Finite Group Databasebeta

← #19144263

Subgroups — #19144263

Order 5504.

484 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063346C211yesmaximal, characteristic, complemented
2C2×#13063333C211yesmaximal, characteristic, complemented
3#14583479C211yesmaximal, characteristic, complemented
4#14583478C211yesmaximal, characteristic, complemented
5#14583146C211yesmaximal, characteristic, complemented
6#14583145C211yesmaximal, characteristic, complemented
7#14583142C211yesmaximal, characteristic, complemented
8#14583139C211yesmaximal, characteristic, complemented
9#14583138C211yesmaximal, characteristic, complemented
10#14583134C211yesmaximal, characteristic, complemented
11#14583133C211yesmaximal, characteristic, complemented
12#107×D43C211yesmaximal, characteristic, complemented
13#14582899C211yesmaximal, characteristic, complemented
14#14582897C211yesmaximal, characteristic, complemented
15C43×#468C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×#10621898C2211yescharacteristic
18C2×#10621900C2211yescharacteristic
19#13063346—24no—
20C2×#10621885C2211yescharacteristic
21C2×#10621873C2211yescharacteristic
22C2×#10621882C2211yescharacteristic
23#13063333—24no—
24C2×#10621872C2211yescharacteristic
25C2×#10621872C2211yescharacteristic
26C22×C43⋊C8C2211yescharacteristic
27C2×C8×D43C2211yescharacteristic
28C2×C8×D43C2211yescharacteristic
29#13063305C2211yescharacteristic
30#13063304C2211yescharacteristic
31#13063303—21no—
32#13063302—21no—
33#13063301C2211yescharacteristic
34#13063300—21no—
35#13063300C2211yescharacteristic
36#13063299C2211yescharacteristic
37#13063298—21no—
38#13063298—21no—
39#13063298—21no—
40#13063297—21no—
41#13063296—21no—
42#13063296C2211yescharacteristic
43C4⋊C4×D43C2211yescharacteristic
44C4⋊C4×D43C2211yescharacteristic
45#13063259C2211yescharacteristic
46#13063258C2211yescharacteristic
47#13063258C2211yescharacteristic
48#13063250C2211yescharacteristic
49#13063249C2211yescharacteristic
50#13063248C2211yescharacteristic
51#13063247C2211yescharacteristic
52#13063246C2211yescharacteristic
53#13063245C2211yescharacteristic
54C2×SD16×C43C2211yescharacteristic
55C2×M16×C43C2211yescharacteristic
56C22⋊Q8×C43C2211yescharacteristic
57#121×C43C2211yescharacteristic
58#107×C43C2211yescharacteristic
59#103×C43C2211yescharacteristic
60#102×C43C2211yescharacteristic
61C2×Q8×C43C2311yescharacteristic
62C2×D4×C43—21no—
63C2×D4×C43C2311yescharacteristic
64C22×C4×C43C2311yescharacteristic
65C2×C22⋊D43—21no—
66C2×C22⋊D43—21no—
67C2×C22⋊D43—21no—
68C2×C22⋊D43D411yescharacteristic
69C2×C22⋊D43D411yescharacteristic
70C22×Dic43—21no—
71#10621902—22no—
72#10621902—22no—
73#10621900—22no—
74#10621900—22no—
75#10621898—22no—
76#10621898—22no—
77C2×D172—21no—
78C2×D172—21no—
79C2×D172D411yescharacteristic
80C2×D172C2311yescharacteristic
81C2×C4×D43—21no—
82C2×C4×D43—21no—
83C2×C4×D43—21no—
84C2×C4×D43C2311yescharacteristic
85C2×C4×D43C2311yescharacteristic
86C2×Dic86D411yescharacteristic
87C2×Dic86C2311yescharacteristic
88SD16×C43—22no—
89M16×C43—22no—
90C2×C8×C43C2311yescharacteristic
91C2×C8×C43C2311yescharacteristic
92C4⋊C4×C43—21no—
