Finite Group Databasebeta

← #24990722

Subgroups — #24990722

Order 11008.

360 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19134714C211yesmaximal, characteristic, complemented
2#19133381C211yesmaximal, characteristic, complemented
3#19133081C211yesmaximal, characteristic
4#19133008C211yesmaximal, characteristic
5#19132487C211yesmaximal, characteristic, complemented
6#19132445C211yesmaximal, characteristic, complemented
7C43×#2992C211yesmaximal, characteristic
8#14582952C2211yescharacteristic
9C2×C4⋊(C43⋊C8)C2211yescharacteristic
10C4×#10621877C2211yescharacteristic
11#14582745C2211yescharacteristic
12#14582653—21no—
13#14582653—21no—
14#14582651—21no—
15#14582649—21no—
16#14582636C411yescharacteristic
17#14582636C411yescharacteristic
18#14582633C411yescharacteristic
19#14582633C411yescharacteristic
20Q8⋊(C43⋊C8)—21no—
21D4⋊(C43⋊C8)—21no—
22C43×#529C2211yescharacteristic
23C43×#446—21no—
24C43×#435—21no—
25C43×#435—21no—
26C8×D4×C43—21no—
27C43×#433—21no—
28C43×#432C2211yescharacteristic
29C43×#424—21no—
30C2×C4⋊C8×C43C2211yescharacteristic
31C2×#10621877—21no—
32C22×C43⋊C8—21no—
33C2×C4×Dic43—21no—
34C4⋊(C43⋊C8)—21no—
35C4⋊(C43⋊C8)—21no—
36C4⋊(C43⋊C8)—21no—
37C22⋊(C43⋊C8)C2×C411yescharacteristic
38C22⋊(C43⋊C8)C2×C411yescharacteristic
39#13063236—21no—
40C4×C43⋊C8—21no—
41C4×C43⋊C8—21no—
42C43⋊#95—21no—
43C43⋊#95C2×C411yescharacteristic
44C43⋊#95C2×C411yescharacteristic
45C2×M16×C43—21no—
46C22×C8×C43—21no—
47C22×C8×C43D411yescharacteristic
48C22×C8×C43D411yescharacteristic
49#126×C43—21no—
50#125×C43Q811yescharacteristic
51#124×C43Q811yescharacteristic
52#123×C43—21no—
53C22⋊Q8×C43C2×C411yescharacteristic
54#121×C43C2×C411yescharacteristic
55C4×Q8×C43D411yescharacteristic
56C4×D4×C43—21no—
57C4×D4×C43D411yescharacteristic
58#117×C43—21no—
59C2×C42×C43C2311yescharacteristic
60C4⋊C8×C43—21no—
61C4⋊C8×C43—21no—
62C4⋊C8×C43—21no—
63C4⋊C8×C43—21no—
64C4⋊C8×C43D411yescharacteristic
65C4⋊C8×C43D411yescharacteristic
66C22⋊C8×C43—21no—
67C22⋊C8×C43—21no—
68C22⋊C8×C43—21no—
69#97×C43—21no—
70#97×C43—21no—
71C4×C8×C43—21no—
72C2×Q8×C43C4⋊C411yescharacteristic
73C2×D4×C43—21no—
74C2×D4×C43C4⋊C411yescharacteristic
75C22×C4×C43—21no—
76C22×C4×C43C22×C411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43#4111yescharacteristic
79C22×Dic43—21no—
80C22×Dic43—21no—
81M16×C43—81no—
82C2×C8×C43—21no—
83C2×C8×C43—21no—
84C2×C8×C43—21no—
85C2×C8×C43—21no—
86C2×C8×C43—41no—
87C2×C8×C43—41no—
88C2×C8×C43—81no—
89C4⋊C4×C43—21no—
90C4⋊C4×C43—21no—
91C4⋊C4×C43—21no—
92C4⋊C4×C43—21no—
93C4⋊C4×C43C4⋊C411yescharacteristic
94C4⋊C4×C43C4⋊C411yescharacteristic
95C22⋊C4×C43—21no—
96C22⋊C4×C43—21no—
97C22⋊C4×C43—21no—
98C22⋊C4×C43—21no—
99C22⋊C4×C43—21no—
100C42×C43—21no—
101C42×C43C2×D411yescharacteristic
102C42×C43C2×D411yescharacteristic
103C42×C43C2×Q811yescharacteristic
104C42×C43#4111yescharacteristic
105C4×Dic43—41no—
106C4×Dic43—41no—
107#10621877—22no—
108#10621877—41no—
109C2×C43⋊C8—21no—
110C2×C43⋊C8—21no—
111C2×C43⋊C8—41no—
112C2×C43⋊C8—42no—
113C2×C43⋊C8—41no—
114C23×C43—21no—
115C23×C43C4×D411yescharacteristic
116Q8×C43—41no—
117D4×C43—41no—
118D4×C43—41no—
119D4×C43—41no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43C2×C4⋊C411yescharacteristic
131C2×C4×C43C4×D411yescharacteristic
132C2×C4×C43#12011yescharacteristic
133C2×C4×C43C22⋊Q811yescharacteristic
134C2×C4×C43C22⋊Q811yescharacteristic
135C2×C4×C43#12311yescharacteristic
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142C8×C43—41no—
143C8×C43—41no—
144C8×C43—41no—
145C8×C43—41no—
146C43⋊C8—41no—
147C43⋊C8—41no—
148C43⋊C8—42no—
149C43⋊C8—81no—
150#8877—431nomaximal, Sylow
151C22×C43—21no—
152C22×C43—21no—
153C22×C43—41no—
154C22×C43—41no—
155C22×C43—41no—
156C22×C43#38511yescharacteristic
157C22×C43#44311yescharacteristic
158C22×C43#44411yescharacteristic
159C4×C43—21no—
160C4×C43—21no—
161C4×C43—21no—
162C4×C43—21no—
163C4×C43—21no—
164C4×C43—41no—
165C4×C43—41no—
166C4×C43—41no—
167C4×C43#45411yescharacteristic
168C4×C43#45511yescharacteristic
169Dic43—81no—
170Dic43—81no—
