Finite Group Databasebeta

← #25067137

Subgroups — #25067137

Order 11008.

630 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145168C211yesmaximal, characteristic
2#19143569C212yesmaximal, complemented
3#19133485C212yesmaximal, complemented
4#19133481C211yesmaximal, characteristic, complemented
5Q16×C43⋊C8C211yesmaximal, characteristic, complemented
6#19133392C212yesmaximal, complemented
7#19133389C211yesmaximal, characteristic, complemented
8#19133357C211yesmaximal, characteristic, complemented
9#19133054C212yesmaximal, complemented
10C82×D43C211yesmaximal, characteristic, complemented
11C43×#1591C211yesmaximal, characteristic, complemented
12#14583436C2212yes—
13#14583300C411yescharacteristic
14#14583284C411yescharacteristic
15#14583255C412yes—
16#14583137C411yescharacteristic
17#14583136C411yescharacteristic
18#14583131C412yes—
19Q8×C43⋊C8C2212yes—
20C4×#10621884C2212yes—
21C4×D344C2211yescharacteristic
22#14582978C2212yes—
23#14582972—22no—
24#14582964—22no—
25#14582964C2212yes—
26#14582959—22no—
27#14582955C2212yes—
28#14582856—22no—
29C4×C8×D43C2211yescharacteristic
30C4×C8×D43C2211yescharacteristic
31C4×C8×D43C2211yescharacteristic
32#14582652C2211yescharacteristic
33#14582649C2212yes—
34Q8⋊(C43⋊C8)C2212yes—
35#14582628C2212yes—
36#14582626C2212yes—
37C8×C43⋊C8C2211yescharacteristic
38C8×C43⋊C8C2211yescharacteristic
39C8×C43⋊C8C2211yescharacteristic
40C43×#446C2212yes—
41C4×Q16×C43C2211yescharacteristic
42C43×#335C2211yescharacteristic
43C43×Q8⋊C8C2212yes—
44C82×C43C2211yescharacteristic
45C2×#10621884C2×C412yes—
46C2×D344C2×C411yescharacteristic
47C2×#10621872—22no—
48C2×C8×D43—21no—
49C2×C8×D43—22no—
50C2×C8×D43C2×C411yescharacteristic
51C2×C8×D43C2×C411yescharacteristic
52C2×C8×D43D411yescharacteristic
53C2×C8×D43D411yescharacteristic
54#13063320—22no—
55#13063316C2×C412yes—
56#13063314C2×C412yes—
57#13063310—22no—
58#13063301C2×C412yes—
59#13063300C2×C412yes—
60C4×D172—22no—
61C4×D172C2312yes—
62#13063282—22no—
63C42×D43C2311yescharacteristic
64#13063259C2×C411yescharacteristic
65#13063256C2×C412yes—
66C4⋊(C43⋊C8)—22no—
67C4⋊(C43⋊C8)C2312yes—
68#13063249C2×C412yes—
69#13063247C2×C412yes—
70#13063245C2×C412yes—
71(C2×D43)⋊C8—22no—
72(C2×D43)⋊C8—22no—
73(C2×D43)⋊C8—22no—
74#13063235—22no—
75C4×C43⋊C8—22no—
76C4×C43⋊C8C2311yescharacteristic
77C4×C43⋊C8C2311yescharacteristic
78C4×C43⋊C8C2311yescharacteristic
79C8×Dic43—21no—
80C8×Dic43C2×C411yescharacteristic
81C8×Dic43C2×C411yescharacteristic
82C8×Dic43D411yescharacteristic
83C8×Dic43D411yescharacteristic
84C2×Q16×C43C2×C411yescharacteristic
85C4×Q8×C43C2312yes—
86#107×C43C2×C411yescharacteristic
87C4⋊C8×C43—22no—
88C4⋊C8×C43C2312yes—
89#103×C43C2×C412yes—
90#97×C43—22no—
91C4×C8×C43C2311yescharacteristic
92C4×C8×C43C2311yescharacteristic
93C4×C8×C43C2311yescharacteristic
94C2×Q8×C43C22×C412yes—
95C2×D172—22no—
96C2×D172C22×C412yes—
97C2×C4×D43—22no—
98C2×C4×D43C22×C411yescharacteristic
99C2×C4×D43C2×D411yescharacteristic
100C2×C4×D43#4111yescharacteristic
101Q16×C43—22no—
102C2×C8×C43—21no—
103C2×C8×C43—22no—
104C2×C8×C43C22×C411yescharacteristic
105C2×C8×C43C22×C411yescharacteristic
106C2×C8×C43C2×D411yescharacteristic
107C2×C8×C43C2×D411yescharacteristic
108C4⋊C4×C43—22no—
