Finite Group Databasebeta

← #24989749

Subgroups — #24989749

Order 11008.

434 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582977C211yesmaximal, characteristic
2#19134732C211yesmaximal, characteristic, complemented
3#19133341C211yesmaximal, characteristic, complemented
4#19133020C211yesmaximal, characteristic
5#19132491C211yesmaximal, characteristic, complemented
6#19132490C211yesmaximal, characteristic, complemented
7C43×#1486C211yesmaximal, characteristic
8C22×#10621877—21no—
9#14582977—21no—
10#14582977—21no—
11#14582977C412yes—
12#14582977C412yes—
13#14582952C2211yescharacteristic
14#14582923C2211yescharacteristic
15C2×C4⋊(C43⋊C8)C2211yescharacteristic
16C2×C22⋊(C43⋊C8)—21no—
17C2×C4×C43⋊C8C2211yescharacteristic
18#14582663—21no—
19#14582663—21no—
20#14582651—21no—
21#14582649—21no—
22D4⋊(C43⋊C8)—22no—
23C2×C4×D4×C43C2211yescharacteristic
24C43×#431C2211yescharacteristic
25C43×#423C2211yescharacteristic
26C43×D4⋊C8—22no—
27C2×#10621877—22no—
28C2×#10621877—22no—
29C2×#10621877—21no—
30C2×#10621877—42no—
31C2×#10621877—42no—
32C22×C43⋊C8—21no—
33C22×C43⋊C8D411yescharacteristic
34C22×C43⋊C8D411yescharacteristic
35C4⋊(C43⋊C8)—21no—
36C4⋊(C43⋊C8)—21no—
37C4⋊(C43⋊C8)—21no—
38C4⋊(C43⋊C8)—21no—
39C4⋊(C43⋊C8)C2×C412yes—
40C22⋊(C43⋊C8)—22no—
41C22⋊(C43⋊C8)—22no—
42C22⋊(C43⋊C8)—21no—
43C4×C43⋊C8—21no—
44C4×C43⋊C8C2×C411yescharacteristic
45C4×C43⋊C8C2×C411yescharacteristic
46C4×C43⋊C8D411yescharacteristic
47C4×C43⋊C8D411yescharacteristic
48C22×D4×C43Q811yescharacteristic
49C23×C4×C43—21no—
50C2×M16×C43—21no—
51C4×D4×C43—21no—
52C4×D4×C43—21no—
53C4×D4×C43C2×C412yes—
54C4×D4×C43D412yes—
55C2×C4⋊C4×C43Q811yescharacteristic
56C2×C22⋊C4×C43—21no—
57C2×C42×C43C2311yescharacteristic
58C4⋊C8×C43—21no—
59C4⋊C8×C43—21no—
60C4⋊C8×C43—21no—
61C22⋊C8×C43—21no—
62C4×C8×C43—21no—
63C24×C43—21no—
64C2×D4×C43—21no—
65C2×D4×C43—42no—
66C2×D4×C43C4⋊C412yes—
67C22×C4×C43—22no—
68C22×C4×C43—22no—
69C22×C4×C43—21no—
70C22×C4×C43—41no—
71C22×C4×C43—41no—
72C22×C4×C43—41no—
73C22×C4×C43—41no—
74C22×C4×C43C2×D411yescharacteristic
75C22×C4×C43C2×Q811yescharacteristic
76C22×C4×C43#4111yescharacteristic
77M16×C43—41no—
78M16×C43—41no—
79C2×C8×C43—41no—
80C2×C8×C43—41no—
81C4⋊C4×C43—21no—
82C4⋊C4×C43C4⋊C412yes—
83C22⋊C4×C43—22no—
84C22⋊C4×C43—22no—
85C42×C43C22×C411yescharacteristic
86C42×C43C2×D411yescharacteristic
87C42×C43C2×D411yescharacteristic
88C42×C43#4111yescharacteristic
89#10621877—44no—
90#10621877—44no—
91#10621877—41no—
92#10621877—41no—
93C2×C43⋊C8—21no—
94C2×C43⋊C8—21no—
95C2×C43⋊C8—21no—
96C2×C43⋊C8—21no—
97C2×C43⋊C8—22no—
98C2×C43⋊C8—41no—
99C2×C43⋊C8—41no—
100C2×C43⋊C8—41no—
101C2×C43⋊C8—41no—
102C2×C43⋊C8C22⋊C411yescharacteristic
