Finite Group Databasebeta

← #24987667

Subgroups — #24987667

Order 11008.

482 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143307C211yesmaximal, characteristic
2#19134460C211yesmaximal, characteristic, complemented
3#19133090C211yesmaximal, characteristic
4#19132879C211yesmaximal, characteristic, complemented
5#19132497C211yesmaximal, characteristic, complemented
6#19132492C211yesmaximal, characteristic, complemented
7C43×#1540C211yesmaximal, characteristic
8C2×#13063332—21no—
9#14582977—21no—
10#14582977C412yescomplemented
11D4×C43⋊C8—21no—
12D4×C43⋊C8C412yescomplemented
13#14582952C2211yescharacteristic
14#14582923C2211yescharacteristic
15#14582866—21no—
16C2×C4×C43⋊C8C2211yescharacteristic
17C2×C8×Dic43—21no—
18C4×C4⋊Dic43C2211yescharacteristic
19#14582653—21no—
20#14582633C414yes—
21#14582621—21no—
22C8×C43⋊C8—21no—
23C43×#532C2211yescharacteristic
24C43×#431C2211yescharacteristic
25C2×C4⋊C8×C43C2211yescharacteristic
26C43×#332C412yescomplemented
27C43×#331C412yescomplemented
28#13063332—42no—
29#13063332—42no—
30C2×#10621877—21no—
31C2×#10621877—22no—
32C22×C43⋊C8—22no—
33C22×C43⋊C8D411yescharacteristic
34C22×C43⋊C8D411yescharacteristic
35C2×C4⋊Dic43—21no—
36C2×C4×Dic43—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)C2×C412yes—
43C4×C43⋊C8—21no—
44C4×C43⋊C8C2×C411yescharacteristic
45C4×C43⋊C8C2×C411yescharacteristic
46C4×C43⋊C8D411yescharacteristic
47C4×C43⋊C8D411yescharacteristic
48C8×Dic43—42no—
49C43⋊#95C2×C412yes—
50C2×#41×C43—21no—
51C22×C8×C43—21no—
52C4⋊Q8×C43C2×C411yescharacteristic
53#127×C43C2×C411yescharacteristic
54#124×C43—21no—
55#121×C43—21no—
56#121×C43C2×C412yes—
57C4×D4×C43—21no—
58C4×D4×C43C2×C412yes—
59C2×C42×C43C2311yescharacteristic
60C4⋊C8×C43—21no—
61C4⋊C8×C43C2×C412yes—
62C4⋊C8×C43C2×C412yes—
63C22⋊C8×C43—21no—
64C4×C8×C43—21no—
65#41×C43—41no—
66#41×C43—41no—
67#41×C43—41no—
68#41×C43—41no—
69C2×Q8×C43—21no—
70C2×D4×C43—21no—
71C2×D4×C43—21no—
72C2×D4×C43—22no—
73C2×D4×C43C4212yes—
74C22×C4×C43—22no—
75C22×C4×C43C22×C411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43#4111yescharacteristic
78C22×Dic43—22no—
79C2×C8×C43—22no—
80C2×C8×C43—22no—
81C2×C8×C43—41no—
82C2×C8×C43—41no—
83C4⋊C4×C43—21no—
84C4⋊C4×C43C4212yes—
85C22⋊C4×C43—22no—
86C22⋊C4×C43—22no—
87C42×C43C22×C411yescharacteristic
88C42×C43C22×C411yescharacteristic
89C42×C43C2×D411yescharacteristic
90C42×C43#4111yescharacteristic
91C4⋊Dic43—24no—
92C4×Dic43—41no—
93C4×Dic43—41no—
94#10621877—41no—
95#10621877—41no—
96#10621877—44no—
97C2×C43⋊C8—21no—
98C2×C43⋊C8—21no—
99C2×C43⋊C8—22no—
100C2×C43⋊C8—22no—
101C2×C43⋊C8—44no—
102C2×C43⋊C8C22⋊C411yescharacteristic
103C2×C43⋊C8C22⋊C411yescharacteristic
104C2×C43⋊C8C22⋊C411yescharacteristic
105C2×C43⋊C8C22⋊C411yescharacteristic
106C2×C43⋊C8D812yes—
107C2×C43⋊C8SD1612yes—
108C23×C43—22no—
