Finite Group Databasebeta

← #19146175

Subgroups — #19146175

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×#13063354C211yesmaximal, characteristic, complemented
2C2×#13063346C211yesmaximal, characteristic, complemented
3#14583569C211yesmaximal, characteristic, complemented
4#14583561C211yesmaximal, characteristic, complemented
5#14583286C211yesmaximal, characteristic, complemented
6#14583151C211yesmaximal, characteristic, complemented
7#14583127C211yesmaximal, characteristic, complemented
8#14583122C211yesmaximal, characteristic, complemented
9#14583062C211yesmaximal, characteristic, complemented
10#14583045C211yesmaximal, characteristic, complemented
11#14583043C211yesmaximal, characteristic, complemented
12#14583036C211yesmaximal, characteristic, complemented
13#14583004C211yesmaximal, characteristic, complemented
14#14582969C211yesmaximal, characteristic, complemented
15C43×#460C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×#10621900C2211yescharacteristic
18C2×#10621900C2211yescharacteristic
19C2×Q8×D43C2211yescharacteristic
20#13063354—24no—
21#13063346—24no—
22C2×Dic172C2211yescharacteristic
23C2×#10621885C2211yescharacteristic
24C2×#10621873C2211yescharacteristic
25C2×#10621883C2211yescharacteristic
26C2×#10621883C2211yescharacteristic
27C2×#10621882C2211yescharacteristic
28C2×#10621882C2211yescharacteristic
29C2×#10621872C2211yescharacteristic
30C2×C8×D43C2211yescharacteristic
31#13063321—21no—
32#13063313—21no—
33#13063313C2211yescharacteristic
34#13063305—21no—
35#13063305C2211yescharacteristic
36#13063300—21no—
37#13063300C2211yescharacteristic
38#13063297—21no—
39#13063297—21no—
40#13063296C2211yescharacteristic
41#13063296C2211yescharacteristic
42C4×Dic86C2211yescharacteristic
43C4×D172—21no—
44C4×D172C2211yescharacteristic
45D4×Dic43—21no—
46#13063256C2211yescharacteristic
47#13063250C2211yescharacteristic
48#13063249C2211yescharacteristic
49#13063248C2211yescharacteristic
50#13063247C2211yescharacteristic
51(C2×D43)⋊C8C2211yescharacteristic
52(C2×D43)⋊C8C2211yescharacteristic
53#13063236C2211yescharacteristic
54C2×SD16×C43C2211yescharacteristic
55C2×SD16×C43C2211yescharacteristic
56#127×C43C2211yescharacteristic
57C4×Q8×C43C2211yescharacteristic
58C4⋊C8×C43C2211yescharacteristic
59#102×C43C2211yescharacteristic
60#102×C43C2211yescharacteristic
61C2×Q8×C43C2311yescharacteristic
62C2×D4×C43—21no—
63C2×D4×C43—21no—
64C2×D4×C43C2311yescharacteristic
65C2×D4×C43C2311yescharacteristic
66C2×C22⋊D43—21no—
67C2×C22⋊D43—21no—
68C2×C22⋊D43—21no—
69C2×C22⋊D43—21no—
70C22×Dic43—21no—
71C22×Dic43—21no—
72#10621902—22no—
73#10621902—41no—
74Q8×D43—22no—
75Q8×D43—41no—
76#10621900—22no—
77#10621900—22no—
78#10621900—41no—
79#10621900—41no—
80C2×D172—21no—
81C2×D172—21no—
82C2×D172D411yescharacteristic
83C2×D172C2311yescharacteristic
84C2×C4×D43—21no—
85C2×C4×D43—21no—
86C2×C4×D43C2311yescharacteristic
