Finite Group Databasebeta

← #19146182

Subgroups — #19146182

Order 5504.

488 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063357C211yesmaximal, characteristic, complemented
2C2×#13063348C211yesmaximal, characteristic, complemented
3#14583571C211yesmaximal, characteristic, complemented
4#14583561C211yesmaximal, characteristic, complemented
5#14583288C211yesmaximal, characteristic, complemented
6#14583153C211yesmaximal, characteristic, complemented
7#14583129C211yesmaximal, characteristic, complemented
8#14583121C211yesmaximal, characteristic, complemented
9#14583099C211yesmaximal, characteristic, complemented
10#14583064C211yesmaximal, characteristic, complemented
11#14583047C211yesmaximal, characteristic, complemented
12#14583047C211yesmaximal, characteristic, complemented
13#14583039C211yesmaximal, characteristic, complemented
14#14582972C211yesmaximal, characteristic, complemented
15C43×#441C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×#10621902C2211yescharacteristic
18C2×#10621902C2211yescharacteristic
19C2×Q8×D43C2211yescharacteristic
20#13063357—24no—
21#13063348—24no—
22C2×#10621885C2211yescharacteristic
23C2×#10621873C2211yescharacteristic
24C2×#10621873C2211yescharacteristic
25C2×#10621884C2211yescharacteristic
26C2×#10621884C2211yescharacteristic
27C2×#10621884C2211yescharacteristic
28C2×D344C2211yescharacteristic
29C2×D344C2211yescharacteristic
30C2×#10621872C2211yescharacteristic
31C2×C8×D43C2211yescharacteristic
32#13063322—21no—
33#13063322C2211yescharacteristic
34#13063313—21no—
35#13063313C2211yescharacteristic
36#13063305—21no—
37#13063305C2211yescharacteristic
38#13063300—21no—
39#13063300—21no—
40#13063300—21no—
41#13063300C2211yescharacteristic
42#13063300C2211yescharacteristic
43#13063300C2211yescharacteristic
44C4×D172—21no—
45C4×D172—21no—
46C4×D172C2211yescharacteristic
47C4⋊(C43⋊C8)C2211yescharacteristic
48#13063248C2211yescharacteristic
49#13063245C2211yescharacteristic
50#13063245C2211yescharacteristic
51#13063245C2211yescharacteristic
52(C2×D43)⋊C8C2211yescharacteristic
53(C2×D43)⋊C8C2211yescharacteristic
54C2×Q16×C43C2211yescharacteristic
55C4×Q8×C43C2211yescharacteristic
56C4×Q8×C43C2211yescharacteristic
57#106×C43C2211yescharacteristic
58#103×C43C2211yescharacteristic
59#103×C43C2211yescharacteristic
60#97×C43C2211yescharacteristic
61C2×Q8×C43C2311yescharacteristic
62C2×Q8×C43C2311yescharacteristic
63#10621902—22no—
64#10621902—22no—
65#10621902—22no—
66#10621902—41no—
67#10621902—41no—
68#10621902—41no—
69Q8×D43—22no—
70Q8×D43—41no—
71C2×D172—21no—
72C2×D172—21no—
73C2×D172—21no—
74C2×D172—21no—
75C2×D172—21no—
76C2×D172—21no—
77C2×D172—21no—
78C2×D172—21no—
79C2×D172D411yescharacteristic
80C2×D172C2311yescharacteristic
81C2×D172C2311yescharacteristic
82C2×D172C2311yescharacteristic
83C2×C4×D43—21no—
84C2×C4×D43—21no—
85C2×C4×D43—21no—
86C2×C4×D43—21no—
87C2×C4×D43C2311yescharacteristic
88C2×C4×D43C2311yescharacteristic
89C2×Dic86—21no—
90C2×Dic86C2311yescharacteristic
91Q16×C43D414yescomplemented
92C2×C8×C43C2311yescharacteristic
93C2×C8×C43C2311yescharacteristic
94C4⋊C4×C43—21no—
95C4⋊C4×C43—21no—
96C4⋊C4×C43C2311yescharacteristic
97C4⋊C4×C43C2311yescharacteristic
98C42×C43—21no—