109C23×C43C4×D411yescharacteristic
110Q8×C43—41no—
111Q8×C43—41no—
112D4×C43—42no—
113D4×C43—42no—
114D4×C43—42no—
115D4×C43—41no—
116D4×C43—41no—
117D4×C43—42no—
118C2×C4×C43—22no—
119C2×C4×C43—22no—
120C2×C4×C43—41no—
121C2×C4×C43—42no—
122C2×C4×C43—42no—
123C2×C4×C43C2×C4211yescharacteristic
124C2×C4×C43C2×C22⋊C411yescharacteristic
125C2×C4×C43#11711yescharacteristic
126C2×C4×C43C4×D411yescharacteristic
127C2×C4×C43C4×D411yescharacteristic
128C2×C4×C43C4×D411yescharacteristic
129C2×C4×C43C2×D811yescharacteristic
130C2×C4×C43C2×SD1611yescharacteristic
131C2×C4×C43#13511yescharacteristic
132C2×C4×C43#13511yescharacteristic
133C2×Dic43—24no—
134C2×Dic43—42no—
135C2×Dic43—42no—
136C8×C43—42no—
137C8×C43—42no—
138C43⋊C8—21no—
139C43⋊C8—21no—
140C43⋊C8—42no—
141C43⋊C8—42no—
142C43⋊C8#10212yes—
143C43⋊C8#10212yes—
144#8251—431nomaximal, Sylow
145C22×C43—21no—
146C22×C43—21no—
147C22×C43—42no—
148C22×C43—42no—
149C22×C43—42no—
150C22×C43C4×C22⋊C411yescharacteristic
151C22×C43C4×D811yescharacteristic
152C22×C43C4×SD1611yescharacteristic
153C4×C43—21no—
154C4×C43—21no—
155C4×C43—21no—
156C4×C43—42no—
157C4×C43C2×#10211yescharacteristic
158C4×C43#41611yescharacteristic
159C4×C43C4×D811yescharacteristic
160C4×C43C4×SD1611yescharacteristic
161C4×C43#44312yes—
162Dic43—44no—
163#2931—431no—
164C8×C4⋊C4—431no—
165#1540D4311yescharacteristic
166#1502—431no—
167#1450—431no—
168#1303—431no—
169#1301—431no—
170C2×C43—21no—
171C2×C43—21no—
172C2×C43—82no—
173C2×C43#175711yescharacteristic
174C2×C43C4×#10211yescharacteristic
175C2×C43#176411yescharacteristic
176C2×#131—861no—
177#532C2×D4311yescharacteristic
178#436—432no—
179#436—861no—
180C8×D4—432no—
181C8×D4—861no—
182#431—431no—
183#431C2×D4311yescharacteristic
184#423—431no—
185C2×C4⋊C8C2×D4311yescharacteristic
186#408—861no—
187C2×C4×C8—431no—
188C2×C4×C8—861no—
189C4×C4⋊C4—431no—
190#336—861no—
191#332Dic4312yescomplemented
192#331Dic4312yescomplemented
193#327—434no—
194#322—861no—
195C82—861no—
196C43#825111yescharacteristic, complemented, Sylow
197C2×#41—21no—
198#131—1722no—
199#131—1722no—
200C2×M16—862no—
201C2×M16—861no—
202C22×C8—21no—
203C22×C8—431no—
204C22×C8—431no—
205C22×C8—862no—
206C4⋊Q8C2×Dic4311yescharacteristic
207#127C2×Dic4311yescharacteristic
208#124—21no—
209#121—21no—
210#121C4×D4312yes—
211C4×D4—21no—
212C4×D4C4×D4312yes—
213C2×C4⋊C4—861no—
214C2×C42—861no—
215C2×C42C22×D4311yescharacteristic
216C4⋊C8—21no—
217C4⋊C8—432no—
218C4⋊C8—861no—
219C4⋊C8—861no—
220C4⋊C8C2×Dic4312yes—
221C4⋊C8C2×Dic4312yes—
222C22⋊C8—21no—
223C22⋊C8—432no—
224C22⋊C8—862no—
225C22⋊C8—862no—
226C4×C8—21no—
227C4×C8—431no—
228C4×C8—431no—
229C4×C8—431no—
230C4×C8—431no—
231C4×C8—861no—
232C4×C8—1722no—
233#95—432no—
234#41—41no—
235#41—41no—
236#41—41no—
237#41—41no—
238C2×Q8—21no—