87C2×C4×D43C2311yescharacteristic
88C2×Dic86—21no—
89C2×Dic86C2311yescharacteristic
90C2×Dic86C2311yescharacteristic
91SD16×C43—22no—
92SD16×C43—22no—
93C2×C8×C43C2311yescharacteristic
94C2×C8×C43C2311yescharacteristic
95C4⋊C4×C43—21no—
96C4⋊C4×C43C2311yescharacteristic
97C42×C43—21no—
98C42×C43C2311yescharacteristic
99C22⋊Dic43—21no—
100C22⋊Dic43—21no—
101#10621885D414yescomplemented
102#10621883—22no—
103#10621883—41no—
104#10621882—22no—
105#10621882—41no—
106(C2×D43)⋊C4—21no—
107(C2×D43)⋊C4—21no—
108(C2×D43)⋊C4—21no—
109(C2×D43)⋊C4—21no—
110(C2×D43)⋊C4D411yescharacteristic
111(C2×D43)⋊C4D411yescharacteristic
112C4⋊Dic43—21no—
113C4⋊Dic43D411yescharacteristic
114C4⋊Dic43C2311yescharacteristic
115Dic43⋊C4—21no—
116C4×Dic43—21no—
117C2×C43⋊C8C2311yescharacteristic
118C2×C43⋊C8C2311yescharacteristic
119Dic172—22no—
120#10621873—22no—
121#10621872—22no—
122C8×D43—22no—
123C23×C43—21no—
124C23×C43—21no—
125C22×D43—21no—
126C22×D43C2×D411yescharacteristic
127C22×D43C2×D411yescharacteristic
128Q8×C43—21no—
129Q8×C43C2×D412yes—
130D4×C43—21no—
131D4×C43—21no—
132D4×C43—21no—
133D4×C43—21no—
134D4×C43—42no—
135D4×C43—81no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43C2×D411yescharacteristic
139C2×C4×C43C2×D411yescharacteristic
140C2×C4×C43C2411yescharacteristic
141C22⋊D43—42no—
142C22⋊D43—42no—
143C22⋊D43—81no—
144C22⋊D43—81no—
145C2×Dic43—21no—
146C2×Dic43—21no—
147C2×Dic43—21no—
148C2×Dic43—42no—
149C2×Dic43—42no—
150C2×Dic43C2×D411yescharacteristic
151C2×Dic43C2×D411yescharacteristic
152D172—21no—
153D172—21no—
154D172—41no—
155D172—42no—
156D172—42no—
157C4×D43—21no—
158C4×D43—21no—
159C4×D43—21no—
160C4×D43—21no—
161C4×D43—42no—
162C4×D43—42no—
163Dic86—21no—
164Dic86—21no—
165Dic86—21no—
166Dic86—42no—
167Dic86C2×D412yes—
168C8×C43—21no—
169C8×C43—21no—
170C43⋊C8—21no—
171C43⋊C8C2×D412yes—
172C22×C43—41no—
173C22×C43—41no—
174C22×C43—41no—
175C22×C43—41no—
176C22×C43—41no—
177C22×C43—41no—
178C22×C43C22×D411yescharacteristic
179C2×D43—21no—
180C2×D43—21no—
181C2×D43—21no—
182C2×D43—21no—
183C2×D43—21no—
184C2×D43—21no—
185C2×D43—41no—
186C2×D43—41no—
187C2×D43—41no—
188C4×C43—22no—
189C4×C43—21no—
190C4×C43—21no—
191C4×C43—41no—
192C4×C43C22×D411yescharacteristic
193C4×C43H(5,𝔽2)11yescharacteristic
194Dic43—22no—
195Dic43—21no—
196Dic43—21no—
197Dic43—41no—
198Dic43—41no—
199#3271—431nomaximal, Sylow
200C2×C43—81no—
201C2×C43—81no—
202C2×C43D4211yescharacteristic
203C2×C43#57511yescharacteristic
204C2×C43#57711yescharacteristic
205D43—41no—
206D43—41no—
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#460D4311yescharacteristic, complemented
217#452—431no—
218#449—431no—
219#449—431no—
220#448—431no—
221#441—431no—
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×Q16—431no—
232C2×SD16—431no—
233C2×SD16—431no—
234C2×SD16—431no—
235C2×SD16C2×D4311yescharacteristic
236C2×SD16C2×D4311yescharacteristic
237C2×D8—431no—
238C2×D8—431no—
