Finite Group Databasebeta

← #19146258

Subgroups — #19146258

Order 5504.

482 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063358C211yesmaximal, characteristic, complemented
2C2×#13063354C211yesmaximal, characteristic, complemented
3#14583567C211yesmaximal, characteristic
4#14583562C211yesmaximal, characteristic, complemented
5#14583270C211yesmaximal, characteristic, complemented
6#14583146C211yesmaximal, characteristic, complemented
7#14583108C211yesmaximal, characteristic, complemented
8#14583098C211yesmaximal, characteristic, complemented
9#14583062C211yesmaximal, characteristic, complemented
10#14583059C211yesmaximal, characteristic, complemented
11#14583039C211yesmaximal, characteristic, complemented
12#14583037C211yesmaximal, characteristic, complemented
13#14582993C211yesmaximal, characteristic, complemented
14#14582975C211yesmaximal, characteristic, complemented
15C43×#468C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×#10621900C2211yescharacteristic
18C22×Dic86C2211yescharacteristic
19C2×Q8×D43C2211yescharacteristic
20#13063358—24no—
21#13063354—24no—
22C2×Dic172C2211yescharacteristic
23C2×Dic172C2211yescharacteristic
24C2×#10621885C2211yescharacteristic
25C2×#10621873C2211yescharacteristic
26C2×#10621873C2211yescharacteristic
27C2×#10621883C2211yescharacteristic
28C2×#10621883C2211yescharacteristic
29C2×#10621884C2211yescharacteristic
30C2×#10621872C2211yescharacteristic
31#13063324—21no—
32#13063323C2211yescharacteristic
33#13063321—21no—
34#13063321C2211yescharacteristic
35#13063305C2211yescharacteristic
36#13063303—21no—
37#13063302—21no—
38#13063300C2211yescharacteristic
39#13063298—21no—
40#13063297—21no—
41#13063290C2211yescharacteristic
42#13063290C2211yescharacteristic
43C4×C22⋊D43C2211yescharacteristic
44(C22⋊D43)⋊C4—21no—
45(C22⋊D43)⋊C4—21no—
46Dic43⋊C8C2211yescharacteristic
47#13063248C2211yescharacteristic
48#13063248C2211yescharacteristic
49#13063248C2211yescharacteristic
50#13063245C2211yescharacteristic
51C22⋊(C43⋊C8)C2211yescharacteristic
52(C2×D43)⋊C8C2211yescharacteristic
53C8×Dic43C2211yescharacteristic
54C2×SD16×C43C2211yescharacteristic
55C2×M16×C43C2211yescharacteristic
56C22⋊Q8×C43C2211yescharacteristic
57#121×C43C2211yescharacteristic
58#107×C43C2211yescharacteristic
59#103×C43C2211yescharacteristic
60#102×C43C2211yescharacteristic
61C2×Q8×C43C2311yescharacteristic
62C2×D4×C43—21no—
63C2×D4×C43C2311yescharacteristic
64C22×C4×C43C2311yescharacteristic
65C2×C22⋊D43—21no—
66C2×C22⋊D43—21no—
67C2×C22⋊D43—21no—
68C2×C22⋊D43—21no—
69C2×C22⋊D43D411yescharacteristic
70C22×Dic43—21no—
71C22×Dic43—21no—
72Q8×D43—22no—
73Q8×D43—41no—
74#10621900—22no—
75#10621900—41no—
76#10621898—22no—
77#10621898—41no—
78C2×D172—21no—
79C2×D172C2311yescharacteristic
80C2×C4×D43—21no—
81C2×C4×D43—21no—
82C2×C4×D43C2311yescharacteristic
83C2×Dic86—22no—
84C2×Dic86—21no—
85C2×Dic86—21no—
86C2×Dic86—41no—
87C2×Dic86C2311yescharacteristic
88C2×Dic86C2311yescharacteristic
89C2×Dic86C2311yescharacteristic
90SD16×C43—22no—
91M16×C43—22no—
92C2×C8×C43C2311yescharacteristic
93C2×C8×C43C2311yescharacteristic
94C4⋊C4×C43—21no—
95C4⋊C4×C43C2311yescharacteristic
