Finite Group Databasebeta

← #25067136

Subgroups — #25067136

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#19145165C211yesmaximal, characteristic
2#19143564C212yesmaximal, complemented
3#19133491C211yesmaximal, characteristic, complemented
4#19133484C212yesmaximal, complemented
5#19133479C211yesmaximal, characteristic, complemented
6#19133401C211yesmaximal, characteristic, complemented
7#19133394C212yesmaximal, complemented
8#19133389C211yesmaximal, characteristic, complemented
9#19133053C212yesmaximal, complemented
10C2×C8×C43⋊C8C211yesmaximal, characteristic, complemented
11C43×#1568C211yesmaximal, characteristic, complemented
12#14583433C2212yes—
13#14583301C411yescharacteristic
14#14583283C411yescharacteristic
15#14583254C412yes—
16#14583140C411yescharacteristic
17#14583135C411yescharacteristic
18#14583128C412yes—
19#14583026C2212yes—
20#14583023C2212yes—
21C4×Dic172C2211yescharacteristic
22C4×#10621873C2212yes—
23C4×D344C2211yescharacteristic
24#14582976C2212yes—
25#14582967—22no—
26#14582964C2212yes—
27(C22⋊D43)⋊C8—22no—
28#14582961—22no—
29#14582856—22no—
30C2×C4×C43⋊C8C2211yescharacteristic
31C2×C4×C43⋊C8C2211yescharacteristic
32#14582629C2212yes—
33#14582629C2212yes—
34#14582626C2212yes—
35#14582626C2212yes—
36C8×C43⋊C8C2211yescharacteristic
37C8×C43⋊C8C2211yescharacteristic
38C8×C43⋊C8C2211yescharacteristic
39C8×C43⋊C8C2211yescharacteristic
40C43×#432C2212yes—
41C2×C4×C8×C43C2211yescharacteristic
42C43×#335C2211yescharacteristic
43C43×#335C2211yescharacteristic
44C43×#334C2212yes—
45C2×Dic172C2×C411yescharacteristic
46C2×#10621873C2×C412yes—
47C2×D344C2×C411yescharacteristic
48C2×#10621872—22no—
49C22×C43⋊C8—21no—
50C22×C43⋊C8D411yescharacteristic
51C22×C43⋊C8D411yescharacteristic
52C2×C8×D43—22no—
53#13063319—22no—
54#13063317C2×C412yes—
55#13063313C2×C412yes—
56#13063308—22no—
57#13063304C2×C412yes—
58#13063299C2×C412yes—
59C4×Dic86C2312yes—
60C4×D172C2312yes—
61C4×C22⋊D43—22no—
62#13063282—22no—
63#13063259C2×C411yescharacteristic
64#13063259C2×C411yescharacteristic
65#13063257C2×C412yes—
66Dic43⋊C8—22no—
67Dic43⋊C8—22no—
68#13063250C2×C412yes—
69#13063250C2×C412yes—
70#13063247C2×C412yes—
71#13063247C2×C412yes—
72(C2×D43)⋊C8—22no—
73(C2×D43)⋊C8—22no—
74#13063235—22no—
75C4×C43⋊C8—21no—
76C4×C43⋊C8D411yescharacteristic
77C4×C43⋊C8D411yescharacteristic
78C4×C43⋊C8C2311yescharacteristic
79C4×C43⋊C8C2311yescharacteristic
80C4×C43⋊C8C2311yescharacteristic
81C4×C43⋊C8C2311yescharacteristic
82C8×Dic43—22no—
83C22×C8×C43C2×C411yescharacteristic
84C22×C8×C43C2×C411yescharacteristic
85C2×C42×C43C2311yescharacteristic
86C4⋊C8×C43C2312yes—
87C4⋊C8×C43C2312yes—
88C22⋊C8×C43—22no—
89#97×C43—22no—
90C4×C8×C43C2×C411yescharacteristic
91C4×C8×C43C2×C411yescharacteristic
92C4×C8×C43C2311yescharacteristic
93C4×C8×C43C2311yescharacteristic
94C22×C4×C43C22×C411yescharacteristic
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43#4111yescharacteristic
97C2×C22⋊D43—22no—
98C2×D172C22×C412yes—
99C2×C4×D43—22no—
100C2×Dic86C22×C412yes—
101C2×C8×C43—22no—
102C2×C8×C43—22no—
103C2×C8×C43—22no—
104C2×C8×C43—22no—
105C2×C8×C43C22×C411yescharacteristic
106C2×C8×C43C22×C411yescharacteristic
107C2×C8×C43C22×C411yescharacteristic
