Finite Group Databasebeta

← #19146174

Subgroups — #19146174

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×#13063348C211yesmaximal, characteristic, complemented
2#14583568C211yesmaximal, characteristic, complemented
3#14583560C211yesmaximal, characteristic, complemented
4#14583285C211yesmaximal, characteristic, complemented
5#14583152C211yesmaximal, characteristic, complemented
6#14583125C211yesmaximal, characteristic, complemented
7#14583123C211yesmaximal, characteristic, complemented
8#14583097C211yesmaximal, characteristic, complemented
9#14583060C211yesmaximal, characteristic, complemented
10#14583044C211yesmaximal, characteristic, complemented
11#14583043C211yesmaximal, characteristic, complemented
12#14583038C211yesmaximal, characteristic, complemented
13#14583006C211yesmaximal, characteristic, complemented
14#14582968C211yesmaximal, characteristic, complemented
15C2×#137×C43C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×#10621902C2211yescharacteristic
18#13063348—24no—
19C2×#10621884C2211yescharacteristic
20C2×#10621884C2211yescharacteristic
21C2×#10621884C2211yescharacteristic
22C2×D344C2211yescharacteristic
23C2×#10621882C2211yescharacteristic
24C2×C8×D43C2211yescharacteristic
25#13063321—21no—
26#13063321C2211yescharacteristic
27#13063314—21no—
28#13063314C2211yescharacteristic
29#13063301—21no—
30#13063301C2211yescharacteristic
31#13063299—21no—
32#13063299—21no—
33#13063299C2211yescharacteristic
34#13063299C2211yescharacteristic
35#13063296—21no—
36#13063296C2211yescharacteristic
37Q8×Dic43C2211yescharacteristic
38Q8×Dic43C2211yescharacteristic
39C4×C22⋊D43—21no—
40C4×C22⋊D43—21no—
41C4×C22⋊D43C2211yescharacteristic
42#13063257C2211yescharacteristic
43Dic43⋊C8C2211yescharacteristic
44#13063249C2211yescharacteristic
45#13063249C2211yescharacteristic
46#13063249C2211yescharacteristic
47#13063247C2211yescharacteristic
48#13063247C2211yescharacteristic
49#13063246C2211yescharacteristic
50C22⋊(C43⋊C8)C2211yescharacteristic
51(C2×D43)⋊C8C2211yescharacteristic
52#13063235C2211yescharacteristic
53C2×#41×C43C2211yescharacteristic
54C22×Q8×C43C2211yescharacteristic
55#137×C43—24no—
56C2×Q16×C43C2211yescharacteristic
57C2×Q16×C43C2211yescharacteristic
58C2×SD16×C43C2211yescharacteristic
59C2×SD16×C43C2211yescharacteristic
60C2×M16×C43C2211yescharacteristic
61#41×C43—22no—
62#41×C43—41no—
63C2×Q8×C43—21no—
64C2×Q8×C43—22no—
65C2×Q8×C43—41no—
66C2×Q8×C43C2311yescharacteristic
67C2×Q8×C43C2311yescharacteristic
68C2×Q8×C43C2311yescharacteristic
69C2×D4×C43—21no—
70C2×D4×C43C2311yescharacteristic
71C22×C4×C43—21no—
72C22×C4×C43—21no—
73C22×C4×C43C2311yescharacteristic
74C2×C22⋊D43—21no—
75C2×C22⋊D43—21no—
76C2×C22⋊D43—21no—
77C2×C22⋊D43—21no—
78C2×C22⋊D43—21no—
79C2×C22⋊D43D411yescharacteristic
80#10621902—22no—
81#10621902—22no—
82#10621902—41no—
83#10621902—41no—
84C2×D172—21no—
85C2×D172—21no—
86C2×D172C2311yescharacteristic
87C2×D172C2311yescharacteristic
88C2×C4×D43—21no—
