Finite Group Databasebeta

← #19146176

Subgroups — #19146176

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×#13063355C211yesmaximal, characteristic, complemented
2C2×#13063345C211yesmaximal, characteristic, complemented
3#14583558C211yesmaximal, characteristic, complemented
4#14583286C211yesmaximal, characteristic, complemented
5#14583150C211yesmaximal, characteristic, complemented
6#14583126C211yesmaximal, characteristic, complemented
7#14583121C211yesmaximal, characteristic, complemented
8#14583096C211yesmaximal, characteristic, complemented
9#14583061C211yesmaximal, characteristic, complemented
10#14583044C211yesmaximal, characteristic, complemented
11#14583042C211yesmaximal, characteristic, complemented
12#14583037C211yesmaximal, characteristic, complemented
13#14583004C211yesmaximal, characteristic, complemented
14#14582971C211yesmaximal, characteristic, complemented
15C43×#550C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C22×Dic86C2211yescharacteristic
18#13063355—24no—
19#13063345—24no—
20C2×#10621885C2211yescharacteristic
21C2×#10621885C2211yescharacteristic
22C2×#10621883C2211yescharacteristic
23C2×#10621883C2211yescharacteristic
24C2×#10621883C2211yescharacteristic
25C2×#10621883C2211yescharacteristic
26C2×#10621884C2211yescharacteristic
27C2×#10621882C2211yescharacteristic
28C2×#10621882C2211yescharacteristic
29C2×#10621877C2211yescharacteristic
30C22×C43⋊C8C2211yescharacteristic
31#13063313C2211yescharacteristic
32#13063311—21no—
33#13063304C2211yescharacteristic
34#13063303—21no—
35#13063299C2211yescharacteristic
36#13063297—21no—
37C4×Dic86C2211yescharacteristic
38(C22⋊D43)⋊C4—21no—
39#13063256C2211yescharacteristic
40C4⋊(C43⋊C8)C2211yescharacteristic
41#13063249C2211yescharacteristic
42#13063248C2211yescharacteristic
43#13063248C2211yescharacteristic
44#13063246C2211yescharacteristic
45#13063246C2211yescharacteristic
46#13063245C2211yescharacteristic
47C22⋊(C43⋊C8)C2211yescharacteristic
48C22⋊(C43⋊C8)C2211yescharacteristic
49#13063236C2211yescharacteristic
50C2×#41×C43C2211yescharacteristic
51C2×#41×C43C2211yescharacteristic
52#127×C43—21no—
53#127×C43C2211yescharacteristic
54#121×C43—21no—
55#121×C43—21no—
56#121×C43C2211yescharacteristic
57#121×C43C2211yescharacteristic
58C4×Q8×C43C2211yescharacteristic
59C4×D4×C43—21no—
60C4×D4×C43C2211yescharacteristic
61#41×C43—22no—
62#41×C43—22no—
63#41×C43—41no—
64#41×C43—41no—
65C2×Q8×C43C2311yescharacteristic
66C2×D4×C43—21no—
67C2×D4×C43—21no—
68C2×D4×C43—21no—
69C2×D4×C43—21no—
70C2×D4×C43—21no—
71C2×D4×C43—21no—
72C2×D4×C43D411yescharacteristic
73C2×D4×C43C2311yescharacteristic
74C2×D4×C43C2311yescharacteristic
75C22×C4×C43—21no—
76C22×C4×C43—21no—
77C22×C4×C43C2311yescharacteristic
78C22×C4×C43C2311yescharacteristic
79C2×C22⋊D43—21no—
80C2×C22⋊D43—21no—
81C22×Dic43—21no—
82#10621898—22no—
83#10621898—41no—
84C2×D172C2311yescharacteristic
85C2×C4×D43—21no—
86C2×Dic86—22no—
87C2×Dic86—21no—
88C2×Dic86—41no—
89C2×Dic86C2311yescharacteristic
90C2×Dic86C2311yescharacteristic
91C4⋊C4×C43—21no—
92C4⋊C4×C43D411yescharacteristic
93C4⋊C4×C43C2311yescharacteristic
94C22⋊C4×C43—21no—
95C22⋊C4×C43—21no—
96C22⋊C4×C43D411yescharacteristic
