Finite Group Databasebeta

← #19146245

Subgroups — #19146245

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×#13063355C211yesmaximal, characteristic, complemented
2C2×#13063354C211yesmaximal, characteristic, complemented
3#14583556C211yesmaximal, characteristic, complemented
4#14583555C211yesmaximal, characteristic, complemented
5#14583282C211yesmaximal, characteristic, complemented
6#14583144C211yesmaximal, characteristic, complemented
7#14583143C211yesmaximal, characteristic, complemented
8#14583120C211yesmaximal, characteristic, complemented
9#14583119C211yesmaximal, characteristic, complemented
10#14583057C211yesmaximal, characteristic, complemented
11#14583056C211yesmaximal, characteristic, complemented
12#14583041C211yesmaximal, characteristic, complemented
13#14582991C211yesmaximal, characteristic, complemented
14#14582974C211yesmaximal, characteristic, complemented
15C43×#449C211yesmaximal, characteristic, complemented
16C2×#10621900C2211yescharacteristic
17C22×Dic86C2211yescharacteristic
18C2×Q8×D43C2211yescharacteristic
19#13063355—24no—
20#13063354—24no—
21C2×Dic172C2211yescharacteristic
22C2×Dic172C2211yescharacteristic
23C2×#10621885C2211yescharacteristic
24C2×#10621885C2211yescharacteristic
25C2×#10621883C2211yescharacteristic
26C2×#10621883C2211yescharacteristic
27C2×#10621883C2211yescharacteristic
28C2×#10621877C2211yescharacteristic
29C2×#10621872C2211yescharacteristic
30#13063312—21no—
31#13063312C2211yescharacteristic
32#13063312C2211yescharacteristic
33#13063311—21no—
34#13063305C2211yescharacteristic
35#13063304—21no—
36#13063304C2211yescharacteristic
37#13063302—21no—
38#13063297—21no—
39#13063296—21no—
40#13063296C2211yescharacteristic
41Q8×Dic43C2211yescharacteristic
42#13063290C2211yescharacteristic
43D4×Dic43—21no—
44C4×C22⋊D43—21no—
45C4×C22⋊D43C2211yescharacteristic
46#13063258C2211yescharacteristic
47Dic43⋊C8C2211yescharacteristic
48#13063250C2211yescharacteristic
49#13063250C2211yescharacteristic
50#13063248C2211yescharacteristic
51#13063246C2211yescharacteristic
52(C2×D43)⋊C8C2211yescharacteristic
53C8×Dic43C2211yescharacteristic
54C2×#41×C43C2211yescharacteristic
55C2×SD16×C43C2211yescharacteristic
56C2×D8×C43C2211yescharacteristic
57#121×C43C2211yescharacteristic
58#103×C43C2211yescharacteristic
59#102×C43C2211yescharacteristic
60C22⋊C8×C43C2211yescharacteristic
61#41×C43—22no—
62#41×C43—41no—
63C2×Q8×C43C2311yescharacteristic
64C2×D4×C43—21no—
65C2×D4×C43—21no—
66C2×D4×C43C2311yescharacteristic
67C2×D4×C43C2311yescharacteristic
68C22×C4×C43—21no—
69C22×C4×C43C2311yescharacteristic
70C2×C22⋊D43—21no—
71C2×C22⋊D43—21no—
72C2×C22⋊D43D411yescharacteristic
73C22×Dic43—21no—
74C22×Dic43—21no—
75Q8×D43—22no—
76Q8×D43—41no—
77#10621900—22no—
78#10621900—41no—
79C2×C4×D43—21no—
80C2×C4×D43C2311yescharacteristic
81C2×Dic86—22no—
82C2×Dic86—21no—
83C2×Dic86—21no—
84C2×Dic86—41no—
85C2×Dic86C2311yescharacteristic
86C2×Dic86C2311yescharacteristic
