Finite Group Databasebeta

← #25067131

Subgroups — #25067131

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#19145163C211yesmaximal, characteristic
2#19143567C212yesmaximal, complemented
3#19133491C211yesmaximal, characteristic, complemented
4#19133488C212yesmaximal, complemented
5#19133480C211yesmaximal, characteristic, complemented
6C8×Dic172C211yesmaximal, characteristic, complemented
7C8×#10621883C212yesmaximal, complemented
8#19133357C211yesmaximal, characteristic, complemented
9#19133052C212yesmaximal, complemented
10C82×D43C211yesmaximal, characteristic, complemented
11C8×D8×C43C211yesmaximal, characteristic, complemented
12#14583431C2212yes—
13#14583300C411yescharacteristic
14#14583282C411yescharacteristic
15#14583252C412yes—
16#14583141C411yescharacteristic
17#14583132C411yescharacteristic
18#14583127C412yes—
19#14583026C2212yes—
20C8×Dic86C2212yes—
21C4×Dic172C2211yescharacteristic
22C4×#10621883C2212yes—
23#14582977C2212yes—
24#14582973—22no—
25C8×C22⋊D43—22no—
26#14582957—22no—
27#14582955C2212yes—
28#14582854—22no—
29C4×C8×D43C2211yescharacteristic
30C4×C8×D43C2211yescharacteristic
31C4×C8×D43C2211yescharacteristic
32#14582652C2211yescharacteristic
33#14582649C2212yes—
34#14582631C2212yes—
35#14582629C2212yes—
36D4⋊(C43⋊C8)C2212yes—
37C8×C43⋊C8C2211yescharacteristic
38C8×C43⋊C8C2211yescharacteristic
39C8×C43⋊C8C2211yescharacteristic
40C4×D8×C43C2211yescharacteristic
41C8×D4×C43C2212yes—
42C43×#335C2211yescharacteristic
43C43×D4⋊C8C2212yes—
44C82×C43C2211yescharacteristic
45C2×Dic172C2×C411yescharacteristic
46C2×#10621883C2×C412yes—
47C2×#10621877—22no—
48C2×C8×D43—21no—
49C2×C8×D43C2×C411yescharacteristic
50C2×C8×D43C2×C411yescharacteristic
51C2×C8×D43D411yescharacteristic
52C2×C8×D43D411yescharacteristic
53#13063318—22no—
54#13063316C2×C412yes—
55#13063312C2×C412yes—
56#13063307—22no—
57#13063305C2×C412yes—
58#13063296C2×C412yes—
59C4×Dic86C2312yes—
60C4×C22⋊D43—22no—
61#13063284—22no—
62C42×D43C2311yescharacteristic
63#13063259C2×C411yescharacteristic
64#13063256C2×C412yes—
65C4⋊(C43⋊C8)C2312yes—
66Dic43⋊C8—22no—
67Dic43⋊C8—22no—
68#13063250C2×C412yes—
69#13063248C2×C412yes—
70#13063246C2×C412yes—
71C22⋊(C43⋊C8)—22no—
72(C2×D43)⋊C8—22no—
73#13063235—22no—
74#13063235—22no—
75C4×C43⋊C8C2311yescharacteristic
76C4×C43⋊C8C2311yescharacteristic
77C4×C43⋊C8C2311yescharacteristic
78C8×Dic43—22no—
79C8×Dic43—21no—
80C8×Dic43C2×C411yescharacteristic
81C8×Dic43C2×C411yescharacteristic
82C8×Dic43D411yescharacteristic
83C8×Dic43D411yescharacteristic
84C2×D8×C43C2×C411yescharacteristic
85C22×C8×C43—22no—
86C4×D4×C43C2312yes—
87#107×C43C2×C411yescharacteristic
88C4⋊C8×C43C2312yes—
89#102×C43C2×C412yes—
90C22⋊C8×C43—22no—
91C4×C8×C43C2311yescharacteristic
92C4×C8×C43C2311yescharacteristic
93C4×C8×C43C2311yescharacteristic
94C2×D4×C43C22×C412yes—
95C22×C4×C43—22no—
96C2×C22⋊D43—22no—
97C2×C4×D43C22×C411yescharacteristic
98C2×C4×D43C2×D411yescharacteristic
99C2×C4×D43#4111yescharacteristic
100C2×Dic86C22×C412yes—
101D8×C43—22no—
102C2×C8×C43—21no—
103C2×C8×C43—22no—
