Finite Group Databasebeta

← #19146246

Subgroups — #19146246

Order 5504.

476 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063357C211yesmaximal, characteristic, complemented
2#14583560C211yesmaximal, characteristic, complemented
3#14583556C211yesmaximal, characteristic, complemented
4#14583280C211yesmaximal, characteristic, complemented
5#14583145C211yesmaximal, characteristic, complemented
6#14583142C211yesmaximal, characteristic, complemented
7#14583123C211yesmaximal, characteristic, complemented
8#14583119C211yesmaximal, characteristic, complemented
9#14583055C211yesmaximal, characteristic, complemented
10#14583053C211yesmaximal, characteristic, complemented
11#14583044C211yesmaximal, characteristic, complemented
12#14583043C211yesmaximal, characteristic, complemented
13Q16×Dic43C211yesmaximal, characteristic, complemented
14#14582975C211yesmaximal, characteristic, complemented
15C2×#137×C43C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×Q8×D43C2211yescharacteristic
18#13063357—24no—
19C2×#10621885C2211yescharacteristic
20C2×#10621885C2211yescharacteristic
21C2×#10621873C2211yescharacteristic
22C2×#10621884C2211yescharacteristic
23C2×#10621882C2211yescharacteristic
24C2×#10621872C2211yescharacteristic
25#13063314—21no—
26#13063314C2211yescharacteristic
27#13063312—21no—
28#13063312C2211yescharacteristic
29#13063304—21no—
30#13063304C2211yescharacteristic
31#13063301—21no—
32#13063301C2211yescharacteristic
33#13063299—21no—
34#13063299C2211yescharacteristic
35#13063296—21no—
36#13063296C2211yescharacteristic
37Q8×Dic43C2211yescharacteristic
38Q8×Dic43C2211yescharacteristic
39C4×C22⋊D43—21no—
40C4×C22⋊D43—21no—
41C4×C22⋊D43C2211yescharacteristic
42#13063259C2211yescharacteristic
43Dic43⋊C8C2211yescharacteristic
44#13063250C2211yescharacteristic
45#13063249C2211yescharacteristic
46#13063249C2211yescharacteristic
47#13063249C2211yescharacteristic
48#13063247C2211yescharacteristic
49#13063246C2211yescharacteristic
50C22⋊(C43⋊C8)C2211yescharacteristic
51(C2×D43)⋊C8C2211yescharacteristic
52C8×Dic43C2211yescharacteristic
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⋊D43D411yescharacteristic
77#10621902—22no—
78#10621902—41no—
79Q8×D43—22no—
80Q8×D43—41no—
81C2×D172—21no—
82C2×D172C2311yescharacteristic
83C2×C4×D43—21no—
84C2×C4×D43—21no—
85C2×C4×D43C2311yescharacteristic
86C2×Dic86—21no—
87C2×Dic86C2311yescharacteristic
88Q16×C43—22no—
89Q16×C43D414yescomplemented
90SD16×C43—22no—
91SD16×C43—22no—
92M16×C43—22no—
93C2×C8×C43C2311yescharacteristic
94C2×C8×C43C2311yescharacteristic
95C22⋊Dic43—21no—
96C22⋊Dic43—21no—
97C22⋊Dic43—21no—
98C22⋊Dic43—21no—
99C22⋊Dic43D411yescharacteristic
100#10621885—22no—
101#10621885—41no—
102#10621884—22no—
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)⋊C4D411yescharacteristic
109C4⋊Dic43—21no—
110C4⋊Dic43—21no—
111C4⋊Dic43C2311yescharacteristic
112C4⋊Dic43C2311yescharacteristic
113Dic43⋊C4—21no—
114Dic43⋊C4—21no—
