Finite Group Databasebeta

← #25012897

Subgroups — #25012897

Order 11008.

404 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#427×D43C211yesmaximal, characteristic
2C2×(C2×D43)⋊C16C211yesmaximal, characteristic
3#19134630C211yesmaximal, characteristic
4#19132692C211yesmaximal, characteristic, complemented
5#19132691C211yesmaximal, characteristic, complemented
6#19132690C211yesmaximal, characteristic, complemented
7C43×#1382C211yesmaximal, characteristic, complemented
8C22×C8×D43C2211yescharacteristic
9#117×D43—21no—
10C22×C43⋊C16C2211yescharacteristic
11C2×#13063261C2211yescharacteristic
12#14582937C2211yescharacteristic
13#14582936C411yescharacteristic
14#14582936C411yescharacteristic
15#14582935—21no—
16#14582934—21no—
17#107×D43C411yescharacteristic
18#107×D43C411yescharacteristic
19#106×D43—21no—
20#14582862—21no—
21(C2×D43)⋊C16—21no—
22(C2×D43)⋊C16—21no—
23#14582663—21no—
24C22×C16×C43C2211yescharacteristic
25C2×#108×C43C2211yescharacteristic
26C43×#427C2211yescharacteristic
27C22×C4×D43D411yescharacteristic
28C2×#10621877—21no—
29C22×C43⋊C8D411yescharacteristic
30C2×C8×D43—21no—
31C2×C8×D43—21no—
32C2×C8×D43—21no—
33C2×C8×D43—21no—
34C2×C8×D43C2×C411yescharacteristic
35C2×C8×D43C2×C411yescharacteristic
36C2×C8×D43D411yescharacteristic
37C2×C8×D43D411yescharacteristic
38#13063284—21no—
39#13063283—21no—
40#13063283—21no—
41#13063282—41no—
42#13063281—41no—
43C4⋊C4×D43—21no—
44C4⋊C4×D43—21no—
45C22⋊C4×D43—41no—
46C42×D43—41no—
47C2×C43⋊C16—21no—
48C2×C43⋊C16—21no—
49C2×C43⋊C16—21no—
50#13063261—21no—
51#13063261—21no—
52#13063259C2×C411yescharacteristic
53#13063259C2×C411yescharacteristic
54#13063258—21no—
55#13063258—21no—
56#13063257—21no—
57#13063256—21no—
58#13063256—21no—
59(C2×D43)⋊C8—41no—
60(C2×D43)⋊C8—41no—
61C2×M16×C43—21no—
62C22×C8×C43C2311yescharacteristic
63#117×C43—21no—
64C2×C16×C43—21no—
65C2×C16×C43—21no—
66C2×C16×C43—21no—
67#108×C43—21no—
68#108×C43—21no—
69#107×C43C2×C411yescharacteristic
70#107×C43C2×C411yescharacteristic
71#106×C43—21no—
72C23×D43SD1611yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C22×Dic43SD1611yescharacteristic
75C2×C4×D43—21no—
76C2×C4×D43—21no—
77C2×C4×D43—21no—
78C2×C4×D43—21no—
79C2×C4×D43—41no—
80C2×C4×D43—41no—
81C2×C4×D43C22⋊C411yescharacteristic
82C2×C4×D43C22⋊C411yescharacteristic
83C2×C4×D43D811yescharacteristic
84C2×C4×D43D811yescharacteristic
85M16×C43—41no—
86M16×C43—41no—
87C2×C8×C43—41no—
88C2×C8×C43C22×C411yescharacteristic
89C2×C8×C43C2×D411yescharacteristic
90C2×C8×C43#4111yescharacteristic
91C2×C8×C43#4111yescharacteristic
92C2×C8×C43#4111yescharacteristic
93C2×C8×C43#4111yescharacteristic
94C4⋊C4×C43—21no—
95C4⋊C4×C43—21no—
96C22⋊C4×C43—41no—
97C42×C43—41no—
98C22⋊Dic43—41no—
99(C2×D43)⋊C4—41no—
100(C2×D43)⋊C4—41no—
101C4⋊Dic43—21no—
102C4⋊Dic43—21no—
103Dic43⋊C4—41no—
104Dic43⋊C4—41no—
105C4×Dic43—41no—
106C4×Dic43—41no—
107C4×Dic43—41no—
108#10621877—41no—
109#10621877—41no—
110C2×C43⋊C8—21no—
111C2×C43⋊C8—21no—
112C2×C43⋊C8—41no—
113C2×C43⋊C8C22⋊C411yescharacteristic
114C2×C43⋊C8C22⋊C411yescharacteristic
115C8×D43—21no—
116C8×D43—21no—
117C8×D43—21no—
118C8×D43—21no—