109C4⋊C4×C43C22×C412yes—
110C42×C43—22no—
111C42×C43C2411yescharacteristic
112#10621884—24no—
113(C2×D43)⋊C4—22no—
114(C2×D43)⋊C4—22no—
115(C2×D43)⋊C4—22no—
116(C2×D43)⋊C4—22no—
117(C2×D43)⋊C4—22no—
118C4⋊Dic43—22no—
119C4⋊Dic43C22×C412yes—
120Dic43⋊C4—22no—
121Dic43⋊C4—22no—
122C4×Dic43C22×C411yescharacteristic
123C4×Dic43C2×D411yescharacteristic
124C4×Dic43#4111yescharacteristic
125C2×C43⋊C8—21no—
126C2×C43⋊C8—22no—
127C2×C43⋊C8C22×C411yescharacteristic
128C2×C43⋊C8C22×C411yescharacteristic
129C2×C43⋊C8C2×D411yescharacteristic
130C2×C43⋊C8C2×D411yescharacteristic
131D344—22no—
132#10621872—44no—
133C8×D43—24no—
134C8×D43—22no—
135C8×D43—22no—
136C8×D43—22no—
137C8×D43—22no—
138C8×D43—44no—
139C22×D43—22no—
140C22×D43C4×D411yescharacteristic
141Q8×C43—22no—
142Q8×C43—22no—
143C2×C4×C43—22no—
144C2×C4×C43—22no—
145C2×C4×C43C23×C411yescharacteristic
146C2×C4×C43C22×D411yescharacteristic
147C2×C4×C43C2×#4111yescharacteristic
148C2×Dic43—22no—
149C2×Dic43C4×D411yescharacteristic
150C2×Dic43C4×D411yescharacteristic
151C2×Dic43C4×D411yescharacteristic
152D172—22no—
153D172—22no—
154D172—44no—
155C4×D43—22no—
156C4×D43—21no—
157C4×D43—21no—
158C4×D43—21no—
159C4×D43—21no—
160C4×D43—42no—
161C4×D43—42no—
162C8×C43—22no—
163C8×C43—21no—
164C8×C43—21no—
165C8×C43—42no—
166C8×C43#13112yes—
167C8×C43#13512yes—
168C43⋊C8—22no—
169C43⋊C8—21no—
170C43⋊C8—21no—
171C43⋊C8—42no—
172C43⋊C8#13112yes—
173C43⋊C8#13512yes—
174#17959—431nomaximal, Sylow
175C22×C43C2×C4×D411yescharacteristic
176C2×D43—21no—
177C2×D43—21no—
178C2×D43—42no—
179C2×D43—42no—
180C2×D43—42no—
181C2×D43#44312yes—
182C4×C43—21no—
183C4×C43—42no—
184C4×C43—42no—
185C4×C43C2×#13111yescharacteristic
186C4×C43C2×#13111yescharacteristic
187C4×C43C2×#13511yescharacteristic
188C4×C43C2×#13511yescharacteristic
189Dic43—21no—
190Dic43—21no—
191Dic43—21no—
192Dic43—42no—
193#3168—431no—
194#2966—432no—
195#1591D4311yescharacteristic, complemented
196#1590—432no—
197#1589—431no—
198C8×Q16—431no—
199C8×SD16—432no—
200C8×D8—431no—
201#1568—431no—
202#1494—432no—
203C2×C82—431no—
204C2×C43#293111yescharacteristic
205C2×C43C4×#13511yescharacteristic
206C2×C43C2×#44311yescharacteristic
207D43—22no—
208D43—82no—
209#529—432no—
210#499—431no—
211#495—431no—
212#488—432no—
213#467—431no—
214#466—431no—
215#465—432no—
216#446C2×D4312yes—
217C8×Q8—432no—
218C4×Q16C2×D4311yescharacteristic
219C4×SD16—432no—
220C4×D8—431no—
221#436—432no—
222#435—862no—
223C8×D4—432no—
224C8×D4—862no—
225#433—862no—
226#432—432no—
227#405—862no—
228C2×C4×C8—431no—
229C2×C4×C8—431no—
230C2×C4×C8—431no—
231#335—431no—
232#335C2×D4311yescharacteristic
233#334—432no—
234Q8⋊C8—432no—
235Q8⋊C8C2×D4312yes—
236D4⋊C8—432no—
237D4⋊C8—432no—
238C82—431no—
239C82—431no—
240C82—431no—
241C82C2×D4311yescharacteristic
242C43#1795911yescharacteristic, complemented, Sylow
243C2×Q16C4×D4311yescharacteristic
244C2×SD16—432no—
245C2×D8—431no—
246C2×M16—862no—
247C22×C8—431no—
248C22×C8—431no—
249C22×C8—431no—
250C22×C8—431no—
251C22×C8—862no—
252C22×C8—861no—
253#126—862no—
254#125—432no—
255#124—432no—
256#123—862no—
257C22⋊Q8—432no—
258#121—432no—
259C4×Q8C22×D4312yes—
260C4×D4—432no—
261C4×D4—862no—
262#117—862no—
263C2×C42—431no—
264#107—431no—