87C2×Dic86C2311yescharacteristic
88SD16×C43—22no—
89D8×C43—41no—
90C2×C8×C43C2311yescharacteristic
91C2×C8×C43C2311yescharacteristic
92C4⋊C4×C43C2311yescharacteristic
93C22⋊C4×C43—21no—
94C22⋊Dic43—21no—
95C22⋊Dic43—21no—
96C22⋊Dic43—21no—
97C22⋊Dic43—21no—
98C22⋊Dic43—21no—
99C22⋊Dic43—21no—
100C22⋊Dic43D411yescharacteristic
101#10621885—22no—
102#10621885D414yescomplemented
103#10621883—22no—
104#10621883—22no—
105#10621883—22no—
106(C2×D43)⋊C4—21no—
107(C2×D43)⋊C4D411yescharacteristic
108C4⋊Dic43—21no—
109C4⋊Dic43—21no—
110C4⋊Dic43C2311yescharacteristic
111Dic43⋊C4—21no—
112Dic43⋊C4—21no—
113Dic43⋊C4D411yescharacteristic
114C4×Dic43—21no—
115C4×Dic43—21no—
116C4×Dic43C2311yescharacteristic
117#10621877—22no—
118C2×C43⋊C8C2311yescharacteristic
119C2×C43⋊C8C2311yescharacteristic
120Dic172—22no—
121Dic172—41no—
122#10621872—22no—
123C23×C43—21no—
124C23×C43—21no—
125C23×C43C2×D411yescharacteristic
126C22×D43C2×D411yescharacteristic
127Q8×C43—21no—
128Q8×C43C2×D412yes—
129D4×C43—21no—
130D4×C43—21no—
131D4×C43—21no—
132D4×C43—21no—
133D4×C43—42no—
134D4×C43—42no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—42no—
140C2×C4×C43C2×D411yescharacteristic
141C2×C4×C43C2411yescharacteristic
142C22⋊D43—41no—
143C22⋊D43—42no—
144C22⋊D43—42no—
145C2×Dic43—21no—
146C2×Dic43—21no—
147C2×Dic43—21no—
148C2×Dic43—21no—
149C2×Dic43—42no—
150C2×Dic43—42no—
151C2×Dic43C2×D411yescharacteristic
152C2×Dic43C2×D411yescharacteristic
153C2×Dic43C2×D411yescharacteristic
154C4×D43—21no—
155C4×D43—21no—
156C4×D43—42no—
157Dic86—21no—
158Dic86—21no—
159Dic86—21no—
160Dic86—21no—
161Dic86—21no—
162Dic86—42no—
163Dic86—42no—
164Dic86C2×D412yes—
165C8×C43—21no—
166C8×C43—21no—
167C43⋊C8—21no—
168C43⋊C8C2×D412yes—
169C22×C43—21no—
170C22×C43—21no—
171C22×C43—21no—
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—
182C4×C43—21no—
183C4×C43—22no—
184C4×C43—41no—
185C4×C43C22×D411yescharacteristic
186C4×C43H(5,𝔽2)11yescharacteristic
187Dic43—22no—
188Dic43—21no—
189Dic43—21no—
190Dic43—21no—
191Dic43—41no—
192Dic43—41no—
193Dic43—41no—
194#3277—431nomaximal, Sylow
195C2×C43—41no—
196C2×C43—81no—
197C2×C43—81no—
198C2×C43D4211yescharacteristic
199C2×C43#57511yescharacteristic
200C2×C43#57811yescharacteristic
201D43—41no—
202C2×#137—431no—
203C2×#137—431no—
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#449D4311yescharacteristic, complemented
215C4×Q16—431no—
216#436—431no—
217C43#327711yescharacteristic, complemented, Sylow
218C2×#41—431no—
219C2×#41C2×D4311yescharacteristic
220C22×Q8—431no—
221C22×Q8—431no—
222#137—864no—
223#137—864no—
224C2×Q16—431no—
225C2×Q16—431no—
226C2×Q16—431no—
227C2×Q16—431no—
228C2×SD16—431no—
229C2×SD16—431no—
230C2×SD16—431no—
231C2×SD16C2×D4311yescharacteristic
232C2×D8C2×D4311yescharacteristic
233C2×M16—431no—
234C2×M16—431no—
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—861no—
245#121—861no—
246#121C2×D4311yescharacteristic