97C22⋊C4×C43D411yescharacteristic
98C42×C43—21no—
99C42×C43C2311yescharacteristic
100C22⋊Dic43—21no—
101#10621885—22no—
102#10621885D414yescomplemented
103#10621884—22no—
104#10621883—22no—
105#10621883—22no—
106#10621883—22no—
107#10621883—41no—
108#10621882—22no—
109#10621882—41no—
110(C2×D43)⋊C4—21no—
111(C2×D43)⋊C4—21no—
112(C2×D43)⋊C4—21no—
113C4⋊Dic43C2311yescharacteristic
114Dic43⋊C4—21no—
115Dic43⋊C4—21no—
116C4×Dic43—21no—
117#10621877—22no—
118C2×C43⋊C8—22no—
119C2×C43⋊C8C2311yescharacteristic
120C2×C43⋊C8C2311yescharacteristic
121C2×C43⋊C8C2311yescharacteristic
122C2×C43⋊C8C2311yescharacteristic
123C23×C43—21no—
124C23×C43—21no—
125C23×C43C2×D411yescharacteristic
126C23×C43C2×D411yescharacteristic
127C22×D43—21no—
128Q8×C43—21no—
129Q8×C43C2×D412yes—
130D4×C43—21no—
131D4×C43—21no—
132D4×C43—21no—
133D4×C43—21no—
134D4×C43—41no—
135D4×C43—42no—
136D4×C43—42no—
137D4×C43—42no—
138D4×C43—81no—
139D4×C43—81no—
140D4×C43—81no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—21no—
145C2×C4×C43—21no—
146C2×C4×C43—21no—
147C2×C4×C43—42no—
148C2×C4×C43—42no—
149C2×C4×C43C2×D411yescharacteristic
150C2×C4×C43C2×D411yescharacteristic
151C2×C4×C43C2×D411yescharacteristic
152C2×C4×C43C2×D411yescharacteristic
153C2×C4×C43C2411yescharacteristic
154C22⋊D43—42no—
155C22⋊D43—42no—
156C2×Dic43—21no—
157C2×Dic43—21no—
158C2×Dic43—21no—
159C2×Dic43—42no—
160D172—21no—
161D172—21no—
162C4×D43—42no—
163Dic86—21no—
164Dic86—21no—
165Dic86—21no—
166Dic86—42no—
167Dic86C2×D412yes—
168C43⋊C8—21no—
169C43⋊C8—21no—
170C43⋊C8—21no—
171C43⋊C8C2×D412yes—
172C22×C43—21no—
173C22×C43—21no—
174C22×C43—21no—
175C22×C43—21no—
176C22×C43—21no—
177C22×C43—21no—
178C22×C43—41no—
179C22×C43—41no—
180C22×C43—41no—
181C22×C43—41no—
182C22×C43—41no—
183C22×C43—41no—
184C22×C43C22×D411yescharacteristic
185C2×D43—41no—
186C2×D43—41no—
187C2×D43—41no—
188C4×C43—21no—
189C4×C43—21no—
190C4×C43—22no—
191C4×C43—21no—
192C4×C43—21no—
193C4×C43—41no—
194C4×C43C22×D411yescharacteristic
195C4×C43H(5,𝔽2)11yescharacteristic
196Dic43—22no—
197Dic43—41no—
198Dic43—41no—
199#3271—431nomaximal, Sylow
200C2×C43—41no—
201C2×C43—41no—
202C2×C43—81no—
203C2×C43—81no—
204C2×C43D4211yescharacteristic
205C2×C43#57511yescharacteristic
206C2×C43#57711yescharacteristic
207D43—81no—
208C2×#137—431no—
209C2×#135—431no—
210#550D4311yescharacteristic, complemented
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#441—431no—
222#435—431no—
223C43#327111yescharacteristic, complemented, Sylow
224C2×#41—431no—
225C2×#41C2×D4311yescharacteristic
226C2×#41C2×D4311yescharacteristic
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×SD16—431no—
236C2×SD16—431no—
237C2×D8—431no—
238C2×D8—431no—
239C2×M16—431no—
240C22×C8—431no—
241#127—21no—
242#127C2×D4311yescharacteristic
243#124—431no—
244#124—861no—
245C22⋊Q8—431no—
246C22⋊Q8—861no—
247#121—21no—
248#121—21no—
249#121—431no—
250#121—861no—
251#121C2×D4311yescharacteristic
252#121C2×D4311yescharacteristic
253C4×Q8—431no—
254C4×Q8C2×D4311yescharacteristic
255C4×D4—21no—
256C4×D4—861no—
257C4×D4C2×D4311yescharacteristic
258#106—431no—
259C4⋊C8—431no—
260#103—431no—
261#103—431no—
262#103—431no—