115Dic43⋊C4D411yescharacteristic
116C4×Dic43—21no—
117C4×Dic43—21no—
118C4×Dic43C2311yescharacteristic
119C2×C43⋊C8C2311yescharacteristic
120C2×C43⋊C8C2311yescharacteristic
121#10621873—22no—
122#10621872—22no—
123C23×C43—21no—
124C23×C43C2×D411yescharacteristic
125C22×D43—21no—
126C22×D43C2×D411yescharacteristic
127Q8×C43—21no—
128Q8×C43—21no—
129Q8×C43—21no—
130Q8×C43—21no—
131Q8×C43—42no—
132Q8×C43C2×D412yes—
133Q8×C43C2×D412yes—
134D4×C43—21no—
135D4×C43—21no—
136D4×C43—42no—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—42no—
143C2×C4×C43—42no—
144C2×C4×C43C2×D411yescharacteristic
145C2×C4×C43C2411yescharacteristic
146C22⋊D43—41no—
147C22⋊D43—42no—
148C22⋊D43—42no—
149C2×Dic43—21no—
150C2×Dic43—21no—
151C2×Dic43—21no—
152C2×Dic43C2×D411yescharacteristic
153C2×Dic43C2×D411yescharacteristic
154C2×Dic43C2×D411yescharacteristic
155D172—21no—
156D172—21no—
157D172—42no—
158C4×D43—21no—
159C4×D43—21no—
160C4×D43—42no—
161C4×D43—42no—
162Dic86—21no—
163Dic86—21no—
164Dic86—42no—
165C8×C43—21no—
166C8×C43C2×D412yes—
167C43⋊C8—21no—
168C43⋊C8—21no—
169C22×C43—21no—
170C22×C43—21no—
171C22×C43—21no—
172C22×C43—41no—
173C22×C43—41no—
174C22×C43—41no—
175C22×C43C22×D411yescharacteristic
176C2×D43—21no—
177C2×D43—21no—
178C2×D43—21no—
179C2×D43—41no—
180C2×D43—41no—
181C2×D43—41no—
182C4×C43—22no—
183C4×C43—22no—
184C4×C43—21no—
185C4×C43—41no—
186C4×C43C22×D411yescharacteristic
187C4×C43H(5,𝔽2)11yescharacteristic
188Dic43—21no—
189Dic43—21no—
190Dic43—21no—
191Dic43—41no—
192Dic43—41no—
193Dic43—41no—
194#3277—431nomaximal, Sylow
195C2×C43—41no—
196C2×C43—81no—
197C2×C43D4211yescharacteristic
198C2×C43#57511yescharacteristic
199C2×C43#57811yescharacteristic
200D43—41no—
201D43—81no—
202C2×#137—431no—
203C2×#137D4311yescharacteristic, complemented
204#548—431no—
205#548—431no—
206#495—431no—
207#468—431no—
208#468—431no—
209#464—431no—
210#464—431no—
211#451—431no—
212#451—431no—
213#449—431no—
214#449—431no—
215C4×Q16—431no—
216#436—431no—
217C43#327711yescharacteristic, complemented, Sylow
218C2×#41—431no—
219C2×#41C2×D4311yescharacteristic
220C22×Q8—431no—
221C22×Q8C2×D4311yescharacteristic
222#137—24no—
223#137—864no—
224C2×Q16—431no—
225C2×Q16—431no—
226C2×Q16C2×D4311yescharacteristic
227C2×Q16C2×D4311yescharacteristic
228C2×SD16—431no—
229C2×SD16—431no—
230C2×SD16C2×D4311yescharacteristic
231C2×SD16C2×D4311yescharacteristic
232C2×D8—431no—
233C2×M16—431no—
234C2×M16C2×D4311yescharacteristic
235#124—431no—
236#124—431no—
237#124—861no—
238#124—861no—
239C22⋊Q8—431no—
240C22⋊Q8—431no—
241C22⋊Q8—861no—
242C22⋊Q8—861no—
243#121—431no—
244#121—431no—
245#121—861no—
246#121—861no—
247C4×Q8—431no—
248C4×Q8—431no—
249C4×D4—431no—
250C4×D4—861no—
251C4×D4—861no—
252#107—431no—
253C4⋊C8—431no—
254#103—431no—
255#103—431no—
256#103—431no—
257#103—431no—
258#102—431no—
259#102—431no—
260C22⋊C8—431no—
261C22⋊C8—431no—
262C4×C8—431no—
263#41—22no—
264#41—41no—
265#41—862no—