103C2×C43⋊C8C22⋊C411yescharacteristic
104C2×C43⋊C8C22⋊C411yescharacteristic
105C2×C43⋊C8C22⋊C411yescharacteristic
106C23×C43—22no—
107C23×C43—42no—
108C23×C43—42no—
109C23×C43—41no—
110C23×C43—41no—
111C23×C43C22⋊Q811yescharacteristic
112D4×C43—24no—
113D4×C43—42no—
114C2×C4×C43—22no—
115C2×C4×C43—22no—
116C2×C4×C43—41no—
117C2×C4×C43—41no—
118C2×C4×C43—41no—
119C2×C4×C43—42no—
120C2×C4×C43—42no—
121C2×C4×C43—42no—
122C2×C4×C43—42no—
123C2×C4×C43C2×C22⋊C411yescharacteristic
124C2×C4×C43C2×C4⋊C411yescharacteristic
125C2×C4×C43#11711yescharacteristic
126C2×C4×C43#12111yescharacteristic
127C2×C4×C43#12111yescharacteristic
128C2×C4×C43C22⋊Q811yescharacteristic
129C2×C4×C43#13511yescharacteristic
130C2×C4×C43#13511yescharacteristic
131C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
133C8×C43—81no—
134C8×C43—81no—
135C43⋊C8—21no—
136C43⋊C8—21no—
137C43⋊C8—21no—
138C43⋊C8—21no—
139C43⋊C8—42no—
140C43⋊C8—81no—
141C43⋊C8—81no—
142#8664—431nomaximal, Sylow
143C22×C43—21no—
144C22×C43—21no—
145C22×C43—42no—
146C22×C43—42no—
147C22×C43—42no—
148C22×C43—82no—
149C22×C43—82no—
150C22×C43#38011yescharacteristic
151C22×C43#47811yescharacteristic
152C22×C43#47811yescharacteristic
153C4×C43—21no—
154C4×C43—21no—
155C4×C43—21no—
156C4×C43—42no—
157C4×C43#41611yescharacteristic
158C4×C43#41811yescharacteristic
159C4×C43#43012yes—
160C4×C43#46311yescharacteristic
161C4×C43#46311yescharacteristic
162C2×#436—431no—
163#1837—431no—
164#1564—431no—
165#1486—431no—
166#1486D4311yescharacteristic
167#1301—431no—
168#1301—431no—
169C2×C43—21no—
170C2×C43—21no—
171C2×C43—82no—
172C2×C43#180411yescharacteristic
173C2×C43#181111yescharacteristic
174C2×C43#181411yescharacteristic
175C22×M16—861no—
176C2×C4×D4C2×D4311yescharacteristic
177#436—432no—
178#436—432no—
179#436—861no—
180#436—861no—
181#431—431no—
182#431C2×D4311yescharacteristic
183#423—431no—
184#423C2×D4311yescharacteristic
185C2×C4⋊C8—431no—
186C2×C22⋊C8—861no—
187C2×C4×C8—431no—
188#341—861no—
189#341—861no—
190#335—861no—
191#334—861no—
192D4⋊C8—22no—
193D4⋊C8—862no—
194C43#866411yescharacteristic, complemented, Sylow
195C22×D4Dic8611yescharacteristic
196C23×C4—21no—
197C2×M16—21no—
198C2×M16—862no—
199C2×M16—862no—
200C2×M16—861no—
201C2×M16—1722no—
202C2×M16—1722no—
203C22×C8—431no—
204C22×C8—431no—
205C22×C8—861no—
206C4×D4—21no—
207C4×D4—21no—
208C4×D4C4×D4312yes—
209C4×D4C22⋊D4312yes—
210C2×C4⋊C4Dic8611yescharacteristic
211C2×C22⋊C4—21no—
212C2×C42C22×D4311yescharacteristic
213C4⋊C8—21no—
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—432no—
217C4⋊C8—861no—
218C4⋊C8—861no—
219C4⋊C8—861no—
220C4⋊C8—861no—
221C22⋊C8—21no—
222C22⋊C8—862no—
223C22⋊C8—862no—
224C22⋊C8—861no—
225C4×C8—21no—
226C4×C8—431no—