265#107C4×D4311yescharacteristic
266#106—432no—
267C4⋊C8—22no—
268C4⋊C8—432no—
269C4⋊C8—862no—
270C4⋊C8C22×D4312yes—
271#103—432no—
272#103C4×D4312yes—
273#102—432no—
274#102—432no—
275C22⋊C8—862no—
276C22⋊C8—862no—
277C22⋊C8—862no—
278#97—22no—
279#97—862no—
280C4×C8—431no—
281C4×C8—431no—
282C4×C8—431no—
283C4×C8—431no—
284C4×C8—431no—
285C4×C8—431no—
286C4×C8—431no—
287C4×C8—862no—
288C4×C8—861no—
289C4×C8C22×D4311yescharacteristic
290C4×C8C22×D4311yescharacteristic
291C4×C8C22×D4311yescharacteristic
292C2×Q8C2×C4×D4312yes—
293C2×D4—432no—
294C2×D4—862no—
295C22×C4—431no—
296C22×C4—431no—
297C22×C4—431no—
298C22×C4—862no—
299Q16—22no—
300SD16—864no—
301D8—862no—
302M16—1724no—
303C2×C8—21no—
304C2×C8—22no—
305C2×C8—431no—
306C2×C8—431no—
307C2×C8—431no—
308C2×C8—431no—
309C2×C8—862no—
310C2×C8—862no—
311C2×C8—864no—
312C2×C8—861no—
313C2×C8—862no—
314C2×C8—862no—
315C2×C8—862no—
316C2×C8—1724no—
317C2×C8C2×C4×D4311yescharacteristic
318C2×C8C2×C4×D4311yescharacteristic
319C2×C8D4×D4311yescharacteristic
320C2×C8D4×D4311yescharacteristic
321C4⋊C4—22no—
322C4⋊C4—432no—
323C4⋊C4—862no—
324C4⋊C4—862no—
325C4⋊C4—862no—
326C4⋊C4C2×C4×D4312yes—
327C22⋊C4—862no—
328C22⋊C4—862no—
329C22⋊C4—862no—
330C22⋊C4—862no—
331C22⋊C4—862no—
332C42—22no—
333C42—431no—
334C42—431no—
335C42—431no—
336C42C23×D4311yescharacteristic
337C23—431no—
338C23—862no—
339Q8—22no—
340Q8—22no—
341D4—862no—
342D4—862no—
343D4—1724no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—431no—
347C2×C4—431no—
348C2×C4—431no—
349C2×C4—862no—
350C2×C4—861no—
351C2×C4—861no—
352C2×C4—861no—
353C2×C4—861no—
354C2×C4—862no—
355C2×C4—1722no—
356C2×C4—1722no—
357C2×C4C22×C4×D4311yescharacteristic
358C2×C4C2×D4×D4311yescharacteristic
359C2×C4#41×D4311yescharacteristic
360C8—22no—
361C8—21no—
362C8—21no—
363C8—42no—
364C8—432no—
365C8—432no—
366C8—862no—
367C8—861no—
368C8—861no—
369C8—1722no—
370C8#1306333312yes—
371C8#1306334812yes—
372C22—432no—
373C22—861no—
374C22—861no—
375C22—1722no—
376C22—1722no—
377C22—1722no—
378C22C4×D4×D4311yescharacteristic
379C4—21no—
380C4—42no—
381C4—42no—
382C4—861no—
383C4—861no—
384C4—861no—
385C4—1722no—
386C4#131×D4311yescharacteristic
387C4C2×#1306333311yescharacteristic
388C4#135×D4311yescharacteristic
389C4C2×#1306334811yescharacteristic
390C2—862no—
391C2—3442no—
392C2#1914330411yescharacteristic
393C2C4×#1306334811yescharacteristic
394C2#443×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1591C2
socleC22×C43C2×C4×D4
prime radical#14583136C4
cosocleC42×C43C24
hypercenter#1591D43
hypocenterC43#17959
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1591

Complements

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

NH ≅ G/Ntype
2. #19143569C2semidirect
3. #19133485C2semidirect
4. #19133481C2semidirect
5. Q16×C43⋊C8C2semidirect
6. #19133392C2semidirect
7. #19133389C2semidirect
8. #19133357C2semidirect
9. #19133054C2semidirect
10. C82×D43C2semidirect
11. C43×#1591C2semidirect
195. #1591D43semidirect
242. C43#17959semidirect

Maximal subgroups

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

subgroupindex
#191451682
#191435692
#191334852
#191334812
Q16×C43⋊C82
#191333922
#191333892
#191333572
#191330542
C82×D432
C43×#15912
#1795943