108C2×C8×C43C22×C411yescharacteristic
109C42×C43C22×C411yescharacteristic
110C42×C43C2×D411yescharacteristic
111C42×C43#4111yescharacteristic
112C42×C43C2411yescharacteristic
113C22⋊Dic43—22no—
114(C2×D43)⋊C4—22no—
115(C2×D43)⋊C4—22no—
116(C2×D43)⋊C4—22no—
117(C2×D43)⋊C4—22no—
118C4⋊Dic43C22×C412yes—
119C4⋊Dic43C22×C412yes—
120Dic43⋊C4—22no—
121Dic43⋊C4—22no—
122Dic43⋊C4—22no—
123Dic43⋊C4—22no—
124C4×Dic43—22no—
125C2×C43⋊C8—24no—
126C2×C43⋊C8—21no—
127C2×C43⋊C8—21no—
128C2×C43⋊C8—22no—
129C2×C43⋊C8—22no—
130C2×C43⋊C8C2×D411yescharacteristic
131C2×C43⋊C8C2×D411yescharacteristic
132C2×C43⋊C8C2×D411yescharacteristic
133C2×C43⋊C8C2×D411yescharacteristic
134Dic172—22no—
135D344—22no—
136#10621873—24no—
137#10621872—44no—
138C8×D43—44no—
139C23×C43C4×D411yescharacteristic
140C22×D43—22no—
141C2×C4×C43—22no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—21no—
145C2×C4×C43—21no—
146C2×C4×C43C4×D411yescharacteristic
147C2×C4×C43C4×D411yescharacteristic
148C2×C4×C43C4×D411yescharacteristic
149C2×C4×C43C23×C411yescharacteristic
150C2×C4×C43C22×D411yescharacteristic
151C2×C4×C43C2×#4111yescharacteristic
152C22⋊D43—44no—
153C2×Dic43—22no—
154C2×Dic43—22no—
155C2×Dic43—22no—
156D172—22no—
157D172—22no—
158C4×D43—42no—
159C4×D43—42no—
160Dic86—22no—
161Dic86—22no—
162C8×C43—21no—
163C8×C43—21no—
164C8×C43—42no—
165C8×C43—42no—
166C8×C43#13112yes—
167C8×C43#13112yes—
168C43⋊C8—22no—
169C43⋊C8—22no—
170C43⋊C8—21no—
171C43⋊C8—21no—
172C43⋊C8#13512yes—
173C43⋊C8#13512yes—
174#17959—431nomaximal, Sylow
175C22×C43—21no—
176C22×C43—21no—
177C22×C43#44312yes—
178C22×C43C2×C4×D411yescharacteristic
179C2×D43—42no—
180C2×D43—42no—
181C2×D43—42no—
182C4×C43—21no—
183C4×C43—21no—
184C4×C43—21no—
185C4×C43—21no—
186C4×C43C2×#13111yescharacteristic
187C4×C43C2×#13111yescharacteristic
188C4×C43C2×#13511yescharacteristic
189C4×C43C2×#13511yescharacteristic
190Dic43—42no—
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×D8—431no—
201#1568D4311yescharacteristic, complemented
202#1494—432no—
203C2×C82—431no—
204C2×C43—22no—
205C2×C43#293111yescharacteristic
206C2×C43C4×#13511yescharacteristic
207C2×C43C2×#44311yescharacteristic
208D43—82no—
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×D8—431no—
221#436—432no—
222#435—862no—
223C8×D4—432no—
224C8×D4—862no—
225#433—862no—
226#432C2×D4312yes—
227#405—862no—
228C2×C4×C8—431no—
229C2×C4×C8—431no—
230C2×C4×C8C2×D4311yescharacteristic
231#335C2×D4311yescharacteristic
232#335C2×D4311yescharacteristic
233#334C2×D4312yes—
234Q8⋊C8—432no—
235Q8⋊C8—432no—
236D4⋊C8—432no—
237D4⋊C8—432no—
238C82—431no—
239C82—431no—
240C82—431no—
241C82—431no—
242C43#1795911yescharacteristic, complemented, Sylow
243C2×Q16—431no—
244C2×SD16—432no—
245C2×D8—431no—
246C2×M16—862no—
247C22×C8—431no—
248C22×C8—431no—
249C22×C8—862no—
250C22×C8—861no—
251C22×C8C4×D4311yescharacteristic
252C22×C8C4×D4311yescharacteristic
253#126—862no—
254#125—432no—
255#124—432no—
256#123—862no—
257C22⋊Q8—432no—
258#121—432no—
259C4×Q8—432no—
260C4×D4—432no—
261C4×D4—862no—
262#117—862no—
263C2×C42C22×D4311yescharacteristic
264#107—431no—
265#107—431no—
266#106—432no—
267C4⋊C8—862no—
268C4⋊C8—862no—
269C4⋊C8C22×D4312yes—