227C4×C8—431no—
228C4×C8—431no—
229C4×C8—431no—
230C4×C8—861no—
231C24—21no—
232C2×D4—21no—
233C2×D4—42no—
234C2×D4Dic43⋊C412yes—
235C22×C4—21no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4C2×Dic8611yescharacteristic
243C22×C4D4×D4311yescharacteristic
244C22×C4#1062190011yescharacteristic
245M16—41no—
246M16—41no—
247M16—1724no—
248M16—1724no—
249M16—1721no—
250M16—1721no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—431no—
254C2×C8—431no—
255C2×C8—431no—
256C2×C8—431no—
257C2×C8—861no—
258C2×C8—861no—
259C2×C8—861no—
260C2×C8—861no—
261C2×C8—862no—
262C2×C8—1721no—
263C2×C8—1721no—
264C2×C8—1721no—
265C2×C8—1721no—
266C4⋊C4—21no—
267C4⋊C4Dic43⋊C412yes—
268C22⋊C4—22no—
269C22⋊C4—22no—
270C42C2×C4×D4311yescharacteristic
271C42D4×D4311yescharacteristic
272C42#1062190011yescharacteristic
273C42C2×C22⋊D4311yescharacteristic
274C23—22no—
275C23—42no—
276C23—42no—
277C23—41no—
278C23—41no—
279C23#1306330211yescharacteristic
280D4—24no—
281D4—42no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4C22⋊C4×D4311yescharacteristic
292C2×C4C2×Dic43⋊C411yescharacteristic
293C2×C4#1306328111yescharacteristic
294C2×C4#1306329711yescharacteristic
295C2×C4#1306329711yescharacteristic
296C2×C4#1306330211yescharacteristic
297C2×C4#1306334411yescharacteristic
298C2×C4#1306334611yescharacteristic
299C2×C4#1306334911yescharacteristic
300C2×C4#1306335211yescharacteristic
301C8—81no—
302C8—81no—
303C8—861no—
304C8—861no—
305C8—861no—
306C8—861no—
307C8—3441no—
308C8—3441no—
309C8—1722no—
310C22—21no—
311C22—21no—
312C22—42no—
313C22—42no—
314C22—42no—
315C22—82no—
316C22—82no—
317C22#1458275711yescharacteristic
318C22#1458319711yescharacteristic
319C22#1458320111yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—42no—
324C4#1458289211yescharacteristic
325C4#1458290211yescharacteristic
326C4#1458294712yes—
327C4#1458311211yescharacteristic
328C4#1458311611yescharacteristic
329C2—21no—
330C2—21no—
331C2—82no—
332C2#1913460311yescharacteristic
333C2#1913463511yescharacteristic
334C2#1913464711yescharacteristic
subgroupG/H
centerC2×C4#13063297
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1486C2
socleC22×C43#380
prime radicalC22×D4×C43Q8
cosocleC2×C42×C43C23
hypercenter#1486D43
hypocenterC43#8664
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1486

Complements

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

NH ≅ G/Ntype
2. #19134732C2semidirect
3. #19133341C2semidirect
5. #19132491C2semidirect
6. #19132490C2semidirect
194. C43#8664semidirect

Maximal subgroups

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

subgroupindex
C2×#145829772
#191347322
#191333412
#191330202
#191324912
#191324902
C43×#14862
#866443