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#103C2×D4311yescharacteristic
258#102—431no—
259#102C2×D4311yescharacteristic
260C22⋊C8—431no—
261C22⋊C8C2×D4311yescharacteristic
262C4×C8—431no—
263#41—22no—
264#41—41no—
265#41—862no—
266#41—1721no—
267C2×Q8—431no—
268C2×Q8—431no—
269C2×Q8—431no—
270C2×Q8—861no—
271C2×Q8—862no—
272C2×Q8—861no—
273C2×Q8—862no—
274C2×Q8—1721no—
275C2×Q8—1721no—
276C2×Q8C22×D4311yescharacteristic
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—431no—
280C2×D4—861no—
281C2×D4—861no—
282C2×D4C22×D4311yescharacteristic
283C2×D4C22×D4311yescharacteristic
284C22×C4—21no—
285C22×C4—431no—
286C22×C4—861no—
287C22×C4—861no—
288C22×C4—861no—
289C22×C4C22×D4311yescharacteristic
290Q16—434no—
291Q16—862no—
292Q16—862no—
293Q16—1721no—
294SD16—22no—
295SD16—862no—
296SD16—862no—
297SD16—862no—
298D8—41no—
299M16—862no—
300M16—862no—
301C2×C8—431no—
302C2×C8—431no—
303C2×C8C22×D4311yescharacteristic
304C2×C8C22×D4311yescharacteristic
305C4⋊C4—431no—
306C4⋊C4—431no—
307C4⋊C4—861no—
308C4⋊C4—861no—
309C4⋊C4—861no—
310C4⋊C4—861no—
311C4⋊C4C22×D4311yescharacteristic
312C22⋊C4—21no—
313C22⋊C4—431no—
314C22⋊C4—431no—
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—21no—
327C23—431no—
328C23D4×D4311yescharacteristic
329Q8—21no—
330Q8—432no—
331Q8—861no—
332Q8—861no—
333Q8—861no—
334Q8—861no—
335Q8—861no—
336Q8—1722no—
337Q8—1722no—
338Q8D4×D4312yes—
339D4—21no—
340D4—21no—
341D4—21no—
342D4—21no—
343D4—42no—
344D4—42no—
345D4—1721no—
346D4—1722no—
347D4—1722no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—42no—
353C2×C4—431no—
354C2×C4—431no—
355C2×C4—431no—
356C2×C4—861no—
357C2×C4—861no—
358C2×C4—861no—
359C2×C4—861no—
360C2×C4—861no—
361C2×C4—861no—
362C2×C4—1722no—
363C2×C4—1722no—
364C2×C4—1722no—
365C2×C4D4×D4311yescharacteristic
366C2×C4C23×D4311yescharacteristic
367C8—21no—
368C8—21no—
369C8—432no—
370C8—861no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—861no—
381C22—861no—
382C22—861no—
383C22C2×D4×D4311yescharacteristic
384C4—21no—
385C4—22no—
386C4—41no—
387C4—861no—
388C4—861no—
389C4—861no—
390C4—862no—
391C4—1721no—
392C4—1721no—
393C4—1721no—
394C4C2×D4×D4311yescharacteristic
395C4#1306337011yescharacteristic
396C2—41no—
397C2—81no—
398C2—81no—
399C2—1721no—
400C2#1458353111yescharacteristic
401C2#1458369511yescharacteristic
402C2#1458371311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#449C2
socleC22×C43C22×D4
hypercenter#449D43
hypocenterC43#3277
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#13063355C2semidirect
2. C2×#13063354C2semidirect
3. #14583556C2semidirect
4. #14583555C2semidirect
5. #14583282C2semidirect
6. #14583144C2semidirect
7. #14583143C2semidirect
8. #14583120C2semidirect
9. #14583119C2semidirect
10. #14583057C2semidirect
11. #14583056C2semidirect
12. #14583041C2semidirect
13. #14582991C2semidirect
14. #14582974C2semidirect
15. C43×#449C2semidirect
102. #10621885D4semidirect
214. #449D43semidirect
217. C43#3277semidirect