104C2×C8×C43—44no—
105C2×C8×C43C22×C411yescharacteristic
106C2×C8×C43C22×C411yescharacteristic
107C2×C8×C43C2×D411yescharacteristic
108C2×C8×C43C2×D411yescharacteristic
109C4⋊C4×C43C22×C412yes—
110C22⋊C4×C43—22no—
111C42×C43C2411yescharacteristic
112C22⋊Dic43—22no—
113C22⋊Dic43—22no—
114C22⋊Dic43—22no—
115#10621883—24no—
116(C2×D43)⋊C4—22no—
117C4⋊Dic43—22no—
118C4⋊Dic43—22no—
119C4⋊Dic43C22×C412yes—
120Dic43⋊C4—22no—
121Dic43⋊C4—22no—
122C4×Dic43—22no—
123C4×Dic43C22×C411yescharacteristic
124C4×Dic43C2×D411yescharacteristic
125C4×Dic43#4111yescharacteristic
126#10621877—44no—
127C2×C43⋊C8—21no—
128C2×C43⋊C8—22no—
129C2×C43⋊C8C22×C411yescharacteristic
130C2×C43⋊C8C22×C411yescharacteristic
131C2×C43⋊C8C2×D411yescharacteristic
132C2×C43⋊C8C2×D411yescharacteristic
133Dic172—22no—
134C8×D43—24no—
135C8×D43—22no—
136C8×D43—22no—
137C8×D43—22no—
138C8×D43—22no—
139C23×C43—22no—
140C22×D43C4×D411yescharacteristic
141D4×C43—22no—
142D4×C43—22no—
143C2×C4×C43—22no—
144C2×C4×C43—42no—
145C2×C4×C43—42no—
146C2×C4×C43C23×C411yescharacteristic
147C2×C4×C43C22×D411yescharacteristic
148C2×C4×C43C2×#4111yescharacteristic
149C22⋊D43—44no—
150C2×Dic43—22no—
151C2×Dic43—22no—
152C2×Dic43C4×D411yescharacteristic
153C2×Dic43C4×D411yescharacteristic
154C2×Dic43C4×D411yescharacteristic
155C4×D43—22no—
156C4×D43—21no—
157C4×D43—21no—
158C4×D43—21no—
159C4×D43—21no—
160Dic86—22no—
161Dic86—22no—
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×C43—42no—
176C22×C43—42no—
177C22×C43—42no—
178C22×C43C2×C4×D411yescharacteristic
179C2×D43—21no—
180C2×D43—21no—
181C2×D43#44312yes—
182C4×C43—21no—
183C4×C43—42no—
184C4×C43C2×#13111yescharacteristic
185C4×C43C2×#13111yescharacteristic
186C4×C43C2×#13511yescharacteristic
187C4×C43C2×#13511yescharacteristic
188Dic43—21no—
189Dic43—21no—
190Dic43—21no—
191Dic43—42no—
192Dic43—42no—
193#3168—431no—
194#2966—432no—
195#1591—431no—
196#1590—432no—
197#1589—431no—
198C8×Q16—431no—
199C8×SD16—432no—
200C8×D8D4311yescharacteristic, complemented
201#1568—431no—
202#1494—432no—
203C2×C82—431no—
204C2×C43—82no—
205C2×C43#293111yescharacteristic
206C2×C43C4×#13511yescharacteristic
207C2×C43C2×#44311yescharacteristic
208D43—22no—
209#529—432no—
210#499—431no—
211#495—431no—
212#488—432no—
213#467—431no—
214#466—431no—
215#465—432no—
216#446—432no—
217C8×Q8—432no—
218C4×Q16—431no—
219C4×SD16—432no—
220C4×D8C2×D4311yescharacteristic
221#436—432no—
222#435—862no—
223C8×D4—862no—
224C8×D4C2×D4312yes—
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⋊C8—432no—
236D4⋊C8—432no—
237D4⋊C8C2×D4312yes—
238C82—431no—
239C82—431no—
240C82—431no—
241C82C2×D4311yescharacteristic
242C43#1795911yescharacteristic, complemented, Sylow
243C2×Q16—431no—
244C2×SD16—432no—
245C2×D8C4×D4311yescharacteristic
246C2×M16—862no—
247C22×C8—22no—
248C22×C8—431no—
249C22×C8—431no—
250C22×C8—431no—
251C22×C8—431no—
252C22×C8—861no—
253#126—862no—
254#125—432no—
255#124—432no—
256#123—862no—
257C22⋊Q8—432no—
258#121—432no—
259C4×Q8—432no—
260C4×D4—862no—
261C4×D4C22×D4312yes—
262#117—862no—