96C4⋊C4×C43C2311yescharacteristic
97C22⋊C4×C43—21no—
98C22⋊C4×C43—21no—
99C22⋊Dic43D411yescharacteristic
100#10621885—22no—
101#10621884—41no—
102#10621883—22no—
103#10621883—41no—
104(C2×D43)⋊C4—21no—
105(C2×D43)⋊C4—21no—
106(C2×D43)⋊C4D411yescharacteristic
107C4⋊Dic43—21no—
108Dic43⋊C4—21no—
109Dic43⋊C4—21no—
110Dic43⋊C4—21no—
111Dic43⋊C4—21no—
112Dic43⋊C4D411yescharacteristic
113C4×Dic43—21no—
114C4×Dic43—21no—
115C4×Dic43C2311yescharacteristic
116C2×C43⋊C8C2311yescharacteristic
117C2×C43⋊C8C2311yescharacteristic
118Dic172—22no—
119Dic172D414yescomplemented
120#10621873—22no—
121#10621873—22no—
122#10621872—22no—
123C23×C43—21no—
124C23×C43C2×D411yescharacteristic
125C22×D43—21no—
126C22×D43C2×D411yescharacteristic
127Q8×C43—21no—
128Q8×C43—21no—
129D4×C43—21no—
130D4×C43—21no—
131D4×C43—81no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43C2×D411yescharacteristic
138C2×C4×C43C2411yescharacteristic
139C22⋊D43—22no—
140C22⋊D43—42no—
141C22⋊D43—42no—
142C22⋊D43—42no—
143C22⋊D43—81no—
144C2×Dic43—21no—
145C2×Dic43—21no—
146C2×Dic43—21no—
147C2×Dic43—42no—
148C2×Dic43—42no—
149C2×Dic43C2×D411yescharacteristic
150C2×Dic43C2×D411yescharacteristic
151C2×Dic43C2×D411yescharacteristic
152D172—21no—
153D172—21no—
154D172—81no—
155C4×D43—21no—
156C4×D43—21no—
157C4×D43—42no—
158C4×D43—42no—
159Dic86—21no—
160Dic86—21no—
161Dic86—21no—
162Dic86—21no—
163Dic86—42no—
164Dic86—42no—
165Dic86C2×D412yes—
166Dic86C2×D412yes—
167C8×C43—21no—
168C8×C43C2×D412yes—
169C43⋊C8—21no—
170C43⋊C8—21no—
171C22×C43—21no—
172C22×C43—21no—
173C22×C43—21no—
174C22×C43—41no—
175C22×C43—41no—
176C22×C43—41no—
177C22×C43C22×D411yescharacteristic
178C2×D43—21no—
179C2×D43—21no—
180C2×D43—21no—
181C2×D43—41no—
182C2×D43—41no—
183C2×D43—41no—
184C4×C43—21no—
185C4×C43—41no—
186C4×C43—41no—
187C4×C43—41no—
188C4×C43C22×D411yescharacteristic
189C4×C43H(5,𝔽2)11yescharacteristic
190Dic43—22no—
191Dic43—22no—
192Dic43—21no—
193Dic43—21no—
194Dic43—41no—
195Dic43#13712yescomplemented
196#3278—431nomaximal, Sylow
197C2×C43—41no—
198C2×C43—81no—
199C2×C43D4211yescharacteristic
200C2×C43C2×#13711yescharacteristic
201C2×C43#57711yescharacteristic
202D43—41no—
203D43—81no—
204C2×#137—431no—
205C2×#137—431no—
206#550—431no—
207D4×Q8—431no—
208#492—431no—
209#468—431no—
210#468D4311yescharacteristic, complemented
211#462—431no—
212#460—431no—
213#452—431no—
214#452—431no—
215#448—431no—
216#448—431no—
217C4×Q16—431no—
218#436—431no—
219C43#327811yescharacteristic, complemented, Sylow
220C2×#41—431no—
221C2×#41—431no—
222C22×Q8—431no—
223C22×Q8—431no—
224#137—864no—
225#137—864no—
226C2×Q16—431no—
227C2×Q16—431no—
228C2×Q16—431no—
229C2×SD16—431no—
230C2×SD16—431no—
231C2×SD16—431no—
232C2×SD16—431no—
233C2×SD16—431no—
234C2×SD16C2×D4311yescharacteristic
235C2×M16—431no—
236C2×M16C2×D4311yescharacteristic
237C4⋊Q8—431no—
238C4⋊Q8—861no—
239#127—431no—
240#127—861no—
241C22⋊Q8—431no—
242C22⋊Q8—861no—
243C22⋊Q8—861no—
244C22⋊Q8C2×D4311yescharacteristic
245#121—431no—
246#121—861no—
247#121—861no—
248#121C2×D4311yescharacteristic
249C4×Q8—431no—
250C4×Q8—431no—
251C4×D4—431no—
252C4×D4—861no—
253C4×D4—861no—
254#107C2×D4311yescharacteristic
