Finite Group Databasebeta

← #25066083

Subgroups — #25066083

Order 11008.

714 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143705C212yesmaximal, complemented
2C4×#13063348C211yesmaximal, characteristic
3#19133420C211yesmaximal, characteristic, complemented
4#19133418C211yesmaximal, characteristic, complemented
5#19133414C211yesmaximal, characteristic, complemented
6C8×#10621884C212yesmaximal, complemented
7#19133392C212yesmaximal, complemented
8#334×D43C211yesmaximal, characteristic, complemented
9#19132981C212yesmaximal, complemented
10#19132880C211yesmaximal, characteristic, complemented
11C43×#1579C211yesmaximal, characteristic, complemented
12C2×#13063348C411yescharacteristic
13C4×#10621902C2212yes—
14Q8×C43⋊C8C2212yes—
15Q16×Dic43C411yescharacteristic
16C4×#10621884C2212yes—
17#14582984C412yes—
18C4×D344C2211yescharacteristic
19#14582981C411yescharacteristic
20C8×D172—22no—
21C8×D172C2212yes—
22#14582964—22no—
23#14582964C2212yes—
24#14582950—22no—
25#14582950C2211yescharacteristic
26#14582950C2211yescharacteristic
27#14582936C411yescharacteristic
28C4⋊C8×D43—22no—
29C4⋊C8×D43C2212yes—
30#14582894C412yes—
31C4×C8×D43C2211yescharacteristic
32#14582650C2211yescharacteristic
33#14582649C2212yes—
34Q8⋊(C43⋊C8)C2212yes—
35#14582628C2212yes—
36#14582626C2212yes—
37#14582620C2211yescharacteristic
38C8×C43⋊C8C2211yescharacteristic
39C8×C43⋊C8C2211yescharacteristic
40C8×Q8×C43C2212yes—
41C4×Q16×C43C2211yescharacteristic
42C43×#334C2211yescharacteristic
43C43×Q8⋊C8C2212yes—
44C43×#322C2211yescharacteristic
45C2×#10621902C2×C412yes—
46#13063348C818yescomplemented
47C2×#10621884C2×C412yes—
48C2×D344C2×C411yescharacteristic
49C2×C8×D43—22no—
50C2×C8×D43—22no—
51C2×C8×D43—22no—
52C2×C8×D43C2×C411yescharacteristic
53C2×C8×D43C2×C411yescharacteristic
54Q8×Dic43C2×C412yes—
55C4×D172—22no—
56C4×D172C2312yes—
57#13063287—22no—
58#13063287C2×C412yes—
59#13063283—22no—
60#13063283C2×C412yes—
61C42×D43—22no—
62C42×D43C2311yescharacteristic
63#13063259C2×C411yescharacteristic
64#13063256C2×C412yes—
65C4⋊(C43⋊C8)—22no—
66C4⋊(C43⋊C8)C2312yes—
67Dic43⋊C8—22no—
68Dic43⋊C8—21no—
69Dic43⋊C8D412yes—
70#13063249C2×C412yes—
71#13063247C2×C412yes—
72#13063245C2×C412yes—
73(C2×D43)⋊C8—21no—
74(C2×D43)⋊C8—22no—
75(C2×D43)⋊C8—22no—
76(C2×D43)⋊C8D412yes—
77C4×C43⋊C8—22no—
78C4×C43⋊C8C2311yescharacteristic
79C4×C43⋊C8C2311yescharacteristic
80C4×C43⋊C8C2311yescharacteristic
81C8×Dic43C2×C411yescharacteristic
82C8×Dic43C2×C411yescharacteristic
83C2×Q16×C43C2×C411yescharacteristic
84C4×Q8×C43C2312yes—
85#107×C43C2×C411yescharacteristic
86C4⋊C8×C43—22no—
87C4⋊C8×C43C2312yes—
88#103×C43C2×C412yes—
89C4×C8×C43—22no—
90C4×C8×C43C2311yescharacteristic
91C4×C8×C43C2311yescharacteristic
92C4×C8×C43C2311yescharacteristic
93C2×Q8×C43C22×C412yes—
94#10621902—24no—
95#10621902C2×C818yescomplemented
96C2×D172—22no—
97C2×D172C22×C412yes—
98C2×C4×D43—22no—
99C2×C4×D43—22no—
100C2×C4×D43—22no—
101C2×C4×D43C22×C411yescharacteristic
102C2×C4×D43C2×D411yescharacteristic
103C2×C4×D43#4111yescharacteristic
104Q16×C43C2×C814yescomplemented
105C2×C8×C43—22no—
106C2×C8×C43—21no—
107C2×C8×C43C22×C411yescharacteristic
108C2×C8×C43C22×C411yescharacteristic
109C2×C8×C43C2×D412yes—
110C4⋊C4×C43—22no—