99C42×C43—21no—
100C42×C43C2311yescharacteristic
101#10621885—22no—
102#10621884—22no—
103#10621884—22no—
104#10621884—22no—
105(C2×D43)⋊C4—21no—
106(C2×D43)⋊C4—21no—
107(C2×D43)⋊C4—21no—
108(C2×D43)⋊C4—21no—
109(C2×D43)⋊C4—21no—
110(C2×D43)⋊C4—21no—
111(C2×D43)⋊C4D411yescharacteristic
112(C2×D43)⋊C4D411yescharacteristic
113C4⋊Dic43—21no—
114C4⋊Dic43D411yescharacteristic
115C2×C43⋊C8C2311yescharacteristic
116C2×C43⋊C8C2311yescharacteristic
117D344—22no—
118D344—41no—
119#10621873—22no—
120#10621873—41no—
121#10621872—22no—
122C8×D43—22no—
123C22×D43—21no—
124C22×D43—21no—
125C22×D43—21no—
126C22×D43C2×D411yescharacteristic
127C22×D43C2×D411yescharacteristic
128Q8×C43—21no—
129Q8×C43—21no—
130Q8×C43C2×D412yes—
131Q8×C43C2×D412yes—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43C2×D411yescharacteristic
137C2×C4×C43C2×D411yescharacteristic
138C2×C4×C43C2411yescharacteristic
139C2×Dic43—21no—
140C2×Dic43C2×D411yescharacteristic
141C2×Dic43C2×D411yescharacteristic
142D172—21no—
143D172—21no—
144D172—21no—
145D172—21no—
146D172—21no—
147D172—21no—
148D172—41no—
149D172—42no—
150D172—42no—
151D172—42no—
152D172—42no—
153D172—42no—
154D172—81no—
155D172—81no—
156D172—81no—
157C4×D43—21no—
158C4×D43—21no—
159C4×D43—21no—
160C4×D43—21no—
161C4×D43—42no—
162C4×D43—42no—
163C4×D43—42no—
164C4×D43—42no—
165Dic86—21no—
166Dic86—21no—
167Dic86—42no—
168C8×C43—21no—
169C8×C43C2×D412yes—
170C43⋊C8—21no—
171C43⋊C8—21no—
172C22×C43C22×D411yescharacteristic
173C2×D43—21no—
174C2×D43—21no—
175C2×D43—21no—
176C2×D43—21no—
177C2×D43—21no—
178C2×D43—21no—
179C2×D43—41no—
180C2×D43—41no—
181C2×D43—41no—
182C2×D43—41no—
183C2×D43—41no—
184C2×D43—41no—
185C2×D43—41no—
186C2×D43—41no—
187C2×D43—41no—
188C4×C43—22no—
189C4×C43—22no—
190C4×C43—21no—
191C4×C43—21no—
192C4×C43—41no—
193C4×C43—41no—
194C4×C43C22×D411yescharacteristic
195C4×C43H(5,𝔽2)11yescharacteristic
196Dic43—21no—
197Dic43—21no—
198Dic43—41no—
199#3271—431nomaximal, Sylow
200C2×C43D4211yescharacteristic
201C2×C43#57511yescharacteristic
202C2×C43#57711yescharacteristic
203D43—41no—
204D43—41no—
205D43—81no—
206D43—81no—
207D43—81no—
208C2×#137—431no—
209C2×#135—431no—
210#550—431no—
211#548—431no—
212#496—431no—
213#469—431no—
214#465—431no—
215#464—431no—
216#460—431no—
217#452—431no—
218#449—431no—
219#449—431no—
220#448—431no—
221#441D4311yescharacteristic, complemented
222#435—431no—
223C43#327111yescharacteristic, complemented, Sylow
224C2×#41—431no—
225C2×#41—431no—
226C2×#41—431no—
227C22×Q8—431no—
228#137—864no—
229#135—864no—
230C2×Q16—431no—
231C2×Q16C2×D4311yescharacteristic
232C2×SD16—431no—
233C2×SD16—431no—
234C2×SD16—431no—
235C2×SD16—431no—
236C2×SD16—431no—
237C2×D8—431no—
238C2×D8—431no—
239C2×M16—431no—
240C22×C8—431no—
241#127—431no—
242#127—861no—
243#124—431no—
244#124—861no—
245C22⋊Q8—431no—
246C22⋊Q8—861no—
247#121—431no—
248#121—431no—
249#121—431no—
250#121—861no—
251#121—861no—
252#121—861no—
253C4×Q8C2×D4311yescharacteristic
254C4×Q8C2×D4311yescharacteristic
255C4×D4—431no—
256C4×D4—861no—
257C4×D4—861no—
258#106C2×D4311yescharacteristic
259C4⋊C8—431no—
260#103—431no—
261#103C2×D4311yescharacteristic
262#103C2×D4311yescharacteristic
263#102—431no—
264#102—431no—
265#102—431no—