89C2×C4×D43—21no—
90C2×C4×D43C2311yescharacteristic
91Q16×C43—22no—
92Q16×C43D414yescomplemented
93SD16×C43—22no—
94SD16×C43—22no—
95M16×C43—22no—
96C2×C8×C43C2311yescharacteristic
97C2×C8×C43C2311yescharacteristic
98C22⋊Dic43—21no—
99C22⋊Dic43D411yescharacteristic
100#10621884—22no—
101#10621884—22no—
102#10621884—41no—
103#10621882—41no—
104(C2×D43)⋊C4—21no—
105(C2×D43)⋊C4—21no—
106(C2×D43)⋊C4—21no—
107(C2×D43)⋊C4—21no—
108(C2×D43)⋊C4—21no—
109(C2×D43)⋊C4D411yescharacteristic
110C4⋊Dic43—21no—
111C4⋊Dic43—21no—
112C4⋊Dic43C2311yescharacteristic
113C4⋊Dic43C2311yescharacteristic
114Dic43⋊C4—21no—
115Dic43⋊C4D411yescharacteristic
116C4×Dic43—21no—
117C4×Dic43—21no—
118C4×Dic43C2311yescharacteristic
119C2×C43⋊C8C2311yescharacteristic
120C2×C43⋊C8C2311yescharacteristic
121D344—22no—
122C8×D43—22no—
123C23×C43—21no—
124C23×C43C2×D411yescharacteristic
125C22×D43—21no—
126C22×D43—21no—
127C22×D43C2×D411yescharacteristic
128Q8×C43—21no—
129Q8×C43—21no—
130Q8×C43—21no—
131Q8×C43—21no—
132Q8×C43—42no—
133Q8×C43C2×D412yes—
134Q8×C43C2×D412yes—
135D4×C43—21no—
136D4×C43—21no—
137D4×C43—42no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—42no—
144C2×C4×C43—42no—
145C2×C4×C43C2×D411yescharacteristic
146C2×C4×C43C2411yescharacteristic
147C22⋊D43—41no—
148C22⋊D43—42no—
149C22⋊D43—42no—
150C22⋊D43—81no—
151C22⋊D43—81no—
152C22⋊D43—81no—
153C2×Dic43—21no—
154C2×Dic43—21no—
155C2×Dic43C2×D411yescharacteristic
156C2×Dic43C2×D411yescharacteristic
157C2×Dic43C2×D411yescharacteristic
158D172—21no—
159D172—21no—
160D172—21no—
161D172—21no—
162D172—42no—
163D172—42no—
164C4×D43—21no—
165C4×D43—21no—
166C4×D43—42no—
167C4×D43—42no—
168C8×C43—21no—
169C8×C43C2×D412yes—
170C43⋊C8—21no—
171C43⋊C8—21no—
172C22×C43—21no—
173C22×C43—21no—
174C22×C43—21no—
175C22×C43—41no—
176C22×C43—41no—
177C22×C43—41no—
178C22×C43C22×D411yescharacteristic
179C2×D43—21no—
180C2×D43—21no—
181C2×D43—21no—
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—41no—
192C4×C43C22×D411yescharacteristic
193C4×C43H(5,𝔽2)11yescharacteristic
194Dic43—21no—
195Dic43—21no—
196Dic43—21no—
197Dic43—41no—
198Dic43—41no—
199#3271—431nomaximal, Sylow
200C2×C43—41no—
201C2×C43—81no—
202C2×C43D4211yescharacteristic
203C2×C43#57511yescharacteristic
204C2×C43#57711yescharacteristic
205D43—41no—
206D43—81no—
207D43—81no—
208C2×#137D4311yescharacteristic, complemented
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#441—431no—
222#435—431no—
223C43#327111yescharacteristic, complemented, Sylow
224C2×#41—431no—
225C2×#41—431no—
226C2×#41C2×D4311yescharacteristic
227C22×Q8C2×D4311yescharacteristic
228#137—24no—
229#135—864no—
230C2×Q16C2×D4311yescharacteristic
231C2×Q16C2×D4311yescharacteristic
232C2×SD16—431no—
233C2×SD16—431no—
234C2×SD16—431no—
235C2×SD16C2×D4311yescharacteristic
236C2×SD16C2×D4311yescharacteristic
237C2×D8—431no—
238C2×D8—431no—
239C2×M16C2×D4311yescharacteristic
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×Q8—431no—
254C4×Q8—431no—