239C2×M16—431no—
240C22×C8—431no—
241#127—861no—
242#127C2×D4311yescharacteristic
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×Q8—431no—
254C4×Q8C2×D4311yescharacteristic
255C4×D4—431no—
256C4×D4—861no—
257C4×D4—861no—
258#106—431no—
259C4⋊C8C2×D4311yescharacteristic
260#103—431no—
261#103—431no—
262#103—431no—
263#102—431no—
264#102C2×D4311yescharacteristic
265#102C2×D4311yescharacteristic
266C22⋊C8—431no—
267C22⋊C8—431no—
268#97—431no—
269#41—862no—
270#41—862no—
271#41—862no—
272#41—1721no—
273#41—1721no—
274#41—1721no—
275C2×Q8—431no—
276C2×Q8—431no—
277C2×Q8—861no—
278C2×Q8—862no—
279C2×Q8—1721no—
280C2×Q8C22×D4311yescharacteristic
281C2×D4—21no—
282C2×D4—21no—
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×D4C22×D4311yescharacteristic
292C2×D4C22×D4311yescharacteristic
293C22×C4—431no—
294C22×C4—431no—
295C22×C4—861no—
296C22×C4—861no—
297C22×C4—861no—
298C22×C4—861no—
299Q16—434no—
300Q16—862no—
301SD16—22no—
302SD16—22no—
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—431no—
316C4⋊C4—431no—
317C4⋊C4—861no—
318C4⋊C4—861no—
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—861no—
330C42C22×D4311yescharacteristic
331C23—21no—
332C23—21no—
333C23—431no—
334C23—431no—
335C23—861no—
336Q8—21no—
337Q8—432no—
338Q8—861no—
339Q8—861no—
340Q8—861no—
341Q8—1722no—
342Q8D4×D4312yes—
343D4—21no—
344D4—21no—
345D4—21no—
346D4—21no—
347D4—42no—
348D4—81no—
349D4—861no—
350D4—861no—
351D4—3441no—
352D4—3441no—
353D4—1721no—
354D4—1722no—
355D4—1722no—
356D4—1722no—
357D4—1722no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—431no—
361C2×C4—431no—
362C2×C4—861no—
363C2×C4—861no—
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—21no—
378C8—432no—
379C8—861no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—861no—
387C22—861no—
388C22—861no—
389C22—861no—
390C22—861no—
391C22—861no—
392C22—1721no—
393C22—1721no—
394C22—1721no—
395C22C2×D4×D4311yescharacteristic
396C4—21no—
397C4—21no—
398C4—22no—
399C4—41no—
400C4—861no—
401C4—861no—
402C4—862no—
403C4—1721no—
404C4—1721no—
405C4C2×D4×D4311yescharacteristic
406C4#1306337111yescharacteristic
407C2—81no—
408C2—81no—
409C2—3441no—
410C2—1721no—
411C2—1721no—
412C2#1458353311yescharacteristic
413C2#1458369511yescharacteristic
414C2#1458370511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#460C2
socleC22×C43C22×D4
hypercenter#460D43
hypocenterC43#3271
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. C2×#13063354C2semidirect
2. C2×#13063346C2semidirect
3. #14583569C2semidirect
4. #14583561C2semidirect
5. #14583286C2semidirect
6. #14583151C2semidirect
7. #14583127C2semidirect
8. #14583122C2semidirect
9. #14583062C2semidirect
10. #14583045C2semidirect
11. #14583043C2semidirect
12. #14583036C2semidirect
13. #14583004C2semidirect
14. #14582969C2semidirect
15. C43×#460C2semidirect
101. #10621885D4semidirect
216. #460D43semidirect
223. C43#3271semidirect