266C22⋊C8—431no—
267C22⋊C8—431no—
268#97C2×D4311yescharacteristic
269#41—862no—
270#41—862no—
271#41—862no—
272#41—1721no—
273#41—1721no—
274#41—1721no—
275C2×Q8—431no—
276C2×Q8—861no—
277C2×Q8—862no—
278C2×Q8—1721no—
279C2×Q8C22×D4311yescharacteristic
280C2×Q8C22×D4311yescharacteristic
281C2×D4—431no—
282C2×D4—431no—
283C2×D4—431no—
284C2×D4—431no—
285C2×D4—861no—
286C2×D4—861no—
287C2×D4—861no—
288C2×D4—861no—
289C2×D4—861no—
290C2×D4—861no—
291C2×D4—861no—
292C2×D4—861no—
293C22×C4—431no—
294C22×C4—431no—
295C22×C4—861no—
296C22×C4—861no—
297C22×C4—861no—
298C22×C4—861no—
299Q16—862no—
300Q16D17214yescomplemented
301SD16—862no—
302SD16—862no—
303SD16—862no—
304SD16—862no—
305SD16—1721no—
306D8—862no—
307D8—1721no—
308M16—862no—
309C2×C8—431no—
310C2×C8—431no—
311C2×C8—862no—
312C2×C8C22×D4311yescharacteristic
313C2×C8C22×D4311yescharacteristic
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—431no—
317C4⋊C4—861no—
318C4⋊C4C22×D4311yescharacteristic
319C4⋊C4C22×D4311yescharacteristic
320C22⋊C4—431no—
321C22⋊C4—431no—
322C22⋊C4—861no—
323C22⋊C4—861no—
324C22⋊C4—861no—
325C22⋊C4—861no—
326C22⋊C4—861no—
327C22⋊C4—861no—
328C42—21no—
329C42—21no—
330C42C22×D4311yescharacteristic
331C23—431no—
332C23—431no—
333C23—861no—
334C23—861no—
335C23—861no—
336Q8—21no—
337Q8—21no—
338Q8—861no—
339Q8—861no—
340Q8—1722no—
341Q8C2×D17212yes—
342Q8C2×D17212yes—
343D4—861no—
344D4—861no—
345D4—861no—
346D4—861no—
347D4—861no—
348D4—861no—
349D4—3441no—
350D4—3441no—
351D4—3441no—
352D4—1721no—
353D4—1722no—
354D4—1722no—
355D4—1722no—
356D4—1722no—
357D4—1722no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—431no—
363C2×C4—431no—
364C2×C4—861no—
365C2×C4—861no—
366C2×C4—861no—
367C2×C4—861no—
368C2×C4—861no—
369C2×C4—1722no—
370C2×C4—1722no—
371C2×C4—1722no—
372C2×C4—1722no—
373C2×C4D4×D4311yescharacteristic
374C2×C4D4×D4311yescharacteristic
375C2×C4C23×D4311yescharacteristic
376C8—21no—
377C8—861no—
378C8—861no—
379C8C2×D17212yes—
380C22—861no—
381C22—861no—
382C22—861no—
383C22—861no—
384C22—861no—
385C22—861no—
386C22—1721no—
387C22—1721no—
388C22—1721no—
389C22—1721no—
390C22—1721no—
391C22—1721no—
392C22—1721no—
393C22—1721no—
394C22—1721no—
395C22C2×D4×D4311yescharacteristic
396C4—21no—
397C4—21no—
398C4—22no—
399C4—22no—
400C4—41no—
401C4—41no—
402C4—861no—
403C4—861no—
404C4—1721no—
405C4C22×D17211yescharacteristic
406C4#1306337111yescharacteristic
407C2—3441no—
408C2—3441no—
409C2—3441no—
410C2—1721no—
411C2—1721no—
412C2D4×D17211yescharacteristic
413C2#1458369811yescharacteristic
414C2#1458370811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#441C2
socleC22×C43C22×D4
hypercenter#441D43
hypocenterC43#3271
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
1. C2×#13063357C2semidirect
2. C2×#13063348C2semidirect
3. #14583571C2semidirect
4. #14583561C2semidirect
5. #14583288C2semidirect
6. #14583153C2semidirect
7. #14583129C2semidirect
8. #14583121C2semidirect
9. #14583099C2semidirect
10. #14583064C2semidirect
11. #14583047C2semidirect
12. #14583047C2semidirect
13. #14583039C2semidirect
14. #14582972C2semidirect
15. C43×#441C2semidirect
91. Q16×C43D4semidirect
221. #441D43semidirect
223. C43#3271semidirect
300. Q16D172semidirect