239C2×D4—22no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4C4×Dic4312yes—
243C22×C4—22no—
244C22×C4—862no—
245C22×C4C2×C4×D4311yescharacteristic
246C22×C4D4×D4311yescharacteristic
247C22×C4#1062190011yescharacteristic
248M16—1724no—
249M16—1721no—
250M16—1721no—
251C2×C8—22no—
252C2×C8—22no—
253C2×C8—41no—
254C2×C8—41no—
255C2×C8—431no—
256C2×C8—431no—
257C2×C8—432no—
258C2×C8—432no—
259C2×C8—431no—
260C2×C8—431no—
261C2×C8—861no—
262C2×C8—861no—
263C2×C8—862no—
264C2×C8—862no—
265C2×C8—1724no—
266C4⋊C4—21no—
267C4⋊C4—864no—
268C4⋊C4C4×Dic4312yes—
269C22⋊C4—22no—
270C22⋊C4—22no—
271C42—1721no—
272C42—1721no—
273C42C2×C4×D4311yescharacteristic
274C42D4×D4311yescharacteristic
275C42#1062190011yescharacteristic
276C42C22×Dic4311yescharacteristic
277C23—22no—
278C23(C22⋊D43)⋊C411yescharacteristic
279Q8—41no—
280Q8—41no—
281D4—42no—
282D4—42no—
283D4—42no—
284D4—41no—
285D4—41no—
286D4—42no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—864no—
293C2×C4—1722no—
294C2×C4—1722no—
295C2×C4C2×C4×Dic4311yescharacteristic
296C2×C4C22⋊C4×D4311yescharacteristic
297C2×C4#1306328111yescharacteristic
298C2×C4(C22⋊D43)⋊C411yescharacteristic
299C2×C4D4×Dic4311yescharacteristic
300C2×C4D4×Dic4311yescharacteristic
301C2×C4D8×D4311yescharacteristic
302C2×C4SD16×D4311yescharacteristic
303C2×C4#1306334411yescharacteristic
304C2×C4#1306334611yescharacteristic
305C8—42no—
306C8—42no—
307C8—432no—
308C8—432no—
309C8—861no—
310C8—861no—
311C8—1722no—
312C8—1722no—
313C22—21no—
314C22—21no—
315C22—42no—
316C22—42no—
317C22—42no—
318C22C22⋊C4×Dic4311yescharacteristic
319C22#1458297911yescharacteristic
320C22#1458299011yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—42no—
325C4—1724no—
326C4#102×D4311yescharacteristic
327C4#1458289211yescharacteristic
328C4D8×Dic4311yescharacteristic
329C4SD16×Dic4311yescharacteristic
330C4#1458301612yes—
331C2—21no—
332C2—21no—
333C2—82no—
334C2#1913439811yescharacteristic
335C2#102×Dic4311yescharacteristic
336C2#1913443511yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D43
commutatorC2×C4×C43C2×C42
FrattiniC2×C42C22×D43
FittingC43×#1540C2
socleC22×C43C4×C22⋊C4
prime radicalC43×#532C22
cosocleC2×C42×C43C23
hypercenter#1540D43
hypocenterC43#8251
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1540

Complements

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

NH ≅ G/Ntype
2. #19134460C2semidirect
4. #19132879C2semidirect
5. #19132497C2semidirect
6. #19132492C2semidirect
10. #14582977C4semidirect
12. D4×C43⋊C8C4semidirect
26. C43×#332C4semidirect
27. C43×#331C4semidirect
191. #332Dic43semidirect
192. #331Dic43semidirect
196. C43#8251semidirect

Maximal subgroups

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

subgroupindex
#191433072
#191344602
#191330902
#191328792
#191324972
#191324922
C43×#15402
#825143