111C4⋊C4×C43C22×C412yes—
112C42×C43—22no—
113C42×C43C2411yescharacteristic
114#10621884C2×C818yescomplemented
115(C2×D43)⋊C4—22no—
116(C2×D43)⋊C4—22no—
117(C2×D43)⋊C4—22no—
118C4⋊Dic43—22no—
119C4⋊Dic43C22×C412yes—
120C4×Dic43—22no—
121C4×Dic43—22no—
122C4×Dic43C22×C411yescharacteristic
123C4×Dic43C2×D411yescharacteristic
124C4×Dic43#4111yescharacteristic
125C2×C43⋊C8—22no—
126C2×C43⋊C8—21no—
127C2×C43⋊C8C22×C411yescharacteristic
128C2×C43⋊C8C22×C411yescharacteristic
129C2×C43⋊C8C2×D412yes—
130D344C2×C814yescomplemented
131C8×D43—22no—
132C8×D43—82no—
133C8×D43—82no—
134C8×D43—82no—
135C8×D43C2×C814yescomplemented
136C22×D43—22no—
137C22×D43C4×D411yescharacteristic
138Q8×C43—22no—
139Q8×C43C22×C814yes—
140C2×C4×C43—22no—
141C2×C4×C43—22no—
142C2×C4×C43C23×C411yescharacteristic
143C2×C4×C43C22×D411yescharacteristic
144C2×C4×C43C2×#4111yescharacteristic
145C2×Dic43—22no—
146C2×Dic43C4×D411yescharacteristic
147C2×Dic43C4×D411yescharacteristic
148C2×Dic43C4×D411yescharacteristic
149D172—28no—
150D172—22no—
151D172C22×C814yes—
152C4×D43—22no—
153C4×D43—28no—
154C4×D43—41no—
155C4×D43—42no—
156C4×D43—42no—
157C4×D43—82no—
158C4×D43C22×C812yes—
159C4×D43#13112yes—
160C8×C43—21no—
161C8×C43—22no—
162C8×C43—41no—
163C8×C43—42no—
164C8×C43C22×C812yes—
165C43⋊C8—21no—
166C43⋊C8—22no—
167C43⋊C8—41no—
168C43⋊C8—42no—
169C43⋊C8C22×C812yes—
170#17858—431nomaximal, Sylow
171C22×C43C2×C4×D411yescharacteristic
172C2×D43—21no—
173C2×D43—21no—
174C2×D43—24no—
175C2×D43—42no—
176C2×D43—42no—
177C2×D43C8×D412yes—
178C4×C43—24no—
179C4×C43—21no—
180C4×C43—42no—
181C4×C43C23×C811yescharacteristic
182C4×C43C2×#13111yescharacteristic
183C4×C43#57712yes—
184Dic43—21no—
185Dic43—21no—
186Dic43—42no—
187Dic43C8×D412yes—
188#2988—432no—
189C4×#135—431no—
190#1580—431no—
191#1580—431no—
192#1579—431no—
193#1579D4311yescharacteristic, complemented
194C8×SD16—432no—
195C8×SD16—432no—
196C2×#334—431no—
197#1477—432no—
198#1450—431no—
199C2×C43C2×C8×D411yescharacteristic
200C2×C43#295211yescharacteristic
201C2×C43#295711yescharacteristic
202D43—22no—
203D43—44no—
204C2×#135—431no—
205C4×#41—432no—
206C8×Q8—432no—
207C8×Q8C2×D4312yes—
208C4×Q16—431no—
209C4×Q16C2×D4311yescharacteristic
210C4×SD16—432no—
211C4×SD16—432no—
212C4×D8—431no—
213C4×D8—431no—
214C8×D4—432no—
215C8×D4—432no—
216C8×D4—862no—
217C8×D4—862no—
218#431—431no—
219#431—431no—
220#431—862no—
221#427—431no—
222C2×C4⋊C8—432no—
223C2×C4⋊C8—862no—
224#416—432no—
225C2×C4×C8—431no—
226#334—432no—
227#334—431no—
228#334C2×D4311yescharacteristic
229Q8⋊C8—432no—
230Q8⋊C8C2×D4312yes—
231D4⋊C8—432no—
232D4⋊C8—432no—
233#322—431no—
234#322C2×D4311yescharacteristic
235C82—431no—
236C82—431no—
237C43#1785811yescharacteristic, complemented, Sylow
238C2×#41—432no—
239#135—438no—
240C2×Q16C4×D4311yescharacteristic
241C2×SD16—432no—
242C2×D8—431no—
243C22×C8—431no—
244C22×C8—431no—
245C22×C8—862no—
246C22×C8—862no—
247C22×C8—862no—
248C4×Q8—432no—
249C4×Q8C22×D4312yes—
250C4×D4—432no—
251C4×D4—432no—
252C4×D4—862no—
253C4×D4—862no—
254#117—432no—
255#117—862no—
256C2×C42—431no—
257C2×C42—862no—
258#107—431no—
259#107C4×D4311yescharacteristic
260#106—432no—
261C4⋊C8—22no—
262C4⋊C8—432no—
263C4⋊C8—432no—
264C4⋊C8—862no—
265C4⋊C8—862no—