266#41—1721no—
267C2×Q8—21no—
268C2×Q8—22no—
269C2×Q8—41no—
270C2×Q8—431no—
271C2×Q8—861no—
272C2×Q8—862no—
273C2×Q8—1721no—
274C2×Q8C22×D4311yescharacteristic
275C2×Q8C22×D4311yescharacteristic
276C2×Q8C22×D4311yescharacteristic
277C2×D4—21no—
278C2×D4—431no—
279C2×D4—431no—
280C2×D4—861no—
281C2×D4—861no—
282C2×D4—861no—
283C2×D4C22×D4311yescharacteristic
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—431no—
287C22×C4—861no—
288C22×C4—861no—
289C22×C4C22×D4311yescharacteristic
290Q16—22no—
291Q16—862no—
292Q16—1721no—
293Q16C22⋊D4314yescomplemented
294SD16—22no—
295SD16—22no—
296SD16—862no—
297SD16—862no—
298D8—1721no—
299M16—22no—
300M16—862no—
301C2×C8—431no—
302C2×C8—431no—
303C2×C8C22×D4311yescharacteristic
304C2×C8C22×D4311yescharacteristic
305C4⋊C4—431no—
306C4⋊C4—431no—
307C4⋊C4—431no—
308C4⋊C4—861no—
309C4⋊C4—861no—
310C4⋊C4—861no—
311C4⋊C4—861no—
312C22⋊C4—431no—
313C22⋊C4—431no—
314C22⋊C4—861no—
315C22⋊C4—861no—
316C22⋊C4—861no—
317C22⋊C4—861no—
318C22⋊C4—861no—
319C22⋊C4—861no—
320C22⋊C4—861no—
321C22⋊C4—861no—
322C42—431no—
323C42—861no—
324C42—861no—
325C23—21no—
326C23—431no—
327C23—861no—
328C23D4×D4311yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—21no—
333Q8—42no—
334Q8—861no—
335Q8—861no—
336Q8—1722no—
337Q8C2×C22⋊D4312yes—
338Q8C2×C22⋊D4312yes—
339D4—21no—
340D4—21no—
341D4—42no—
342D4—861no—
343D4—861no—
344D4—1722no—
345D4—1721no—
346D4—1722no—
347D4—1722no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—431no—
356C2×C4—431no—
357C2×C4—431no—
358C2×C4—861no—
359C2×C4—861no—
360C2×C4—861no—
361C2×C4—861no—
362C2×C4—861no—
363C2×C4—1722no—
364C2×C4—1722no—
365C2×C4D4×D4311yescharacteristic
366C2×C4C23×D4311yescharacteristic
367C8—21no—
368C8—861no—
369C8—861no—
370C8C2×C22⋊D4312yes—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—861no—
378C22—861no—
379C22—861no—
380C22—1721no—
381C22—1721no—
382C22—1721no—
383C22C2×D4×D4311yescharacteristic
384C4—21no—
385C4—22no—
386C4—22no—
387C4—41no—
388C4—861no—
389C4—861no—
390C4—861no—
391C4—1721no—
392C4—1721no—
393C4—1721no—
394C4C22×C22⋊D4311yescharacteristic
395C4#1306337011yescharacteristic
396C2—41no—
397C2—81no—
398C2—3441no—
399C2—1721no—
400C2D4×C22⋊D4311yescharacteristic
401C2#1458369811yescharacteristic
402C2#1458371511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC2×#137×C43C2
socleC22×C43C22×D4
hypercenterC2×#137D43
hypocenterC43#3277
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×#13063357C2semidirect
2. #14583560C2semidirect
3. #14583556C2semidirect
4. #14583280C2semidirect
5. #14583145C2semidirect
6. #14583142C2semidirect
7. #14583123C2semidirect
8. #14583119C2semidirect
9. #14583055C2semidirect
10. #14583053C2semidirect
11. #14583044C2semidirect
12. #14583043C2semidirect
13. Q16×Dic43C2semidirect
14. #14582975C2semidirect
15. C2×#137×C43C2semidirect
89. Q16×C43D4semidirect
203. C2×#137D43semidirect
217. C43#3277semidirect
293. Q16C22⋊D43semidirect