Finite Group Databasebeta

← #24990902

Subgroups — #24990902

Order 11008.

392 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143261C211yesmaximal, characteristic
2#19133367C211yesmaximal, characteristic, complemented
3#19133353C211yesmaximal, characteristic, complemented
4#19132977C211yesmaximal, characteristic
5#19132498C211yesmaximal, characteristic, complemented
6#19132436C211yesmaximal, characteristic, complemented
7C43×#1806C211yesmaximal, characteristic
8#14582960—22no—
9#14582956—21no—
10#14582952—21no—
11#14582952C2211yescharacteristic
12#14582923C2211yescharacteristic
13C2×C4⋊(C43⋊C8)C2211yescharacteristic
14#14582866—21no—
15#14582855—21no—
16C2×C4×C43⋊C8C2211yescharacteristic
17#14582651—22no—
18#14582649—21no—
19#14582649—21no—
20Q8⋊(C43⋊C8)C411yescharacteristic, complemented
21Q8⋊(C43⋊C8)C411yescharacteristic, complemented
22D4⋊(C43⋊C8)C411yescharacteristic, complemented
23D4⋊(C43⋊C8)C411yescharacteristic, complemented
24C4×#41×C43C2211yescharacteristic
25C43×#423C2211yescharacteristic
26C2×#104×C43—21no—
27C4×C4⋊C4×C43C2211yescharacteristic
28C43×#339—21no—
29C2×#10621877—21no—
30C22×C43⋊C8—21no—
31C22×C43⋊C8—21no—
32C4⋊(C43⋊C8)—21no—
33C4⋊(C43⋊C8)—21no—
34C4⋊(C43⋊C8)C2×C411yescharacteristic
35C4⋊(C43⋊C8)C2×C411yescharacteristic
36C4⋊(C43⋊C8)D411yescharacteristic
37C4⋊(C43⋊C8)D411yescharacteristic
38C4⋊(C43⋊C8)D412yes—
39C22⋊(C43⋊C8)—22no—
40C22⋊(C43⋊C8)—22no—
41C22⋊(C43⋊C8)—21no—
42#13063236—22no—
43C4×C43⋊C8—22no—
44C4×C43⋊C8—21no—
45C4×C43⋊C8—21no—
46C4×C43⋊C8C2×C411yescharacteristic
47C4×C43⋊C8C2×C411yescharacteristic
48C2×#41×C43D411yescharacteristic
49C2×M16×C43—21no—
50C4×Q8×C43C2×C411yescharacteristic
51C4×Q8×C43Q811yescharacteristic
52C4×D4×C43—21no—
53C4×D4×C43—21no—
54C4×D4×C43C2×C411yescharacteristic
55C4×D4×C43Q811yescharacteristic
56#117×C43—21no—
57#117×C43D411yescharacteristic
58C2×C4⋊C4×C43—21no—
59C2×C42×C43—21no—
60C2×C42×C43—21no—
61C2×C42×C43C2311yescharacteristic
62C4⋊C8×C43—21no—
63C4⋊C8×C43—21no—
64#104×C43—42no—
65#95×C43—21no—
66#41×C43—21no—
67#41×C43—21no—
68#41×C43—21no—
69#41×C43—21no—
70C2×Q8×C43C4⋊C411yescharacteristic
71C2×D4×C43—21no—
72C2×D4×C43C4⋊C411yescharacteristic
73C22×C4×C43—21no—
74C22×C4×C43—21no—
75C22×C4×C43—21no—
76C22×C4×C43—41no—
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43#4111yescharacteristic
79C22×C4×C43#4111yescharacteristic
80M16×C43—41no—
81M16×C43—41no—
82C2×C8×C43—41no—
83C4⋊C4×C43—21no—
84C4⋊C4×C43—21no—
85C4⋊C4×C43—22no—
86C4⋊C4×C43—41no—
87C4⋊C4×C43C4⋊C411yescharacteristic
88C4⋊C4×C43C4⋊C411yescharacteristic
89C22⋊C4×C43—21no—
90C22⋊C4×C43—21no—
91C22⋊C4×C43—21no—
92C42×C43—21no—
93C42×C43—21no—
94C42×C43—21no—
95C42×C43—41no—
96C42×C43—41no—
97C42×C43C22×C411yescharacteristic
98C42×C43C2×D411yescharacteristic
99C42×C43C2×D411yescharacteristic
100C42×C43C2×Q811yescharacteristic
101#10621877—41no—