93C4⋊C4×C43C2311yescharacteristic
94C4⋊C4×C43C2311yescharacteristic
95C22⋊C4×C43—21no—
96C22⋊C4×C43—21no—
97C22⋊Dic43—21no—
98C22⋊Dic43—21no—
99#10621885—22no—
100#10621882—22no—
101(C2×D43)⋊C4—21no—
102(C2×D43)⋊C4—21no—
103(C2×D43)⋊C4—21no—
104(C2×D43)⋊C4—21no—
105C4⋊Dic43—21no—
106C4⋊Dic43C2311yescharacteristic
107C4⋊Dic43C2311yescharacteristic
108Dic43⋊C4—21no—
109Dic43⋊C4—21no—
110Dic43⋊C4—21no—
111Dic43⋊C4—21no—
112C2×C43⋊C8—22no—
113C2×C43⋊C8C2311yescharacteristic
114C2×C43⋊C8C2311yescharacteristic
115#10621873—22no—
116#10621872—22no—
117#10621872—22no—
118C8×D43—22no—
119C8×D43D414yescomplemented
120C23×C43—21no—
121C23×C43C2×D411yescharacteristic
122C22×D43—21no—
123C22×D43C2×D411yescharacteristic
124C22×D43C2×D411yescharacteristic
125Q8×C43—21no—
126Q8×C43—21no—
127D4×C43—21no—
128D4×C43—21no—
129D4×C43—81no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43C2×D411yescharacteristic
136C2×C4×C43C2411yescharacteristic
137C22⋊D43—22no—
138C22⋊D43—22no—
139C22⋊D43—42no—
140C22⋊D43—81no—
141C22⋊D43—81no—
142C2×Dic43—21no—
143C2×Dic43—21no—
144C2×Dic43—21no—
145C2×Dic43—42no—
146C2×Dic43C2×D411yescharacteristic
147C2×Dic43C2×D411yescharacteristic
148D172—22no—
149D172—21no—
150D172—21no—
151D172—42no—
152D172—81no—
153C4×D43—21no—
154C4×D43—21no—
155C4×D43—42no—
156C4×D43—81no—
157C4×D43—81no—
158C4×D43C2×D412yes—
159C4×D43#4112yes—
160Dic86—22no—
161Dic86—21no—
162Dic86—21no—
163C8×C43—21no—
164C8×C43C2×D412yes—
165C43⋊C8—21no—
166C43⋊C8C2×D412yes—
167C22×C43—21no—
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—41no—
171C22×C43—41no—
172C22×C43—41no—
173C22×C43C22×D411yescharacteristic
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#12112yes—
183C4×C43—21no—
184C4×C43—41no—
185C4×C43—41no—
186C4×C43—41no—
187C4×C43C22×D411yescharacteristic
188C4×C43C2×#4111yescharacteristic
189Dic43—21no—
190Dic43—41no—
191Dic43—41no—
192Dic43—41no—
193Dic43#12112yes—
194#3061—431nomaximal, Sylow
195C2×C43—41no—
196C2×C43—81no—
197C2×C43C2×#12111yescharacteristic
198C2×C43#57611yescharacteristic
199C2×C43#57811yescharacteristic
200D43—22no—
201D43—41no—
202D43—81no—
203C2×#135—431no—
204C2×#131—431no—
205#537—431no—
206#537—431no—
207#468—431no—
208#468—431no—
209#468—431no—
210#468D4311yescharacteristic, complemented
211#467—431no—
212#467—431no—
213#466—431no—
214#466—431no—
215C2×#107—431no—
216#417—431no—
217#417—431no—
218C43#306111yescharacteristic, complemented, Sylow
219C2×#41—431no—
220C2×#41—431no—
221C2×#41—431no—
222#135—864no—
223C2×Q16—431no—
224C2×SD16—431no—
225C2×SD16C2×D4311yescharacteristic
226C2×D8—431no—
227#131—864no—
228C2×M16—431no—
229C2×M16—431no—
230C2×M16C2×D4311yescharacteristic
231C22×C8—431no—
232C22×C8—431no—
233C22×C8—431no—
234C22⋊Q8—431no—
235C22⋊Q8—431no—
236C22⋊Q8—431no—
237C22⋊Q8—861no—
238C22⋊Q8—861no—
239C22⋊Q8C2×D4311yescharacteristic
240#121—431no—
241#121—431no—
242#121—431no—
243#121—861no—
244#121—861no—
245#121—861no—
246#121—861no—
247#121—861no—
248#121—861no—
249#121C2×D4311yescharacteristic
250C2×C4⋊C4—431no—
251C2×C4⋊C4—431no—
252#107—431no—
253#107—431no—
254#107—431no—
255#107C2×D4311yescharacteristic