119C8×D43—21no—
120C8×D43—21no—
121C8×D43—21no—
122C8×D43—21no—
123C16×C43—41no—
124C43⋊C16—41no—
125C23×C43C2×SD1611yescharacteristic
126C22×D43—21no—
127C22×D43—21no—
128C22×D43—22no—
129C22×D43—41no—
130C22×D43#10211yescharacteristic
131C22×D43#10211yescharacteristic
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43C2×C22⋊C411yescharacteristic
135C2×C4×C43#12311yescharacteristic
136C2×C4×C43#12311yescharacteristic
137C2×C4×C43C2×D811yescharacteristic
138C2×C4×C43#13711yescharacteristic
139C2×C4×C43#13711yescharacteristic
140C2×Dic43—21no—
141C2×Dic43—21no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43#10211yescharacteristic
145C2×Dic43#10211yescharacteristic
146C4×D43—21no—
147C4×D43—21no—
148C4×D43—21no—
149C4×D43—21no—
150C4×D43—21no—
151C4×D43—21no—
152C4×D43—21no—
153C4×D43—21no—
154C4×D43—82no—
155C4×D43—82no—
156C8×C43—81no—
157C8×C43#11711yescharacteristic
158C8×C43#11711yescharacteristic
159C8×C43#12311yescharacteristic
160C8×C43#12311yescharacteristic
161C43⋊C8—21no—
162C43⋊C8—21no—
163C43⋊C8—81no—
164#12869—431nomaximal, Sylow
165C22×C43—21no—
166C22×C43—21no—
167C22×C43C2×#10211yescharacteristic
168C22×C43#48311yescharacteristic
169C22×C43#48311yescharacteristic
170C2×D43—21no—
171C2×D43—21no—
172C2×D43—21no—
173C2×D43—21no—
174C2×D43—21no—
175C2×D43—42no—
176C2×D43—42no—
177C2×D43#35912yes—
178C4×C43—81no—
179C4×C43—81no—
180C4×C43#38111yescharacteristic
181C4×C43#41911yescharacteristic
182C4×C43#48011yescharacteristic
183C4×C43#48011yescharacteristic
184Dic43—21no—
185Dic43—21no—
186Dic43—81no—
187Dic43—81no—
188C2×#427—431no—
189C2×C22⋊C16—431no—
190#1810—431no—
191#1382—431no—
192#1382—431no—
193#1382—431no—
194#1382D4311yescharacteristic, complemented
195C2×C43—21no—
196C2×C43—21no—
197C2×C43#182311yescharacteristic
198C2×C43C2×#35911yescharacteristic
199C2×C43#214311yescharacteristic
200D43—22no—
201D43—41no—
202C23×C8—431no—
203C2×#117—861no—
204C22×C16—431no—
205C22×C16C2×D4311yescharacteristic
206C2×#108—431no—
207C2×#108C2×D4311yescharacteristic
208#427—431no—
209#427—431no—
210#427—431no—
211#427—861no—
212#427—861no—
213#427C2×D4311yescharacteristic
214C2×#107—431no—
215C2×#107—431no—
216C2×#106—861no—
217#407—861no—
218C22⋊C16—861no—
219C22⋊C16—861no—
220#341—861no—
221C43#1286911yescharacteristic, complemented, Sylow
222C23×C4—431no—
223C2×M16—21no—
224C2×M16—861no—
225C22×C8—431no—
226C22×C8—431no—
227C22×C8—431no—
228C22×C8—431no—
229C22×C8—431no—
230C22×C8—861no—
231C22×C8—861no—
232C22×C8—861no—
233C22×C8—861no—
234C22×C8C22×D4311yescharacteristic
235#117—21no—
236#117—861no—
237#117—861no—
238#117—861no—
239#117—1721no—
240#117—1721no—
241C2×C4⋊C4—861no—
242C2×C4⋊C4—861no—
243C2×C22⋊C4—1721no—
244C2×C42—1721no—
245C2×C16—21no—
246C2×C16—21no—
247C2×C16—21no—
248C2×C16—861no—
249C2×C16—861no—
250C2×C16—861no—
251#108—21no—
252#108—21no—
253#108—861no—
254#108—861no—
255#107—431no—
256#107—431no—
257#107—861no—
258#107—861no—
259#107C4×D4311yescharacteristic
260#107C4×D4311yescharacteristic
261#106—21no—
262#106—861no—
263#106—861no—
264#106—861no—
265C22⋊C8—1721no—
266C22⋊C8—1721no—
267C24—431no—