102#10621877—41no—
103C2×C43⋊C8—21no—
104C2×C43⋊C8—21no—
105C2×C43⋊C8—21no—
106C2×C43⋊C8—21no—
107C2×C43⋊C8—21no—
108C2×C43⋊C8—22no—
109C2×C43⋊C8—21no—
110C2×C43⋊C8—42no—
111C2×C43⋊C8—41no—
112C2×C43⋊C8—41no—
113C23×C43—21no—
114C23×C43#12311yescharacteristic
115Q8×C43—21no—
116Q8×C43—21no—
117D4×C43—21no—
118D4×C43—21no—
119D4×C43—41no—
120D4×C43—41no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—42no—
132C2×C4×C43—81no—
133C2×C4×C43—81no—
134C2×C4×C43—81no—
135C2×C4×C43C2×C4⋊C411yescharacteristic
136C2×C4×C43C4×D411yescharacteristic
137C2×C4×C43C4×D411yescharacteristic
138C2×C4×C43#12011yescharacteristic
139C2×C4×C43C22⋊Q811yescharacteristic
140C2×C4×C43C22⋊Q811yescharacteristic
141C2×C4×C43#13511yescharacteristic
142C2×C4×C43#13511yescharacteristic
143C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C43#13711yescharacteristic
145C8×C43—81no—
146C43⋊C8—22no—
147C43⋊C8—41no—
148C43⋊C8—41no—
149C43⋊C8—41no—
150C43⋊C8—42no—
151C43⋊C8—41no—
152C43⋊C8—41no—
153#8903—431nomaximal, Sylow
154C22×C43—21no—
155C22×C43—21no—
156C22×C43—41no—
157C22×C43—41no—
158C22×C43—41no—
159C22×C43#38511yescharacteristic
160C22×C43#48211yescharacteristic
161C22×C43#48511yescharacteristic
162C4×C43—21no—
163C4×C43—21no—
164C4×C43—21no—
165C4×C43—41no—
166C4×C43—41no—
167C4×C43—41no—
168C4×C43—82no—
169C4×C43#42711yescharacteristic
170C4×C43#42811yescharacteristic
171C4×C43#44311yescharacteristic
172C4×C43#44411yescharacteristic
173C4×C43#44911yescharacteristic
174C4×C43#45211yescharacteristic
175#2925—431no—
176#1806D4311yescharacteristic
177#1570—431no—
178#1567—431no—
179#1476—431no—
180#1303—431no—
181#1279—431no—
182C2×C43—21no—
183C2×C43—21no—
184C2×C43—81no—
185C2×C43#185411yescharacteristic
186C2×C43#186111yescharacteristic
187C2×C43#186611yescharacteristic
188C4×#41C2×D4311yescharacteristic
189#433—862no—
190#432—861no—
191#431—431no—
192#431—861no—
193#423—431no—
194#423C2×D4311yescharacteristic
195C2×C4⋊C8—431no—
196C2×#104—21no—
197#408—861no—
198#405—861no—
199C2×C4×C8—431no—
200C4×C4⋊C4C2×D4311yescharacteristic
201#339—21no—
202#335—862no—
203#334—861no—
204#334—861no—
205Q8⋊C8—431no—
206Q8⋊C8—431no—
207D4⋊C8—431no—
208D4⋊C8—431no—
209C43#890311yescharacteristic, complemented, Sylow
210C2×#41C22⋊D4311yescharacteristic
211C2×M16—21no—
212C2×M16—861no—
213C22×C8—861no—
214C22×C8—861no—
215C4×Q8Dic8611yescharacteristic
216C4×Q8C4×D4311yescharacteristic
217C4×D4—21no—
218C4×D4—21no—
219C4×D4Dic8611yescharacteristic
220C4×D4C4×D4311yescharacteristic
221#117—21no—
222#117C22⋊D4311yescharacteristic
223C2×C4⋊C4—21no—
224C2×C42—21no—
225C2×C42—21no—
226C2×C42C22×D4311yescharacteristic
227C4⋊C8—21no—
228C4⋊C8—21no—
229C4⋊C8—431no—
230C4⋊C8—431no—
231C4⋊C8—431no—
232C4⋊C8—431no—
233C4⋊C8—432no—
234C4⋊C8—861no—
235C4⋊C8—861no—
236#104—42no—
237C22⋊C8—862no—
238C22⋊C8—862no—
239C22⋊C8—861no—
240#97—862no—
