cosocleC2×C42×C43C23
hypercenter#1806D43
hypocenterC43#9207
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
3. #19133093C2semidirect
4. #19133049C2semidirect
5. #19132490C2semidirect
6. #19132436C2semidirect
11. #14583194C4semidirect
12. #14583189C4semidirect
13. #14583184C4semidirect
14. #14583179C4semidirect
241. C43#9207semidirect

Maximal subgroups

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

subgroupindex
#191443832
#41×C43⋊C82
#191330932
#191330492
#191324902
#191324362
C43×#18062
#920743