171#2992D4311yescharacteristic
172#1832—431no—
173#1573—431no—
174#1500—431no—
175#1483—431no—
176#1300—431no—
177#1283—431no—
178C2×C43—21no—
179C2×C43—21no—
180C2×C43—81no—
181C2×C43#186011yescharacteristic
182C2×C43#186611yescharacteristic
183C2×C43#186811yescharacteristic
184#529C2×D4311yescharacteristic
185#446—21no—
186#435—21no—
187#435—21no—
188C8×D4—21no—
189#433—21no—
190#432C2×D4311yescharacteristic
191#431—431no—
192#424—21no—
193C2×C4⋊C8—431no—
194C2×C4⋊C8C2×D4311yescharacteristic
195C4×M16—431no—
196#376—431no—
197#336—861no—
198#336—861no—
199#335—861no—
200#334—861no—
201#328—431no—
202#328—431no—
203#327—431no—
204#327—431no—
205Q8⋊C8—861no—
206D4⋊C8—861no—
207C43#887711yescharacteristic, complemented, Sylow
208C2×M16—21no—
209C2×M16—861no—
210C22×C8—21no—
211C22×C8—861no—
212C22×C8C22⋊D4311yescharacteristic
213C22×C8C22⋊D4311yescharacteristic
214#126—21no—
215#125Dic8611yescharacteristic
216#124Dic8611yescharacteristic
217#123—21no—
218C22⋊Q8C4×D4311yescharacteristic
219#121C4×D4311yescharacteristic
220C4×Q8C22⋊D4311yescharacteristic
221C4×D4—21no—
222C4×D4C22⋊D4311yescharacteristic
223#117—21no—
224C2×C42—861no—
225C2×C42C22×D4311yescharacteristic
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8—21no—
229C4⋊C8—21no—
230C4⋊C8—861no—
231C4⋊C8—861no—
232C4⋊C8—861no—
233C4⋊C8C22⋊D4311yescharacteristic
234C4⋊C8C22⋊D4311yescharacteristic
235C22⋊C8—21no—
236C22⋊C8—21no—
237C22⋊C8—21no—
238C22⋊C8—431no—
239C22⋊C8—431no—
240#97—21no—
241#97—21no—
242#97—861no—
243C4×C8—21no—
244C4×C8—861no—
245C4×C8—861no—
246#95—431no—
247#95—431no—
248#95—861no—
249C2×Q8Dic43⋊C411yescharacteristic
250C2×D4—21no—
251C2×D4Dic43⋊C411yescharacteristic
252C22×C4—21no—
253C22×C4—861no—
254C22×C4—861no—
255C22×C4C2×C4×D4311yescharacteristic
256C22×C4#1062189811yescharacteristic
257C22×C4C2×C22⋊D4311yescharacteristic
258M16—81no—
259M16—862no—
260M16—1721no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—81no—
268C2×C8—861no—
269C2×C8—861no—
270C2×C8—1722no—
271C2×C8—1721no—
272C2×C8—1721no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4Dic43⋊C411yescharacteristic
278C4⋊C4Dic43⋊C411yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C42—21no—
285C42—1721no—
286C42—1721no—
287C42C2×Dic8611yescharacteristic
288C42#1062189811yescharacteristic
289C42C2×C22⋊D4311yescharacteristic
290C42C2×C22⋊D4311yescharacteristic
291C23—21no—
292C23C4×C22⋊D4311yescharacteristic
293Q8—41no—
294D4—41no—
295D4—41no—
296D4—41no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—1721no—
308C2×C4—1721no—
309C2×C4—1721no—
310C2×C4—1721no—
311C2×C4—1721no—
312C2×C4—1721no—
313C2×C4C2×Dic43⋊C411yescharacteristic
314C2×C4C4×C22⋊D4311yescharacteristic
315C2×C4#1306329411yescharacteristic
316C2×C4#1306330411yescharacteristic
317C2×C4#1306330411yescharacteristic
318C2×C4#1306330811yescharacteristic
319C8—41no—
320C8—41no—
321C8—41no—
322C8—41no—
323C8—3441no—
324C8—1721no—
325C8—1721no—
326C8—1722no—
327C22—21no—
328C22—21no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22#1458277211yescharacteristic
333C22#1458301411yescharacteristic
334C22#1458301911yescharacteristic
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—3441no—
344C4—3441no—
345C4#1458307211yescharacteristic
346C4#1458307711yescharacteristic
347C2—21no—
348C2—21no—
349C2—81no—
350C2#1913482811yescharacteristic
351C2#1913487011yescharacteristic
352C2#1913488111yescharacteristic
subgroupG/H
centerC2×C4#13063294
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2992C2
socleC22×C43#385
prime radical#121×C43C2×C4
cosocleC2×C42×C43C23
hypercenter#2992D43
hypocenterC43#8877
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2992

Complements

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

NH ≅ G/Ntype
1. #19134714C2semidirect
2. #19133381C2semidirect
5. #19132487C2semidirect
6. #19132445C2semidirect
207. C43#8877semidirect

Maximal subgroups

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

subgroupindex
#191347142
#191333812
#191330812
#191330082
#191324872
#191324452
C43×#29922
#887743