255C4⋊C8—431no—
256#103—431no—
257#103—431no—
258#103—431no—
259#103C2×D4311yescharacteristic
260#102—431no—
261#102C2×D4311yescharacteristic
262C22⋊C8—431no—
263C22⋊C8—431no—
264C4×C8—431no—
265#41—862no—
266#41—862no—
267#41—1721no—
268#41—1721no—
269C2×Q8—431no—
270C2×Q8—431no—
271C2×Q8—431no—
272C2×Q8—861no—
273C2×Q8—862no—
274C2×Q8—861no—
275C2×Q8—862no—
276C2×Q8—1721no—
277C2×Q8—1721no—
278C2×Q8C22×D4311yescharacteristic
279C2×D4—21no—
280C2×D4—431no—
281C2×D4—431no—
282C2×D4—861no—
283C2×D4—861no—
284C2×D4—861no—
285C2×D4—861no—
286C2×D4—861no—
287C2×D4C22×D4311yescharacteristic
288C22×C4—431no—
289C22×C4—861no—
290C22×C4—861no—
291C22×C4—861no—
292C22×C4—861no—
293C22×C4C22×D4311yescharacteristic
294Q16—434no—
295Q16—862no—
296Q16—862no—
297SD16—22no—
298SD16—862no—
299SD16—862no—
300SD16—862no—
301SD16—1721no—
302SD16—1721no—
303M16—22no—
304M16—862no—
305C2×C8—431no—
306C2×C8—431no—
307C2×C8C22×D4311yescharacteristic
308C2×C8C22×D4311yescharacteristic
309C4⋊C4—21no—
310C4⋊C4—431no—
311C4⋊C4—861no—
312C4⋊C4—861no—
313C4⋊C4—861no—
314C4⋊C4—861no—
315C4⋊C4—861no—
316C4⋊C4C22×D4311yescharacteristic
317C4⋊C4C22×D4311yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—21no—
320C22⋊C4—431no—
321C22⋊C4—431no—
322C22⋊C4—861no—
323C22⋊C4—861no—
324C42—431no—
325C42—861no—
326C42—861no—
327C23—21no—
328C23—431no—
329C23—861no—
330C23D4×D4311yescharacteristic
331Q8—21no—
332Q8—21no—
333Q8—432no—
334Q8—432no—
335Q8—861no—
336Q8—861no—
337Q8—861no—
338Q8—861no—
339Q8—1722no—
340Q8—1722no—
341D4—21no—
342D4—21no—
343D4—81no—
344D4—862no—
345D4—861no—
346D4—861no—
347D4—3441no—
348D4—3441no—
349D4—1722no—
350D4—1722no—
351D4—1722no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—431no—
358C2×C4—431no—
359C2×C4—431no—
360C2×C4—861no—
361C2×C4—861no—
362C2×C4—861no—
363C2×C4—861no—
364C2×C4—861no—
365C2×C4—1722no—
366C2×C4—1722no—
367C2×C4—1722no—
368C2×C4—1722no—
369C2×C4D4×D4311yescharacteristic
370C2×C4C23×D4311yescharacteristic
371C8—21no—
372C8—861no—
373C8—861no—
374C8D4×D4312yes—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—861no—
382C22—861no—
383C22—861no—
384C22—1721no—
385C22—1721no—
386C22—1721no—
387C22C2×D4×D4311yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—432no—
393C4—861no—
394C4—861no—
395C4—862no—
396C4—862no—
397C4—1721no—
398C4C2×D4×D4311yescharacteristic
399C4#1306337111yescharacteristic
400C2—41no—
401C2—81no—
402C2—3441no—
403C2—1721no—
404C2#1458353311yescharacteristic
405C2#137×D4311yescharacteristic
406C2#1458370911yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#468C2
socleC22×C43C22×D4
hypercenter#468D43
hypocenterC43#3278
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#13063358C2semidirect
2. C2×#13063354C2semidirect
4. #14583562C2semidirect
5. #14583270C2semidirect
6. #14583146C2semidirect
7. #14583108C2semidirect
8. #14583098C2semidirect
9. #14583062C2semidirect
10. #14583059C2semidirect
11. #14583039C2semidirect
12. #14583037C2semidirect
13. #14582993C2semidirect
14. #14582975C2semidirect
15. C43×#468C2semidirect
119. Dic172D4semidirect
195. Dic43#137semidirect
210. #468D43semidirect
219. C43#3278semidirect