270C4⋊C8C22×D4312yes—
271#103—432no—
272#103—432no—
273#102—432no—
274#102—432no—
275C22⋊C8—22no—
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—862no—
287C4×C8—861no—
288C4×C8C4×D4311yescharacteristic
289C4×C8C4×D4311yescharacteristic
290C4×C8C22×D4311yescharacteristic
291C4×C8C22×D4311yescharacteristic
292C2×Q8—432no—
293C2×D4—432no—
294C2×D4—862no—
295C22×C4—862no—
296C22×C4C2×C4×D4311yescharacteristic
297C22×C4D4×D4311yescharacteristic
298C22×C4#1062190211yescharacteristic
299Q16—862no—
300SD16—864no—
301D8—862no—
302M16—1724no—
303C2×C8—22no—
304C2×C8—22no—
305C2×C8—22no—
306C2×C8—22no—
307C2×C8—431no—
308C2×C8—431no—
309C2×C8—431no—
310C2×C8—431no—
311C2×C8—862no—
312C2×C8—862no—
313C2×C8—864no—
314C2×C8—861no—
315C2×C8—861no—
316C2×C8—1724no—
317C2×C8C2×C4×D4311yescharacteristic
318C2×C8C2×C4×D4311yescharacteristic
319C2×C8C2×C4×D4311yescharacteristic
320C2×C8C2×C4×D4311yescharacteristic
321C4⋊C4—432no—
322C4⋊C4—432no—
323C4⋊C4—862no—
324C4⋊C4—862no—
325C4⋊C4—862no—
326C4⋊C4—862no—
327C22⋊C4—862no—
328C22⋊C4—862no—
329C22⋊C4—862no—
330C22⋊C4—862no—
331C22⋊C4—862no—
332C42—862no—
333C42C2×C4×D4311yescharacteristic
334C42D4×D4311yescharacteristic
335C42#1062190211yescharacteristic
336C42C23×D4311yescharacteristic
337C23—862no—
338C23#1306328711yescharacteristic
339Q8—862no—
340Q8—862no—
341D4—862no—
342D4—862no—
343D4—1724no—
344C2×C4—22no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—862no—
350C2×C4—862no—
351C2×C4—862no—
352C2×C4—1722no—
353C2×C4—1722no—
354C2×C4#1306328711yescharacteristic
355C2×C4#1306328711yescharacteristic
356C2×C4#1306328711yescharacteristic
357C2×C4C22×C4×D4311yescharacteristic
358C2×C4C2×D4×D4311yescharacteristic
359C2×C4C2×#1062190211yescharacteristic
360C8—21no—
361C8—21no—
362C8—42no—
363C8—42no—
364C8—432no—
365C8—432no—
366C8—862no—
367C8—862no—
368C8—861no—
369C8—861no—
370C8#1306333312yes—
371C8#1306333312yes—
372C22—21no—
373C22—21no—
374C22—1722no—
375C22—1722no—
376C22—1722no—
377C22#1458301512yes—
378C22C2×#1306328711yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—1722no—
384C4—1722no—
385C4—1722no—
386C4C2×#1306333311yescharacteristic
387C4C2×#1306333311yescharacteristic
388C4#135×D4311yescharacteristic
389C4#135×D4311yescharacteristic
390C2—22no—
391C2—3442no—
392C2#1914330611yescharacteristic
393C2#1914336611yescharacteristic
394C2C2×#1458301511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1568C2
socleC22×C43C2×C4×D4
prime radical#14583135C4
cosocleC42×C43C24
hypercenter#1568D43
hypocenterC43#17959
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1568

Complements

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

NH ≅ G/Ntype
2. #19143564C2semidirect
3. #19133491C2semidirect
4. #19133484C2semidirect
5. #19133479C2semidirect
6. #19133401C2semidirect
7. #19133394C2semidirect
8. #19133389C2semidirect
9. #19133053C2semidirect
10. C2×C8×C43⋊C8C2semidirect
11. C43×#1568C2semidirect
201. #1568D43semidirect
242. C43#17959semidirect

Maximal subgroups

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

subgroupindex
#191451652
#191435642
#191334912
#191334842
#191334792
#191334012
#191333942
#191333892
#191330532
C2×C8×C43⋊C82
C43×#15682
#1795943