263C2×C42—431no—
264#107—431no—
265#107C4×D4311yescharacteristic
266#106—432no—
267C4⋊C8—432no—
268C4⋊C8—862no—
269C4⋊C8—862no—
270C4⋊C8C22×D4312yes—
271#103—432no—
272#103—432no—
273#102—432no—
274#102C4×D4312yes—
275C22⋊C8—22no—
276C22⋊C8—862no—
277C22⋊C8—862no—
278#97—862no—
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—861no—
288C4×C8—862no—
289C4×C8C22×D4311yescharacteristic
290C4×C8C22×D4311yescharacteristic
291C4×C8C22×D4311yescharacteristic
292C2×Q8—432no—
293C2×D4—862no—
294C2×D4C2×C4×D4312yes—
295C22×C4—22no—
296C22×C4—431no—
297C22×C4—431no—
298C22×C4—431no—
299Q16—862no—
300SD16—864no—
301D8—22no—
302M16—1724no—
303C2×C8—21no—
304C2×C8—22no—
305C2×C8—44no—
306C2×C8—431no—
307C2×C8—431no—
308C2×C8—431no—
309C2×C8—431no—
310C2×C8—862no—
311C2×C8—862no—
312C2×C8—864no—
313C2×C8—861no—
314C2×C8—862no—
315C2×C8—862no—
316C2×C8—862no—
317C2×C8C2×C4×D4311yescharacteristic
318C2×C8C2×C4×D4311yescharacteristic
319C2×C8D4×D4311yescharacteristic
320C2×C8D4×D4311yescharacteristic
321C4⋊C4—432no—
322C4⋊C4—862no—
323C4⋊C4—862no—
324C4⋊C4—862no—
325C4⋊C4—862no—
326C4⋊C4C2×C4×D4312yes—
327C22⋊C4—22no—
328C22⋊C4—862no—
329C22⋊C4—862no—
330C22⋊C4—862no—
331C22⋊C4—862no—
332C42—431no—
333C42—431no—
334C42—431no—
335C42—862no—
336C42C23×D4311yescharacteristic
337C23—22no—
338C23—431no—
339Q8—862no—
340Q8—862no—
341D4—22no—
342D4—22no—
343D4—1724no—
344C2×C4—22no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—431no—
348C2×C4—431no—
349C2×C4—431no—
350C2×C4—862no—
351C2×C4—861no—
352C2×C4—861no—
353C2×C4—861no—
354C2×C4—861no—
355C2×C4—862no—
356C2×C4—862no—
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#1306333112yes—
371C8#1306334412yes—
372C22—42no—
373C22—42no—
374C22—42no—
375C22—432no—
376C22—861no—
377C22—861no—
378C22C4×D4×D4311yescharacteristic
379C4—21no—
380C4—42no—
381C4—861no—
382C4—861no—
383C4—861no—
384C4—1722no—
385C4—1722no—
386C4#131×D4311yescharacteristic
387C4C2×#1306333111yescharacteristic
388C4#135×D4311yescharacteristic
389C4C2×#1306334411yescharacteristic
390C2—82no—
391C2—862no—
392C2#1914330211yescharacteristic
393C2C4×#1306334411yescharacteristic
394C2#443×D4311yescharacteristic
subgroupG/H
centerC2×C8D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC8×D8×C43C2
socleC22×C43C2×C4×D4
prime radical#14583132C4
cosocleC42×C43C24
hypercenterC8×D8D43
hypocenterC43#17959
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C8 ◁ C4×C8 ◁ C8×D8

Complements

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

NH ≅ G/Ntype
2. #19143567C2semidirect
3. #19133491C2semidirect
4. #19133488C2semidirect
5. #19133480C2semidirect
6. C8×Dic172C2semidirect
7. C8×#10621883C2semidirect
8. #19133357C2semidirect
9. #19133052C2semidirect
10. C82×D43C2semidirect
11. C8×D8×C43C2semidirect
200. C8×D8D43semidirect
242. C43#17959semidirect

Maximal subgroups

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

subgroupindex
#191451632
#191435672
#191334912
#191334882
#191334802
C8×Dic1722
C8×#106218832
#191333572
#191330522
C82×D432
C8×D8×C432
#1795943