266C4⋊C8—861no—
267C4⋊C8C22×D4312yes—
268#103—432no—
269#103C4×D4312yes—
270#102—432no—
271#102—432no—
272C22⋊C8—432no—
273C22⋊C8—862no—
274C22⋊C8—861no—
275C22⋊C8—862no—
276C4×C8—22no—
277C4×C8—431no—
278C4×C8—431no—
279C4×C8—431no—
280C4×C8—431no—
281C4×C8—431no—
282C4×C8—862no—
283C4×C8C22×D4311yescharacteristic
284C4×C8C22×D4311yescharacteristic
285C4×C8C22×D4311yescharacteristic
286#41—438no—
287#41—864no—
288C2×Q8C2×C4×D4312yes—
289C2×D4—432no—
290C2×D4—862no—
291C22×C4—431no—
292C22×C4—431no—
293C22×C4—431no—
294C22×C4—862no—
295C22×C4—862no—
296C22×C4—862no—
297Q16C8×D4314yescomplemented
298SD16—438no—
299D8—434no—
300C2×C8—22no—
301C2×C8—21no—
302C2×C8—431no—
303C2×C8—434no—
304C2×C8—431no—
305C2×C8—432no—
306C2×C8—862no—
307C2×C8—862no—
308C2×C8—861no—
309C2×C8—3442no—
310C2×C8—3442no—
311C2×C8—3442no—
312C2×C8C2×C4×D4311yescharacteristic
313C2×C8C2×C4×D4311yescharacteristic
314C2×C8D4×D4312yes—
315C4⋊C4—22no—
316C4⋊C4—432no—
317C4⋊C4—862no—
318C4⋊C4C2×C4×D4312yes—
319C22⋊C4—862no—
320C22⋊C4—862no—
321C22⋊C4—862no—
322C42—22no—
323C42—431no—
324C42—431no—
325C42—431no—
326C42—862no—
327C42—862no—
328C42C23×D4311yescharacteristic
329C23—431no—
330C23—862no—
331Q8—22no—
332Q8C2×C8×D4314yes—
333D4—434no—
334D4—868no—
335D4—862no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—431no—
339C2×C4—432no—
340C2×C4—432no—
341C2×C4—431no—
342C2×C4—431no—
343C2×C4—868no—
344C2×C4—862no—
345C2×C4—862no—
346C2×C4—3442no—
347C2×C4—1721no—
348C2×C4—1722no—
349C2×C4—1722no—
350C2×C4C22×C4×D4311yescharacteristic
351C2×C4C2×D4×D4311yescharacteristic
352C2×C4#41×D4311yescharacteristic
353C8—21no—
354C8—22no—
355C8—41no—
356C8—42no—
357C8—432no—
358C8—861no—
359C8—862no—
360C8—1721no—
361C8—1722no—
362C8C2×C8×D4312yes—
363C22—432no—
364C22—861no—
365C22—861no—
366C22—864no—
367C22—1722no—
368C22—1722no—
369C22C4×D4×D4311yescharacteristic
370C4—21no—
371C4—24no—
372C4—42no—
373C4—432no—
374C4—861no—
375C4—861no—
376C4—1722no—
377C4C22×C8×D4311yescharacteristic
378C4#131×D4311yescharacteristic
379C4#1458370812yes—
380C2—862no—
381C2—1724no—
382C2C8×D4×D4311yescharacteristic
383C2#1914347511yescharacteristic
384C2#1914350911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC4×C43C23×C8
FrattiniC42C23×D43
FittingC43×#1579C2
socleC22×C43C2×C4×D4
prime radicalC2×#13063348C4
cosocleC42×C43C24
hypercenter#1579D43
hypocenterC43#17858
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1579

Complements

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

NH ≅ G/Ntype
1. #19143705C2semidirect
3. #19133420C2semidirect
4. #19133418C2semidirect
5. #19133414C2semidirect
6. C8×#10621884C2semidirect
7. #19133392C2semidirect
8. #334×D43C2semidirect
9. #19132981C2semidirect
10. #19132880C2semidirect
11. C43×#1579C2semidirect
46. #13063348C8semidirect
95. #10621902C2×C8semidirect
104. Q16×C43C2×C8semidirect
114. #10621884C2×C8semidirect
130. D344C2×C8semidirect
135. C8×D43C2×C8semidirect
193. #1579D43semidirect
237. C43#17858semidirect
297. Q16C8×D43semidirect

Maximal subgroups

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

subgroupindex
#191437052
C4×#130633482
#191334202
#191334182
#191334142
C8×#106218842
#191333922
#334×D432
#191329812
#191328802
C43×#15792
#1785843