263#102—431no—
264#102—431no—
265#102—431no—
266C22⋊C8—431no—
267C22⋊C8—431no—
268#97—431no—
269#41—22no—
270#41—22no—
271#41—41no—
272#41—41no—
273#41—862no—
274#41—1721no—
275C2×Q8—431no—
276C2×Q8—431no—
277C2×Q8—862no—
278C2×Q8—861no—
279C2×Q8—1721no—
280C2×Q8C22×D4311yescharacteristic
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—431no—
288C2×D4—861no—
289C2×D4—861no—
290C2×D4C22⋊D4311yescharacteristic
291C2×D4C22×D4311yescharacteristic
292C2×D4C22×D4311yescharacteristic
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—861no—
296C22×C4—861no—
297C22×C4C22×D4311yescharacteristic
298C22×C4C22×D4311yescharacteristic
299Q16—434no—
300Q16—862no—
301SD16—862no—
302SD16—862no—
303SD16—862no—
304SD16—862no—
305SD16—1721no—
306D8—862no—
307D8—1721no—
308M16—862no—
309C2×C8—431no—
310C2×C8—431no—
311C2×C8—431no—
312C2×C8—431no—
313C2×C8—862no—
314C4⋊C4—21no—
315C4⋊C4—431no—
316C4⋊C4—861no—
317C4⋊C4—861no—
318C4⋊C4C22⋊D4311yescharacteristic
319C4⋊C4C22×D4311yescharacteristic
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—861no—
323C22⋊C4—861no—
324C22⋊C4—861no—
325C22⋊C4—861no—
326C22⋊C4C22⋊D4311yescharacteristic
327C22⋊C4C22⋊D4311yescharacteristic
328C42—21no—
329C42—861no—
330C42C22×D4311yescharacteristic
331C23—21no—
332C23—21no—
333C23—861no—
334C23C2×C22⋊D4311yescharacteristic
335C23C2×C22⋊D4311yescharacteristic
336Q8—21no—
337Q8—432no—
338Q8—861no—
339Q8—861no—
340Q8—861no—
341Q8—1722no—
342Q8D4×D4312yes—
343D4—21no—
344D4—21no—
345D4—21no—
346D4—21no—
347D4—41no—
348D4—42no—
349D4—42no—
350D4—42no—
351D4—81no—
352D4—81no—
353D4—81no—
354D4—861no—
355D4—861no—
356D4—1722no—
357D4—1722no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—861no—
367C2×C4—861no—
368C2×C4—861no—
369C2×C4—1722no—
370C2×C4—1722no—
371C2×C4C2×C22⋊D4311yescharacteristic
372C2×C4C2×C22⋊D4311yescharacteristic
373C2×C4C2×C22⋊D4311yescharacteristic
374C2×C4C2×C22⋊D4311yescharacteristic
375C2×C4C23×D4311yescharacteristic
376C8—432no—
377C8—861no—
378C8—861no—
379C8—861no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—1721no—
393C22—1721no—
394C22—1721no—
395C22C22×C22⋊D4311yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—22no—
401C4—41no—
402C4—862no—
403C4—1721no—
404C4—1721no—
405C4C2×D4×D4311yescharacteristic
406C4#1306337011yescharacteristic
407C2—41no—
408C2—41no—
409C2—81no—
410C2—81no—
411C2—3441no—
412C2D4×C22⋊D4311yescharacteristic
413C2#1458369711yescharacteristic
414C2#1458371011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#550C2
socleC22×C43C22×D4
hypercenter#550D43
hypocenterC43#3271
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ #550

Complements

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

NH ≅ G/Ntype
1. C2×#13063355C2semidirect
2. C2×#13063345C2semidirect
3. #14583558C2semidirect
4. #14583286C2semidirect
5. #14583150C2semidirect
6. #14583126C2semidirect
7. #14583121C2semidirect
8. #14583096C2semidirect
9. #14583061C2semidirect
10. #14583044C2semidirect
11. #14583042C2semidirect
12. #14583037C2semidirect
13. #14583004C2semidirect
14. #14582971C2semidirect
15. C43×#550C2semidirect
102. #10621885D4semidirect
210. #550D43semidirect
223. C43#3271semidirect