256#103—431no—
257#103—431no—
258#103—431no—
259#103C2×D4311yescharacteristic
260#102—431no—
261#102—431no—
262#102—431no—
263#102C2×D4311yescharacteristic
264#41—862no—
265#41—862no—
266#41—862no—
267#41—862no—
268#41—862no—
269#41—862no—
270C2×Q8—431no—
271C2×Q8—431no—
272C2×Q8C22×D4311yescharacteristic
273C2×D4—21no—
274C2×D4—431no—
275C2×D4—431no—
276C2×D4—431no—
277C2×D4—431no—
278C2×D4—861no—
279C2×D4—861no—
280C2×D4—861no—
281C2×D4—861no—
282C2×D4—861no—
283C2×D4C22×D4311yescharacteristic
284C22×C4—431no—
285C22×C4—431no—
286C22×C4—861no—
287C22×C4—861no—
288C22×C4—861no—
289C22×C4—861no—
290C22×C4C22×D4311yescharacteristic
291Q16—862no—
292SD16—22no—
293SD16—862no—
294D8—862no—
295M16—22no—
296M16—862no—
297M16—862no—
298C2×C8—431no—
299C2×C8—434no—
300C2×C8—431no—
301C2×C8—862no—
302C2×C8—862no—
303C2×C8C22×D4311yescharacteristic
304C2×C8C22×D4311yescharacteristic
305C4⋊C4—21no—
306C4⋊C4—431no—
307C4⋊C4—431no—
308C4⋊C4—861no—
309C4⋊C4—861no—
310C4⋊C4—861no—
311C4⋊C4—861no—
312C4⋊C4—861no—
313C4⋊C4C22×D4311yescharacteristic
314C4⋊C4C22×D4311yescharacteristic
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—861no—
318C22⋊C4—861no—
319C22⋊C4—861no—
320C22⋊C4—861no—
321C22⋊C4—861no—
322C22⋊C4—861no—
323C23—21no—
324C23—431no—
325C23—431no—
326C23—861no—
327C23D4×D4311yescharacteristic
328Q8—21no—
329Q8—21no—
330Q8—862no—
331Q8—861no—
332Q8—861no—
333D4—21no—
334D4—21no—
335D4—81no—
336D4—862no—
337D4—862no—
338D4—862no—
339D4—861no—
340D4—861no—
341D4—3441no—
342D4—3441no—
343D4—3441no—
344D4—1722no—
345D4—1722no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—431no—
352C2×C4—432no—
353C2×C4—432no—
354C2×C4—431no—
355C2×C4—861no—
356C2×C4—861no—
357C2×C4—861no—
358C2×C4—861no—
359C2×C4—861no—
360C2×C4—3441no—
361C2×C4—3441no—
362C2×C4—1722no—
363C2×C4—1722no—
364C2×C4D4×D4311yescharacteristic
365C2×C4C23×D4311yescharacteristic
366C8—21no—
367C8—432no—
368C8—861no—
369C8D4×D4312yes—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—432no—
377C22—861no—
378C22—861no—
379C22—861no—
380C22—861no—
381C22—861no—
382C22—1721no—
383C22—1721no—
384C22—1721no—
385C22C2×D4×D4311yescharacteristic
386C4—21no—
387C4—41no—
388C4—41no—
389C4—41no—
390C4—432no—
391C4—861no—
392C4—1721no—
393C4—1721no—
394C4—1721no—
395C4C2×D4×D4311yescharacteristic
396C4#41×D4311yescharacteristic
397C2—41no—
398C2—81no—
399C2—862no—
400C2—3441no—
401C2—1721no—
402C2#121×D4311yescharacteristic
403C2#1458370311yescharacteristic
404C2#1458371511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#468C2
socleC22×C43C22×D4
hypercenter#468D43
hypocenterC43#3061
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#13063346C2semidirect
2. C2×#13063333C2semidirect
3. #14583479C2semidirect
4. #14583478C2semidirect
5. #14583146C2semidirect
6. #14583145C2semidirect
7. #14583142C2semidirect
8. #14583139C2semidirect
9. #14583138C2semidirect
10. #14583134C2semidirect
11. #14583133C2semidirect
12. #107×D43C2semidirect
13. #14582899C2semidirect
14. #14582897C2semidirect
15. C43×#468C2semidirect
119. C8×D43D4semidirect
210. #468D43semidirect
218. C43#3061semidirect