Finite Group Databasebeta

← #19146248

Subgroups — #19146248

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×#13063356C211yesmaximal, characteristic, complemented
2C2×#13063355C211yesmaximal, characteristic, complemented
3#14583558C211yesmaximal, characteristic, complemented
4#14583281C211yesmaximal, characteristic, complemented
5#14583147C211yesmaximal, characteristic, complemented
6#14583143C211yesmaximal, characteristic, complemented
7#14583121C211yesmaximal, characteristic, complemented
8#14583118C211yesmaximal, characteristic, complemented
9#14583055C211yesmaximal, characteristic, complemented
10#14583054C211yesmaximal, characteristic, complemented
11#14583044C211yesmaximal, characteristic, complemented
12#14583042C211yesmaximal, characteristic, complemented
13C4×#10621885C211yesmaximal, characteristic, complemented
14#14582977C211yesmaximal, characteristic, complemented
15C43×#548C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C22×Dic86C2211yescharacteristic
18#13063356—24no—
19#13063355—24no—
20C2×#10621885C2211yescharacteristic
21C2×#10621885C2211yescharacteristic
22C2×#10621885C2211yescharacteristic
23C2×#10621885C2211yescharacteristic
24C2×#10621883C2211yescharacteristic
25C2×#10621883C2211yescharacteristic
26C2×#10621884C2211yescharacteristic
27C2×#10621884C2211yescharacteristic
28C2×#10621882C2211yescharacteristic
29C2×#10621877C2211yescharacteristic
30C2×#10621877C2211yescharacteristic
31#13063313C2211yescharacteristic
32#13063311—21no—
33#13063304C2211yescharacteristic
34#13063303—21no—
35#13063299C2211yescharacteristic
36#13063297—21no—
37C4×Dic86C2211yescharacteristic
38(C22⋊D43)⋊C4—21no—
39#13063258C2211yescharacteristic
40C4⋊(C43⋊C8)C2211yescharacteristic
41#13063249C2211yescharacteristic
42#13063249C2211yescharacteristic
43#13063248C2211yescharacteristic
44#13063248C2211yescharacteristic
45#13063246C2211yescharacteristic
46#13063245C2211yescharacteristic
47C22⋊(C43⋊C8)C2211yescharacteristic
48C22⋊(C43⋊C8)C2211yescharacteristic
49C4×C43⋊C8C2211yescharacteristic
50C2×#41×C43C2211yescharacteristic
51C22×Q8×C43C2211yescharacteristic
52#124×C43—21no—
53#124×C43C2211yescharacteristic
54C22⋊Q8×C43—21no—
55C22⋊Q8×C43C2211yescharacteristic
56#121×C43—21no—
57#121×C43C2211yescharacteristic
58C4×Q8×C43C2211yescharacteristic
59C4×D4×C43—21no—
60C4×D4×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×D4×C43—21no—
69C2×D4×C43—21no—
70C2×D4×C43D411yescharacteristic
71C2×D4×C43C2311yescharacteristic
72C22×C4×C43—21no—
73C22×C4×C43—21no—
74C22×C4×C43C2311yescharacteristic
75C22×C4×C43C2311yescharacteristic
76C2×C22⋊D43—21no—
77C2×C22⋊D43—21no—
78C22×Dic43—21no—
79#10621898—22no—
80#10621898—41no—
81C2×D172C2311yescharacteristic
82C2×C4×D43—21no—
83C2×Dic86—22no—
84C2×Dic86—21no—
85C2×Dic86—41no—
86C2×Dic86C2311yescharacteristic
87C2×Dic86C2311yescharacteristic
88C4⋊C4×C43—21no—
89C4⋊C4×C43—21no—
90C4⋊C4×C43D411yescharacteristic
91C4⋊C4×C43C2311yescharacteristic
92C22⋊C4×C43—21no—
93C22⋊C4×C43—21no—
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#10621885—22no—
103#10621885—41no—
104#10621885D414yescomplemented
105#10621884—22no—
106#10621884—22no—
107#10621883—22no—
108#10621883—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—
118#10621877—22no—
119C2×C43⋊C8C2311yescharacteristic
120C2×C43⋊C8C2311yescharacteristic
121C2×C43⋊C8C2311yescharacteristic
122C2×C43⋊C8C2311yescharacteristic
123C23×C43—21no—
124C23×C43C2×D411yescharacteristic
125C23×C43C2×D411yescharacteristic
126C22×D43—21no—
127Q8×C43—21no—
128Q8×C43—21no—
129Q8×C43—21no—
130Q8×C43—42no—
131Q8×C43C2×D412yes—
132D4×C43—21no—
133D4×C43—21no—
134D4×C43—41no—
135D4×C43—42no—
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—21no—
143C2×C4×C43—21no—
144C2×C4×C43—42no—
145C2×C4×C43—42no—
146C2×C4×C43C2×D411yescharacteristic
147C2×C4×C43C2×D411yescharacteristic
148C2×C4×C43C2×D411yescharacteristic
149C2×C4×C43C2×D411yescharacteristic
150C2×C4×C43C2411yescharacteristic
151C22⋊D43—42no—
152C22⋊D43—42no—
153C2×Dic43—21no—
154C2×Dic43—21no—
155C2×Dic43—21no—
156C2×Dic43—42no—
157D172—21no—
158D172—21no—
159C4×D43—42no—
160Dic86—21no—
161Dic86—21no—