268C22×C4—431no—
269C22×C4—431no—
270C22×C4—431no—
271C22×C4—431no—
272C22×C4—431no—
273C22×C4—861no—
274C22×C4—861no—
275C22×C4—861no—
276C22×C4—861no—
277C22×C4—1721no—
278C22×C4—1721no—
279C22×C4D4×D4311yescharacteristic
280M16—41no—
281M16—41no—
282M16—1721no—
283M16—1721no—
284C2×C8—41no—
285C2×C8—431no—
286C2×C8—431no—
287C2×C8—861no—
288C2×C8—861no—
289C2×C8—861no—
290C2×C8—861no—
291C2×C8—861no—
292C2×C8—861no—
293C2×C8—861no—
294C2×C8—861no—
295C2×C8—861no—
296C2×C8—861no—
297C2×C8—1721no—
298C2×C8C2×C4×D4311yescharacteristic
299C2×C8#1062189811yescharacteristic
300C2×C8#1062189811yescharacteristic
301C2×C8D4×D4311yescharacteristic
302C2×C8#1062190011yescharacteristic
303C2×C8#1062190211yescharacteristic
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—861no—
307C4⋊C4—861no—
308C4⋊C4—1721no—
309C4⋊C4—1721no—
310C22⋊C4—41no—
311C22⋊C4—1721no—
312C22⋊C4—1721no—
313C22⋊C4—1721no—
314C42—41no—
315C42—1721no—
316C42—1721no—
317C42—1721no—
318C16—41no—
319C16—1721no—
320C23—431no—
321C23—431no—
322C23—862no—
323C23—861no—
324C23—861no—
325C23—1721no—
326C23SD16×D4311yescharacteristic
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—431no—
330C2×C4—431no—
331C2×C4—861no—
332C2×C4—861no—
333C2×C4—861no—
334C2×C4—861no—
335C2×C4—861no—
336C2×C4—861no—
337C2×C4—861no—
338C2×C4—861no—
339C2×C4—861no—
340C2×C4—861no—
341C2×C4—3442no—
342C2×C4—3442no—
343C2×C4—1721no—
344C2×C4—1721no—
345C2×C4C22⋊C4×D4311yescharacteristic
346C2×C4#1306330711yescharacteristic
347C2×C4#1306331011yescharacteristic
348C2×C4D8×D4311yescharacteristic
349C2×C4#1306335411yescharacteristic
350C2×C4#1306335711yescharacteristic
351C8—81no—
352C8—861no—
353C8—861no—
354C8—3441no—
355C8#1306328211yescharacteristic
356C8#1306328311yescharacteristic
357C8#1306330711yescharacteristic
358C8#1306331011yescharacteristic
359C22—21no—
360C22—21no—
361C22—432no—
362C22—861no—
363C22—861no—
364C22—861no—
365C22—861no—
366C22—861no—
367C22—1722no—
368C22—1722no—
369C22#102×D4311yescharacteristic
370C22#1458322811yescharacteristic
371C22#1458323111yescharacteristic
372C4—81no—
373C4—81no—
374C4—861no—
375C4—861no—
376C4—3441no—
377C4—3441no—
378C4#1458276111yescharacteristic
379C4#1458290611yescharacteristic
380C4#1458321111yescharacteristic
381C4#1458321411yescharacteristic
382C2—21no—
383C2—21no—
384C2—862no—
385C2—1721no—
386C2#1913468011yescharacteristic
387C2#359×D4311yescharacteristic
388C2#1913632111yescharacteristic
subgroupG/H
centerC2×C4D8×D43
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC43×#1382C2
socleC22×C43C2×#102
prime radicalC23×D43SD16
cosocleC22×C8×C43C23
hypercenter#1382D43
hypocenterC43#12869
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ #1382

Complements

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

NH ≅ G/Ntype
4. #19132692C2semidirect
5. #19132691C2semidirect
6. #19132690C2semidirect
7. C43×#1382C2semidirect
194. #1382D43semidirect
221. C43#12869semidirect

Maximal subgroups

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

subgroupindex
#427×D432
C2×(C2×D43)⋊C162
#191346302
#191326922
#191326912
#191326902
C43×#13822
#1286943