241C4×C8—431no—
242C4×C8—431no—
243C4×C8—862no—
244C4×C8—861no—
245C4×C8—861no—
246#95—21no—
247#41—21no—
248#41—21no—
249#41—21no—
250#41—21no—
251C2×Q8Dic43⋊C411yescharacteristic
252C2×D4—21no—
253C2×D4Dic43⋊C411yescharacteristic
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—41no—
258C22×C4#1062190011yescharacteristic
259C22×C4#1062190011yescharacteristic
260C22×C4C2×C22⋊D4311yescharacteristic
261M16—41no—
262M16—41no—
263M16—1721no—
264M16—1721no—
265C2×C8—41no—
266C2×C8—861no—
267C2×C8—861no—
268C2×C8—861no—
269C2×C8—861no—
270C2×C8—861no—
271C2×C8—862no—
272C2×C8—861no—
273C2×C8—1722no—
274C2×C8—1721no—
275C2×C8—1721no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—22no—
279C4⋊C4—41no—
280C4⋊C4Dic43⋊C411yescharacteristic
281C4⋊C4Dic43⋊C411yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C42—21no—
286C42—21no—
287C42—21no—
288C42—41no—
289C42—41no—
290C42C2×Dic8611yescharacteristic
291C42C2×C4×D4311yescharacteristic
292C42D4×D4311yescharacteristic
293C42D4×D4311yescharacteristic
294C23—21no—
295C23#1306330611yescharacteristic
296Q8—21no—
297Q8—21no—
298D4—21no—
299D4—21no—
300D4—41no—
301D4—41no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4C2×Dic43⋊C411yescharacteristic
317C2×C4(C22⋊D43)⋊C411yescharacteristic
318C2×C4(C22⋊D43)⋊C411yescharacteristic
319C2×C4#1306329311yescharacteristic
320C2×C4#1306330211yescharacteristic
321C2×C4#1306330211yescharacteristic
322C2×C4#1306334511yescharacteristic
323C2×C4#1306334511yescharacteristic
324C2×C4#1306335111yescharacteristic
325C2×C4#1306335611yescharacteristic
326C8—81no—
327C8—862no—
328C8—1721no—
329C8—1722no—
330C8—1721no—
331C8—1721no—
332C8—1721no—
333C8—1721no—
334C22—21no—
335C22—21no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22#1458277111yescharacteristic
340C22#1458322011yescharacteristic
341C22#1458323711yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—82no—
349C4#1458293511yescharacteristic
350C4#1458293911yescharacteristic
351C4#1458301311yescharacteristic
352C4#1458301811yescharacteristic
353C4#1458304211yescharacteristic
354C4#1458305911yescharacteristic
355C2—21no—
356C2—21no—
357C2—81no—
358C2#1913479211yescharacteristic
359C2#1913483311yescharacteristic
360C2#1913486811yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1806C2
socleC22×C43#385
prime radicalC2×#41×C43D4
cosocleC2×C42×C43C23
hypercenter#1806D43
hypocenterC43#8903
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
2. #19133367C2semidirect
3. #19133353C2semidirect
5. #19132498C2semidirect
6. #19132436C2semidirect
20. Q8⋊(C43⋊C8)C4semidirect
21. Q8⋊(C43⋊C8)C4semidirect
22. D4⋊(C43⋊C8)C4semidirect
23. D4⋊(C43⋊C8)C4semidirect
209. C43#8903semidirect

Maximal subgroups

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

subgroupindex
#191432612
#191333672
#191333532
#191329772
#191324982
#191324362
C43×#18062
#890343