162Dic86—21no—
163Dic86—42no—
164Dic86C2×D412yes—
165C43⋊C8—21no—
166C43⋊C8—21no—
167C43⋊C8—21no—
168C43⋊C8C2×D412yes—
169C22×C43—21no—
170C22×C43—21no—
171C22×C43—21no—
172C22×C43—21no—
173C22×C43—21no—
174C22×C43—21no—
175C22×C43—41no—
176C22×C43—41no—
177C22×C43—41no—
178C22×C43C22×D411yescharacteristic
179C2×D43—41no—
180C2×D43—41no—
181C2×D43—41no—
182C4×C43—21no—
183C4×C43—21no—
184C4×C43—22no—
185C4×C43—21no—
186C4×C43—21no—
187C4×C43—41no—
188C4×C43—41no—
189C4×C43C22×D411yescharacteristic
190C4×C43H(5,𝔽2)11yescharacteristic
191Dic43—22no—
192Dic43—41no—
193Dic43—41no—
194#3277—431nomaximal, Sylow
195C2×C43—41no—
196C2×C43—41no—
197C2×C43—81no—
198C2×C43D4211yescharacteristic
199C2×C43#57511yescharacteristic
200C2×C43#57811yescharacteristic
201D43—81no—
202C2×#137—431no—
203C2×#137—431no—
204#548—431no—
205#548D4311yescharacteristic, complemented
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—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×SD16—431no—
232C2×D8—431no—
233C2×M16—431no—
234C2×M16—431no—
235#124—21no—
236#124—431no—
237#124—861no—
238#124C2×D4311yescharacteristic
239C22⋊Q8—21no—
240C22⋊Q8—431no—
241C22⋊Q8—861no—
242C22⋊Q8C2×D4311yescharacteristic
243#121—21no—
244#121—431no—
245#121—861no—
246#121C2×D4311yescharacteristic
247C4×Q8—431no—
248C4×Q8C2×D4311yescharacteristic
249C4×D4—21no—
250C4×D4—861no—
251C4×D4C2×D4311yescharacteristic
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—431no—
272C2×Q8—862no—
273C2×Q8—861no—
274C2×Q8—1721no—
275C2×Q8C22×D4311yescharacteristic
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—21no—
286C22×C4—861no—
287C22×C4—861no—
288C22×C4C22×D4311yescharacteristic
289C22×C4C22×D4311yescharacteristic
290Q16—434no—
291Q16—862no—
292Q16—862no—
293Q16—1721no—
294SD16—862no—
295SD16—862no—
296SD16—862no—
297SD16—862no—
298D8—1721no—
299M16—862no—
300M16—862no—
301C2×C8—431no—
302C2×C8—431no—
303C2×C8—431no—
304C2×C8—431no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—431no—
308C4⋊C4—861no—
309C4⋊C4—861no—
310C4⋊C4C22⋊D4311yescharacteristic
311C4⋊C4C22×D4311yescharacteristic
312C22⋊C4—21no—
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—861no—
317C22⋊C4—861no—
318C22⋊C4—861no—
319C22⋊C4—861no—
320C22⋊C4C22⋊D4311yescharacteristic
321C22⋊C4C22⋊D4311yescharacteristic
322C42—21no—
323C42—861no—
324C42C22×D4311yescharacteristic
325C23—21no—
326C23—861no—
327C23C2×C22⋊D4311yescharacteristic
328C23C2×C22⋊D4311yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—42no—
333Q8—432no—
334Q8—861no—
335Q8—861no—
336Q8—861no—
337Q8—1722no—
338Q8D4×D4312yes—
339D4—21no—
340D4—21no—
341D4—41no—
342D4—42no—
343D4—42no—
344D4—861no—
345D4—861no—
346D4—1722no—
347D4—1722no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—861no—
358C2×C4—861no—
359C2×C4—861no—
360C2×C4—1722no—
361C2×C4—1722no—
362C2×C4C2×C22⋊D4311yescharacteristic
363C2×C4C2×C22⋊D4311yescharacteristic
364C2×C4C2×C22⋊D4311yescharacteristic
365C2×C4C2×C22⋊D4311yescharacteristic
366C2×C4C23×D4311yescharacteristic
367C8—432no—
368C8—861no—
369C8—861no—
370C8—861no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—1721no—
381C22—1721no—
382C22—1721no—
383C22C22×C22⋊D4311yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—22no—
389C4—41no—
390C4—41no—
391C4—862no—
392C4—1721no—
393C4—1721no—
394C4C2×D4×D4311yescharacteristic
395C4#1306337011yescharacteristic
396C2—41no—
397C2—41no—
398C2—81no—
399C2—3441no—
400C2D4×C22⋊D4311yescharacteristic
401C2#1458369711yescharacteristic
402C2#1458371411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#548C2
socleC22×C43C22×D4
hypercenter#548D43
hypocenterC43#3277
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#13063356C2semidirect
2. C2×#13063355C2semidirect
3. #14583558C2semidirect
4. #14583281C2semidirect
5. #14583147C2semidirect
6. #14583143C2semidirect
7. #14583121C2semidirect
8. #14583118C2semidirect
9. #14583055C2semidirect
10. #14583054C2semidirect
11. #14583044C2semidirect
12. #14583042C2semidirect
13. C4×#10621885C2semidirect
14. #14582977C2semidirect
15. C43×#548C2semidirect
104. #10621885D4semidirect
205. #548D43semidirect
217. C43#3277semidirect