255C4×D4—431no—
256C4×D4—861no—
257C4×D4—861no—
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—41no—
271#41—862no—
272#41—862no—
273#41—1721no—
274#41—1721no—
275C2×Q8—21no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8C22×D4311yescharacteristic
279C2×Q8C22×D4311yescharacteristic
280C2×Q8C22×D4311yescharacteristic
281C2×D4—21no—
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×D4C22×D4311yescharacteristic
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—431no—
296C22×C4—861no—
297C22×C4—861no—
298C22×C4C22×D4311yescharacteristic
299Q16—22no—
300Q16C22⋊D4314yescomplemented
301SD16—22no—
302SD16—22no—
303SD16—862no—
304SD16—862no—
305SD16—1721no—
306D8—862no—
307D8—1721no—
308M16—22no—
309C2×C8—431no—
310C2×C8—431no—
311C2×C8—862no—
312C2×C8C22×D4311yescharacteristic
313C2×C8C22×D4311yescharacteristic
314C4⋊C4—431no—
315C4⋊C4—431no—
316C4⋊C4—431no—
317C4⋊C4—861no—
318C4⋊C4—861no—
319C4⋊C4—861no—
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—431no—
329C42—861no—
330C42—861no—
331C23—21no—
332C23—431no—
333C23—861no—
334C23—861no—
335C23D4×D4311yescharacteristic
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—21no—
340Q8—42no—
341Q8C2×C22⋊D4312yes—
342Q8C2×C22⋊D4312yes—
343D4—21no—
344D4—21no—
345D4—42no—
346D4—861no—
347D4—861no—
348D4—861no—
349D4—861no—
350D4—3441no—
351D4—3441no—
352D4—3441no—
353D4—1722no—
354D4—1722no—
355D4—1721no—
356D4—1722no—
357D4—1722no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—431no—
366C2×C4—431no—
367C2×C4—431no—
368C2×C4—861no—
369C2×C4—861no—
370C2×C4—861no—
371C2×C4—861no—
372C2×C4—1722no—
373C2×C4—1722no—
374C2×C4D4×D4311yescharacteristic
375C2×C4C23×D4311yescharacteristic
376C8—21no—
377C8—861no—
378C8—861no—
379C8C2×C22⋊D4312yes—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—861no—
387C22—861no—
388C22—861no—
389C22—1721no—
390C22—1721no—
391C22—1721no—
392C22—1721no—
393C22—1721no—
394C22—1721no—
395C22C2×D4×D4311yescharacteristic
396C4—21no—
397C4—22no—
398C4—22no—
399C4—41no—
400C4—861no—
401C4—861no—
402C4—861no—
403C4—1721no—
404C4—1721no—
405C4C22×C22⋊D4311yescharacteristic
406C4#1306337011yescharacteristic
407C2—41no—
408C2—81no—
409C2—3441no—
410C2—3441no—
411C2—1721no—
412C2D4×C22⋊D4311yescharacteristic
413C2#1458369811yescharacteristic
414C2#1458370811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC2×#137×C43C2
socleC22×C43C22×D4
hypercenterC2×#137D43
hypocenterC43#3271
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#13063348C2semidirect
2. #14583568C2semidirect
3. #14583560C2semidirect
4. #14583285C2semidirect
5. #14583152C2semidirect
6. #14583125C2semidirect
7. #14583123C2semidirect
8. #14583097C2semidirect
9. #14583060C2semidirect
10. #14583044C2semidirect
11. #14583043C2semidirect
12. #14583038C2semidirect
13. #14583006C2semidirect
14. #14582968C2semidirect
15. C2×#137×C43C2semidirect
92. Q16×C43D4semidirect
208. C2×#137D43semidirect
223. C43#3271semidirect
300. Q16C22⋊D43semidirect